Finite Group Databasebeta

← #11904224

Subgroups — #11904224

Order 1152.

2343 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3832C211yesmaximal, characteristic, complemented
2C3×#5584C211yesmaximal, characteristic, complemented
3C3×#5567C211yesmaximal, characteristic, complemented
4#10595368C212yesmaximal, complemented
5#10595341C212yesmaximal, complemented
6#10594565C212yesmaximal, complemented
7#10594465C214yesmaximal, complemented
8#10594462C214yesmaximal, complemented
9#10594362C212yesmaximal, complemented
10#10593947C212yesmaximal, complemented
11#10593943C212yesmaximal, complemented
12#10593903C211yesmaximal, characteristic, complemented
13#10593901C212yesmaximal, complemented
14C4×#3797C212yesmaximal, complemented
15C4×#3796C211yesmaximal, characteristic, complemented
16#10593869C211yesmaximal, characteristic, complemented
17#10593866C211yesmaximal, characteristic, complemented
18#87017—31nomaximal
19#86981—31nomaximal
20C2×#3832C2211yescharacteristic
21C2×#3799C2212yes—
22C2×#3797C2212yes—
23C2×#3796C2211yescharacteristic
24C32×C4×Q8C2211yescharacteristic
25Q8×C3⋊Dic3C2211yescharacteristic
26#64102C2211yescharacteristic
27#64102C2212yes—
28#64101C2211yescharacteristic
29#64101C2212yes—
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31C4×C4⋊(C3⋊D3)C2212yes—
32C42×C3⋊D3C2211yescharacteristic
33C42×C3⋊D3C2212yes—
34C3×#946C2212yes—
35C3×#944C2212yes—
36C3×#898C2214yes—
37C3×#892C2212yes—
38C3×#889C2214yes—
39C3×#887C2212yes—
40C3×#875C2212yes—
41C3×C4×D12C2211yescharacteristic
42C3×#870C2212yes—
43C3×#869C2211yescharacteristic
44C3×#869C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46C3×C4×Dic6C2212yes—
47C3×C4×Dic6C2212yes—
48#63918C2212yes—
49C4×#627C2214yes—
50#63916C2212yes—
51#63910C2214yes—
52C4×#626C2212yes—
53#63900C2212yes—
54#63898C2211yescharacteristic
55#63897C2214yes—
56#63895C2214yes—
57#63894C2212yes—
58#63893C2214yes—
59#63883C2214yes—
60C4×#624C2214yes—
61#63881C2214yes—
62#63881C2212yes—
63#63880C2214yes—
64#63878C2214yes—
65#63878C2212yes—
66C4×D3×Dic3C2212yes—
67#63872C2212yes—
68#63871C2212yes—
69#63871C2212yes—
70#63871C2212yes—
71#63868C2214yes—
72#63862C2214yes—
73#63856C2212yes—
74#63854C2214yes—
75#63853C2214yes—
76#63852C2214yes—
77#63849C2212yes—
78#63849C2211yescharacteristic
79#63845C2214yes—
80#63843C2212yes—
81#63843C2212yes—
82#63843C2211yescharacteristic
83#63838C2214yes—
84#63836C2214yes—
85C3×#557—31no—
86C3×#556—31no—
87#5728—32no—
88#5728—31no—
89#5728—31no—
90#5727—31no—
91#5726—32no—
92#5726—31no—
93#5708—34no—
94#5706—34no—
95#5694—34no—
96#5694—32no—
97#5691—34no—
98#5691—32no—
99#5680—32no—
100#5677—32no—
101#5631—32no—
102#5622—32no—
103#5584—32no—
104#5584D311yescharacteristic, complemented
105#5581—32no—
106#5576—32no—
