Finite Group Databasebeta

← #11909802

Subgroups — #11909802

Order 1152.

2322 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596201C211yesmaximal, characteristic, complemented
2C3×#5725C211yesmaximal, characteristic, complemented
3C3×#5722C211yesmaximal, characteristic, complemented
4#10595383C214yesmaximal, complemented
5#10595358C214yesmaximal, complemented
6#10594566C212yesmaximal, complemented
7#10594460C212yesmaximal, complemented
8#10594426C212yesmaximal, complemented
9#10594382C212yesmaximal, complemented
10#10594373C212yesmaximal, complemented
11#10594369C212yesmaximal, complemented
12#10594361C212yesmaximal, complemented
13#10594341C212yesmaximal, complemented
14#10593951C211yesmaximal, characteristic, complemented
15#10593900C211yesmaximal, characteristic, complemented
16C4×D3×Dic6C211yesmaximal, characteristic, complemented
17#10593870C211yesmaximal, characteristic, complemented
18#87043—31nomaximal
19#86229—31nomaximal
20C2×C3×#239C2212yes—
21C2×#3796C2212yes—
22C2×#3796C2214yes—
23C2×D3×Dic6C2211yescharacteristic
24C32×C4⋊Q8C2211yescharacteristic
25#64155C2214yes—
26#64106C2212yes—
27#64102C2212yes—
28C4⋊C4×C3⋊D3C2212yes—
29#64099C2212yes—
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31C4×#634C2211yescharacteristic
32C3×#947C2212yes—
33C3×#944C2214yes—
34C3×#895C2212yes—
35C3×#895C2212yes—
36C3×#893C2212yes—
37C3×#893C2212yes—
38C3×#888C2212yes—
39C3×#888C2212yes—
40C3×#887C2212yes—
41C3×#887C2212yes—
42C3×#874C2211yescharacteristic
43C3×C42×D3C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46C4×#627C2212yes—
47#63916C2212yes—
48#63911C2212yes—
49#63909C2211yescharacteristic
50#63907C2214yes—
51C4×#626C2214yes—
52C4×#626C2212yes—
53#63898C2212yes—
54#63893C2214yes—
55Dic3×D12C2214yes—
56Dic3×D12C2212yes—
57Dic3×D12C2212yes—
58D3×C4⋊Dic3C2211yescharacteristic
59#63887C2214yes—
60#63886C2214yes—
61#63886C2214yes—
62#63884C2214yes—
63#63884C2214yes—
64#63881C2214yes—
65#63877C2214yes—
66D3×Dic3⋊C4C2212yes—
67D3×Dic3⋊C4C2214yes—
68C4×D3×Dic3C2212yes—
69#63874C2212yes—
70#63869C2211yescharacteristic
71#63868C2212yes—
72#63864C2211yescharacteristic
73#63863C2212yes—
74#63861C2214yes—
75#63860C2212yes—
76#63856C2214yes—
77#63856C2211yescharacteristic
78#63853C2214yes—
79#63852C2214yes—
80#63850C2214yes—
81#63850C2212yes—
82#63844C2211yescharacteristic
83Dic3×Dic6C2211yescharacteristic
84#63837C2212yes—
85C3×Q82—31no—
86C3×#532—31no—
87#5824—34no—
88#5733—34no—
89#5733—32no—
90#5730—31no—
91#5730—31no—
92#5730—32no—
93#5730—61no—
94#5726—34no—
95#5726—32no—
96#5725—32no—
97#5725D311yescharacteristic, complemented
98#5722D311yescharacteristic, complemented
99#5718—31no—
100#5713—31no—
101#5669—34no—
102#5611—32no—
103#5600—32no—
104#5598—32no—
