Finite Group Databasebeta

← C2×#6377437 #72257683

Subgroups — C2×#6377437 #72257683

Order 1024.

13665 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#532C211yesmaximal, characteristic
2#6377437C2132yesmaximal, direct product factor
3C2×#22395C214yesmaximal, complemented
4C2×#22339C214yesmaximal, complemented
5C2×#22311C212yesmaximal, complemented
6C2×#22260C212yesmaximal, complemented
7C2×#22135C214yesmaximal, complemented
8C2×#21379C214yesmaximal, complemented
9C2×#21270C212yesmaximal, complemented
10C2×#21107C214yesmaximal, complemented
11C2×#20778C211yesmaximal, characteristic, complemented
12C2×D4×#97C212yesmaximal, complemented
13C2×#20463C211yesmaximal, characteristic, complemented
14C22×#532C411yescharacteristic
15C22×C4×#41C2212yes—
16C22×C8×D4C2214yes—
17C22×#432C2214yes—
18C22×#431C2212yes—
19C23×#97C2214yes—
20C4×#532C4116yes—
21C4×#532C22116yes—
22C2×C4×C4⋊Q8C411yescharacteristic
23C2×C4×C4⋊Q8C2211yescharacteristic
24C2×C4×#127C411yescharacteristic
25C2×C4×#127C2211yescharacteristic
26C2×C4×#124C412yes—
27C2×C4×#124C2212yes—
28C2×C4×#121C412yes—
29C2×C4×#121C412yes—
30C2×C4×#121C2212yes—
31C2×C4×#121C2212yes—
32C2×#2297C412yes—
33C2×#2293C412yes—
34C2×#2293C412yes—
35C2×#2285C411yescharacteristic
36C2×C42×D4C2212yes—
37C2×C42×D4C2212yes—
38C22×C43C2211yescharacteristic
39#22395C22164yescomplemented
40#22339C22164yescomplemented
41#22311C22132yescomplemented
42#22260C22132yescomplemented
43#22135C22164yescomplemented
44#21379C22164yescomplemented
45C2×#1985C2218yes—
46#21270C22132yescomplemented
47C2×#1955C2218yes—
48C2×#1954C2214yes—
49C2×#1939C2214yes—
50#21107C22164yescomplemented
51C2×#1924C2218yes—
52C2×#1924C2218yes—
53C2×#1917C2218yes—
54C2×#1869C2218yes—
55C2×#1869C2218yes—
56C2×#1869C2218yes—
57C2×#1850C2218yes—
58#20778C22116yescomplemented
59C2×#1839C2212yes—
60C2×#1831C2212yes—
61C2×#1817C2212yes—
62C2×#1797C2212yes—
63D4×#97C22132yescomplemented
64#20463C22116yescomplemented
65C2×#1770C2214yes—
66C2×#1767C2212yes—
67C2×#1767C2212yes—
68C2×#1767C2212yes—
69C2×#1752C2218yes—
70C2×#1749C2212yes—
71C2×#1749C2212yes—
72C2×#1749C2214yes—
73C2×#1749C2214yes—
74C2×#1749C2212yes—
75C2×#1745C2212yes—
76C2×#1744C2212yes—
77C2×C4×#97C2211yescharacteristic
78C2×C4×#97C2211yescharacteristic
79C23×#41C2×C412yes—
80C24×C8C2318yes—
81C2×#532—216no—
82C2×#532C2×C4116yes—
83C22×C4⋊Q8C2×C411yescharacteristic
84C22×#127C2×C411yescharacteristic
85C22×#124C2×C412yes—
86C22×#121C2×C412yes—
87C22×#121C2×C412yes—
88C2×C4×#41—416no—
89C2×C4×#41C2×C4116yes—
90C2×C4×#41C23116yes—
91C22×C4×Q8C2×C412yes—
92C22×C4×Q8C2312yes—
93C22×C4×D4C2×C412yes—
94C22×C4×D4C2×C412yes—
95C22×C4×D4C2×C414yes—
96C22×C4×D4C2×C412yes—
97C22×C4×D4C2×C412yes—
98C22×C4×D4C2×C412yes—
99C22×C4×D4C2312yes—
100C22×C4×D4C2312yes—
101C22×C4×D4C2312yes—
102C22×C4×D4C2314yes—
103C22×#117C2×C412yes—
104C22×#117C2×C414yes—
105C23×C42C2×C411yescharacteristic
106C23×C42C2×C411yescharacteristic
107C23×C42C2×C411yescharacteristic
108C23×C42C2×C411yescharacteristic
109C23×C42C2311yescharacteristic
110C23×C42C2314yes—
111C23×C42C2311yescharacteristic
