Finite Group Databasebeta

← #11889774

Subgroups — #11889774

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#10594629C211yesmaximal, characteristic
2#10594393C211yesmaximal, characteristic, complemented
3#10592581C211yesmaximal, characteristic, complemented
4C3×#4890C211yesmaximal, characteristic, complemented
5C3×#4887C211yesmaximal, characteristic, complemented
6#10590965C211yesmaximal, characteristic, complemented
7D3×#821C211yesmaximal, characteristic, complemented
8#10590801C211yesmaximal, characteristic, complemented
9#10590727C211yesmaximal, characteristic, complemented
10#10590612C211yesmaximal, characteristic, complemented
11#10590596C211yesmaximal, characteristic, complemented
12#10590535C211yesmaximal, characteristic, complemented
13#10590522C211yesmaximal, characteristic, complemented
14#10590478C211yesmaximal, characteristic, complemented
15#10590440C211yesmaximal, characteristic, complemented
16#80982—31nomaximal
17#80777—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20#64104C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
22C2×C3×Dic12C2211yescharacteristic, complemented
23C2×C3×D3×C8C2211yescharacteristic
24C3×#897C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#888C2211yescharacteristic, complemented
28#63923—21no—
29D3×(C2×D3)⋊C4—21no—
30#63909—21no—
31C4×#626C2211yescharacteristic
32#63890—21no—
33D3×C4⋊Dic3C2211yescharacteristic
34#63887—21no—
35#63881—21no—
36#63871—21no—
37#63871C2211yescharacteristic, complemented
38#63864C2211yescharacteristic
39#63846—21no—
40Dic3×Dic6C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×#3712C2211yescharacteristic, complemented
44C32×#107C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63647C2211yescharacteristic, complemented
47#63636C2211yescharacteristic
48#63634C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#807C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5730—31no—
62#5635—31no—
63#5630—31no—
64#5554—31no—
65C3×#474—31no—
66C3×#467—31no—
67#5187—31no—
68#5185—31no—
69C2×#821—31no—
70#5111—31no—
71#5089—31no—
72#5046—31no—
73#5044—31no—
74#5018—31no—
75#4890D311yescharacteristic, complemented
76#4887D311yescharacteristic, complemented
77#4886—31no—
78#4884—31no—
79#4882—31no—
80#4882—31no—
81#4882—61no—
82#4845—31no—
83#4836—31no—
84#4817—31no—
85#4812—31no—
86#4803—31no—
87#4794—31no—
88#4783—31no—
89#4776—31no—
90#4771—31no—
91D3×#102—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#626—21no—
104C2×#626—21no—
105C2×#626D411yescharacteristic
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108D3×D12—22no—
109D3×D12—41no—
110#3796—22no—
111#3796—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×Dic12—41no—
130C3×D3×C8—41no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3D411yescharacteristic
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141#3717—41no—
142#3715—22no—
143#3712—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×#237—31no—
147C2×D3×D4—31no—
148C22×D12—31no—
149C2×C3×Q16—31no—
150C22×C3×C8—31no—
151C3×C4⋊Q8—31no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C4×D4—31no—
155#947—31no—
156#946—31no—
157#946—61no—
158#946—61no—
159Q8×Dic3—31no—
160C2×#215—31no—
161C2×#215—31no—
162C2×#214—31no—
163#930—61no—
164C4×#67—31no—
165C2×(C2×D3)⋊C4—61no—
166C2×C4⋊Dic3—31no—
167C2×Dic12C2×D311yescharacteristic, complemented
168C2×#204—31no—
169C2×ΓL(1,𝔽25)—31no—
170C2×ΓL(1,𝔽25)—31no—
171C2×D3×C8C2×D311yescharacteristic
172#897—31no—
173#897—61no—
174#897C2×D311yescharacteristic
175#897C2×D311yescharacteristic
176#895—31no—
177#895—31no—
178#895—61no—
179#895—61no—
180#894—61no—
181#893—61no—
182#893C2×D311yescharacteristic
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#886—61no—
191#882—61no—
192#882—61no—
193#67⋊C4—61no—
194D3×C22⋊C4—61no—
195#878—61no—
196#875—31no—
197C4×D12—31no—
198C4×Dic6—31no—
199C3×#107—21no—
200C3×#107—31no—
201C3×#107C2×D311yescharacteristic, complemented
202C3×#107C2×D311yescharacteristic, complemented
203C3×C4⋊C8—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#102—31no—
207C3×#102—31no—
208#835—31no—
209#835—31no—
210#832—31no—
211#830—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—61no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—61no—
222#816—31no—
223#815—31no—
