Finite Group Databasebeta

← #11909914

Subgroups — #11909914

Order 1152.

2095 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596199C211yesmaximal, characteristic, complemented
2C3×#5727C211yesmaximal, characteristic, complemented
3C3×#5721C211yesmaximal, characteristic, complemented
4#10595403C212yesmaximal, complemented
5#10595349C212yesmaximal, complemented
6#10595347C212yesmaximal, complemented
7#10595344C212yesmaximal, complemented
8#10594447C212yesmaximal
9#10594397C212yesmaximal, complemented
10#10594336C214yesmaximal, complemented
11#10594335C212yesmaximal, complemented
12#10594334C214yesmaximal, complemented
13#10594318C212yesmaximal, complemented
14C4×#3797C211yesmaximal, characteristic, complemented
15#10593879C211yesmaximal, characteristic, complemented
16#10593875C211yesmaximal, characteristic
17#10593860C211yesmaximal, characteristic, complemented
18#87025—31nomaximal
19#86753—31nomaximal
20C2×C3×D3×Q8C2212yes—
21C2×#3797C2211yescharacteristic
22C32×C4⋊Q8C2211yescharacteristic
23#64155C2212yes—
24Q8×C3⋊Dic3C2212yes—
25#64106C2212yes—
26#64101C2212yes—
27#64099C2212yes—
28#64096C2212yes—
29C42×C3⋊D3C2211yescharacteristic
30#64078C2211yescharacteristic
31C3×#946C2212yes—
32C3×Q8×Dic3C2212yes—
33C3×#944C2212yes—
34C3×#896C2214yes—
35C3×#893C2212yes—
36C3×#890C2212yes—
37C3×#889C2214yes—
38C3×#888C2212yes—
39C3×#887C2212yes—
40C3×C4×D12C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C4×#627C2212yes—
45#63916C2211yescharacteristic
46#63904C2214yes—
47C4×#626C2212yes—
48#63900C2211yescharacteristic
49#63888C2214yes—
50#63883C2212yes—
51C4×#624C2212yes—
52#63872C2211yescharacteristic
53#63871C2211yescharacteristic
54#63870C2214yes—
55#63869C2212yes—
56#63866C2212yes—
57#63863C2211yescharacteristic
58#63862C2214yes—
59#63862C2212yes—
60#63861C2214yes—
61#63861C2214yes—
62#63860C2212yes—
63#63859C2214yes—
64#63856C2212yes—
65#63855C2212yes—
66#63855C2214yes—
67#63854C2214yes—
68#63853C2212yes—
69#63851C2214yes—
70#63847C2214yes—
71#63845C2214yes—
72#63845C2214yes—
73#63844C2212yes—
74#63844C2212yes—
75#63843C2214yes—
76#63843C2211yescharacteristic
77#63843C2211yescharacteristic
78Dic3×Dic6C2214yes—
79Dic3×Dic6C2212yes—
80#63841C2212yes—
81#63841C2214yes—
82#63839C2214yes—
83#63838C2212yes—
84#63836C2214yes—
85C3×#557—31no—
86C3×D4×Q8—31no—
87Q8×#67—32no—
88#5812—32no—
89#5731—32no—
90#5728—31no—
91#5728—31no—
92#5728—32no—
93#5728—61no—
94#5727—32no—
95#5727D311yescharacteristic, complemented
96#5721—32no—
97#5721D311yescharacteristic, complemented
98#5696—34no—
99#5693—34no—
100#5691—32no—