105#5596—32no—
106#5585—32no—
107#5585—31no—
108#5580—32no—
109#5580—31no—
110#5577—31no—
111#5576—32no—
112#5574—32no—
113C4×D3×Q8—31no—
114#5561—32no—
115#5559—32no—
116#5546—32no—
117#5539—32no—
118#5479—31no—
119C2×C4×Dic6—31no—
120C2×C32×Q8C2312yes—
121C2×C4⋊(C3⋊D3)C2311yescharacteristic
122C2×C4×C3⋊D3C2312yes—
123C2×C4×C3⋊D3C2314yes—
124C2×#634C2311yescharacteristic
125C3×#239—44no—
126C2×C3×D12C2312yes—
127C2×C3×D12C2312yes—
128C2×C3×D12C2314yes—
129C2×C3×D12C2312yes—
130C2×C3×C4×D3C2311yescharacteristic
131C2×C3×C4×D3C2311yescharacteristic
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×C4×D3C2314yes—
134C2×C3×Dic6C2311yescharacteristic
135C2×C3×Dic6C2314yes—
136C2×C3×Dic6C2311yescharacteristic
137C2×#627C2312yes—
138C2×#626C2312yes—
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×D3×Dic3C2312yes—
142C2×D3×Dic3C2312yes—
143C2×D3×Dic3C2314yes—
144C2×D3×Dic3C2314yes—
145#3796—28no—
146#3796—48no—
147D3×Dic6—24no—
148C32×C4⋊C4C2312yes—
149C32×C4⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151#3752C2312yes—
152#3752C2314yes—
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154C4⋊(C3⋊Dic3)C2311yescharacteristic
155C4⋊(C3⋊Dic3)C2314yes—
156#3750C2312yes—
157#3750C2314yes—
158C4×C3⋊Dic3C2312yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×(C2×D3)⋊C4C2314yes—
161C3×C4⋊Dic3C2311yescharacteristic
162C3×C4⋊Dic3C2311yescharacteristic
163C3×Dic3⋊C4C2314yes—
164C3×Dic3⋊C4C2314yes—
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2312yes—
167C3×C4×Dic3C2314yes—
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2311yescharacteristic
173#3724C2312yes—
174#3724C2312yes—
175#3724C2312yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2312yes—
179#3722C2312yes—
180#3722C2312yes—
181#3722C2312yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187Dic32C2312yes—
188Dic32C2312yes—
189#3522—91noSylow
190C2×C3×#41—32no—
191C2×#239—32no—
192C2×#239—34no—
193C2×#239C2×D312yes—
194C2×D3×Q8—31no—
195C2×#237—32no—
196C2×#237—34no—
197C22×Dic6—31no—
198C3×C4⋊Q8—21no—
199C3×C4⋊Q8—34no—
200C3×C4⋊Q8—32no—
201C3×C4⋊Q8—32no—
202C3×C4⋊Q8C2×D311yescharacteristic
203C3×C4⋊Q8C2×D311yescharacteristic
204C3×#127—31no—
205C3×#124—32no—
206C3×#121—32no—
207C3×#121—32no—
208C3×C4×Q8—32no—
209C3×C4×Q8—32no—
210C3×C4×Q8—31no—
211C3×C4×Q8—31no—
212C3×C4×D4—32no—
213C3×C4×D4—32no—
214C2×C3×C42—31no—
215#947—32no—
216#947—34no—
217#947—31no—
218#947C2×D312yes—
219#946—34no—
220#946—34no—
221#946—34no—
222#946—31no—
223#946—34no—
224#946—64no—
225Q8×Dic3—31no—
226#944C2×D314yes—
227#940—32no—
228#939—34no—
229#939—34no—
230#938—32no—
231#936—32no—
232#936—32no—
233#935—34no—
234#935—34no—
235D4×Dic3—32no—
236D4×Dic3—32no—
237D4×Dic3—32no—
238D4×Dic3—34no—
239#930—31no—
