Finite Group Databasebeta

← #11878438

Subgroups — #11878438

Order 1152.

830 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5816C211yesmaximal, characteristic
2#10594884C211yesmaximal, characteristic
3#10592927C211yesmaximal, characteristic, complemented
4C3×#5228C211yesmaximal, characteristic, complemented
5#10591653C211yesmaximal, characteristic, complemented
6#10591653C211yesmaximal, characteristic, complemented
7#10591638C211yesmaximal, characteristic, complemented
8#10591635C211yesmaximal, characteristic, complemented
9#10591598C211yesmaximal, characteristic, complemented
10#10591596C211yesmaximal, characteristic, complemented
11#10591559C211yesmaximal, characteristic, complemented
12#10591558C211yesmaximal, characteristic, complemented
13#10591145C211yesmaximal, characteristic
14#10591134C211yesmaximal, characteristic, complemented
15#10591102C211yesmaximal, characteristic, complemented
16#83413—31nomaximal
17#80192—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23#64133C2211yescharacteristic
24C3×#947—21no—
25C3×#946C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C3×#946C2211yescharacteristic
28C3×#946C2211yescharacteristic
29C3×#944—21no—
30C2×C3×#216C2211yescharacteristic
31C2×C3×#216C2211yescharacteristic
32C3×#929—21no—
33C3×#929—21no—
34C3×#926C2211yescharacteristic
35C3×#924C2211yescharacteristic
36#63969—21no—
37#63959—21no—
38#63884—21no—
39#63857C2211yescharacteristic
40#63856C2211yescharacteristic
41#63841C2211yescharacteristic
42#63839—21no—
43C2×#3711C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63657C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63576C2211yescharacteristic
52#63575C2211yescharacteristic
53#63574C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#536—31no—
62#5825—31no—
63#5816D311yescharacteristic
64#5628—31no—
65C3×#451—31no—
66#5234—31no—
67#5228—31no—
68#5228—31no—
69#5228—61no—
70#5228D311yescharacteristic, complemented
71#5189—31no—
72#5188—31no—
73#5186—31no—
74#5186—31no—
75#5052—31no—
76#5052—31no—
77#5051—31no—
78#5051—31no—
79#5050—31no—
80#5050—31no—
81#5045—31no—
82#5045—31no—
83#5045—31no—
84#4996—31no—
85#4996—31no—
86#4816—31no—
87#4815—31no—
88#4814—31no—
89#4813—31no—
90#4727—31no—
91#4723—31no—
92C2×C32×Q8—21no—
93C2×C32×Q8—41no—
94C2×C32×Q8—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C2×C3×#67D411yescharacteristic
102C3×#235—41no—
103C3×#235—41no—
104C2×C3×D12D411yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6D411yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C2×D3×Dic3—21no—
111D3×Dic6—41no—
112D3×Dic6—41no—
113#3757—21no—
114#3756—41no—
115#3756—41no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#217—21no—
122C3×#216—41no—
123C3×#216—41no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3—21no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139#3724—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144Dic32—21no—
145#3711—41no—
146D3×C3⋊C8—41no—
147#3202—91noSylow
148C2×C3×#41—31no—
149C22×C3×Q8—21no—
150C22×C3×Q8C2×D311yescharacteristic
151C22×C3×Q8C2×D311yescharacteristic
152C2×D3×Q8—31no—
153C2×#235C2×D311yescharacteristic
154C22×Dic6—31no—
155C2×C3×Q16—31no—
156C2×C3×Q16—31no—
157C3×C4⋊Q8—61no—
158C3×#124—61no—
159C3×#123—61no—
160C3×#123—61no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×#117—31no—
167#947—21no—
168#946—31no—
169#946C2×D311yescharacteristic
170#946C2×D311yescharacteristic
171#946C2×D311yescharacteristic
172#946C2×D311yescharacteristic
173#944—21no—
174#944—61no—
175C2×#216—31no—
176C2×#216—31no—
177C2×#216—31no—
178C2×#216—31no—
179C2×#216—61no—
180C2×#216—61no—
181C2×#216C2×D311yescharacteristic
182C2×#216C2×D311yescharacteristic
183#936—61no—
184#935—61no—
185#935—61no—
186#929—21no—
187#929—21no—
188#926—31no—
189#926C2×D311yescharacteristic
190#924—31no—
191#924—31no—
192#924—31no—
193#924—31no—
194#924—61no—
195#924C2×D311yescharacteristic
196C2×#208—31no—
197C22×C3⋊C8—31no—
198C2×ΓL(1,𝔽25)—31no—
199C2×D3×C8—31no—
200#897—31no—
201#894—61no—
202#892—31no—
203#888—61no—
204#885—61no—
205#883—61no—
206C3×#103—31no—
207C3×#103—31no—
208C3×C22⋊C8—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—31no—
215#835—61no—
216#835—61no—
217#835C2×D311yescharacteristic
218#835C2×D311yescharacteristic
219#830—31no—
220#830—31no—
221#830—31no—
222#830—31no—
223#830—61no—
224#830C2×D311yescharacteristic
