Finite Group Databasebeta

← #11904209

Subgroups — #11904209

Order 1152.

2294 conjugacy classes of subgroups.

The subgroup lattice has 937 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596203C211yesmaximal, characteristic, complemented
2C3×#5728C211yesmaximal, characteristic, complemented
3C3×#5727C211yesmaximal, characteristic, complemented
4#10595402C212yesmaximal, complemented
5#10595380C212yesmaximal, complemented
6#10595376C212yesmaximal, complemented
7D3×Q8×Dic3C212yesmaximal, complemented
8#10594557C212yesmaximal, complemented
9#10594449C214yesmaximal, complemented
10#10594402C214yesmaximal, complemented
11#10594397C212yesmaximal, complemented
12#10594381C212yesmaximal, complemented
13#10594360C212yesmaximal, complemented
14C4×#3799C211yesmaximal, characteristic, complemented
15#10593896C211yesmaximal, characteristic, complemented
16C4×#3795C211yesmaximal, characteristic, complemented
17#10593861C211yesmaximal, characteristic, complemented
18#86744—31nomaximal
19#86278—31nomaximal
20C2×C3×D3×Q8C2212yes—
21C2×#3799C2211yescharacteristic
22C2×#3796C2212yes—
23C2×#3795C2211yescharacteristic
24C32×C4⋊Q8C2211yescharacteristic
25#64156C2212yes—
26Q8×C3⋊Dic3C2212yes—
27#64107C2214yes—
28#64106C2212yes—
29#64101C2212yes—
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31C4×#634C2211yescharacteristic
32C3×#946C2212yes—
33C3×#946C2212yes—
34C3×Q8×Dic3C2212yes—
35C3×#897C2212yes—
36C3×#896C2214yes—
37C3×#893C2212yes—
38C3×#892C2212yes—
39C3×#890C2212yes—
40C3×#888C2212yes—
41C3×#887C2212yes—
42C3×C4×D12C2211yescharacteristic
43C3×C42×D3C2211yescharacteristic
44C3×#869C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46#63909C2212yes—
47#63907C2214yes—
48#63906C2214yes—
49#63904C2214yes—
50#63904C2212yes—
51C4×#626C2212yes—
52C4×#625C2212yes—
53#63894C2211yescharacteristic
54Dic3×D12C2211yescharacteristic
55#63891C2214yes—
56#63890C2214yes—
57#63890C2214yes—
58D3×C4⋊Dic3C2212yes—
59D3×C4⋊Dic3C2214yes—
60#63888C2214yes—
61C4×#624C2212yes—
62#63880C2214yes—
63#63879C2212yes—
64#63878C2214yes—
65#63877C2212yes—
66C4×D3×Dic3C2212yes—
67C4×D3×Dic3C2214yes—
68#63872C2212yes—
69#63871C2212yes—
70#63866C2212yes—
71#63862C2214yes—
72#63848C2214yes—
73#63846C2214yes—
74#63845C2214yes—
75#63844C2211yescharacteristic
76#63843C2212yes—
77#63843C2214yes—
78Dic3×Dic6C2211yescharacteristic
79Dic3×Dic6C2214yes—
80Dic3×Dic6C2212yes—
81#63841C2211yescharacteristic
82#63841C2211yescharacteristic
83#63836C2214yes—
84#63836C2212yes—
85C3×D4×Q8—31no—
86C3×#533—31no—
87#5817—32no—
88C2×Q8×Dic3—32no—
89#5732—31no—
90#5732—31no—
91#5732—32no—
92#5732—61no—
93#5728—32no—
94#5728D311yescharacteristic, complemented