112C23×C42C2311yescharacteristic
113C2×C8×D4—232no—
114C2×C8×D4C23132yes—
115C2×#432—416no—
116C2×#432C23132yes—
117C2×#431—216no—
118C2×#431C23116yes—
119C22×C4⋊C8C2314yes—
120C22×C4⋊C8C2314yes—
121C22×C4⋊C8C2318yes—
122C22×C22⋊C8C2318yes—
123C22×C22⋊C8C2314yes—
124C22×C22⋊C8C2318yes—
125C22×C22⋊C8C2318yes—
126C22×C22⋊C8C2314yes—
127C22×#97—416no—
128C22×#97C2312yes—
129C22×#97C2312yes—
130C22×#97C2314yes—
131C22×#97C23132yes—
132C22×#97C2318yes—
133C22×#97C2312yes—
134C22×#97C2312yes—
135C22×C4×C8C2312yes—
136C22×C4×C8C2312yes—
137C4×C4⋊Q8C2×C4116yes—
138C4×C4⋊Q8C2×C418yes—
139C4×C4⋊Q8C2318yes—
140C4×#127C2×C4116yes—
141C4×#127C2×C418yes—
142C4×#127C2318yes—
143C4×#124C2×C4132yes—
144C4×#124C2×C4116yes—
145C4×#124C23116yes—
146C4×#121C2×C4132yes—
147C4×#121C2×C4132yes—
148C4×#121C2×C4116yes—
149C4×#121C2×C4116yes—
150C4×#121C23116yes—
151C4×#121C23116yes—
152#2297C2×C4132yes—
153C2×#391C2×C412yes—
154C2×#391C2×C412yes—
155#2293C2×C4132yes—
156#2293C2×C4132yes—
157C2×#390C2×C412yes—
158C2×#390C2×C412yes—
159C2×#390C2×C412yes—
160C2×#390C2×C412yes—
161C2×#390C2×C412yes—
162C2×#390C2×C412yes—
163C2×#389C2×C412yes—
164C2×#389C2×C412yes—
165C2×#389C2×C412yes—
166C2×#389C2×C412yes—
167C2×#388C2×C414yes—
168C2×#388C2×C414yes—
169C2×#388C2×C414yes—
170C2×#388C2×C414yes—
171C2×#386C2×C414yes—
172C2×#386C2×C414yes—
173#2285C2×C4116yes—
174C2×#384C2×C411yescharacteristic
175C2×#384C2×C411yescharacteristic
176C2×#382C2×C412yes—
177C2×#380C2×C412yes—
178C2×#380C2×C412yes—
179C42×D4C2×C4116yes—
180C42×D4C2×C4116yes—
181C42×D4C23116yes—
182C42×D4C23116yes—
183C2×C4×C4⋊C4C2×C412yes—
184C2×C4×C4⋊C4C2×C412yes—
185C2×C4×C4⋊C4C2×C412yes—
186C2×C4×C4⋊C4C2×C412yes—
187C2×C4×C4⋊C4C2312yes—
188C2×C4×C4⋊C4C2312yes—
189C2×C4×C22⋊C4C2×C414yes—
190C2×C4×C22⋊C4C2×C414yes—
191C2×C4×C22⋊C4C2×C414yes—
192C2×C4×C22⋊C4C2×C414yes—
193C2×C4×C22⋊C4C2314yes—
194C2×C4×C22⋊C4C2314yes—
195C2×C43C2×C411yescharacteristic
196C2×C43C2×C411yescharacteristic
197C2×C43C2×C411yescharacteristic
198C2×C43C2×C411yescharacteristic
199C2×C43C2×C418yes—
200C2×C43C2311yescharacteristic
201C2×C43C2311yescharacteristic
202C2×C43C2318yes—
203C2×C43C2311yescharacteristic
204C2×C43C2311yescharacteristic
205#1985C23164yes—
206#1955C23164yes—
207#1954C23132yes—
208#1939C23132yes—
209#1924C23164yes—
210#1924C23164yes—
211#1917C23164yes—
212#1869C23164yes—
213#1869C23164yes—
214#1869C23164yes—
215#1850C23164yes—
216#1839C23116yes—
217#1831C23116yes—
218#1817C23116yes—
219#1797C23116yes—
220#1770C23132yes—
221#1767C23116yes—
222#1767C23116yes—
223#1767C23116yes—
224#1752C23164yes—
225#1749C23132yes—
226#1749C23132yes—
227#1749C23116yes—
228#1749C23116yes—
229#1749C23116yes—
230#1745C23116yes—
231#1744C23116yes—
232C2×#336C2314yes—
233C2×#336C2314yes—
234C2×#336C2314yes—
235C2×#336C2318yes—
236C2×#336C2318yes—
237C2×#336C2314yes—
238C2×#336C2314yes—
239C2×#336C2314yes—
240C4×#97C2318yes—
241C4×#97C2318yes—
242C22×#41—216no—
243C22×#41—48no—
244C22×#41—48no—
245C22×#41C22×C4116yes—
246C23×Q8C22×C412yes—
247C23×D4C22×C414yes—
248C23×D4C22×C412yes—
249C23×D4C22×C412yes—
250C23×D4C22×C412yes—