107Q8×D12—31no—
108C4×#239—31no—
109C4×#239—31no—
110C4×#239—32no—
111C4×#239—31no—
112C4×#239—61no—
113C4×D3×Q8—32no—
114C4×D3×Q8—32no—
115#5567D311yescharacteristic, complemented
116#5551—31no—
117C4×#237—31no—
118#5533—32no—
119#5522—32no—
120C2×C32×Q8C2311yescharacteristic
121#3832—24no—
122C2×C4⋊(C3⋊D3)C2312yes—
123C2×C4⋊(C3⋊D3)C2311yescharacteristic
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×C4×C3⋊D3C2312yes—
126C2×C4×C3⋊D3C2312yes—
127C2×C4×C3⋊D3C2311yescharacteristic
128C2×C4×C3⋊D3C2311yescharacteristic
129C2×C4×C3⋊D3C2312yes—
130C2×C3×D12C2311yescharacteristic
131C2×C3×C4×D3C2312yes—
132C2×C3×Dic6C2312yes—
133C2×C3×Dic6C2312yes—
134C2×C3×Dic6C2311yescharacteristic
135C2×#627C2314yes—
136C2×#626C2312yes—
137C2×#626C2314yes—
138C2×#624C2314yes—
139C2×#624C2314yes—
140C2×D3×Dic3C2312yes—
141C2×D3×Dic3C2312yes—
142#3799—28no—
143#3797—28no—
144#3796—24no—
145C32×C4⋊C4C2311yescharacteristic
146C32×C4⋊C4C2312yes—
147C32×C42C2312yes—
148C32×C42C2311yescharacteristic
149#3752C2312yes—
150#3752C2312yes—
151#3752C2312yes—
152C4⋊(C3⋊Dic3)C2312yes—
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154C4×C3⋊Dic3C2311yescharacteristic
155C4×C3⋊Dic3C2312yes—
156C4×C3⋊Dic3C2311yescharacteristic
157C4×C3⋊Dic3C2312yes—
158C4×C3⋊Dic3C2311yescharacteristic
159C3×(C2×D3)⋊C4C2314yes—
160C3×(C2×D3)⋊C4C2312yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2311yescharacteristic
166C3×C4⋊Dic3C2312yes—
167C3×C4⋊Dic3C2311yescharacteristic
168C3×Dic3⋊C4C2314yes—
169C3×Dic3⋊C4C2312yes—
170C3×Dic3⋊C4C2314yes—
171C3×Dic3⋊C4C2314yes—
172C3×Dic3⋊C4C2314yes—
173C3×C4×Dic3C2314yes—
174C3×C4×Dic3C2312yes—
175C3×C4×Dic3C2314yes—
176#3724C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2314yes—
181#3722C2314yes—
182#3722C2314yes—
183#3722C2312yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2312yes—
186Dic32C2312yes—
187Dic32C2312yes—
188Dic32C2314yes—
189#3482—91noSylow
190C2×#239—31no—
191C2×#239—31no—
192C2×#239—31no—
193C2×#239—32no—
194C2×#239—61no—
195C2×D3×Q8—32no—
196C2×D3×Q8—32no—
197C2×#237—31no—
198C2×#235—32no—
199C3×C4⋊Q8—32no—
200C3×C4⋊Q8—31no—
201C3×C4⋊Q8—31no—
202C3×#126—34no—
203C3×#125—34no—
204C3×#125—32no—
205C3×#124—32no—
206C3×C22⋊Q8—32no—
207C3×C4×Q8—21no—
208C3×C4×Q8—32no—
209C3×C4×Q8—32no—
210C3×C4×Q8—32no—
211C3×C4×Q8—31no—
212C3×C4×Q8C2×D311yescharacteristic
213C3×C4×Q8C2×D311yescharacteristic
214C3×C4×D4—31no—
215C3×#117—32no—
216#946—32no—
217#946—32no—
218#946—32no—
219#946—32no—
220#946C2×D312yes—
221Q8×Dic3—31no—
222Q8×Dic3—31no—
223Q8×Dic3—32no—
224Q8×Dic3—32no—
225Q8×Dic3—31no—
226Q8×Dic3—61no—
227#944C2×D312yes—
228#938—32no—
229D4×Dic3—31no—
230C4×#67—32no—
231#924—32no—
232C2×C4×Dic3—32no—
233#898—34no—
234#898—34no—
235#898C2×D314yes—
236#897—32no—
