Finite Group Databasebeta

← C2×C4×D4×C22⋊C4 #72299616

Subgroups — C2×C4×D4×C22⋊C4 #72299616

Order 1024.

88545 conjugacy classes of subgroups.

The subgroup lattice has 1474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C4×D4C211yesmaximal, characteristic
2C22×D4×C22⋊C4C212yesmaximal
3C22×C42×D4C212yesmaximal, complemented
4C23×C4×C22⋊C4C212yesmaximal, complemented
5C4×D4×C22⋊C4C2132yesmaximal, direct product factor
6C2×#13820C212yesmaximal, complemented
7C2×#13813C214yesmaximal, complemented
8C2×D4×#95C212yesmaximal, complemented
9C2×C22⋊C4×C4⋊C4C212yesmaximal, complemented
10C2×C22⋊C42C214yesmaximal, complemented
11C2×C4×#380C211yesmaximal, characteristic, complemented
12C2×C4×#379C212yesmaximal, complemented
13C2×C4×#390C212yesmaximal, complemented
14C2×C4×#386C214yesmaximal, complemented
15C2×C42×C22⋊C4C211yesmaximal, characteristic, complemented
16C25×D4C2211yescharacteristic
17C26×C4C2212yes—
18C23×C4×D4—232no—
19C23×C4×D4C4132yescomplemented
20C23×C4×D4C2211yescharacteristic
21C23×C4×D4C2212yes—
22C23×C4×D4C2211yescharacteristic
23C23×C4×D4C2212yes—
24C23×C4×D4C2211yescharacteristic
25C23×C4×D4C22116yes—
26C23×C4×D4C2214yes—
27C23×C4×D4C2211yescharacteristic
28C24×C4⋊C4C2211yescharacteristic
29C24×C22⋊C4C2212yes—
30C24×C22⋊C4C2214yes—
31C24×C42C2211yescharacteristic
32C24×C42C2214yescomplemented
33C2×D4×C22⋊C4C4164yesdirect product factor
34C2×D4×C22⋊C4C22132yes—
35C22×#390C2214yes—
36C22×#386C2218yes—
37C22×#380C2212yes—
38C22×#379C2214yes—
39C2×C42×D4—232no—
40C2×C42×D4C22132yescomplemented
41C22×C4×C4⋊C4C2212yescomplemented
42C22×C4×C4⋊C4C2214yescomplemented
43C22×C4×C22⋊C4—232no—
44C22×C4×C22⋊C4C2211yescharacteristic
45C22×C4×C22⋊C4C2212yes—
46C22×C4×C22⋊C4C2212yes—
47C22×C4×C22⋊C4C2214yes—
48C22×C4×C22⋊C4C2212yes—
49C22×C4×C22⋊C4C2211yescharacteristic
50C22×C4×C22⋊C4C2214yescomplemented
51C22×C4×C22⋊C4C2214yescomplemented
52C22×C4×C22⋊C4C2218yescomplemented
53C22×C4×C22⋊C4C2214yescomplemented
54C22×C4×C22⋊C4C2214yescomplemented
55C22×C4×C22⋊C4C22132yescomplemented
56C23×#95C2214yescomplemented
57C22×C43C2212yescomplemented
58#13820C22132yescomplemented
59#13813C22164yescomplemented
60D4×#95C22132yescomplemented
61C22⋊C4×C4⋊C4C22132yescomplemented
62C22⋊C42C22164yescomplemented
63C4×#380C22116yescomplemented
64C4×#379C22132yescomplemented
65C4×#390C22132yescomplemented
66C4×#386C22164yescomplemented
67C2×#1437C2218yescomplemented
68C2×#1437C2218yescomplemented
69C2×#1436C2218yescomplemented
70C2×C4⋊#95C2214yescomplemented
71C2×C4⋊#95C2212yescomplemented
72C2×#1434C2212yescomplemented
73C2×C22⋊#95C2214yes—
74C2×C22⋊#95C2212yes—
75C2×C22⋊#95C2218yescomplemented
76C2×C22⋊#95C2214yescomplemented
77C2×C22⋊#95C2214yescomplemented
78C42×C22⋊C4C22116yescomplemented
79C2×C4×#95C2212yescomplemented
80C2×C4×#95C2212yescomplemented
81C2×C4×#95C2212yescomplemented
82C2×C4×#95C2212yescomplemented
83C27C2312yes—
84C24×D4—216no—
85C24×D4—216no—
86C24×D4C2×C4132yes—
87C24×D4C2×C4116yes—
88C24×D4C2318yes—
89C24×D4C2312yes—
90C24×D4C2311yescharacteristic
91C24×D4C2311yescharacteristic
92C25×C4—232no—
93C25×C4—216no—
94C25×C4—216no—
95C25×C4—416no—
96C25×C4C2×C4132yescomplemented
97C25×C4C2312yes—
98C25×C4C2312yes—
99C25×C4C2312yes—
100C25×C4C2312yes—
101C25×C4C2311yescharacteristic
102C25×C4C23116yes—
103C25×C4C2318yes—
104C25×C4C2311yescharacteristic
105C25×C4C2312yes—
106C25×C4C2311yescharacteristic
107C22×C4×D4—216no—
108C22×C4×D4—216no—
109C22×C4×D4—232no—
110C22×C4×D4—232no—
111C22×C4×D4—232no—
112C22×C4×D4—2512no—
113C22×C4×D4—2256no—
114C22×C4×D4—216no—
115C22×C4×D4—232no—
116C22×C4×D4C2×C4116yes—
117C22×C4×D4C2×C4116yes—
118C22×C4×D4C2×C4132yescomplemented
119C22×C4×D4C2×C4116yescomplemented
120C22×C4×D4C2×C4116yescomplemented
121C22×C4×D4C2×C4132yescomplemented
122C22×C4×D4C2×C41256yescomplemented
123C22×C4×D4C2×C4164yescomplemented
124C22×C4×D4D4132yes—
125C22×C4×D4C2318yes—
126C22×C4×D4C23132yes—
127C22×C4×D4C23116yes—
128C22×C4×D4C2318yes—
129C22×C4×D4C23116yes—
130C22×C4×D4C2318yes—
131C22×C4×D4C2318yes—
132C23×C4⋊C4—216no—
133C23×C4⋊C4C2×C4116yescomplemented
134C23×C4⋊C4C2311yescharacteristic
135C23×C4⋊C4C2312yes—
136C23×C4⋊C4C2318yes—
137C23×C4⋊C4C2314yes—
138C23×C4⋊C4C2311yescharacteristic
139C23×C22⋊C4—232no—
140C23×C22⋊C4—232no—
141C23×C22⋊C4—232no—
142C23×C22⋊C4C2×C4132yescomplemented
143C23×C22⋊C4C2×C4164yescomplemented
144C23×C22⋊C4C2312yes—
145C23×C22⋊C4C2312yes—
146C23×C22⋊C4C2312yes—
147C23×C22⋊C4C2314yes—
148C23×C22⋊C4C2312yes—
149C23×C22⋊C4C23132yes—
150C23×C22⋊C4C23116yes—
151C23×C22⋊C4C2318yes—
152C23×C22⋊C4C2318yes—
