Finite Group Databasebeta

← #11904793

Subgroups — #11904793

Order 1152.

3209 conjugacy classes of subgroups.

The subgroup lattice has 1023 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64316C211yesmaximal, characteristic, complemented
2C2×#64306C211yesmaximal, characteristic, complemented
3#10596098C211yesmaximal, characteristic, complemented
4C3×#5628C212yesmaximal, complemented
5D3×#946C212yesmaximal, complemented
6#10595404C211yesmaximal, characteristic, complemented
7#10594925C211yesmaximal, characteristic, complemented
8#10594894C212yesmaximal, complemented
9#10594627C212yesmaximal, complemented
10#10594616C212yesmaximal, complemented
11#10594529C211yesmaximal, characteristic, complemented
12#10594511C211yesmaximal, characteristic, complemented
13#10594379C212yesmaximal, complemented
14#10594372C214yesmaximal, complemented
15#10594282C214yesmaximal, complemented
16#10594191C212yesmaximal, complemented
17#10594185C212yesmaximal, complemented
18#86356—32nomaximal
19C2×#3832C2211yescharacteristic, complemented
20C22×C4×C3⋊D3C2211yescharacteristic
21C2×C3×D3×Q8C2212yescomplemented
22C2×C3×#235C2212yes—
23C2×#3811C2212yes—
24C2×#3805C2211yescharacteristic
25C2×#3805C2211yescharacteristic
26#64316—28no—
27#64306—28no—
28C2×#3802C2211yescharacteristic
29C2×C4×D32C2212yes—
30C2×#3799C2212yescomplemented
31C2×#3799C2214yescomplemented
32C2×#3798C2211yescharacteristic
33C2×#3798C2211yescharacteristic
34C2×#3798C2212yescomplemented
35C2×#3797C2211yescharacteristic
36C2×#3797C2212yescomplemented
37C2×#3797C2211yescharacteristic, complemented
38C2×#3796C2212yes—
39C32×C22⋊Q8C2211yescharacteristic, complemented
40#64155C2211yescharacteristic
41#64139C2211yescharacteristic, complemented
42#64104C2211yescharacteristic
43#64103C2212yescomplemented
44#64102C2212yes—
45#64101C2211yescharacteristic, complemented
46#64091C2212yes—
47#64090C2212yescomplemented
48C3×#946C2212yescomplemented
49C3×#924C2212yescomplemented
50C3×#897C2212yescomplemented
51C3×#894C2214yescomplemented
52C3×#892C2212yescomplemented
53C3×#888C2214yescomplemented
54C3×#885C2214yescomplemented
55C3×#883C2214yescomplemented
56#63982C2212yescomplemented
57#63974C2212yes—
58#63971C2214yescomplemented
59#63958C2214yescomplemented
60#63923C2214yes—
61D3×(C2×D3)⋊C4C2214yes—
62#63919C2212yescomplemented
63C4×#627C2212yescomplemented
64#63915C2212yescomplemented
65#63912C2212yescomplemented
66#63910C2214yescomplemented
67#63909C2212yescomplemented
68#63902C2212yescomplemented
69#63900C2211yescharacteristic, complemented
70#63894C2214yes—
71#63890C2214yescomplemented
72D3×C4⋊Dic3C2212yescomplemented
73#63888C2214yes—
74#63888C2214yescomplemented
75#63887C2214yescomplemented
76#63886C2214yescomplemented
