Finite Group Databasebeta

← #11887620

Subgroups — #11887620

Order 1152.

890 conjugacy classes of subgroups.

The subgroup lattice has 787 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596106C211yesmaximal, characteristic
2#10594803C211yesmaximal, characteristic
3C3×#5051C211yesmaximal, characteristic, complemented
4C3×#5050C211yesmaximal, characteristic, complemented
5#10591654C211yesmaximal, characteristic, complemented
6#10591633C211yesmaximal, characteristic, complemented
7#10591601C211yesmaximal, characteristic, complemented
8#10591581C211yesmaximal, characteristic, complemented
9#10591148C211yesmaximal, characteristic
10#10591103C211yesmaximal, characteristic, complemented
11C2×#63566C211yesmaximal, characteristic, complemented
12#10590601C211yesmaximal, characteristic, complemented
13#10590567C211yesmaximal, characteristic, complemented
14#10590528C211yesmaximal, characteristic, complemented
15#10590496C211yesmaximal, characteristic, complemented
16#80781—31nomaximal
17#80193—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C2×#3797C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21#64155C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23C4×#638C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25#64106—21no—
26C4⋊C4×C3⋊D3C2211yescharacteristic
27#64098—21no—
28#64097C2211yescharacteristic
29#64090—21no—
30#64087—21no—
31C2×C3×#216C2211yescharacteristic
32C2×C3×#216C2211yescharacteristic
33C2×C3×#216C2211yescharacteristic
34C3×#924C2211yescharacteristic
35C22×C3×C3⋊C8C2211yescharacteristic
36#63964—21no—
37#63952—21no—
38#63888—21no—
39#63873C2211yescharacteristic
40#63871C2211yescharacteristic
41#63843C2211yescharacteristic
42#63839—21no—
43C2×#3710C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#830C2211yescharacteristic
46C3×#810C2211yescharacteristic
47C3×#810C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#807C2211yescharacteristic
50#63575C2211yescharacteristic
51#63575C2211yescharacteristic
52#63572C2211yescharacteristic
53#63566C2211yescharacteristic
54#63566C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63557C2211yescharacteristic
60#63553C2211yescharacteristic
61Q8×#67—31no—
62#5635—31no—
63#5635—31no—
64#5635—61no—
65#5632—31no—
66C3×#467—31no—
67C3×#451—31no—
68C2×#835—31no—
69#5188—31no—
70#5186—31no—
71#5186—31no—
72#5182—31no—
73#5182—31no—
74Dic3×Q16—31no—
75C8×#67—31no—
76C2×#816—31no—
77#5051D311yescharacteristic, complemented
78#5050D311yescharacteristic, complemented
79#5044—31no—
80#4884—31no—
81#4875—31no—
82#4813—31no—
83#4811—31no—
84D3×#103—31no—
85D3×#103—31no—
86#4793—31no—
87#4792—31no—
88#4792—31no—
89#4790—31no—
90#67⋊C8—31no—
91#4722—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638D411yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634—21no—
99C22×C3×Dic3—21no—
100C2×C3×Dic6—22no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6—41no—
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#627—21no—
107C2×#624—21no—
108#3797—22no—
109#3797—41no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113#3757D411yescharacteristic
114#3752—21no—
115#3752D411yescharacteristic
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121#3750—21no—
122#3750—21no—
123#3750D411yescharacteristic
124C4×C3⋊Dic3—21no—
125C4×C3⋊Dic3C2311yescharacteristic
126C3×#217—21no—
127C3×#216—22no—
128C3×#216—41no—
129C3×#216—41no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C2×C3×C3⋊C8—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138#3724—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141#3722—21no—
