Finite Group Databasebeta

← #11904200

Subgroups — #11904200

Order 1152.

2288 conjugacy classes of subgroups.

The subgroup lattice has 933 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596192C211yesmaximal, characteristic, complemented
2C3×#5728C211yesmaximal, characteristic, complemented
3C3×#5726C211yesmaximal, characteristic, complemented
4#10595413C212yesmaximal, complemented
5Dic3×#239C212yesmaximal, complemented
6#10595367C212yesmaximal, complemented
7#10595357C212yesmaximal, complemented
8#10594551C212yesmaximal, complemented
9#10594525C212yesmaximal, complemented
10#10594429C214yesmaximal, complemented
11#10594426C212yesmaximal, complemented
12#10594404C214yesmaximal, complemented
13D3×#887C212yesmaximal, complemented
14#10593904C211yesmaximal, characteristic, complemented
15C4×#3795C211yesmaximal, characteristic, complemented
16C4×#3795C211yesmaximal, characteristic, complemented
17#10593863C211yesmaximal, characteristic, complemented
18#86676—31nomaximal
19#86278—31nomaximal
20C2×C3×#239C2212yes—
21C2×#3795C2211yescharacteristic
22C2×#3795C2211yescharacteristic
23C2×D3×Dic6C2212yes—
24C32×C4⋊Q8C2211yescharacteristic
25Q8×C3⋊Dic3C2212yes—
26#64153C2212yes—
27#64099C2212yes—
28#64098C2214yes—
29#64096C2212yes—
30C4×#634C2211yescharacteristic
31C4×#634C2211yescharacteristic
32C3×#946C2212yes—
33C3×#946C2212yes—
34C3×Q8×Dic3C2212yes—
35C3×#897C2212yes—
36C3×#895C2212yes—
37C3×#894C2214yes—
38C3×#892C2212yes—
39C3×D3×C4⋊C4C2212yes—
40C3×#890C2212yes—
41C3×#887C2212yes—
42C3×C4×D12C2211yescharacteristic
43C3×C4×D12C2211yescharacteristic
44C3×C42×D3C2211yescharacteristic
45C3×#869C2211yescharacteristic
46#63919C2212yes—
47#63915C2214yes—
48#63905C2214yes—
49C4×#625C2212yes—
50C4×#625C2212yes—
51#63899C2214yes—
52#63899C2214yes—
53#63898C2212yes—
54#63898C2214yes—
55Dic3×D12C2211yescharacteristic
56Dic3×D12C2214yes—
57Dic3×D12C2211yescharacteristic
58#63885C2214yes—
59#63884C2214yes—
60#63879C2212yes—
61#63879C2212yes—
62#63877C2214yes—
63#63877C2212yes—
64#63877C2212yes—
65D3×Dic3⋊C4C2214yes—
66C4×D3×Dic3C2212yes—
67C4×D3×Dic3C2214yes—
68C4×D3×Dic3C2212yes—
69#63863C2212yes—
70#63861C2214yes—
71#63861C2214yes—
72#63858C2214yes—
73#63857C2212yes—
74#63856C2212yes—
75#63847C2214yes—
76#63844C2211yescharacteristic
77#63844C2211yescharacteristic
78#63843C2212yes—
79#63841C2212yes—
80#63841C2214yes—
81#63841C2211yescharacteristic
82#63841C2211yescharacteristic
83#63838C2214yes—
84#63837C2214yes—
85C3×#547—31no—
86C3×#533—31no—
87Dic3×#41—32no—
88#5824—32no—
89#5732—31no—
90#5728D311yescharacteristic, complemented
91#5727—31no—
92#5726D311yescharacteristic, complemented
93#5721—31no—
94#5721—31no—
95#5721—61no—
96#5693—34no—
97#5650—34no—
