Finite Group Databasebeta

← #11889766

Subgroups — #11889766

Order 1152.

877 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595229C211yesmaximal, characteristic
2#10594393C211yesmaximal, characteristic, complemented
3#10592473C211yesmaximal, characteristic, complemented
4C3×#4776C211yesmaximal, characteristic, complemented
5C3×#4765C211yesmaximal, characteristic, complemented
6#10591464C211yesmaximal, characteristic, complemented
7#10591442C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590961C211yesmaximal, characteristic, complemented
10#10590766C211yesmaximal, characteristic, complemented
11#10590728C211yesmaximal, characteristic, complemented
12#10590682C211yesmaximal, characteristic, complemented
13#10590612C211yesmaximal, characteristic, complemented
14#10590518C211yesmaximal, characteristic, complemented
15#10590463C211yesmaximal, characteristic, complemented
16#81700—31nomaximal
17#80163—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20#64147C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
22C3×#936C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×#888C2211yescharacteristic, complemented
27#63977—21no—
28#63971—21no—
29#63969—21no—
30D3×#217—21no—
31C4×#626C2211yescharacteristic
32Dic3×D12C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63887—21no—
35#63881—21no—
36#63871—21no—
37#63871C2211yescharacteristic, complemented
38#63856C2211yescharacteristic
39#63846—21no—
40Dic3×Dic6C2211yescharacteristic, complemented
41C2×#3718C2211yescharacteristic, complemented
42C2×#3712C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63647C2211yescharacteristic, complemented
47#63645C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×#810C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61#5806—31no—
62#5730—31no—
63#5676—31no—
64#5635—31no—
65C3×#489—31no—
66C3×#450—31no—
67C2×#832—31no—
68#5174—31no—
69#5173—31no—
70#5166—31no—
71#5164—31no—
72#5087—31no—
73#5054—31no—
74#5051—31no—
75#4813—31no—
76#4811—31no—
77#4808—31no—
78#4803—31no—
79#4780—31no—
80#4776D311yescharacteristic, complemented
81#4774—31no—
82#4774—31no—
83#4774—61no—
84#4771—31no—
85D3×#102—31no—
86#4765D311yescharacteristic, complemented
87#4759—31no—
88#4730—31no—
89#4722—31no—
90#4710—31no—
91#4706—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×#67—21no—
98C3×D3×D4—22no—
99C3×D3×D4—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#626D411yescharacteristic
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3796—22no—
111#3796—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3757—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217—21no—
121C3×#214—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×#204—22no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3D411yescharacteristic
135#3722—21no—
136#3722D411yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141#3718—41no—
142#3712—41no—
143D3×C3⋊C8—41no—
144#3314—91noSylow
145C22×C3×D4—31no—
146C2×#239—31no—
147C2×#237—31no—
148C2×D3×D4C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C3×C4⋊Q8—31no—
152C3×#124—31no—
153C3×C22⋊Q8—31no—
154#953—61no—
155C2×#217—61no—
156#946—31no—
157#946—31no—
158#946—61no—
159#946—61no—
160Q8×Dic3—31no—
161C2×#216—31no—
162C2×#216—31no—
163#939—61no—
164#938—31no—
165#938—31no—
166#938—61no—
167#936C2×D311yescharacteristic
168#935—61no—
169D4×Dic3—31no—
170C2×#214C2×D311yescharacteristic
171C4×#67—31no—
172C2×C4⋊Dic3—31no—
173#924—31no—
174C22×C3⋊C8—31no—
175C2×#204C2×D311yescharacteristic
176C2×ΓL(1,𝔽25)—31no—
177C2×ΓL(1,𝔽25)—31no—
178C2×D3×C8—31no—
179#897—31no—
180#897—61no—
181#897C2×D311yescharacteristic
182#893—61no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—61no—
187#890—61no—
188#889—61no—
189#888C2×D311yescharacteristic, complemented
190#884—61no—
191#883—61no—
192#882—61no—
193#67⋊C4—61no—
194D3×C22⋊C4—61no—
195#878—61no—
196C4×D12—31no—
197C4×D12—31no—
198C4×Dic6—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#102—21no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102C2×D311yescharacteristic
205C3×#102C2×D311yescharacteristic
206C3×C22⋊C8—31no—
207C3×#97—31no—
208#835—31no—
209#835—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—61no—
215#832C2×D311yescharacteristic
216#821—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—61no—
220(C2×D3)⋊C8C2×D311yescharacteristic
221#818—31no—
222#818—31no—
223#818—31no—
224#818—61no—
225#816—31no—
226#816—31no—
