Finite Group Databasebeta

← C2×#72239325 #72315722

Subgroups — C2×#72239325 #72315722

Order 2048.

29264 conjugacy classes of subgroups.

The subgroup lattice has 1896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#7622691C212yesmaximal
2C2×#493286C212yesmaximal, complemented
3C2×#493273C214yesmaximal, complemented
4C2×#493318C218yesmaximal, complemented
5C22×D4×#97C211yesmaximal, characteristic
6C2×D4×#347C218yesmaximal, complemented
7#72239325C2132yesmaximal, direct product factor
8C22×#12605C214yesmaximal, complemented
9C2×#493177C212yesmaximal, complemented
10C23×C8×D4C411yescharacteristic
11C23×C8×D4C2211yescharacteristic
12C24×#97C2212yes—
13C22×C42×D4C411yescharacteristic
14#7622691C4132yescomplemented
15#7622691C22132yes—
16C2×#33489C414yescomplemented
17C2×#33488C4116yescomplemented
18C2×#33487C418yescomplemented
19C2×#33486C414yescomplemented
20C2×D4×M32C22116yes—
21C2×#33418C2214yes—
22C22×#2112C2218yes—
23C23×#347C2218yescomplemented
24C2×D4×#97C4116yes—
25C2×D4×#97C414yes—
26C2×D4×#97C414yes—
27C2×D4×#97C2214yes—
28C2×D4×#97C2214yes—
29C2×D4×#97C22116yes—
30C22×#1770C411yescharacteristic
31C22×#1770C2211yescharacteristic
32C22×#1767C411yescharacteristic
33C22×#1752C412yes—
34C22×#1752C2212yes—
35C22×#1749C412yes—
36C22×C4×#97C2211yescharacteristic
37#493318C221128yescomplemented
38#493286C22132yescomplemented
39#493273C22164yescomplemented
40D4×#347C221128yescomplemented
41#493177C22132yescomplemented
42C2×#12666C22116yescomplemented
43C2×#12658C2214yescomplemented
44C2×#12658C2214yescomplemented
45C2×#12616C22132yescomplemented
46C2×#12605C2214yes—
47C2×#12605C2214yes—
48C2×#12605C2218yes—
49C2×#12605C2218yescomplemented
50C2×#12605C2218yescomplemented
51C2×#12605C22164yescomplemented
52C2×#12594C2214yescomplemented
53C22×#1375C2218yescomplemented
54C2×C4×#347C2214yescomplemented
55C25×C8C2×C412yes—
56C25×C8C2312yes—
57C23×C4×D4—21no—
58C23×C4×D4C2×C411yescharacteristic
59C24×C42C2×C412yes—
60C23×M32C23116yes—
61C22×C8×D4—24no—
62C22×C8×D4—28no—
63C22×C8×D4—22no—
64C22×C8×D4—21no—
65C22×C8×D4—21no—
66C22×C8×D4C2×C412yes—
67C22×C8×D4C2×C414yes—
68C22×C8×D4C2×C418yes—
69C22×C8×D4C2×C412yes—
70C22×C8×D4C2×C4116yes—
71C22×C8×D4C2×C414yes—
72C22×C8×D4C2×C414yes—
73C22×C8×D4C2×C4116yes—
74C22×C8×D4C2×C414yes—
75C22×C8×D4C2×C418yes—
76C22×C8×D4C2318yes—
77C22×C8×D4C2314yes—
78C23×C4⋊C8C2×C411yescharacteristic
79C23×C4⋊C8C2×C411yescharacteristic
80C23×C22⋊C8C2×C412yes—
81C23×C22⋊C8C2×C412yes—
82C23×#97—416no—
83C23×#97C2×C411yescharacteristic
84C23×#97C2×C412yes—
85C23×#97C2×C412yes—
86C23×#97C2×C411yescharacteristic
87C23×#97C2×C414yes—
88C23×#97C2×C4116yes—
89C23×#97C2×C414yes—
90C23×#97C2314yes—
91C23×#97C2311yescharacteristic
92C23×#97C2311yescharacteristic
93C23×#97C2312yes—
94C23×#97C2314yes—
95C23×#97C23116yes—
96C23×C4×C8C2×C411yescharacteristic
97C23×C4×C8C2311yescharacteristic
98C2×C42×D4—24no—
99C2×C42×D4—28no—
100C2×C42×D4C2×C414yes—
101C2×C42×D4C2×C414yes—
102C2×C42×D4C2×C4116yes—
103C22×C4×C4⋊C4—21no—
104C22×C4×C4⋊C4C2×C411yescharacteristic
105C22×C4×C22⋊C4—22no—
106C22×C4×C22⋊C4C2×C412yes—
107C22×C43C2×C411yescharacteristic
108#33489C2×C4164yescomplemented
109#33488C2×C41256yescomplemented
110#33487C2×C41128yescomplemented
111#33486C2×C4164yescomplemented
112D4×M32C2×C41128yescomplemented
113D4×M32C231128yes—
114C2×#2169C2×C4132yescomplemented
115C2×#2168C2×C4164yescomplemented
116C2×D4×C16C2×C4132yescomplemented
117#33418C2×C4132yescomplemented
118#33418C23132yes—
119C2×#2163C2×C418yescomplemented
120C2×#2163C2×C418yescomplemented
121C2×#2162C2×C418yescomplemented
122C2×#2162C2×C418yescomplemented
123C2×#2150C2318yes—
124C2×#2112C2×C4116yescomplemented
125C2×#2112C2×C4116yescomplemented
126C2×#2112C2×C4164yescomplemented
127C2×#2112C2318yes—
128C2×#2112C23164yes—
129C2×#2112C23116yes—
130C22×C22⋊C16C2×C4116yescomplemented
131C22×C22⋊C16C2×C4116yescomplemented
132C22×#347—432no—
133C22×#347C2318yes—
134C22×#347C23116yes—
135C22×#347C2318yes—
136C22×#347C23164yescomplemented
137C2×C4×M32C2318yes—
138D4×#97C2×C4132yes—
139D4×#97C2×C4132yes—
140D4×#97C2×C4164yes—
141D4×#97C2×C4164yes—
142D4×#97C23132yes—
143D4×#97C23132yes—
144C2×#1770C2×C414yes—
145C2×#1770C2×C414yes—
146C2×#1770C2×C4116yes—
147C2×#1770C2×C414yes—
148C2×#1770C2×C418yes—
149C2×#1770C2314yes—
150C2×#1770C2318yes—
151C2×#1767C2×C414yes—
152C2×#1767C2×C414yes—
153C2×#1767C2×C4116yes—
154C2×#1752C2×C418yes—
155C2×#1752C2×C418yes—
156C2×#1752C2×C4132yes—
157C2×#1752C2×C418yes—
158C2×#1752C2×C4116yes—
159C2×#1752C2318yes—
160C2×#1752C23116yes—
161C2×#1749C2×C418yes—
162C2×#1749C2×C418yes—
163C2×#1749C2×C4132yes—
164C22×#336C2×C412yes—
165C22×#336C2×C412yes—
166C22×#336C2×C412yes—
167C2×C4×#97C2×C412yes—
168C2×C4×#97C2×C412yes—
169C2×C4×#97C2×C418yes—
170C2×C4×#97C2312yes—
171C2×C4×#97C2312yes—
172C2×C4×#97C2318yes—
173#12666C231128yescomplemented
174#12658C23132yescomplemented
175#12658C23132yescomplemented
176#12616C231256yescomplemented
177#12605C23132yes—
178#12605C23132yes—
179#12605C23164yes—
180#12605C23164yescomplemented
181#12605C23164yescomplemented
182#12594C23132yescomplemented
183C2×#1375C2318yes—
184C2×#1375C23116yes—
185C2×#1375C2318yes—
186C2×#1375C23164yescomplemented
187C4×#347C23132yescomplemented
188C24×D4M1611yescharacteristic
189C25×C4—22no—
190C25×C4C22×C412yes—
191C24×C8—24no—
192C24×C8—28no—
193C24×C8—22no—
194C24×C8—22no—
195C24×C8—48no—
196C24×C8—48no—