240#929—32no—
241#929—34no—
242C4×#67—32no—
243C4×#67—34no—
244C2×C4⋊Dic3—31no—
245#924—31no—
246#924—34no—
247C2×Dic3⋊C4—32no—
248C2×Dic3⋊C4—34no—
249C2×C4×Dic3—32no—
250#898—34no—
251#898—32no—
252#897—32no—
253#897—32no—
254#897—34no—
255#897—62no—
256#895—34no—
257#895—34no—
258#895—32no—
259#895—31no—
260#895C2×D312yes—
261#895C2×D312yes—
262#894—34no—
263#894—34no—
264#894—32no—
265#894—34no—
266#894—34no—
267#893—32no—
268#893—32no—
269#893—32no—
270#893—34no—
271#893—62no—
272#893C2×D312yes—
273#893C2×D312yes—
274D3×C4⋊C4—32no—
275D3×C4⋊C4—31no—
276D3×C4⋊C4—34no—
277D3×C4⋊C4—32no—
278D3×C4⋊C4—32no—
279D3×C4⋊C4—62no—
280#890—32no—
281#890—32no—
282#890—31no—
283#890—62no—
284#888C2×D312yes—
285#888C2×D312yes—
286#887—32no—
287#887—31no—
288#887C2×D312yes—
289#887C2×D312yes—
290#885—34no—
291#885—34no—
292#883—34no—
293#67⋊C4—34no—
294#879—34no—
295#878—34no—
296#878—34no—
297#877—34no—
298#876—32no—
299#875—32no—
300#875—31no—
301#875—34no—
302#874—32no—
303#874C2×D311yescharacteristic
304C4×D12—32no—
305C4×D12—34no—
306C4×D12—32no—
307C4×D12—34no—
308C4×D12—32no—
309C4×D12—31no—
310C4×D12—31no—
311C4×D12—61no—
312#872—34no—
313#872—32no—
314#872—32no—
315C42×D3—32no—
316C42×D3C2×D311yescharacteristic
317#870—31no—
318C4×Dic6—31no—
319C4×Dic6—31no—
320C4×Dic6—31no—
321C4×Dic6—31no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—61no—
326C4×Dic6C2×D311yescharacteristic
327C4×Dic6C2×D311yescharacteristic
328C22×C3⋊D3C2412yes—
329C22×C3×D3C2414yes—
330C22×C3×D3C2411yescharacteristic
331C32×Q8—42no—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2414yes—
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C3⋊Dic3C2412yes—
337C2×C3⋊Dic3C2412yes—
338C2×C3⋊Dic3C2412yes—
339C4⋊(C3⋊D3)—22no—
340C4×C3⋊D3—24no—
341C4×C3⋊D3—44no—
342#634—22no—
343C2×C3×Dic3C2411yescharacteristic
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2411yescharacteristic
348C2×C3×Dic3C2411yescharacteristic
349C2×C3×Dic3C2412yes—
350C3×D12—28no—
351C3×D12—24no—
352C3×D12—24no—
353C3×D12—42no—
354C3×C4×D3—22no—
355C3×C4×D3—22no—
356C3×C4×D3—22no—
357C3×C4×D3—44no—
358C3×Dic6—22no—
359C3×Dic6—44no—
360C3×Dic6#4114yescomplemented
361#627—24no—
362#626—24no—
363#626—28no—
364#626—44no—
365D3×Dic3—24no—
366D3×Dic3—24no—
367D3×Dic3—28no—
368D3×Dic3—44no—
369#559—92no—
370#559—91no—
371Q82—31no—
372#554—92no—
373#554—91no—
374#550—91no—
375#548—92no—
376#547—92no—
377#547—94no—
378#542—92no—
379#542—94no—
380#532—31no—
381#532—92no—
382#529—91no—
383#529—92no—
384#520—92no—
385C2×C4×Q8—91no—
386C3×#41—124no—
387C2×C3×Q8—22no—
388C2×C3×Q8—31no—
389C2×C3×Q8—31no—
390C2×C3×Q8—34no—
391C2×C3×Q8C22×D312yes—
392C2×C3×Q8C22×D312yes—
393C2×C3×D4—32no—
394C2×C3×D4—34no—
395C2×C3×D4—32no—
