Finite Group Databasebeta

← #11904223

Subgroups — #11904223

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#10596055C211yesmaximal, characteristic, complemented
2C3×C4×#239C211yesmaximal, characteristic, complemented
3C3×#5567C211yesmaximal, characteristic, complemented
4#10595374C212yesmaximal, complemented
5#10595358C212yesmaximal, complemented
6#10594565C212yesmaximal, complemented
7#10594412C214yesmaximal, complemented
8#10594403C214yesmaximal, complemented
9#10594360C212yesmaximal, complemented
10#10593976C212yesmaximal, complemented
11C4×#3799C211yesmaximal, characteristic, complemented
12#10593920C212yesmaximal, complemented
13#10593899C212yesmaximal, complemented
14Dic6×D12C211yesmaximal, characteristic, complemented
15#10593896C211yesmaximal, characteristic, complemented
16C4×D3×Dic6C212yesmaximal, complemented
17#10593859C211yesmaximal, characteristic, complemented
18#87017—31nomaximal
19#85826—31nomaximal
20C2×C3×#239C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C2×#3796C2212yes—
23C2×D3×Dic6C2212yes—
24C32×C4×Q8C2211yescharacteristic
25#64155C2212yes—
26#64107C2214yes—
27#64101C2212yes—
28#64084C2212yes—
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30#64078C2211yescharacteristic
31C4×#634C2212yes—
32C3×Q8×Dic3C2211yescharacteristic
33C3×#944C2212yes—
34C3×#893C2211yescharacteristic
35C3×#893C2212yes—
36C3×#892C2211yescharacteristic
37C3×#892C2212yes—
38C3×#889C2214yes—
39C3×#887C2212yes—
40C3×C4×D12C2211yescharacteristic
41C3×C4×D12C2212yes—
42C3×C42×D3C2211yescharacteristic
43C3×C42×D3C2212yes—
44C3×#870C2212yes—
45C3×#869C2211yescharacteristic
46C3×C4×Dic6C2212yes—
47C3×C4×Dic6C2211yescharacteristic
48#63918C2212yes—
49C4×#627C2214yes—
50#63909C2212yes—
51#63904C2214yes—
52#63904C2212yes—
53C4×#626C2212yes—
54#63895C2214yes—
55#63894C2211yescharacteristic
56#63893C2214yes—
57Dic3×D12C2212yes—
58#63890C2214yes—
59D3×C4⋊Dic3C2212yes—
60#63886C2214yes—
61#63884C2214yes—
62C4×#624C2212yes—
63#63880C2214yes—
64#63878C2214yes—
65D3×Dic3⋊C4C2214yes—
66C4×D3×Dic3C2214yes—
67#63871C2212yes—
68#63869C2212yes—
69#63868C2214yes—
70#63862C2214yes—
71#63857C2212yes—
72#63857C2212yes—
73#63856C2212yes—
74#63852C2214yes—
75#63850C2214yes—
76#63846C2214yes—
77#63844C2212yes—
78Dic3×Dic6C2212yes—
79Dic3×Dic6C2211yescharacteristic
80#63841C2212yes—
81#63841C2211yescharacteristic
82#63837C2214yes—
83#63836C2214yes—
84#63836C2212yes—
85C3×#557—31no—
86C3×C4×#41—31no—
87#5824—32no—
88#5728—32no—
89#5728—31no—
90#5726—32no—
91#5726—31no—
92#5694—34no—
93#5694—32no—
94#5691—34no—
95#5691—32no—
96#5584—31no—
97#5584—31no—
98#5584—32no—
99#5584—61no—