197C24×C8—48no—
198C24×C8—48no—
199C24×C8C22×C411yescharacteristic
200C24×C8C22×C414yes—
201C24×C8C22×C414yes—
202C24×C8C22×C412yes—
203C24×C8C22×C4116yes—
204C24×C8C22×C411yescharacteristic
205C24×C8C22×C412yes—
206C24×C8C22×C418yes—
207C24×C8C22×C414yes—
208C24×C8C22×C411yescharacteristic
209C24×C8C22×C414yes—
210C24×C8C22×C418yes—
211C24×C8C22×C414yes—
212C24×C8C22×C4116yes—
213C24×C8C2411yescharacteristic
214C24×C8C2414yes—
215C24×C8C2418yes—
216C22×C4×D4—24no—
217C22×C4×D4—24no—
218C22×C4×D4—216no—
219C22×C4×D4—416no—
220C22×C4×D4C4212yes—
221C22×C4×D4C4214yes—
222C22×C4×D4C4211yescharacteristic
223C22×C4×D4C4218yes—
224C22×C4×D4C4211yescharacteristic
225C22×C4×D4M1614yes—
226C22×C4×D4M1618yes—
227C22×C4×D4M1611yescharacteristic
228C22×C4×D4M1612yes—
229C22×C4×D4M1611yescharacteristic
230C22×C4×D4M1614yes—
231C22×C4×D4M1618yes—
232C22×C4×D4C22×C414yes—
233C22×C4×D4C22×C418yes—
234C23×C4⋊C4—21no—
235C23×C4⋊C4M1611yescharacteristic
236C23×C22⋊C4—22no—
237C23×C22⋊C4M1612yes—
238C23×C42—22no—
239C23×C42—24no—
240C23×C42—28no—
241C23×C42—21no—
242C23×C42—21no—
243C23×C42—48no—
244C23×C42—48no—
245C23×C42C22×C411yescharacteristic
246C23×C42C22×C414yes—
247C23×C42C22×C414yes—
248C23×C42C22×C412yes—
249C23×C42C22×C411yescharacteristic
250C23×C42C22×C4116yes—
251C23×C42C22×C411yescharacteristic
252C22×M32—432no—
253C22×M32—432no—
254C22×M32C22×C4132yescomplemented
255C22×M32C22×C4164yescomplemented
256C22×M32C24116yes—
257C22×M32C24164yes—
258C23×C16C22×C4132yescomplemented
259C2×C8×D4—28no—
260C2×C8×D4—24no—
261C2×C8×D4—216no—
262C2×C8×D4—28no—
263C2×C8×D4—24no—
264C2×C8×D4—216no—
265C2×C8×D4—24no—
266C2×C8×D4—24no—
267C2×C8×D4—264no—
268C2×C8×D4—232no—
269C2×C8×D4—216no—
270C2×C8×D4—216no—
271C2×C8×D4C4218yes—
272C2×C8×D4C42116yes—
273C2×C8×D4C42116yes—
274C2×C8×D4C42132yes—
275C2×C8×D4C4218yes—
276C2×C8×D4C42164yes—
277C2×C8×D4C42116yes—
278C2×C8×D4C42132yes—
279C2×C8×D4C22×C418yes—
280C2×C8×D4C22×C4116yes—
281C2×C8×D4C22×C418yes—
282C2×C8×D4C22×C4132yes—
283C2×C8×D4C22×C4116yes—
284C2×C8×D4C22×C4132yes—
285C2×C8×D4C22×C4164yes—
286C2×C8×D4C22×C4116yes—
287C2×C8×D4C22×C4132yes—
288C2×C8×D4C22×C4132yes—
289C2×C8×D4C22×C4116yes—
290C2×C8×D4C22×C4132yes—
291C2×C8×D4C24116yes—
292C22×C4⋊C8—22no—
293C22×C4⋊C8—24no—
294C22×C4⋊C8—21no—
295C22×C4⋊C8—21no—
296C22×C4⋊C8C4212yes—
297C22×C4⋊C8C4212yes—
298C22×C4⋊C8C4214yes—
299C22×C4⋊C8C4218yes—
300C22×C4⋊C8C22×C414yes—
301C22×C4⋊C8C22×C418yes—
302C22×C4⋊C8C22×C414yes—
303C22×C4⋊C8C22×C418yes—
304C22×C22⋊C8—24no—
305C22×C22⋊C8—28no—
306C22×C22⋊C8—22no—
307C22×C22⋊C8—22no—
308C22×C22⋊C8C4214yes—
309C22×C22⋊C8C4214yes—
310C22×C22⋊C8C4218yes—
311C22×C22⋊C8C42116yes—
312C22×C22⋊C8C22×C418yes—
313C22×C22⋊C8C22×C4116yes—
314C22×C22⋊C8C22×C418yes—
315C22×C22⋊C8C22×C4116yes—
316C22×#97—232no—
317C22×#97—28no—
318C22×#97—48no—
319C22×#97—416no—
320C22×#97—48no—
321C22×#97—416no—
322C22×#97—44no—
323C22×#97—44no—
324C22×#97—464no—
325C22×#97—464no—
326C22×#97—416no—
327C22×#97—48no—
328C22×#97—44no—
329C22×#97C22×C4116yes—
330C22×#97C22×C414yes—
331C22×#97C22×C411yescharacteristic
332C22×#97C22×C411yescharacteristic
333C22×#97C22×C412yes—
334C22×#97C22×C412yes—
335C22×#97C22×C414yes—
336C22×#97C22×C414yes—
337C22×#97C22×C4116yes—
338C22×#97C22×C4132yes—
339C22×#97C22×C4132yes—
340C22×#97C22×C412yes—
341C22×#97C22×C414yes—
342C22×#97C22×C412yes—
343C22×#97C22×C418yes—
344C22×#97C22×C418yes—
345C22×#97C22×C412yes—
346C22×#97C22×C414yes—
347C22×#97C22×C4116yes—
348C22×#97C22×C4116yes—
349C22×#97C22×C414yes—
350C22×#97C22×C414yes—
351C22×#97C22×C418yes—
352C22×#97C2411yescharacteristic
353C22×#97C2412yes—
354C22×#97C2414yes—
355C22×#97C24116yes—
356C22×#97C2414yes—
357C22×#97C24116yes—
358C22×#97C2414yes—
359C22×#97C2418yes—
360C22×#97C2411yescharacteristic
361C22×C4×C8—22no—
362C22×C4×C8—24no—
363C22×C4×C8—21no—
364C22×C4×C8—21no—
365C22×C4×C8C22×C412yes—
366C22×C4×C8C22×C414yes—
367C22×C4×C8C22×C412yes—
368C22×C4×C8C22×C418yes—
369C22×C4×C8C22×C418yes—
370C22×C4×C8C22×C412yes—
371C22×C4×C8C22×C412yes—
372C22×C4×C8C22×C412yes—
373C22×C4×C8C22×C414yes—
374C22×C4×C8C2412yes—
375C22×C4×C8C2414yes—
376C42×D4—216no—
377C42×D4—216no—
378C42×D4—264no—
379C42×D4C22×C4132yes—
380C42×D4C22×C4132yes—
381C2×C4×C4⋊C4—22no—
382C2×C4×C4⋊C4—24no—
383C2×C4×C4⋊C4—24no—
384C2×C4×C4⋊C4—24no—
385C2×C4×C4⋊C4—216no—
386C2×C4×C4⋊C4C22×C414yes—
387C2×C4×C4⋊C4C22×C418yes—
388C2×C4×C22⋊C4—24no—
389C2×C4×C22⋊C4—28no—
390C2×C4×C22⋊C4—28no—
391C2×C4×C22⋊C4—28no—
392C2×C4×C22⋊C4—232no—
393C2×C4×C22⋊C4C22×C418yes—
394C2×C4×C22⋊C4C22×C4116yes—
395C22×#95—21no—
396C22×#95—22no—
397C2×C43—22no—
398C2×C43—24no—
399C2×C43C22×C418yes—
400C2×C43C22×C412yes—
401C2×C43C22×C412yes—
402#2169C22×C41256yescomplemented
403#2168C22×C41512yescomplemented
404D4×C16C22×C41256yescomplemented
405#2163C22×C4164yescomplemented
406#2163C22×C4164yescomplemented
407#2162C22×C4164yescomplemented
408#2162C22×C4164yescomplemented
409#2150C22×C4132yescomplemented
410#2150C24132yes—
411C2×C4⋊C16C22×C4116yescomplemented
412C2×C4⋊C16C22×C4116yescomplemented
413#2112C22×C4132yes—
414#2112C22×C41128yescomplemented
415#2112C22×C41128yescomplemented
416#2112C22×C4164yescomplemented
417#2112C24132yes—
418#2112C24164yes—
419C2×C22⋊C16C22×C4116yes—
420C2×C22⋊C16C22×C4116yes—
421C2×C22⋊C16C22×C41128yescomplemented
422C2×C22⋊C16C22×C41128yescomplemented
423C2×C22⋊C16C22×C4132yescomplemented
424C2×C22⋊C16C22×C4132yescomplemented
