Finite Group Databasebeta

← #11889720

Subgroups — #11889720

Order 1152.

877 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594988C211yesmaximal, characteristic, complemented
2#10594886C211yesmaximal, characteristic
3#10592815C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5C3×#5111C211yesmaximal, characteristic, complemented
6#10591172C211yesmaximal, characteristic, complemented
7#10591135C211yesmaximal, characteristic, complemented
8#10590969C211yesmaximal, characteristic, complemented
9#10590895C211yesmaximal, characteristic, complemented
10#10590861C211yesmaximal, characteristic, complemented
11#10590828C211yesmaximal, characteristic, complemented
12#10590762C211yesmaximal, characteristic, complemented
13#10590747C211yesmaximal, characteristic, complemented
14#10590680C211yesmaximal, characteristic, complemented
15#10590670C211yesmaximal, characteristic, complemented
16#79503—31nomaximal
17#78763—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21#64133C2211yescharacteristic
22#64133C2211yescharacteristic
23C2×#3746C2211yescharacteristic, complemented
24C3×C4×#67C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
27#63976—21no—
28Dic3×#67—21no—
29D3×#217—21no—
30#63964—21no—
31#63918C2211yescharacteristic, complemented
32#63908C2211yescharacteristic
33#63899—21no—
34Dic3×D12C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic, complemented
36#63885—21no—
37#63884—21no—
38#63860C2211yescharacteristic
39#63857C2211yescharacteristic, complemented
40#63846—21no—
41#63844C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44#63645C2211yescharacteristic, complemented
45#63643C2211yescharacteristic, complemented
46#63643C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54C3×Dic3⋊C8C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5806—31no—
62#5550—31no—
63#5543—31no—
64#5511—31no—
65C3×#435—31no—
66C2×C3×#102—31no—
67#5218—31no—
68#5134—31no—
69#5133—31no—
70#5116—31no—
71#5116—31no—
72#5116—61no—
73C2×#821D311yescharacteristic, complemented
74#5111D311yescharacteristic, complemented
75#4970—31no—
76#4846—31no—
77#4845—31no—
78#4783—31no—
79#4780—31no—
80#4774—31no—
81#4771—31no—
82#4767—31no—
83#4765—31no—
84#4759—31no—
85#4757—31no—
86#4736—31no—
87#4733—31no—
88#4731—31no—
89#4722—31no—
90#4714—31no—
91#4710—31no—
92C23×C3×D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67D411yescharacteristic
97C22×C3×Dic3—21no—
98C2×C3×D12—22no—
99C2×C3×D12—21no—
100C2×C3×D12—41no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×#627—21no—
105C2×#625—21no—
106C2×#625—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795—41no—
112C2×C32×C8—41no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115#3757—21no—
116#3757—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120#3750—21no—
121#3746—41no—
122C3×#217D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×ΓL(1,𝔽25)—41no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3716—22no—
143#3716—41no—
144#3314—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#235—31no—
148C22×D12C2×D311yescharacteristic
149C2×C3×M16—31no—
150C22×C3×C8—21no—
151C22×C3×C8C2×D311yescharacteristic
152C22×C3×C8C2×D311yescharacteristic
153C3×C4×D4—31no—
154C2×C3×C4⋊C4—31no—
155#953—61no—
156C2×#217—61no—
157#939—61no—
158#938—31no—
159#937—61no—
160#936—31no—
161#935—61no—
162D4×Dic3—31no—
163D4×Dic3—61no—
164C2×#214—31no—
165C2×#214—31no—
166#930—31no—
167C4×#67—61no—
168C4×#67C2×D311yescharacteristic
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3C2×D311yescharacteristic
171#924—31no—
172#924—31no—
173#924—31no—
174#924—31no—
175#924—31no—
176#924—61no—
177#924—61no—
178#924—61no—
179C2×Dic12—31no—
180C2×Dic12—31no—
181C2×Dic12—61no—
182C2×#204—31no—
183C2×#204—31no—
184C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
185#897—31no—
186#896—61no—
187#894—61no—
188D3×C4⋊C4—31no—
189#890—61no—
190#889—61no—
191#888—31no—
192#887—31no—
193#884—61no—
194D3×C22⋊C4—61no—
195#878—61no—
196#878—61no—
197#875—31no—
198C4×D12—31no—
199#869—31no—
200C4×Dic6—31no—
201C3×C4⋊C8—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—31no—
207C3×C22⋊C8—31no—
208C3×#97—31no—
209#832—31no—
210#832—31no—
211#830C2×D311yescharacteristic
212#821—31no—
213#821—31no—
214#821C2×D311yescharacteristic
215#821C2×D311yescharacteristic
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8C2×D311yescharacteristic, complemented
219#818—31no—
220#818—31no—
221#818—31no—