100#5578—32no—
101#5576—32no—
102Q8×D12—31no—
103C4×#239—32no—
104C4×#239—31no—
105C4×#239D311yescharacteristic, complemented
106C4×D3×Q8—32no—
107#5567D311yescharacteristic, complemented
108#5555—31no—
109#5552—32no—
110#5541—32no—
111#5538—34no—
112D4×Dic6—31no—
113C4×#237—32no—
114#5533—32no—
115#5531—34no—
116#5479—32no—
117C4×#235—31no—
118#5470—31no—
119C2×C4×Dic6—32no—
120C2×C32×Q8C2311yescharacteristic
121C2×C4⋊(C3⋊D3)C2311yescharacteristic
122C2×C4×C3⋊D3C2312yes—
123C2×#634C2312yes—
124C3×#239—24no—
125C2×C3×D12C2312yes—
126C2×C3×D12C2311yescharacteristic
127C2×C3×C4×D3C2312yes—
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×C4×D3C2312yes—
131C2×C3×C4×D3C2312yes—
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×Dic6C2312yes—
134C2×C3×Dic6C2311yescharacteristic
135C2×#627C2314yes—
136C2×#626C2314yes—
137C2×#626C2312yes—
138C2×#624C2312yes—
139C2×#624C2312yes—
140C2×D3×Dic3C2314yes—
141C2×D3×Dic3C2314yes—
142#3799—24no—
143#3796—28no—
144D3×Dic6—28no—
145C32×C4⋊C4C2311yescharacteristic
146C32×C4⋊C4C2312yes—
147C32×C42C2312yes—
148C32×C42C2311yescharacteristic
149#3752C2312yes—
150#3752C2314yes—
151#3752C2314yes—
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153C4⋊(C3⋊Dic3)C2312yes—
154C4⋊(C3⋊Dic3)C2312yes—
155#3750C2314yes—
156C4×C3⋊Dic3C2314yes—
157C3×(C2×D3)⋊C4C2312yes—
158C3×(C2×D3)⋊C4C2312yes—
159C3×(C2×D3)⋊C4C2312yes—
160C3×C4⋊Dic3C2312yes—
161C3×C4⋊Dic3C2312yes—
162C3×C4⋊Dic3C2311yescharacteristic
163C3×C4⋊Dic3C2311yescharacteristic
164C3×C4⋊Dic3C2312yes—
165C3×Dic3⋊C4C2314yes—
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2314yes—
168C3×Dic3⋊C4C2314yes—
169C3×C4×Dic3C2314yes—
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2312yes—
173C3×C4×Dic3C2312yes—
174C3×C4×Dic3C2311yescharacteristic
175C3×C4×Dic3C2311yescharacteristic
176#3724C2314yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181#3722C2312yes—
182#3722C2314yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2314yes—
186Dic32C2314yes—
187Dic32C2312yes—
188Dic32C2312yes—
189#3482—91noSylow
190C2×C3×#41—31no—
191C2×#239—32no—
192C2×#239—31no—
193C2×#239C2×D311yescharacteristic
194C2×D3×Q8—32no—
195C2×#237—32no—
196C2×#235—31no—
197C22×Dic6—32no—
198C3×C4⋊Q8—32no—
199C3×C4⋊Q8—31no—
200C3×#125—34no—
201C3×#125—32no—
202C3×C4×Q8—21no—
203C3×C4×Q8—31no—
204C3×C4×Q8—32no—
205C3×C4×Q8—32no—
206C3×C4×Q8—31no—
207C3×C4×Q8C2×D311yescharacteristic
208C3×C4×Q8C2×D311yescharacteristic
209C3×C4×D4—31no—
210C3×C4×D4—32no—
211C3×C4×D4—31no—
212C3×C4×D4—32no—
213C3×#117—32no—
214C3×#117—31no—
215C2×C3×C42—32no—
216C2×C3×C42—31no—
217#946—32no—
218#946—32no—
219#946—32no—