425C2×#347—232no—
426C2×#347—4128no—
427C2×#347—432no—
428C2×#347—416no—
429C2×#347C24132yes—
430C2×#347C24164yes—
431C2×#347C24132yes—
432C4×M32C22×C4132yescomplemented
433C4×M32C24132yes—
434C2×#346C22×C4116yescomplemented
435C2×C4×C16C22×C4116yescomplemented
436#1770C22×C4116yes—
437#1770C22×C4132yes—
438#1770C22×C4132yes—
439#1770C22×C4132yes—
440#1770C24116yes—
441#1767C22×C4132yes—
442#1767C22×C4132yes—
443#1752C22×C4132yes—
444#1752C22×C4164yes—
445#1752C22×C4164yes—
446#1752C22×C4164yes—
447#1752C24132yes—
448#1749C22×C4164yes—
449#1749C22×C4164yes—
450C2×#336C22×C418yes—
451C2×#336C22×C4116yes—
452C2×#336C22×C418yes—
453C2×#336C22×C4116yes—
454C2×#336C22×C418yes—
455C2×#336C22×C4116yes—
456C4×#97C22×C418yes—
457C4×#97C22×C4116yes—
458C4×#97C22×C4116yes—
459C4×#97C22×C418yes—
460C4×#97C2418yes—
461C4×#97C2418yes—
462#1375C24132yes—
463#1375C24164yes—
464#1375C24132yes—
465C26C2×M1612yes—
466C23×D4—216no—
467C23×D4#9712yes—
468C23×D4#9714yes—
469C23×D4#9718yes—
470C23×D4#9711yescharacteristic
471C23×D4#9711yescharacteristic
472C23×D4C2×M1614yes—
473C23×D4C2×M1618yes—
474C24×C4—21no—
475C24×C4—22no—
476C24×C4—21no—
477C24×C4—24no—
478C24×C4—24no—
479C24×C4—216no—
480C24×C4—44no—
481C24×C4—44no—
482C24×C4—44no—
483C24×C4—44no—
484C24×C4—416no—
485C24×C4—416no—
486C24×C4—88no—
487C24×C4C2×C4218yes—
488C24×C4C2×C4214yes—
489C24×C4C2×C4212yes—
490C24×C4C2×C4212yes—
491C24×C4C2×M1611yescharacteristic
492C24×C4C2×M1614yes—
493C24×C4C2×M1612yes—
494C24×C4C2×M1618yes—
495C24×C4C2×M1612yes—
496C24×C4C2×M1612yes—
497C24×C4C2×M1618yes—
498C24×C4C2×M1614yes—
499C24×C4C2×M1611yescharacteristic
500C24×C4C23×C411yescharacteristic
501C24×C4C23×C414yes—
502C24×C4C23×C418yes—
503C23×C8—22no—
504C23×C8—21no—
505C23×C8—21no—
506C23×C8—24no—
507C23×C8—24no—
508C23×C8—24no—
509C23×C8—216no—
510C23×C8—24no—
511C23×C8—216no—
512C23×C8—22no—
513C23×C8—21no—
514C23×C8—21no—
515C23×C8—24no—
516C23×C8—22no—
517C23×C8—22no—
518C23×C8—24no—
519C23×C8—28no—
520C23×C8—24no—
521C23×C8—24no—
522C23×C8—28no—
523C23×C8—24no—
524C23×C8—232no—
525C23×C8—216no—
526C23×C8—216no—
527C23×C8—216no—
528C23×C8—216no—
529C23×C8—416no—
530C23×C8—432no—
531C23×C8—416no—
532C23×C8—416no—
533C23×C8—416no—
534C23×C8—432no—
535C23×C8—416no—
536C23×C8—464no—
537C23×C8—432no—
538C23×C8—416no—
539C23×C8—48no—
540C23×C8—48no—
541C23×C8—44no—
542C23×C8—44no—
543C23×C8—42no—
544C23×C8—42no—
545C23×C8—42no—
546C23×C8—42no—
547C23×C8—48no—
548C23×C8—44no—
549C23×C8—48no—
550C23×C8—44no—
551C23×C8—416no—
552C23×C8—432no—
553C23×C8—464no—
554C23×C8—416no—
555C23×C8C2×C4214yes—
556C23×C8C2×C4212yes—
557C23×C8C2×C4212yes—
558C23×C8C2×C4218yes—
559C23×C8C2×C4214yes—
560C23×C8C2×C4214yes—
561C23×C8C2×C42116yes—
562C23×C8C2×C42132yes—
563C23×C8C2×C42116yes—
564C23×C8C2×C42116yes—
565C23×C8C2×C4218yes—
566C23×C8C2×C4218yes—
567C23×C8C23×C414yes—
568C23×C8C23×C412yes—
569C23×C8C23×C414yes—
570C23×C8C23×C4116yes—
571C23×C8C23×C4116yes—
572C23×C8C23×C411yescharacteristic
573C23×C8C23×C411yescharacteristic
574C23×C8C23×C412yes—
575C23×C8C23×C412yes—
576C23×C8C23×C414yes—
577C23×C8C23×C418yes—
578C23×C8C23×C418yes—
579C23×C8C23×C4116yes—
580C23×C8C23×C411yescharacteristic
581C23×C8C23×C412yes—
582C23×C8C23×C412yes—
583C23×C8C23×C414yes—
584C23×C8C23×C418yes—
585C23×C8C23×C414yes—
586C23×C8C23×C418yes—
587C23×C8C23×C4116yes—
588C23×C8C23×C4132yes—
589C23×C8C23×C4116yes—
590C23×C8C23×C414yes—
591C23×C8C23×C418yes—
592C23×C8C23×C4116yes—
593C23×C8C2512yes—
594C23×C8C2518yes—
595C23×C8C2511yescharacteristic
596C2×C4×D4—232no—
597C2×C4×D4—232no—
598C2×C4×D4—432no—
599C2×C4×D4—432no—
600C2×C4×D4—4128no—
601C2×C4×D4#9718yes—
602C2×C4×D4#9718yes—
603C2×C4×D4#97132yes—
604C2×C4×D4#97132yes—
605C2×C4×D4#9714yes—
606C2×C4×D4#9714yes—
607C2×C4×D4#97132yes—
608C2×C4×D4#97116yes—
609C2×C4×D4#97116yes—
610C2×C4×D4#9718yes—
611C2×C4×D4#9718yes—
612C2×C4×D4#9714yes—
613C2×C4×D4#9714yes—
614C2×C4×D4#9718yes—
615C2×C4×D4#9718yes—
616C2×C4×D4C2×C42116yes—
617C2×C4×D4C2×C42116yes—
618C2×C4×D4C2×C42132yes—
619C2×C4×D4C2×C4218yes—
620C2×C4×D4C2×C4218yes—
621C2×C4×D4C2×C4218yes—
622C2×C4×D4C2×C4214yes—
623C2×C4×D4C2×C4214yes—
624C2×C4×D4C2×M16116yes—
625C2×C4×D4C2×M16132yes—
626C2×C4×D4C2×M1618yes—
627C2×C4×D4C2×M1614yes—
628C2×C4×D4C2×M16116yes—
629C2×C4×D4C2×M1614yes—
630C2×C4×D4C2×M16132yes—
631C2×C4×D4C2×M16116yes—
632C2×C4×D4C2×M1618yes—
633C2×C4×D4C2×M1618yes—
634C2×C4×D4C23×C4116yes—
635C22×C4⋊C4—24no—
636C22×C4⋊C4—28no—
637C22×C4⋊C4—48no—
638C22×C4⋊C4#9712yes—
639C22×C4⋊C4#9718yes—
640C22×C4⋊C4#9714yes—
641C22×C4⋊C4#9711yescharacteristic
642C22×C4⋊C4#9711yescharacteristic
643C22×C4⋊C4C2×M1614yes—
644C22×C4⋊C4C2×M1618yes—
645C22×C22⋊C4—28no—
646C22×C22⋊C4—216no—
647C22×C22⋊C4—416no—
648C22×C22⋊C4#9718yes—
649C22×C22⋊C4#9712yes—
650C22×C22⋊C4#9712yes—
651C22×C22⋊C4#97116yes—
652C22×C22⋊C4#9712yes—
653C22×C22⋊C4#9712yes—
654C22×C22⋊C4C2×M1618yes—
655C22×C22⋊C4C2×M16116yes—
656C22×C42—21no—
657C22×C42—22no—
658C22×C42—24no—
659C22×C42—24no—
660C22×C42—216no—
661C22×C42—216no—
662C22×C42—24no—
663C22×C42—24no—
664C22×C42—216no—
665C22×C42—22no—
666C22×C42—24no—
667C22×C42—28no—
668C22×C42—28no—
669C22×C42—232no—
670C22×C42—22no—
671C22×C42—22no—
672C22×C42—28no—
673C22×C42—21no—
674C22×C42—22no—
675C22×C42—28no—
676C22×C42—22no—
677C22×C42—22no—
678C22×C42—432no—
679C22×C42—432no—
680C22×C42—48no—
681C22×C42—44no—
682C22×C42—42no—
