Finite Group Databasebeta

← #11909819

Subgroups — #11909819

Order 1152.

2325 conjugacy classes of subgroups.

The subgroup lattice has 971 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595950C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic, complemented
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4#10594949C212yesmaximal, complemented
5#10594928C212yesmaximal, complemented
6#10594910C212yesmaximal, complemented
7#10594900C212yesmaximal, complemented
8#10594885C214yesmaximal, complemented
9#10593978C212yesmaximal, complemented
10#10593958C211yesmaximal, characteristic, complemented
11#10593951C211yesmaximal, characteristic, complemented
12#10593929C212yesmaximal, complemented
13#10593927C214yesmaximal, complemented
14#10593900C211yesmaximal, characteristic, complemented
15#10593889C212yesmaximal, complemented
16#10593876C212yesmaximal, complemented
17#10593856C211yesmaximal, characteristic, complemented
18#86229—31nomaximal
19#85821—31nomaximal
20C2×C3×#235C2212yes—
21C22×C3×Dic6C2211yescharacteristic
22C2×#3804C2214yes—
23C2×#3796C2212yes—
24C2×C32×C42C2211yescharacteristic
25#64139C2211yescharacteristic
26#64138C2212yes—
27C4×#638C2212yes—
28#64133C2211yescharacteristic
29#64085C2212yes—
30#64084C2211yescharacteristic
31C4×C4⋊(C3⋊D3)C2211yescharacteristic
32#64081C2212yes—
33#64079C2211yescharacteristic
34C4×#634C2211yescharacteristic
35C3×#930C2212yes—
36C3×#930C2212yes—
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×Dic3⋊C4C2212yes—
39C2×C3×C4×Dic3C2212yes—
40C3×#875C2212yes—
41C3×#874C2211yescharacteristic
42C3×C4×D12C2212yes—
43C3×C4×D12C2212yes—
44C3×#869C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46C3×C4×Dic6C2211yescharacteristic
47C3×C4×Dic6C2211yescharacteristic
48C3×C4×Dic6C2212yes—
49C3×C4×Dic6C2212yes—
50C3×C4×Dic6C2211yescharacteristic
51#63978C2214yes—
52Dic3×#67C2214yes—
53#63961C2214yes—
54#63919C2212yes—
55#63918C2212yes—
56#63916C2212yes—
57#63911C2212yes—
58#63907C2214yes—
59#63904C2214yes—
60#63900C2212yes—
61#63899C2214yes—
62#63898C2212yes—
63#63894C2212yes—
64Dic3×D12C2212yes—
65Dic3×D12C2212yes—
66#63888C2214yes—
67#63887C2214yes—
68#63886C2214yes—
69#63884C2214yes—
70#63880C2214yes—
71#63877C2214yes—
72D3×Dic3⋊C4C2214yes—
73#63871C2212yes—
74#63869C2212yes—
75#63863C2212yes—
76#63860C2212yes—
77#63859C2214yes—
78#63854C2214yes—
79#63852C2214yes—
80#63851C2214yes—
81#63850C2214yes—
82#63844C2212yes—
83#63843C2212yes—
84#63839C2214yes—