77#63883C2212yescomplemented
78#63880C2214yescomplemented
79#63880C2214yescomplemented
80D3×Dic3⋊C4C2214yescomplemented
81#63871C2212yes—
82#63865C2212yes—
83#63865C2212yescomplemented
84#63856C2212yescomplemented
85#63854C2214yescomplemented
86C2×D3×#41—32no—
87C2×#1007—32no—
88C3×#536—32no—
89#5833—32no—
90C2×#946—32no—
91#5727—34no—
92#5726—34no—
93#5677—34no—
94#5676—34no—
95#5655—34no—
96#5655—34no—
97#5654—34no—
98#5654—34no—
99#5629—32no—
100#5629—32no—
101#5628—32no—
102#5628D312yescomplemented
103#5627—32no—
104#5627—32no—
105#5627—61no—
106D3×C22⋊Q8—32no—
107D3×C22⋊Q8—32no—
108#5524—32no—
109#5523—32no—
110C23×C3⋊D3C2311yescharacteristic
111C22×D32C2312yes—
112C2×C32×Q8C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C2×#638C2312yes—
115C22×C3⋊Dic3C2311yescharacteristic
116#3832—24no—
117C2×C4⋊(C3⋊D3)C2312yes—
118C2×C4⋊(C3⋊D3)C2311yescharacteristic
119C2×C4⋊(C3⋊D3)C2312yes—
120C2×C4×C3⋊D3—24no—
121C2×C4×C3⋊D3C2311yescharacteristic
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2312yes—
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×C4×C3⋊D3C2311yescharacteristic
126C2×C3×#67C2312yes—
127C2×C3×#67C2312yes—
128C3×D3×Q8—28no—
129C3×#235—28no—
130C2×C3×D12C2312yes—
131C2×C3×C4×D3C2314yes—
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2312yes—
134C2×C3×Dic6C2314yes—
135C2×C3×Dic6C2312yes—
136C2×C3×Dic6C2312yes—
137#3811—28no—
138C2×#627C2311yescharacteristic
139C2×#627C2312yes—
140C2×#627C2311yescharacteristic
141C2×#626C2312yes—
142C2×#626C2314yes—
143C2×#626C2314yes—
144C2×#626C2312yes—
145C2×#625C2311yescharacteristic
146C2×#625C2311yescharacteristic
147C2×#624C2312yes—
148C2×#624C2312yes—
149C2×#624C2314yes—
150C2×#624C2312yes—
151#3805—24no—
152#3805—24no—
153C2×D3×Dic3C2312yes—
154C2×D3×Dic3C2312yes—
155C2×D3×Dic3C2314yes—
156#3802—24no—
157C4×D32—28no—
158#3799—28no—
159#3799—216no—
160#3798—24no—
161#3798—28no—
162#3798D418yescomplemented
163#3797—24no—
164#3797—24no—
165#3797—28no—
166#3796—28no—
167C32×C4⋊C4C2312yes—
168C32×C4⋊C4C2311yescharacteristic
169C32×C22⋊C4C2312yes—
170#3752C2312yes—
171#3752C2312yes—
172#3752C2312yes—
173#3752C2312yes—
174C4⋊(C3⋊Dic3)C2311yescharacteristic
175#3750C2312yes—
176C4×C3⋊Dic3C2312yes—
177C3×#217C2314yes—
178C3×(C2×D3)⋊C4C2314yes—
179C3×(C2×D3)⋊C4C2314yes—
180C3×(C2×D3)⋊C4C2314yes—
181C3×C4⋊Dic3C2314yes—
182C3×C4⋊Dic3C2312yes—
183C3×Dic3⋊C4C2314yes—
184C3×Dic3⋊C4C2314yes—
185C3×C4×Dic3C2314yes—
186#3724C2314yes—
187#3724C2312yes—
188Dic3⋊Dic3C2314yes—
189Dic3⋊Dic3C2314yes—
190#3722C2314yes—
191#3722C2314yes—
192(C2×D3)⋊Dic3C2314yes—
193#3489—91noSylow
194C2×C3×#41—32no—
195C22×C3×Q8—32no—
196D3×#41—616no—
197#1007—616no—
198C2×#239—32no—
199C2×#239—32no—
200C2×#239—34no—