683C22×C42—42no—
684C22×C42—48no—
685C22×C42—44no—
686C22×C42—464no—
687C22×C42—432no—
688C22×C42—416no—
689C22×C42—48no—
690C22×C42—84no—
691C22×C42C2×C4214yes—
692C22×C42C2×C4212yes—
693C22×C42C2×C4211yescharacteristic
694C22×C42C2×C4211yescharacteristic
695C22×C42C2×M1612yes—
696C22×C42C2×M1614yes—
697C22×C42C2×M1611yescharacteristic
698C22×C42C2×M1611yescharacteristic
699C22×C42C2×M1612yes—
700C22×C42C2×M1614yes—
701C22×C42C23×C414yes—
702C22×C42C23×C414yes—
703C22×C42C23×C412yes—
704C22×C42C23×C4116yes—
705C22×C42C23×C4116yes—
706C22×C42C23×C411yescharacteristic
707C22×C42C23×C411yescharacteristic
708C22×C42C23×C418yes—
709C22×C42C23×C414yes—
710C22×C42C23×C414yes—
711C22×C42C23×C412yes—
712C2×M32—232no—
713C2×M32—232no—
714C2×M32—464no—
715C2×M32—464no—
716C2×M32—4128no—
717C2×M32—464no—
718C2×M32C23×C4132yes—
719C2×M32C23×C41128yescomplemented
720C2×M32C25132yes—
721C22×C16—464no—
722C22×C16C23×C4132yes—
723C22×C16C23×C41128yescomplemented
724C8×D4—264no—
725C8×D4—232no—
726C8×D4—264no—
727C8×D4—232no—
728C8×D4—232no—
729C8×D4—232no—
730C8×D4C2×C42132yes—
731C8×D4C2×C42164yes—
732C8×D4C2×C42132yes—
733C8×D4C2×C42164yes—
734C8×D4C2×C421128yes—
735C8×D4C2×C42164yes—
736C8×D4C23×C4132yes—
737C8×D4C23×C4164yes—
738C8×D4C23×C4132yes—
739C2×C4⋊C8—216no—
740C2×C4⋊C8—24no—
741C2×C4⋊C8—24no—
742C2×C4⋊C8—28no—
743C2×C4⋊C8—28no—
744C2×C4⋊C8—28no—
745C2×C4⋊C8C2×C42116yes—
746C2×C4⋊C8C2×C42116yes—
747C2×C4⋊C8C2×C42116yes—
748C2×C4⋊C8C2×C42132yes—
749C2×C4⋊C8C2×C4218yes—
750C2×C4⋊C8C2×C4218yes—
751C2×C4⋊C8C23×C4116yes—
752C2×C4⋊C8C23×C4116yes—
753C2×C22⋊C8—28no—
754C2×C22⋊C8—216no—
755C2×C22⋊C8—28no—
756C2×C22⋊C8—232no—
757C2×C22⋊C8—216no—
758C2×C22⋊C8—216no—
759C2×C22⋊C8C2×C42132yes—
760C2×C22⋊C8C2×C42116yes—
761C2×C22⋊C8C2×C42116yes—
762C2×C22⋊C8C2×C42132yes—
763C2×C22⋊C8C2×C42132yes—
764C2×C22⋊C8C2×C42164yes—
765C2×C22⋊C8C23×C4132yes—
766C2×C22⋊C8C23×C4132yes—
767C2×#97—24no—
768C2×#97—216no—
769C2×#97—28no—
770C2×#97—24no—
771C2×#97—216no—
772C2×#97—28no—
773C2×#97—24no—
774C2×#97—216no—
775C2×#97—28no—
776C2×#97—216no—
777C2×#97—264no—
778C2×#97—216no—
779C2×#97—264no—
780C2×#97—464no—
781C2×#97—432no—
782C2×#97—416no—
783C2×#97—432no—
784C2×#97—464no—
785C2×#97—432no—
786C2×#97—416no—
787C2×#97—416no—
788C2×#97—432no—
789C2×#97—48no—
790C2×#97—416no—
791C2×#97—48no—
792C2×#97—48no—
793C2×#97—48no—
794C2×#97—48no—
795C2×#97—44no—
796C2×#97—44no—
797C2×#97—44no—
798C2×#97C23×C414yes—
799C2×#97C23×C412yes—
800C2×#97C23×C414yes—
801C2×#97C23×C4116yes—
802C2×#97C23×C418yes—
803C2×#97C23×C4116yes—
804C2×#97C23×C418yes—
805C2×#97C23×C418yes—
806C2×#97C23×C414yes—
807C2×#97C23×C4116yes—
808C2×#97C23×C4116yes—
809C2×#97C23×C4116yes—
810C2×#97C23×C418yes—
811C2×#97C23×C418yes—
812C2×#97C23×C418yes—
813C2×#97C23×C412yes—
814C2×#97H(5,𝔽2)18yes—
815C2×#97C2512yes—
816C2×#97C2518yes—
817C2×#97C2514yes—
818C2×#97C2512yes—
819C2×C4×C8—216no—
820C2×C4×C8—22no—
821C2×C4×C8—22no—
822C2×C4×C8—22no—
823C2×C4×C8—22no—
824C2×C4×C8—28no—
825C2×C4×C8—24no—
826C2×C4×C8—24no—
827C2×C4×C8—28no—
828C2×C4×C8C2×C4218yes—
829C2×C4×C8C2×C4218yes—
830C2×C4×C8C2×C42116yes—
831C2×C4×C8C2×C4218yes—
832C2×C4×C8C2×C4214yes—
833C2×C4×C8C2×C4214yes—
834C2×C4×C8C23×C418yes—
835C2×C4×C8C23×C418yes—
836C2×C4×C8C23×C414yes—
837C2×C4×C8C23×C414yes—
838C2×C4×C8C23×C418yes—
839C2×C4×C8C23×C418yes—
840C2×C4×C8C23×C4116yes—
841C2×C4×C8C23×C418yes—
842C2×C4×C8C23×C418yes—
843C2×C4×C8C23×C414yes—
844C2×C4×C8C2514yes—
845C4×C4⋊C4—232no—
846C4×C4⋊C4—232no—
847C4×C4⋊C4—216no—
848C4×C4⋊C4—28no—
849C4×C4⋊C4C23×C4116yes—
850C4×C22⋊C4—216no—
851C4×C22⋊C4—232no—
852C4×C22⋊C4—264no—
853C4×C22⋊C4—264no—
854C4×C22⋊C4C23×C4132yes—
855C2×#95—28no—
856C2×#95—24no—
857C2×#95—28no—
858C2×#95—216no—
859C43—216no—
860C43—24no—
861C43—24no—
862C43C23×C418yes—
863C43C23×C418yes—
864C4⋊C16C23×C4164yescomplemented
865C4⋊C16C23×C4164yescomplemented
866C22⋊C16C23×C4164yes—
867C22⋊C16C23×C4164yes—
868C22⋊C16C23×C41128yescomplemented
869C22⋊C16C23×C41128yescomplemented
870#347—264no—
871#347—464no—
872#347—432no—
873#346C23×C4164yescomplemented
874C4×C16C23×C4164yescomplemented
875#336C23×C4132yes—
876#336C23×C4132yes—
877#336C23×C4132yes—
878C25—216no—
879C25—44no—
880C25—44no—
881C25—48no—
882C25C2×#9714yes—
883C25C2×#9712yes—
884C25C2×#9718yes—
885C25C2×#9712yes—
886C25C22×M1611yescharacteristic
887C25C22×M1614yes—
888C25C22×M1618yes—
889C22×D4—216no—
890C22×D4—232no—
891C22×D4—264no—
892C22×D4—232no—
893C22×D4—264no—
894C22×D4—28no—
895C22×D4#347116yescomplemented
896C22×D4C2×#9718yes—
897C22×D4C2×#97116yes—
898C22×D4C2×#97132yes—
899C22×D4C2×#97116yes—
900C22×D4C2×#9714yes—
901C22×D4C2×#9718yes—
902C22×D4C2×#9714yes—
903C22×D4C2×#9718yes—
904C22×D4C22×M16116yes—
905C23×C4—28no—
906C23×C4—22no—
907C23×C4—28no—
908C23×C4—22no—
909C23×C4—28no—
910C23×C4—22no—
911C23×C4—28no—
912C23×C4—22no—
913C23×C4—28no—
914C23×C4—28no—
915C23×C4—24no—
916C23×C4—21no—
917C23×C4—21no—
918C23×C4—24no—
919C23×C4—22no—
920C23×C4—28no—
921C23×C4—24no—
922C23×C4—216no—
923C23×C4—216no—
924C23×C4—48no—
925C23×C4—416no—
926C23×C4—44no—
927C23×C4—48no—
928C23×C4—44no—
929C23×C4—44no—
930C23×C4—48no—
931C23×C4—416no—
932C23×C4—44no—
933C23×C4—48no—
934C23×C4—48no—
935C23×C4—416no—
936C23×C4—44no—
937C23×C4—48no—
938C23×C4—44no—
939C23×C4—416no—
940C23×C4—44no—
941C23×C4—48no—
942C23×C4—416no—
943C23×C4—44no—
944C23×C4—416no—
945C23×C4—48no—
946C23×C4—48no—
947C23×C4—44no—