220#946—32no—
221#946—62no—
222Q8×Dic3—32no—
223Q8×Dic3—31no—
224Q8×Dic3C2×D311yescharacteristic
225#944C2×D312yes—
226#939—34no—
227#935—34no—
228D4×Dic3—32no—
229#930—32no—
230#929—34no—
231C4×#67—32no—
232C4×#67—34no—
233C4×#67—32no—
234#926—32no—
235#926—31no—
236C2×C4⋊Dic3—32no—
237#924—32no—
238#924—32no—
239#924—32no—
240C2×Dic3⋊C4—34no—
241C2×C4×Dic3—34no—
242#898—34no—
243#898—34no—
244#898—34no—
245#898—34no—
246#898—64no—
247#897—32no—
248#897—32no—
249#897—32no—
250#897—34no—
251#897—34no—
252#896—34no—
253#895—34no—
254#895—32no—
255#894—34no—
256#894—34no—
257#894—34no—
258#893—32no—
259#893—34no—
260#893—31no—
261#893C2×D312yes—
262#893C2×D311yescharacteristic
263#892—32no—
264#892—31no—
265#892—32no—
266#892—32no—
267#892—34no—
268#892—34no—
269#892—32no—
270#892—62no—
271#892C2×D312yes—
272#892C2×D311yescharacteristic
273D3×C4⋊C4—34no—
274D3×C4⋊C4—32no—
275#890—34no—
276#890—32no—
277#889—34no—
278#889C2×D314yes—
279#888—32no—
280#887—34no—
281#887—32no—
282#887C2×D312yes—
283#886—34no—
284#885—34no—
285#67⋊C4—34no—
286#879—34no—
287#878—34no—
288#877—34no—
289#876—34no—
290#875—32no—
291#875—32no—
292#875—34no—
293#875—62no—
294C4×D12—32no—
295C4×D12—32no—
296C4×D12—31no—
297C4×D12—31no—
298C4×D12—34no—
299C4×D12—31no—
300C4×D12—61no—
301C4×D12C2×D312yes—
302C4×D12C2×D311yescharacteristic
303#872—32no—
304#872—34no—
305C42×D3—34no—
306C42×D3—32no—
307C42×D3—32no—
308C42×D3C2×D312yes—
309C42×D3C2×D311yescharacteristic
310#870—32no—
311#870C2×D312yes—
312#869—31no—
313#869—31no—
314#869—32no—
315#869—61no—
316#869C2×D311yescharacteristic
317C4×Dic6—31no—
318C4×Dic6—32no—
319C4×Dic6—32no—
320C4×Dic6—32no—
321C4×Dic6—32no—
322C4×Dic6—34no—
323C4×Dic6—34no—
324C4×Dic6—34no—
325C4×Dic6—62no—
326C4×Dic6C2×D312yes—
327C4×Dic6C2×D311yescharacteristic
328C22×C3⋊D3C2412yes—
329C22×C3×D3C2411yescharacteristic
330C22×C3×D3C2412yes—
331C32×Q8—22no—
332C2×C32×C4C2412yes—
333C2×C32×C4C2412yes—
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C3⋊Dic3C2412yes—
338C2×C3⋊Dic3C2414yes—
339C4⋊(C3⋊D3)—22no—
340C4×C3⋊D3—24no—
341#634—24no—
342C2×C3×Dic3C2411yescharacteristic
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2414yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2411yescharacteristic
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2411yescharacteristic
349C3×D12—24no—
350C3×D12#4114yescomplemented
351C3×C4×D3—24no—
352C3×C4×D3—24no—
353C3×C4×D3—22no—
354C3×C4×D3—22no—
355C3×C4×D3—24no—
356C3×C4×D3—22no—
357C3×Dic6—24no—
358C3×Dic6#4114yescomplemented
359#627—28no—
360#626—28no—
361#626—24no—
362#624—24no—
363#624—24no—
364D3×Dic3—28no—
365D3×Dic3—28no—