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—31no—
227#818—31no—
228#817—31no—
229#816—31no—
230#816—31no—
231#810—31no—
232#810—31no—
233#810—31no—
234#810—31no—
235#808—31no—
236#808—31no—
237#808—31no—
238#807—31no—
239#807—31no—
240#807—31no—
241C23×C32C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C22×C3×D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8—21no—
246C32×Q8—21no—
247C32×Q8—21no—
248C32×Q8—42no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—42no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258#634—21no—
259#634—21no—
260C3×#67—41no—
261C3×#67—41no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—41no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3×Dic6—41no—
276#627—42no—
277D3×Dic3—42no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#536—31no—
283#536—91no—
284#485—91no—
285#485—91no—
286#485—91no—
287#485—91no—
288#470—91no—
289#470—91no—
290#467—91no—
291#467—91no—
292#451—31no—
293#451—91no—
294#451—91no—
295#451—91no—
296#408—91no—
297C3×#41—121no—
298C3×#41—121no—
299C2×C3×Q8—21no—
300C2×C3×Q8—21no—
301C2×C3×Q8—21no—
302C2×C3×Q8—21no—
303C2×C3×Q8—31no—
304C2×C3×Q8—31no—
305C2×C3×Q8—41no—
306C2×C3×Q8—41no—
307C2×C3×Q8—41no—
308C2×C3×Q8—41no—
309C2×C3×Q8—41no—
310C2×C3×Q8—42no—
311C2×C3×Q8—42no—
312C2×C3×Q8C22×D311yescharacteristic
313C2×C3×Q8C22×D311yescharacteristic
314C2×C3×Q8C22×D311yescharacteristic
315C2×C3×Q8C22×D311yescharacteristic
316C2×C3×D4—31no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—41no—
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C2×#67#6711yescharacteristic
328C2×#67#6711yescharacteristic
329C22×Dic3—61no—
330D3×Q8—121no—
331D3×Q8—121no—
332#235—41no—
333#235—41no—
334C2×D12#6711yescharacteristic
335C2×C4×D3—61no—
336C2×C4×D3C22×D311yescharacteristic
337C2×C4×D3C22×D311yescharacteristic
338C2×Dic6—31no—
339C2×Dic6—31no—
340C2×Dic6—61no—
341C2×Dic6—61no—
342C2×Dic6—61no—
343C2×Dic6—121no—
344C2×Dic6—121no—
345C2×Dic6#6711yescharacteristic
346C2×Dic6C22×D311yescharacteristic
347C3×Q16—121no—
348C3×Q16—121no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C42—61no—
366#217—21no—
367#217—21no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—121no—
374#216—41no—
375#216—41no—
376#216—121no—
377#216—121no—
378#216—121no—
379#216—121no—
380#216—122no—
381#216—122no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—121no—
407C4×Dic3—21no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410#208—121no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—61no—
416C2×C3⋊C8—61no—
417C2×C3⋊C8—121no—
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420ΓL(1,𝔽25)—121no—
421D3×C8—121no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32C22×D411yescharacteristic
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C32×C4—21no—
433C32×C4—41no—
434C32×C4—41no—
435C32×C4H(5,𝔽2)11yescharacteristic
436C32×C4H(5,𝔽2)11yescharacteristic
437C3⋊Dic3—41no—
438C3⋊Dic3—41no—
439C3×Dic3—21no—
440C3×Dic3—21no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C2×#41—31no—
446C22×Q8—91no—
447C22×Q8D3211yescharacteristic
448C2×Q16—31no—
449C2×Q16—31no—
450C2×Q16—91no—
451C2×Q16—91no—
452C2×M16—91no—
453C22×C8—91no—
454C4⋊Q8—61no—
455C4⋊Q8—181no—
456#124—61no—
457#124—181no—
458#123—61no—
459#123—61no—
460#123—181no—
461#123—181no—
462C22⋊Q8—31no—
463C22⋊Q8—31no—
464C22⋊Q8—31no—
465C22⋊Q8—31no—
466C22⋊Q8—31no—
467C22⋊Q8—91no—
468C22⋊Q8—91no—
469C22⋊Q8—91no—
470#117—31no—
471#117—91no—
472#107—91no—
473#107—91no—
474#106—91no—
475#106—91no—
476#103—31no—
477#103—31no—
478#103—91no—
479#103—91no—
480#103—91no—
481#103—91no—
482#103—91no—
483#103—91no—
484C22⋊C8—31no—
485C22⋊C8—91no—
486C22⋊C8—91no—
487C22⋊C8—91no—
488C23×C3—21no—
489C23×C3—31no—
490C23×C3—31no—
491C23×C3D3×D411yescharacteristic
492C23×C3C2×#6711yescharacteristic
493C22×D3C2×#6711yescharacteristic
494C22×D3C2×#6711yescharacteristic
495C3×Q8—22no—
496C3×Q8—22no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—41no—
506C3×Q8—41no—
507C3×Q8—42no—
508C3×Q8—42no—
509C3×Q8—44no—
510C3×Q8—61no—
511C3×Q8—61no—
512C3×Q8—121no—
513C3×D4—121no—
514C3×D4—121no—
515C3×D4—121no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—42no—
533C2×C3×C4—42no—
534C2×C3×C4—44no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4D3×D411yescharacteristic