201C2×#239—32no—
202C2×#239—61no—
203C2×D3×Q8—32no—
204C2×D3×Q8—34no—
205C2×D3×Q8—32no—
206C2×D3×Q8C2×D312yescomplemented
207C2×#237—32no—
208C2×#237—32no—
209C2×#237—32no—
210C2×D3×D4—32no—
211C2×D3×D4—32no—
212C2×D3×D4—32no—
213C2×#235—32no—
214C2×#235—34no—
215C2×#235—32no—
216C2×#235—34no—
217C2×#235—32no—
218C2×#235C2×D312yes—
219C22×C4×D3—32no—
220C22×C4×D3—32no—
221C22×C4×D3—32no—
222C22×C4×D3—61no—
223C3×C4⋊Q8—34no—
224C3×#124—34no—
225C3×#123—34no—
226C3×#123—34no—
227C3×C22⋊Q8—21no—
228C3×C22⋊Q8—32no—
229C3×C22⋊Q8—32no—
230C3×C22⋊Q8—32no—
231C3×C22⋊Q8C2×D312yescomplemented
232C3×#117—32no—
233#946—32no—
234#946—32no—
235#946—34no—
236#946—32no—
237#946—34no—
238#946—34no—
239#946—61no—
240#946C2×D312yescomplemented
241#939—34no—
242#939—34no—
243#938—34no—
244#930—32no—
245#930—32no—
246#930—61no—
247C2×(C2×D3)⋊C4—34no—
248C2×C4⋊Dic3—32no—
249#924—32no—
250#924C2×D312yescomplemented
251C2×Dic3⋊C4—34no—
252#897—32no—
253#897C2×D312yescomplemented
254#896—34no—
255#896—34no—
256#896—34no—
257#896—34no—
258#895—34no—
259#895—32no—
260#895—32no—
261#895—34no—
262#895—61no—
263#894—34no—
264#894—34no—
265#894—34no—
266#894—62no—
267#894C2×D314yescomplemented
268#893—34no—
269#893—34no—
270#893—62no—
271#892—32no—
272#892—61no—
273#892C2×D312yescomplemented
274D3×C4⋊C4—34no—
275D3×C4⋊C4—32no—
276D3×C4⋊C4—32no—
277D3×C4⋊C4—34no—
278#888—34no—
279#888C2×D314yescomplemented
280#886—34no—
281#885—34no—
282#885C2×D314yescomplemented
283#884—34no—
284#884—34no—
285#884—34no—
286#884—34no—
287#883—34no—
288#883C2×D314yescomplemented
289#882—34no—
290#882—34no—
291#882—34no—
292#882—62no—
293#67⋊C4—34no—
294#67⋊C4—34no—
295#67⋊C4—34no—
296#67⋊C4—34no—
297#67⋊C4—62no—
298D3×C22⋊C4—34no—
299D3×C22⋊C4—34no—
300#878—34no—
301#878—34no—
302C4×D12—34no—
303C4×D12—34no—
304C4×D12—34no—
305C4×Dic6—34no—
306C23×C32C2411yescharacteristic
307C22×C3⋊D3—22no—
308C22×C3⋊D3—22no—
309C22×C3⋊D3—41no—
310C22×C3⋊D3C2412yes—
311C22×C3⋊D3C2411yescharacteristic
312C22×C3⋊D3C2411yescharacteristic
313C22×C3×D3C2412yes—
314C22×C3×D3C2412yes—
315C2×D32—24no—
316C2×D32—24no—
317C2×D32—42no—
318C32×Q8—22no—
319C2×C32×C4—22no—
320C2×C32×C4C2412yes—
321C2×C32×C4C2411yescharacteristic
322C2×C32×C4C2412yes—
323C2×C32×C4C2411yescharacteristic
324#638—42no—
325C2×C3⋊Dic3—22no—
326C2×C3⋊Dic3C2412yes—
327C2×C3⋊Dic3C2411yescharacteristic
328C2×C3⋊Dic3C2411yescharacteristic
329C4⋊(C3⋊D3)—24no—
330C4⋊(C3⋊D3)—24no—
331C4⋊(C3⋊D3)—22no—
332C4×C3⋊D3—22no—
333C4×C3⋊D3—22no—
334C4×C3⋊D3—24no—
335C4×C3⋊D3—22no—
336C4×C3⋊D3C2×D414yes—
337C3×#67—24no—
338C3×#67—24no—
339C2×C3×Dic3C2414yes—
340C2×C3×Dic3C2414yes—
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C3×D12—24no—
344C3×C4×D3—28no—
345C3×C4×D3—24no—