153C23×C22⋊C4C2318yes—
154C23×C22⋊C4C2312yes—
155C23×C22⋊C4C2312yes—
156C23×C42—216no—
157C23×C42—232no—
158C23×C42—232no—
159C23×C42—416no—
160C23×C42C2×C4116yescomplemented
161C23×C42C2318yes—
162C23×C42C2314yes—
163C23×C42C2311yescharacteristic
164C23×C42C2311yescharacteristic
165C23×C42C2318yes—
166C23×C42C2314yes—
167C23×C42C2314yes—
168C23×C42C2312yes—
169C23×C42C2311yescharacteristic
170C23×C42C2312yes—
171C23×C42C2311yescharacteristic
172C23×C42C23132yescomplemented
173D4×C22⋊C4C2×C41512yesdirect product factor
174C2×#390C2×C4164yescomplemented
175C2×#390C23132yes—
176C2×#386C2×C41128yescomplemented
177C2×#386C23164yes—
178C2×#380C2×C4132yescomplemented
179C2×#380C23116yes—
180C2×#379C2×C4164yescomplemented
181C2×#379C23132yes—
182C42×D4—2256no—
183C2×C4×C4⋊C4—216no—
184C2×C4×C4⋊C4—232no—
185C2×C4×C4⋊C4C23116yescomplemented
186C2×C4×C4⋊C4C23132yescomplemented
187C2×C4×C22⋊C4—232no—
188C2×C4×C22⋊C4—2256no—
189C2×C4×C22⋊C4—232no—
190C2×C4×C22⋊C4—216no—
191C2×C4×C22⋊C4—232no—
192C2×C4×C22⋊C4—28no—
193C2×C4×C22⋊C4—232no—
194C2×C4×C22⋊C4—264no—
195C2×C4×C22⋊C4—216no—
196C2×C4×C22⋊C4—416no—
197C2×C4×C22⋊C4C2×C4132yescomplemented
198C2×C4×C22⋊C4D4116yesdirect product factor
199C2×C4×C22⋊C4C2318yes—
200C2×C4×C22⋊C4C23116yes—
201C2×C4×C22⋊C4C23116yes—
202C2×C4×C22⋊C4C23132yes—
203C2×C4×C22⋊C4C23116yes—
204C2×C4×C22⋊C4C2318yes—
205C2×C4×C22⋊C4C23132yescomplemented
206C2×C4×C22⋊C4C23132yescomplemented
207C2×C4×C22⋊C4C23132yescomplemented
208C2×C4×C22⋊C4C23164yescomplemented
209C2×C4×C22⋊C4C23132yescomplemented
210C22×#95—232no—
211C22×#95C2312yes—
212C22×#95C2314yes—
213C22×#95C2318yes—
214C22×#95C2314yes—
215C22×#95C2314yes—
216C22×#95C2318yes—
217C22×#95C2314yes—
218C22×#95C2318yes—
219C22×#95C2314yes—
220C22×#95C2314yes—
221C22×#95C2312yes—
222C22×#95C23132yescomplemented
223C2×C43—216no—
224C2×C43C23116yescomplemented
225#1437C23164yescomplemented
226#1437C23164yescomplemented
227#1436C23164yescomplemented
228C4⋊#95C23132yescomplemented
229C4⋊#95C23116yescomplemented
230#1434C23116yescomplemented
231C22⋊#95C23132yes—
232C22⋊#95C23116yes—
233C22⋊#95C23164yescomplemented
234C22⋊#95C23132yescomplemented
235C22⋊#95C23132yescomplemented
236C4×#95C23116yescomplemented
237C4×#95C23116yescomplemented
238C4×#95C23116yescomplemented
239C4×#95C23116yescomplemented
240C26—216no—
241C26—28no—
242C26—28no—
243C26—216no—
244C26—216no—
245C26—48no—
246C26—48no—
247C26C22×C4116yes—
248C26C22×C4132yes—
249C26C2412yes—
250C26C2418yes—
251C26C2412yes—
252C26C2411yescharacteristic
253C23×D4—216no—
254C23×D4—216no—
255C23×D4—2128no—
256C23×D4—2128no—
257C23×D4—2512no—
258C23×D4—264no—
259C23×D4—264no—
260C23×D4—28no—
261C23×D4—28no—
262C23×D4C421256yescomplemented
263C23×D4C22×C41128yes—
264C23×D4C22×C4116yes—
265C23×D4C22×C4164yes—
266C23×D4C22×C418yes—
267C23×D4C22×C4132yes—
268C23×D4C22×C4116yes—
269C23×D4C22×C418yes—
270C23×D4C22×C4116yes—
271C23×D4C2×D4116yes—
272C23×D4#41116yes—
273C23×D4C2418yes—
274C23×D4C2414yes—
275C23×D4C2414yes—
276C24×C4—28no—
277C24×C4—28no—
278C24×C4—28no—
279C24×C4—28no—
280C24×C4—28no—
281C24×C4—28no—
282C24×C4—216no—
283C24×C4—216no—
284C24×C4—28no—
285C24×C4—232no—
286C24×C4—28no—
287C24×C4—232no—
288C24×C4—28no—
289C24×C4—2256no—
290C24×C4—2256no—
291C24×C4—216no—
292C24×C4—216no—
293C24×C4—2128no—
294C24×C4—216no—
295C24×C4—28no—
296C24×C4—28no—
297C24×C4—264no—
298C24×C4—28no—
299C24×C4—28no—
300C24×C4—232no—
301C24×C4—28no—
302C24×C4—264no—
303C24×C4—28no—
304C24×C4—28no—
305C24×C4—232no—
306C24×C4—216no—
307C24×C4—4128no—
308C24×C4—464no—
309C24×C4—48no—
310C24×C4—48no—
311C24×C4—48no—
312C24×C4—416no—
313C24×C4—44no—
314C24×C4—416no—
315C24×C4—4256no—
316C24×C4—4256no—
317C24×C4C22×C4116yes—
318C24×C4C22×C4116yes—
319C24×C4C22×C4116yes—
320C24×C4C22×C4116yes—
321C24×C4C22×C418yes—
322C24×C4C22×C418yes—
323C24×C4C22×C4116yes—
324C24×C4C22×C4116yes—
325C24×C4C22×C418yes—
326C24×C4C22×C41128yescomplemented
327C24×C4C22×C4164yescomplemented
328C24×C4C2×D4132yes—
329C24×C4C2×D418yes—
330C24×C4#4118yes—
331C24×C4C2412yes—
332C24×C4C2418yes—
333C24×C4C2418yes—
334C24×C4C2411yescharacteristic
335C24×C4C2414yes—
336C24×C4C2418yes—
337C24×C4C2418yes—
338C24×C4C2418yes—
339C24×C4C2414yes—
340C24×C4C24132yes—
341C24×C4C2411yescharacteristic
342C24×C4C2414yes—
343C24×C4C2412yes—
344C24×C4C2418yes—
345C24×C4C2411yescharacteristic
346C24×C4C2411yescharacteristic
347C24×C4C2414yes—
348C24×C4C2414yes—
349C24×C4C2411yescharacteristic
350C24×C4C2411yescharacteristic
351C2×C4×D4—2128no—
352C2×C4×D4—2512no—
353C2×C4×D4—264no—
354C2×C4×D4—2128no—
355C2×C4×D4—2128no—