251C24×C4C22×C411yescharacteristic
252C24×C4C22×C411yescharacteristic
253C24×C4C22×C411yescharacteristic
254C24×C4C22×C414yes—
255C24×C4C22×C411yescharacteristic
256C24×C4C22×C411yescharacteristic
257C24×C4C22×C411yescharacteristic
258C24×C4C22×C414yes—
259C24×C4C2411yescharacteristic
260C24×C4C2414yes—
261C23×C8—232no—
262C23×C8—416no—
263C23×C8—416no—
264C23×C8C2414yes—
265C23×C8C2418yes—
266C23×C8C2414yes—
267C23×C8C24132yes—
268#532—2128no—
269C2×C4⋊Q8—28no—
270C2×C4⋊Q8C22×C418yes—
271C2×#127M16116yes—
272C2×#127C22×C418yes—
273C2×#124—216no—
274C2×#124C22×C4116yes—
275C2×#121—216no—
276C2×#121—216no—
277C2×#121C22×C4116yes—
278C2×#121C22×C4116yes—
279C4×#41—464no—
280C4×#41—464no—
281C2×C4×Q8—48no—
282C2×C4×Q8—48no—
283C2×C4×Q8C22×C4116yes—
284C2×C4×Q8C22×C418yes—
285C2×C4×Q8C2418yes—
286C2×C4×D4—216no—
287C2×C4×D4—216no—
288C2×C4×D4—216no—
289C2×C4×D4—48no—
290C2×C4×D4—48no—
291C2×C4×D4—48no—
292C2×C4×D4—416no—
293C2×C4×D4—48no—
294C2×C4×D4—48no—
295C2×C4×D4—48no—
296C2×C4×D4—48no—
297C2×C4×D4C22×C418yes—
298C2×C4×D4C22×C4116yes—
299C2×C4×D4C22×C4116yes—
300C2×C4×D4C22×C4116yes—
301C2×C4×D4C22×C4116yes—
302C2×C4×D4C22×C4116yes—
303C2×C4×D4C22×C418yes—
304C2×C4×D4C22×C418yes—
305C2×C4×D4C22×C4132yes—
306C2×C4×D4C22×C4116yes—
307C2×C4×D4C2418yes—
308C2×C4×D4C2418yes—
309C2×C4×D4C2418yes—
310C2×C4×D4C24116yes—
311C2×#117—416no—
312C2×#117—48no—
313C2×#117C22×C4116yes—
314C2×#117C22×C4132yes—
315C22×C4⋊C4C22×C412yes—
316C22×C4⋊C4C22×C412yes—
317C22×C4⋊C4C22×C412yes—
318C22×C4⋊C4C22×C412yes—
319C22×C4⋊C4C22×C412yes—
320C22×C4⋊C4C22×C414yes—
321C22×C4⋊C4C22×C412yes—
322C22×C4⋊C4C22×C414yes—
323C22×C4⋊C4C22×C412yes—
324C22×C4⋊C4C22×C412yes—
325C22×C22⋊C4C22×C414yes—
326C22×C22⋊C4C22×C414yes—
327C22×C22⋊C4C22×C414yes—
328C22×C22⋊C4C22×C414yes—
329C22×C22⋊C4C22×C414yes—
330C22×C22⋊C4C22×C414yes—
331C22×C22⋊C4C22×C414yes—
332C22×C22⋊C4C22×C414yes—
333C22×C22⋊C4C22×C414yes—
334C22×C42—28no—
335C22×C42—28no—
336C22×C42—216no—
337C22×C42—28no—
338C22×C42—216no—
339C22×C42—44no—
340C22×C42—44no—
341C22×C42—44no—
342C22×C42—44no—
343C22×C42C22×C411yescharacteristic
344C22×C42C22×C411yescharacteristic
345C22×C42C22×C411yescharacteristic
346C22×C42C22×C411yescharacteristic
347C22×C42C22×C411yescharacteristic
348C22×C42C22×C418yes—
349C22×C42C22×C411yescharacteristic
350C22×C42C22×C411yescharacteristic
351C22×C42C22×C411yescharacteristic
352C22×C42C22×C414yes—
353C22×C42C22×C411yescharacteristic
354C22×C42C22×C414yes—
355C22×C42C22×C414yes—
356C22×C42C22×C4116yes—
357C22×C42C22×C411yescharacteristic
358C22×C42C22×C411yescharacteristic
359C22×C42C22×C414yes—
360C22×C42C22×C411yescharacteristic
361C22×C42C22×C411yescharacteristic
362C22×C42C22×C411yescharacteristic
363C22×C42C22×C411yescharacteristic
364C22×C42C22×C411yescharacteristic
365C22×C42C22×C411yescharacteristic
366C22×C42C22×C411yescharacteristic
367C22×C42C22×C411yescharacteristic
368C22×C42C22×C418yes—
369C22×C42C22×C418yes—
370C22×C42C22×C418yes—
371C22×C42C22×C411yescharacteristic
372C22×C42C22×C411yescharacteristic
373C22×C42C22×C414yes—
374C22×C42C22×C411yescharacteristic