396C2×C3×D4—32no—
397C22×C3×C4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—31no—
400C22×C3×C4—34no—
401C2×#67—34no—
402C2×#67—32no—
403C2×#67—34no—
404C22×Dic3—34no—
405C22×Dic3—32no—
406C22×Dic3—32no—
407C22×Dic3—34no—
408#239—44no—
409#239—68no—
410#239—128no—
411D3×Q8—64no—
412#237—68no—
413#237—128no—
414C2×D12—34no—
415C2×D12—32no—
416C2×D12—31no—
417C2×D12—31no—
418C2×D12—34no—
419C2×D12—61no—
420C2×D12C22×D312yes—
421C2×D12C22×D312yes—
422C2×D12C22×D314yes—
423C2×D12C22×D312yes—
424C2×C4×D3—32no—
425C2×C4×D3—32no—
426C2×C4×D3—34no—
427C2×C4×D3—32no—
428C2×C4×D3—32no—
429C2×C4×D3—34no—
430C2×C4×D3—34no—
431C2×C4×D3—34no—
432C2×C4×D3—62no—
433C2×C4×D3—64no—
434C2×C4×D3C22×D311yescharacteristic
435C2×C4×D3C22×D311yescharacteristic
436C2×C4×D3C22×D311yescharacteristic
437C2×C4×D3C22×D314yes—
438C2×Dic6—31no—
439C2×Dic6—31no—
440C2×Dic6—32no—
441C2×Dic6—32no—
442C2×Dic6—61no—
443C2×Dic6—64no—
444C2×Dic6C22×D311yescharacteristic
445C2×Dic6C22×D314yes—
446C2×Dic6C22×D311yescharacteristic
447C3×C4⋊C4—22no—
448C3×C4⋊C4—22no—
449C3×C4⋊C4—32no—
450C3×C4⋊C4—31no—
451C3×C4⋊C4—31no—
452C3×C4⋊C4—34no—
453C3×C4⋊C4—34no—
454C3×C4⋊C4—32no—
455C3×C4⋊C4C22×D312yes—
456C3×C4⋊C4C22×D312yes—
457C3×C4⋊C4C22×D312yes—
458C3×C4⋊C4C22×D312yes—
459C3×C22⋊C4—34no—
460C3×C22⋊C4—34no—
461C3×C42—21no—
462C3×C42—31no—
463C3×C42—31no—
464C3×C42—31no—
465C3×C42—32no—
466C3×C42—34no—
467C3×C42—32no—
468C3×C42C22×D311yescharacteristic
469C3×C42C22×D311yescharacteristic
470#217—34no—
471#217—34no—
472#217—34no—
473#217—34no—
474#217—32no—
475(C2×D3)⋊C4—34no—
476(C2×D3)⋊C4—32no—
477(C2×D3)⋊C4—34no—
478(C2×D3)⋊C4—34no—
479(C2×D3)⋊C4—34no—
480(C2×D3)⋊C4—32no—
481(C2×D3)⋊C4—32no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—32no—
485(C2×D3)⋊C4—32no—
486(C2×D3)⋊C4—32no—
487(C2×D3)⋊C4—32no—
488(C2×D3)⋊C4—32no—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—62no—
491(C2×D3)⋊C4—64no—
492(C2×D3)⋊C4C22×D314yes—
493(C2×D3)⋊C4C22×D314yes—
494C4⋊Dic3—31no—
495C4⋊Dic3—31no—
496C4⋊Dic3—31no—
497C4⋊Dic3—31no—
498C4⋊Dic3—34no—
499C4⋊Dic3—34no—
500C4⋊Dic3—32no—
501C4⋊Dic3—32no—
502C4⋊Dic3—32no—
503C4⋊Dic3—61no—
504C4⋊Dic3—61no—
505C4⋊Dic3—64no—
506C4⋊Dic3C22×D311yescharacteristic
507C4⋊Dic3C22×D311yescharacteristic
508Dic3⋊C4—32no—
509Dic3⋊C4—32no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—32no—
513Dic3⋊C4—32no—
514Dic3⋊C4—32no—
515Dic3⋊C4—32no—
516Dic3⋊C4—32no—
517Dic3⋊C4—32no—
518Dic3⋊C4—32no—
519Dic3⋊C4—32no—
520Dic3⋊C4—32no—
521Dic3⋊C4—62no—
522Dic3⋊C4—64no—
523Dic3⋊C4C22×D312yes—
524Dic3⋊C4C22×D312yes—
525Dic3⋊C4C22×D314yes—
526Dic3⋊C4C22×D314yes—
527C4×Dic3—32no—
528C4×Dic3—32no—
529C4×Dic3—32no—
530C4×Dic3—32no—
531C4×Dic3—32no—
532C4×Dic3—32no—
533C4×Dic3—62no—
534C4×Dic3C22×D311yescharacteristic