356C2×C4×D4—2256no—
357C2×C4×D4—2128no—
358C2×C4×D4—22048no—
359C2×C4×D4—2128no—
360C2×C4×D4—264no—
361C2×C4×D4—2256no—
362C2×C4×D4—2128no—
363C2×C4×D4—2128no—
364C2×C4×D4—264no—
365C2×C4×D4C22⋊C41256yesdirect product factor
366C2×C4×D4C22×C4164yes—
367C2×C4×D4C22×C4164yes—
368C2×C4×D4C22×C4164yescomplemented
369C2×C4×D4C22×C41128yescomplemented
370C2×C4×D4C22×C41128yescomplemented
371C2×C4×D4C22×C4164yescomplemented
372C2×C4×D4C22×C41256yescomplemented
373C2×C4×D4C2×D41128yes—
374C22×C4⋊C4—216no—
375C22×C4⋊C4—28no—
376C22×C4⋊C4—216no—
377C22×C4⋊C4—216no—
378C22×C4⋊C4—2128no—
379C22×C4⋊C4—264no—
380C22×C4⋊C4C22×C418yes—
381C22×C4⋊C4C22×C4116yes—
382C22×C4⋊C4C22×C418yes—
383C22×C4⋊C4C22×C4164yescomplemented
384C22×C4⋊C4C22×C4132yescomplemented
385C22×C4⋊C4C2×D4116yes—
386C22×C4⋊C4C2414yes—
387C22×C4⋊C4C2418yes—
388C22×C4⋊C4C24116yes—
389C22×C4⋊C4C2414yes—
390C22×C22⋊C4—216no—
391C22×C22⋊C4—216no—
392C22×C22⋊C4—232no—
393C22×C22⋊C4—216no—
394C22×C22⋊C4—232no—
395C22×C22⋊C4—28no—
396C22×C22⋊C4—28no—
397C22×C22⋊C4—216no—
398C22×C22⋊C4—216no—
399C22×C22⋊C4—232no—
400C22×C22⋊C4—232no—
401C22×C22⋊C4—2256no—
402C22×C22⋊C4—2512no—
403C22×C22⋊C4—2128no—
404C22×C22⋊C4—2128no—
405C22×C22⋊C4—2128no—
406C22×C22⋊C4—416no—
407C22×C22⋊C4—416no—
408C22×C22⋊C4C22×C4116yes—
409C22×C22⋊C4C22×C4116yes—
410C22×C22⋊C4C22×C4116yes—
411C22×C22⋊C4C22×C4132yes—
412C22×C22⋊C4C22×C4116yes—
413C22×C22⋊C4C22×C4116yes—
414C22×C22⋊C4C22×C4116yes—
415C22×C22⋊C4C22×C41128yescomplemented
416C22×C22⋊C4C22×C41256yescomplemented
417C22×C22⋊C4C22×C4164yescomplemented
418C22×C22⋊C4C22×C4164yescomplemented
419C22×C22⋊C4C22×C4164yescomplemented
420C22×C22⋊C4C2×D4132yes—
421C22×C22⋊C4C2×D4116yes—
422C22×C22⋊C4#41116yes—
423C22×C22⋊C4C2418yes—
424C22×C22⋊C4C2418yes—
425C22×C22⋊C4C2418yes—
426C22×C22⋊C4C24116yes—
427C22×C22⋊C4C2418yes—
428C22×C22⋊C4C24132yes—
429C22×C22⋊C4C24132yes—
430C22×C22⋊C4C24132yes—
431C22×C22⋊C4C2418yes—
432C22×C22⋊C4C2418yes—
433C22×C42—28no—
434C22×C42—28no—
435C22×C42—28no—
436C22×C42—28no—
437C22×C42—216no—
438C22×C42—216no—
439C22×C42—28no—
440C22×C42—2128no—
441C22×C42—264no—
442C22×C42—232no—
443C22×C42—216no—
444C22×C42—232no—
445C22×C42—216no—
446C22×C42—2128no—
447C22×C42—216no—
448C22×C42—28no—
449C22×C42—216no—
450C22×C42—28no—
451C22×C42—216no—
452C22×C42—28no—
453C22×C42—2128no—
454C22×C42—464no—
455C22×C42—4256no—
456C22×C42—416no—
457C22×C42—48no—
458C22×C42C22×C418yes—
459C22×C42C22×C418yes—
460C22×C42C22×C418yes—
461C22×C42C22×C418yes—
462C22×C42C22×C4164yescomplemented
463C22×C42C22×C4132yescomplemented
464C22×C42C2×D4116yes—
465C22×C42C2×D4116yescomplemented
466C22×C42C24116yes—
467C22×C42C2418yes—
468C22×C42C24132yes—
469C22×C42C24116yes—
470C22×C42C2414yes—
471C22×C42C2414yes—
472C22×C42C2414yes—
473C22×C42C24116yes—
474C22×C42C2418yes—
475C22×C42C2414yes—
476#390C22×C41256yescomplemented
477#386C22×C41512yescomplemented
478#380C22×C41128yescomplemented
479#379C22×C41256yescomplemented
480C4×C4⋊C4—2128no—
481C4×C4⋊C4—264no—
482C4×C22⋊C4—264no—
483C4×C22⋊C4—2128no—
484C4×C22⋊C4—232no—
485C4×C22⋊C4—2128no—
486C4×C22⋊C4—2256no—
487C4×C22⋊C4—264no—
488C4×C22⋊C4—2128no—
489C4×C22⋊C4—2128no—
490C4×C22⋊C4—464no—
491C4×C22⋊C4C22×C41128yescomplemented
492C4×C22⋊C4C2×D4164yesdirect product factor
493C2×#95—216no—
494C2×#95—232no—
495C2×#95—232no—
496C2×#95—216no—
497C2×#95—28no—
498C2×#95—216no—
499C2×#95—2128no—
500C2×#95—48no—
501C2×#95—416no—
502C2×#95C22×C4132yescomplemented
503C2×#95C22×C4132yescomplemented
504C2×#95C2×D4116yescomplemented
505C2×#95C2418yes—
506C2×#95C24116yes—
507C2×#95C24132yes—
508C2×#95C24116yes—
509C2×#95C24116yes—
510C2×#95C24132yes—
511C2×#95C24116yes—
512C2×#95C24132yes—
513C2×#95C24116yes—
514C2×#95C24116yes—
515C2×#95C2418yes—
516C43—264no—
517C25—24no—
518C25—24no—
519C25—24no—
520C25—28no—
521C25—24no—
522C25—28no—
523C25—24no—
524C25—28no—
525C25—24no—
526C25—264no—
527C25—264no—
528C25—2128no—
529C25—264no—
530C25—2256no—
531C25—2128no—
532C25—264no—
533C25—216no—
534C25—24no—
535C25—232no—
536C25—28no—
537C25—232no—
538C25—28no—
539C25—216no—
540C25—24no—
541C25—232no—
542C25—28no—
543C25—28no—
544C25—28no—
545C25—432no—
546C25—416no—
547C25—432no—
548C25—4128no—
549C25—416no—
550C25—464no—
551C25—464no—
552C25—464no—
553C25—4128no—
554C25—464no—
555C25—4128no—
556C25C2×C421128yescomplemented
557C25C23×C418yes—
558C25C23×C4116yes—
559C25C23×C4132yes—
560C25C23×C4164yes—
561C25C23×C418yes—
562C25C23×C4116yes—
563C25C23×C418yes—
564C25C23×C414yes—
565C25C22×D4116yes—
566C25C22×D414yes—
567C25C2×#41116yes—
568C25C2×#4118yes—