375C22×C42C2414yes—
376C22×C42C24116yes—
377C22×C42C2414yes—
378C22×C42C2411yescharacteristic
379C22×C42C2414yes—
380C22×C42C2411yescharacteristic
381C22×C42C2411yescharacteristic
382C22×C42C2411yescharacteristic
383C22×C42C2414yes—
384C22×C42C2411yescharacteristic
385C22×C42C2411yescharacteristic
386C8×D4—2128no—
387#432—464no—
388#431—264no—
389C2×C4⋊C8—216no—
390C2×C4⋊C8—216no—
391C2×C4⋊C8—416no—
392C2×C4⋊C8C24116yes—
393C2×C4⋊C8C24116yes—
394C2×C4⋊C8C24132yes—
395C2×C22⋊C8—216no—
396C2×C22⋊C8—232no—
397C2×C22⋊C8—48no—
398C2×C22⋊C8—416no—
399C2×C22⋊C8—416no—
400C2×C22⋊C8C24116yes—
401C2×C22⋊C8C24132yes—
402C2×C22⋊C8C24116yes—
403C2×C22⋊C8C24132yes—
404C2×C22⋊C8C24132yes—
405C2×#97—28no—
406C2×#97—216no—
407C2×#97—28no—
408C2×#97—464no—
409C2×#97—416no—
410C2×#97—44no—
411C2×#97—44no—
412C2×#97C2418yes—
413C2×#97C24116yes—
414C2×#97C2418yes—
415C2×#97C24132yes—
416C2×#97C2418yes—
417C2×#97C2418yes—
418C2×C4×C8—28no—
419C2×C4×C8#41116yescomplemented
420C2×C4×C8C2418yes—
421C2×C4×C8C2418yes—
422#391C22×C4116yes—
423#391C22×C4116yes—
424#390C22×C4116yes—
425#390C22×C4116yes—
426#390C22×C4116yes—
427#390C22×C4116yes—
428#390C22×C4116yes—
429#390C22×C4116yes—
430#389C22×C4116yes—
431#389C22×C4116yes—
432#389C22×C4116yes—
433#389C22×C4116yes—
434#388C22×C4132yes—
435#388C22×C4132yes—
436#388C22×C4132yes—
437#388C22×C4132yes—
438#386C22×C4132yes—
439#386C22×C4132yes—
440#384C22×C418yes—
441#384C22×C418yes—
442#382C22×C4116yes—
443#380C22×C4116yes—
444#380C22×C4116yes—
445C4×C4⋊C4C22×C4116yes—
446C4×C4⋊C4C22×C4116yes—
447C4×C4⋊C4C22×C418yes—
448C4×C4⋊C4C22×C418yes—
449C4×C4⋊C4C22×C4116yes—
450C4×C4⋊C4C22×C4116yes—
451C4×C4⋊C4C2418yes—
452C4×C4⋊C4C2418yes—
453C4×C22⋊C4C22×C4132yes—
454C4×C22⋊C4C22×C4132yes—
455C4×C22⋊C4C22×C4132yes—
456C4×C22⋊C4C22×C4132yes—
457C4×C22⋊C4C22×C4116yes—
458C4×C22⋊C4C22×C4116yes—
459C4×C22⋊C4C24116yes—
460C4×C22⋊C4C24116yes—
461C2×#95C22×C414yes—
462C2×#95C22×C414yes—
463C2×#95C22×C414yes—
464C2×#95C22×C414yes—
465C2×#95C22×C414yes—
466C2×#95C22×C414yes—
467C43C22×C414yes—
468C43C22×C418yes—
469C43C22×C414yes—
470C43C22×C414yes—
471C43C22×C418yes—
472C43C22×C418yes—
473C43C22×C414yes—
474C43C22×C418yes—
475C43C2414yes—
476C43C2414yes—
477C43C2414yes—
478C43C2414yes—
479#336C24116yes—
480#336C24116yes—
481#336C24116yes—
482#336C24116yes—
483#336C24132yes—
484#336C24116yes—
485#336C24116yes—
486#336C24132yes—
487C25C23×C414yes—
488C25C23×C411yescharacteristic
489C2×#41—264no—
490C2×#41—432no—
491C2×#41—432no—
492C2×#41—4128no—
493C22×Q8—28no—
494C22×Q8—44no—
495C22×Q8—44no—
496C22×Q8C23×C418yes—
497C22×D4—216no—
498C22×D4—216no—
499C22×D4—28no—
500C22×D4—28no—
501C22×D4—44no—
502C22×D4—48no—
503C22×D4—44no—
504C22×D4—44no—
505C22×D4—44no—
506C22×D4C2×M16116yes—
507C22×D4C2×M16116yes—
508C22×D4C2×M16116yes—
509C22×D4C23×C4116yes—
510C22×D4C23×C418yes—
511C22×D4C23×C418yes—
512C22×D4C23×C418yes—
513C23×C4—24no—
514C23×C4—24no—
515C23×C4—24no—
516C23×C4—24no—
517C23×C4—24no—
518C23×C4—24no—
519C23×C4—216no—
520C23×C4—24no—
521C23×C4—24no—
522C23×C4—216no—
523C23×C4—24no—
524C23×C4—24no—