222#818—31no—
223#818—61no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—61no—
231#816—61no—
232#815C2×D311yescharacteristic, complemented
233Dic3⋊C8C2×D311yescharacteristic, complemented
234#810—31no—
235#810—31no—
236#807—31no—
237#807—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253#634—21no—
254#634—21no—
255#634—21no—
256#634—21no—
257C3×#67—22no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—42no—
268C3×D12#4112yes—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271#627—81no—
272#625—42no—
273#625—81no—
274D3×Dic3—42no—
275D3×Dic3—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C32×C8—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—91no—
283#489—91no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—31no—
294#417—91no—
295C2×#102—31no—
296C24×C3—61no—
297C23×D3—21no—
298C2×C3×D4—31no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—62no—
302C2×C3×D4—61no—
303C2×C3×D4—121no—
304C22×C3×C4—21no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67D1211yescharacteristic
314C22×Dic3—21no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318#237—62no—
319#237—121no—
320#235—62no—
321#235—121no—
322C2×D12—22no—
323C2×D12—21no—
324C2×D12—41no—
325C2×D12C22×D311yescharacteristic
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—31no—
332C2×Dic6—31no—
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C3×M16—121no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—41no—
345C2×C3×C8—41no—
346C2×C3×C8—42no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C22×D311yescharacteristic
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—61no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—31no—
357C3×C42—31no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—121no—
368#217—121no—
369#217D1211yescharacteristic
370#214—62no—
371#214—121no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4D1211yescharacteristic
378C4⋊Dic3—21no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—121no—
400Dic3⋊C4—121no—
401Dic3⋊C4D1211yescharacteristic
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407Dic12—121no—
408Dic12—121no—
409Dic12—122no—
410#204—62no—
411#204—121no—
412ΓL(1,𝔽25)—41no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32#13712yes—
416C22×C32C22×D411yescharacteristic
417C2×C3×D3—22no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—84no—
427C32×C4—21no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—31no—
441C2×Q16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C2×M16—31no—
445C22×C8D3211yescharacteristic
446C4⋊Q8—91no—
447#125—181no—
448#124—91no—
449#123—181no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455#121—91no—
456#121—181no—
457#120—181no—
458C4×Q8—91no—
459C4×D4—31no—
460C4×D4—91no—
461C4×D4—181no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—181no—
465#107—91no—
466#107—91no—
467#107—91no—
468C4⋊C8—31no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8—31no—
481#97—31no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3—122no—
487C23×C3—122no—
488C23×C3—241no—
489C23×C3C2×D1211yescharacteristic
490C23×C3D3×D411yescharacteristic
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—42no—
494C22×D3—42no—
495C22×D3—81no—
496C22×D3C2×D1211yescharacteristic
497C3×D4—32no—
498C3×D4—62no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—122no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—241no—
519C2×C3×C4C2×D1211yescharacteristic
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—22no—
524#67—122no—
525#67—122no—
526#67—241no—
527#67—241no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—81no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—122no—
544C2×Dic3—241no—
545C2×Dic3—241no—
546C2×Dic3C2×D1211yescharacteristic
547C2×Dic3C2×D1211yescharacteristic
548C2×Dic3C2×D1211yescharacteristic
549D12—21no—
550D12—21no—
551D12—21no—
552D12—42no—
553D12#23512yes—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—122no—
557C4×D3—241no—
558C4×D3—241no—
559Dic6—61no—
560Dic6—61no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—61no—
567Dic6—121no—
568Dic6—121no—
569Dic6—121no—
570Dic6—121no—
571Dic6—241no—
572Dic6—241no—
573C3×C8—22no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—21no—
578C3×C8—41no—
579C3×C8—61no—
580C3×C8—61no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C2×C32—22no—
584C2×C32#54611yescharacteristic
585C2×C32C2×#13711yescharacteristic
586C2×C32#57611yescharacteristic
587C3×D3—41no—