95#5727D311yescharacteristic, complemented
96#5726—31no—
97#5721—31no—
98#5693—34no—
99#5642—32no—
100#5642—34no—
101#5641—32no—
102#5639—32no—
103#5633—32no—
104#5631—32no—
105#5624—32no—
106#5624—34no—
107#5580—32no—
108#5578—32no—
109C4×#239—32no—
110C4×#239—31no—
111C4×D3×Q8—32no—
112#5570—31no—
113#5555—32no—
114#5555—31no—
115C4×#237—32no—
116C4×#237—31no—
117#5528—34no—
118C4×#235—31no—
119C4×#235—31no—
120C2×C32×Q8C2312yes—
121C2×C4⋊(C3⋊D3)C2311yescharacteristic
122C2×C4×C3⋊D3C2312yes—
123C2×#634C2311yescharacteristic
124C3×D3×Q8—28no—
125C2×C3×D12C2311yescharacteristic
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×C4×D3C2314yes—
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×C4×D3C2312yes—
131C2×C3×Dic6C2312yes—
132C2×C3×Dic6C2314yes—
133C2×C3×Dic6C2311yescharacteristic
134C2×#626C2314yes—
135C2×#626C2312yes—
136C2×#625C2312yes—
137C2×#624C2312yes—
138C2×#624C2312yes—
139C2×D3×Dic3C2312yes—
140C2×D3×Dic3C2314yes—
141C2×D3×Dic3C2312yes—
142#3799—24no—
143#3796—28no—
144#3795—24no—
145C32×C4⋊C4C2312yes—
146C32×C4⋊C4C2312yes—
147C32×C42C2311yescharacteristic
148#3752C2312yes—
149#3752C2314yes—
150#3752C2314yes—
151C4⋊(C3⋊Dic3)C2311yescharacteristic
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153C4⋊(C3⋊Dic3)C2314yes—
154#3750C2312yes—
155C4×C3⋊Dic3C2312yes—
156C4×C3⋊Dic3C2314yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×(C2×D3)⋊C4C2314yes—
159C3×(C2×D3)⋊C4C2312yes—
160C3×C4⋊Dic3C2311yescharacteristic
161C3×C4⋊Dic3C2312yes—
162C3×C4⋊Dic3C2314yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2311yescharacteristic
165C3×Dic3⋊C4C2314yes—
166C3×Dic3⋊C4C2314yes—
167C3×Dic3⋊C4C2312yes—
168C3×C4×Dic3C2311yescharacteristic
169C3×C4×Dic3C2314yes—
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2311yescharacteristic
173#3724C2312yes—
174Dic3⋊Dic3C2312yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179#3722C2312yes—
180#3722C2314yes—
181(C2×D3)⋊Dic3C2312yes—
182(C2×D3)⋊Dic3C2312yes—
183(C2×D3)⋊Dic3C2312yes—
184Dic32C2312yes—
185Dic32C2312yes—
186Dic32C2312yes—
187Dic32C2312yes—
188Dic32C2314yes—
189#3482—91noSylow
190C22×C3×Q8—32no—
191C2×#239—32no—
192C2×#239—31no—
193C2×D3×Q8C2×D312yes—
194C2×#237—31no—
195C2×#237—32no—
196C2×#235—31no—
197C2×#235—31no—
198C3×C4⋊Q8—21no—
199C3×C4⋊Q8—32no—
200C3×C4⋊Q8—31no—
201C3×C4⋊Q8C2×D311yescharacteristic
202C3×C4⋊Q8C2×D311yescharacteristic
203C3×#125—32no—
204C3×C22⋊Q8—32no—
205C3×C22⋊Q8—32no—
206C3×C22⋊Q8—32no—
207C3×C22⋊Q8—34no—
208C3×C4×Q8—32no—
209C3×C4×Q8—32no—
210C3×C4×Q8—31no—
211C3×C4×D4—32no—
212C3×C4×D4—31no—
213C3×#117—32no—
214C2×C3×C42—31no—
215#947—32no—
216#947—32no—
217#947—34no—
218#947—62no—