101#5685—32no—
102#5639—32no—
103#5639—34no—
104#5625—32no—
105#5625—34no—
106#5584—31no—
107#5581—32no—
108#5580—31no—
109#5578—32no—
110#5572—32no—
111C4×D3×Q8—31no—
112C4×D3×Q8—31no—
113#5570—31no—
114#5568—32no—
115#5567—31no—
116#5557—32no—
117#5557—31no—
118#5542—32no—
119#5542—31no—
120C2×C32×Q8C2312yes—
121C2×C4×C3⋊D3C2311yescharacteristic
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×#634C2312yes—
125C3×D3×Q8—28no—
126C2×C3×D12C2311yescharacteristic
127C2×C3×C4×D3C2314yes—
128C2×C3×C4×D3C2312yes—
129C2×C3×Dic6C2311yescharacteristic
130C2×C3×Dic6C2314yes—
131C2×C3×Dic6C2311yescharacteristic
132C2×C3×Dic6C2311yescharacteristic
133C2×#627C2312yes—
134C2×#626C2312yes—
135C2×#624C2312yes—
136C2×#624C2312yes—
137#3797—24no—
138C32×C4⋊C4C2312yes—
139C32×C4⋊C4C2312yes—
140C32×C42C2311yescharacteristic
141#3752C2314yes—
142C4⋊(C3⋊Dic3)C2312yes—
143C4⋊(C3⋊Dic3)C2312yes—
144C4⋊(C3⋊Dic3)C2314yes—
145#3750C2314yes—
146C4×C3⋊Dic3C2311yescharacteristic
147C4×C3⋊Dic3C2311yescharacteristic
148C4×C3⋊Dic3C2311yescharacteristic
149C4×C3⋊Dic3C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2312yes—
152C3×C4⋊Dic3C2311yescharacteristic
153C3×C4⋊Dic3C2314yes—
154C3×C4⋊Dic3C2311yescharacteristic
155C3×C4⋊Dic3C2311yescharacteristic
156C3×C4⋊Dic3C2311yescharacteristic
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2312yes—
160C3×Dic3⋊C4C2312yes—
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2312yes—
163C3×C4×Dic3C2314yes—
164C3×C4×Dic3C2312yes—
165C3×C4×Dic3C2312yes—
166C3×C4×Dic3C2312yes—
167#3724C2312yes—
168#3724C2314yes—
169#3724C2314yes—
170Dic3⋊Dic3C2314yes—
171Dic3⋊Dic3C2312yes—
172Dic3⋊Dic3C2312yes—
173Dic3⋊Dic3C2314yes—
174Dic3⋊Dic3C2312yes—
175Dic3⋊Dic3C2312yes—
176Dic3⋊Dic3C2312yes—
177#3722C2312yes—
178(C2×D3)⋊Dic3C2314yes—
179(C2×D3)⋊Dic3C2312yes—
180(C2×D3)⋊Dic3C2312yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2312yes—
183Dic32C2314yes—
184Dic32C2312yes—
185Dic32C2312yes—
186Dic32C2314yes—
187#3523—91noSylow
188C22×C3×Q8—32no—
189C2×D3×Q8—31no—
190C2×D3×Q8—31no—
191C2×D3×Q8C2×D312yes—
192C3×C4⋊Q8—21no—
193C3×C4⋊Q8—32no—
194C3×C4⋊Q8—32no—
195C3×C4⋊Q8C2×D311yescharacteristic
196C3×C4⋊Q8C2×D311yescharacteristic
197C3×#125—34no—
198C3×#125—32no—
199C3×C22⋊Q8—32no—
200C3×C22⋊Q8—34no—
201C3×C4×Q8—32no—
202C3×C4×Q8—32no—
203C3×C4×Q8—31no—
204C3×C4×Q8—31no—
205C3×C4×Q8—31no—
206C3×C4×D4—32no—
207C3×C4×D4—31no—
208#947—31no—
209#946—32no—
210#946—32no—
211#946—32no—
212#946—31no—
213#946—34no—
214#946—62no—
215#946C2×D312yes—
216Q8×Dic3—32no—
217Q8×Dic3—32no—
218Q8×Dic3—34no—
219Q8×Dic3—31no—