366#557—31no—
367#556—92no—
368#556—91no—
369#552—94no—
370#552—92no—
371D4×Q8—91no—
372#548—92no—
373#547—91no—
374#547—92no—
375#533—91no—
376#533—92no—
377#529—92no—
378#529—94no—
379C4×#41—31no—
380C4×#41—91no—
381C4×#41—92no—
382C2×C4×Q8—92no—
383C3×#41—64no—
384C2×C3×Q8—21no—
385C2×C3×Q8—31no—
386C2×C3×Q8—32no—
387C2×C3×Q8C22×D311yescharacteristic
388C2×C3×Q8C22×D311yescharacteristic
389C2×C3×D4—31no—
390C2×C3×D4—32no—
391C22×C3×C4—32no—
392C22×C3×C4—32no—
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—32no—
396C22×C3×C4—31no—
397C2×#67—34no—
398C2×#67—32no—
399C22×Dic3—34no—
400C22×Dic3—34no—
401#239—24no—
402#239—64no—
403#239—68no—
404D3×Q8—68no—
405#237—68no—
406#235—64no—
407C2×D12—32no—
408C2×D12—34no—
409C2×D12—31no—
410C2×D12—31no—
411C2×D12—61no—
412C2×D12C22×D312yes—
413C2×D12C22×D311yescharacteristic
414C2×C4×D3—34no—
415C2×C4×D3—34no—
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—62no—
423C2×C4×D3C22×D312yes—
424C2×C4×D3C22×D311yescharacteristic
425C2×C4×D3C22×D312yes—
426C2×C4×D3C22×D311yescharacteristic
427C2×C4×D3C22×D312yes—
428C2×C4×D3C22×D311yescharacteristic
429C2×Dic6—32no—
430C2×Dic6—32no—
431C2×Dic6—34no—
432C2×Dic6—34no—
433C2×Dic6—62no—
434C2×Dic6—68no—
435C2×Dic6C22×D312yes—
436C2×Dic6C22×D311yescharacteristic
437C3×C4⋊C4—21no—
438C3×C4⋊C4—22no—
439C3×C4⋊C4—34no—
440C3×C4⋊C4—32no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—32no—
443C3×C4⋊C4—34no—
444C3×C4⋊C4—32no—
445C3×C4⋊C4—32no—
446C3×C4⋊C4—31no—
447C3×C4⋊C4—34no—
448C3×C4⋊C4C22×D311yescharacteristic
449C3×C4⋊C4C22×D312yes—
450C3×C4⋊C4C22×D311yescharacteristic
451C3×C4⋊C4C22×D312yes—
452C3×C22⋊C4—32no—
453C3×C22⋊C4—32no—
454C3×C22⋊C4—32no—
455C3×C42—22no—
456C3×C42—21no—
457C3×C42—31no—
458C3×C42—31no—
459C3×C42—32no—
460C3×C42—32no—
461C3×C42—34no—
462C3×C42—32no—
463C3×C42—31no—
464C3×C42C22×D312yes—
465C3×C42C22×D312yes—
466C3×C42C22×D311yescharacteristic
467C3×C42C22×D311yescharacteristic
468#217—34no—
469#217—32no—
470#217—34no—
471(C2×D3)⋊C4—34no—
472(C2×D3)⋊C4—32no—
473(C2×D3)⋊C4—34no—
474(C2×D3)⋊C4—32no—
475(C2×D3)⋊C4—34no—
476(C2×D3)⋊C4—34no—
477(C2×D3)⋊C4—32no—
478(C2×D3)⋊C4—34no—
479(C2×D3)⋊C4—34no—
480(C2×D3)⋊C4—32no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—32no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—62no—
485(C2×D3)⋊C4—64no—
486(C2×D3)⋊C4—64no—
487(C2×D3)⋊C4C22×D312yes—
488(C2×D3)⋊C4C22×D312yes—
489(C2×D3)⋊C4C22×D312yes—
490C4⋊Dic3—31no—
491C4⋊Dic3—31no—
492C4⋊Dic3—32no—
493C4⋊Dic3—32no—
494C4⋊Dic3—32no—
495C4⋊Dic3—32no—
496C4⋊Dic3—32no—
497C4⋊Dic3—34no—
498C4⋊Dic3—34no—
499C4⋊Dic3—34no—
500C4⋊Dic3—61no—
501C4⋊Dic3—62no—