142Dic32—21no—
143#3710—41no—
144#3299—91noSylow
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8—31no—
148C22×Dic6C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C2×C3×Q16—31no—
152C22×C3×C8—31no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8C2×D311yescharacteristic
156C3×C22⋊Q8C2×D311yescharacteristic
157#946—31no—
158#946—31no—
159#946—31no—
160#946—61no—
161#946—61no—
162Q8×Dic3—31no—
163Q8×Dic3—31no—
164Q8×Dic3—31no—
165Q8×Dic3—61no—
166#944—31no—
167#944—31no—
168#944—61no—
169C2×#216C2×D311yescharacteristic
170C2×#216C2×D311yescharacteristic
171C2×#216C2×D311yescharacteristic
172C4×#67—31no—
173C4×#67—31no—
174C4×#67—61no—
175C4×#67—61no—
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—61no—
179#924—61no—
180#924C2×D311yescharacteristic
181C22×C3⋊C8C2×D311yescharacteristic
182C2×D3×C8—31no—
183C2×D3×C8—31no—
184#897—31no—
185#897—61no—
186#897—61no—
187#897—62no—
188#896—61no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—31no—
191D3×C4⋊C4—61no—
192#889—61no—
193#889—61no—
194#889—62no—
195#888—31no—
196#888—31no—
197#888—61no—
198#888—61no—
199#887—31no—
200#67⋊C4—61no—
201#67⋊C4—61no—
202#67⋊C4—62no—
203#67⋊C4—61no—
204#878—61no—
205#878—61no—
206#878—61no—
207#878—62no—
208C3×#107—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×C22⋊C8—31no—
214#835—31no—
215#835—31no—
216#835—31no—
217#835—31no—
218#835—31no—
219#835—31no—
220#835C2×D311yescharacteristic
221#830C2×D311yescharacteristic
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224#818—31no—
225#818—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232Dic3⋊C8—31no—
233Dic3⋊C8—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#810C2×D311yescharacteristic
237#810C2×D311yescharacteristic
238#810C2×D311yescharacteristic
239#807—31no—
240#807—31no—
241#807C2×D311yescharacteristic
242C23×C32C2×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
252#638Q1614yescomplemented
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—81no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C4×C3⋊D3—21no—
260C4×C3⋊D3—21no—
261C4×C3⋊D3—81no—
262#634—81no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—42no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—42no—
274C3×Dic6#4112yes—
275#627—42no—
276#624—42no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282D4×Q8—91no—
283#487—91no—
284#484—91no—
285#484—91no—
286#477—91no—
287#467—31no—
288#467—91no—
289#462—91no—
290#451—31no—
291#451—91no—
292C4×Q16—91no—
293C8×D4—91no—
294C2×#103—91no—
295C2×#103—91no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×Q8—62no—
301C2×C3×Q8—61no—
302C2×C3×Q8—121no—
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C22×D311yescharacteristic
305C22×C3×C4—21no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—31no—
310C2×#67—31no—
311C2×#67—61no—
312C22×Dic3—21no—
313C22×Dic3—62no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316D3×Q8—62no—
317D3×Q8—62no—
318D3×Q8—121no—
319D3×Q8—121no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—62no—
328C2×Dic6—22no—
329C2×Dic6—21no—
330C2×Dic6—41no—
331C2×Dic6—61no—
332C2×Dic6—61no—
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6—62no—
336C2×Dic6C22×D311yescharacteristic
337C2×Dic6C22×D311yescharacteristic
338C2×Dic6C22×D311yescharacteristic
339C3×Q16—62no—
340C3×Q16—121no—
341C3×Q16—121no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—121no—
347C3×C4⋊C4—22no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C22⋊C4—22no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—61no—
359#217—21no—
360#217—31no—
361#217—31no—