220Q8×Dic3—31no—
221Q8×Dic3—34no—
222Q8×Dic3—32no—
223Q8×Dic3—62no—
224Q8×Dic3C2×D312yes—
225#944—34no—
226#944—32no—
227#944C2×D312yes—
228#938—31no—
229#936—31no—
230#936—32no—
231C4×#67—34no—
232C4×#67—32no—
233#926—32no—
234#926—34no—
235#926—34no—
236#926—32no—
237#924—32no—
238#924—34no—
239#898—34no—
240#898—34no—
241#898—34no—
242#898—32no—
243#897—31no—
244#897—32no—
245#897—32no—
246#897—62no—
247#896—34no—
248#896—34no—
249#896C2×D314yes—
250#895—31no—
251#894—34no—
252#894—32no—
253#893—34no—
254#893C2×D312yes—
255#892—34no—
256#892—32no—
257#892—32no—
258#892—32no—
259#892—34no—
260#892—62no—
261D3×C4⋊C4—31no—
262D3×C4⋊C4—31no—
263D3×C4⋊C4—32no—
264D3×C4⋊C4—32no—
265#890—32no—
266#890—32no—
267#890—31no—
268#890—31no—
269#890—34no—
270#890—34no—
271#890—32no—
272#890—62no—
273#890C2×D312yes—
274#889—34no—
275#889—34no—
276#889—34no—
277#889—34no—
278#889—34no—
279#889—34no—
280#889C2×D314yes—
281#888—34no—
282#888C2×D312yes—
283#887—34no—
284#887—31no—
285#887—31no—
286#887—32no—
287#887—32no—
288#887—32no—
289#887—32no—
290#887—32no—
291#887—32no—
292#887—62no—
293#887C2×D312yes—
294#883—34no—
295#883—32no—
296#879—34no—
297#879—34no—
298#879—34no—
299#879—32no—
300#879—34no—
301#876—34no—
302#875—32no—
303C4×D12—32no—
304C4×D12C2×D311yescharacteristic
305#872—34no—
306#872—32no—
307#872—34no—
308C42×D3—31no—
309C42×D3—31no—
310C42×D3—32no—
311C42×D3—32no—
312C42×D3—61no—
313#870—32no—
314#869—32no—
315#869—31no—
316#869—31no—
317#869—61no—
318C4×Dic6—34no—
319C4×Dic6—32no—
320C4×Dic6—32no—
321C4×Dic6—32no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6C2×D311yescharacteristic
325C4×Dic6C2×D311yescharacteristic
326C4×Dic6C2×D311yescharacteristic
327C22×C3⋊D3C2411yescharacteristic
328C22×C3×D3C2412yes—
329C32×Q8—24no—
330C2×C32×C4C2414yes—
331C2×C32×C4C2411yescharacteristic
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C3⋊Dic3C2411yescharacteristic
335C2×C3⋊Dic3C2414yes—
336C2×C3⋊Dic3C2411yescharacteristic
337C2×C3⋊Dic3C2411yescharacteristic
338C4×C3⋊D3—22no—
339C4×C3⋊D3—22no—
340C4×C3⋊D3—22no—
341#634—24no—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C3×D12—22no—
350C3×C4×D3—24no—
351C3×C4×D3—28no—
352C3×Dic6—22no—
353C3×Dic6—22no—
354C3×Dic6—28no—
355C3×Dic6#4114yes—
356#627—24no—
357#626—24no—
358#624—24no—
359#624—24no—
360#557—31no—
361#557—91no—
362#557—92no—
363#556—92no—
364#556—91no—
365#552—92no—
366#552—94no—
367D4×Q8—31no—
368D4×Q8—92no—
369#541—94no—
370#541—92no—
371#533—92no—
372#533—91no—
373#529—91no—
374#529—92no—
375#519—92no—
376C2×C4×Q8—91no—
377C2×C3×Q8—22no—