502C4⋊Dic3—62no—
503C4⋊Dic3C22×D312yes—
504C4⋊Dic3C22×D311yescharacteristic
505C4⋊Dic3C22×D311yescharacteristic
506C4⋊Dic3C22×D312yes—
507C4⋊Dic3C22×D312yes—
508Dic3⋊C4—34no—
509Dic3⋊C4—34no—
510Dic3⋊C4—32no—
511Dic3⋊C4—34no—
512Dic3⋊C4—34no—
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—64no—
517Dic3⋊C4C22×D314yes—
518Dic3⋊C4C22×D312yes—
519Dic3⋊C4C22×D314yes—
520Dic3⋊C4C22×D314yes—
521C4×Dic3—34no—
522C4×Dic3—34no—
523C4×Dic3—32no—
524C4×Dic3—34no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—34no—
528C4×Dic3—32no—
529C4×Dic3—64no—
530C4×Dic3C22×D312yes—
531C4×Dic3C22×D314yes—
532C4×Dic3C22×D312yes—
533C4×Dic3C22×D311yescharacteristic
534C4×Dic3C22×D311yescharacteristic
535C4×Dic3C22×D312yes—
536C4×Dic3C22×D311yescharacteristic
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—22no—
548C32×C4—22no—
549C32×C4—21no—
550C32×C4C2×#4112yes—
551C32×C4C2×#4112yes—
552C3⋊Dic3—22no—
553C3⋊Dic3—24no—
554C3×Dic3—24no—
555C3×Dic3—21no—
556C3×Dic3—22no—
557C3×Dic3—21no—
558C3×Dic3—22no—
559C3×Dic3C2×#4114yes—
560C3×Dic32−1+412yes—
561C2×#41—31no—
562C2×#41—91no—
563C2×#41—92no—
564C22×Q8—92no—
565C4⋊Q8—32no—
566C4⋊Q8—31no—
567C4⋊Q8—92no—
568C4⋊Q8—91no—
569#126—94no—
570#126—94no—
571#126—94no—
572#125—34no—
573#125—32no—
574#125—92no—
575#125—94no—
576#124—94no—
577#124—92no—
578#123—94no—
579#123—94no—
580#123—94no—
581C22⋊Q8—94no—
582C22⋊Q8—94no—
583C22⋊Q8—92no—
584C22⋊Q8—92no—
585C22⋊Q8—92no—
586C22⋊Q8—92no—
587C22⋊Q8—92no—
588#121—92no—
589#121—94no—
590C4×Q8—31no—
591C4×Q8—32no—
592C4×Q8—32no—
593C4×Q8—31no—
594C4×Q8—94no—
595C4×Q8—92no—
596C4×Q8—94no—
597C4×Q8—91no—
598C4×Q8—92no—
599C4×Q8—92no—
600C4×Q8D3211yescharacteristic
601C4×D4—31no—
602C4×D4—32no—
603C4×D4—31no—
604C4×D4—32no—
605C4×D4—94no—
606C4×D4—91no—
607C4×D4—92no—
608C4×D4—92no—
609C4×D4—92no—
610C4×D4—94no—
611C4×D4—91no—
612#117—32no—
613#117—31no—
614#117—92no—
615#117—94no—
616#117—94no—
617#117—91no—
618#117—92no—
619#117—92no—
620C2×C4⋊C4—94no—
621C2×C4⋊C4—92no—
622C2×C42—32no—
623C2×C42—31no—
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—22no—
634C3×Q8—22no—
635C3×Q8—34no—
636C3×Q8—42no—
637C3×Q8—64no—
638C3×D4—34no—
639C3×D4—64no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—21no—
645C2×C3×C4—31no—
646C2×C3×C4—32no—
647C2×C3×C4—31no—
648C2×C3×C4—34no—
649C2×C3×C4—32no—
650C2×C3×C4—31no—
651C2×C3×C4—32no—
652C2×C3×C4—64no—
653C2×C3×C4—62no—
654C2×C3×C4—64no—
655C2×C3×C4—64no—
656C2×C3×C4—62no—
657C2×C3×C4—62no—
658C2×C3×C4C23×D312yes—
659C2×C3×C4C23×D312yes—
660C2×C3×C4C23×D312yes—
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D312yes—
663C2×C3×C4C23×D311yescharacteristic