98#5649—34no—
99#5641—32no—
100#5641—32no—
101#5639—32no—
102#5633—32no—
103#5631—32no—
104#5622—32no—
105#5600—32no—
106#5598—32no—
107#5580—32no—
108#5578—32no—
109C4×#239—32no—
110C4×D3×Q8—32no—
111#5542—31no—
112D4×Dic6—31no—
113C4×#237—31no—
114C4×#237—31no—
115#5528—34no—
116#5513—32no—
117C2×#887—32no—
118C4×#235—31no—
119C4×#235—31no—
120C2×C32×Q8C2312yes—
121C2×#634C2311yescharacteristic
122C2×#634C2311yescharacteristic
123C3×#239—28no—
124C2×C3×D12C2314yes—
125C2×C3×D12C2311yescharacteristic
126C2×C3×D12C2311yescharacteristic
127C2×C3×C4×D3C2314yes—
128C2×C3×C4×D3C2312yes—
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×C4×D3C2311yescharacteristic
131C2×C3×C4×D3C2311yescharacteristic
132C2×C3×C4×D3C2312yes—
133C2×C3×Dic6C2312yes—
134C2×#627C2314yes—
135C2×#625C2312yes—
136C2×#625C2312yes—
137C2×D3×Dic3C2314yes—
138C2×D3×Dic3C2312yes—
139C2×D3×Dic3C2312yes—
140C2×D3×Dic3C2312yes—
141C2×D3×Dic3C2312yes—
142#3795—24no—
143#3795—24no—
144D3×Dic6—28no—
145C32×C4⋊C4C2312yes—
146C32×C4⋊C4C2312yes—
147C32×C42C2311yescharacteristic
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150C4⋊(C3⋊Dic3)C2314yes—
151#3750C2312yes—
152#3750C2312yes—
153#3750C2314yes—
154#3750C2314yes—
155C4×C3⋊Dic3C2312yes—
156C4×C3⋊Dic3C2312yes—
157C4×C3⋊Dic3C2314yes—
158C3×(C2×D3)⋊C4C2314yes—
159C3×(C2×D3)⋊C4C2312yes—
160C3×(C2×D3)⋊C4C2312yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2314yes—
164C3×C4⋊Dic3C2311yescharacteristic
165C3×C4⋊Dic3C2312yes—
166C3×C4⋊Dic3C2311yescharacteristic
167C3×Dic3⋊C4C2314yes—
168C3×Dic3⋊C4C2314yes—
169C3×C4×Dic3C2311yescharacteristic
170C3×C4×Dic3C2314yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2311yescharacteristic
173#3724C2312yes—
174#3724C2312yes—
175#3724C2314yes—
176Dic3⋊Dic3C2314yes—
177(C2×D3)⋊Dic3C2312yes—
178(C2×D3)⋊Dic3C2314yes—
179(C2×D3)⋊Dic3C2314yes—
180(C2×D3)⋊Dic3C2312yes—
181(C2×D3)⋊Dic3C2312yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2312yes—
184Dic32C2312yes—
185Dic32C2312yes—
186Dic32C2312yes—
187Dic32C2314yes—
188Dic32C2312yes—
189#3482—91noSylow
190C2×C3×#41—32no—
191C2×#239C2×D312yes—
192C2×D3×Q8—32no—
193C2×#237—31no—
194C2×#237—31no—
195C2×#235—31no—
196C2×#235—31no—
197C22×Dic6—32no—
198C3×C4⋊Q8—21no—
199C3×C4⋊Q8—31no—
200C3×C4⋊Q8C2×D311yescharacteristic
201C3×C4⋊Q8C2×D311yescharacteristic
202C3×#125—32no—
203C3×#123—34no—
204C3×C22⋊Q8—32no—
205C3×C22⋊Q8—32no—
206C3×C22⋊Q8—32no—
207C3×#121—32no—
208C3×C4×Q8—32no—
209C3×C4×Q8—32no—
210C3×C4×D4—31no—
211C3×C4×D4—31no—
212C3×#117—32no—
213C2×C3×C4⋊C4—32no—
214C2×C3×C42—31no—
215#947—32no—
216#946—32no—
217#946C2×D312yes—
218#946C2×D312yes—
219Q8×Dic3—32no—
220Q8×Dic3—32no—
221Q8×Dic3—32no—
222Q8×Dic3—62no—
223Q8×Dic3C2×D312yes—