227#816C2×D311yescharacteristic, complemented
228#815C2×D311yescharacteristic, complemented
229Dic3⋊C8—31no—
230#810C2×D311yescharacteristic, complemented
231#809—31no—
232#809C2×D311yescharacteristic
233#807—31no—
234#807—31no—
235#807—31no—
236#807—61no—
237C4⋊(C3⋊C8)—31no—
238C23×C32—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249#638—81no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C4×C3⋊D3—81no—
256C3×#67—42no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—81no—
272#626—22no—
273#626—42no—
274D3×Dic3—42no—
275D3×Dic3—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—91no—
283#489—31no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—31no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C24×C3—61no—
297C23×D3—21no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×Q8—61no—
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C2×C3×D4—62no—
305C2×C3×D4—121no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C22×C3×C4—31no—
309C2×#67—21no—
310C2×#67—31no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—121no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318#239—62no—
319#239—121no—
320#237—62no—
321#237—121no—
322D3×D4—22no—
323D3×D4—41no—
324C2×D12—31no—
325C2×D12—61no—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—121no—
336C2×C4×D3C22×D311yescharacteristic
337C2×Dic6—21no—
338C2×Dic6C22×D311yescharacteristic
339C2×Dic6C22×D311yescharacteristic
340C3×SD16—62no—
341C3×SD16—121no—
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—31no—
357#217—21no—
358#217—21no—
359#217—31no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—121no—
365#216—121no—
366#216—121no—
367#214—41no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376C4⋊Dic3—21no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—31no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—121no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407#204—22no—
408ΓL(1,𝔽25)—121no—
409ΓL(1,𝔽25)—121no—
410D3×C8—121no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—84no—
424C2×C3×D3#13712yes—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C22×D4—31no—
439C2×Q16—91no—
440C2×SD16—31no—
441C2×SD16—31no—
442C2×M16—91no—
443C22×C8—91no—
444C4⋊Q8—31no—
445#125—181no—
446#124—31no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451C22⋊Q8—181no—
452C22⋊Q8—181no—
453#121—91no—
454#121—181no—
455#120—181no—
456C4×Q8—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—181no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4—91no—
462C2×C22⋊C4—181no—
463#107—91no—
464#107—91no—
465#107—91no—
466C4⋊C8—91no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102D3211yescharacteristic
477C22⋊C8—31no—
478C22⋊C8—91no—
479#97—31no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3—41no—
484C23×C3—61no—
485C23×C3—122no—
486C23×C3—122no—
487C23×C3—241no—
488C22×D3—21no—
489C22×D3—31no—
490C22×D3—31no—
491C22×D3—42no—
492C22×D3—42no—
493C22×D3—61no—
494C22×D3—81no—
495C22×D3D3×D411yescharacteristic
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×Q8—241no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—32no—
506C3×D4—41no—
507C3×D4—41no—
508C3×D4—61no—
509C3×D4—122no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
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—42no—
525#67—62no—
526#67—122no—
527#67—241no—
528#67—241no—
529#67—242no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—122no—
543C2×Dic3—241no—
544C2×Dic3—241no—
545C2×Dic3D3×D411yescharacteristic
546C2×Dic3D3×D411yescharacteristic
547C2×Dic3D3×D411yescharacteristic
548D12—21no—
549D12—62no—
550D12—122no—
551D12#23712yes—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—61no—
555C4×D3—61no—
556C4×D3—61no—
557C4×D3—61no—
558C4×D3—121no—
559C4×D3—121no—
560C4×D3—122no—
561C4×D3—241no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—241no—
565C4×D3—242no—
566Dic6—21no—
567Dic6—21no—
568Dic6—21no—
569Dic6—21no—
570Dic6—81no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—41no—
574C3×C8—61no—
575C3×C8—61no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—121no—
581C2×C32—81no—
582C2×C32#54611yescharacteristic
583C2×C32C2×#13711yescharacteristic
584C2×C32#57611yescharacteristic
585C3⋊D3—41no—
586C3×D3—22no—
587C3×D3—42no—
588C24—61no—
589#41—182no—
590#41—361no—
591C2×Q8—31no—
592C2×Q8—31no—
593C2×Q8—61no—
594C2×D4—31no—
595C2×D4—61no—
596C2×D4—62no—
597C2×D4—91no—
598C2×D4—121no—
599C2×D4—181no—
