Finite Group Databasebeta

← #11889312

Subgroups — #11889312

Order 1152.

852 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594630C211yesmaximal, characteristic
2#10594557C211yesmaximal, characteristic, complemented
3#10592567C211yesmaximal, characteristic, complemented
4C3×#4870C211yesmaximal, characteristic, complemented
5C3×#4864C211yesmaximal, characteristic, complemented
6#10590954C211yesmaximal, characteristic, complemented
7#10590943C211yesmaximal, characteristic, complemented
8#10590859C211yesmaximal, characteristic, complemented
9#10590727C211yesmaximal, characteristic, complemented
10#10590614C211yesmaximal, characteristic, complemented
11#10590594C211yesmaximal, characteristic, complemented
12#10590531C211yesmaximal, characteristic, complemented
13#10590524C211yesmaximal, characteristic, complemented
14#10590478C211yesmaximal, characteristic, complemented
15#10590449C211yesmaximal, characteristic, complemented
16#81078—31nomaximal
17#80686—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64106C2211yescharacteristic
21#64101C2211yescharacteristic
22C2×C3×#204C2211yescharacteristic
23C2×C3×D3×C8C2211yescharacteristic, complemented
24C3×#897C2211yescharacteristic, complemented
25C3×#895C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#888C2211yescharacteristic, complemented
28#63922—21no—
29D3×(C2×D3)⋊C4—21no—
30#63908—21no—
31#63907—21no—
32C4×#626C2211yescharacteristic
33#63891—21no—
34#63871C2211yescharacteristic
35#63862—21no—
36#63860C2211yescharacteristic
37#63848—21no—
38#63843—21no—
39Dic3×Dic6C2211yescharacteristic, complemented
40#63841C2211yescharacteristic, complemented
41C2×#3719C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic
43C2×#3712C2211yescharacteristic
44C32×#106C2211yescharacteristic, complemented
45#63647C2211yescharacteristic
46#63643C2211yescharacteristic, complemented
47#63637C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic
54C3×#808C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61#5732—31no—
62#5641—31no—
63#5612—31no—
64#5554—31no—
65C3×#476—31no—
66C3×#465—31no—
67#5169—31no—
68#5166—31no—
69#5113—31no—
70#5111—31no—
71#5089—31no—
72#5047—31no—
73#5035—31no—
74#5018—31no—
75#4870D311yescharacteristic, complemented
76#4868—31no—
77#4868—31no—
78#4868—61no—
79#4867—31no—
80#4866—31no—
81#4864D311yescharacteristic, complemented
82#4845—31no—
83#4836—31no—
84#4817—31no—
85#4816—31no—
86#4783—31no—
87#4776—31no—
88#4772—31no—
89#4770—31no—
90#4770—31no—
91#4765—31no—
92C22×D32—21no—
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×D12—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×#626D411yescharacteristic
103C2×#625—21no—
104C2×#625—21no—
105C2×D3×Dic3—21no—
106#3802—22no—
107#3802—41no—
108#3795—22no—
109#3795—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3752—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3—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⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×#204—41no—
129C3×D3×C8—41no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133#3722—21no—
134#3722D411yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139Dic32—21no—
140Dic32—21no—
141#3719—41no—
142#3715—22no—
143#3712—41no—
144#3311—91noSylow
145C2×#237—31no—
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×#235—31no—
149C2×C3×SD16—31no—
150C22×C3×C8—31no—
151C3×C4⋊Q8—31no—
152C3×C22⋊Q8—31no—
153C3×#121—31no—
154C3×C4×D4—31no—
155#947—61no—
156#946—31no—
157Q8×Dic3—31no—
158Q8×Dic3—61no—
159C2×#216—31no—
160C2×#215—31no—
161#938—61no—
162#937—61no—
163#936—31no—
164C2×#214—31no—
165#930—61no—
166C4×#67—31no—
167C2×(C2×D3)⋊C4—61no—
168#926—31no—
169C2×Dic12—31no—
170C2×#204C2×D311yescharacteristic
171C2×ΓL(1,𝔽25)—31no—
172C2×ΓL(1,𝔽25)—31no—
173C2×D3×C8C2×D311yescharacteristic, complemented
174#898—61no—
175#898—61no—
176#898—61no—
177#897—31no—
178#897—31no—
179#897—31no—
180#897—61no—
181#897C2×D311yescharacteristic, complemented
182#895C2×D311yescharacteristic
183#893C2×D311yescharacteristic
184#892—31no—
185#892—31no—
186#892—31no—
187#892—61no—
188#888C2×D311yescharacteristic, complemented
189#887—61no—
190#886—61no—
191#885—61no—
192#883—61no—
193#882—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196#875—31no—
197C4×D12—31no—
198C4×Dic6—31no—
199C3×#106—21no—
200C3×#106—31no—
201C3×#106C2×D311yescharacteristic, complemented
202C3×#106C2×D311yescharacteristic, complemented
203C3×C4⋊C8—31no—
204C3×#103—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#830—31no—
212#821—31no—
213#821—31no—
214#821C2×D311yescharacteristic
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—61no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—61no—
