Finite Group Databasebeta

← #11878434

Subgroups — #11878434

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×#5628C211yesmaximal, characteristic
2#10594856C211yesmaximal, characteristic
3#10592749C211yesmaximal, characteristic, complemented
4C3×#5045C211yesmaximal, characteristic, complemented
5#10591598C211yesmaximal, characteristic, complemented
6#10591596C211yesmaximal, characteristic, complemented
7#10591595C211yesmaximal, characteristic, complemented
8#10591595C211yesmaximal, characteristic, complemented
9#10591190C211yesmaximal, characteristic, complemented
10#10591145C211yesmaximal, characteristic
11#10591102C211yesmaximal, characteristic, complemented
12#10590587C211yesmaximal, characteristic, complemented
13#10590579C211yesmaximal, characteristic, complemented
14#10590429C211yesmaximal, characteristic, complemented
15#10590428C211yesmaximal, characteristic, complemented
16#83413—31nomaximal
17#81551—31nomaximal
18C22×#634C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23C2×#3756C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#897C2211yescharacteristic
28C3×#894—21no—
29C3×#892C2211yescharacteristic
30C3×#888—21no—
31C3×#885—21no—
32C3×#883—21no—
33#63962—21no—
34#63962—21no—
35#63866—21no—
36#63860—21no—
37#63857C2211yescharacteristic
38#63857C2211yescharacteristic
39#63857C2211yescharacteristic
40#63857C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63657C2211yescharacteristic
46#63637C2211yescharacteristic
47#63637C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63576C2211yescharacteristic
54#63574C2211yescharacteristic
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#5628D311yescharacteristic
64#5526—31no—
65C3×#485—31no—
66#5234—31no—
67#5228—31no—
68#5228—31no—
69#5052—31no—
70#5052—31no—
71#5051—31no—
72#5051—31no—
73#5050—31no—
74#5050—31no—
75#5050—31no—
76#5050—61no—
77#5045—31no—
78#5045D311yescharacteristic, complemented
79#4996—31no—
80#4996—31no—
81#4996—31no—
82#4888—31no—
83#4887—31no—
84#4868—31no—
85#4867—31no—
86#4816—31no—
87#4813—31no—
88#4809—31no—
89#4809—31no—
90#4739—31no—
91#4727—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634—21no—
96C2×#634—41no—
97C2×#634—41no—
98C2×#634C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C2×C3×#67D411yescharacteristic
102C3×D3×Q8—41no—
103C3×D3×Q8—41no—
104C3×#235—41no—
105C3×#235—41no—
106C2×C3×D12D411yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6—21no—
111C2×C3×Dic6D411yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116#3756—41no—
117#3756—41no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#217—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3719—41no—
144#3719—41no—
145#3711—41no—
146D3×C3⋊C8—41no—
147#3202—91noSylow
148C2×C3×#41—31no—
149C22×C3×Q8—31no—
150C2×D3×Q8C2×D311yescharacteristic
151C2×#235C2×D311yescharacteristic
152C22×Dic6—31no—
153C22×Dic6—31no—
154C22×Dic6—61no—
155C3×C4⋊Q8—61no—
156C3×#124—61no—
157C3×#123—61no—
158C3×#123—61no—
159C3×C22⋊Q8—21no—
160C3×C22⋊Q8—31no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8C2×D311yescharacteristic
164C3×C22⋊Q8C2×D311yescharacteristic
165C3×#117—31no—
166C3×#117—31no—
167#946C2×D311yescharacteristic
168#944—61no—
169C2×#216—31no—
170C2×#216—31no—
171C2×#216—31no—
172C2×#216—31no—
173C2×#216—31no—
174C2×#216—31no—
175C2×#216—61no—
176C2×#216—61no—
177#936—61no—
178#935—61no—
179#935—61no—
180#926C2×D311yescharacteristic
181#924—31no—
182#924—31no—
183#924—31no—
184#924—31no—
185#924C2×D311yescharacteristic
186C2×#208—31no—
187C22×C3⋊C8—31no—
188C2×Dic12—31no—
189C2×Dic12—31no—
190C2×ΓL(1,𝔽25)—31no—
191C2×D3×C8—31no—
192#897—31no—
193#897—31no—
194#897—31no—
195#897—31no—
196#897C2×D311yescharacteristic
197#894—21no—
198#892C2×D311yescharacteristic
199#888—21no—
200#886—61no—
201#886—61no—
202#885—21no—
203#883—21no—
204#875—61no—
205#869—61no—
206C3×#107—31no—
207C3×#106—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×C22⋊C8—31no—
211#835—31no—
212#835—31no—
213#835C2×D311yescharacteristic
214#835C2×D311yescharacteristic
215#830—31no—
216#830—31no—
217#830—31no—
218#830—31no—
219#830—61no—
220#830C2×D311yescharacteristic
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223#816—31no—
224#816—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—31no—
233#810—61no—
234#810—61no—
235#808—31no—
236#808—31no—
237#808C2×D311yescharacteristic
238#807—31no—
239#807—31no—
240#807C2×D311yescharacteristic
241C23×C32C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C22×C3×D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—42no—
255#634—21no—
256#634—21no—
257#634—21no—
258#634—21no—
259#634—42no—
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×C4×D3—42no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276C3×Dic6—41no—
277C3×Dic6—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—31no—
285#485—91no—
286#485—91no—
287#485—91no—
288#470—91no—
289#470—91no—
290#467—91no—
291#467—91no—
292#451—91no—
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—31no—
301C2×C3×Q8—31no—
302C2×C3×Q8—61no—
303C2×C3×Q8—121no—
304C2×C3×Q8—121no—
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C2×#67#6711yescharacteristic
317C2×#67#6711yescharacteristic
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—121no—
321D3×Q8—41no—
322D3×Q8—41no—
323#235—41no—
324#235—41no—