535C4×Dic3C22×D312yes—
536C4×Dic3C22×D312yes—
537C4×Dic3C22×D311yescharacteristic
538C4×Dic3C22×D311yescharacteristic
539C4×Dic3C22×D314yes—
540C22×C32C2511yescharacteristic
541C2×C3⋊D3—22no—
542C2×C3⋊D3—22no—
543C2×C3⋊D3—22no—
544C2×C3×D3—21no—
545C2×C3×D3—21no—
546C2×C3×D3—24no—
547C2×C3×D3—24no—
548C2×C3×D3—24no—
549C2×C3×D3H(5,𝔽2)12yes—
550C32×C4—24no—
551C32×C4—21no—
552C32×C4C2×#4112yes—
553C32×C42−1+412yes—
554C3⋊Dic3—22no—
555C3⋊Dic3—22no—
556C3⋊Dic3—22no—
557C3×Dic3—21no—
558C3×Dic3—22no—
559C3×Dic3—22no—
560C3×Dic3—21no—
561C3×Dic3—22no—
562C3×Dic3—21no—
563C3×Dic3C2×#4114yes—
564C2×#41—32no—
565C2×#41—92no—
566C2×#41—94no—
567C22×Q8—91no—
568C4⋊Q8—34no—
569C4⋊Q8—32no—
570C4⋊Q8—32no—
571C4⋊Q8D3211yescharacteristic
572#127—31no—
573#127—92no—
574#126—92no—
575#126—94no—
576#125—91no—
577#125—92no—
578#124—32no—
579#124—94no—
580#124—92no—
581#124—91no—
582#124—94no—
583#124—92no—
584#123—94no—
585#123—92no—
586#123—94no—
587#123—94no—
588#123—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—91no—
592C22⋊Q8—94no—
593C22⋊Q8—94no—
594C22⋊Q8—92no—
595#121—32no—
596#121—32no—
597#121—91no—
598#121—94no—
599#121—92no—
600#121—94no—
601C4×Q8—32no—
602C4×Q8—32no—
603C4×Q8—31no—
604C4×Q8—31no—
605C4×Q8—92no—
606C4×Q8—91no—
607C4×Q8—92no—
608C4×Q8—91no—
609C4×Q8—91no—
610C4×D4—32no—
611C4×D4—32no—
612C4×D4—94no—
613C4×D4—92no—
614C4×D4—92no—
615C4×D4—94no—
616C4×D4—92no—
617C4×D4—94no—
618C4×D4—92no—
619C4×D4—92no—
620C4×D4—91no—
621#117—92no—
622#117—94no—
623C2×C4⋊C4—92no—
624C2×C4⋊C4—91no—
625C2×C4⋊C4—94no—
626C2×C4⋊C4—92no—
627C2×C42—31no—
628C2×C42—92no—
629C23×C3—31no—
630C23×C3—34no—
631C22×D3—32no—
632C22×D3—32no—
633C22×D3—62no—
634C22×D3C23×D314yes—
635C22×D3C23×D311yescharacteristic
636C3×Q8—34no—
637C3×Q8—42no—
638C3×Q8—42no—
639C3×Q8—62no—
640C3×Q8—82no—
641C3×Q8—124no—
642C3×D4—68no—
643C3×D4—64no—
644C3×D4—64no—
645C3×D4—122no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—24no—
650C2×C3×C4—32no—
651C2×C3×C4—31no—
652C2×C3×C4—32no—
653C2×C3×C4—31no—
654C2×C3×C4—31no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—62no—
658C2×C3×C4—62no—
659C2×C3×C4—62no—
660C2×C3×C4—124no—
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D314yes—
663C2×C3×C4C23×D311yescharacteristic
664C2×C3×C4C23×D314yes—
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D311yescharacteristic
668C2×C3×C4C23×D311yescharacteristic
669#67—64no—
670#67—68no—
671#67—124no—
672C2×Dic3—32no—
673C2×Dic3—32no—
674C2×Dic3—32no—
675C2×Dic3—32no—
676C2×Dic3—32no—
677C2×Dic3—32no—
678C2×Dic3—62no—
679C2×Dic3—62no—
680C2×Dic3—62no—
681C2×Dic3—64no—
682C2×Dic3—64no—
683C2×Dic3—68no—
684C2×Dic3—124no—
685C2×Dic3C23×D311yescharacteristic
686C2×Dic3C23×D312yes—