362#217—61no—
363#216—22no—
364#216—41no—
365#216—41no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—62no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—62no—
385C4⋊Dic3—62no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—31no—
391Dic3⋊C4—31no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—62no—
406Dic3⋊C4—62no—
407Dic3⋊C4—62no—
408C4×Dic3—31no—
409C4×Dic3—31no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413C4×Dic3—61no—
414C4×Dic3—61no—
415C4×Dic3—62no—
416C2×C3⋊C8—41no—
417C2×C3⋊C8C22×D311yescharacteristic
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421D3×C8—121no—
422D3×C8—121no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32C2×Q1612yes—
426C22×C32C22×D411yescharacteristic
427C2×C3⋊D3—21no—
428C2×C3⋊D3—21no—
429C2×C3⋊D3C2×Q1612yes—
430C32×C4—21no—
431C32×C4—41no—
432C32×C4—41no—
433C32×C4C2×#4111yescharacteristic
434C32×C4H(5,𝔽2)11yescharacteristic
435C3⋊Dic3—21no—
436C3⋊Dic3—21no—
437C3⋊Dic3—41no—
438C3⋊Dic3—41no—
439C3⋊Dic3C2×Q1612yes—
440C3×Dic3—22no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C22×Q8—31no—
445C22×Q8—91no—
446C2×Q16—31no—
447C2×Q16—31no—
448C2×Q16—31no—
449C22×C8—31no—
450C22×C8—91no—
451C4⋊Q8—91no—
452C4⋊Q8—91no—
453C4⋊Q8—181no—
454#125—181no—
455C22⋊Q8—31no—
456C22⋊Q8—91no—
457C22⋊Q8—91no—
458C22⋊Q8—181no—
459C22⋊Q8—181no—
460C22⋊Q8—181no—
461C22⋊Q8—181no—
462C22⋊Q8D3211yescharacteristic
463C4×Q8—91no—
464C4×Q8—91no—
465C4×D4—91no—
466C4×D4—181no—
467C4×D4—181no—
468C2×C4⋊C4—91no—
469C2×C4⋊C4—91no—
470#107—31no—
471#107—91no—
472#107—91no—
473C4⋊C8—91no—
474#103—31no—
475#103—31no—
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—
486C4×C8—91no—
487C23×C3—21no—
488C23×C3D3×D411yescharacteristic
489C23×C3D3×D411yescharacteristic
490C22×D3—31no—
491C22×D3—31no—
492C22×D3—61no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—32no—
498C3×Q8—41no—
499C3×Q8—41no—
500C3×Q8—61no—
501C3×Q8—61no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×Q8—61no—
505C3×Q8—122no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
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—41no—
519C2×C3×C4—41no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—122no—
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—34no—
530#67—34no—
531#67—64no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—42no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—62no—
547C2×Dic3—62no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—241no—
553C2×Dic3—241no—
554C2×Dic3—242no—
555C4×D3—61no—
556C4×D3—61no—
557C4×D3—61no—
558C4×D3—61no—
559C4×D3—121no—
560C4×D3—121no—
561C4×D3—122no—
562C4×D3—122no—
563C4×D3—241no—
564C4×D3—241no—
565C4×D3—242no—
566Dic6—21no—
567Dic6—21no—
568Dic6—21no—
569Dic6—21no—
570Dic6—21no—
571Dic6—42no—
572Dic6—122no—
573Dic6—122no—
574Dic6—241no—
575Dic6—241no—
576Dic6—242no—
577Dic6#23712yes—
578C3×C8—61no—
579C3×C8—61no—
580C3×C8—61no—
581C3×C8—61no—
582C3⋊C8—21no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C3⋊C8—21no—
586C2×C32—22no—
587C2×C32#54611yescharacteristic
588C2×C32C22×Q1611yescharacteristic
589C2×C32#57711yescharacteristic
590C3⋊D3—22no—
591C2×Q8—31no—
592C2×Q8—31no—
593C2×Q8—31no—
594C2×Q8—62no—
595C2×Q8—61no—
596C2×Q8—121no—
597C2×Q8—181no—
598C2×Q8—181no—
599C2×Q8—182no—
600C2×Q8—361no—
601C2×Q8C2×D3211yescharacteristic
602C2×D4—91no—
603C22×C4—61no—
604C22×C4—91no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4C2×D3211yescharacteristic
609Q16—62no—
610Q16—121no—
611Q16—121no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—121no—
617C2×C8—361no—
618C4⋊C4—21no—