224#944—32no—
225#944—32no—
226#944—62no—
227#939—34no—
228#936—32no—
229#935—34no—
230D4×Dic3—34no—
231D4×Dic3—32no—
232D4×Dic3—34no—
233D4×Dic3—31no—
234D4×Dic3—31no—
235#929—34no—
236C4×#67—32no—
237C4×#67—32no—
238C4×#67—32no—
239C4×#67—32no—
240C4×#67—32no—
241C4×#67—32no—
242#926—31no—
243#926—31no—
244#926—32no—
245#926—34no—
246#924—32no—
247#924—32no—
248C2×Dic3⋊C4—34no—
249C2×C4×Dic3—34no—
250C2×C4×Dic3—32no—
251C2×C4×Dic3—32no—
252#898—34no—
253#898—34no—
254#898—34no—
255#897—32no—
256#897C2×D312yes—
257#896—34no—
258#896—34no—
259#895C2×D312yes—
260#894—34no—
261#894C2×D314yes—
262#893—34no—
263#893—32no—
264#892—34no—
265#892—31no—
266#892—32no—
267#892—31no—
268#892C2×D312yes—
269D3×C4⋊C4—34no—
270D3×C4⋊C4C2×D312yes—
271#890—32no—
272#890—32no—
273#890—62no—
274#890C2×D312yes—
275#889—34no—
276#889—34no—
277#889—34no—
278#889—34no—
279#889—64no—
280#888—32no—
281#888—32no—
282#887—32no—
283#887—32no—
284#887—32no—
285#887—34no—
286#887—34no—
287#887—34no—
288#887—31no—
289#887—31no—
290#887—62no—
291#887C2×D312yes—
292#885—34no—
293#885—34no—
294#884—34no—
295#883—34no—
296#67⋊C4—32no—
297#67⋊C4—32no—
298#879—34no—
299#879—34no—
300#879—34no—
301#878—34no—
302#878—34no—
303#877—34no—
304#877—32no—
305#877—32no—
306C4×D12—31no—
307C4×D12—31no—
308C4×D12—34no—
309C4×D12C2×D311yescharacteristic
310C4×D12C2×D311yescharacteristic
311#872—32no—
312#872—32no—
313#872—34no—
314C42×D3—32no—
315C42×D3—32no—
316C42×D3—34no—
317C42×D3C2×D311yescharacteristic
318#869C2×D311yescharacteristic
319C4×Dic6—31no—
320C4×Dic6—31no—
321C4×Dic6—31no—
322C4×Dic6—31no—
323C4×Dic6—31no—
324C4×Dic6—31no—
325C4×Dic6—34no—
326C4×Dic6—61no—
327C4×Dic6—61no—
328C22×C3×D3C2412yes—
329C22×C3×D3C2411yescharacteristic
330C22×C3×D3C2412yes—
331C32×Q8—24no—
332C2×C32×C4C2414yes—
333C2×C32×C4C2411yescharacteristic
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C3⋊Dic3C2412yes—
337C2×C3⋊Dic3C2412yes—
338C2×C3⋊Dic3C2412yes—
339C2×C3⋊Dic3C2412yes—
340#634—22no—
341#634#4114yescomplemented
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2411yescharacteristic
344C2×C3×Dic3C2411yescharacteristic
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2414yes—
347C2×C3×Dic3C2411yescharacteristic
348C3×D12—28no—
349C3×D12—22no—
350C3×D12#4114yescomplemented
351C3×C4×D3—28no—
352C3×C4×D3—24no—
353C3×C4×D3—22no—
354C3×C4×D3—22no—
355C3×C4×D3—24no—
356C3×C4×D3—22no—
357C3×Dic6—24no—
358#627—28no—
359#625—24no—
360#625—24no—
361D3×Dic3—24no—
362D3×Dic3—28no—
363D3×Dic3—24no—
364D3×Dic3—24no—
365D3×Dic3—24no—
366#557—91no—
367#556—91no—
368#556—92no—
369#552—92no—
370#552—94no—
371D4×Q8—91no—
372#548—92no—
373#547—31no—
374#547—92no—
375#533—31no—
376#533—92no—
377#529—94no—
378#529—92no—