588C3×D3—42no—
589C3×D3—81no—
590C24—61no—
591#41—182no—
592#41—361no—
593C2×Q8—91no—
594C2×Q8—91no—
595C2×Q8—181no—
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—62no—
600C2×D4—61no—
601C2×D4—121no—
602C2×D4—181no—
603C2×D4—181no—
604C22×C4—31no—
605C22×C4—61no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4C2×D3211yescharacteristic
610Q16—361no—
611SD16—182no—
612SD16—361no—
613M16—121no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—41no—
617C2×C8C2×D3211yescharacteristic
618C2×C8C2×D3211yescharacteristic
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—91no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—31no—
641C42—181no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—22no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—62no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—244no—
660C22×C3#90912yes—
661C22×C3#91512yes—
662C22×C3C22×D1211yescharacteristic
663C22×C3C2×D3×D411yescharacteristic
664C2×D3—22no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—84no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—41no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4C2×#23511yescharacteristic
685C3×C4#100411yescharacteristic
686C3×C4#100411yescharacteristic
687C3×C4D3×#4111yescharacteristic
688Dic3—21no—
689Dic3—21no—
690Dic3—21no—
691Dic3—41no—
692Dic3—41no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—121no—
701Dic3—241no—
702Dic3—241no—
703Dic3—241no—
704Dic3—241no—
705C32#331411yescharacteristic, complemented, Sylow
706C23—31no—
707C23—61no—
708C23—61no—
709C23—122no—
710C23—122no—
711C23—241no—
712C23D3×D1211yescharacteristic
713Q8—181no—
714Q8—181no—
715Q8—181no—
716Q8—181no—
717Q8—721no—
718D4—32no—
719D4—62no—
720D4—61no—
721D4—61no—
722D4—61no—
723D4—122no—
724D4—362no—
725D4—721no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—241no—
740C2×C4—362no—
741C2×C4—721no—
742C2×C4—721no—
743C2×C4D3×D1211yescharacteristic
744C2×C4C22×D3211yescharacteristic
745C8—21no—
746C8—21no—
747C8—61no—
748C8—61no—
749C2×C3—22no—
750C2×C3—22no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—42no—
755C2×C3—122no—
756C2×C3—121no—
757C2×C3—241no—
758C2×C3#549011yescharacteristic
759C2×C3#555411yescharacteristic
760C2×C3C2×#90911yescharacteristic
761C2×C3#575211yescharacteristic
762C2×C3#575711yescharacteristic
763C2×C3C2×#91511yescharacteristic
764D3—41no—
765D3—42no—
766D3—81no—
767C22—21no—
768C22—21no—
769C22—61no—
770C22—62no—
771C22—61no—
772C22—61no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—244no—
779C22#6380012yes—
780C22C2×D3×D1211yescharacteristic
781C4—21no—
782C4—61no—
783C4—61no—
784C4—61no—
785C4—121no—
786C4—121no—
787C4—361no—
788C4—361no—
789C4—361no—
790C4—361no—
791C4D3×#23511yescharacteristic
792C4#6433011yescharacteristic
793C3—21no—
794C3#7876311yescharacteristic, complemented
795C3#7950311yescharacteristic, complemented
796C2—22no—
797C2—121no—
798C2—122no—
799C2—241no—
800C2#1059467811yescharacteristic
801C2C2×#6380011yescharacteristic
802C2#1059507311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10594886C2
hypercenterC22×C8D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #10594988C2semidirect
3. #10592815C2semidirect
4. C2×C3×#821C2semidirect
5. C3×#5111C2semidirect
6. #10591172C2semidirect
7. #10591135C2semidirect
8. #10590969C2semidirect
9. #10590895C2semidirect
10. #10590861C2semidirect
11. #10590828C2semidirect
12. #10590762C2semidirect
13. #10590747C2semidirect
14. #10590680C2semidirect
15. #10590670C2semidirect
23. C2×#3746C22semidirect
26. C2×C3×ΓL(1,𝔽25)C22semidirect
31. #63918C22semidirect
35. D3×C4⋊Dic3C22semidirect
39. #63857C22semidirect
41. #63844C22semidirect
44. #63645C22semidirect
45. #63643C22semidirect
46. #63643C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×#815C22semidirect
54. C3×Dic3⋊C8C22semidirect
55. #63575C22semidirect
56. #63575C22semidirect
57. #63567C22semidirect
58. #63567C22semidirect
73. C2×#821D3semidirect
74. #5111D3semidirect
184. C2×ΓL(1,𝔽25)C2×D3semidirect
218. (C2×D3)⋊C8C2×D3semidirect
232. #815C2×D3semidirect
233. Dic3⋊C8C2×D3semidirect
705. C32#3314semidirect
794. C3#78763semidirect
795. C3#79503semidirect

Maximal subgroups

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

subgroupindex
#105949882
#105948862
#105928152
C2×C3×#8212
C3×#51112
#105911722
#105911352
#105909692
#105908952
#105908612
#105908282
#105907622
#105907472
#105906802
#105906702
#795033
#787633