569C25C2×#4114yes—
570C25C2514yes—
571C25C2514yes—
572C25C2512yes—
573C25C2511yescharacteristic
574C22×D4—264no—
575C22×D4—264no—
576C22×D4—2256no—
577C22×D4—232no—
578C22×D4—232no—
579C22×D4—2256no—
580C22×D4—2256no—
581C22×D4—21024no—
582C22×D4—22048no—
583C22×D4—232no—
584C22×D4—232no—
585C22×D4—2128no—
586C22×D4—216no—
587C22×D4—216no—
588C22×D4C2×C42164yes—
589C22×D4C2×C421128yescomplemented
590C22×D4C2×C42164yescomplemented
591C22×D4C2×C421512yescomplemented
592C22×D4C2×C22⋊C4164yes—
593C22×D4#117164yes—
594C22×D4C4×D41256yes—
595C22×D4C23×C4132yes—
596C22×D4C23×C4116yes—
597C22×D4C23×C4164yes—
598C22×D4C23×C4132yes—
599C22×D4C23×C4116yes—
600C22×D4C23×C4132yes—
601C22×D4C22×D4132yes—
602C22×D4C2×#41132yes—
603C23×C4—24no—
604C23×C4—24no—
605C23×C4—24no—
606C23×C4—28no—
607C23×C4—24no—
608C23×C4—28no—
609C23×C4—24no—
610C23×C4—24no—
611C23×C4—24no—
612C23×C4—28no—
613C23×C4—28no—
614C23×C4—28no—
615C23×C4—24no—
616C23×C4—232no—
617C23×C4—232no—
618C23×C4—232no—
619C23×C4—264no—
620C23×C4—2128no—
621C23×C4—232no—
622C23×C4—264no—
623C23×C4—264no—
624C23×C4—2128no—
625C23×C4—264no—
626C23×C4—2128no—
627C23×C4—216no—
628C23×C4—216no—
629C23×C4—216no—
630C23×C4—216no—
631C23×C4—216no—
632C23×C4—216no—
633C23×C4—232no—
634C23×C4—264no—
635C23×C4—2256no—
636C23×C4—264no—
637C23×C4—232no—
638C23×C4—24no—
639C23×C4—28no—
640C23×C4—216no—
641C23×C4—28no—
642C23×C4—216no—
643C23×C4—232no—
644C23×C4—264no—
645C23×C4—24no—
646C23×C4—216no—
647C23×C4—216no—
648C23×C4—28no—
649C23×C4—216no—
650C23×C4—28no—
651C23×C4—28no—
652C23×C4—264no—
653C23×C4—216no—
654C23×C4—24no—
655C23×C4—24no—
656C23×C4—216no—
657C23×C4—28no—
658C23×C4—216no—
659C23×C4—28no—
660C23×C4—28no—
661C23×C4—216no—
662C23×C4—24no—
663C23×C4—232no—
664C23×C4—264no—
665C23×C4—264no—
666C23×C4—264no—
667C23×C4—2512no—
668C23×C4—264no—
669C23×C4—264no—
670C23×C4—264no—
671C23×C4—2256no—
672C23×C4—2512no—
673C23×C4—264no—
674C23×C4—216no—
675C23×C4—232no—
676C23×C4—264no—
677C23×C4—232no—
678C23×C4—232no—
679C23×C4—216no—
680C23×C4—216no—
681C23×C4—216no—
682C23×C4—264no—
683C23×C4—216no—
684C23×C4—216no—
685C23×C4—216no—
686C23×C4—232no—
687C23×C4—4256no—
688C23×C4—432no—
689C23×C4—432no—
690C23×C4—432no—
691C23×C4—416no—
692C23×C4—416no—
693C23×C4—416no—
694C23×C4—416no—
695C23×C4—4128no—
696C23×C4—48no—
697C23×C4—432no—
698C23×C4—432no—
699C23×C4—464no—
700C23×C4—464no—
701C23×C4—42048no—
702C23×C4—4512no—
703C23×C4—4512no—
704C23×C4—4128no—
705C23×C4—464no—
706C23×C4—4128no—
707C23×C4—4128no—
708C23×C4—464no—
709C23×C4—464no—
710C23×C4—464no—
711C23×C4—464no—
712C23×C4—4128no—
713C23×C4—464no—
714C23×C4—464no—
715C23×C4C2×C42164yescomplemented
716C23×C4C2×C22⋊C41128yescomplemented
717C23×C4C4×D4164yescomplemented
718C23×C4C23×C414yes—
719C23×C4C23×C418yes—
720C23×C4C23×C4116yes—
721C23×C4C23×C4132yes—
722C23×C4C23×C4132yes—
723C23×C4C23×C4116yes—
724C23×C4C23×C4132yes—
725C23×C4C23×C4132yes—
726C23×C4C23×C4132yes—
727C23×C4C23×C414yes—
728C23×C4C23×C418yes—
729C23×C4C23×C4132yes—
730C23×C4C23×C414yes—
731C23×C4C23×C4116yes—
732C23×C4C23×C4116yes—
733C23×C4C23×C414yes—
734C23×C4C23×C418yes—
735C23×C4C23×C4116yes—
736C23×C4C23×C4132yes—
737C23×C4C23×C414yes—
738C23×C4C23×C414yes—
739C23×C4C23×C418yes—
740C23×C4C23×C41128yescomplemented
741C23×C4C22×D418yes—
742C23×C4C22×D4116yes—
743C23×C4C22×D4164yes—
744C23×C4C22×D414yes—
745C23×C4C22×D4116yes—
746C23×C4C22×D4116yes—
747C23×C4C22×D418yes—
748C23×C4C22×D418yes—
749C23×C4C22×D414yes—
750C23×C4C2×#4114yes—
751C23×C4C2×#41116yes—
752C23×C4C2×#41116yes—
753C23×C4C2×#4118yes—
754C23×C4C2×#4114yes—
755C23×C4H(5,𝔽2)18yes—
756C23×C4C2518yes—
757C23×C4C25116yes—
758C23×C4C2512yes—
759C23×C4C2514yes—
760C23×C4C2512yes—
761C23×C4C2512yes—
762C23×C4C2514yes—
763C23×C4C2518yes—
764C23×C4C2512yes—
765C23×C4C2512yes—
766C23×C4C2512yes—
767C4×D4—2256no—
768C4×D4—21024no—
769C4×D4—2512no—
770C4×D4—2256no—
771C4×D4—2512no—
772C4×D4—2256no—
773C4×D4C2×C22⋊C41512yesdirect product factor
774C2×C4⋊C4—264no—
775C2×C4⋊C4—232no—
776C2×C4⋊C4—2128no—
777C2×C4⋊C4—232no—
778C2×C4⋊C4—216no—
779C2×C4⋊C4—232no—
780C2×C4⋊C4—232no—
781C2×C4⋊C4—2256no—
782C2×C4⋊C4C2×C22⋊C4164yescomplemented
783C2×C4⋊C4C23×C4116yes—
784C2×C4⋊C4C23×C4132yes—
785C2×C4⋊C4C23×C4116yes—
786C2×C4⋊C4C23×C4164yescomplemented
787C2×C4⋊C4C22×D4132yes—
788C2×C22⋊C4—264no—
789C2×C22⋊C4—2128no—
790C2×C22⋊C4—2256no—
791C2×C22⋊C4—264no—
792C2×C22⋊C4—232no—
793C2×C22⋊C4—232no—
794C2×C22⋊C4—264no—
795C2×C22⋊C4—232no—
796C2×C22⋊C4—264no—
797C2×C22⋊C4—216no—
798C2×C22⋊C4—216no—
799C2×C22⋊C4—264no—
800C2×C22⋊C4—264no—