346C3×C4×D3C2×D418yes—
347C3×Dic6—24no—
348C3×Dic6—24no—
349C3×Dic6—28no—
350#627—24no—
351#627—22no—
352#627C2×D414yes—
353#626—24no—
354#626—28no—
355#626—44no—
356#626C2×D418yes—
357#625—22no—
358#625C2×D414yes—
359#624—24no—
360#624—28no—
361#624—24no—
362#624—42no—
363D3×Dic3—24no—
364D3×Dic3—24no—
365D3×Dic3—44no—
366C2×2−1+4—91no—
367C22×#41—91no—
368D4×Q8—92no—
369#548—92no—
370#547—92no—
371#547—94no—
372#546—92no—
373#546—94no—
374#537—91no—
375#537—92no—
376#536—32no—
377#536—91no—
378#525—92no—
379#525—91no—
380C2×C22⋊Q8—91no—
381C2×C22⋊Q8—92no—
382#520—91no—
383C23×D3—32no—
384C23×D3—32no—
385C23×D3—32no—
386C23×D3—61no—
387C3×#41—68no—
388C2×C3×Q8—21no—
389C2×C3×Q8—32no—
390C2×C3×Q8—34no—
391C2×C3×Q8—32no—
392C2×C3×Q8—68no—
393C2×C3×Q8C22×D312yes—
394C2×C3×D4—32no—
395C2×C3×D4—32no—
396C2×C3×D4—32no—
397C22×C3×C4—21no—
398C22×C3×C4—32no—
399C22×C3×C4—34no—
400C22×C3×C4—32no—
401C22×C3×C4C22×D312yes—
402C2×#67—32no—
403C2×#67—32no—
404C2×#67—34no—
405C2×#67—32no—
406C2×#67—34no—
407C2×#67—32no—
408C2×#67—34no—
409C2×#67—62no—
410C2×#67C22×D312yes—
411C2×#67C22×D312yes—
412C22×Dic3—32no—
413C22×Dic3—32no—
414C22×Dic3—32no—
415C22×Dic3—34no—
416C22×Dic3—61no—
417#239—616no—
418#239—68no—
419#239—68no—
420#239—68no—
421#239—124no—
422D3×Q8—28no—
423D3×Q8—616no—
424D3×Q8—68no—
425D3×Q8—68no—
426#237—68no—
427#237—68no—
428#237—68no—
429D3×D4—68no—
430D3×D4—68no—
431D3×D4—68no—
432#235—28no—
433#235—316no—
434#235—616no—
435#235—68no—
436#235—68no—
437#235—616no—
438C2×D12—32no—
439C2×D12—34no—
440C2×D12—32no—
441C2×D12—34no—
442C2×D12—34no—
443C2×D12—32no—
444C2×D12—34no—
445C2×D12—62no—
446C2×D12—62no—
447C2×D12—61no—
448C2×D12C22×D312yes—
449C2×C4×D3—32no—
450C2×C4×D3—32no—
451C2×C4×D3—32no—
452C2×C4×D3—34no—
453C2×C4×D3—32no—
454C2×C4×D3—32no—
455C2×C4×D3—32no—
456C2×C4×D3—34no—
457C2×C4×D3—32no—
458C2×C4×D3—34no—
459C2×C4×D3—34no—
460C2×C4×D3—32no—
461C2×C4×D3—34no—
462C2×C4×D3—34no—
463C2×C4×D3—61no—
464C2×C4×D3—62no—
465C2×C4×D3—61no—
466C2×C4×D3—61no—
467C2×C4×D3—61no—
468C2×C4×D3—68no—
469C2×C4×D3—68no—
470C2×C4×D3—68no—
471C2×C4×D3—124no—
472C2×C4×D3C22×D314yes—
473C2×C4×D3C22×D312yes—
474C2×C4×D3C22×D312yes—
475C2×Dic6—32no—
476C2×Dic6—34no—
477C2×Dic6—32no—
478C2×Dic6C22×D314yes—
479C2×Dic6C22×D312yes—
480C2×Dic6C22×D312yes—
481C3×C4⋊C4—21no—
482C3×C4⋊C4—22no—
483C3×C4⋊C4—34no—
484C3×C4⋊C4—32no—
485C3×C4⋊C4—34no—
486C3×C4⋊C4—34no—
487C3×C4⋊C4C22×D314yes—
488C3×C4⋊C4C22×D312yes—
489C3×C22⋊C4—22no—
490C3×C22⋊C4—34no—
491C3×C22⋊C4—34no—
492C3×C22⋊C4—34no—
493C3×C22⋊C4—34no—
494C3×C22⋊C4C22×D314yes—
495C3×C42—34no—
496#217—34no—
497#217C22×D314yes—
498(C2×D3)⋊C4—34no—
499(C2×D3)⋊C4—34no—
500(C2×D3)⋊C4—34no—
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—34no—