544C2×C3×C4C2×#6711yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546C2×C3×C4C23×D311yescharacteristic
547#67—41no—
548#67—41no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—121no—
558C2×Dic3—121no—
559C2×Dic3—122no—
560C2×Dic3C2×#6711yescharacteristic
561C2×Dic3C2×#6711yescharacteristic
562D12—41no—
563C4×D3—21no—
564C4×D3—21no—
565C4×D3—21no—
566C4×D3—21no—
567C4×D3—122no—
568Dic6—21no—
569Dic6—21no—
570Dic6—41no—
571Dic6—61no—
572Dic6—61no—
573Dic6—61no—
574Dic6—61no—
575Dic6—121no—
576Dic6—121no—
577Dic6—122no—
578Dic6—122no—
579C3×C8—61no—
580C3×C8—61no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C3⋊C8—61no—
584C3⋊C8—61no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—121no—
588C3⋊C8—121no—
589C2×C32—41no—
590C2×C32#53411yescharacteristic
591C2×C32#57811yescharacteristic
592C2×C32#57811yescharacteristic
593C3×D3—41no—
594C3×D3—41no—
595#41—121no—
596#41—121no—
597C2×Q8—21no—
598C2×Q8—31no—
599C2×Q8—31no—
600C2×Q8—41no—
601C2×Q8—41no—
602C2×Q8—91no—
603C2×Q8—181no—
604C2×Q8—361no—
605C2×Q8—361no—
606C2×Q8C2×D3211yescharacteristic
607C2×Q8C2×D3211yescharacteristic
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—31no—
611C22×C4—21no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—181no—
615C22×C4C2×D3211yescharacteristic
616Q16—121no—
617Q16—121no—
618Q16—361no—
619Q16—361no—
620M16—361no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—91no—
624C2×C8—91no—
625C2×C8—361no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—91no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C4⋊C4—181no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—61no—
649C42—181no—
650C22×C3—22no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—61no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3C2×D3×D411yescharacteristic
667C22×C3C22×#6711yescharacteristic
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—41no—
679C3×C4—42no—
680C3×C4—42no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4#100411yescharacteristic
692C3×C4#100411yescharacteristic
693C3×C4#100411yescharacteristic
694C3×C4#100411yescharacteristic
695Dic3—21no—
696Dic3—21no—
697Dic3—41no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—241no—
706Dic3—241no—
707C32#320211yescharacteristic, complemented, Sylow
708C23—31no—
709C23—31no—
710C23D3×#6711yescharacteristic
711Q8—21no—
712Q8—21no—
713Q8—21no—
714Q8—21no—
715Q8—42no—
716Q8—61no—
717Q8—61no—
718Q8—121no—
719Q8—181no—
720Q8—181no—
721Q8—362no—
722D4—121no—
723D4—121no—
724D4—121no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—42no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—362no—
743C2×C4D3×#6711yescharacteristic
744C2×C4C22×D3211yescharacteristic
745C8—61no—
746C8—61no—
747C8—181no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—42no—
753C2×C3—41no—
754C2×C3—41no—
755C2×C3—121no—
756C2×C3—121no—
757C2×C3#558911yescharacteristic
758C2×C3#576611yescharacteristic
759C2×C3#577911yescharacteristic
760C2×C3#580411yescharacteristic
761C2×C3#583811yescharacteristic
762C2×C3#583811yescharacteristic
763D3—41no—
764D3—41no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—61no—
773C22—61no—
774C22C2×D3×#6711yescharacteristic
775C4—21no—
776C4—41no—
777C4—41no—
778C4—61no—
779C4—61no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—361no—
785C4—361no—
786C4#6433011yescharacteristic
787C4#6433011yescharacteristic
788C3—21no—
789C3#8019211yescharacteristic, complemented
790C3#8341311yescharacteristic, complemented
791C2—41no—
792C2—121no—
793C2—121no—
794C2#1059532711yescharacteristic
795C2#1059532811yescharacteristic
796C2#1059552411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
hypercenterC22×Q8D32
hypocenterC32#3202
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #10592927C2semidirect
4. C3×#5228C2semidirect
5. #10591653C2semidirect
6. #10591653C2semidirect
7. #10591638C2semidirect
8. #10591635C2semidirect
9. #10591598C2semidirect
10. #10591596C2semidirect
11. #10591559C2semidirect
12. #10591558C2semidirect
14. #10591134C2semidirect
15. #10591102C2semidirect
70. #5228D3semidirect
707. C32#3202semidirect
789. C3#80192semidirect
790. C3#83413semidirect

Maximal subgroups

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

subgroupindex
C3×#58162
#105948842
#105929272
C3×#52282
#105916532
#105916382
#105916352
#105915982
#105915962
#105915592
#105915582
#105911452
#105911342
#105911022
#834133
#801923