219#946—32no—
220#946—34no—
221#946C2×D312yes—
222#946C2×D312yes—
223Q8×Dic3—32no—
224Q8×Dic3—32no—
225Q8×Dic3—34no—
226Q8×Dic3—32no—
227Q8×Dic3—32no—
228Q8×Dic3—34no—
229Q8×Dic3—31no—
230Q8×Dic3—62no—
231Q8×Dic3C2×D312yes—
232#944—32no—
233D4×Dic3—31no—
234#930—34no—
235#930—32no—
236C4×#67—32no—
237C4×#67—32no—
238C4×#67—32no—
239C4×#67—34no—
240C4×#67—32no—
241C4×#67—32no—
242#926—31no—
243#926—31no—
244C2×C4⋊Dic3—32no—
245C2×C4⋊Dic3—34no—
246C2×C4×Dic3—32no—
247C2×C4×Dic3—34no—
248#898—34no—
249#898—34no—
250#898—34no—
251#898—34no—
252#898—34no—
253#898—64no—
254#897—32no—
255#897—32no—
256#897—32no—
257#897—62no—
258#897C2×D312yes—
259#896—34no—
260#896C2×D314yes—
261#895—32no—
262#894—34no—
263#894—34no—
264#893—34no—
265#893—32no—
266#893—31no—
267#893C2×D312yes—
268#892—31no—
269#892—31no—
270#892—32no—
271#892—32no—
272#892—34no—
273#892—32no—
274#892—34no—
275#892—62no—
276#892C2×D312yes—
277D3×C4⋊C4—32no—
278D3×C4⋊C4—34no—
279#890—32no—
280#890—34no—
281#890—32no—
282#890—34no—
283#890C2×D312yes—
284#889—34no—
285#889—34no—
286#888C2×D312yes—
287#887—32no—
288#887—34no—
289#887—31no—
290#887C2×D312yes—
291#886—34no—
292#886—34no—
293#886—34no—
294#885—34no—
295#884—34no—
296#883—34no—
297#67⋊C4—32no—
298#67⋊C4—34no—
299#879—34no—
300#877—34no—
301#877—32no—
302C4×D12—31no—
303C4×D12—32no—
304C4×D12—31no—
305C4×D12—31no—
306C4×D12—34no—
307C4×D12—31no—
308C4×D12—61no—
309C4×D12C2×D311yescharacteristic
310#872—32no—
311#872—32no—
312#872—34no—
313C42×D3—32no—
314C42×D3—34no—
315C42×D3—32no—
316C42×D3—32no—
317C42×D3C2×D311yescharacteristic
318#869—32no—
319#869C2×D311yescharacteristic
320C4×Dic6—31no—
321C4×Dic6—32no—
322C4×Dic6—34no—
323C4×Dic6—31no—
324C4×Dic6—31no—
325C4×Dic6—31no—
326C4×Dic6—61no—
327C4×Dic6C2×D311yescharacteristic
328C22×C3⋊D3C2412yes—
329C22×C3×D3C2411yescharacteristic
330C22×C3×D3C2412yes—
331C32×Q8—24no—
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—
341#634—22no—
342C2×C3×Dic3C2411yescharacteristic
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2411yescharacteristic
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2414yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2411yescharacteristic
349C3×D12#4114yescomplemented
350C3×C4×D3—22no—
351C3×C4×D3—22no—
352C3×C4×D3—24no—
353C3×C4×D3—28no—
354C3×C4×D3—22no—
355C3×Dic6—24no—
356C3×Dic6—28no—
357C3×Dic6#4114yescomplemented
358#626—28no—
359#626—24no—
360#625—24no—
361#624—24no—
362#624—24no—
363D3×Dic3—24no—
364D3×Dic3—28no—
365D3×Dic3—24no—
366#557—91no—
367#556—92no—
368#556—91no—
369#552—92no—
370#552—94no—
371D4×Q8—31no—
372#548—92no—
373#547—92no—
374#547—91no—
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—