379C4×#41—91no—
380C4×#41—91no—
381C4×#41—92no—
382C2×C4×Q8—92no—
383C3×#41—68no—
384C2×C3×Q8—22no—
385C2×C3×Q8—32no—
386C2×C3×Q8C22×D312yes—
387C2×C3×Q8C22×D312yes—
388C2×C3×D4—31no—
389C2×C3×D4—34no—
390C2×C3×D4—31no—
391C22×C3×C4—34no—
392C22×C3×C4—32no—
393C22×C3×C4—32no—
394C22×C3×C4—31no—
395C22×C3×C4—31no—
396C22×C3×C4—31no—
397C2×#67—32no—
398C2×#67—32no—
399C2×#67—32no—
400C2×#67—32no—
401C22×Dic3—32no—
402C22×Dic3—32no—
403C22×Dic3—32no—
404C22×Dic3—34no—
405C22×Dic3—32no—
406#239—28no—
407D3×Q8—68no—
408#237—64no—
409#237—64no—
410#235—64no—
411#235—64no—
412C2×D12C22×D311yescharacteristic
413C2×D12C22×D314yes—
414C2×D12C22×D311yescharacteristic
415C2×C4×D3—32no—
416C2×C4×D3—32no—
417C2×C4×D3—32no—
418C2×C4×D3—32no—
419C2×C4×D3—34no—
420C2×C4×D3C22×D312yes—
421C2×C4×D3C22×D312yes—
422C2×C4×D3C22×D314yes—
423C2×C4×D3C22×D311yescharacteristic
424C2×C4×D3C22×D311yescharacteristic
425C2×C4×D3C22×D311yescharacteristic
426C2×Dic6—31no—
427C2×Dic6—31no—
428C2×Dic6—31no—
429C2×Dic6—31no—
430C2×Dic6—34no—
431C2×Dic6—34no—
432C2×Dic6—61no—
433C2×Dic6—61no—
434C2×Dic6—68no—
435C2×Dic6C22×D312yes—
436C3×C4⋊C4—22no—
437C3×C4⋊C4—22no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—34no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—34no—
442C3×C4⋊C4—32no—
443C3×C4⋊C4—34no—
444C3×C4⋊C4—32no—
445C3×C4⋊C4C22×D312yes—
446C3×C4⋊C4C22×D312yes—
447C3×C4⋊C4C22×D312yes—
448C3×C4⋊C4C22×D312yes—
449C3×C22⋊C4—32no—
450C3×C22⋊C4—34no—
451C3×C22⋊C4—32no—
452C3×C22⋊C4—34no—
453C3×C42—21no—
454C3×C42—31no—
455C3×C42—31no—
456C3×C42—34no—
457C3×C42—31no—
458C3×C42C22×D311yescharacteristic
459C3×C42C22×D311yescharacteristic
460#217—34no—
461#217—32no—
462#217—32no—
463#217—34no—
464#217—32no—
465#217—32no—
466#217—34no—
467(C2×D3)⋊C4—32no—
468(C2×D3)⋊C4—32no—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—34no—
471(C2×D3)⋊C4—34no—
472(C2×D3)⋊C4—32no—
473(C2×D3)⋊C4—32no—
474(C2×D3)⋊C4C22×D312yes—
475(C2×D3)⋊C4C22×D312yes—
476(C2×D3)⋊C4C22×D314yes—
477(C2×D3)⋊C4C22×D314yes—
478C4⋊Dic3—31no—
479C4⋊Dic3—31no—
480C4⋊Dic3—31no—
481C4⋊Dic3—31no—
482C4⋊Dic3—34no—
483C4⋊Dic3—34no—
484C4⋊Dic3—34no—
485C4⋊Dic3—61no—
486C4⋊Dic3—61no—
487C4⋊Dic3—64no—
488C4⋊Dic3C22×D311yescharacteristic
489C4⋊Dic3C22×D311yescharacteristic
490C4⋊Dic3C22×D312yes—
491C4⋊Dic3C22×D312yes—
492C4⋊Dic3C22×D314yes—
493Dic3⋊C4—32no—
494Dic3⋊C4—32no—
495Dic3⋊C4—32no—
496Dic3⋊C4—32no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—32no—
502Dic3⋊C4—32no—
503Dic3⋊C4—34no—
504Dic3⋊C4—32no—
505Dic3⋊C4—34no—
506Dic3⋊C4—32no—
507Dic3⋊C4—34no—
508Dic3⋊C4—62no—
509Dic3⋊C4—62no—
510Dic3⋊C4—64no—
511Dic3⋊C4—64no—
512Dic3⋊C4C22×D314yes—
513Dic3⋊C4C22×D314yes—
514C4×Dic3—32no—
515C4×Dic3—32no—