619C4⋊C4—31no—
620C4⋊C4—61no—
621C4⋊C4—91no—
622C4⋊C4—91no—
623C4⋊C4—91no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4—181no—
632C4⋊C4—181no—
633C4⋊C4C2×D3211yescharacteristic
634C22⋊C4—21no—
635C22⋊C4—61no—
636C22⋊C4—91no—
637C22⋊C4—91no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—91no—
641C42—181no—
642C42—181no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—22no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3D3×Q1612yes—
652C22×C3D3×Q1612yes—
653C22×C3C2×D3×D411yescharacteristic
654C22×C3C2×D3×D411yescharacteristic
655C2×D3—32no—
656C2×D3—32no—
657C2×D3—62no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—121no—
663C2×D3—121no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—41no—
669C3×C4—42no—
670C3×C4—42no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—62no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4C2×#23711yescharacteristic
680C3×C4#100411yescharacteristic
681C3×C4#100411yescharacteristic
682C3×C4D3×#4111yescharacteristic
683Dic3—22no—
684Dic3—32no—
685Dic3—32no—
686Dic3—41no—
687Dic3—41no—
688Dic3—41no—
689Dic3—62no—
690Dic3—61no—
691Dic3—61no—
692Dic3—61no—
693Dic3—61no—
694Dic3—121no—
695Dic3—121no—
696Dic3—122no—
697Dic3—122no—
698Dic3—121no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702C32#329911yescharacteristic, complemented, Sylow
703C23—91no—
704C23#381111yescharacteristic
705Q8—21no—
706Q8—21no—
707Q8—32no—
708Q8—61no—
709Q8—61no—
710Q8—61no—
711Q8—61no—
712Q8—61no—
713Q8—122no—
714Q8—362no—
715Q8—721no—
716D4—94no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—91no—
726C2×C4—91no—
727C2×C4—91no—
728C2×C4—122no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—362no—
734C2×C4—721no—
735C2×C4—721no—
736C2×C4#381111yescharacteristic
737C2×C4C22×D3211yescharacteristic
738C8—61no—
739C8—61no—
740C8—61no—
741C8—61no—
742C2×C3—22no—
743C2×C3—22no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—42no—
748C2×C3#559111yescharacteristic
749C2×C3#561011yescharacteristic
750C2×C3C2×D3×Q1611yescharacteristic
751C2×C3C2×D3×Q1611yescharacteristic
752C2×C3#577011yescharacteristic
753C2×C3#577811yescharacteristic
754D3—62no—
755D3—62no—
756D3—122no—
757C22—21no—
758C22—21no—
759C22—92no—
760C22—181no—
761C22—181no—
762C22#6394412yes—
763C22C2×#381111yescharacteristic
764C4—21no—
765C4—41no—
766C4—41no—
767C4—62no—
768C4—92no—
769C4—121no—
770C4—121no—
771C4—121no—
772C4—181no—
773C4—181no—
774C4—361no—
775C4—361no—
776C4D3×#23711yescharacteristic
777C4#6431311yescharacteristic
778C3—21no—
779C3#8019311yescharacteristic, complemented
780C3#8078111yescharacteristic, complemented
781C2—22no—
782C2—182no—
783C2#1059530711yescharacteristic
784C2C2×#6394411yescharacteristic
785C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#638D4
hypercenterC22⋊Q8D32
hypocenterC32#3299
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. C3×#5051C2semidirect
4. C3×#5050C2semidirect
5. #10591654C2semidirect
6. #10591633C2semidirect
7. #10591601C2semidirect
8. #10591581C2semidirect
10. #10591103C2semidirect
11. C2×#63566C2semidirect
12. #10590601C2semidirect
13. #10590567C2semidirect
14. #10590528C2semidirect
15. #10590496C2semidirect
77. #5051D3semidirect
78. #5050D3semidirect
252. #638Q16semidirect
702. C32#3299semidirect
779. C3#80193semidirect
780. C3#80781semidirect

Maximal subgroups

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

subgroupindex
#105961062
#105948032
C3×#50512
C3×#50502
#105916542
#105916332
#105916012
#105915812
#105911482
#105911032
C2×#635662
#105906012
#105905672
#105905282
#105904962
#807813
#801933