948C23×C4—48no—
949C23×C4—44no—
950C23×C4—44no—
951C23×C4—416no—
952C23×C4—416no—
953C23×C4—464no—
954C23×C4—44no—
955C23×C4—44no—
956C23×C4—44no—
957C23×C4—48no—
958C23×C4—416no—
959C23×C4—416no—
960C23×C4—464no—
961C23×C4—48no—
962C23×C4—48no—
963C23×C4—44no—
964C23×C4—44no—
965C23×C4—88no—
966C23×C4—88no—
967C23×C4—832no—
968C23×C4—8128no—
969C23×C4C2×#9712yes—
970C23×C4C2×#9711yescharacteristic
971C23×C4C2×#9712yes—
972C23×C4C2×#9714yes—
973C23×C4C2×#9714yes—
974C23×C4C2×#9711yescharacteristic
975C23×C4C2×#9711yescharacteristic
976C23×C4C2×#9718yes—
977C23×C4C2×#9712yes—
978C23×C4C2×#9712yes—
979C23×C4C2×#9714yes—
980C23×C4C2×#97116yes—
981C23×C4C2×#97116yes—
982C23×C4C2×#9718yes—
983C23×C4C2×#9718yes—
984C23×C4C2×#9718yes—
985C23×C4C2×#9718yes—
986C23×C4C2×#9714yes—
987C23×C4C2×#9714yes—
988C23×C4C2×#97116yes—
989C23×C4C2×#9714yes—
990C23×C4C2×#9714yes—
991C23×C4C2×#9711yescharacteristic
992C23×C4C22×C4218yes—
993C23×C4C22×C4212yes—
994C23×C4C22×C4214yes—
995C23×C4C22×C4214yes—
996C23×C4C22×C4211yescharacteristic
997C23×C4C22×C4211yescharacteristic
998C23×C4C22×C42116yes—
999C23×C4C22×C4218yes—
1000C23×C4C22×C4218yes—
1001C23×C4C22×M1614yes—
1002C23×C4C22×M1612yes—
1003C23×C4C22×M1614yes—
1004C23×C4C22×M1618yes—
1005C23×C4C22×M1611yescharacteristic
1006C23×C4C22×M1612yes—
1007C23×C4C22×M1614yes—
1008C23×C4C22×M1618yes—
1009C23×C4C22×M1614yes—
1010C23×C4C22×M1612yes—
1011C23×C4C22×M1611yescharacteristic
1012C23×C4C22×M1611yescharacteristic
1013C23×C4C22×M1614yes—
1014C23×C4C22×M1612yes—
1015C23×C4C22×M1618yes—
1016C23×C4C22×M16116yes—
1017C23×C4C22×M16116yes—
1018C23×C4C22×M1618yes—
1019C23×C4C22×M1618yes—
1020C23×C4C24×C418yes—
1021C23×C4C24×C412yes—
1022C23×C4C24×C411yescharacteristic
1023C22×C8—216no—
1024C22×C8—28no—
1025C22×C8—28no—
1026C22×C8—22no—
1027C22×C8—22no—
1028C22×C8—28no—
1029C22×C8—22no—
1030C22×C8—28no—
1031C22×C8—24no—
1032C22×C8—24no—
1033C22×C8—21no—
1034C22×C8—21no—
1035C22×C8—21no—
1036C22×C8—21no—
1037C22×C8—22no—
1038C22×C8—24no—
1039C22×C8—24no—
1040C22×C8—24no—
1041C22×C8—216no—
1042C22×C8—24no—
1043C22×C8—216no—
1044C22×C8—28no—
1045C22×C8—24no—
1046C22×C8—216no—
1047C22×C8—24no—
1048C22×C8—216no—
1049C22×C8—28no—
1050C22×C8—28no—
1051C22×C8—216no—
1052C22×C8—232no—
1053C22×C8—264no—
1054C22×C8—232no—
1055C22×C8—28no—
1056C22×C8—28no—
1057C22×C8—24no—
1058C22×C8—28no—
1059C22×C8—28no—
1060C22×C8—24no—
1061C22×C8—24no—
1062C22×C8—216no—
1063C22×C8—216no—
1064C22×C8—216no—
1065C22×C8—216no—
1066C22×C8—24no—
1067C22×C8—24no—
1068C22×C8—22no—
1069C22×C8—22no—
1070C22×C8—28no—
1071C22×C8—24no—
1072C22×C8—232no—
1073C22×C8—232no—
1074C22×C8—432no—
1075C22×C8—464no—
1076C22×C8—432no—
1077C22×C8—432no—
1078C22×C8—464no—
1079C22×C8—432no—
1080C22×C8—432no—
1081C22×C8—416no—
1082C22×C8—416no—
1083C22×C8—416no—
1084C22×C8—48no—
1085C22×C8—48no—
1086C22×C8—416no—
1087C22×C8—416no—
1088C22×C8—48no—
1089C22×C8—48no—
1090C22×C8—416no—
1091C22×C8—416no—
1092C22×C8—48no—
1093C22×C8—48no—
1094C22×C8—48no—
1095C22×C8—44no—
1096C22×C8—44no—
1097C22×C8—44no—
1098C22×C8—44no—
1099C22×C8—44no—
1100C22×C8—44no—
1101C22×C8—416no—
1102C22×C8—432no—
1103C22×C8—416no—
1104C22×C8—416no—
1105C22×C8—432no—
1106C22×C8—416no—
1107C22×C8—464no—
1108C22×C8—4128no—
1109C22×C8—464no—
1110C22×C8—48no—
1111C22×C8—44no—
1112C22×C8—44no—
1113C22×C8—416no—
1114C22×C8—48no—
1115C22×C8—48no—
1116C22×C8C22×C4212yes—
1117C22×C8C22×C4214yes—
1118C22×C8C22×C4214yes—
1119C22×C8C22×C4218yes—
1120C22×C8C22×C42116yes—
1121C22×C8C22×C42116yes—
1122C22×C8C22×C4214yes—
1123C22×C8C22×C4212yes—
1124C22×C8C22×C4218yes—
1125C22×C8C22×C4214yes—
1126C22×C8C22×C42116yes—
1127C22×C8C22×C42116yes—
1128C22×C8C22×C42132yes—
1129C22×C8C22×C42132yes—
1130C22×C8C22×C4218yes—
1131C22×C8C22×C4218yes—
1132C22×C8#51814yes—
1133C22×C8#56814yes—
1134C22×C8C24×C418yes—
1135C22×C8C24×C414yes—
1136C22×C8C24×C414yes—
1137C22×C8C24×C414yes—
1138C22×C8C24×C4116yes—
1139C22×C8C24×C4116yes—
1140C22×C8C24×C412yes—
1141C22×C8C24×C418yes—
1142C22×C8C24×C414yes—
1143C22×C8C24×C412yes—
1144C22×C8C24×C412yes—
1145C22×C8C24×C412yes—
1146C22×C8C24×C412yes—
1147C22×C8C24×C411yescharacteristic
1148C22×C8C2×H(5,𝔽2)14yes—
1149C22×C8#58514yes—
1150C22×C8C2611yescharacteristic
1151C4×D4—4128no—
1152C4×D4—4128no—
1153C4×D4C2×#97132yes—
1154C4×D4C2×#97132yes—
1155C4×D4C2×#97116yes—
1156C4×D4C2×#97116yes—
1157C4×D4C2×#97116yes—
1158C4×D4C2×#97116yes—
1159C4×D4C2×#97164yes—
1160C4×D4C2×#97164yes—
1161C4×D4C2×#97132yes—
1162C4×D4C2×#97132yes—
1163C4×D4C2×#97132yes—
1164C4×D4C2×#97132yes—
1165C4×D4C22×C42132yes—
1166C4×D4C22×C42116yes—
1167C4×D4C22×C42116yes—
1168C4×D4C22×M16132yes—
1169C4×D4C22×M16116yes—
1170C4×D4C22×M16116yes—
1171C2×C4⋊C4—216no—
1172C2×C4⋊C4—416no—
1173C2×C4⋊C4—432no—
1174C2×C4⋊C4C2×#9718yes—
1175C2×C4⋊C4C2×#97116yes—
1176C2×C4⋊C4C2×#97116yes—
1177C2×C4⋊C4C2×#97132yes—
1178C2×C4⋊C4C2×#9714yes—
1179C2×C4⋊C4C2×#9714yes—
1180C2×C4⋊C4C2×#9718yes—
1181C2×C4⋊C4C2×#9718yes—
1182C2×C4⋊C4C22×M16116yes—
1183C2×C22⋊C4—232no—
1184C2×C22⋊C4—432no—
1185C2×C22⋊C4—464no—
1186C2×C22⋊C4C2×#9718yes—
1187C2×C22⋊C4C2×#9718yes—
1188C2×C22⋊C4C2×#9718yes—
1189C2×C22⋊C4C2×#9718yes—
1190C2×C22⋊C4C2×#97164yes—
1191C2×C22⋊C4C2×#97132yes—
1192C2×C22⋊C4C2×#97116yes—
1193C2×C22⋊C4C2×#97116yes—
1194C2×C22⋊C4C2×#97116yes—
1195C2×C22⋊C4C2×#97116yes—
1196C2×C22⋊C4C22×M16132yes—
1197C2×C42—28no—
1198C2×C42—216no—
1199C2×C42—22no—
1200C2×C42—24no—