378C2×C3×Q8—31no—
379C2×C3×Q8—31no—
380C2×C3×Q8—34no—
381C2×C3×Q8—31no—
382C2×C3×Q8—68no—
383C2×C3×Q8C22×D312yes—
384C2×C3×Q8C22×D312yes—
385C2×C3×D4—31no—
386C22×C3×C4—34no—
387C22×C3×C4—32no—
388C2×#67—32no—
389D3×Q8—28no—
390D3×Q8—64no—
391D3×Q8—64no—
392C2×D12—32no—
393C2×D12C22×D311yescharacteristic
394C2×C4×D3—31no—
395C2×C4×D3—31no—
396C2×C4×D3—31no—
397C2×C4×D3—31no—
398C2×C4×D3—31no—
399C2×C4×D3—31no—
400C2×C4×D3—32no—
401C2×C4×D3—32no—
402C2×C4×D3—32no—
403C2×C4×D3—32no—
404C2×C4×D3—61no—
405C2×C4×D3—61no—
406C2×C4×D3—61no—
407C2×C4×D3C22×D312yes—
408C2×C4×D3C22×D314yes—
409C2×Dic6—32no—
410C2×Dic6—32no—
411C2×Dic6—32no—
412C2×Dic6—32no—
413C2×Dic6—62no—
414C2×Dic6C22×D314yes—
415C2×Dic6C22×D311yescharacteristic
416C2×Dic6C22×D311yescharacteristic
417C2×Dic6C22×D311yescharacteristic
418C3×C4⋊C4—22no—
419C3×C4⋊C4—22no—
420C3×C4⋊C4—31no—
421C3×C4⋊C4—31no—
422C3×C4⋊C4—34no—
423C3×C4⋊C4—32no—
424C3×C4⋊C4—31no—
425C3×C4⋊C4—31no—
426C3×C4⋊C4—32no—
427C3×C4⋊C4—34no—
428C3×C4⋊C4—34no—
429C3×C4⋊C4—32no—
430C3×C4⋊C4—34no—
431C3×C4⋊C4C22×D312yes—
432C3×C4⋊C4C22×D312yes—
433C3×C4⋊C4C22×D312yes—
434C3×C4⋊C4C22×D312yes—
435C3×C22⋊C4—32no—
436C3×C22⋊C4—34no—
437C3×C42—21no—
438C3×C42—32no—
439C3×C42—32no—
440C3×C42—32no—
441C3×C42—34no—
442C3×C42C22×D311yescharacteristic
443C3×C42C22×D311yescharacteristic
444#217—34no—
445#217—32no—
446#217—32no—
447#217—32no—
448#217—34no—
449(C2×D3)⋊C4—32no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4—32no—
452(C2×D3)⋊C4—32no—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4—34no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—32no—
457(C2×D3)⋊C4—32no—
458(C2×D3)⋊C4—64no—
459(C2×D3)⋊C4C22×D312yes—
460(C2×D3)⋊C4C22×D314yes—
461C4⋊Dic3—32no—
462C4⋊Dic3—34no—
463C4⋊Dic3—32no—
464C4⋊Dic3—32no—
465C4⋊Dic3—32no—
466C4⋊Dic3—34no—
467C4⋊Dic3—32no—
468C4⋊Dic3—32no—
469C4⋊Dic3—34no—
470C4⋊Dic3—34no—
471C4⋊Dic3—32no—
472C4⋊Dic3—32no—
473C4⋊Dic3—32no—
474C4⋊Dic3—62no—
475C4⋊Dic3—62no—
476C4⋊Dic3—64no—
477C4⋊Dic3C22×D311yescharacteristic
478C4⋊Dic3C22×D311yescharacteristic
479C4⋊Dic3C22×D311yescharacteristic
480C4⋊Dic3C22×D311yescharacteristic
481C4⋊Dic3C22×D314yes—
482Dic3⋊C4—34no—
483Dic3⋊C4—34no—
484Dic3⋊C4—32no—
485Dic3⋊C4—34no—
486Dic3⋊C4—32no—
487Dic3⋊C4—32no—
488Dic3⋊C4—32no—
489Dic3⋊C4—32no—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4—34no—
494Dic3⋊C4—32no—
495Dic3⋊C4—34no—
496Dic3⋊C4—32no—
497Dic3⋊C4—64no—
498Dic3⋊C4C22×D312yes—
499Dic3⋊C4C22×D312yes—
500Dic3⋊C4C22×D312yes—
501Dic3⋊C4C22×D314yes—
502Dic3⋊C4C22×D314yes—
503Dic3⋊C4C22×D314yes—
504C4×Dic3—31no—