525C23×C4—24no—
526C23×C4—24no—
527C23×C4—216no—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—28no—
531C23×C4—28no—
532C23×C4—216no—
533C23×C4—24no—
534C23×C4—216no—
535C23×C4—48no—
536C23×C4—42no—
537C23×C4—42no—
538C23×C4—42no—
539C23×C4—42no—
540C23×C4—42no—
541C23×C4—42no—
542C23×C4—48no—
543C23×C4—48no—
544C23×C4C23×C414yes—
545C23×C4C23×C411yescharacteristic
546C23×C4C23×C414yes—
547C23×C4C23×C411yescharacteristic
548C23×C4C23×C411yescharacteristic
549C23×C4C23×C411yescharacteristic
550C23×C4C23×C411yescharacteristic
551C23×C4C23×C411yescharacteristic
552C23×C4C23×C414yes—
553C23×C4C23×C414yes—
554C23×C4C23×C418yes—
555C23×C4C23×C412yes—
556C23×C4C23×C414yes—
557C23×C4C23×C414yes—
558C23×C4C23×C4116yes—
559C23×C4C23×C411yescharacteristic
560C23×C4C23×C411yescharacteristic
561C23×C4C23×C411yescharacteristic
562C23×C4C23×C411yescharacteristic
563C23×C4C23×C411yescharacteristic
564C23×C4C23×C411yescharacteristic
565C23×C4C23×C4116yes—
566C23×C4C23×C414yes—
567C23×C4C23×C414yes—
568C23×C4C23×C414yes—
569C23×C4C23×C411yescharacteristic
570C23×C4C2518yes—
571C23×C4C2512yes—
572C23×C4C2511yescharacteristic
573C22×C8—28no—
574C22×C8—28no—
575C22×C8—216no—
576C22×C8—28no—
577C22×C8—216no—
578C22×C8—28no—
579C22×C8—216no—
580C22×C8—28no—
581C22×C8—264no—
582C22×C8—432no—
583C22×C8—432no—
584C22×C8—4128no—
585C22×C8C2×#41116yes—
586C22×C8C25116yes—
587C22×C8C2518yes—
588C22×C8C2518yes—
589C4⋊Q8—232no—
590#127C2×M16164yes—
591#124—264no—
592#121—264no—
593#121—264no—
594C4×Q8—432no—
595C4×Q8—416no—
596C4×Q8—416no—
597C4×D4—264no—
598C4×D4—264no—
599C4×D4—232no—
600C4×D4—232no—
601C4×D4—432no—
602C4×D4—432no—
603C4×D4—416no—
604C4×D4—416no—
605C4×D4—432no—
606C4×D4—432no—
607C4×D4—464no—
608C4×D4—416no—
609C4×D4—416no—
610C4×D4—416no—
611C4×D4—416no—
612#117—432no—
613#117—464no—
614C2×C4⋊C4—28no—
615C2×C4⋊C4—28no—
616C2×C4⋊C4—28no—
617C2×C4⋊C4—28no—
618C2×C4⋊C4—44no—
619C2×C4⋊C4—44no—
620C2×C4⋊C4—48no—
621C2×C4⋊C4—48no—
622C2×C4⋊C4—44no—
623C2×C4⋊C4—44no—
624C2×C4⋊C4C23×C418yes—
625C2×C4⋊C4C23×C418yes—
626C2×C4⋊C4C23×C418yes—
627C2×C4⋊C4C23×C418yes—
628C2×C4⋊C4C23×C418yes—
629C2×C4⋊C4C23×C4116yes—
630C2×C4⋊C4C23×C418yes—
631C2×C4⋊C4C23×C4116yes—
632C2×C4⋊C4C23×C418yes—
633C2×C4⋊C4C23×C418yes—
634C2×C22⋊C4—216no—
635C2×C22⋊C4—216no—
636C2×C22⋊C4—216no—
637C2×C22⋊C4—216no—
638C2×C22⋊C4—48no—
639C2×C22⋊C4—48no—
640C2×C22⋊C4—48no—
641C2×C22⋊C4—48no—
642C2×C22⋊C4—48no—
643C2×C22⋊C4C23×C4116yes—
644C2×C22⋊C4C23×C4116yes—
645C2×C22⋊C4C23×C4116yes—
646C2×C22⋊C4C23×C4116yes—
647C2×C22⋊C4C23×C4116yes—
648C2×C22⋊C4C23×C4116yes—
649C2×C22⋊C4C23×C4116yes—
650C2×C22⋊C4C23×C4116yes—
651C2×C22⋊C4C23×C4116yes—
652C2×C42—24no—
653C2×C42—24no—
654C2×C42—24no—
655C2×C42—216no—
656C2×C42—24no—
657C2×C42—216no—
658C2×C42—24no—
659C2×C42—24no—
660C2×C42—24no—
661C2×C42—24no—
662C2×C42—24no—
663C2×C42—24no—
664C2×C42—24no—
665C2×C42—24no—
666C2×C42—24no—
667C2×C42—28no—
668C2×C42—28no—
669C2×C42—24no—
670C2×C42—24no—
671C2×C42—216no—
672C2×C42—216no—
673C2×C42—264no—
674C2×C42—232no—
675C2×C42—216no—
676C2×C42—216no—
677C2×C42—232no—