85C3×#532—31no—
86C2×C3×C4×Q8—31no—
87#5824—34no—
88#5817—32no—
89#5730—31no—
90#5722—31no—
91#5718—31no—
92#5713—31no—
93#5669—34no—
94#5611—32no—
95#5600—32no—
96#5598—32no—
97#5596—32no—
98#5585—31no—
99#5585—32no—
100#5582—34no—
101#5582—32no—
102#5579—32no—
103#5579—31no—
104#5577—31no—
105#5574—32no—
106Q8×Dic6—31no—
107#5561—32no—
108#5559—32no—
109#5546—32no—
110#5539—32no—
111#5507—34no—
112#5507—32no—
113#5479—31no—
114#5479—31no—
115#5479—32no—
116#5479—61no—
117#5477—32no—
118#5477D311yescharacteristic, complemented
119C2×C4×Dic6D311yescharacteristic, complemented
120C22×C32×C4C2311yescharacteristic
121C22×C32×C4C2311yescharacteristic
122C22×C32×C4C2311yescharacteristic
123C2×#638C2312yes—
124C2×C4⋊(C3⋊D3)C2311yescharacteristic
125C2×C4×C3⋊D3C2312yes—
126C2×#634C2311yescharacteristic
127C2×C3×#67C2314yes—
128C22×C3×Dic3C2312yes—
129C22×C3×Dic3C2312yes—
130C3×#235—44no—
131C2×C3×D12C2312yes—
132C2×C3×D12C2312yes—
133C2×C3×D12C2312yes—
134C2×C3×C4×D3C2314yes—
135C2×C3×Dic6—24no—
136C2×C3×Dic6C2311yescharacteristic
137C2×C3×Dic6C2312yes—
138C2×C3×Dic6C2312yes—
139C2×C3×Dic6C2311yescharacteristic
140C2×#627C2314yes—
141C2×#626C2314yes—
142C2×#626C2314yes—
143C2×#624C2314yes—
144#3804—48no—
145C2×D3×Dic3C2314yes—
146C2×D3×Dic3C2314yes—
147#3796—28no—
148C32×C42C2311yescharacteristic
149C32×C42C2311yescharacteristic
150C32×C42C2311yescharacteristic
151C32×C42C2311yescharacteristic
152#3757C2312yes—
153#3752C2312yes—
154#3752C2312yes—
155#3752C2312yes—
156#3752C2312yes—
157C4⋊(C3⋊Dic3)C2311yescharacteristic
158C4⋊(C3⋊Dic3)C2311yescharacteristic
159#3750C2312yes—
160#3750C2312yes—
161#3750C2312yes—
162#3750C2312yes—
163C4×C3⋊Dic3C2312yes—
164C3×(C2×D3)⋊C4C2314yes—
165C3×(C2×D3)⋊C4C2314yes—
166C3×C4⋊Dic3C2312yes—
167C3×C4⋊Dic3C2311yescharacteristic
168C3×C4⋊Dic3C2311yescharacteristic
169C3×C4⋊Dic3C2312yes—
170C3×C4⋊Dic3C2312yes—
171C3×Dic3⋊C4C2312yes—
172C3×Dic3⋊C4C2312yes—
173C3×Dic3⋊C4C2312yes—
174C3×Dic3⋊C4C2312yes—
175C3×C4×Dic3C2312yes—
176C3×C4×Dic3C2312yes—
177C3×C4×Dic3C2312yes—
178C3×C4×Dic3C2312yes—
179#3724C2314yes—
180#3724C2314yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2314yes—
183#3722C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2314yes—
188Dic32C2314yes—
189#3522—91noSylow
190C2×C3×#41—32no—
191C22×C3×Q8—31no—
192C2×#239—32no—
193C2×#237—34no—
194C2×#237—32no—
195C2×#235—34no—
196C2×#235C2×D312yes—
197C22×Dic6C2×D311yescharacteristic
198C3×C4⋊Q8—31no—
199C3×#127—31no—