801C2×C22⋊C4—2256no—
802C2×C22⋊C4—232no—
803C2×C22⋊C4—232no—
804C2×C22⋊C4—264no—
805C2×C22⋊C4—264no—
806C2×C22⋊C4—2512no—
807C2×C22⋊C4—21024no—
808C2×C22⋊C4—4128no—
809C2×C22⋊C4—432no—
810C2×C22⋊C4—432no—
811C2×C22⋊C4C2×C22⋊C41128yescomplemented
812C2×C22⋊C4C4×D41128yesdirect product factor
813C2×C22⋊C4C23×C4132yes—
814C2×C22⋊C4C23×C4132yes—
815C2×C22⋊C4C23×C4132yes—
816C2×C22⋊C4C23×C4164yes—
817C2×C22⋊C4C23×C4132yes—
818C2×C22⋊C4C23×C4132yes—
819C2×C22⋊C4C23×C4132yes—
820C2×C22⋊C4C23×C41128yescomplemented
821C2×C22⋊C4C23×C41128yescomplemented
822C2×C22⋊C4C23×C41128yescomplemented
823C2×C22⋊C4C22×D4164yes—
824C2×C22⋊C4C22×D4132yes—
825C2×C22⋊C4C2×#41132yes—
826C2×C42—232no—
827C2×C42—232no—
828C2×C42—232no—
829C2×C42—2128no—
830C2×C42—264no—
831C2×C42—216no—
832C2×C42—216no—
833C2×C42—216no—
834C2×C42—232no—
835C2×C42—216no—
836C2×C42—232no—
837C2×C42—216no—
838C2×C42—2256no—
839C2×C42—232no—
840C2×C42—216no—
841C2×C42—264no—
842C2×C42—232no—
843C2×C42—264no—
844C2×C42—232no—
845C2×C42—232no—
846C2×C42—216no—
847C2×C42—216no—
848C2×C42—232no—
849C2×C42—4512no—
850C2×C42—432no—
851C2×C42—416no—
852C2×C42—464no—
853C2×C42—4128no—
854C2×C42—464no—
855C2×C42—432no—
856C2×C42C2×C22⋊C4164yescomplemented
857C2×C42C23×C4116yes—
858C2×C42C23×C4116yes—
859C2×C42C23×C4116yes—
860C2×C42C23×C4116yes—
861C2×C42C23×C4164yescomplemented
862C2×C42C22×D4132yes—
863C2×C42C22×D4132yescomplemented
864#95—264no—
865#95—232no—
866#95—264no—
867#95—232no—
868#95—232no—
869#95—216no—
870#95—416no—
871#95—432no—
872#95C23×C4164yescomplemented
873#95C23×C4164yescomplemented
874#95C22×D4132yescomplemented
875C24—24no—
876C24—24no—
877C24—24no—
878C24—28no—
879C24—24no—
880C24—28no—
881C24—24no—
882C24—28no—
883C24—24no—
884C24—28no—
885C24—28no—
886C24—216no—
887C24—232no—
888C24—232no—
889C24—216no—
890C24—232no—
891C24—28no—
892C24—216no—
893C24—28no—
894C24—216no—
895C24—264no—
896C24—232no—
897C24—232no—
898C24—216no—
899C24—216no—
900C24—232no—
901C24—232no—
902C24—232no—
903C24—264no—
904C24—216no—
905C24—216no—
906C24—232no—
907C24—264no—
908C24—232no—
909C24—24no—
910C24—28no—
911C24—28no—
912C24—24no—
913C24—28no—
914C24—28no—
915C24—28no—
916C24—264no—
917C24—216no—
918C24—264no—
919C24—216no—
920C24—2128no—
921C24—232no—
922C24—264no—
923C24—216no—
924C24—2256no—
925C24—264no—
926C24—2128no—
927C24—264no—
928C24—216no—
929C24—232no—
930C24—216no—
931C24—216no—
932C24—264no—
933C24—2512no—
934C24—2512no—
935C24—432no—
936C24—4256no—
937C24—432no—
938C24—4128no—
939C24—4256no—
940C24—464no—
941C24—464no—
942C24—4256no—
943C24—4256no—
944C24—4256no—
945C24—41024no—
946C24—41024no—
947C24—464no—
948C24—4128no—
949C24—464no—
950C24—4128no—
951C24—416no—
952C24—416no—
953C24—432no—
954C24—416no—
955C24—416no—
956C24—432no—
957C24C22×C42132yes—
958C24C22×C42132yes—
959C24C22×C42116yes—
960C24C22×C421128yescomplemented
961C24C22×C22⋊C4132yes—
962C24C2×#117132yes—
963C24C2×C4×D41128yes—
964C24C2×C4×D4132yes—
965C24C2×C4×D4116yes—
966C24C4×#41132yes—
967C24C4×#41116yes—
968C24C24×C418yes—
969C24C24×C4116yes—
970C24C24×C418yes—
971C24C24×C4116yes—
972C24C24×C418yes—
973C24C24×C414yes—
974C24C24×C412yes—
975C24C24×C414yes—
976C24C23×D4116yes—
977C24C23×D414yes—
978C24C23×D414yes—
979C24C23×D412yes—
980C24C22×#41116yes—
981C24C22×#4118yes—
982C24C22×#4114yes—
983C24C22×#4114yes—
984C24C22×#4112yes—
985C24C22×#4114yes—
986C24C2×H(5,𝔽2)14yes—
987C24#58514yes—
988C24C2611yescharacteristic
989C2×D4—264no—
990C2×D4—264no—
991C2×D4—2256no—
992C2×D4—2512no—
993C2×D4—22048no—
994C2×D4—232no—
995C2×D4—232no—
996C2×D4—2128no—
997C2×D4—2256no—
998C2×D4C4×C22⋊C41512yesdirect product factor
999C2×D4C22×C42164yes—
1000C2×D4C22×C421128yescomplemented
1001C2×D4C22×C42164yescomplemented
1002C2×D4C22×C22⋊C4164yes—
1003C2×D4C2×#117164yes—
1004C2×D4C2×C4×D41256yes—
1005C22×C4—28no—
1006C22×C4—24no—
1007C22×C4—24no—
1008C22×C4—24no—
1009C22×C4—24no—
1010C22×C4—28no—
1011C22×C4—24no—
1012C22×C4—24no—
1013C22×C4—28no—
1014C22×C4—28no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—28no—
1018C22×C4—28no—
1019C22×C4—28no—
1020C22×C4—28no—
1021C22×C4—232no—
1022C22×C4—216no—
1023C22×C4—232no—
1024C22×C4—28no—
1025C22×C4—28no—
1026C22×C4—216no—
1027C22×C4—28no—
1028C22×C4—232no—
1029C22×C4—232no—
1030C22×C4—232no—
1031C22×C4—216no—
1032C22×C4—216no—
1033C22×C4—232no—
1034C22×C4—232no—
1035C22×C4—232no—
1036C22×C4—232no—
1037C22×C4—232no—
1038C22×C4—2256no—
1039C22×C4—2512no—
1040C22×C4—232no—
1041C22×C4—232no—
1042C22×C4—232no—
1043C22×C4—264no—
1044C22×C4—2128no—
1045C22×C4—232no—
1046C22×C4—264no—