664C2×C3×C4C23×D311yescharacteristic
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D311yescharacteristic
668#67—68no—
669#67—64no—
670C2×Dic3—32no—
671C2×Dic3—32no—
672C2×Dic3—34no—
673C2×Dic3—34no—
674C2×Dic3—62no—
675C2×Dic3—64no—
676C2×Dic3—68no—
677C2×Dic3—68no—
678C2×Dic3C23×D311yescharacteristic
679C2×Dic3C23×D312yes—
680C2×Dic3C23×D314yes—
681C2×Dic3C23×D311yescharacteristic
682C2×Dic3C23×D312yes—
683C2×Dic3C23×D312yes—
684C2×Dic3C23×D311yescharacteristic
685D12—24no—
686D12—64no—
687D12—68no—
688D12—62no—
689D12—62no—
690D12—122no—
691D12#23514yescomplemented
692C4×D3—24no—
693C4×D3—22no—
694C4×D3—24no—
695C4×D3—22no—
696C4×D3—24no—
697C4×D3—22no—
698C4×D3—64no—
699C4×D3—64no—
700C4×D3—68no—
701C4×D3—68no—
702C4×D3—64no—
703C4×D3—64no—
704C4×D3—64no—
705C4×D3—64no—
706C4×D3—124no—
707Dic6—24no—
708Dic6—68no—
709Dic6—64no—
710Dic6—64no—
711Dic6—68no—
712Dic6—124no—
713Dic6#23914yescomplemented
714C2×C32C22×#4111yescharacteristic
715C2×C32C22×#4111yescharacteristic
716C2×C32C2×2−1+411yescharacteristic
717C3⋊D3—42no—
718C3×D3—24no—
719C3×D3—41no—
720#41—64no—
721#41—184no—
722#41—188no—
723C2×Q8—31no—
724C2×Q8—32no—
725C2×Q8—94no—
726C2×Q8—92no—
727C2×Q8—188no—
728C2×Q8C2×D3211yescharacteristic
729C2×D4—31no—
730C2×D4—32no—
731C2×D4—94no—
732C2×D4—92no—
733C2×D4—91no—
734C22×C4—32no—
735C22×C4—32no—
736C22×C4—32no—
737C22×C4—31no—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—92no—
741C22×C4—92no—
742C22×C4—94no—
743C22×C4—94no—
744C22×C4—92no—
745C4⋊C4—34no—
746C4⋊C4—32no—
747C4⋊C4—32no—
748C4⋊C4—31no—
749C4⋊C4—32no—
750C4⋊C4—31no—
751C4⋊C4—34no—
752C4⋊C4—34no—
753C4⋊C4—32no—
754C4⋊C4—92no—
755C4⋊C4—94no—
756C4⋊C4—94no—
757C4⋊C4—94no—
758C4⋊C4—94no—
759C4⋊C4—91no—
760C4⋊C4—94no—
761C4⋊C4—92no—
762C4⋊C4—92no—
763C4⋊C4C2×D3211yescharacteristic
764C4⋊C4C2×D3212yes—
765C22⋊C4—32no—
766C22⋊C4—32no—
767C22⋊C4—32no—
768C22⋊C4—92no—
769C22⋊C4—94no—
770C22⋊C4—94no—
771C22⋊C4—92no—
772C22⋊C4—94no—
773C22⋊C4—92no—
774C22⋊C4—94no—
775C22⋊C4—94no—
776C42—31no—
777C42—31no—
778C42—31no—
779C42—32no—
780C42—32no—
781C42—32no—
782C42—34no—
783C42—92no—
784C42—92no—
785C42—94no—
786C42—94no—
787C42C2×D3211yescharacteristic
788C42C2×D3212yes—
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×#23514yes—
813C3×C4—22no—
814C3×C4—22no—
815C3×C4—22no—
816C3×C4—21no—
817C3×C4—22no—
818C3×C4—21no—
819C3×C4—22no—
820C3×C4—22no—
821C3×C4—34no—
822C3×C4—32no—
823C3×C4—42no—
824C3×C4—42no—
825C3×C4—41no—
826C3×C4—64no—
827C3×C4—62no—
828C3×C4—61no—
829C3×C4—61no—
830C3×C4—62no—
831C3×C4C2×#23512yes—
832C3×C4C2×#23912yes—
833C3×C4D3×#4112yes—
834C3×C4D3×#4112yes—