505C4×Dic3—31no—
506C4×Dic3—31no—
507C4×Dic3—31no—
508C4×Dic3—31no—
509C4×Dic3—31no—
510C4×Dic3—34no—
511C4×Dic3—34no—
512C4×Dic3—32no—
513C4×Dic3—34no—
514C4×Dic3—34no—
515C4×Dic3—34no—
516C4×Dic3—32no—
517C4×Dic3—32no—
518C4×Dic3—32no—
519C4×Dic3—34no—
520C4×Dic3—61no—
521C4×Dic3—61no—
522C4×Dic3—61no—
523C4×Dic3—64no—
524C4×Dic3C22×D312yes—
525C4×Dic3C22×D312yes—
526C4×Dic3C22×D312yes—
527C4×Dic3C22×D314yes—
528C22×C32C2511yescharacteristic
529C2×C3⋊D3—21no—
530C2×C3⋊D3—21no—
531C2×C3⋊D32−1+412yes—
532C2×C3×D3—22no—
533C2×C3×D3—22no—
534C2×C3×D3—22no—
535C32×C4—21no—
536C32×C4—24no—
537C32×C4C2×#4112yes—
538C32×C42−1+412yes—
539C3⋊Dic3—21no—
540C3⋊Dic3—21no—
541C3⋊Dic3—24no—
542C3⋊Dic3—21no—
543C3×Dic3—22no—
544C3×Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—22no—
549C3×Dic3C2×#4114yes—
550C22×Q8—32no—
551C22×Q8—91no—
552C4⋊Q8—32no—
553C4⋊Q8—32no—
554C4⋊Q8—92no—
555C4⋊Q8—94no—
556C4⋊Q8—91no—
557C4⋊Q8D3211yescharacteristic
558#126—94no—
559#126—94no—
560#126—92no—
561#126—94no—
562#126—94no—
563#125—32no—
564#125—34no—
565#125—92no—
566#125—91no—
567#125—94no—
568#125—94no—
569#125—94no—
570#125—94no—
571#125—92no—
572#124—92no—
573#124—91no—
574#123—92no—
575#123—94no—
576C22⋊Q8—32no—
577C22⋊Q8—34no—
578C22⋊Q8—94no—
579C22⋊Q8—91no—
580C22⋊Q8—94no—
581C22⋊Q8—92no—
582C22⋊Q8—92no—
583C22⋊Q8—92no—
584#121—91no—
585C4×Q8—32no—
586C4×Q8—32no—
587C4×Q8—31no—
588C4×Q8—31no—
589C4×Q8—31no—
590C4×Q8—92no—
591C4×Q8—92no—
592C4×Q8—92no—
593C4×Q8—94no—
594C4×Q8—92no—
595C4×Q8—92no—
596C4×Q8—91no—
597C4×Q8—91no—
598C4×Q8—94no—
599C4×Q8—92no—
600C4×Q8—92no—
601C4×D4—32no—
602C4×D4—31no—
603C4×D4—92no—
604C4×D4—94no—
605#117—94no—
606#117—92no—
607#117—94no—
608#117—94no—
609#117—92no—
610#117—92no—
611C2×C4⋊C4—91no—
612C2×C4⋊C4—92no—
613C2×C42—92no—
614C2×C42—91no—
615C23×C3—32no—
616C22×D3—31no—
617C22×D3—31no—
618C22×D3—61no—
619C22×D3C23×D312yes—
620C3×Q8—24no—
621C3×Q8—24no—
622C3×Q8—34no—
623C3×Q8—44no—
624C3×Q8—68no—
625C3×Q8—62no—
626C3×Q8—62no—
627C3×D4—62no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—24no—
632C2×C3×C4—32no—
633C2×C3×C4—32no—
634C2×C3×C4—32no—
635C2×C3×C4—32no—
636C2×C3×C4—32no—
637C2×C3×C4—32no—
638C2×C3×C4—32no—
639C2×C3×C4—68no—
640C2×C3×C4—64no—
641C2×C3×C4C23×D314yes—
642C2×C3×C4C23×D314yes—
643C2×C3×C4C23×D311yescharacteristic
644C2×C3×C4C23×D311yescharacteristic
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647C2×C3×C4C23×D311yescharacteristic
648C2×C3×C4C23×D311yescharacteristic
649#67—64no—
650C2×Dic3—31no—
651C2×Dic3—31no—
652C2×Dic3—31no—
653C2×Dic3—31no—
654C2×Dic3—34no—