1201C2×C42—21no—
1202C2×C42—21no—
1203C2×C42—22no—
1204C2×C42—28no—
1205C2×C42—28no—
1206C2×C42—28no—
1207C2×C42—24no—
1208C2×C42—24no—
1209C2×C42—28no—
1210C2×C42—232no—
1211C2×C42—232no—
1212C2×C42—28no—
1213C2×C42—28no—
1214C2×C42—24no—
1215C2×C42—22no—
1216C2×C42—216no—
1217C2×C42—216no—
1218C2×C42—28no—
1219C2×C42—24no—
1220C2×C42—28no—
1221C2×C42—28no—
1222C2×C42—416no—
1223C2×C42—48no—
1224C2×C42—44no—
1225C2×C42—44no—
1226C2×C42—416no—
1227C2×C42—48no—
1228C2×C42—432no—
1229C2×C42—432no—
1230C2×C42—4128no—
1231C2×C42—416no—
1232C2×C42—416no—
1233C2×C42—48no—
1234C2×C42—48no—
1235C2×C42—432no—
1236C2×C42—44no—
1237C2×C42—48no—
1238C2×C42—464no—
1239C2×C42—48no—
1240C2×C42—416no—
1241C2×C42—816no—
1242C2×C42—84no—
1243C2×C42—84no—
1244C2×C42C2×#9712yes—
1245C2×C42C2×#9712yes—
1246C2×C42C2×#9718yes—
1247C2×C42C2×#9718yes—
1248C2×C42C2×#9712yes—
1249C2×C42C2×#9712yes—
1250C2×C42C2×#9718yes—
1251C2×C42C2×#9714yes—
1252C2×C42C2×#9714yes—
1253C2×C42C2×#9714yes—
1254C2×C42C2×#9714yes—
1255C2×C42C22×C4218yes—
1256C2×C42C22×C4214yes—
1257C2×C42C22×C4214yes—
1258C2×C42C22×C4214yes—
1259C2×C42C22×C4212yes—
1260C2×C42C22×C4212yes—
1261C2×C42#51814yes—
1262C2×C42C22×M1618yes—
1263C2×C42C22×M1614yes—
1264C2×C42C22×M1618yes—
1265C2×C42C22×M1612yes—
1266C2×C42C22×M1612yes—
1267C2×C42C22×M1614yes—
1268C2×C42C22×M1614yes—
1269C2×C42C22×M1614yes—
1270C2×C42#56814yes—
1271C2×C42C24×C414yes—
1272C2×C42C24×C418yes—
1273C2×C42C24×C412yes—
1274C2×C42C24×C412yes—
1275C2×C42C24×C414yes—
1276M32—232no—
1277M32—232no—
1278M32—264no—
1279M32—4128no—
1280C2×C16—264no—
1281C2×C16—4128no—
1282C2×C16C24×C4164yes—
1283C4⋊C8—216no—
1284C4⋊C8—216no—
1285C4⋊C8C22×C42132yes—
1286C4⋊C8C22×C42132yes—
1287C22⋊C8—232no—
1288C22⋊C8—232no—
1289C22⋊C8C22×C42164yes—
1290C22⋊C8C22×C42164yes—
1291#97—216no—
1292#97—24no—
1293#97—28no—
1294#97—28no—
1295#97—24no—
1296#97—232no—
1297#97—216no—
1298#97—28no—
1299#97—216no—
1300#97—28no—
1301#97—232no—
1302#97—216no—
1303#97—416no—
1304#97—416no—
1305#97—416no—
1306#97—48no—
1307#97—48no—
1308#97—48no—
1309#97#51818yes—
1310#97C2×H(5,𝔽2)18yes—
1311C4×C8—28no—
1312C4×C8—28no—
1313C4×C8—28no—
1314C4×C8—28no—
1315C4×C8C22×C42116yes—
1316C4×C8C22×C42116yes—
1317C4×C8C22×C4218yes—
1318C4×C8C22×C4218yes—
1319C4×C8C24×C418yes—
1320C4×C8C24×C418yes—
1321#95—216no—
1322#95—232no—
1323C24—24no—
1324C24—24no—
1325C24—22no—
1326C24—22no—
1327C24—216no—
1328C24—216no—
1329C24—28no—
1330C24—232no—
1331C24—232no—
1332C24—216no—
1333C24—28no—
1334C24—28no—
1335C24—48no—
1336C24—48no—
1337C24—44no—
1338C24—48no—
1339C24—416no—
1340C24—44no—
1341C24—48no—
1342C24—416no—
1343C24—44no—
1344C24—416no—
1345C24—44no—
1346C24—464no—
1347C24—464no—
1348C24C2×#347116yescomplemented
1349C24C22×#9714yes—
1350C24C22×#9712yes—
1351C24C22×#97116yes—
1352C24C22×#9718yes—
1353C24C22×#9714yes—
1354C24C22×#9711yescharacteristic
1355C24C22×#9711yescharacteristic
1356C24C22×#9718yes—
1357C24C22×#9718yes—
1358C24C23×M1612yes—
1359C24C23×M1618yes—
1360C24C23×M1611yescharacteristic
1361C2×D4—232no—
1362C2×D4—264no—
1363C2×D4—264no—
1364C2×D4—264no—
1365C2×D4—2128no—
1366C2×D4—216no—
1367C2×D4—232no—
1368C2×D4C2×#347132yescomplemented
1369C2×D4C2×#347164yescomplemented
1370C2×D4C22×#97132yes—
1371C2×D4C22×#97116yes—
1372C2×D4C22×#97116yes—
1373C22×C4—24no—
1374C22×C4—28no—
1375C22×C4—22no—
1376C22×C4—28no—
1377C22×C4—22no—
1378C22×C4—28no—
1379C22×C4—28no—
1380C22×C4—28no—
1381C22×C4—216no—
1382C22×C4—216no—
1383C22×C4—24no—
1384C22×C4—216no—
1385C22×C4—24no—
1386C22×C4—22no—
1387C22×C4—22no—
1388C22×C4—28no—
1389C22×C4—216no—
1390C22×C4—28no—
1391C22×C4—22no—
1392C22×C4—28no—
1393C22×C4—22no—
1394C22×C4—28no—
1395C22×C4—24no—
1396C22×C4—24no—
1397C22×C4—22no—
1398C22×C4—22no—
1399C22×C4—216no—
1400C22×C4—28no—
1401C22×C4—216no—
1402C22×C4—28no—
1403C22×C4—24no—
1404C22×C4—22no—
1405C22×C4—22no—
1406C22×C4—216no—
1407C22×C4—28no—
1408C22×C4—28no—
1409C22×C4—22no—
1410C22×C4—28no—
1411C22×C4—22no—
1412C22×C4—28no—
1413C22×C4—24no—
1414C22×C4—22no—
1415C22×C4—22no—
1416C22×C4—216no—
1417C22×C4—28no—
1418C22×C4—28no—
1419C22×C4—216no—
1420C22×C4—24no—
1421C22×C4—24no—
1422C22×C4—22no—
1423C22×C4—22no—
1424C22×C4—24no—
1425C22×C4—28no—
1426C22×C4—48no—
1427C22×C4—416no—
1428C22×C4—48no—
1429C22×C4—48no—
1430C22×C4—416no—
1431C22×C4—48no—
1432C22×C4—48no—
1433C22×C4—416no—
1434C22×C4—48no—
1435C22×C4—416no—
1436C22×C4—416no—
1437C22×C4—432no—
1438C22×C4—432no—
1439C22×C4—416no—
1440C22×C4—416no—
1441C22×C4—48no—
1442C22×C4—416no—
1443C22×C4—48no—
1444C22×C4—416no—
1445C22×C4—48no—
1446C22×C4—48no—
1447C22×C4—44no—
1448C22×C4—416no—
1449C22×C4—48no—
1450C22×C4—48no—
1451C22×C4—48no—
1452C22×C4—432no—
1453C22×C4—48no—
1454C22×C4—48no—
1455C22×C4—416no—
1456C22×C4—44no—
1457C22×C4—44no—
1458C22×C4—48no—
1459C22×C4—48no—
1460C22×C4—42no—
1461C22×C4—42no—
1462C22×C4—432no—
1463C22×C4—432no—
1464C22×C4—48no—
1465C22×C4—42no—
1466C22×C4—42no—
1467C22×C4—48no—
1468C22×C4—42no—
1469C22×C4—42no—
1470C22×C4—432no—
1471C22×C4—416no—
1472C22×C4—48no—
1473C22×C4—44no—
1474C22×C4—48no—
1475C22×C4—48no—
1476C22×C4—44no—
1477C22×C4—416no—
1478C22×C4—48no—
1479C22×C4—432no—
1480C22×C4—432no—
1481C22×C4—416no—
1482C22×C4—48no—
1483C22×C4—48no—
1484C22×C4—44no—
1485C22×C4—816no—
1486C22×C4—816no—
1487C22×C4—864no—
1488C22×C4—864no—
1489C22×C4—8256no—
1490C22×C4—816no—
1491C22×C4—832no—
1492C22×C4C2×#34718yescomplemented