1047C22×C4—2128no—
1048C22×C4—264no—
1049C22×C4—264no—
1050C22×C4—2128no—
1051C22×C4—2256no—
1052C22×C4—24no—
1053C22×C4—28no—
1054C22×C4—216no—
1055C22×C4—216no—
1056C22×C4—24no—
1057C22×C4—28no—
1058C22×C4—24no—
1059C22×C4—28no—
1060C22×C4—28no—
1061C22×C4—28no—
1062C22×C4—216no—
1063C22×C4—216no—
1064C22×C4—24no—
1065C22×C4—28no—
1066C22×C4—28no—
1067C22×C4—216no—
1068C22×C4—24no—
1069C22×C4—216no—
1070C22×C4—28no—
1071C22×C4—28no—
1072C22×C4—216no—
1073C22×C4—264no—
1074C22×C4—232no—
1075C22×C4—264no—
1076C22×C4—264no—
1077C22×C4—2256no—
1078C22×C4—264no—
1079C22×C4—216no—
1080C22×C4—232no—
1081C22×C4—232no—
1082C22×C4—28no—
1083C22×C4—216no—
1084C22×C4—28no—
1085C22×C4—232no—
1086C22×C4—264no—
1087C22×C4—232no—
1088C22×C4—264no—
1089C22×C4—264no—
1090C22×C4—264no—
1091C22×C4—264no—
1092C22×C4—264no—
1093C22×C4—264no—
1094C22×C4—2256no—
1095C22×C4—264no—
1096C22×C4—432no—
1097C22×C4—432no—
1098C22×C4—432no—
1099C22×C4—416no—
1100C22×C4—4128no—
1101C22×C4—4256no—
1102C22×C4—464no—
1103C22×C4—464no—
1104C22×C4—42048no—
1105C22×C4—4128no—
1106C22×C4—4128no—
1107C22×C4—41024no—
1108C22×C4—4128no—
1109C22×C4—464no—
1110C22×C4—4128no—
1111C22×C4—4128no—
1112C22×C4—4256no—
1113C22×C4—4256no—
1114C22×C4—464no—
1115C22×C4—464no—
1116C22×C4—464no—
1117C22×C4—464no—
1118C22×C4—432no—
1119C22×C4—416no—
1120C22×C4—416no—
1121C22×C4—416no—
1122C22×C4—416no—
1123C22×C4—416no—
1124C22×C4—432no—
1125C22×C4—432no—
1126C22×C4—416no—
1127C22×C4—416no—
1128C22×C4—432no—
1129C22×C4—4256no—
1130C22×C4—464no—
1131C22×C4—464no—
1132C22×C4C22×C42116yes—
1133C22×C4C22×C42116yes—
1134C22×C4C22×C42164yescomplemented
1135C22×C4C22×C22⋊C4116yes—
1136C22×C4C22×C22⋊C4132yes—
1137C22×C4C22×C22⋊C4116yes—
1138C22×C4C22×C22⋊C4116yes—
1139C22×C4C22×C22⋊C41128yescomplemented
1140C22×C4C2×#117116yes—
1141C22×C4C2×C4×D4116yes—
1142C22×C4C2×C4×D4116yes—
1143C22×C4C2×C4×D4164yes—
1144C22×C4C2×C4×D4164yescomplemented
1145C22×C4C2×C4×D4164yescomplemented
1146C22×C4#518116yes—
1147C22×C4D42132yes—
1148C22×C4#546132yes—
1149C22×C4C24×C4116yes—
1150C22×C4C24×C4132yes—
1151C22×C4C24×C414yes—
1152C22×C4C24×C418yes—
1153C22×C4C24×C418yes—
1154C22×C4C24×C414yes—
1155C22×C4C24×C414yes—
1156C22×C4C24×C418yes—
1157C22×C4C24×C414yes—
1158C22×C4C24×C4116yes—
1159C22×C4C24×C414yes—
1160C22×C4C24×C418yes—
1161C22×C4C24×C414yes—
1162C22×C4C23×D418yes—
1163C22×C4C23×D4116yes—
1164C22×C4C23×D414yes—
1165C22×C4C23×D4116yes—
1166C22×C4C23×D418yes—
1167C22×C4C23×D418yes—
1168C22×C4C23×D414yes—
1169C22×C4C22×#4114yes—
1170C22×C4C22×#41116yes—
1171C22×C4C22×#4118yes—
1172C22×C4C22×#4114yes—
1173C22×C4C2×H(5,𝔽2)18yes—
1174C4⋊C4—264no—
1175C4⋊C4—232no—
1176C4⋊C4—2128no—
1177C4⋊C4C22×C22⋊C4164yescomplemented
1178C22⋊C4—264no—
1179C22⋊C4—2128no—
1180C22⋊C4—2256no—
1181C22⋊C4—264no—
1182C22⋊C4—264no—
1183C22⋊C4—264no—
1184C22⋊C4—2256no—
1185C22⋊C4—4128no—
1186C22⋊C4C22×C22⋊C41128yescomplemented
1187C22⋊C4C2×C4×D41128yesdirect product factor
1188C42—232no—
1189C42—232no—
1190C42—232no—
1191C42—2128no—
1192C42—264no—
1193C42—464no—
1194C42—4128no—
1195C42—464no—
1196C42—432no—
1197C42C22×C22⋊C4164yescomplemented
1198C23—232no—
1199C23—264no—
1200C23—232no—
1201C23—264no—
1202C23—232no—
1203C23—264no—
1204C23—232no—
1205C23—264no—
1206C23—2256no—
1207C23—2128no—
1208C23—2128no—
1209C23—2256no—
1210C23—24no—
1211C23—24no—
1212C23—28no—
1213C23—216no—
1214C23—216no—
1215C23—28no—
1216C23—216no—
1217C23—24no—
1218C23—28no—
1219C23—24no—
1220C23—28no—
1221C23—232no—
1222C23—216no—
1223C23—232no—
1224C23—264no—
1225C23—232no—
1226C23—264no—
1227C23—216no—
1228C23—28no—
1229C23—28no—
1230C23—216no—
1231C23—216no—
1232C23—216no—
1233C23—232no—
1234C23—28no—
1235C23—28no—
1236C23—216no—
1237C23—232no—
1238C23—216no—
1239C23—28no—
1240C23—28no—
1241C23—216no—
1242C23—28no—
1243C23—232no—
1244C23—28no—
1245C23—216no—
1246C23—28no—
1247C23—28no—
1248C23—232no—
1249C23—264no—
1250C23—2256no—
1251C23—264no—
1252C23—2256no—
1253C23—264no—
1254C23—4128no—
1255C23—4128no—
1256C23—4128no—
1257C23—4128no—
1258C23—4128no—
1259C23—4512no—
1260C23—4512no—
1261C23—42048no—
1262C23—432no—
1263C23—432no—
1264C23—432no—
1265C23—432no—
1266C23—4128no—
1267C23—4128no—
1268C23—48no—
1269C23—48no—
1270C23—48no—
1271C23—416no—
1272C23—48no—
1273C23—416no—
1274C23C2×C4×C22⋊C41128yescomplemented
1275C23C42×D4164yescomplemented
1276C23C23×C42116yes—
1277C23C23×C42116yes—
1278C23C23×C4218yes—
1279C23C23×C4214yes—
1280C23C23×C22⋊C4116yes—
1281C23C23×C22⋊C414yes—
1282C23C22×#117116yes—
1283C23C22×#11714yes—
1284C23C22×C4×D4164yes—
1285C23C22×C4×D4116yes—