200C3×#124—32no—
201C3×#121—32no—
202C3×#121—32no—
203C3×C4×Q8—31no—
204C3×C4×Q8—31no—
205C3×C4×Q8—32no—
206C3×C4×Q8—31no—
207C3×C4×Q8—32no—
208C3×C4×Q8—31no—
209C3×C4×D4—32no—
210C3×C4×D4—32no—
211C2×C3×C4⋊C4—32no—
212C2×C3×C4⋊C4—31no—
213C2×C3×C42—21no—
214C2×C3×C42—32no—
215C2×C3×C42C2×D311yescharacteristic
216C2×C3×C42C2×D311yescharacteristic
217#947—32no—
218#947—34no—
219#946—34no—
220#946—32no—
221#946—34no—
222Q8×Dic3—32no—
223#944—34no—
224#940—32no—
225#939—34no—
226#939—34no—
227#938—32no—
228#936—32no—
229#936—32no—
230#935—34no—
231#935—34no—
232D4×Dic3—34no—
233D4×Dic3—32no—
234D4×Dic3—32no—
235D4×Dic3—32no—
236#930—31no—
237#930—31no—
238#930—34no—
239#930—61no—
240#930C2×D312yes—
241#930C2×D312yes—
242#929—32no—
243#929—32no—
244#929—34no—
245#929—34no—
246#929—62no—
247C4×#67—32no—
248C4×#67—32no—
249C4×#67—34no—
250C4×#67—34no—
251C4×#67—62no—
252C2×C4⋊Dic3C2×D311yescharacteristic
253#924—31no—
254#924—31no—
255#924—34no—
256#924—61no—
257C2×Dic3⋊C4—34no—
258C2×Dic3⋊C4C2×D312yes—
259C2×C4×Dic3C2×D312yes—
260#897—32no—
261#896—34no—
262#896—34no—
263#896—34no—
264#895—34no—
265#895—32no—
266#894—34no—
267#894—34no—
268#894—34no—
269#893—32no—
270#893—34no—
271#893—32no—
272D3×C4⋊C4—34no—
273D3×C4⋊C4—32no—
274D3×C4⋊C4—32no—
275#890—32no—
276#888—34no—
277#888—32no—
278#888—32no—
279#888—32no—
280#887—32no—
281#887—32no—
282#885—34no—
283#885—34no—
284#883—34no—
285#67⋊C4—34no—
286#879—34no—
287#878—34no—
288#878—34no—
289#877—34no—
290#876—32no—
291#876—32no—
292#876—34no—
293#876—62no—
294#875—32no—
295#875—31no—
296#875—31no—
297#875—34no—
298#875—61no—
299#875C2×D312yes—
300#874—32no—
301#874C2×D311yescharacteristic
302C4×D12—32no—
303C4×D12—32no—
304C4×D12—31no—
305C4×D12—31no—
306C4×D12—34no—
307C4×D12—32no—
308C4×D12—61no—
309C4×D12C2×D312yes—
310C4×D12C2×D312yes—
311#872—32no—
312#872—32no—
313#872—34no—
314#872—62no—
315#870—31no—
316#870—31no—
317#870—32no—
318#870—61no—
319#869—32no—
320#869C2×D311yescharacteristic
321C4×Dic6—31no—
322C4×Dic6—31no—
323C4×Dic6—32no—
324C4×Dic6—61no—
325C4×Dic6C2×D312yes—
326C4×Dic6C2×D311yescharacteristic
327C4×Dic6C2×D311yescharacteristic
328C4×Dic6C2×D312yes—
329C4×Dic6C2×D311yescharacteristic
330C4×Dic6C2×D311yescharacteristic
331C23×C32C2411yescharacteristic
332C22×C3⋊D3C2412yes—
333C22×C3×D3C2414yes—
334C2×C32×C4—22no—
335C2×C32×C4—22no—
336C2×C32×C4—22no—
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C32×C4C2411yescharacteristic