383C2×C3×Q8—22no—
384C2×C3×Q8—31no—
385C2×C3×Q8—32no—
386C2×C3×Q8—34no—
387C2×C3×Q8—68no—
388C2×C3×Q8C22×D312yes—
389C2×C3×Q8C22×D312yes—
390C2×C3×D4—31no—
391C22×C3×C4—34no—
392C22×C3×C4—32no—
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—31no—
396C2×#67—32no—
397C2×#67—32no—
398C2×#67—34no—
399C2×#67—32no—
400C22×Dic3—34no—
401C22×Dic3—32no—
402C22×Dic3—32no—
403#239—64no—
404#239—68no—
405D3×Q8—28no—
406#237—68no—
407#237—64no—
408#235—64no—
409#235—64no—
410C2×D12—34no—
411C2×D12—32no—
412C2×D12—31no—
413C2×D12—31no—
414C2×D12—61no—
415C2×D12C22×D311yescharacteristic
416C2×C4×D3—32no—
417C2×C4×D3—32no—
418C2×C4×D3—34no—
419C2×C4×D3—32no—
420C2×C4×D3—32no—
421C2×C4×D3—32no—
422C2×C4×D3—32no—
423C2×C4×D3—32no—
424C2×C4×D3—32no—
425C2×C4×D3—62no—
426C2×C4×D3C22×D312yes—
427C2×C4×D3C22×D314yes—
428C2×C4×D3C22×D311yescharacteristic
429C2×C4×D3C22×D311yescharacteristic
430C2×C4×D3C22×D311yescharacteristic
431C2×Dic6—31no—
432C2×Dic6—31no—
433C2×Dic6—61no—
434C2×Dic6C22×D312yes—
435C2×Dic6C22×D314yes—
436C2×Dic6C22×D311yescharacteristic
437C3×C4⋊C4—22no—
438C3×C4⋊C4—22no—
439C3×C4⋊C4—32no—
440C3×C4⋊C4—34no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—32no—
443C3×C4⋊C4—34no—
444C3×C4⋊C4—32no—
445C3×C4⋊C4—31no—
446C3×C4⋊C4—34no—
447C3×C4⋊C4C22×D312yes—
448C3×C4⋊C4C22×D312yes—
449C3×C4⋊C4C22×D312yes—
450C3×C4⋊C4C22×D312yes—
451C3×C22⋊C4—32no—
452C3×C22⋊C4—34no—
453C3×C22⋊C4—34no—
454C3×C42—21no—
455C3×C42—32no—
456C3×C42—31no—
457C3×C42—31no—
458C3×C42—34no—
459C3×C42—31no—
460C3×C42C22×D311yescharacteristic
461C3×C42C22×D311yescharacteristic
462#217—32no—
463#217—32no—
464#217—32no—
465(C2×D3)⋊C4—32no—
466(C2×D3)⋊C4—32no—
467(C2×D3)⋊C4—32no—
468(C2×D3)⋊C4—32no—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—34no—
471(C2×D3)⋊C4—32no—
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4—34no—
474(C2×D3)⋊C4—32no—
475(C2×D3)⋊C4—34no—
476(C2×D3)⋊C4—32no—
477(C2×D3)⋊C4—34no—
478(C2×D3)⋊C4—62no—
479(C2×D3)⋊C4—64no—
480(C2×D3)⋊C4—64no—
481(C2×D3)⋊C4C22×D312yes—
482(C2×D3)⋊C4C22×D314yes—
483(C2×D3)⋊C4C22×D314yes—
484C4⋊Dic3—31no—
485C4⋊Dic3—31no—
486C4⋊Dic3—31no—
487C4⋊Dic3—34no—
488C4⋊Dic3—31no—
489C4⋊Dic3—34no—
490C4⋊Dic3—34no—
491C4⋊Dic3—34no—
492C4⋊Dic3—34no—
493C4⋊Dic3—32no—
494C4⋊Dic3—34no—
495C4⋊Dic3—61no—
496C4⋊Dic3—61no—
497C4⋊Dic3—64no—
498C4⋊Dic3C22×D311yescharacteristic
499C4⋊Dic3C22×D311yescharacteristic
500C4⋊Dic3C22×D312yes—
501C4⋊Dic3C22×D312yes—
502C4⋊Dic3C22×D314yes—
503Dic3⋊C4—32no—
504Dic3⋊C4—32no—
505Dic3⋊C4—32no—
506Dic3⋊C4—32no—
507Dic3⋊C4—34no—
508Dic3⋊C4—34no—
509Dic3⋊C4—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—32no—
512Dic3⋊C4—62no—