504(C2×D3)⋊C4—34no—
505(C2×D3)⋊C4—34no—
506(C2×D3)⋊C4—34no—
507(C2×D3)⋊C4—62no—
508(C2×D3)⋊C4—62no—
509(C2×D3)⋊C4—62no—
510(C2×D3)⋊C4—62no—
511(C2×D3)⋊C4C22×D314yes—
512(C2×D3)⋊C4C22×D314yes—
513(C2×D3)⋊C4C22×D314yes—
514C4⋊Dic3—32no—
515C4⋊Dic3—34no—
516C4⋊Dic3—34no—
517C4⋊Dic3—61no—
518C4⋊Dic3C22×D314yes—
519C4⋊Dic3C22×D312yes—
520Dic3⋊C4—34no—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—34no—
526Dic3⋊C4—62no—
527Dic3⋊C4C22×D314yes—
528Dic3⋊C4C22×D314yes—
529C4×Dic3—34no—
530C4×Dic3—62no—
531C4×Dic3C22×D314yes—
532C22×C32—21no—
533C22×C32—21no—
534C22×C32—21no—
535C22×C32C2511yescharacteristic
536C2×C3⋊D3—21no—
537C2×C3⋊D3—21no—
538C2×C3⋊D3—21no—
539C2×C3⋊D3—21no—
540C2×C3⋊D3—22no—
541C2×C3⋊D3—22no—
542C2×C3⋊D3—22no—
543C2×C3⋊D3—44no—
544C2×C3⋊D3C22×D412yes—
545C2×C3⋊D32−1+412yescomplemented
546C2×C3×D3—22no—
547C2×C3×D3—22no—
548C2×C3×D3—22no—
549C2×C3×D3—22no—
550C2×C3×D3—22no—
551C2×C3×D3C22×D414yes—
552D32—48no—
553C32×C4—22no—
554C32×C4—21no—
555C32×C4—22no—
556C32×C4C22×D412yes—
557C3⋊Dic3—21no—
558C3⋊Dic3—22no—
559C3⋊Dic3C22×D412yes—
560C3×Dic3—22no—
561C3×Dic3—24no—
562C3×Dic3—24no—
563C3×Dic3C22×D414yes—
5642−1+4—188no—
565C2×#41—32no—
566C2×#41—91no—
567C2×#41—91no—
568C2×#41—92no—
569C2×#41—92no—
570C2×#41—94no—
571C2×#41—91no—
572C2×#41—91no—
573C2×#41—92no—
574C2×#41—91no—
575C2×#41—188no—
576C22×Q8—32no—
577C22×Q8—91no—
578C22×Q8—92no—
579C22×Q8—91no—
580C22×D4—92no—
581C22×D4—91no—
582C23×C4—92no—
583C23×C4—91no—
584C4⋊Q8—34no—
585C4⋊Q8—92no—
586#124—34no—
587#124—92no—
588#123—34no—
589#123—34no—
590#123—94no—
591#123—94no—
592#123—92no—
593C22⋊Q8—32no—
594C22⋊Q8—32no—
595C22⋊Q8—32no—
596C22⋊Q8—92no—
597C22⋊Q8—94no—
598C22⋊Q8—92no—
599C22⋊Q8—92no—
600C22⋊Q8—92no—
601C22⋊Q8—94no—
602C22⋊Q8—94no—
603C22⋊Q8—92no—
604C22⋊Q8—91no—
605C22⋊Q8D3211yescharacteristic, complemented
606#121—92no—
607#121—94no—
608#121—94no—
609#121—94no—
610#121—92no—
611#121—94no—
612#121—91no—
613#121—91no—
614#120—94no—
615#120—92no—
616C4×Q8—92no—
617C4×D4—94no—
618C4×D4—94no—
619C4×D4—94no—
620C4×D4—92no—
621C4×D4—92no—
622C4×D4—92no—
623#117—32no—
624#117—91no—
625C2×C4⋊C4—91no—
626C2×C4⋊C4—92no—
627C2×C4⋊C4—92no—
628C2×C4⋊C4—94no—
629C2×C22⋊C4—92no—
630C2×C22⋊C4—94no—
631C23×C3—21no—
632C23×C3—32no—
633C23×C3—32no—
634C23×C3C23×D312yes—
635C22×D3—32no—
636C22×D3—32no—
637C22×D3—34no—
638C22×D3—61no—
639C22×D3—61no—
640C22×D3—62no—
641C22×D3—64no—
642C22×D3—64no—
643C22×D3—64no—
644C22×D3—64no—
645C22×D3—64no—
646C22×D3—64no—
647C22×D3—122no—
648C22×D3—122no—
649C22×D3—122no—
650C22×D3—122no—
651C22×D3—122no—
652C22×D3—122no—
653C22×D3C23×D312yes—
654C22×D3C23×D312yes—
655C3×Q8—24no—
656C3×Q8—42no—
657C3×Q8—68no—
658C3×Q8—64no—