341C2×C32×C4C2411yescharacteristic
342C2×C32×C4C2411yescharacteristic
343#638—24no—
344C2×C3⋊Dic3C2412yes—
345C2×C3⋊Dic3C2412yes—
346C2×C3⋊Dic3C2412yes—
347C4⋊(C3⋊D3)—22no—
348C4×C3⋊D3—24no—
349#634—22no—
350C3×#67—28no—
351C2×C3×Dic3—24no—
352C2×C3×Dic3—24no—
353C2×C3×Dic3C2414yes—
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2412yes—
356C2×C3×Dic3C2412yes—
357C2×C3×Dic3C2412yes—
358C3×D12—24no—
359C3×D12—24no—
360C3×D12—42no—
361C3×C4×D3—44no—
362C3×Dic6—22no—
363C3×Dic6—24no—
364C3×Dic6—42no—
365C3×Dic6#4114yescomplemented
366#627—44no—
367#626—28no—
368#626—44no—
369#624—44no—
370D3×Dic3—28no—
371D3×Dic3—44no—
372#559—92no—
373#559—91no—
374Q82—91no—
375#554—92no—
376#554—91no—
377#550—91no—
378#548—92no—
379#547—92no—
380#547—94no—
381#542—92no—
382#542—94no—
383#532—31no—
384#532—92no—
385#529—92no—
386#529—91no—
387#520—92no—
388C2×C4×Q8—31no—
389C3×#41—124no—
390C2×C3×Q8—31no—
391C2×C3×Q8—32no—
392C2×C3×Q8—31no—
393C2×C3×Q8—32no—
394C2×C3×Q8—64no—
395C2×C3×D4—34no—
396C2×C3×D4—32no—
397C2×C3×D4—32no—
398C2×C3×D4—32no—
399C22×C3×C4—21no—
400C22×C3×C4—21no—
401C22×C3×C4—21no—
402C22×C3×C4—32no—
403C22×C3×C4—32no—
404C22×C3×C4—34no—
405C22×C3×C4C22×D311yescharacteristic
406C22×C3×C4C22×D311yescharacteristic
407C22×C3×C4C22×D311yescharacteristic
408C22×C3×C4C22×D311yescharacteristic
409C22×C3×C4C22×D311yescharacteristic
410C22×C3×C4C22×D311yescharacteristic
411C2×#67—32no—
412C2×#67—32no—
413C2×#67—34no—
414C2×#67—34no—
415C2×#67—62no—
416C2×#67C22×D314yes—
417C22×Dic3—34no—
418C22×Dic3—34no—
419C22×Dic3C22×D312yes—
420C22×Dic3C22×D312yes—
421#239—68no—
422#237—68no—
423#237—128no—
424#235—44no—
425#235—128no—
426C2×D12—34no—
427C2×D12—31no—
428C2×D12—31no—
429C2×D12—34no—
430C2×D12—61no—
431C2×D12C22×D312yes—
432C2×D12C22×D312yes—
433C2×D12C22×D312yes—
434C2×C4×D3—34no—
435C2×C4×D3—32no—
436C2×C4×D3—32no—
437C2×C4×D3—34no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—62no—
441C2×C4×D3C22×D314yes—
442C2×Dic6—24no—
443C2×Dic6—31no—
444C2×Dic6—31no—
445C2×Dic6—34no—
446C2×Dic6—34no—
447C2×Dic6—61no—
448C2×Dic6C22×D312yes—
449C2×Dic6C22×D311yescharacteristic
450C2×Dic6C22×D312yes—
451C2×Dic6C22×D311yescharacteristic
452C3×C4⋊C4—32no—
453C3×C4⋊C4—32no—
454C3×C4⋊C4—32no—
455C3×C4⋊C4—31no—
456C3×C4⋊C4—32no—
457C3×C4⋊C4—31no—
458C3×C4⋊C4—32no—
459C3×C4⋊C4—32no—
460C3×C4⋊C4—32no—
461C3×C22⋊C4—34no—
462C3×C22⋊C4—34no—
463C3×C42—21no—
464C3×C42—21no—
465C3×C42—21no—
466C3×C42—21no—
467C3×C42—32no—
468C3×C42—32no—
