Finite Group Databasebeta

← #11889299

Subgroups — #11889299

Order 1152.

883 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595431C211yesmaximal, characteristic
2#10594565C211yesmaximal, characteristic, complemented
3#10592503C211yesmaximal, characteristic, complemented
4C3×#4815C211yesmaximal, characteristic, complemented
5C3×#4798C211yesmaximal, characteristic, complemented
6#10591638C211yesmaximal, characteristic, complemented
7#10591624C211yesmaximal, characteristic, complemented
8#10591602C211yesmaximal, characteristic, complemented
9#10590942C211yesmaximal, characteristic, complemented
10#10590843C211yesmaximal, characteristic, complemented
11#10590759C211yesmaximal, characteristic, complemented
12#10590737C211yesmaximal, characteristic, complemented
13#10590592C211yesmaximal, characteristic, complemented
14#10590512C211yesmaximal, characteristic, complemented
15#10590457C211yesmaximal, characteristic, complemented
16#81526—31nomaximal
17#80617—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic, complemented
21#64101C2211yescharacteristic, complemented
22C3×#947C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic, complemented
25C2×C3×#204C2211yescharacteristic
26C3×#892C2211yescharacteristic
27C3×#887C2211yescharacteristic, complemented
28#63923—21no—
29#63921—21no—
30#63918C2211yescharacteristic, complemented
31C4×#627—21no—
32#63916C2211yescharacteristic
33#63910—21no—
34C4×#626C2211yescharacteristic
35#63894C2211yescharacteristic
36#63871C2211yescharacteristic, complemented
37#63868—21no—
38#63862—21no—
39#63856C2211yescharacteristic
40#63853—21no—
41#63852—21no—
42C2×#3717C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C32×#103C2211yescharacteristic, complemented
45#63662C2211yescharacteristic, complemented
46#63648C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#835C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#817C2211yescharacteristic, complemented
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61#5676—31no—
62#5630—31no—
63#5584—31no—
64#5533—31no—
65C3×#485—31no—
66C3×#464—31no—
67#5189—31no—
68#5187—31no—
69#5171—31no—
70#5169—31no—
71#5055—31no—
72#5052—31no—
73#5026—31no—
74#5001—31no—
75#4889—31no—
76#4885—31no—
77#4870—31no—
78#4864—31no—
79#4842—31no—
80#4836—31no—
81#4815D311yescharacteristic, complemented
82#4808—31no—
83#4804—31no—
84#4804—31no—
85#4804—61no—
86#4798D311yescharacteristic, complemented
87#4794—31no—
88#4779—31no—
89#4770—31no—
90#4731—31no—
91#4728—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94#3832—22no—
95#3832—41no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#627—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#626D411yescharacteristic
107C2×#624—21no—
108D3×D12—22no—
109D3×D12—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4×C3⋊Dic3—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C8×C3⋊D3—41no—
117C3×#216—41no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204—41no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722—21no—
137#3722—21no—
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142#3717—22no—
143#3711—41no—
144#3311—91noSylow
145C2×#239—31no—
146C2×#239—31no—
147C2×#239—61no—
148C2×D3×D4—31no—
149C22×D12—31no—
150C2×C3×Q16—31no—
151C2×C3×SD16—31no—
152C3×#124—31no—
153C3×C22⋊Q8—31no—
154C3×C4×Q8—31no—
155C3×#117—31no—
156#947C2×D311yescharacteristic
157#946—31no—
158#946—31no—
159#946C2×D311yescharacteristic
160C2×#216C2×D311yescharacteristic, complemented
161C2×#215—31no—
162#938—31no—
163C4×#67—31no—
164#924—31no—
165C2×#208—31no—
166C2×#204—31no—
167C2×#204C2×D311yescharacteristic
168C2×ΓL(1,𝔽25)—31no—
169C2×D3×C8—31no—
170C2×D3×C8—31no—
171C2×D3×C8—61no—
172#898—61no—
173#898—61no—
174#897—31no—
175#895—31no—
176#895—61no—
177#894—61no—
178#893—31no—
179#892—31no—
180#892—31no—
181#892—61no—
182#892C2×D311yescharacteristic
183#888—31no—
184#887C2×D311yescharacteristic, complemented
185#885—61no—
186#884—61no—
187#883—61no—
188#882—61no—
189#882—61no—
190D3×C22⋊C4—61no—
191D3×C22⋊C4—61no—
192#879—61no—
193#876—61no—
194#875—61no—
195C4×D12—31no—
196C4×D12—31no—
197#869—31no—
198C4×Dic6—61no—
199C4×Dic6—61no—
200C3×#107—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103C2×D311yescharacteristic, complemented
206C3×#103C2×D311yescharacteristic, complemented
207C3×#102—31no—
208C3×C22⋊C8—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—61no—
213#835C2×D311yescharacteristic, complemented
214#832—31no—
215#832—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8C2×D311yescharacteristic