237#897—32no—
238#897—32no—
239#897—34no—
240#897—34no—
241#896—34no—
242#895—32no—
243#895—34no—
244#894—34no—
245#894—34no—
246#894—34no—
247#894—34no—
248#893—31no—
249#893—32no—
250#893—32no—
251#893—31no—
252#893—31no—
253#893—32no—
254#893—34no—
255#893—32no—
256#893—61no—
257#893—62no—
258#892—32no—
259#892—32no—
260#892—31no—
261#892—31no—
262#892—34no—
263#892—32no—
264#892—32no—
265#892—31no—
266#892—32no—
267#892—31no—
268#892—34no—
269#892—62no—
270#892—61no—
271#892C2×D312yes—
272D3×C4⋊C4—32no—
273D3×C4⋊C4—32no—
274D3×C4⋊C4—34no—
275D3×C4⋊C4—34no—
276#890—32no—
277#890—32no—
278#890—34no—
279#889—34no—
280#889C2×D314yes—
281#888—32no—
282#887—32no—
283#887—32no—
284#887—31no—
285#887—34no—
286#887—34no—
287#887C2×D312yes—
288#885—34no—
289#884—34no—
290#883—34no—
291#883—34no—
292#67⋊C4—34no—
293#67⋊C4—32no—
294#67⋊C4—34no—
295#879—34no—
296#878—34no—
297#877—34no—
298#877—32no—
299#876—34no—
300#875—34no—
301#875C2×D312yes—
302C4×D12—32no—
303C4×D12—32no—
304C4×D12—32no—
305C4×D12—31no—
306C4×D12—31no—
307C4×D12—34no—
308C4×D12—32no—
309C4×D12—61no—
310C4×D12—62no—
311C4×D12C2×D311yescharacteristic
312#872—34no—
313C42×D3—32no—
314C42×D3—32no—
315C42×D3—32no—
316C42×D3—31no—
317C42×D3—31no—
318C42×D3—34no—
319C42×D3—34no—
320C42×D3—62no—
321C42×D3—61no—
322#870C2×D312yes—
323#869—32no—
324#869C2×D311yescharacteristic
325#869C2×D311yescharacteristic
326C4×Dic6—34no—
327C4×Dic6—34no—
328C4×Dic6C2×D312yes—
329C4×Dic6C2×D312yes—
330C4×Dic6C2×D311yescharacteristic
331C22×C3⋊D3C2411yescharacteristic
332C22×C3⋊D3C2412yes—
333C22×C3×D3C2412yes—
334C32×Q8—22no—
335C2×C32×C4C2412yes—
336C2×C32×C4C2412yes—
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C3⋊Dic3C2411yescharacteristic
341C2×C3⋊Dic3C2411yescharacteristic
342C2×C3⋊Dic3C2412yes—
343C2×C3⋊Dic3C2411yescharacteristic
344C4⋊(C3⋊D3)—24no—
345C4⋊(C3⋊D3)#4114yescomplemented
346C4×C3⋊D3—24no—
347C4×C3⋊D3—22no—
348C4×C3⋊D3—22no—
349C4×C3⋊D3—24no—
350C4×C3⋊D3—24no—
351C4×C3⋊D3—22no—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2414yes—
355C2×C3×Dic3C2414yes—
356C2×C3×Dic3C2412yes—
357C3×D12—22no—
358C3×C4×D3—24no—
359C3×Dic6—24no—
360C3×Dic6—24no—
361C3×Dic6#4114yescomplemented
362#627—28no—
363#626—28no—
364#626—24no—
365#624—28no—
366#624—28no—
367D3×Dic3—24no—
368D3×Dic3—24no—
369#557—31no—
370#556—31no—
371#556—92no—
372#552—92no—
373#552—94no—
374D4×Q8—91no—
375#548—92no—
376#547—91no—
377#547—92no—
378#533—92no—
379#533—91no—
380#529—92no—
381#529—94no—
382C4×#41—92no—
383C4×#41—91no—
384C4×#41—91no—
385C2×C4×Q8—92no—
386C2×C3×Q8—21no—
387C2×C3×Q8—31no—
388C2×C3×Q8—32no—
389C2×C3×Q8—32no—
390C2×C3×Q8C22×D311yescharacteristic
391C2×C3×Q8C22×D311yescharacteristic
392C2×C3×D4—31no—
393C22×C3×C4—32no—
394C2×#67—34no—