469C3×C42—32no—
470C3×C42—32no—
471C3×C42C22×D311yescharacteristic
472C3×C42C22×D311yescharacteristic
473C3×C42C22×D311yescharacteristic
474C3×C42C22×D311yescharacteristic
475C3×C42C22×D311yescharacteristic
476C3×C42C22×D311yescharacteristic
477C3×C42C22×D311yescharacteristic
478C3×C42C22×D311yescharacteristic
479#217—32no—
480#217—32no—
481#217—34no—
482#217—34no—
483#217—34no—
484#217—34no—
485#217—62no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4—32no—
491(C2×D3)⋊C4—32no—
492(C2×D3)⋊C4—32no—
493(C2×D3)⋊C4—32no—
494(C2×D3)⋊C4—32no—
495(C2×D3)⋊C4—32no—
496(C2×D3)⋊C4—32no—
497(C2×D3)⋊C4—32no—
498(C2×D3)⋊C4—34no—
499(C2×D3)⋊C4—34no—
500(C2×D3)⋊C4—62no—
501(C2×D3)⋊C4—62no—
502(C2×D3)⋊C4—62no—
503(C2×D3)⋊C4—62no—
504(C2×D3)⋊C4C22×D314yes—
505(C2×D3)⋊C4C22×D314yes—
506C4⋊Dic3—31no—
507C4⋊Dic3—31no—
508C4⋊Dic3—31no—
509C4⋊Dic3—31no—
510C4⋊Dic3—34no—
511C4⋊Dic3—34no—
512C4⋊Dic3—61no—
513C4⋊Dic3—61no—
514C4⋊Dic3C22×D312yes—
515C4⋊Dic3C22×D312yes—
516C4⋊Dic3C22×D311yescharacteristic
517C4⋊Dic3C22×D311yescharacteristic
518C4⋊Dic3C22×D312yes—
519Dic3⋊C4—32no—
520Dic3⋊C4—32no—
521Dic3⋊C4—32no—
522Dic3⋊C4—32no—
523Dic3⋊C4—32no—
524Dic3⋊C4—32no—
525Dic3⋊C4—32no—
526Dic3⋊C4—32no—
527Dic3⋊C4—34no—
528Dic3⋊C4—34no—
529Dic3⋊C4—34no—
530Dic3⋊C4—34no—
531Dic3⋊C4—34no—
532Dic3⋊C4—34no—
533Dic3⋊C4—62no—
534Dic3⋊C4—62no—
535Dic3⋊C4—62no—
536Dic3⋊C4—62no—
537Dic3⋊C4C22×D312yes—
538Dic3⋊C4C22×D312yes—
539Dic3⋊C4C22×D312yes—
540Dic3⋊C4C22×D312yes—
541C4×Dic3—32no—
542C4×Dic3—32no—
543C4×Dic3—34no—
544C4×Dic3—34no—
545C4×Dic3—62no—
546C4×Dic3C22×D312yes—
547C4×Dic3C22×D312yes—
548C4×Dic3C22×D312yes—
549C4×Dic3C22×D312yes—
550C22×C32—21no—
551C22×C32—21no—
552C22×C32H(5,𝔽2)12yes—
553C22×C32C2511yescharacteristic
554C2×C3⋊D3—22no—
555C2×C3⋊D3—22no—
556C2×C3⋊D3—22no—
557C2×C3×D3—24no—
558C2×C3×D3—24no—
559C2×C3×D3—24no—
560C32×C4—21no—
561C32×C4—21no—
562C32×C4—21no—
563C32×C4—21no—
564C32×C4C2×#4112yes—
565C32×C42−1+412yes—
566C3⋊Dic3—22no—
567C3⋊Dic3—22no—
568C3⋊Dic3—22no—
569C3×Dic3—22no—
570C3×Dic3—22no—
571C3×Dic3—24no—
572C3×Dic3—22no—
573C3×Dic3C2×#4114yes—
574C2×#41—32no—
575C2×#41—94no—
576C2×#41—92no—
577C22×Q8—31no—
578C4⋊Q8—31no—
579C4⋊Q8—92no—
580C4⋊Q8—92no—
581C4⋊Q8—94no—
582#127—31no—
583#127—92no—
584#126—94no—
585#126—92no—
586#125—92no—
587#125—91no—
588#124—32no—
589#124—94no—
590#124—92no—
591#124—94no—
592#124—92no—
593#124—91no—
594#123—94no—
595#123—94no—
596#123—94no—
597#123—94no—
598#123—92no—