835Dic3—21no—
836Dic3—24no—
837Dic3—22no—
838Dic3—21no—
839Dic3—22no—
840Dic3—62no—
841Dic3—64no—
842Dic3—64no—
843Dic3—62no—
844Dic3—124no—
845Dic3—122no—
846Dic3C2×#23914yes—
847Dic3#101012yes—
848C32#348211yescharacteristic, complemented, Sylow
849C23—32no—
850C23—31no—
851C23—92no—
852Q8—22no—
853Q8—34no—
854Q8—64no—
855Q8—188no—
856Q8—184no—
857D4—34no—
858D4—64no—
859D4—184no—
860D4—188no—
861D4—182no—
862C2×C4—31no—
863C2×C4—32no—
864C2×C4—31no—
865C2×C4—31no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—34no—
869C2×C4—64no—
870C2×C4—62no—
871C2×C4—64no—
872C2×C4—62no—
873C2×C4—64no—
874C2×C4—62no—
875C2×C4—92no—
876C2×C4—94no—
877C2×C4—184no—
878C2×C4—184no—
879C2×C4—188no—
880C2×C4—188no—
881C2×C4—184no—
882C2×C4C22×D3212yes—
883C2×C4C22×D3211yescharacteristic
884C2×C4C22×D3212yes—
885C2×C4C22×D3211yescharacteristic
886C2×C4C22×D3211yescharacteristic
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—64no—
891C2×C3—121no—
892C2×C3C22×#23511yescharacteristic
893C2×C3C22×#23911yescharacteristic
894C2×C3C2×D3×#4111yescharacteristic
895C2×C3C2×D3×#4111yescharacteristic
896C2×C3C2×#101011yescharacteristic
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—22no—
914C4—22no—
915C4—21no—
916C4—34no—
917C4—32no—
918C4—61no—
919C4—64no—
920C4—61no—
921C4—62no—
922C4—62no—
923C4—182no—
924C4—184no—
925C4D3×#23512yes—
926C4D3×#23912yes—
927C3—21no—
928C3#8582611yescharacteristic, complemented
929C3#8701711yescharacteristic, complemented
930C2—64no—
931C2—121no—
932C2—362no—
933C2C2×D3×#23511yescharacteristic
934C2C2×D3×#23911yescharacteristic
935C2D3×#101011yescharacteristic
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. #10596055C2semidirect
2. C3×C4×#239C2semidirect
3. C3×#5567C2semidirect
4. #10595374C2semidirect
5. #10595358C2semidirect
6. #10594565C2semidirect
7. #10594412C2semidirect
8. #10594403C2semidirect
9. #10594360C2semidirect
10. #10593976C2semidirect
11. C4×#3799C2semidirect
12. #10593920C2semidirect
13. #10593899C2semidirect
14. Dic6×D12C2semidirect
15. #10593896C2semidirect
16. C4×D3×Dic6C2semidirect
17. #10593859C2semidirect
105. C4×#239D3semidirect
107. #5567D3semidirect
350. C3×D12#41semidirect
358. C3×Dic6#41semidirect
691. D12#235semidirect
713. Dic6#239semidirect
848. C32#3482semidirect
928. C3#85826semidirect
929. C3#87017semidirect

Maximal subgroups

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

subgroupindex
#105960552
C3×C4×#2392
C3×#55672
#105953742
#105953582
#105945652
#105944122
#105944032
#105943602
#105939762
C4×#37992
#105939202
#105938992
Dic6×D122
#105938962
C4×D3×Dic62
#105938592
#870173
#858263