395C2×#67—32no—
396C22×Dic3—32no—
397C22×Dic3—32no—
398#239—68no—
399#239—64no—
400#239—64no—
401#239—64no—
402#239—68no—
403D3×Q8—68no—
404D3×Q8—68no—
405#237—64no—
406#235—68no—
407C2×D12—31no—
408C2×D12—31no—
409C2×D12—32no—
410C2×D12—34no—
411C2×D12—32no—
412C2×D12—32no—
413C2×D12—61no—
414C2×D12—62no—
415C2×D12C22×D311yescharacteristic
416C2×C4×D3—32no—
417C2×C4×D3—32no—
418C2×C4×D3—32no—
419C2×C4×D3—32no—
420C2×C4×D3—32no—
421C2×C4×D3—32no—
422C2×C4×D3—31no—
423C2×C4×D3—31no—
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×C4×D3—32no—
427C2×C4×D3—32no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—34no—
431C2×C4×D3—34no—
432C2×C4×D3—34no—
433C2×C4×D3—34no—
434C2×C4×D3—62no—
435C2×C4×D3—61no—
436C2×C4×D3—62no—
437C2×C4×D3—61no—
438C2×C4×D3—62no—
439C2×C4×D3—61no—
440C2×C4×D3C22×D312yes—
441C2×Dic6—34no—
442C2×Dic6—34no—
443C2×Dic6C22×D312yes—
444C2×Dic6C22×D312yes—
445C2×Dic6C22×D311yescharacteristic
446C3×C4⋊C4—21no—
447C3×C4⋊C4—22no—
448C3×C4⋊C4—32no—
449C3×C4⋊C4—34no—
450C3×C4⋊C4—31no—
451C3×C4⋊C4—34no—
452C3×C4⋊C4—32no—
453C3×C4⋊C4—34no—
454C3×C4⋊C4—32no—
455C3×C4⋊C4—32no—
456C3×C4⋊C4—32no—
457C3×C4⋊C4—31no—
458C3×C4⋊C4—34no—
459C3×C4⋊C4C22×D311yescharacteristic
460C3×C4⋊C4C22×D312yes—
461C3×C4⋊C4C22×D311yescharacteristic
462C3×C4⋊C4C22×D312yes—
463C3×C22⋊C4—34no—
464C3×C22⋊C4—32no—
465C3×C22⋊C4—34no—
466C3×C42—21no—
467C3×C42—22no—
468C3×C42—34no—
469C3×C42—34no—
470C3×C42—32no—
471C3×C42C22×D311yescharacteristic
472C3×C42C22×D312yes—
473C3×C42C22×D312yes—
474C3×C42C22×D311yescharacteristic
475#217—34no—
476#217—32no—
477(C2×D3)⋊C4—32no—
478(C2×D3)⋊C4—34no—
479(C2×D3)⋊C4—32no—
480(C2×D3)⋊C4—32no—
481(C2×D3)⋊C4—32no—
482(C2×D3)⋊C4—32no—
483(C2×D3)⋊C4—32no—
484(C2×D3)⋊C4—32no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—32no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—62no—
492(C2×D3)⋊C4—62no—
493(C2×D3)⋊C4—62no—
494(C2×D3)⋊C4C22×D314yes—
495(C2×D3)⋊C4C22×D312yes—
496(C2×D3)⋊C4C22×D314yes—
497C4⋊Dic3—31no—
498C4⋊Dic3—32no—
499C4⋊Dic3—31no—
500C4⋊Dic3—32no—
501C4⋊Dic3—32no—
502C4⋊Dic3—34no—
503C4⋊Dic3—34no—
504C4⋊Dic3—34no—
505C4⋊Dic3—62no—
506C4⋊Dic3—61no—
507C4⋊Dic3C22×D311yescharacteristic
508C4⋊Dic3C22×D312yes—
509C4⋊Dic3C22×D311yescharacteristic
510C4⋊Dic3C22×D312yes—
511C4⋊Dic3C22×D312yes—
512C4⋊Dic3C22×D312yes—
513Dic3⋊C4—32no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—34no—
519Dic3⋊C4C22×D312yes—
520Dic3⋊C4C22×D314yes—
521Dic3⋊C4C22×D314yes—
522Dic3⋊C4C22×D314yes—
523Dic3⋊C4C22×D314yes—
524C4×Dic3—32no—
525C4×Dic3—32no—
526C4×Dic3—31no—
527C4×Dic3—31no—
528C4×Dic3—31no—
529C4×Dic3—32no—
530C4×Dic3—31no—
531C4×Dic3—32no—
532C4×Dic3—31no—
533C4×Dic3—31no—
534C4×Dic3—32no—
535C4×Dic3—32no—
536C4×Dic3—34no—
537C4×Dic3—34no—
538C4×Dic3—32no—