224Dic3⋊C8C2×D311yescharacteristic, complemented
225#810—31no—
226#810C2×D311yescharacteristic, complemented
227#810C2×D311yescharacteristic, complemented
228#809—31no—
229#809—31no—
230#809—31no—
231#809—61no—
232#809C2×D311yescharacteristic
233#807—31no—
234#807—31no—
235#807—61no—
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—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—81no—
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C4×C3⋊D3—81no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—81no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—81no—
272#626—22no—
273#626—42no—
274#626—42no—
275D3×Dic3—42no—
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—91no—
284#484—91no—
285#480—91no—
286#474—31no—
287#468—91no—
288#467—31no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×Q8—61no—
301C2×C3×D4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C2×#67—31no—
305C2×#67—61no—
306C2×#67—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309#239—62no—
310#239—121no—
311#237—62no—
312#237—121no—
313D3×D4—62no—
314D3×D4—121no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—62no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—121no—
325C2×D12—121no—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
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×Q16—121no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—121no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C42—31no—
361#217—31no—
362#215—62no—
363#215—121no—
364#214—62no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
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—61no—
379(C2×D3)⋊C4—121no—
380C4⋊Dic3—21no—
381C4⋊Dic3—21no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—31no—
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⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406Dic12—41no—
407#204—121no—
408ΓL(1,𝔽25)—121no—
409ΓL(1,𝔽25)—121no—
410D3×C8—41no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—21no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3#13712yes—
424D32—84no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—21no—
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—91no—
439C2×Q16—31no—
440C2×SD16—91no—
441C2×SD16—91no—
442C2×M16—91no—
443C22×C8—31no—
444C4⋊Q8—31no—
445#125—181no—
446#124—91no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451C22⋊Q8—181no—
452C22⋊Q8—181no—
453#121—91no—
454#121—181no—
455#120—181no—
456C4×Q8—91no—
457C4×D4—31no—
458C4×D4—91no—
459C4×D4—181no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4—91no—
462C2×C22⋊C4—181no—
463#107—31no—
464#107—91no—
465#107D3211yescharacteristic, complemented
466C4⋊C8—31no—
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#102—91no—
477C22⋊C8—91no—
478C22⋊C8—91no—
479#97—91no—
480C23×C3—31no—
481C23×C3—61no—
482C22×D3—21no—
483C22×D3—31no—
484C22×D3—31no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—121no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—241no—
494C22×D3—241no—
495C22×D3D3×D411yescharacteristic
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×Q8—241no—
501C3×D4—32no—
502C3×D4—61no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—241no—
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—62no—
522#67—122no—
523#67—122no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—121no—
533C2×Dic3—122no—
534C2×Dic3—241no—
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537C2×Dic3D3×D411yescharacteristic
538D12—21no—
539D12—62no—
540D12—61no—
541D12—61no—
542D12—61no—
543D12—61no—
544D12—121no—
545D12—121no—
546D12—122no—
547D12—122no—
548D12—241no—
549D12—241no—
550D12—242no—
551D12#23912yes—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—61no—
555C4×D3—61no—
556C4×D3—61no—
557C4×D3—61no—
558C4×D3—81no—
559C4×D3—121no—
560C4×D3—121no—
561C4×D3—122no—
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#54611yescharacteristic
582C2×C32C2×#13711yescharacteristic
583C2×C32#57611yescharacteristic
584C3⋊D3—41no—
585C3⋊D3—81no—
586C3×D3—22no—
587C3×D3—42no—
588C24—181no—
589#41—182no—
590#41—361no—
591C2×Q8—31no—
592C2×Q8—31no—
593C2×Q8—61no—
594C2×D4—31no—
595C2×D4—91no—
596C2×D4—91no—
597C2×D4—181no—
598C2×D4—181no—
599C2×D4—182no—
600C2×D4—181no—
601C2×D4—361no—
602C22×C4—31no—
603C22×C4—61no—