513Dic3⋊C4C22×D312yes—
514Dic3⋊C4C22×D314yes—
515Dic3⋊C4C22×D314yes—
516C4×Dic3—32no—
517C4×Dic3—32no—
518C4×Dic3—34no—
519C4×Dic3—34no—
520C4×Dic3—32no—
521C4×Dic3—32no—
522C4×Dic3—34no—
523C4×Dic3—32no—
524C4×Dic3—32no—
525C4×Dic3—32no—
526C4×Dic3—34no—
527C4×Dic3—32no—
528C4×Dic3—32no—
529C4×Dic3—32no—
530C4×Dic3—62no—
531C4×Dic3—64no—
532C4×Dic3C22×D312yes—
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—22no—
542C2×C3×D3—22no—
543C2×C3×D3—21no—
544C2×C3×D3—21no—
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×Dic3—21no—
555C3×Dic3—24no—
556C3×Dic3—21no—
557C3×Dic3—22no—
558C3×Dic3—22no—
559C3×Dic3C2×#4114yes—
560C3×Dic32−1+412yes—
561C2×#41—91no—
562C2×#41—91no—
563C2×#41—92no—
564C22×Q8—32no—
565C4⋊Q8—32no—
566C4⋊Q8—31no—
567C4⋊Q8—92no—
568C4⋊Q8D3211yescharacteristic
569#126—94no—
570#126—94no—
571#126—94no—
572#125—32no—
573#125—94no—
574#125—92no—
575#125—94no—
576#124—94no—
577#124—92no—
578#123—94no—
579#123—94no—
580#123—94no—
581C22⋊Q8—32no—
582C22⋊Q8—32no—
583C22⋊Q8—34no—
584C22⋊Q8—32no—
585C22⋊Q8—92no—
586C22⋊Q8—94no—
587C22⋊Q8—92no—
588#121—94no—
589#121—92no—
590C4×Q8—32no—
591C4×Q8—32no—
592C4×Q8—31no—
593C4×Q8—91no—
594C4×Q8—91no—
595C4×Q8—94no—
596C4×Q8—92no—
597C4×Q8—92no—
598C4×Q8—94no—
599C4×Q8—92no—
600C4×Q8—91no—
601C4×D4—32no—
602C4×D4—31no—
603C4×D4—94no—
604C4×D4—91no—
605C4×D4—92no—
606C4×D4—91no—
607C4×D4—92no—
608C4×D4—92no—
609C4×D4—94no—
610C4×D4—92no—
611C4×D4—91no—
612#117—32no—
613#117—92no—
614#117—92no—
615#117—94no—
616#117—94no—
617#117—91no—
618#117—91no—
619#117—92no—
620C2×C4⋊C4—92no—
621C2×C4⋊C4—94no—
622C2×C42—31no—
623C2×C42—92no—
624C2×C42—92no—
625C2×C42—94no—
626C23×C3—32no—
627C23×C3—31no—
628C22×D3—32no—
629C22×D3—32no—
630C22×D3—62no—
631C22×D3C23×D311yescharacteristic
632C22×D3C23×D312yes—
633C3×Q8—24no—
634C3×Q8—24no—
635C3×Q8—34no—
636C3×Q8—44no—
637C3×Q8—68no—
638C3×Q8—64no—
639C3×D4—34no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—24no—
643C2×C3×C4—21no—
644C2×C3×C4—31no—
645C2×C3×C4—32no—
646C2×C3×C4—31no—
647C2×C3×C4—31no—
648C2×C3×C4—32no—
649C2×C3×C4—34no—
650C2×C3×C4—32no—
651C2×C3×C4—62no—
652C2×C3×C4—68no—
653C2×C3×C4—62no—
654C2×C3×C4—62no—
655C2×C3×C4—64no—
656C2×C3×C4C23×D314yes—
657C2×C3×C4C23×D314yes—
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664#67—68no—
665#67—64no—
666#67—64no—
667#67—64no—
668C2×Dic3—32no—
669C2×Dic3—32no—
670C2×Dic3—32no—
671C2×Dic3—32no—
672C2×Dic3—32no—
673C2×Dic3—32no—
674C2×Dic3—62no—
675C2×Dic3—62no—
676C2×Dic3—62no—
677C2×Dic3—68no—
678C2×Dic3—64no—
679C2×Dic3—64no—
680C2×Dic3C23×D311yescharacteristic
681C2×Dic3C23×D311yescharacteristic
682C2×Dic3C23×D312yes—