659C3×Q8—64no—
660C3×D4—64no—
661C3×D4—64no—
662C3×D4—64no—
663C2×C3×C4—24no—
664C2×C3×C4—21no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—21no—
668C2×C3×C4—32no—
669C2×C3×C4—38no—
670C2×C3×C4—34no—
671C2×C3×C4—34no—
672C2×C3×C4—32no—
673C2×C3×C4—42no—
674C2×C3×C4—68no—
675C2×C3×C4—64no—
676C2×C3×C4C23×D314yes—
677C2×C3×C4C23×D314yes—
678C2×C3×C4C23×D312yes—
679C2×C3×C4C23×D312yes—
680#67—24no—
681#67—24no—
682#67—38no—
683#67—38no—
684#67—64no—
685#67—68no—
686#67—64no—
687#67—124no—
688#67—124no—
689#67—124no—
690C2×Dic3—32no—
691C2×Dic3—34no—
692C2×Dic3—32no—
693C2×Dic3—61no—
694C2×Dic3—62no—
695C2×Dic3—61no—
696C2×Dic3—64no—
697C2×Dic3—64no—
698C2×Dic3—64no—
699C2×Dic3—122no—
700C2×Dic3—124no—
701C2×Dic3C23×D314yes—
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D314yes—
704C2×Dic3C23×D312yes—
705D12—24no—
706D12—38no—
707D12—68no—
708D12—68no—
709D12—64no—
710D12—68no—
711D12—64no—
712D12—122no—
713D12—124no—
714D12—124no—
715D12—124no—
716C4×D3—28no—
717C4×D3—24no—
718C4×D3—38no—
719C4×D3—64no—
720C4×D3—64no—
721C4×D3—68no—
722C4×D3—68no—
723C4×D3—64no—
724C4×D3—68no—
725C4×D3—64no—
726C4×D3—64no—
727C4×D3—64no—
728C4×D3—64no—
729C4×D3—64no—
730C4×D3—68no—
731C4×D3—122no—
732C4×D3—124no—
733C4×D3—122no—
734C4×D3—122no—
735C4×D3—124no—
736C4×D3—124no—
737C4×D3D3×D418yes—
738Dic6—24no—
739Dic6—24no—
740Dic6—28no—
741Dic6—38no—
742Dic6—64no—
743Dic6—68no—
744C2×C32—41no—
745C2×C32C23×D411yescharacteristic
746C2×C32C2×2−1+411yescharacteristic
747C2×C32#58511yescharacteristic
748C3⋊D3—22no—
749C3⋊D3—22no—
750C3⋊D3—42no—
751C3×D3—24no—
752C3×D3—42no—
753C24—92no—
754C24—91no—
755#41—68no—
756#41—98no—
757#41—188no—
758#41—184no—
759#41—188no—
760#41—1816no—
761#41—184no—
762#41—184no—
763#41—184no—
764#41—188no—
765C2×Q8—32no—
766C2×Q8—34no—
767C2×Q8—32no—
768C2×Q8—68no—
769C2×Q8—91no—
770C2×Q8—92no—
771C2×Q8—91no—
772C2×Q8—184no—
773C2×Q8—184no—
774C2×Q8—188no—
775C2×Q8C2×D3211yescharacteristic
776C2×D4—32no—
777C2×D4—32no—
778C2×D4—32no—
779C2×D4—92no—
780C2×D4—94no—
781C2×D4—92no—
782C2×D4—94no—
783C2×D4—91no—
784C2×D4—91no—
785C2×D4—92no—
786C2×D4—92no—
787C2×D4—92no—
788C2×D4—91no—
789C2×D4—184no—
790C2×D4—188no—
791C22×C4—32no—
792C22×C4—34no—
793C22×C4—32no—
794C22×C4—92no—
795C22×C4—94no—
796C22×C4—92no—
797C22×C4—92no—
798C22×C4—92no—
799C22×C4—92no—
800C22×C4—94no—
801C22×C4—91no—
802C22×C4—91no—
803C22×C4—91no—
804C22×C4—92no—
805C22×C4—91no—
806C22×C4—91no—
807C22×C4—184no—
808C22×C4—188no—
809C22×C4C2×D3211yescharacteristic
810C4⋊C4—32no—
811C4⋊C4—34no—
812C4⋊C4—34no—
813C4⋊C4—34no—
814C4⋊C4—94no—
815C4⋊C4—92no—
816C4⋊C4—94no—
817C4⋊C4—94no—
818C4⋊C4—91no—
819C4⋊C4—92no—
820C4⋊C4C2×D3211yescharacteristic
821C4⋊C4C2×D3212yes—