678C2×C42—232no—
679C2×C42—48no—
680C2×C42—416no—
681C2×C42—416no—
682C2×C42—48no—
683C2×C42—42no—
684C2×C42—42no—
685C2×C42—42no—
686C2×C42—42no—
687C2×C42—42no—
688C2×C42—42no—
689C2×C42—42no—
690C2×C42—42no—
691C2×C42—416no—
692C2×C42—42no—
693C2×C42—42no—
694C2×C42C2×M1618yes—
695C2×C42C23×C414yes—
696C2×C42C23×C4116yes—
697C2×C42C23×C414yes—
698C2×C42C23×C412yes—
699C2×C42C23×C412yes—
700C2×C42C23×C414yes—
701C2×C42C23×C414yes—
702C2×C42C23×C414yes—
703C2×C42C23×C414yes—
704C2×C42C23×C4116yes—
705C2×C42C23×C418yes—
706C2×C42C23×C414yes—
707C2×C42C23×C412yes—
708C2×C42C23×C412yes—
709C2×C42C23×C414yes—
710C2×C42C23×C414yes—
711C2×C42C23×C414yes—
712C2×C42C23×C414yes—
713C2×C42C23×C414yes—
714C2×C42C23×C414yes—
715C2×C42C23×C414yes—
716C2×C42C23×C414yes—
717C2×C42C23×C414yes—
718C2×C42C23×C414yes—
719C2×C42C23×C414yes—
720C2×C42C23×C414yes—
721C2×C42C23×C414yes—
722C2×C42C23×C414yes—
723C2×C42C23×C412yes—
724C2×C42C23×C412yes—
725C2×C42C23×C414yes—
726C2×C42C2×#4118yes—
727C2×C42H(5,𝔽2)18yes—
728C2×C42C2512yes—
729C2×C42C2512yes—
730C2×C42C2518yes—
731C2×C42C2512yes—
732C2×C42C2512yes—
733C2×C42C2512yes—
734C2×C42C2512yes—
735C4⋊C8—232no—
736C4⋊C8—232no—
737C4⋊C8—432no—
738C22⋊C8—232no—
739C22⋊C8—264no—
740C22⋊C8—432no—
741C22⋊C8—416no—
742C22⋊C8—432no—
743#97—216no—
744#97—232no—
745#97—216no—
746#97—432no—
747#97—48no—
748#97—48no—
749C4×C8—216no—
750C4×C8C2×#41132yescomplemented
751#95C23×C4116yes—
752#95C23×C4116yes—
753#95C23×C4116yes—
754#95C23×C4116yes—
755#95C23×C4116yes—
756#95C23×C4116yes—
757C24—28no—
758C24—22no—
759C24—22no—
760C24—28no—
761C24—28no—
762C24—22no—
763C24—22no—
764C24—28no—
765C24—28no—
766C24—22no—
767C24—22no—
768C24—28no—
769C24C22×M16116yes—
770C24#56814yes—
771C24C24×C418yes—
772C24C24×C412yes—
773C24C24×C411yescharacteristic
774#41—4256no—
775C2×Q8—216no—
776C2×Q8—48no—
777C2×Q8—48no—
778C2×Q8—432no—
779C2×D4—232no—
780C2×D4—232no—
781C2×D4—216no—
782C2×D4—264no—
783C2×D4—216no—
784C2×D4—48no—
785C2×D4—416no—
786C2×D4—48no—
787C2×D4—48no—
788C2×D4—432no—
789C2×D4—432no—
790C2×D4—48no—
791C2×D4—464no—
792C2×D4C22×M16132yes—
793C2×D4C22×M16132yes—
794C2×D4C22×M16132yes—
795C22×C4—232no—
796C22×C4—232no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—28no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—28no—
811C22×C4—28no—
812C22×C4—28no—
813C22×C4—28no—
814C22×C4—28no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—28no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—28no—
821C22×C4—28no—
822C22×C4—28no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—28no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—28no—
831C22×C4—232no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—28no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—28no—
842C22×C4—28no—
843C22×C4—28no—
844C22×C4—24no—
845C22×C4—216no—
846C22×C4—28no—
847C22×C4—24no—
848C22×C4—28no—
849C22×C4—24no—
850C22×C4—216no—
851C22×C4—24no—
852C22×C4—28no—
853C22×C4—216no—
854C22×C4—232no—
855C22×C4—28no—
856C22×C4—24no—
857C22×C4—216no—
858C22×C4—24no—
859C22×C4—216no—
860C22×C4—28no—
861C22×C4—28no—