683C2×Dic3C23×D312yes—
684C2×Dic3C23×D314yes—
685C2×Dic3C23×D312yes—
686C2×Dic3C23×D311yescharacteristic
687D12—64no—
688D12—68no—
689D12—62no—
690D12—62no—
691D12—122no—
692D12#23914yescomplemented
693C4×D3—24no—
694C4×D3—22no—
695C4×D3—22no—
696C4×D3—28no—
697C4×D3—22no—
698C4×D3—64no—
699C4×D3—64no—
700C4×D3—64no—
701C4×D3—64no—
702C4×D3—68no—
703C4×D3—64no—
704C4×D3—64no—
705C4×D3—64no—
706C4×D3—64no—
707C4×D3—124no—
708Dic6—24no—
709Dic6—28no—
710Dic6—62no—
711Dic6—62no—
712Dic6—122no—
713Dic6#23714yescomplemented
714C2×C32C22×#4111yescharacteristic
715C2×C32C22×#4111yescharacteristic
716C2×C32C2×2−1+411yescharacteristic
717C3⋊D3—42no—
718C3×D3—24no—
719C3×D3—41no—
720#41—184no—
721#41—184no—
722#41—188no—
723C2×Q8—31no—
724C2×Q8—32no—
725C2×Q8—34no—
726C2×Q8—68no—
727C2×Q8—91no—
728C2×Q8C2×D3212yes—
729C2×D4—31no—
730C2×D4—94no—
731C2×D4—92no—
732C2×D4—92no—
733C2×D4—91no—
734C22×C4—31no—
735C22×C4—31no—
736C22×C4—31no—
737C22×C4—34no—
738C22×C4—32no—
739C22×C4—92no—
740C22×C4—92no—
741C22×C4—92no—
742C22×C4—92no—
743C22×C4—94no—
744C22×C4—92no—
745C4⋊C4—32no—
746C4⋊C4—34no—
747C4⋊C4—32no—
748C4⋊C4—31no—
749C4⋊C4—32no—
750C4⋊C4—31no—
751C4⋊C4—34no—
752C4⋊C4—34no—
753C4⋊C4—92no—
754C4⋊C4—94no—
755C4⋊C4—94no—
756C4⋊C4—92no—
757C4⋊C4—94no—
758C4⋊C4—94no—
759C4⋊C4—91no—
760C4⋊C4—94no—
761C4⋊C4—91no—
762C4⋊C4—92no—
763C4⋊C4C2×D3212yes—
764C4⋊C4C2×D3212yes—
765C22⋊C4—34no—
766C22⋊C4—34no—
767C22⋊C4—32no—
768C22⋊C4—92no—
769C22⋊C4—94no—
770C22⋊C4—92no—
771C22⋊C4—92no—
772C22⋊C4—92no—
773C22⋊C4—92no—
774C22⋊C4—94no—
775C22⋊C4—94no—
776C42—31no—
777C42—31no—
778C42—31no—
779C42—34no—
780C42—32no—
781C42—92no—
782C42—92no—
783C42—92no—
784C42—92no—
785C42—94no—
786C42—94no—
787C42—92no—
788C42C2×D3211yescharacteristic
789C22×C3—21no—
790C22×C3—34no—
791C22×C3—62no—
792C22×C3—62no—
793C22×C3—61no—
794C22×C3—61no—
795C22×C3—61no—
796C22×C3C24×D311yescharacteristic
797C22×C3C24×D311yescharacteristic
798C2×D3—22no—
799C2×D3—22no—
800C2×D3—21no—
801C2×D3—21no—
802C2×D3—21no—
803C2×D3—62no—
804C2×D3—62no—
805C2×D3—62no—
806C2×D3—62no—
807C2×D3—62no—
808C2×D3—62no—
809C2×D3—122no—
810C2×D3—122no—
811C2×D3—122no—
812C2×D3C2×#23914yes—
813C3×C4—24no—
814C3×C4—21no—
815C3×C4—24no—
816C3×C4—21no—
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—34no—
820C3×C4—32no—
821C3×C4—44no—
822C3×C4—41no—
823C3×C4—61no—
824C3×C4—61no—
825C3×C4—64no—
826C3×C4—62no—
827C3×C4—62no—
828C3×C4C2×#23712yes—
829C3×C4C2×#23912yes—
830C3×C4D3×#4112yes—
831C3×C4D3×#4112yes—
832Dic3—22no—
833Dic3—24no—
834Dic3—21no—
835Dic3—21no—
836Dic3—22no—
837Dic3—62no—
838Dic3—62no—
839Dic3—62no—
840Dic3—62no—
841Dic3—62no—
842Dic3—62no—
843Dic3—122no—