599C22⋊Q8—94no—
600C22⋊Q8—94no—
601C22⋊Q8—94no—
602C22⋊Q8—94no—
603C22⋊Q8—92no—
604C22⋊Q8—91no—
605#121—32no—
606#121—32no—
607#121—92no—
608#121—94no—
609#121—94no—
610#121—91no—
611C4×Q8—31no—
612C4×Q8—32no—
613C4×Q8—31no—
614C4×Q8—31no—
615C4×Q8—31no—
616C4×Q8—32no—
617C4×Q8—92no—
618C4×Q8—92no—
619C4×Q8—91no—
620C4×D4—32no—
621C4×D4—32no—
622C4×D4—94no—
623C4×D4—92no—
624C4×D4—92no—
625C4×D4—92no—
626C4×D4—94no—
627C4×D4—92no—
628C4×D4—94no—
629C4×D4—92no—
630C4×D4—91no—
631#117—94no—
632#117—92no—
633C2×C4⋊C4—32no—
634C2×C4⋊C4—31no—
635C2×C4⋊C4—92no—
636C2×C4⋊C4—94no—
637C2×C42—32no—
638C2×C42D3211yescharacteristic
639C23×C3—21no—
640C23×C3—34no—
641C23×C3C23×D311yescharacteristic
642C23×C3C23×D311yescharacteristic
643C22×D3—32no—
644C22×D3—32no—
645C22×D3—62no—
646C22×D3C23×D314yes—
647C3×Q8—34no—
648C3×Q8—64no—
649C3×Q8—62no—
650C3×Q8—122no—
651C3×D4—68no—
652C3×D4—64no—
653C3×D4—64no—
654C3×D4—122no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—32no—
668C2×C3×C4—34no—
669C2×C3×C4—32no—
670C2×C3×C4—32no—
671C2×C3×C4—32no—
672C2×C3×C4—42no—
673C2×C3×C4—42no—
674C2×C3×C4—42no—
675C2×C3×C4—64no—
676C2×C3×C4—64no—
677C2×C3×C4—124no—
678C2×C3×C4C23×D311yescharacteristic
679C2×C3×C4C23×D311yescharacteristic
680C2×C3×C4C23×D311yescharacteristic
681C2×C3×C4C23×D311yescharacteristic
682C2×C3×C4C23×D311yescharacteristic
683C2×C3×C4C23×D311yescharacteristic
684C2×C3×C4C23×D311yescharacteristic
685C2×C3×C4C23×D311yescharacteristic
686C2×C3×C4C23×D311yescharacteristic
687C2×C3×C4C23×D311yescharacteristic
688C2×C3×C4C23×D311yescharacteristic
689C2×C3×C4C23×D311yescharacteristic
690#67—28no—
691#67—64no—
692#67—64no—
693#67—68no—
694#67—124no—
695#67—124no—
696C2×Dic3—24no—
697C2×Dic3—24no—
698C2×Dic3—32no—
699C2×Dic3—32no—
700C2×Dic3—32no—
701C2×Dic3—32no—
702C2×Dic3—32no—
703C2×Dic3—32no—
704C2×Dic3—62no—
705C2×Dic3—62no—
706C2×Dic3—62no—
707C2×Dic3—68no—
708C2×Dic3—124no—
709C2×Dic3C23×D314yes—
710C2×Dic3C23×D312yes—
711C2×Dic3C23×D312yes—
712C2×Dic3C23×D312yes—
713C2×Dic3C23×D312yes—
714D12—24no—
715D12—24no—
716D12—42no—
717D12—68no—
718D12—62no—
719D12—62no—
720D12—122no—
721D12—124no—
722C4×D3—44no—
723C4×D3—68no—
724C4×D3—64no—
725C4×D3—64no—
726C4×D3—124no—
727C4×D3—124no—
728C4×D3—124no—
729C4×D3—124no—
730Dic6—22no—
731Dic6—24no—
732Dic6—42no—
733Dic6—62no—
734Dic6—62no—
735Dic6—122no—
736Dic6—124no—
737Dic6—124no—
738Dic6#23514yescomplemented
739C2×C32—22no—
740C2×C32C22×#4111yescharacteristic