1493C22×C4C22×#9718yes—
1494C22×C4C22×#9712yes—
1495C22×C4C22×#9712yes—
1496C22×C4C22×#9714yes—
1497C22×C4C22×#9712yes—
1498C22×C4C22×#9718yes—
1499C22×C4C22×#9714yes—
1500C22×C4C22×#9712yes—
1501C22×C4C22×#9711yescharacteristic
1502C22×C4C22×#9711yescharacteristic
1503C22×C4C22×#9712yes—
1504C22×C4C22×#9712yes—
1505C22×C4C22×#9712yes—
1506C22×C4C22×#9712yes—
1507C22×C4C22×#9718yes—
1508C22×C4C22×#9714yes—
1509C22×C4C22×#9714yes—
1510C22×C4C22×#9718yes—
1511C22×C4C22×#9718yes—
1512C22×C4C22×#9718yes—
1513C22×C4C22×#9718yes—
1514C22×C4C22×#9714yes—
1515C22×C4C22×#9714yes—
1516C22×C4C22×#9714yes—
1517C22×C4C22×#9718yes—
1518C22×C4C22×#9718yes—
1519C22×C4C22×#97116yes—
1520C22×C4C22×#97116yes—
1521C22×C4C22×#97116yes—
1522C22×C4C22×#97116yes—
1523C22×C4C22×#97116yes—
1524C22×C4C22×#9712yes—
1525C22×C4C22×#9714yes—
1526C22×C4C23×C4218yes—
1527C22×C4C23×C4218yes—
1528C22×C4C23×C4212yes—
1529C22×C4C23×C4212yes—
1530C22×C4C23×C4211yescharacteristic
1531C22×C4C23×C4211yescharacteristic
1532C22×C4C2×#51812yes—
1533C22×C4#342812yes—
1534C22×C4C23×M1618yes—
1535C22×C4C23×M1618yes—
1536C22×C4C23×M1612yes—
1537C22×C4C23×M1612yes—
1538C22×C4C23×M1618yes—
1539C22×C4C23×M1612yes—
1540C22×C4C23×M1614yes—
1541C22×C4C23×M1614yes—
1542C22×C4C23×M1611yescharacteristic
1543C22×C4C23×M1611yescharacteristic
1544C22×C4C23×M1611yescharacteristic
1545C22×C4C2×#56812yes—
1546C22×C4C2×#56812yes—
1547C22×C4C25×C411yescharacteristic
1548C2×C8—216no—
1549C2×C8—216no—
1550C2×C8—24no—
1551C2×C8—24no—
1552C2×C8—24no—
1553C2×C8—24no—
1554C2×C8—22no—
1555C2×C8—22no—
1556C2×C8—24no—
1557C2×C8—24no—
1558C2×C8—22no—
1559C2×C8—28no—
1560C2×C8—28no—
1561C2×C8—22no—
1562C2×C8—22no—
1563C2×C8—28no—
1564C2×C8—22no—
1565C2×C8—28no—
1566C2×C8—24no—
1567C2×C8—24no—
1568C2×C8—216no—
1569C2×C8—216no—
1570C2×C8—232no—
1571C2×C8—232no—
1572C2×C8—28no—
1573C2×C8—28no—
1574C2×C8—28no—
1575C2×C8—28no—
1576C2×C8—232no—
1577C2×C8—232no—
1578C2×C8—24no—
1579C2×C8—28no—
1580C2×C8—24no—
1581C2×C8—28no—
1582C2×C8—28no—
1583C2×C8—24no—
1584C2×C8—432no—
1585C2×C8—432no—
1586C2×C8—416no—
1587C2×C8—416no—
1588C2×C8—48no—
1589C2×C8—48no—
1590C2×C8—432no—
1591C2×C8—432no—
1592C2×C8—432no—
1593C2×C8—432no—
1594C2×C8—48no—
1595C2×C8—48no—
1596C2×C8—416no—
1597C2×C8—416no—
1598C2×C8—48no—
1599C2×C8—48no—
1600C2×C8—44no—
1601C2×C8—44no—
1602C2×C8C23×C4218yes—
1603C2×C8C23×C4214yes—
1604C2×C8C23×C42116yes—
1605C2×C8C23×C4212yes—
1606C2×C8C2×#51814yes—
1607C2×C8C2×#51812yes—
1608C2×C8#342812yes—
1609C2×C8C4×H(5,𝔽2)18yes—
1610C2×C8C4×H(5,𝔽2)18yes—
1611C2×C8C2×#56814yes—
1612C2×C8C25×C412yes—
1613C2×C8C22×H(5,𝔽2)12yes—
1614C2×C8C2×#58512yes—
1615C4⋊C4—432no—
1616C4⋊C4C22×#97132yes—
1617C4⋊C4C22×#97116yes—
1618C4⋊C4C22×#97116yes—
1619C22⋊C4—464no—
1620C22⋊C4C22×#97132yes—
1621C22⋊C4C22×#97132yes—
1622C22⋊C4C22×#97132yes—
1623C22⋊C4C22×#97132yes—
1624C42—216no—
1625C42—24no—
1626C42—24no—
1627C42—22no—
1628C42—22no—
1629C42—24no—
1630C42—28no—
1631C42—28no—
1632C42—24no—
1633C42—432no—
1634C42—432no—
1635C42—48no—
1636C42—416no—
1637C42—416no—
1638C42—416no—
1639C42—48no—
1640C42—44no—
1641C42—88no—
1642C42—88no—
1643C42C22×#9718yes—
1644C42C22×#9718yes—
1645C42C22×#9718yes—
1646C42C22×#9718yes—
1647C42C22×#9714yes—
1648C42C22×#9714yes—
1649C42C22×#9714yes—
1650C42C22×#9714yes—
1651C42C23×C4214yes—
1652C42C23×C4214yes—
1653C42C2×#51814yes—
1654C42C23×M1614yes—
1655C42C23×M1614yes—
1656C42C2×#56814yes—
1657C16—264no—
1658C23—216no—
1659C23—216no—
1660C23—24no—
1661C23—22no—
1662C23—24no—
1663C23—22no—
1664C23—24no—
1665C23—22no—
1666C23—24no—
1667C23—22no—
1668C23—28no—
1669C23—22no—
1670C23—24no—
1671C23—22no—
1672C23—22no—
1673C23—28no—
1674C23—22no—
1675C23—216no—
1676C23—216no—
1677C23—232no—
1678C23—216no—
1679C23—28no—
1680C23—232no—
1681C23—28no—
1682C23—28no—
1683C23—216no—
1684C23—28no—
1685C23—28no—
1686C23—48no—
1687C23—416no—
1688C23—48no—
1689C23—48no—
1690C23—48no—
1691C23—48no—
1692C23—48no—
1693C23—432no—
1694C23—432no—
1695C23—432no—
1696C23—464no—
1697C23—464no—
1698C23—464no—
1699C23—4128no—
1700C23—432no—
1701C23C22×#34714yes—
1702C23C22×#347116yes—
1703C23C22×#347132yescomplemented
1704C23#3332914yes—
1705C23C23×#9718yes—
1706C23C23×#9718yes—
1707C23C23×#9712yes—
1708C23C23×#9712yes—
1709C23C23×#9711yescharacteristic
1710C23C23×#9711yescharacteristic
1711C23#6023012yes—
1712C23#6028212yes—
1713C23C24×M1611yescharacteristic
1714D4—264no—
1715D4—232no—
1716D4C22×#347164yescomplemented
1717C2×C4—28no—
1718C2×C4—24no—
1719C2×C4—216no—
1720C2×C4—24no—
1721C2×C4—24no—
1722C2×C4—22no—
1723C2×C4—28no—
1724C2×C4—24no—
1725C2×C4—22no—
1726C2×C4—22no—
1727C2×C4—216no—
1728C2×C4—28no—
1729C2×C4—28no—
1730C2×C4—22no—
1731C2×C4—28no—
1732C2×C4—28no—
1733C2×C4—28no—
1734C2×C4—216no—
1735C2×C4—22no—
1736C2×C4—22no—
1737C2×C4—28no—
1738C2×C4—28no—
1739C2×C4—24no—
1740C2×C4—24no—
1741C2×C4—24no—
1742C2×C4—24no—
1743C2×C4—216no—
1744C2×C4—216no—
1745C2×C4—216no—
1746C2×C4—216no—
1747C2×C4—22no—
1748C2×C4—22no—
1749C2×C4—28no—
1750C2×C4—28no—
1751C2×C4—22no—
1752C2×C4—22no—
1753C2×C4—28no—
1754C2×C4—28no—
1755C2×C4—22no—
1756C2×C4—22no—
1757C2×C4—28no—
1758C2×C4—28no—
1759C2×C4—24no—
1760C2×C4—24no—
1761C2×C4—44no—
1762C2×C4—416no—
1763C2×C4—416no—
1764C2×C4—416no—
1765C2×C4—416no—
1766C2×C4—48no—
1767C2×C4—48no—
1768C2×C4—416no—
1769C2×C4—44no—
1770C2×C4—44no—
1771C2×C4—44no—
1772C2×C4—42no—
1773C2×C4—42no—
1774C2×C4—42no—
1775C2×C4—42no—
1776C2×C4—432no—