655C2×Dic3—34no—
656C2×Dic3—31no—
657C2×Dic3—31no—
658C2×Dic3—61no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—64no—
662C2×Dic3C23×D312yes—
663C2×Dic3C23×D312yes—
664C2×Dic3C23×D312yes—
665C2×Dic3C23×D312yes—
666C2×Dic3C23×D312yes—
667C2×Dic3C23×D312yes—
668C2×Dic3C23×D312yes—
669D12—22no—
670D12—64no—
671C4×D3—24no—
672C4×D3—28no—
673C4×D3—64no—
674C4×D3—64no—
675C4×D3—64no—
676C4×D3—62no—
677C4×D3—62no—
678C4×D3—64no—
679C4×D3—62no—
680C4×D3—62no—
681C4×D3—62no—
682C4×D3—62no—
683C4×D3—64no—
684C4×D3—122no—
685C4×D3—122no—
686Dic6—22no—
687Dic6—22no—
688Dic6—28no—
689Dic6—64no—
690Dic6—64no—
691Dic6—64no—
692Dic6—64no—
693Dic6—124no—
694Dic6#23714yes—
695C2×C32C22×#4111yescharacteristic
696C2×C32C2×2−1+411yescharacteristic
697C2×C32C2×2−1+411yescharacteristic
698C3⋊D3—22no—
699C3×D3—42no—
700C2×Q8—31no—
701C2×Q8—31no—
702C2×Q8—31no—
703C2×Q8—34no—
704C2×Q8—68no—
705C2×Q8—92no—
706C2×Q8—92no—
707C2×Q8—184no—
708C2×Q8C2×D3212yes—
709C2×D4—31no—
710C2×D4—92no—
711C22×C4—34no—
712C22×C4—32no—
713C22×C4—92no—
714C22×C4—92no—
715C22×C4—91no—
716C22×C4—91no—
717C22×C4—91no—
718C4⋊C4—31no—
719C4⋊C4—32no—
720C4⋊C4—31no—
721C4⋊C4—32no—
722C4⋊C4—34no—
723C4⋊C4—34no—
724C4⋊C4—31no—
725C4⋊C4—34no—
726C4⋊C4—31no—
727C4⋊C4—34no—
728C4⋊C4—32no—
729C4⋊C4—92no—
730C4⋊C4—92no—
731C4⋊C4—92no—
732C4⋊C4—94no—
733C4⋊C4—92no—
734C4⋊C4—92no—
735C4⋊C4—94no—
736C4⋊C4—92no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—92no—
740C4⋊C4—94no—
741C4⋊C4—92no—
742C4⋊C4—94no—
743C4⋊C4C2×D3212yes—
744C4⋊C4C2×D3212yes—
745C22⋊C4—34no—
746C22⋊C4—32no—
747C22⋊C4—92no—
748C22⋊C4—92no—
749C22⋊C4—94no—
750C22⋊C4—92no—
751C22⋊C4—92no—
752C22⋊C4—94no—
753C22⋊C4—94no—
754C42—32no—
755C42—32no—
756C42—34no—
757C42—32no—
758C42—92no—
759C42—92no—
760C42—94no—
761C42—94no—
762C42—91no—
763C42—91no—
764C42—91no—
765C42—94no—
766C42C2×D3211yescharacteristic
767C22×C3—21no—
768C22×C3—62no—
769C22×C3—62no—
770C22×C3—62no—
771C22×C3C24×D311yescharacteristic
772C22×C3C24×D311yescharacteristic
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—32no—
777C2×D3—32no—
778C2×D3—62no—
779C2×D3—61no—
780C2×D3—61no—
781C2×D3—61no—
782C2×D3—61no—
783C2×D3—121no—
784C2×D3—121no—
785C3×C4—22no—
786C3×C4—24no—
787C3×C4—24no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—22no—
791C3×C4—22no—
792C3×C4—34no—
793C3×C4—44no—
794C3×C4—62no—
795C3×C4—62no—
796C3×C4—62no—
797C3×C4—62no—
798C3×C4—62no—
799C3×C4—62no—
800C3×C4C2×#23712yes—
801C3×C4#100712yes—
802C3×C4#100712yes—
803C3×C4D3×#4112yes—
804Dic3—22no—
805Dic3—22no—
806Dic3—22no—
807Dic3—22no—