741C2×C32C2×H(5,𝔽2)11yescharacteristic
742C2×C32C2×2−1+411yescharacteristic
743C3⋊D3—42no—
744C3×D3—44no—
745#41—124no—
746#41—188no—
747#41—368no—
748C2×Q8—31no—
749C2×Q8—32no—
750C2×Q8—31no—
751C2×Q8—32no—
752C2×Q8—64no—
753C2×Q8—94no—
754C2×Q8—91no—
755C2×D4—34no—
756C2×D4—32no—
757C2×D4—32no—
758C2×D4—32no—
759C2×D4—94no—
760C2×D4—94no—
761C2×D4—92no—
762C2×D4—91no—
763C22×C4—32no—
764C22×C4—32no—
765C22×C4—34no—
766C22×C4—94no—
767C22×C4—94no—
768C22×C4—94no—
769C22×C4—92no—
770C22×C4C2×D3211yescharacteristic
771C22×C4C2×D3211yescharacteristic
772C22×C4C2×D3211yescharacteristic
773C4⋊C4—32no—
774C4⋊C4—31no—
775C4⋊C4—32no—
776C4⋊C4—31no—
777C4⋊C4—32no—
778C4⋊C4—32no—
779C4⋊C4—32no—
780C4⋊C4—32no—
781C4⋊C4—32no—
782C4⋊C4—94no—
783C4⋊C4—94no—
784C4⋊C4—94no—
785C4⋊C4—94no—
786C4⋊C4—92no—
787C4⋊C4—92no—
788C4⋊C4—91no—
789C4⋊C4—91no—
790C4⋊C4—92no—
791C4⋊C4—92no—
792C22⋊C4—34no—
793C22⋊C4—34no—
794C22⋊C4—94no—
795C22⋊C4—94no—
796C22⋊C4—94no—
797C22⋊C4—94no—
798C22⋊C4—94no—
799C22⋊C4—92no—
800C22⋊C4—92no—
801C22⋊C4—92no—
802C22⋊C4—92no—
803C22⋊C4—92no—
804C42—32no—
805C42—32no—
806C42—32no—
807C42—32no—
808C42—94no—
809C42—92no—
810C42C2×D3211yescharacteristic
811C42C2×D3211yescharacteristic
812C42C2×D3211yescharacteristic
813C42C2×D3211yescharacteristic
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—22no—
819C22×C3—21no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—64no—
823C22×C3—64no—
824C22×C3—64no—
825C22×C3#100412yes—
826C22×C3#100912yes—
827C22×C3C24×D311yescharacteristic
828C22×C3C24×D311yescharacteristic
829C2×D3—24no—
830C2×D3—24no—
831C2×D3—24no—
832C2×D3—62no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—62no—
837C2×D3—62no—
838C2×D3—122no—
839C2×D3—122no—
840C2×D3—122no—
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—21no—
849C3×C4—22no—
850C3×C4—22no—
851C3×C4—34no—
852C3×C4—41no—
853C3×C4—41no—
854C3×C4—41no—
855C3×C4—41no—
856C3×C4—62no—
857C3×C4—62no—
858C3×C4—62no—
859C3×C4—64no—
860C3×C4C2×#23512yes—
861C3×C4#100712yes—
862C3×C4D3×#4112yes—
863C3×C4#101012yes—
864Dic3—22no—
865Dic3—24no—
866Dic3—22no—
867Dic3—22no—
868Dic3—62no—
869Dic3—62no—
870Dic3—62no—
871Dic3—62no—
872Dic3—62no—
873Dic3—62no—
874Dic3—122no—
875Dic3—122no—
876Dic3—122no—
877Dic3C2×#23514yes—
878C32#352211yescharacteristic, complemented, Sylow
879C23—34no—
880C23—92no—
881C23C22×D3211yescharacteristic
882Q8—34no—
883Q8—64no—
884Q8—62no—
885Q8—122no—
886Q8—182no—
887Q8—364no—
888D4—68no—
889D4—64no—