516C4×Dic3—32no—
517C4×Dic3—32no—
518C4×Dic3—34no—
519C4×Dic3—34no—
520C4×Dic3—32no—
521C4×Dic3—32no—
522C4×Dic3—32no—
523C4×Dic3—32no—
524C4×Dic3—34no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—32no—
528C4×Dic3—34no—
529C4×Dic3—32no—
530C4×Dic3—62no—
531C4×Dic3—62no—
532C4×Dic3—64no—
533C4×Dic3C22×D311yescharacteristic
534C4×Dic3C22×D311yescharacteristic
535C4×Dic3C22×D311yescharacteristic
536C4×Dic3C22×D314yes—
537C22×C32C2511yescharacteristic
538C2×C3×D3—22no—
539C2×C3×D3—22no—
540C2×C3×D3—22no—
541C2×C3×D3—21no—
542C2×C3×D3—21no—
543C2×C3×D3—22no—
544C2×C3×D3—22no—
545C2×C3×D3—21no—
546C2×C3×D3C2×#4114yes—
547C32×C4—24no—
548C32×C4—21no—
549C32×C4C2×#4112yes—
550C32×C4C2×#4112yes—
551C3⋊Dic3—22no—
552C3⋊Dic3—22no—
553C3⋊Dic3—22no—
554C3⋊Dic3C2×#4114yes—
555C3×Dic3—21no—
556C3×Dic3—21no—
557C3×Dic3—24no—
558C3×Dic3—22no—
559C3×Dic3—22no—
560C3×Dic32−1+412yes—
561C2×#41—32no—
562C2×#41—91no—
563C2×#41—91no—
564C22×Q8—92no—
565C4⋊Q8—31no—
566C4⋊Q8—92no—
567C4⋊Q8—92no—
568C4⋊Q8D3211yescharacteristic
569#126—94no—
570#126—94no—
571#126—94no—
572#125—32no—
573#125—94no—
574#125—94no—
575#125—92no—
576#124—94no—
577#124—92no—
578#123—34no—
579#123—94no—
580#123—94no—
581C22⋊Q8—32no—
582C22⋊Q8—32no—
583C22⋊Q8—32no—
584C22⋊Q8—94no—
585C22⋊Q8—94no—
586C22⋊Q8—92no—
587C22⋊Q8—92no—
588#121—32no—
589#121—94no—
590C4×Q8—32no—
591C4×Q8—32no—
592C4×Q8—91no—
593C4×Q8—94no—
594C4×Q8—91no—
595C4×Q8—94no—
596C4×Q8—92no—
597C4×Q8—92no—
598C4×Q8—92no—
599C4×Q8—91no—
600C4×Q8—91no—
601C4×D4—31no—
602C4×D4—31no—
603C4×D4—91no—
604C4×D4—91no—
605C4×D4—94no—
606C4×D4—92no—
607C4×D4—92no—
608C4×D4—92no—
609C4×D4—94no—
610C4×D4—92no—
611C4×D4—92no—
612#117—32no—
613#117—92no—
614#117—92no—
615#117—94no—
616#117—91no—
617#117—94no—
618#117—91no—
619#117—92no—
620C2×C4⋊C4—32no—
621C2×C4⋊C4—94no—
622C2×C42—31no—
623C2×C42—92no—
624C2×C42—94no—
625C2×C42—92no—
626C23×C3—32no—
627C23×C3—32no—
628C23×C3—31no—
629C22×D3C23×D312yes—
630C22×D3C23×D311yescharacteristic
631C22×D3C23×D312yes—
632C3×Q8—24no—
633C3×Q8—24no—
634C3×Q8—44no—
635C3×Q8—64no—
636C3×D4—34no—
637C3×D4—68no—
638C3×D4—62no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—24no—
642C2×C3×C4—21no—
643C2×C3×C4—31no—
644C2×C3×C4—32no—
645C2×C3×C4—32no—
646C2×C3×C4—31no—
647C2×C3×C4—31no—
648C2×C3×C4—34no—
649C2×C3×C4—62no—
650C2×C3×C4—68no—
651C2×C3×C4—62no—
652C2×C3×C4—64no—
653C2×C3×C4—62no—
654C2×C3×C4—64no—
655C2×C3×C4C23×D314yes—
656C2×C3×C4C23×D314yes—
657C2×C3×C4C23×D311yescharacteristic
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663#67—64no—
664#67—64no—
665#67—64no—
666#67—64no—
667C2×Dic3—32no—
668C2×Dic3—32no—
669C2×Dic3—32no—
670C2×Dic3—32no—
671C2×Dic3—32no—
672C2×Dic3—32no—
673C2×Dic3—32no—