539C4×Dic3—32no—
540C4×Dic3—61no—
541C4×Dic3—61no—
542C4×Dic3—62no—
543C4×Dic3—61no—
544C4×Dic3—62no—
545C4×Dic3C22×D314yes—
546C4×Dic3C22×D314yes—
547C4×Dic3C22×D312yes—
548C22×C32C2511yescharacteristic
549C2×C3⋊D3—21no—
550C2×C3⋊D3—22no—
551C2×C3⋊D3—22no—
552C2×C3⋊D3—21no—
553C2×C3⋊D3—21no—
554C2×C3⋊D3C2×#4114yes—
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C32×C4—22no—
559C32×C4—22no—
560C32×C4—21no—
561C32×C4C2×#4112yes—
562C32×C4C2×#4112yes—
563C3⋊Dic3—21no—
564C3⋊Dic3—21no—
565C3⋊Dic3—22no—
566C3⋊Dic32−1+412yes—
567C3×Dic3—22no—
568C3×Dic3—24no—
569C3×Dic3—24no—
570C3×Dic3—22no—
571C3×Dic3C2×#4114yes—
572C2×#41—92no—
573C2×#41—91no—
574C2×#41—91no—
575C22×Q8—92no—
576C4⋊Q8—32no—
577C4⋊Q8—31no—
578C4⋊Q8—31no—
579C4⋊Q8—92no—
580#126—34no—
581#126—94no—
582#126—94no—
583#125—34no—
584#125—32no—
585#125—94no—
586#125—92no—
587#124—32no—
588#124—94no—
589#123—94no—
590#123—94no—
591#123—94no—
592C22⋊Q8—32no—
593C22⋊Q8—94no—
594C22⋊Q8—94no—
595C22⋊Q8—92no—
596C22⋊Q8—92no—
597C22⋊Q8—92no—
598C22⋊Q8—92no—
599#121—94no—
600#121—92no—
601C4×Q8—32no—
602C4×Q8—32no—
603C4×Q8—32no—
604C4×Q8—31no—
605C4×Q8—94no—
606C4×Q8—94no—
607C4×Q8—91no—
608C4×Q8—92no—
609C4×Q8—92no—
610C4×Q8—91no—
611C4×Q8D3211yescharacteristic
612C4×D4—31no—
613C4×D4—94no—
614C4×D4—92no—
615C4×D4—92no—
616C4×D4—92no—
617C4×D4—94no—
618C4×D4—91no—
619C4×D4—91no—
620C4×D4—92no—
621C4×D4—91no—
622C4×D4—92no—
623#117—32no—
624#117—94no—
625#117—92no—
626#117—94no—
627#117—91no—
628#117—92no—
629#117—92no—
630#117—91no—
631C2×C4⋊C4—92no—
632C2×C4⋊C4—94no—
633C2×C42—94no—
634C2×C42—92no—
635C2×C42—92no—
636C2×C42—91no—
637C23×C3—32no—
638C22×D3—32no—
639C22×D3—32no—
640C22×D3—31no—
641C22×D3—31no—
642C22×D3—62no—
643C22×D3—61no—
644C22×D3C23×D312yes—
645C3×Q8—24no—
646C3×Q8—22no—
647C3×Q8—22no—
648C3×Q8—34no—
649C3×Q8—64no—
650C3×Q8—64no—
651C3×D4—62no—
652C2×C3×C4—22no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—22no—
656C2×C3×C4—21no—
657C2×C3×C4—32no—
658C2×C3×C4—32no—
659C2×C3×C4—34no—
660C2×C3×C4—34no—
661C2×C3×C4—32no—
662C2×C3×C4—64no—
663C2×C3×C4C23×D312yes—
664C2×C3×C4C23×D312yes—
665C2×C3×C4C23×D312yes—
666C2×C3×C4C23×D312yes—
667C2×C3×C4C23×D311yescharacteristic
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D311yescharacteristic
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C23×D311yescharacteristic
672C2×C3×C4C23×D311yescharacteristic
673#67—68no—
674#67—64no—
675C2×Dic3—31no—
676C2×Dic3—31no—
677C2×Dic3—31no—
678C2×Dic3—31no—
679C2×Dic3—31no—
680C2×Dic3—31no—
681C2×Dic3—32no—
682C2×Dic3—32no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—62no—
687C2×Dic3—64no—
688C2×Dic3—64no—
689C2×Dic3C23×D312yes—
690C2×Dic3C23×D312yes—
691C2×Dic3C23×D314yes—
692C2×Dic3C23×D314yes—
693C2×Dic3C23×D312yes—