1286C23C22×C4×D418yes—
1287C23C22×C4×D414yes—
1288C23C22×C4×D418yes—
1289C23C22×C4×D4116yes—
1290C23C2×C4×#41116yes—
1291C23C2×C4×#4118yes—
1292C23C2×C4×#4114yes—
1293C23C2×C4×#4118yes—
1294C23C2×#51814yes—
1295C23#342814yes—
1296C23C4×H(5,𝔽2)116yes—
1297C23C2×D4218yes—
1298C23C2×#54618yes—
1299C23D4×#41116yes—
1300C23D4×#4118yes—
1301C23#347518yes—
1302C23#3481116yes—
1303C23C25×C411yescharacteristic
1304C23C25×C412yes—
1305C23C24×D412yes—
1306C23C24×D411yescharacteristic
1307C23C23×#4112yes—
1308C23C23×#4111yescharacteristic
1309C23C23×#4112yes—
1310C23C22×H(5,𝔽2)12yes—
1311C23C2×#58512yes—
1312D4—2256no—
1313D4—2128no—
1314D4C2×C4×C22⋊C41256yesdirect product factor
1315C2×C4—232no—
1316C2×C4—264no—
1317C2×C4—232no—
1318C2×C4—2128no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—216no—
1323C2×C4—28no—
1324C2×C4—216no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—28no—
1328C2×C4—24no—
1329C2×C4—216no—
1330C2×C4—232no—
1331C2×C4—216no—
1332C2×C4—216no—
1333C2×C4—28no—
1334C2×C4—28no—
1335C2×C4—216no—
1336C2×C4—216no—
1337C2×C4—216no—
1338C2×C4—216no—
1339C2×C4—216no—
1340C2×C4—2128no—
1341C2×C4—2256no—
1342C2×C4—2128no—
1343C2×C4—24no—
1344C2×C4—28no—
1345C2×C4—216no—
1346C2×C4—232no—
1347C2×C4—232no—
1348C2×C4—28no—
1349C2×C4—216no—
1350C2×C4—24no—
1351C2×C4—28no—
1352C2×C4—24no—
1353C2×C4—216no—
1354C2×C4—232no—
1355C2×C4—4128no—
1356C2×C4—464no—
1357C2×C4—4512no—
1358C2×C4—4128no—
1359C2×C4—4128no—
1360C2×C4—432no—
1361C2×C4—416no—
1362C2×C4—4128no—
1363C2×C4—464no—
1364C2×C4—416no—
1365C2×C4—48no—
1366C2×C4—48no—
1367C2×C4—48no—
1368C2×C4—48no—
1369C2×C4—48no—
1370C2×C4—416no—
1371C2×C4—416no—
1372C2×C4—48no—
1373C2×C4—48no—
1374C2×C4—416no—
1375C2×C4—4128no—
1376C2×C4C2×C4×C22⋊C4164yescomplemented
1377C2×C4D4×C22⋊C4164yesdirect product factor
1378C2×C4C23×C4218yes—
1379C2×C4C23×C4218yes—
1380C2×C4C23×C22⋊C418yes—
1381C2×C4C23×C22⋊C4116yes—
1382C2×C4C23×C22⋊C418yes—
1383C2×C4C23×C22⋊C418yes—
1384C2×C4C22×#11718yes—
1385C2×C4C22×C4×D418yes—
1386C2×C4C22×C4×D418yes—
1387C2×C4C22×C4×D4132yes—
1388C2×C4C22×C4×D4132yescomplemented
1389C2×C4C2×#51818yes—
1390C2×C4C2×D42116yes—
1391C2×C4C2×#546116yes—
1392C22—28no—
1393C22—216no—
1394C22—28no—
1395C22—216no—
1396C22—28no—
1397C22—216no—
1398C22—28no—
1399C22—216no—
1400C22—264no—
1401C22—232no—
1402C22—232no—
1403C22—264no—
1404C22—2128no—
1405C22—2256no—
1406C22—28no—
1407C22—216no—
1408C22—28no—
1409C22—216no—
1410C22—216no—
1411C22—216no—
1412C22—216no—
1413C22—4512no—
1414C22—48no—
1415C22—48no—
1416C22—48no—
1417C22—48no—
1418C22—432no—
1419C22—432no—
1420C22—4128no—
1421C22C22×C4×C22⋊C418yes—
1422C22C22×C4×C22⋊C4132yescomplemented
1423C22C2×C42×D418yes—
1424C22C2×C42×D4116yescomplemented
1425C22C4×#51818yes—
1426C22C2×D4×C22⋊C418yes—
1427C22C22⋊C4×#4118yes—
1428C22D4×#11718yes—
1429C22#3412618yes—
1430C22C4×D42132yes—
1431C22C4×#546132yes—
1432C22C24×C4211yescharacteristic
1433C22C24×C22⋊C411yescharacteristic
1434C22C23×#11711yescharacteristic
1435C22C23×C4×D411yescharacteristic
1436C22C23×C4×D412yes—
1437C22C23×C4×D414yes—
1438C22C22×C4×#4111yescharacteristic
1439C22C22×C4×#4112yes—
1440C22C22×#51811yescharacteristic
1441C22C2×#342811yescharacteristic
1442C22C2×C4×H(5,𝔽2)14yes—
1443C22C22×D4212yes—
1444C22C22×#54612yes—
1445C22C2×D4×#4112yes—
1446C22C2×D4×#4114yes—
1447C22C2×#347512yes—
1448C22C2×#348114yes—
1449C4—28no—
1450C4—216no—
1451C4—28no—
1452C4—232no—
1453C4—28no—
1454C4—48no—
1455C4—44no—
1456C4—432no—
1457C4—416no—
1458C4C22×C4×C22⋊C4116yescomplemented
1459C4C2×D4×C22⋊C4116yesdirect product factor
1460C2—216no—
1461C2—232no—
1462C2—416no—
1463C2C4×D4×C22⋊C4116yesdirect product factor
1464C2C23×C4×C22⋊C411yescharacteristic
1465C2C22×C42×D411yescharacteristic
1466C2C2×C4×#51811yescharacteristic
1467C2C22×D4×C22⋊C411yescharacteristic
1468C2C2×D4×#11711yescharacteristic
1469C2C2×C22⋊C4×#4111yescharacteristic
1470C2C2×#3412611yescharacteristic
1471C2C2×C4×D4214yes—
1472C2C2×C4×#54614yes—
subgroupG/H
center, socleC24×C4C24
commutatorC22C24×C42
Frattini, cosocleC24C26
prime radicalC25×D4C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C4 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C22×C42×D4C2semidirect
4. C23×C4×C22⋊C4C2semidirect
5. C4×D4×C22⋊C4C2direct (N × H)
6. C2×#13820C2semidirect
7. C2×#13813C2semidirect
8. C2×D4×#95C2semidirect
9. C2×C22⋊C4×C4⋊C4C2semidirect
10. C2×C22⋊C42C2semidirect
11. C2×C4×#380C2semidirect
12. C2×C4×#379C2semidirect
13. C2×C4×#390C2semidirect
14. C2×C4×#386C2semidirect
15. C2×C42×C22⋊C4C2semidirect
19. C23×C4×D4C4semidirect
32. C24×C42C22semidirect