674C2×Dic3—32no—
675C2×Dic3—62no—
676C2×Dic3—62no—
677C2×Dic3—62no—
678C2×Dic3—62no—
679C2×Dic3—68no—
680C2×Dic3—64no—
681C2×Dic3—64no—
682C2×Dic3—64no—
683C2×Dic3—64no—
684C2×Dic3C23×D312yes—
685C2×Dic3C23×D311yescharacteristic
686C2×Dic3C23×D311yescharacteristic
687C2×Dic3C23×D312yes—
688C2×Dic3C23×D314yes—
689C2×Dic3C23×D311yescharacteristic
690D12—28no—
691D12—22no—
692D12#23714yescomplemented
693C4×D3—28no—
694C4×D3—24no—
695C4×D3—22no—
696C4×D3—22no—
697C4×D3—24no—
698C4×D3—22no—
699C4×D3—64no—
700C4×D3—68no—
701C4×D3—64no—
702C4×D3—64no—
703C4×D3—64no—
704Dic6—24no—
705Dic6—34no—
706Dic6—34no—
707Dic6—64no—
708Dic6—68no—
709Dic6—68no—
710Dic6—62no—
711Dic6—62no—
712Dic6—122no—
713C2×C32C22×#4111yescharacteristic
714C2×C32C22×#4111yescharacteristic
715C2×C32C2×2−1+411yescharacteristic
716C3×D3—24no—
717C3×D3—41no—
718C3×D3—42no—
719#41—68no—
720#41—184no—
721#41—184no—
722C2×Q8—32no—
723C2×Q8—94no—
724C2×Q8—91no—
725C2×Q8—91no—
726C2×Q8—188no—
727C2×Q8C2×D3212yes—
728C2×D4—31no—
729C2×D4—31no—
730C2×D4—34no—
731C2×D4—92no—
732C2×D4—92no—
733C22×C4—31no—
734C22×C4—31no—
735C22×C4—31no—
736C22×C4—34no—
737C22×C4—32no—
738C22×C4—32no—
739C22×C4—92no—
740C22×C4—92no—
741C22×C4—94no—
742C22×C4—92no—
743C22×C4—92no—
744C4⋊C4—31no—
745C4⋊C4—34no—
746C4⋊C4—34no—
747C4⋊C4—32no—
748C4⋊C4—31no—
749C4⋊C4—34no—
750C4⋊C4—32no—
751C4⋊C4—92no—
752C4⋊C4—94no—
753C4⋊C4—92no—
754C4⋊C4—94no—
755C4⋊C4—94no—
756C4⋊C4—91no—
757C4⋊C4—92no—
758C4⋊C4—91no—
759C4⋊C4—92no—
760C4⋊C4—94no—
761C4⋊C4—94no—
762C4⋊C4C2×D3212yes—
763C4⋊C4C2×D3212yes—
764C22⋊C4—34no—
765C22⋊C4—32no—
766C22⋊C4—32no—
767C22⋊C4—34no—
768C22⋊C4—92no—
769C22⋊C4—94no—
770C22⋊C4—92no—
771C22⋊C4—92no—
772C22⋊C4—94no—
773C22⋊C4—92no—
774C22⋊C4—94no—
775C42—31no—
776C42—31no—
777C42—31no—
778C42—34no—
779C42—92no—
780C42—92no—
781C42—92no—
782C42—92no—
783C42—94no—
784C42—92no—
785C42—94no—
786C42—92no—
787C42C2×D3211yescharacteristic
788C22×C3—21no—
789C22×C3—34no—
790C22×C3—62no—
791C22×C3—62no—
792C22×C3—61no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3—61no—
796C22×C3—62no—
797C22×C3—61no—
798C22×C3C24×D311yescharacteristic
799C22×C3C24×D311yescharacteristic
800C2×D3—22no—
801C2×D3—22no—
802C2×D3—22no—
803C2×D3—21no—
804C2×D3—21no—
805C2×D3—21no—
806C2×D3—22no—
807C2×D3—22no—
808C2×D3C2×#23714yes—
809C3×C4—24no—
810C3×C4—21no—
811C3×C4—24no—
812C3×C4—21no—
813C3×C4—22no—
814C3×C4—22no—
815C3×C4—32no—
816C3×C4—44no—
817C3×C4—41no—
818C3×C4—61no—
819C3×C4—62no—
820C3×C4—64no—
821C3×C4—61no—
822C3×C4—62no—
823C3×C4C2×#23712yes—
824C3×C4D3×#4112yes—
825C3×C4D3×#4112yes—
826C3×C4D3×#4112yes—
827Dic3—22no—
828Dic3—24no—
829Dic3—22no—
830Dic3—21no—
831Dic3—21no—
832Dic3—34no—
833Dic3—34no—