694D12—22no—
695D12—34no—
696D12—34no—
697D12—64no—
698D12—64no—
699D12—64no—
700D12—68no—
701D12—64no—
702D12—68no—
703C4×D3—24no—
704C4×D3—68no—
705C4×D3—68no—
706C4×D3—68no—
707C4×D3—64no—
708C4×D3—62no—
709C4×D3—64no—
710C4×D3—62no—
711C4×D3—64no—
712C4×D3—64no—
713C4×D3—64no—
714C4×D3—68no—
715C4×D3—64no—
716C4×D3—64no—
717C4×D3—62no—
718C4×D3—64no—
719C4×D3—64no—
720C4×D3—62no—
721C4×D3—62no—
722C4×D3—62no—
723C4×D3—68no—
724C4×D3—124no—
725C4×D3—122no—
726C4×D3—124no—
727C4×D3—122no—
728Dic6—24no—
729Dic6—24no—
730Dic6—68no—
731Dic6—68no—
732Dic6#23914yescomplemented
733C2×C32C22×#4111yescharacteristic
734C2×C32C22×#4111yescharacteristic
735C2×C32C2×2−1+411yescharacteristic
736C3⋊D3—24no—
737C3⋊D3—41no—
738C3×D3—42no—
739#41—188no—
740#41—184no—
741#41—184no—
742C2×Q8—31no—
743C2×Q8—32no—
744C2×Q8—32no—
745C2×Q8—94no—
746C2×Q8—188no—
747C2×Q8C2×D3211yescharacteristic
748C2×D4—31no—
749C2×D4—94no—
750C2×D4—92no—
751C2×D4—91no—
752C2×D4—92no—
753C22×C4—32no—
754C22×C4—94no—
755C22×C4—94no—
756C22×C4—92no—
757C22×C4—92no—
758C22×C4—92no—
759C22×C4—92no—
760C22×C4—92no—
761C22×C4—91no—
762C22×C4—91no—
763C22×C4—91no—
764C4⋊C4—31no—
765C4⋊C4—34no—
766C4⋊C4—32no—
767C4⋊C4—34no—
768C4⋊C4—32no—
769C4⋊C4—32no—
770C4⋊C4—31no—
771C4⋊C4—34no—
772C4⋊C4—32no—
773C4⋊C4—34no—
774C4⋊C4—32no—
775C4⋊C4—92no—
776C4⋊C4—94no—
777C4⋊C4—94no—
778C4⋊C4—94no—
779C4⋊C4—94no—
780C4⋊C4—92no—
781C4⋊C4—91no—
782C4⋊C4C2×D3211yescharacteristic
783C4⋊C4C2×D3212yes—
784C22⋊C4—34no—
785C22⋊C4—32no—
786C22⋊C4—34no—
787C22⋊C4—94no—
788C22⋊C4—92no—
789C22⋊C4—94no—
790C22⋊C4—92no—
791C22⋊C4—94no—
792C22⋊C4—92no—
793C22⋊C4—92no—
794C22⋊C4—92no—
795C42—34no—
796C42—32no—
797C42—34no—
798C42—92no—
799C42—92no—
800C42—94no—
801C42—91no—
802C42—91no—
803C42—91no—
804C42—92no—
805C42—92no—
806C42C2×D3211yescharacteristic
807C42C2×D3212yes—
808C22×C3—21no—
809C22×C3—62no—
810C22×C3—62no—
811C22×C3—62no—
812C22×C3C24×D311yescharacteristic
813C22×C3C24×D311yescharacteristic
814C2×D3—22no—
815C2×D3—22no—
816C2×D3—22no—
817C2×D3—34no—
818C2×D3—34no—
819C2×D3—64no—
820C2×D3—62no—
821C2×D3—62no—
822C2×D3—62no—
823C2×D3—62no—
824C2×D3—62no—
825C2×D3—61no—
826C2×D3—61no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—61no—
831C2×D3—122no—
832C2×D3—122no—
833C2×D3—121no—
834C2×D3—121no—
835C3×C4—24no—
836C3×C4—22no—
837C3×C4—22no—
838C3×C4—22no—
839C3×C4—21no—
840C3×C4—22no—
841C3×C4—21no—
842C3×C4—22no—
843C3×C4—22no—
844C3×C4—34no—
845C3×C4—42no—
846C3×C4—41no—
847C3×C4—64no—
848C3×C4—62no—
849C3×C4—64no—
850C3×C4—62no—
851C3×C4C2×#23912yes—
852C3×C4D3×#4112yes—
853C3×C4D3×#4112yes—
854C3×C4D3×#4112yes—
855Dic3—24no—
856Dic3—24no—
857Dic3—22no—
858Dic3—22no—
859Dic3—32no—
860Dic3—32no—
861Dic3—62no—
862Dic3—62no—
863Dic3—62no—