224#817—31no—
225#817C2×D311yescharacteristic, complemented
226#815—31no—
227Dic3⋊C8C2×D311yescharacteristic, complemented
228#810—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#809C2×D311yescharacteristic
235#808—31no—
236#807C2×D311yescharacteristic, complemented
237#803—31no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—42no—
254C4⋊(C3⋊D3)#4112yes—
255C4×C3⋊D3—21no—
256C4×C3⋊D3—21no—
257C4×C3⋊D3—42no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#627—42no—
271#626—41no—
272#626—42no—
273#626—81no—
274#624—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—91no—
281#489—91no—
282#485—31no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—91no—
287#464—31no—
288#452—91no—
289#450—91no—
290#440—91no—
291#435—91no—
292#418—91no—
293#416—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×D4—31no—
301C22×C3×C4—31no—
302C2×#67—31no—
303C2×#67—61no—
304C2×#67—61no—
305#239—62no—
306#239—62no—
307#239—64no—
308#239—121no—
309#239—121no—
310#239—122no—
311D3×D4—62no—
312D3×D4—121no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×D12—62no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—121no—
323C2×D12—121no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—121no—
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6C22×D311yescharacteristic
337C3×Q16—121no—
338C3×SD16—121no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—31no—
356C3×C42—61no—
357C3×C42—61no—
358#217—31no—
359#217—61no—
360#217—61no—
361#216—41no—
362#215—62no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
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)⋊C4—61no—
378(C2×D3)⋊C4—121no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—31no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394C4×Dic3—21no—
395C4×Dic3—21no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—121no—
399C4×Dic3C22×D311yescharacteristic
400#208—121no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406#204—41no—
407#204—62no—
408ΓL(1,𝔽25)—121no—
409D3×C8—121no—
410D3×C8—121no—
411D3×C8—122no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—21no—
414C2×C3⋊D3—22no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425D32—84no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—91no—
439C22×D4—91no—
440C2×Q16—31no—
441C2×SD16—31no—
442C2×SD16—91no—
443C2×M16—91no—
444C22×C8—91no—
445C4⋊Q8—91no—
446#126—181no—
447#126—181no—
448#124—31no—
449#124—181no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—91no—
453C22⋊Q8—91no—
454#121—91no—
455#121—181no—
456#120—181no—
457C4×Q8—31no—
458C4×Q8—181no—
459C4×D4—91no—
460C4×D4—91no—
461#117—31no—
462#117—91no—
463C2×C22⋊C4—181no—
464#107—31no—
465#106—31no—
466#106—91no—
467C4⋊C8—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#103D3211yescharacteristic, complemented
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8—91no—
480#97—91no—
481C23×C3—31no—
482C23×C3—61no—
483C22×D3—21no—
484C22×D3—31no—
485C22×D3—31no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—121no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—241no—
495C22×D3—241no—
496C22×D3D3×D411yescharacteristic
497C3×Q8—22no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—41no—
503C3×Q8—61no—
504C3×Q8—61no—
505C3×D4—61no—
506C3×D4—61no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—121no—
525#67—122no—
526#67—241no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—121no—
536C2×Dic3D3×D411yescharacteristic
537C2×Dic3D3×D411yescharacteristic
538C2×Dic3D3×D411yescharacteristic
539D12—21no—
540D12—21no—
541D12—32no—
542D12—32no—
543D12—62no—
544D12—61no—
545D12—61no—
546D12—121no—
547D12—122no—
548D12—122no—
549D12—124no—
550D12—121no—
551D12—122no—
552D12—241no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—62no—
556C4×D3—62no—
557C4×D3—61no—
558C4×D3—61no—
559C4×D3—61no—
560C4×D3—61no—
561C4×D3—122no—
562C4×D3—122no—
563C4×D3—124no—
564C4×D3—241no—
565C4×D3—241no—
566Dic6—21no—
567Dic6—21no—
568Dic6—122no—
569Dic6—122no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—41no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—121no—
580C2×C32#54611yescharacteristic
581C2×C32#57511yescharacteristic
582C2×C32#57711yescharacteristic
583C3⋊D3—41no—
584C3⋊D3—42no—
585C3×D3—41no—
586C3×D3—81no—
587C24—181no—
588#41—182no—
589#41—361no—
590C2×Q8—31no—
591C2×Q8—181no—
592C2×Q8C2×D3211yescharacteristic
593C2×D4—31no—
594C2×D4—91no—
595C2×D4—91no—
596C2×D4—181no—
597C2×D4—181no—
598C2×D4—182no—
599C2×D4—181no—
600C2×D4—361no—