33. C2×D4×C22⋊C4C4direct (N × H)
40. C2×C42×D4C22semidirect
41. C22×C4×C4⋊C4C22semidirect
42. C22×C4×C4⋊C4C22semidirect
50. C22×C4×C22⋊C4C22semidirect
51. C22×C4×C22⋊C4C22semidirect
52. C22×C4×C22⋊C4C22semidirect
53. C22×C4×C22⋊C4C22semidirect
54. C22×C4×C22⋊C4C22semidirect
55. C22×C4×C22⋊C4C22semidirect
56. C23×#95C22semidirect
57. C22×C43C22semidirect
58. #13820C22semidirect
59. #13813C22semidirect
60. D4×#95C22semidirect
61. C22⋊C4×C4⋊C4C22semidirect
62. C22⋊C42C22semidirect
63. C4×#380C22semidirect
64. C4×#379C22semidirect
65. C4×#390C22semidirect
66. C4×#386C22semidirect
67. C2×#1437C22semidirect
68. C2×#1437C22semidirect
69. C2×#1436C22semidirect
70. C2×C4⋊#95C22semidirect
71. C2×C4⋊#95C22semidirect
72. C2×#1434C22semidirect
75. C2×C22⋊#95C22semidirect
76. C2×C22⋊#95C22semidirect
77. C2×C22⋊#95C22semidirect
78. C42×C22⋊C4C22semidirect
79. C2×C4×#95C22semidirect
80. C2×C4×#95C22semidirect
81. C2×C4×#95C22semidirect
82. C2×C4×#95C22semidirect
96. C25×C4C2×C4semidirect
118. C22×C4×D4C2×C4semidirect
119. C22×C4×D4C2×C4semidirect
120. C22×C4×D4C2×C4semidirect
121. C22×C4×D4C2×C4semidirect
122. C22×C4×D4C2×C4semidirect
123. C22×C4×D4C2×C4semidirect
133. C23×C4⋊C4C2×C4semidirect
142. C23×C22⋊C4C2×C4semidirect
143. C23×C22⋊C4C2×C4semidirect
160. C23×C42C2×C4semidirect
172. C23×C42C23semidirect
173. D4×C22⋊C4C2×C4direct (N × H)
174. C2×#390C2×C4semidirect
176. C2×#386C2×C4semidirect
178. C2×#380C2×C4semidirect
180. C2×#379C2×C4semidirect
185. C2×C4×C4⋊C4C23semidirect
186. C2×C4×C4⋊C4C23semidirect
197. C2×C4×C22⋊C4C2×C4semidirect
198. C2×C4×C22⋊C4D4direct (N × H)
205. C2×C4×C22⋊C4C23semidirect
206. C2×C4×C22⋊C4C23semidirect
207. C2×C4×C22⋊C4C23semidirect
208. C2×C4×C22⋊C4C23semidirect
209. C2×C4×C22⋊C4C23semidirect
222. C22×#95C23semidirect
224. C2×C43C23semidirect
225. #1437C23semidirect
226. #1437C23semidirect
227. #1436C23semidirect
228. C4⋊#95C23semidirect
229. C4⋊#95C23semidirect
230. #1434C23semidirect
233. C22⋊#95C23semidirect
234. C22⋊#95C23semidirect
235. C22⋊#95C23semidirect
236. C4×#95C23semidirect
237. C4×#95C23semidirect
238. C4×#95C23semidirect
239. C4×#95C23semidirect
262. C23×D4C42semidirect
326. C24×C4C22×C4semidirect
327. C24×C4C22×C4semidirect
365. C2×C4×D4C22⋊C4direct (N × H)
368. C2×C4×D4C22×C4semidirect
369. C2×C4×D4C22×C4semidirect
370. C2×C4×D4C22×C4semidirect
371. C2×C4×D4C22×C4semidirect
372. C2×C4×D4C22×C4semidirect
383. C22×C4⋊C4C22×C4semidirect
384. C22×C4⋊C4C22×C4semidirect
415. C22×C22⋊C4C22×C4semidirect
416. C22×C22⋊C4C22×C4semidirect
417. C22×C22⋊C4C22×C4semidirect
418. C22×C22⋊C4C22×C4semidirect
419. C22×C22⋊C4C22×C4semidirect
462. C22×C42C22×C4semidirect
463. C22×C42C22×C4semidirect
465. C22×C42C2×D4semidirect
476. #390C22×C4semidirect
477. #386C22×C4semidirect
478. #380C22×C4semidirect
479. #379C22×C4semidirect
491. C4×C22⋊C4C22×C4semidirect
492. C4×C22⋊C4C2×D4direct (N × H)
502. C2×#95C22×C4semidirect
503. C2×#95C22×C4semidirect
504. C2×#95C2×D4semidirect
556. C25C2×C42semidirect
589. C22×D4C2×C42semidirect
590. C22×D4C2×C42semidirect
591. C22×D4C2×C42semidirect
715. C23×C4C2×C42semidirect
716. C23×C4C2×C22⋊C4semidirect
717. C23×C4C4×D4semidirect
740. C23×C4C23×C4semidirect
773. C4×D4C2×C22⋊C4direct (N × H)
782. C2×C4⋊C4C2×C22⋊C4semidirect
786. C2×C4⋊C4C23×C4semidirect
811. C2×C22⋊C4C2×C22⋊C4semidirect
812. C2×C22⋊C4C4×D4direct (N × H)
820. C2×C22⋊C4C23×C4semidirect
821. C2×C22⋊C4C23×C4semidirect
822. C2×C22⋊C4C23×C4semidirect
856. C2×C42C2×C22⋊C4semidirect
861. C2×C42C23×C4semidirect
863. C2×C42C22×D4semidirect
872. #95C23×C4semidirect
873. #95C23×C4semidirect
874. #95C22×D4semidirect
960. C24C22×C42semidirect
998. C2×D4C4×C22⋊C4direct (N × H)
1000. C2×D4C22×C42semidirect
1001. C2×D4C22×C42semidirect
1134. C22×C4C22×C42semidirect
1139. C22×C4C22×C22⋊C4semidirect
1144. C22×C4C2×C4×D4semidirect
1145. C22×C4C2×C4×D4semidirect
1177. C4⋊C4C22×C22⋊C4semidirect
1186. C22⋊C4C22×C22⋊C4semidirect
1187. C22⋊C4C2×C4×D4direct (N × H)
1197. C42C22×C22⋊C4semidirect
1274. C23C2×C4×C22⋊C4semidirect
1275. C23C42×D4semidirect
1314. D4C2×C4×C22⋊C4direct (N × H)
1376. C2×C4C2×C4×C22⋊C4semidirect
1377. C2×C4D4×C22⋊C4direct (N × H)
1388. C2×C4C22×C4×D4semidirect
1422. C22C22×C4×C22⋊C4semidirect
1424. C22C2×C42×D4semidirect
1458. C4C22×C4×C22⋊C4semidirect
1459. C4C2×D4×C22⋊C4direct (N × H)
1463. C2C4×D4×C22⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C4×D42
C22×D4×C22⋊C42
C22×C42×D42
C23×C4×C22⋊C42
C4×D4×C22⋊C42
C2×#138202
C2×#138132
C2×D4×#952
C2×C22⋊C4×C4⋊C42
C2×C22⋊C422
C2×C4×#3802
C2×C4×#3792
C2×C4×#3902
C2×C4×#3862
C2×C42×C22⋊C42