223#815—31no—
224Dic3⋊C8C2×D311yescharacteristic, complemented
225#810—31no—
226#810—31no—
227#810—31no—
228#810—61no—
229#810C2×D311yescharacteristic, complemented
230#809—31no—
231#809C2×D311yescharacteristic
232#809C2×D311yescharacteristic
233#808C2×D311yescharacteristic, complemented
234#807—31no—
235#807—31no—
236#807—61no—
237#803—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3—21no—
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⋊Dic3—21no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4×C3⋊D3—21no—
252C4×C3⋊D3—21no—
253#634—21no—
254#634—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—81no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—81no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—42no—
271#626—41no—
272#625—42no—
273#625—42no—
274D3×Dic3—42no—
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—91no—
283#482—91no—
284#476—31no—
285#470—91no—
286#465—31no—
287#464—91no—
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—31no—
297C2×C3×Q8—61no—
298C2×C3×D4—31no—
299C2×C3×D4—31no—
300C2×C3×D4—61no—
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C2×#67—31no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C22×Dic3—61no—
309#237—62no—
310#237—121no—
311D3×D4—62no—
312D3×D4—62no—
313D3×D4—121no—
314D3×D4—121no—
315#235—62no—
316#235—121no—
317C2×D12—21no—
318C2×D12—31no—
319C2×D12C22×D311yescharacteristic
320C2×D12C22×D311yescharacteristic
321C2×C4×D3—21no—
322C2×C4×D3—31no—
323C2×C4×D3—31no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3C22×D311yescharacteristic
327C2×Dic6—21no—
328C2×Dic6—31no—
329C2×Dic6—31no—
330C2×Dic6—61no—
331C2×Dic6C22×D311yescharacteristic
332C3×SD16—121no—
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—121no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C42—31no—
352#217—31no—
353#217—61no—
354#217—61no—
355#217—61no—
356#216—121no—
357#215—62no—
358#214—62no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
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—61no—
374(C2×D3)⋊C4—121no—
375(C2×D3)⋊C4—121no—
376C4⋊Dic3—21no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—121no—
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—31no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—121no—
398C4×Dic3C22×D311yescharacteristic
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404Dic12—121no—
405#204—41no—
406ΓL(1,𝔽25)—121no—
407ΓL(1,𝔽25)—121no—
408D3×C8—41no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—21no—
413C2×C3×D3—22no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422D32—84no—
423C32×C4—41no—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—21no—
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—91no—
436C22×D4—91no—
437C2×Q16—91no—
438C2×SD16—31no—
439C2×SD16—91no—
440C2×M16—91no—
441C22×C8—31no—
442C4⋊Q8—31no—
443#126—181no—
444#126—181no—
445#124—91no—
446#124—181no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451#121—31no—
452#121—181no—
453#120—181no—
454C4×Q8—91no—
455C4×Q8—181no—
456C4×D4—31no—
457C4×D4—91no—
458#117—91no—
459#117—91no—
460C2×C22⋊C4—181no—
461#107—91no—
462#106—31no—
463#106D3211yescharacteristic, complemented
464C4⋊C8—31no—
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—31no—
471#102—31no—
472#102—91no—
473#102—91no—
474#102—91no—
475C22⋊C8—91no—
476C22⋊C8—91no—
477#97—91no—
478C23×C3—31no—
479C23×C3—61no—
480C23×C3—61no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—31no—
484C22×D3—31no—
485C22×D3—61no—
486C22×D3—122no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—241no—
491C22×D3—241no—
492C22×D3D3×D411yescharacteristic
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—122no—
496C3×D4—32no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—61no—
500C3×D4—241no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—241no—
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—121no—
519#67—122no—
520#67—122no—
521#67—122no—
522#67—122no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—122no—
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537C2×Dic3D3×D411yescharacteristic
538D12—21no—
539D12—21no—
540D12—21no—
541D12—81no—
542D12—121no—
543D12#23912yes—
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—61no—
547C4×D3—61no—
548C4×D3—61no—
549C4×D3—61no—
550C4×D3—81no—
551C4×D3—121no—
552C4×D3—121no—
553C4×D3—122no—
554Dic6—21no—
555Dic6—21no—
556Dic6—42no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—61no—
561Dic6—121no—
562Dic6—121no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—41no—
566C3×C8—61no—
567C3×C8—61no—
568C3⋊C8—21no—
569C3⋊C8—21no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C2×C32#54611yescharacteristic