822C22⋊C4—34no—
823C22⋊C4—34no—
824C22⋊C4—34no—
825C22⋊C4—34no—
826C22⋊C4—94no—
827C22⋊C4—94no—
828C22⋊C4—94no—
829C22⋊C4—92no—
830C22⋊C4—92no—
831C22⋊C4—92no—
832C22⋊C4—92no—
833C22⋊C4C2×D3212yes—
834C42—34no—
835C42—92no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—21no—
841C22×C3—34no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—62no—
847C22×C3—62no—
848C22×C3—62no—
849C22×C3C24×D312yes—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—22no—
853C2×D3—22no—
854C2×D3—22no—
855C2×D3—34no—
856C2×D3—34no—
857C2×D3—62no—
858C2×D3—62no—
859C2×D3—62no—
860C2×D3—62no—
861C2×D3—62no—
862C2×D3—62no—
863C2×D3—64no—
864C2×D3—64no—
865C2×D3—64no—
866C2×D3—121no—
867C2×D3—121no—
868C2×D3—121no—
869C2×D3—121no—
870C2×D3—122no—
871C2×D3—122no—
872C2×D3—122no—
873C2×D3—128no—
874C2×D3—128no—
875C2×D3—128no—
876C2×D3—128no—
877C2×D3C2×D3×D414yes—
878C3×C4—24no—
879C3×C4—22no—
880C3×C4—24no—
881C3×C4—22no—
882C3×C4—34no—
883C3×C4—41no—
884C3×C4—42no—
885C3×C4—42no—
886C3×C4—62no—
887C3×C4—64no—
888C3×C4—64no—
889C3×C4C2×D3×D414yes—
890Dic3—24no—
891Dic3—22no—
892Dic3—24no—
893Dic3—34no—
894Dic3—62no—
895Dic3—62no—
896Dic3—64no—
897Dic3—121no—
898Dic3—122no—
899Dic3C2×D3×D414yes—
900C32#348911yescharacteristic, complemented, Sylow
901C23—32no—
902C23—32no—
903C23—91no—
904C23—91no—
905C23—92no—
906C23—182no—
907C23—182no—
908C23—184no—
909C23—184no—
910C23—361no—
911C23—362no—
912C23C22×D3211yescharacteristic
913Q8—22no—
914Q8—68no—
915Q8—64no—
916Q8—64no—
917Q8—94no—
918Q8—184no—
919Q8—182no—
920D4—64no—
921D4—64no—
922D4—64no—
923D4—98no—
924D4—94no—
925D4—184no—
926D4—184no—
927D4—188no—
928D4—184no—
929D4—182no—
930D4—182no—
931D4—364no—
932D4—362no—
933C2×C4—22no—
934C2×C4—32no—
935C2×C4—38no—
936C2×C4—34no—
937C2×C4—34no—
938C2×C4—32no—
939C2×C4—68no—
940C2×C4—64no—
941C2×C4—91no—
942C2×C4—94no—
943C2×C4—92no—
944C2×C4—91no—
945C2×C4—182no—
946C2×C4—184no—
947C2×C4—182no—
948C2×C4—184no—
949C2×C4—188no—
950C2×C4—184no—
951C2×C4—184no—
952C2×C4—184no—
953C2×C4—182no—
954C2×C4—182no—
955C2×C4—362no—
956C2×C4—364no—
957C2×C4C22×D3212yes—
958C2×C4C22×D3212yes—
959C2×C4C22×D3211yescharacteristic
960C2×C4C22×D3211yescharacteristic
961C2×C3—21no—
962C2×C3—21no—
963C2×C3—21no—
964C2×C3—42no—
965C2×C3—42no—
966C2×C3—64no—
967C2×C3—122no—
968C2×C3C22×D3×D412yes—
969C2×C3D3×2−1+412yes—
970C2×C3#596812yes—
971D3—24no—
972D3—42no—
973D3—64no—
974D3—64no—
975D3—122no—
976D3—122no—
977D3—124no—
978D3—242no—
979C22—21no—
980C22—21no—
981C22—21no—
982C22—34no—
983C22—62no—
984C22—62no—
985C22—62no—
986C22—62no—
987C22—62no—
988C22—92no—
989C22—92no—
990C22—181no—
991C22—181no—
992C22—181no—
993C22—181no—
994C22—182no—
995C22—182no—
996C22—182no—
997C22—364no—
998C22—368no—