687C2×Dic3C23×D312yes—
688C2×Dic3C23×D311yescharacteristic
689C2×Dic3C23×D311yescharacteristic
690C2×Dic3C23×D312yes—
691C2×Dic3C23×D312yes—
692D12—28no—
693D12—24no—
694D12—24no—
695D12—42no—
696D12—64no—
697D12—68no—
698D12—64no—
699D12—62no—
700D12—62no—
701D12—124no—
702C4×D3—22no—
703C4×D3—22no—
704C4×D3—22no—
705C4×D3—44no—
706C4×D3—64no—
707C4×D3—68no—
708C4×D3—64no—
709C4×D3—64no—
710C4×D3—64no—
711C4×D3—124no—
712C4×D3—124no—
713C4×D3—124no—
714C4×D3—124no—
715C4×D3—244no—
716Dic6—22no—
717Dic6—44no—
718Dic6—64no—
719Dic6—62no—
720Dic6—62no—
721Dic6—64no—
722Dic6—122no—
723Dic6#23914yescomplemented
724C2×C32C22×#4111yescharacteristic
725C2×C32C2×H(5,𝔽2)11yescharacteristic
726C2×C32C2×2−1+411yescharacteristic
727C3⋊D3—42no—
728C3×D3—22no—
729C3×D3—44no—
730#41—124no—
731#41—188no—
732#41—368no—
733C2×Q8—31no—
734C2×Q8—31no—
735C2×Q8—34no—
736C2×Q8—92no—
737C2×Q8—91no—
738C2×Q8—184no—
739C2×Q8C2×D3212yes—
740C2×D4—32no—
741C2×D4—32no—
742C2×D4—34no—
743C2×D4—32no—
744C2×D4—94no—
745C2×D4—92no—
746C2×D4—94no—
747C2×D4—91no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—31no—
751C22×C4—34no—
752C22×C4—92no—
753C22×C4—92no—
754C22×C4—94no—
755C22×C4—94no—
756C22×C4—92no—
757C22×C4—94no—
758C4⋊C4—34no—
759C4⋊C4—32no—
760C4⋊C4—31no—
761C4⋊C4—31no—
762C4⋊C4—34no—
763C4⋊C4—32no—
764C4⋊C4—92no—
765C4⋊C4—92no—
766C4⋊C4—92no—
767C4⋊C4—92no—
768C4⋊C4—92no—
769C4⋊C4—92no—
770C4⋊C4—91no—
771C4⋊C4—94no—
772C4⋊C4—92no—
773C4⋊C4—91no—
774C4⋊C4—94no—
775C4⋊C4C2×D3212yes—
776C4⋊C4C2×D3212yes—
777C22⋊C4—34no—
778C22⋊C4—34no—
779C22⋊C4—92no—
780C22⋊C4—92no—
781C22⋊C4—92no—
782C22⋊C4—94no—
783C22⋊C4—92no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—92no—
788C22⋊C4—94no—
789C42—31no—
790C42—31no—
791C42—31no—
792C42—32no—
793C42—34no—
794C42—32no—
795C42—92no—
796C42—92no—
797C42—92no—
798C42C2×D3211yescharacteristic
799C22×C3—21no—
800C22×C3—32no—
801C22×C3—61no—
802C22×C3—61no—
803C22×C3—64no—
804C22×C3—64no—
805C22×C3—64no—
806C22×C3C24×D311yescharacteristic
807C22×C3C24×D311yescharacteristic
808C2×D3—21no—
809C2×D3—21no—
810C2×D3—24no—
811C2×D3—24no—
812C2×D3—24no—
813C2×D3—64no—
814C2×D3—62no—
815C2×D3—62no—
816C2×D3—62no—
817C2×D3—62no—
818C2×D3—62no—
819C2×D3—62no—
820C2×D3—122no—
821C2×D3—122no—
822C2×D3#100412yes—
823C3×C4—21no—
824C3×C4—24no—
825C3×C4—24no—
826C3×C4—21no—
827C3×C4—22no—
828C3×C4—22no—
829C3×C4—34no—
830C3×C4—44no—
831C3×C4—41no—
832C3×C4—62no—
833C3×C4—62no—
834C3×C4—61no—
835C3×C4—61no—
836C3×C4—62no—
837C3×C4—61no—
838C3×C4C2×#23912yes—
839C3×C4#100712yes—
840C3×C4D3×#4112yes—
841C3×C4#101012yes—
842Dic3—21no—
843Dic3—22no—
844Dic3—21no—
845Dic3—21no—
846Dic3—22no—
847Dic3—22no—
848Dic3—62no—
849Dic3—62no—
850Dic3—62no—
851Dic3—62no—
852Dic3—62no—