325C2×D12#6711yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3C22×D311yescharacteristic
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6—21no—
330C2×Dic6—31no—
331C2×Dic6—31no—
332C2×Dic6—31no—
333C2×Dic6—31no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—121no—
339C2×Dic6—121no—
340C2×Dic6—121no—
341C2×Dic6—121no—
342C2×Dic6—121no—
343C2×Dic6—122no—
344C2×Dic6—122no—
345C2×Dic6#6711yescharacteristic
346C2×Dic6C22×D311yescharacteristic
347C2×C3×C8—31no—
348C2×C3×C8—31no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—41no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—41no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C42—61no—
370C3×C42—61no—
371#217—21no—
372#217—21no—
373#217—61no—
374#217—61no—
375#217—61no—
376#217—61no—
377#216—121no—
378#216—121no—
379#216—121no—
380#216—121no—
381#216—121no—
382#216—121no—
383#216—122no—
384#216—122no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392C4⋊Dic3—21no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399C4⋊Dic3C22×D311yescharacteristic
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406C4×Dic3—21no—
407C4×Dic3—21no—
408#208—121no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—61no—
414C2×C3⋊C8—61no—
415C2×C3⋊C8—121no—
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418Dic12—121no—
419Dic12—121no—
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—31no—
447C22×Q8—91no—
448C2×Q16—91no—
449C2×Q16—91no—
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—91no—
466C22⋊Q8—91no—
467C22⋊Q8—91no—
468C22⋊Q8—91no—
469C22⋊Q8D3211yescharacteristic
470#117—31no—
471#117—31no—
472#107—31no—
473#107—91no—
474#106—31no—
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—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—41no—
500C3×Q8—41no—
501C3×Q8—61no—
502C3×Q8—61no—
503C3×Q8—121no—
504C3×Q8—122no—
505C3×D4—121no—
506C3×D4—121no—
507C3×D4—121no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—122no—
533C2×C3×C4D3×D411yescharacteristic
534C2×C3×C4C2×#6711yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—41no—
538#67—41no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—122no—
550C2×Dic3—122no—
551C2×Dic3—124no—
552C2×Dic3C2×#6711yescharacteristic
553C2×Dic3C2×#6711yescharacteristic
554D12—41no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—42no—
560Dic6—21no—
561Dic6—21no—
562Dic6—41no—
563Dic6—42no—
564Dic6—62no—
565Dic6—62no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—61no—
570Dic6—61no—
571Dic6—61no—
572Dic6—61no—
573Dic6—61no—
574Dic6—121no—
575Dic6—121no—
576Dic6—122no—
577Dic6—122no—
578Dic6—124no—
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—31no—
598C2×Q8—31no—
599C2×Q8—61no—
600C2×Q8—91no—
601C2×Q8—91no—
602C2×Q8—121no—
603C2×Q8—121no—
604C2×Q8—181no—
605C2×Q8—361no—
606C2×Q8—361no—
607C2×Q8C2×D3211yescharacteristic
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—31no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—61no—
614C22×C4—181no—
615C22×C4C2×D3211yescharacteristic
616Q16—361no—
617Q16—361no—
618Q16—361no—
619Q16—361no—
620M16—361no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—91no—
624C2×C8—91no—
625C2×C8—361no—
626C4⋊C4—21no—
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C4⋊C4C2×D3211yescharacteristic
638C22⋊C4—21no—
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—61no—
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—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—81no—
686C3×C4—81no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4#100411yescharacteristic
692C3×C4#100411yescharacteristic
693C3×C4#100911yescharacteristic
694C3×C4#100911yescharacteristic
695Dic3—21no—
696Dic3—21no—
697Dic3—41no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—122no—
702Dic3—122no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—121no—
707C32#320211yescharacteristic, complemented, Sylow
708C23—31no—
709C23—31no—
710C23D3×#6711yescharacteristic
711Q8—21no—
712Q8—21no—
713Q8—61no—
714Q8—61no—
715Q8—121no—
716Q8—122no—
717Q8—181no—
718Q8—181no—
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—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—122no—
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#565311yescharacteristic
758C2×C3#577111yescharacteristic
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#6431411yescharacteristic
787C4#6431411yescharacteristic
788C3—21no—
789C3#8155111yescharacteristic, complemented
790C3#8341311yescharacteristic, complemented
791C2—41no—
792C2—121no—
793C2—121no—
794C2#1059523411yescharacteristic
795C2#1059532811yescharacteristic
796C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊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. #10592749C2semidirect
4. C3×#5045C2semidirect
5. #10591598C2semidirect
6. #10591596C2semidirect
7. #10591595C2semidirect
8. #10591595C2semidirect
9. #10591190C2semidirect
11. #10591102C2semidirect
12. #10590587C2semidirect
13. #10590579C2semidirect
14. #10590429C2semidirect
15. #10590428C2semidirect
78. #5045D3semidirect
707. C32#3202semidirect
789. C3#81551semidirect
790. C3#83413semidirect

Maximal subgroups

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

subgroupindex
C3×#56282
#105948562
#105927492
C3×#50452
#105915982
#105915962
#105915952
#105911902
#105911452
#105911022
#105905872
#105905792
#105904292
#105904282
#834133
#815513