844Dic3—122no—
845Dic3—122no—
846Dic3C2×#23714yes—
847Dic3#100712yes—
848C32#348211yescharacteristic, complemented, Sylow
849C23—32no—
850C23—31no—
851C23—92no—
852Q8—24no—
853Q8—34no—
854Q8—68no—
855Q8—64no—
856Q8—182no—
857D4—34no—
858D4—184no—
859D4—188no—
860D4—184no—
861D4—182no—
862C2×C4—31no—
863C2×C4—32no—
864C2×C4—31no—
865C2×C4—31no—
866C2×C4—32no—
867C2×C4—34no—
868C2×C4—32no—
869C2×C4—68no—
870C2×C4—62no—
871C2×C4—64no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—92no—
875C2×C4—92no—
876C2×C4—92no—
877C2×C4—184no—
878C2×C4—184no—
879C2×C4—184no—
880C2×C4—184no—
881C2×C4—188no—
882C2×C4—184no—
883C2×C4C22×D3214yes—
884C2×C4C22×D3211yescharacteristic
885C2×C4C22×D3211yescharacteristic
886C2×C4C22×D3211yescharacteristic
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—64no—
891C2×C3—121no—
892C2×C3C22×#23711yescharacteristic
893C2×C3C22×#23911yescharacteristic
894C2×C3C2×#100711yescharacteristic
895C2×C3C2×D3×#4111yescharacteristic
896C2×C3C2×D3×#4111yescharacteristic
897C2×C3D3×2−1+411yescharacteristic
898D3—24no—
899D3—41no—
900D3—122no—
901D3—122no—
902D3—242no—
903C22—34no—
904C22—62no—
905C22—62no—
906C22—61no—
907C22—61no—
908C22—61no—
909C22—182no—
910C22—182no—
911C22—182no—
912C22C23×D3211yescharacteristic
913C4—24no—
914C4—21no—
915C4—34no—
916C4—32no—
917C4—61no—
918C4—62no—
919C4—61no—
920C4—64no—
921C4—62no—
922C4—182no—
923C4—182no—
924C4—182no—
925C4D3×#23712yes—
926C4D3×#23912yes—
927C3—21no—
928C3#8627811yescharacteristic, complemented
929C3#8674411yescharacteristic, complemented
930C2—64no—
931C2—121no—
932C2—362no—
933C2C2×D3×#23711yescharacteristic
934C2C2×D3×#23911yescharacteristic
935C2D3×#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. #10596203C2semidirect
2. C3×#5728C2semidirect
3. C3×#5727C2semidirect
4. #10595402C2semidirect
5. #10595380C2semidirect
6. #10595376C2semidirect
7. D3×Q8×Dic3C2semidirect
8. #10594557C2semidirect
9. #10594449C2semidirect
10. #10594402C2semidirect
11. #10594397C2semidirect
12. #10594381C2semidirect
13. #10594360C2semidirect
14. C4×#3799C2semidirect
15. #10593896C2semidirect
16. C4×#3795C2semidirect
17. #10593861C2semidirect
94. #5728D3semidirect
95. #5727D3semidirect
349. C3×D12#41semidirect
357. C3×Dic6#41semidirect
692. D12#239semidirect
713. Dic6#237semidirect
848. C32#3482semidirect
928. C3#86278semidirect
929. C3#86744semidirect

Maximal subgroups

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

subgroupindex
#105962032
C3×#57282
C3×#57272
#105954022
#105953802
#105953762
D3×Q8×Dic32
#105945572
#105944492
#105944022
#105943972
#105943812
#105943602
C4×#37992
#105938962
C4×#37952
#105938612
#867443
#862783