1777C2×C4—48no—
1778C2×C4—48no—
1779C2×C4—44no—
1780C2×C4—44no—
1781C2×C4—48no—
1782C2×C4—48no—
1783C2×C4—44no—
1784C2×C4—48no—
1785C2×C4—864no—
1786C2×C4—864no—
1787C2×C4—816no—
1788C2×C4—88no—
1789C2×C4—832no—
1790C2×C4—816no—
1791C2×C4C22×#34718yes—
1792C2×C4C22×#347116yescomplemented
1793C2×C4C4×#51812yes—
1794C2×C4C4×#51812yes—
1795C2×C4C23×#9712yes—
1796C2×C4C23×#9712yes—
1797C2×C4C23×#9714yes—
1798C2×C4C23×#9714yes—
1799C2×C4C23×#9714yes—
1800C2×C4C23×#9718yes—
1801C2×C4C23×#9718yes—
1802C2×C4C23×#9714yes—
1803C2×C4C23×#9711yescharacteristic
1804C2×C4C23×#9711yescharacteristic
1805C2×C4C4×#56812yes—
1806C2×C4C4×#56812yes—
1807C2×C4#6023012yes—
1808C2×C4#6023012yes—
1809C2×C4#6023012yes—
1810C2×C4#6028212yes—
1811C2×C4#6028212yes—
1812C2×C4#6028212yes—
1813C2×C4C24×C4211yescharacteristic
1814C2×C4C22×#51811yescharacteristic
1815C2×C4C2×#342811yescharacteristic
1816C2×C4C24×M1611yescharacteristic
1817C2×C4C22×#56811yescharacteristic
1818C2×C4C22×#56811yescharacteristic
1819C8—24no—
1820C8—24no—
1821C8—28no—
1822C8—24no—
1823C8—216no—
1824C8—44no—
1825C8—48no—
1826C8C4×#51814yes—
1827C8C2×C4×H(5,𝔽2)14yes—
1828C22—28no—
1829C22—28no—
1830C22—216no—
1831C22—21no—
1832C22—22no—
1833C22—21no—
1834C22—21no—
1835C22—22no—
1836C22—21no—
1837C22—28no—
1838C22—22no—
1839C22—22no—
1840C22—28no—
1841C22—24no—
1842C22—24no—
1843C22—28no—
1844C22—28no—
1845C22—232no—
1846C22—28no—
1847C22—28no—
1848C22—28no—
1849C22—432no—
1850C22—416no—
1851C22—416no—
1852C22—464no—
1853C22—432no—
1854C22—432no—
1855C22—416no—
1856C22#637038012yes—
1857C22#637038012yes—
1858C22C23×#34714yes—
1859C22C23×#347116yes—
1860C22C23×#34712yes—
1861C22C2×#3332914yes—
1862C22C2×#3332912yes—
1863C22C24×#9711yescharacteristic
1864C22C2×#6023011yescharacteristic
1865C22C2×#6028211yescharacteristic
1866C4—24no—
1867C4—24no—
1868C4—24no—
1869C4—22no—
1870C4—22no—
1871C4—28no—
1872C4—28no—
1873C4—44no—
1874C4—44no—
1875C4—84no—
1876C4—88no—
1877C4#637038012yes—
1878C4#637038012yes—
1879C4C23×#34718yes—
1880C4C2×C4×#51811yescharacteristic
1881C4C2×C4×#56811yescharacteristic
1882C4C2×#6023011yescharacteristic
1883C4C2×#6028211yescharacteristic
1884C2—21no—
1885C2—21no—
1886C2—24no—
1887C2—24no—
1888C2—22no—
1889C2—216no—
1890C2—48no—
1891C2C22×#3332911yescharacteristic
1892C2C2×#637038011yescharacteristic
1893C2#7223932514yesdirect product factor
1894C2C24×#34711yescharacteristic
subgroupG/H
centerC22×C4C23×C42
commutatorC2×C4C24×C42
Frattini, cosocleC22×C8C26
socleC23C23×#97
prime radicalC24×D4M16
LCSG ▷ C2×C4 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#493286C2semidirect
3. C2×#493273C2semidirect
4. C2×#493318C2semidirect
6. C2×D4×#347C2semidirect
7. #72239325C2direct (N × H)
8. C22×#12605C2semidirect
9. C2×#493177C2semidirect
14. #7622691C4semidirect
16. C2×#33489C4semidirect
17. C2×#33488C4semidirect
18. C2×#33487C4semidirect
19. C2×#33486C4semidirect
23. C23×#347C22semidirect
37. #493318C22semidirect
38. #493286C22semidirect
39. #493273C22semidirect
40. D4×#347C22semidirect
41. #493177C22semidirect
42. C2×#12666C22semidirect
43. C2×#12658C22semidirect
44. C2×#12658C22semidirect
45. C2×#12616C22semidirect
49. C2×#12605C22semidirect
50. C2×#12605C22semidirect
51. C2×#12605C22semidirect
52. C2×#12594C22semidirect
53. C22×#1375C22semidirect
54. C2×C4×#347C22semidirect
108. #33489C2×C4semidirect
109. #33488C2×C4semidirect
110. #33487C2×C4semidirect
111. #33486C2×C4semidirect
112. D4×M32C2×C4semidirect
114. C2×#2169C2×C4semidirect
115. C2×#2168C2×C4semidirect
116. C2×D4×C16C2×C4semidirect
117. #33418C2×C4semidirect
119. C2×#2163C2×C4semidirect
120. C2×#2163C2×C4semidirect
121. C2×#2162C2×C4semidirect
122. C2×#2162C2×C4semidirect
124. C2×#2112C2×C4semidirect
125. C2×#2112C2×C4semidirect
126. C2×#2112C2×C4semidirect
130. C22×C22⋊C16C2×C4semidirect
131. C22×C22⋊C16C2×C4semidirect
136. C22×#347C23semidirect
173. #12666C23semidirect
174. #12658C23semidirect
175. #12658C23semidirect
176. #12616C23semidirect
180. #12605C23semidirect
181. #12605C23semidirect
182. #12594C23semidirect
186. C2×#1375C23semidirect
187. C4×#347C23semidirect
254. C22×M32C22×C4semidirect
255. C22×M32C22×C4semidirect
258. C23×C16C22×C4semidirect
402. #2169C22×C4semidirect
403. #2168C22×C4semidirect
404. D4×C16C22×C4semidirect
405. #2163C22×C4semidirect
406. #2163C22×C4semidirect
407. #2162C22×C4semidirect
408. #2162C22×C4semidirect
409. #2150C22×C4semidirect
411. C2×C4⋊C16C22×C4semidirect
412. C2×C4⋊C16C22×C4semidirect
414. #2112C22×C4semidirect
415. #2112C22×C4semidirect
416. #2112C22×C4semidirect
421. C2×C22⋊C16C22×C4semidirect
422. C2×C22⋊C16C22×C4semidirect
423. C2×C22⋊C16C22×C4semidirect
424. C2×C22⋊C16C22×C4semidirect
432. C4×M32C22×C4semidirect
434. C2×#346C22×C4semidirect
435. C2×C4×C16C22×C4semidirect
719. C2×M32C23×C4semidirect
723. C22×C16C23×C4semidirect
864. C4⋊C16C23×C4semidirect
865. C4⋊C16C23×C4semidirect
868. C22⋊C16C23×C4semidirect
869. C22⋊C16C23×C4semidirect
873. #346C23×C4semidirect
874. C4×C16C23×C4semidirect
895. C22×D4#347semidirect
1348. C24C2×#347semidirect
1368. C2×D4C2×#347semidirect
1369. C2×D4C2×#347semidirect
1492. C22×C4C2×#347semidirect
1703. C23C22×#347semidirect
1716. D4C22×#347semidirect
1792. C2×C4C22×#347semidirect
1893. C2#72239325direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#76226912
C2×#4932862
C2×#4932732
C2×#4933182
C22×D4×#972
C2×D4×#3472
#722393252
C22×#126052
C2×#4931772