574C2×C32#57511yescharacteristic
575C2×C32#57711yescharacteristic
576C3⋊D3—41no—
577C3×D3—42no—
578C3×D3—41no—
579C3×D3—81no—
580C24—181no—
581#41—182no—
582#41—361no—
583C2×Q8—31no—
584C2×Q8—61no—
585C2×Q8—91no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—91no—
590C2×D4—181no—
591C2×D4—182no—
592C2×D4—181no—
593C2×D4—361no—
594C22×C4—31no—
595C22×C4—61no—
596C22×C4—91no—
597C22×C4—181no—
598Q16—361no—
599SD16—121no—
600SD16—182no—
601M16—361no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—91no—
605C2×C8—121no—
606C2×C8C2×D3211yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4C2×D3211yescharacteristic
616C4⋊C4C2×D3211yescharacteristic
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—91no—
621C22⋊C4—91no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C42—31no—
629C42—181no—
630C42—181no—
631C42—181no—
632C22×C3—21no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—62no—
636C22×C3—61no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C2×D3×D411yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—22no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—244no—
663C2×D3—244no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—81no—
674C3×C4—81no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4#100411yescharacteristic
678C3×C4C2×#23911yescharacteristic
679C3×C4D3×#4111yescharacteristic
680C3×C4#100911yescharacteristic
681Dic3—21no—
682Dic3—21no—
683Dic3—21no—
684Dic3—41no—
685Dic3—41no—
686Dic3—61no—
687Dic3—61no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—241no—
694Dic3—241no—
695C32#331111yescharacteristic, complemented, Sylow
696C23—31no—
697C23—61no—
698C23—61no—
699C23—91no—
700C23—362no—
701C23—362no—
702C23—721no—
703Q8—61no—
704Q8—61no—
705Q8—122no—
706Q8—181no—
707Q8—181no—
708D4—32no—
709D4—61no—
710D4—61no—
711D4—61no—
712D4—241no—
713D4—361no—
714D4—362no—
715D4—362no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—91no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—241no—
731C2×C4—362no—
732C2×C4C22×D3211yescharacteristic
733C8—21no—
734C8—61no—
735C8—61no—
736C8—181no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—122no—
741C2×C3—121no—
742C2×C3—241no—
743C2×C3#561011yescharacteristic
744C2×C3#563011yescharacteristic
745C2×C3#576211yescharacteristic
746C2×C3#576211yescharacteristic
747C2×C3#576811yescharacteristic
748C2×C3#577311yescharacteristic
749D3—41no—
750D3—42no—
751D3—81no—
752D3—121no—
753D3—121no—
754D3—241no—
755C22—61no—
756C22—62no—
757C22—61no—
758C22—61no—
759C22—121no—
760C22—121no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22—181no—
765C22—181no—
766C22—181no—
767C22—724no—
768C22D32×D411yescharacteristic
769C4—41no—
770C4—41no—
771C4—61no—
772C4—61no—
773C4—61no—
774C4—121no—
775C4—121no—
776C4—181no—
777C4—361no—
778C4—361no—
779C4#6430711yescharacteristic
780C4D3×#23911yescharacteristic
781C3—21no—
782C3#8068611yescharacteristic, complemented
783C3#8107811yescharacteristic, complemented
784C2—121no—
785C2—122no—
786C2—241no—
787C2—361no—
788C2#1059462211yescharacteristic
789C2#1059474511yescharacteristic
790C2#1059474811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10594630C2
hypercenter#106D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594557C2semidirect
3. #10592567C2semidirect
4. C3×#4870C2semidirect
5. C3×#4864C2semidirect
6. #10590954C2semidirect
7. #10590943C2semidirect
8. #10590859C2semidirect
9. #10590727C2semidirect
10. #10590614C2semidirect
11. #10590594C2semidirect
12. #10590531C2semidirect
13. #10590524C2semidirect
14. #10590478C2semidirect
15. #10590449C2semidirect
23. C2×C3×D3×C8C22semidirect
24. C3×#897C22semidirect
27. C3×#888C22semidirect
39. Dic3×Dic6C22semidirect
40. #63841C22semidirect
41. C2×#3719C22semidirect
44. C32×#106C22semidirect
46. #63643C22semidirect
47. #63637C22semidirect
48. #63634C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#810C22semidirect
54. C3×#808C22semidirect
55. #63567C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
75. #4870D3semidirect
81. #4864D3semidirect
173. C2×D3×C8C2×D3semidirect
181. #897C2×D3semidirect
188. #888C2×D3semidirect
201. C3×#106C2×D3semidirect
202. C3×#106C2×D3semidirect
224. Dic3⋊C8C2×D3semidirect
229. #810C2×D3semidirect
233. #808C2×D3semidirect
463. #106D32semidirect
695. C32#3311semidirect
782. C3#80686semidirect
783. C3#81078semidirect

Maximal subgroups

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

subgroupindex
#105946302
#105945572
#105925672
C3×#48702
C3×#48642
#105909542
#105909432
#105908592
#105907272
#105906142
#105905942
#105905312
#105905242
#105904782
#105904492
#810783
#806863