999C22C23×D3211yescharacteristic
1000C4—21no—
1001C4—22no—
1002C4—22no—
1003C4—34no—
1004C4—62no—
1005C4—64no—
1006C4—64no—
1007C4—92no—
1008C4—181no—
1009C4—182no—
1010C4D32×D412yes—
1011C3—21no—
1012C3#8635612yescomplemented
1013C2—41no—
1014C2—64no—
1015C2—122no—
1016C2—182no—
1017C2—182no—
1018C2—362no—
1019C2C2×D32×D411yescharacteristic
1020C2#1059668911yescharacteristic
1021C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C22⋊Q8C22
hypercenterC22⋊Q8D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64316C2semidirect
2. C2×#64306C2semidirect
3. #10596098C2semidirect
4. C3×#5628C2semidirect
5. D3×#946C2semidirect
6. #10595404C2semidirect
7. #10594925C2semidirect
8. #10594894C2semidirect
9. #10594627C2semidirect
10. #10594616C2semidirect
11. #10594529C2semidirect
12. #10594511C2semidirect
13. #10594379C2semidirect
14. #10594372C2semidirect
15. #10594282C2semidirect
16. #10594191C2semidirect
17. #10594185C2semidirect
19. C2×#3832C22semidirect
21. C2×C3×D3×Q8C22semidirect
30. C2×#3799C22semidirect
31. C2×#3799C22semidirect
34. C2×#3798C22semidirect
36. C2×#3797C22semidirect
37. C2×#3797C22semidirect
39. C32×C22⋊Q8C22semidirect
41. #64139C22semidirect
43. #64103C22semidirect
45. #64101C22semidirect
47. #64090C22semidirect
48. C3×#946C22semidirect
49. C3×#924C22semidirect
50. C3×#897C22semidirect
51. C3×#894C22semidirect
52. C3×#892C22semidirect
53. C3×#888C22semidirect
54. C3×#885C22semidirect
55. C3×#883C22semidirect
56. #63982C22semidirect
58. #63971C22semidirect
59. #63958C22semidirect
62. #63919C22semidirect
63. C4×#627C22semidirect
64. #63915C22semidirect
65. #63912C22semidirect
66. #63910C22semidirect
67. #63909C22semidirect
68. #63902C22semidirect
69. #63900C22semidirect
71. #63890C22semidirect
72. D3×C4⋊Dic3C22semidirect
74. #63888C22semidirect
75. #63887C22semidirect
76. #63886C22semidirect
77. #63883C22semidirect
78. #63880C22semidirect
79. #63880C22semidirect
80. D3×Dic3⋊C4C22semidirect
83. #63865C22semidirect
84. #63856C22semidirect
85. #63854C22semidirect
102. #5628D3semidirect
162. #3798D4semidirect
206. C2×D3×Q8C2×D3semidirect
231. C3×C22⋊Q8C2×D3semidirect
240. #946C2×D3semidirect
250. #924C2×D3semidirect
253. #897C2×D3semidirect
267. #894C2×D3semidirect
273. #892C2×D3semidirect
279. #888C2×D3semidirect
282. #885C2×D3semidirect
288. #883C2×D3semidirect
545. C2×C3⋊D32−1+4semidirect
605. C22⋊Q8D32semidirect
900. C32#3489semidirect
1012. C3#86356semidirect

Maximal subgroups

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

subgroupindex
C2×#643162
C2×#643062
#105960982
C3×#56282
D3×#9462
#105954042
#105949252
#105948942
#105946272
#105946162
#105945292
#105945112
#105943792
#105943722
#105942822
#105941912
#105941852
#863563