834Dic3—64no—
835Dic3—62no—
836Dic3—62no—
837Dic3—62no—
838Dic3—62no—
839Dic3—62no—
840Dic3—62no—
841Dic3—122no—
842Dic3—122no—
843Dic3—122no—
844Dic3#100712yes—
845C32#348211yescharacteristic, complemented, Sylow
846C23—32no—
847C23—31no—
848C23—32no—
849Q8—24no—
850Q8—64no—
851Q8—94no—
852Q8—188no—
853Q8—182no—
854D4—34no—
855D4—68no—
856D4—62no—
857D4—184no—
858D4—184no—
859C2×C4—31no—
860C2×C4—31no—
861C2×C4—31no—
862C2×C4—34no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—62no—
866C2×C4—68no—
867C2×C4—64no—
868C2×C4—62no—
869C2×C4—64no—
870C2×C4—62no—
871C2×C4—92no—
872C2×C4—92no—
873C2×C4—92no—
874C2×C4—92no—
875C2×C4—184no—
876C2×C4—184no—
877C2×C4—188no—
878C2×C4—184no—
879C2×C4—184no—
880C2×C4C22×D3214yes—
881C2×C4C22×D3211yescharacteristic
882C2×C4C22×D3211yescharacteristic
883C2×C4C22×D3211yescharacteristic
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—64no—
888C2×C3—122no—
889C2×C3—121no—
890C2×C3C22×#23711yescharacteristic
891C2×C3C2×#100711yescharacteristic
892C2×C3C2×D3×#4111yescharacteristic
893C2×C3C2×D3×#4111yescharacteristic
894C2×C3C2×D3×#4111yescharacteristic
895C2×C3D3×2−1+411yescharacteristic
896D3—24no—
897D3—41no—
898D3—42no—
899C22—34no—
900C22—62no—
901C22—62no—
902C22—62no—
903C22—61no—
904C22—61no—
905C22—62no—
906C22—61no—
907C22—62no—
908C22C23×D3211yescharacteristic
909C4—24no—
910C4—21no—
911C4—32no—
912C4—62no—
913C4—61no—
914C4—61no—
915C4—62no—
916C4—64no—
917C4—94no—
918C4—182no—
919C4—182no—
920C4—182no—
921C4D3×#23712yes—
922C4#6431912yes—
923C3—21no—
924C3#8627811yescharacteristic, complemented
925C3#8667611yescharacteristic, complemented
926C2—64no—
927C2—122no—
928C2—121no—
929C2C2×D3×#23711yescharacteristic
930C2C2×#6431911yescharacteristic
931C2D3×#100711yescharacteristic
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. #10596192C2semidirect
2. C3×#5728C2semidirect
3. C3×#5726C2semidirect
4. #10595413C2semidirect
5. Dic3×#239C2semidirect
6. #10595367C2semidirect
7. #10595357C2semidirect
8. #10594551C2semidirect
9. #10594525C2semidirect
10. #10594429C2semidirect
11. #10594426C2semidirect
12. #10594404C2semidirect
13. D3×#887C2semidirect
14. #10593904C2semidirect
15. C4×#3795C2semidirect
16. C4×#3795C2semidirect
17. #10593863C2semidirect
90. #5728D3semidirect
92. #5726D3semidirect
341. #634#41semidirect
350. C3×D12#41semidirect
692. D12#237semidirect
845. C32#3482semidirect
924. C3#86278semidirect
925. C3#86676semidirect

Maximal subgroups

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

subgroupindex
#105961922
C3×#57282
C3×#57262
#105954132
Dic3×#2392
#105953672
#105953572
#105945512
#105945252
#105944292
#105944262
#105944042
D3×#8872
#105939042
C4×#37952
#105938632
#866763
#862783