864Dic3—61no—
865Dic3—62no—
866Dic3—61no—
867Dic3—61no—
868Dic3—61no—
869Dic3—121no—
870Dic3—122no—
871Dic3C2×#23914yes—
872C32#348211yescharacteristic, complemented, Sylow
873C23—32no—
874C23—92no—
875C23—91no—
876Q8—22no—
877Q8—34no—
878Q8—64no—
879Q8—64no—
880Q8—188no—
881D4—62no—
882D4—94no—
883D4—184no—
884D4—184no—
885D4—188no—
886C2×C4—32no—
887C2×C4—32no—
888C2×C4—34no—
889C2×C4—32no—
890C2×C4—34no—
891C2×C4—64no—
892C2×C4—91no—
893C2×C4—91no—
894C2×C4—91no—
895C2×C4—92no—
896C2×C4—184no—
897C2×C4—182no—
898C2×C4—184no—
899C2×C4—188no—
900C2×C4—184no—
901C2×C4—188no—
902C2×C4—184no—
903C2×C4—182no—
904C2×C4—184no—
905C2×C4—182no—
906C2×C4C22×D3212yes—
907C2×C4C22×D3211yescharacteristic
908C2×C4C22×D3212yes—
909C2×C4C22×D3211yescharacteristic
910C2×C4C22×D3211yescharacteristic
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—122no—
915C2×C3C22×#23911yescharacteristic
916C2×C3C2×D3×#4111yescharacteristic
917C2×C3C2×D3×#4111yescharacteristic
918C2×C3C2×D3×#4111yescharacteristic
919C2×C3D3×2−1+411yescharacteristic
920C2×C3D3×2−1+411yescharacteristic
921D3—42no—
922D3—64no—
923D3—64no—
924D3—124no—
925D3—122no—
926D3—121no—
927D3—121no—
928C22—62no—
929C22—62no—
930C22—62no—
931C22—94no—
932C22—182no—
933C22—182no—
934C22—181no—
935C22—181no—
936C22—181no—
937C22C23×D3211yescharacteristic
938C4—22no—
939C4—22no—
940C4—21no—
941C4—34no—
942C4—62no—
943C4—64no—
944C4—64no—
945C4—62no—
946C4—92no—
947C4—181no—
948C4—181no—
949C4—182no—
950C4#6430612yes—
951C4D3×#23912yes—
952C3—21no—
953C3#8698111yescharacteristic, complemented
954C3#8701711yescharacteristic, complemented
955C2—122no—
956C2—184no—
957C2—361no—
958C2C2×#6430611yescharacteristic
959C2C2×D3×#23911yescharacteristic
960C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3482
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×#3832C2semidirect
2. C3×#5584C2semidirect
3. C3×#5567C2semidirect
4. #10595368C2semidirect
5. #10595341C2semidirect
6. #10594565C2semidirect
7. #10594465C2semidirect
8. #10594462C2semidirect
9. #10594362C2semidirect
10. #10593947C2semidirect
11. #10593943C2semidirect
12. #10593903C2semidirect
13. #10593901C2semidirect
14. C4×#3797C2semidirect
15. C4×#3796C2semidirect
16. #10593869C2semidirect
17. #10593866C2semidirect
104. #5584D3semidirect
115. #5567D3semidirect
345. C4⋊(C3⋊D3)#41semidirect
361. C3×Dic6#41semidirect
732. Dic6#239semidirect
872. C32#3482semidirect
953. C3#86981semidirect
954. C3#87017semidirect

Maximal subgroups

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

subgroupindex
C4×#38322
C3×#55842
C3×#55672
#105953682
#105953412
#105945652
#105944652
#105944622
#105943622
#105939472
#105939432
#105939032
#105939012
C4×#37972
C4×#37962
#105938692
#105938662
#870173
#869813