601C22×C4—31no—
602C22×C4—91no—
603C22×C4—181no—
604C22×C4—181no—
605Q16—121no—
606SD16—121no—
607SD16—182no—
608M16—361no—
609C2×C8—31no—
610C2×C8—31no—
611C2×C8—91no—
612C2×C8—361no—
613C2×C8C2×D3211yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—91no—
619C4⋊C4—91no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4C2×D3211yescharacteristic
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—91no—
629C22⋊C4—91no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C42—31no—
636C42—61no—
637C42—61no—
638C42—181no—
639C22×C3—21no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3C2×D3×D411yescharacteristic
647C22×C3C2×D3×D411yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—62no—
655C2×D3—61no—
656C2×D3—62no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—62no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—122no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—241no—
671C2×D3—241no—
672C2×D3—244no—
673C2×D3—244no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—42no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—81no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4#100411yescharacteristic
689C3×C4D3×#4111yescharacteristic
690C3×C4D3×#4111yescharacteristic
691C3×C4#100911yescharacteristic
692Dic3—21no—
693Dic3—21no—
694Dic3—21no—
695Dic3—41no—
696Dic3—41no—
697Dic3—41no—
698Dic3—62no—
699Dic3—61no—
700Dic3—61no—
701Dic3—121no—
702Dic3—121no—
703Dic3—241no—
704C32#331111yescharacteristic, complemented, Sylow
705C23—31no—
706C23—61no—
707C23—91no—
708C23—181no—
709C23—362no—
710C23—362no—
711C23—721no—
712Q8—21no—
713Q8—21no—
714Q8—61no—
715Q8—61no—
716Q8—362no—
717D4—61no—
718D4—61no—
719D4—92no—
720D4—181no—
721D4—362no—
722D4—361no—
723D4—362no—
724D4—721no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—91no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—362no—
740C2×C4—721no—
741C2×C4C22×D3211yescharacteristic
742C8—21no—
743C8—61no—
744C8—61no—
745C8—181no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—121no—
750C2×C3—241no—
751C2×C3#561211yescharacteristic
752C2×C3#565411yescharacteristic
753C2×C3#577011yescharacteristic
754C2×C3#577011yescharacteristic
755C2×C3#577711yescharacteristic
756C2×C3#577711yescharacteristic
757D3—41no—
758D3—81no—
759D3—122no—
760D3—121no—
761D3—122no—
762D3—121no—
763D3—122no—
764D3—242no—
765C22—61no—
766C22—61no—
767C22—61no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—181no—
772C22—181no—
773C22—181no—
774C22—182no—
775C22—361no—
776C22—361no—
777C22—724no—
778C22D32×D411yescharacteristic
779C4—41no—
780C4—41no—
781C4—61no—
782C4—61no—
783C4—61no—
784C4—121no—
785C4—121no—
786C4—121no—
787C4—181no—
788C4—361no—
789C4#6430611yescharacteristic
790C4#6431411yescharacteristic
791C3—21no—
792C3#8061711yescharacteristic, complemented
793C3#8152611yescharacteristic, complemented
794C2—121no—
795C2—241no—
796C2—361no—
797C2—362no—
798C2#1059427911yescharacteristic
799C2#1059475711yescharacteristic
800C2#1059476211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10595431C2
hypercenter#103D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. #10594565C2semidirect
3. #10592503C2semidirect
4. C3×#4815C2semidirect
5. C3×#4798C2semidirect
6. #10591638C2semidirect
7. #10591624C2semidirect
8. #10591602C2semidirect
9. #10590942C2semidirect
10. #10590843C2semidirect
11. #10590759C2semidirect
12. #10590737C2semidirect
13. #10590592C2semidirect
14. #10590512C2semidirect
15. #10590457C2semidirect
20. C2×C8×C3⋊D3C22semidirect
21. #64101C22semidirect
24. C2×C3×#216C22semidirect
27. C3×#887C22semidirect
30. #63918C22semidirect
36. #63871C22semidirect
44. C32×#103C22semidirect
45. #63662C22semidirect
48. C3×#835C22semidirect
50. C3×#817C22semidirect
51. C3×Dic3⋊C8C22semidirect
53. C3×#807C22semidirect
54. #63573C22semidirect
55. #63565C22semidirect
59. #63557C22semidirect
60. #63554C22semidirect
81. #4815D3semidirect
86. #4798D3semidirect
160. C2×#216C2×D3semidirect
184. #887C2×D3semidirect
205. C3×#103C2×D3semidirect
206. C3×#103C2×D3semidirect
213. #835C2×D3semidirect
225. #817C2×D3semidirect
227. Dic3⋊C8C2×D3semidirect
236. #807C2×D3semidirect
471. #103D32semidirect
704. C32#3311semidirect
792. C3#80617semidirect
793. C3#81526semidirect

Maximal subgroups

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

subgroupindex
#105954312
#105945652
#105925032
C3×#48152
C3×#47982
#105916382
#105916242
#105916022
#105909422
#105908432
#105907592
#105907372
#105905922
#105905122
#105904572
#815263
#806173