862C22×C4—28no—
863C22×C4—232no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—416no—
871C22×C4—416no—
872C22×C4—416no—
873C22×C4—464no—
874C22×C4—416no—
875C22×C4—416no—
876C22×C4—416no—
877C22×C4—432no—
878C22×C4—432no—
879C22×C4—416no—
880C22×C4—416no—
881C22×C4—832no—
882C22×C4C4×#4114yes—
883C22×C4C4×#4114yes—
884C22×C4#51814yes—
885C22×C4#51814yes—
886C22×C4C22×M1614yes—
887C22×C4C22×M1614yes—
888C22×C4C22×M1614yes—
889C22×C4#56814yes—
890C22×C4#56814yes—
891C22×C4C24×C412yes—
892C22×C4C24×C412yes—
893C22×C4C24×C412yes—
894C22×C4C24×C412yes—
895C22×C4C24×C418yes—
896C22×C4C24×C418yes—
897C22×C4C24×C418yes—
898C22×C4C24×C412yes—
899C22×C4C24×C412yes—
900C22×C4C24×C412yes—
901C22×C4C24×C412yes—
902C22×C4C24×C412yes—
903C22×C4C24×C412yes—
904C22×C4C24×C412yes—
905C22×C4C24×C412yes—
906C22×C4C24×C411yescharacteristic
907C22×C4C24×C412yes—
908C22×C4C22×#4114yes—
909C22×C4C2×H(5,𝔽2)14yes—
910C22×C4#58514yes—
911C22×C4C2611yescharacteristic
912C2×C8—28no—
913C2×C8—28no—
914C2×C8—232no—
915C2×C8—28no—
916C2×C8—216no—
917C2×C8—216no—
918C2×C8—28no—
919C2×C8—28no—
920C2×C8—216no—
921C2×C8—4128no—
922C2×C8—416no—
923C2×C8—432no—
924C2×C8C22×#41116yes—
925C4⋊C4—216no—
926C4⋊C4—216no—
927C4⋊C4—216no—
928C4⋊C4—216no—
929C4⋊C4—48no—
930C4⋊C4—48no—
931C4⋊C4—416no—
932C4⋊C4—416no—
933C4⋊C4—48no—
934C4⋊C4—48no—
935C22⋊C4—232no—
936C22⋊C4—232no—
937C22⋊C4—232no—
938C22⋊C4—232no—
939C22⋊C4—416no—
940C22⋊C4—416no—
941C22⋊C4—416no—
942C22⋊C4—416no—
943C22⋊C4—416no—
944C42—24no—
945C42—28no—
946C42—28no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—24no—
951C42—28no—
952C42—28no—
953C42—232no—
954C42—28no—
955C42—28no—
956C42—24no—
957C42—232no—
958C42—216no—
959C42—24no—
960C42—24no—
961C42—28no—
962C42—28no—
963C42—28no—
964C42—28no—
965C42—28no—
966C42—28no—
967C42—28no—
968C42—44no—
969C42—44no—
970C42—44no—
971C42—44no—
972C42—44no—
973C42—44no—
974C42—44no—
975C42—44no—
976C42—44no—
977C42—44no—
978C42C4×#4118yes—
979C42#51818yes—
980C42C22×M16116yes—
981C42C22×#4118yes—
982C42C2×H(5,𝔽2)18yes—
983C23—232no—
984C23—28no—
985C23—28no—
986C23—232no—
987C23—22no—
988C23—28no—
989C23—28no—
990C23—22no—
991C23—22no—
992C23—28no—
993C23—232no—
994C23—28no—
995C23—28no—
996C23—22no—
997C23—22no—
998C23—28no—
999C23—28no—
1000C23—22no—
1001C23—416no—
1002C23—44no—
1003C23—44no—
1004C23—416no—
1005C23—44no—
1006C23—416no—
1007C23—44no—
1008C23—416no—
1009C23C2×C4×#4112yes—
1010C23C2×#51812yes—
1011C23#342812yes—
1012C23C23×M16116yes—
1013C23C23×M1612yes—
1014C23C2×#56814yes—
1015C23C2×#56812yes—
1016C23C2×#56812yes—
1017C23C2×#56812yes—
1018C23C25×C411yescharacteristic
1019Q8—432no—
1020D4—264no—
1021D4—432no—
1022D4—432no—
1023D4—464no—
1024C2×C4—232no—
1025C2×C4—232no—
1026C2×C4—28no—
1027C2×C4—28no—
1028C2×C4—28no—
1029C2×C4—28no—
1030C2×C4—28no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—28no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—28no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—28no—
1056C2×C4—28no—
1057C2×C4—28no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—28no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—28no—