600C2×D4—181no—
601C2×D4C2×D3211yescharacteristic
602C22×C4—31no—
603C22×C4—91no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4—181no—
608Q16—361no—
609SD16—62no—
610SD16—121no—
611M16—361no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—91no—
615C2×C8—361no—
616C2×C8C2×D3211yescharacteristic
617C4⋊C4—31no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—91no—
621C4⋊C4—91no—
622C4⋊C4—91no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4C2×D3211yescharacteristic
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—91no—
633C22⋊C4—91no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—31no—
639C42—181no—
640C22×C3—21no—
641C22×C3—32no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—62no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—244no—
657C22×C3C2×D3×D411yescharacteristic
658C22×C3C2×D3×D411yescharacteristic
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—22no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—62no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—84no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3#91512yes—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—81no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4C2×#23711yescharacteristic
687C3×C4#100411yescharacteristic
688C3×C4D3×#4111yescharacteristic
689C3×C4#100911yescharacteristic
690Dic3—21no—
691Dic3—21no—
692Dic3—21no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—61no—
697Dic3—61no—
698Dic3—121no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—241no—
704Dic3—241no—
705C32#331411yescharacteristic, complemented, Sylow
706C23—21no—
707C23—31no—
708C23—61no—
709C23—91no—
710C23—122no—
711C23—122no—
712C23—241no—
713Q8—61no—
714Q8—61no—
715Q8—61no—
716Q8—61no—
717Q8—241no—
718D4—21no—
719D4—21no—
720D4—32no—
721D4—61no—
722D4—122no—
723D4—182no—
724D4—362no—
725D4—721no—
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—181no—
740C2×C4—362no—
741C2×C4—721no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4C22×D3211yescharacteristic
745C8—21no—
746C8—61no—
747C8—61no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—62no—
753C2×C3—81no—
754C2×C3—81no—
755C2×C3—122no—
756C2×C3—161no—
757C2×C3#559111yescharacteristic
758C2×C3#567611yescharacteristic
759C2×C3C2×#91511yescharacteristic
760C2×C3#577411yescharacteristic
761C2×C3#577411yescharacteristic
762C2×C3D3×#13711yescharacteristic
763D3—22no—
764D3—42no—
765D3—122no—
766D3—121no—
767D3—121no—
768C22—32no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—61no—
773C22—61no—
774C22—62no—
775C22—121no—
776C22—121no—
777C22—181no—
778C22—181no—
779C22—181no—
780C22—244no—
781C22D32×D411yescharacteristic
782C4—41no—
783C4—61no—
784C4—61no—
785C4—61no—
786C4—121no—
787C4—121no—
788C4—121no—
789C4—181no—
790C4—361no—
791C4—361no—
792C4#6430711yescharacteristic
793C4D3×#23711yescharacteristic
794C3—21no—
795C3#8016311yescharacteristic, complemented
796C3#8170011yescharacteristic, complemented
797C2—62no—
798C2—81no—
799C2—122no—
800C2—361no—
801C2#1059428111yescharacteristic
802C2#1059473511yescharacteristic
803C2D3×#91511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595229C2
hypercenter#102D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594393C2semidirect
3. #10592473C2semidirect
4. C3×#4776C2semidirect
5. C3×#4765C2semidirect
6. #10591464C2semidirect
7. #10591442C2semidirect
8. D3×#832C2semidirect
9. #10590961C2semidirect
10. #10590766C2semidirect
11. #10590728C2semidirect
12. #10590682C2semidirect
13. #10590612C2semidirect
14. #10590518C2semidirect
15. #10590463C2semidirect
21. C4⋊C4×C3⋊D3C22semidirect
26. C3×#888C22semidirect
37. #63871C22semidirect
40. Dic3×Dic6C22semidirect
41. C2×#3718C22semidirect
42. C2×#3712C22semidirect
46. #63647C22semidirect
47. #63645C22semidirect
48. #63634C22semidirect
51. C3×#816C22semidirect
52. C3×#815C22semidirect
53. C3×#810C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
58. #63566C22semidirect
80. #4776D3semidirect
86. #4765D3semidirect
189. #888C2×D3semidirect
227. #816C2×D3semidirect
228. #815C2×D3semidirect
230. #810C2×D3semidirect
705. C32#3314semidirect
795. C3#80163semidirect
796. C3#81700semidirect

Maximal subgroups

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

subgroupindex
#105952292
#105943932
#105924732
C3×#47762
C3×#47652
#105914642
#105914422
D3×#8322
#105909612
#105907662
#105907282
#105906822
#105906122
#105905182
#105904632
#817003
#801633