808Dic3—22no—
809Dic3—22no—
810Dic3—62no—
811Dic3—61no—
812Dic3—64no—
813Dic3—64no—
814Dic3—61no—
815Dic3—61no—
816Dic3—61no—
817Dic3—61no—
818Dic3—61no—
819Dic3—124no—
820Dic3—121no—
821Dic3—121no—
822Dic3C2×#23714yes—
823C32#352311yescharacteristic, complemented, Sylow
824C23—32no—
825C23—91no—
826Q8—24no—
827Q8—34no—
828Q8—68no—
829Q8—62no—
830Q8—62no—
831Q8—184no—
832Q8—184no—
833D4—62no—
834D4—184no—
835C2×C4—32no—
836C2×C4—32no—
837C2×C4—32no—
838C2×C4—32no—
839C2×C4—32no—
840C2×C4—32no—
841C2×C4—32no—
842C2×C4—68no—
843C2×C4—64no—
844C2×C4—91no—
845C2×C4—91no—
846C2×C4—94no—
847C2×C4—91no—
848C2×C4—182no—
849C2×C4—184no—
850C2×C4—184no—
851C2×C4—182no—
852C2×C4—182no—
853C2×C4C22×D3214yes—
854C2×C4C22×D3211yescharacteristic
855C2×C4C22×D3211yescharacteristic
856C2×C4C22×D3211yescharacteristic
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—122no—
861C2×C3C22×#23711yescharacteristic
862C2×C3C2×#100711yescharacteristic
863C2×C3C2×#100711yescharacteristic
864C2×C3C2×D3×#4111yescharacteristic
865C2×C3D3×2−1+411yescharacteristic
866C2×C3D3×2−1+411yescharacteristic
867D3—42no—
868D3—62no—
869D3—62no—
870D3—122no—
871C22—62no—
872C22—62no—
873C22—62no—
874C22—92no—
875C22—181no—
876C22—181no—
877C22C23×D3211yescharacteristic
878C4—24no—
879C4—21no—
880C4—34no—
881C4—62no—
882C4—62no—
883C4—62no—
884C4—62no—
885C4—62no—
886C4—62no—
887C4—181no—
888C4—181no—
889C4—184no—
890C4—181no—
891C4D3×#23712yes—
892C4#6431612yes—
893C3—21no—
894C3#8675311yescharacteristic, complemented
895C3#8702511yescharacteristic, complemented
896C2—122no—
897C2—182no—
898C2C2×D3×#23711yescharacteristic
899C2C2×#6431611yescharacteristic
900C2#1059668711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radical#63916C22
hypercenterC4⋊Q8D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
2. C3×#5727C2semidirect
3. C3×#5721C2semidirect
4. #10595403C2semidirect
5. #10595349C2semidirect
6. #10595347C2semidirect
7. #10595344C2semidirect
9. #10594397C2semidirect
10. #10594336C2semidirect
11. #10594335C2semidirect
12. #10594334C2semidirect
13. #10594318C2semidirect
14. C4×#3797C2semidirect
15. #10593879C2semidirect
17. #10593860C2semidirect
95. #5727D3semidirect
97. #5721D3semidirect
823. C32#3523semidirect
894. C3#86753semidirect
895. C3#87025semidirect

Maximal subgroups

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

subgroupindex
#105961992
C3×#57272
C3×#57212
#105954032
#105953492
#105953472
#105953442
#105944472
#105943972
#105943362
#105943352
#105943342
#105943182
C4×#37972
#105938792
#105938752
#105938602
#870253
#867533