604C22×C4—91no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4—181no—
608Q16—121no—
609SD16—182no—
610SD16—361no—
611M16—361no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—91no—
615C2×C8—121no—
616C2×C8C2×D3211yescharacteristic
617C4⋊C4—31no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—91no—
622C4⋊C4—91no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4C2×D3211yescharacteristic
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—61no—
643C22×C3—61no—
644C22×C3—62no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3C2×D3×D411yescharacteristic
648C22×C3C2×D3×D411yescharacteristic
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—22no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—62no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—241no—
670C2×D3—241no—
671C2×D3—241no—
672C2×D3—244no—
673C2×D3—244no—
674C2×D3#91812yes—
675C3×C4—21no—
676C3×C4—21no—
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—81no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4#100411yescharacteristic
690C3×C4C2×#23911yescharacteristic
691C3×C4D3×#4111yescharacteristic
692C3×C4#100911yescharacteristic
693Dic3—21no—
694Dic3—21no—
695Dic3—21no—
696Dic3—41no—
697Dic3—41no—
698Dic3—41no—
699Dic3—61no—
700Dic3—61no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—241no—
705C32#331411yescharacteristic, complemented, Sylow
706C23—31no—
707C23—61no—
708C23—91no—
709C23—181no—
710C23—362no—
711C23—362no—
712C23—721no—
713Q8—61no—
714Q8—61no—
715Q8—61no—
716Q8—61no—
717Q8—241no—
718D4—32no—
719D4—61no—
720D4—182no—
721D4—181no—
722D4—181no—
723D4—362no—
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—61no—
736C2×C4—91no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—241no—
741C2×C4—362no—
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—122no—
754C2×C3#561011yescharacteristic
755C2×C3#563011yescharacteristic
756C2×C3#575711yescharacteristic
757C2×C3C2×#91811yescharacteristic
758C2×C3#576911yescharacteristic
759C2×C3D3×#13711yescharacteristic
760D3—22no—
761D3—42no—
762D3—122no—
763D3—121no—
764D3—121no—
765D3—241no—
766D3—241no—
767D3—481no—
768C22—32no—
769C22—61no—
770C22—61no—
771C22—62no—
772C22—121no—
773C22—121no—
774C22—181no—
775C22—181no—
776C22—181no—
777C22—361no—
778C22—361no—
779C22—361no—
780C22—724no—
781C22D32×D411yescharacteristic
782C4—41no—
783C4—41no—
784C4—61no—
785C4—61no—
786C4—61no—
787C4—121no—
788C4—121no—
789C4—121no—
790C4—181no—
791C4—361no—
792C4#6430711yescharacteristic
793C4D3×#23911yescharacteristic
794C3—21no—
795C3#8077711yescharacteristic, complemented
796C3#8098211yescharacteristic, complemented
797C2—62no—
798C2—122no—
799C2—361no—
800C2—721no—
801C2#1059462211yescharacteristic
802C2#1059473411yescharacteristic
803C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#10594629C2
hypercenter#107D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594393C2semidirect
3. #10592581C2semidirect
4. C3×#4890C2semidirect
5. C3×#4887C2semidirect
6. #10590965C2semidirect
7. D3×#821C2semidirect
8. #10590801C2semidirect
9. #10590727C2semidirect
10. #10590612C2semidirect
11. #10590596C2semidirect
12. #10590535C2semidirect
13. #10590522C2semidirect
14. #10590478C2semidirect
15. #10590440C2semidirect
21. C4⋊C4×C3⋊D3C22semidirect
22. C2×C3×Dic12C22semidirect
27. C3×#888C22semidirect
37. #63871C22semidirect
40. Dic3×Dic6C22semidirect
43. C2×#3712C22semidirect
44. C32×#107C22semidirect
46. #63647C22semidirect
48. #63634C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#810C22semidirect
52. C3×#810C22semidirect
54. C3×#807C22semidirect
55. #63566C22semidirect
56. #63565C22semidirect
60. #63554C22semidirect
75. #4890D3semidirect
76. #4887D3semidirect
167. C2×Dic12C2×D3semidirect
189. #888C2×D3semidirect
201. C3×#107C2×D3semidirect
202. C3×#107C2×D3semidirect
224. Dic3⋊C8C2×D3semidirect
226. #810C2×D3semidirect
227. #810C2×D3semidirect
236. #807C2×D3semidirect
465. #107D32semidirect
705. C32#3314semidirect
795. C3#80777semidirect
796. C3#80982semidirect

Maximal subgroups

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

subgroupindex
#105946292
#105943932
#105925812
C3×#48902
C3×#48872
#105909652
D3×#8212
#105908012
#105907272
#105906122
#105905962
#105905352
#105905222
#105904782
#105904402
#809823
#807773