890D4—64no—
891D4—122no—
892D4—188no—
893D4—184no—
894D4—182no—
895D4—364no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—32no—
900C2×C4—32no—
901C2×C4—32no—
902C2×C4—32no—
903C2×C4—34no—
904C2×C4—64no—
905C2×C4—64no—
906C2×C4—92no—
907C2×C4—92no—
908C2×C4—92no—
909C2×C4—124no—
910C2×C4—188no—
911C2×C4—184no—
912C2×C4—364no—
913C2×C4—364no—
914C2×C4C22×D3211yescharacteristic
915C2×C4C22×D3211yescharacteristic
916C2×C4C22×D3211yescharacteristic
917C2×C4C22×D3211yescharacteristic
918C2×C4C22×D3211yescharacteristic
919C2×C4C22×D3211yescharacteristic
920C2×C3—22no—
921C2×C3—22no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—42no—
926C2×C3—124no—
927C2×C3C22×#23511yescharacteristic
928C2×C3C2×#100411yescharacteristic
929C2×C3C2×#100711yescharacteristic
930C2×C3C2×D3×#4111yescharacteristic
931C2×C3C2×#100911yescharacteristic
932C2×C3C2×#101011yescharacteristic
933D3—44no—
934D3—122no—
935D3—122no—
936D3—242no—
937C22—21no—
938C22—21no—
939C22—64no—
940C22—64no—
941C22—64no—
942C22—182no—
943C22—182no—
944C22—182no—
945C22#6430712yes—
946C22C23×D3211yescharacteristic
947C4—21no—
948C4—21no—
949C4—21no—
950C4—21no—
951C4—34no—
952C4—62no—
953C4—62no—
954C4—62no—
955C4—64no—
956C4—182no—
957C4—182no—
958C4—182no—
959C4#6429712yes—
960C4D3×#23512yes—
961C3—21no—
962C3#8582111yescharacteristic, complemented
963C3#8622911yescharacteristic, complemented
964C2—22no—
965C2—124no—
966C2—362no—
967C2C2×#6429711yescharacteristic
968C2C2×D3×#23511yescharacteristic
969C2C2×#6430711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595950C2semidirect
2. C3×#5477C2semidirect
3. C2×C3×C4×Dic6C2semidirect
4. #10594949C2semidirect
5. #10594928C2semidirect
6. #10594910C2semidirect
7. #10594900C2semidirect
8. #10594885C2semidirect
9. #10593978C2semidirect
10. #10593958C2semidirect
11. #10593951C2semidirect
12. #10593929C2semidirect
13. #10593927C2semidirect
14. #10593900C2semidirect
15. #10593889C2semidirect
16. #10593876C2semidirect
17. #10593856C2semidirect
118. #5477D3semidirect
119. C2×C4×Dic6D3semidirect
365. C3×Dic6#41semidirect
738. Dic6#235semidirect
878. C32#3522semidirect
962. C3#85821semidirect
963. C3#86229semidirect

Maximal subgroups

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

subgroupindex
#105959502
C3×#54772
C2×C3×C4×Dic62
#105949492
#105949282
#105949102
#105949002
#105948852
#105939782
#105939582
#105939512
#105939292
#105939272
#105939002
#105938892
#105938762
#105938562
#862293
#858213