853Dic3—62no—
854Dic3—122no—
855Dic3—122no—
856Dic3—122no—
857Dic3C2×#23914yes—
858C32#352211yescharacteristic, complemented, Sylow
859C23—31no—
860C23—34no—
861C23—92no—
862Q8—34no—
863Q8—42no—
864Q8—62no—
865Q8—124no—
866Q8—184no—
867Q8—182no—
868D4—68no—
869D4—64no—
870D4—64no—
871D4—122no—
872D4—188no—
873D4—184no—
874D4—182no—
875D4—364no—
876C2×C4—32no—
877C2×C4—32no—
878C2×C4—31no—
879C2×C4—31no—
880C2×C4—31no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—62no—
884C2×C4—62no—
885C2×C4—62no—
886C2×C4—92no—
887C2×C4—92no—
888C2×C4—92no—
889C2×C4—124no—
890C2×C4—184no—
891C2×C4—188no—
892C2×C4—184no—
893C2×C4—184no—
894C2×C4—364no—
895C2×C4—364no—
896C2×C4C22×D3211yescharacteristic
897C2×C4C22×D3214yes—
898C2×C4C22×D3211yescharacteristic
899C2×C4C22×D3211yescharacteristic
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—62no—
904C2×C3—124no—
905C2×C3C2×#100411yescharacteristic
906C2×C3C22×#23911yescharacteristic
907C2×C3C2×#100711yescharacteristic
908C2×C3C2×D3×#4111yescharacteristic
909C2×C3C2×#101011yescharacteristic
910C2×C3D3×H(5,𝔽2)11yescharacteristic
911D3—22no—
912D3—44no—
913D3—124no—
914D3—122no—
915D3—122no—
916C22—32no—
917C22—61no—
918C22—61no—
919C22—64no—
920C22—64no—
921C22—64no—
922C22—182no—
923C22—182no—
924C22—182no—
925C22C23×D3211yescharacteristic
926C4—21no—
927C4—24no—
928C4—34no—
929C4—61no—
930C4—62no—
931C4—62no—
932C4—61no—
933C4—62no—
934C4—61no—
935C4—182no—
936C4—182no—
937C4—182no—
938C4#6431512yes—
939C4D3×#23912yes—
940C3—21no—
941C3#8622911yescharacteristic, complemented
942C3#8704311yescharacteristic, complemented
943C2—62no—
944C2—124no—
945C2—362no—
946C2D3×#100411yescharacteristic
947C2C2×#6431511yescharacteristic
948C2C2×D3×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
hypercenterC4⋊Q8D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596201C2semidirect
2. C3×#5725C2semidirect
3. C3×#5722C2semidirect
4. #10595383C2semidirect
5. #10595358C2semidirect
6. #10594566C2semidirect
7. #10594460C2semidirect
8. #10594426C2semidirect
9. #10594382C2semidirect
10. #10594373C2semidirect
11. #10594369C2semidirect
12. #10594361C2semidirect
13. #10594341C2semidirect
14. #10593951C2semidirect
15. #10593900C2semidirect
16. C4×D3×Dic6C2semidirect
17. #10593870C2semidirect
97. #5725D3semidirect
98. #5722D3semidirect
360. C3×Dic6#41semidirect
723. Dic6#239semidirect
858. C32#3522semidirect
941. C3#86229semidirect
942. C3#87043semidirect

Maximal subgroups

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

subgroupindex
#105962012
C3×#57252
C3×#57222
#105953832
#105953582
#105945662
#105944602
#105944262
#105943822
#105943732
#105943692
#105943612
#105943412
#105939512
#105939002
C4×D3×Dic62
#105938702
#870433
#862293