1064C2×C4—28no—
1065C2×C4—28no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—28no—
1071C2×C4—464no—
1072C2×C4—416no—
1073C2×C4—416no—
1074C2×C4—416no—
1075C2×C4—44no—
1076C2×C4—416no—
1077C2×C4—44no—
1078C2×C4—416no—
1079C2×C4—44no—
1080C2×C4—416no—
1081C2×C4—44no—
1082C2×C4—44no—
1083C2×C4—44no—
1084C2×C4—48no—
1085C2×C4—432no—
1086C2×C4—416no—
1087C2×C4—416no—
1088C2×C4—48no—
1089C2×C4—416no—
1090C2×C4—832no—
1091C2×C4#2970116yes—
1092C2×C4C2×C4×#4114yes—
1093C2×C4C2×C4×#4112yes—
1094C2×C4C2×C4×#4114yes—
1095C2×C4C2×#51814yes—
1096C2×C4C2×#51814yes—
1097C2×C4C2×#51812yes—
1098C2×C4#342812yes—
1099C2×C4#3460116yes—
1100C2×C4C23×M1614yes—
1101C2×C4C23×M1614yes—
1102C2×C4C23×M1614yes—
1103C2×C4C2×#56814yes—
1104C2×C4C2×#56814yes—
1105C2×C4C23×#4112yes—
1106C2×C4C22×H(5,𝔽2)12yes—
1107C2×C4C2×#58512yes—
1108C8—216no—
1109C8—48no—
1110C8—416no—
1111C22—216no—
1112C22—24no—
1113C22—216no—
1114C22—24no—
1115C22—24no—
1116C22—216no—
1117C22—42no—
1118C22—48no—
1119C22—48no—
1120C22—42no—
1121C22—42no—
1122C22—48no—
1123C22—42no—
1124C22—48no—
1125C22—464no—
1126C22—416no—
1127C22#3408614yes—
1128C22C2×#297014yes—
1129C22#6020714yes—
1130C22#6023014yes—
1131C22#6023214yes—
1132C22#6028214yes—
1133C22#6028514yes—
1134C22C22×C4×#4111yescharacteristic
1135C22C22×#51811yescharacteristic
1136C22C2×#342811yescharacteristic
1137C22C24×M1611yescharacteristic
1138C22C22×#56811yescharacteristic
1139C22C22×#56811yescharacteristic
1140C22C22×#56811yescharacteristic
1141C4—24no—
1142C4—24no—
1143C4—24no—
1144C4—24no—
1145C4—24no—
1146C4—24no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—48no—
1152C4—42no—
1153C4—48no—
1154C4—42no—
1155C4—48no—
1156C4#3408614yes—
1157C4C2×#297018yes—
1158C4C2×#346014yes—
1159C2—416no—
1160C2—44no—
1161C2#637743718yesdirect product factor
1162C2C2×#3408611yescharacteristic
1163C2C22×#297011yescharacteristic
1164C2C2×#6020711yescharacteristic
1165C2C2×#6023011yescharacteristic
1166C2C2×#6023211yescharacteristic
1167C2C2×#6028211yescharacteristic
1168C2C2×#6028511yescharacteristic
subgroupG/H
centerC23×C4C25
commutatorC23C25×C4
Frattini, cosocleC22×C4C26
socleC24C24×C4
prime radicalC22×#532C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #6377437C2direct (N × H)
3. C2×#22395C2semidirect
4. C2×#22339C2semidirect
5. C2×#22311C2semidirect
6. C2×#22260C2semidirect
7. C2×#22135C2semidirect
8. C2×#21379C2semidirect
9. C2×#21270C2semidirect
10. C2×#21107C2semidirect
11. C2×#20778C2semidirect
12. C2×D4×#97C2semidirect
13. C2×#20463C2semidirect
39. #22395C22semidirect
40. #22339C22semidirect
41. #22311C22semidirect
42. #22260C22semidirect
43. #22135C22semidirect
44. #21379C22semidirect
46. #21270C22semidirect
50. #21107C22semidirect
58. #20778C22semidirect
63. D4×#97C22semidirect
64. #20463C22semidirect
419. C2×C4×C8#41semidirect
750. C4×C8C2×#41semidirect
1161. C2#6377437direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#5322
#63774372
C2×#223952
C2×#223392
C2×#223112
C2×#222602
C2×#221352
C2×#213792
C2×#212702
C2×#211072
C2×#207782
C2×D4×#972
C2×#204632