Finite Group Databasebeta

← #11889159

Subgroups — #11889159

Order 1152.

960 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594618C211yesmaximal, characteristic
2#10594550C211yesmaximal, characteristic, complemented
3#10592588C211yesmaximal, characteristic, complemented
4C3×#4885C211yesmaximal, characteristic, complemented
5C3×#4882C211yesmaximal, characteristic, complemented
6#10590946C211yesmaximal, characteristic, complemented
7#10590946C211yesmaximal, characteristic, complemented
8#10590888C211yesmaximal, characteristic, complemented
9#10590725C211yesmaximal, characteristic, complemented
10#10590592C211yesmaximal, characteristic, complemented
11D3×#809C211yesmaximal, characteristic, complemented
12#10590588C211yesmaximal, characteristic, complemented
13#10590578C211yesmaximal, characteristic, complemented
14#10590553C211yesmaximal, characteristic, complemented
15#10590435C211yesmaximal, characteristic, complemented
16#81383—31nomaximal
17#81303—31nomaximal
18C2×#3802—21no—
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22#64102C2211yescharacteristic
23#64096C2211yescharacteristic, complemented
24C3×#895C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#892C2211yescharacteristic, complemented
27C3×D3×C4⋊C4C2211yescharacteristic, complemented
28#63922—21no—
29#63922—21no—
30#63914C2211yescharacteristic
31#63912—21no—
32#63905—21no—
33C4×#625C2211yescharacteristic
34#63872C2211yescharacteristic, complemented
35#63867—21no—
36#63862—21no—
37#63857C2211yescharacteristic, complemented
38#63857C2211yescharacteristic, complemented
39#63855—21no—
40C2×#3716C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic, complemented
42C2×#3711C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#107C2211yescharacteristic, complemented
45#63642C2211yescharacteristic, complemented
46#63637C2211yescharacteristic, complemented
47#63636C2211yescharacteristic
48C3×#821C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61#5609—31no—
62#5609—31no—
63#5529—31no—
64#5513—31no—
65C3×#482—31no—
66C3×#480—31no—
67#5042—31no—
68#5041—31no—
69#5001—31no—
70C2×#809—31no—
71#4891—31no—
72#4889—31no—
73#4889—31no—
74#4889—61no—
75#4886—31no—
76#4885D311yescharacteristic, complemented
77#4882D311yescharacteristic, complemented
78#4871—31no—
79#4864—31no—
80#4776—31no—
81#4776—31no—
82#4770—31no—
83D3×#102—31no—
84#4764—31no—
85#4764—31no—
86#4762—31no—
87#4762—31no—
88#4731—31no—
89#4731—31no—
90#4730—31no—
91#4728—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×D12—21no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×#625—21no—
108C2×#625D411yescharacteristic
109#3802—44no—
110D3×D12—22no—
111D3×D12—22no—
112D3×D12—41no—
113D3×D12—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117#3752—21no—
118#3750—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122#3744—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132#3724D411yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141#3716—41no—
142#3716—41no—
143#3711—41no—
144D3×C3⋊C8—41no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—61no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12—31no—
152C3×#121—31no—
153C3×#121—31no—
154C3×#117—31no—
155C2×C3×C4⋊C4—31no—
156#940—31no—
157#940—31no—
158#937—61no—
159#937—61no—
160C2×#214—31no—
161C2×#214—31no—
162#929—61no—
163C4×#67—31no—
164C4×#67—31no—
165#926—61no—
166#924—31no—
167#924—31no—
168C2×#208—31no—
169C22×C3⋊C8—31no—
170C2×#204—31no—
171C2×#204—31no—
172C2×#204—31no—
173C2×#204—31no—
174C2×#204—61no—
175C2×ΓL(1,𝔽25)—31no—
176C2×D3×C8—31no—
177#898—61no—
178#897—31no—
179#897—31no—
180#895C2×D311yescharacteristic
181#895C2×D311yescharacteristic
182#893—31no—
183#893—31no—
184#893—61no—
185#892C2×D311yescharacteristic, complemented
186D3×C4⋊C4C2×D311yescharacteristic, complemented
187#890—31no—
188#890—31no—
189#889—61no—
190#887—31no—
191#887—31no—
192#887—61no—
193#884—61no—
194#884—61no—
195#883—61no—
196#882—61no—
197#882—61no—
198#879—61no—
199#872—61no—
200#870—61no—
201C3×#107—21no—
202C3×#107—31no—
203C3×#107C2×D311yescharacteristic, complemented
204C3×#107C2×D311yescharacteristic, complemented
205C3×#106—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×C22⋊C8—31no—
211C3×C22⋊C8—31no—
212#832—31no—
213#832—31no—
214#821—31no—
215#821—31no—
216#821C2×D311yescharacteristic, complemented
217#821C2×D311yescharacteristic, complemented
218(C2×D3)⋊C8C2×D311yescharacteristic, complemented
219(C2×D3)⋊C8C2×D311yescharacteristic, complemented
220#815—31no—
221#815—31no—
222#815—61no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225#810—31no—
226#810—31no—
227#810—61no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—61no—
235#809C2×D311yescharacteristic, complemented
236#809C2×D311yescharacteristic, complemented
237#808C2×D311yescharacteristic, complemented
238#807C2×D311yescharacteristic, complemented
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3C2×D411yescharacteristic
243C22×C3×D3C2×D411yescharacteristic
244C2×D32—42no—
245C2×D32—42no—
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—81no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D411yescharacteristic
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)#4112yes—
258C4×C3⋊D3—42no—
259#634—21no—
260#634—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—42no—
270C3×D12—42no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—42no—
276#626—42no—
277#626—42no—
278#625—22no—
279#625—42no—
280#625—81no—
281C32×C8—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—91no—
287#490—91no—
288#482—31no—
289#480—31no—
290#478—91no—
291#468—91no—
292#465—91no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C23×D3—61no—
301C23×D3—61no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C2×#67—31no—
312C2×#67—31no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319D3×D4—62no—
320D3×D4—62no—
321D3×D4—121no—
322D3×D4—121no—
323D3×D4—124no—
324D3×D4—124no—
325C2×D12—21no—
326C2×D12—21no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12—62no—
331C2×D12—62no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—121no—
335C2×D12—121no—
336C2×D12C22×D311yescharacteristic
337C2×D12C22×D311yescharacteristic
338C2×C4×D3—21no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—121no—
342C2×C4×D3C22×D311yescharacteristic
343C2×C4×D3C22×D311yescharacteristic
344C2×Dic6—31no—
345C2×Dic6—31no—
346C2×Dic6—61no—
347C2×C3×C8—21no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8C22×D311yescharacteristic
351C2×C3×C8C22×D311yescharacteristic
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—61no—
365#217—31no—
366#217—31no—
367#217—61no—
368#217—61no—
369#214—121no—
370#214—121no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—121no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—31no—
389Dic3⋊C4—31no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—121no—
397C4×Dic3—21no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—121no—
404#208—121no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411#204—62no—
412#204—62no—
413#204—64no—
414#204—121no—
415#204—121no—
416ΓL(1,𝔽25)—121no—
417D3×C8—121no—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—22no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3AGL(1,ℤ/8)12yes—
434D32—84no—
435D32—84no—
436C32×C4—41no—
437C32×C4—41no—
438C32×C4C2×#4111yescharacteristic
439C32×C4H(5,𝔽2)11yescharacteristic
440C3⋊Dic3—21no—
441C3⋊Dic3—21no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C22×D4—91no—
448C22×D4—91no—
449C22×D4—181no—
450C2×SD16—91no—
451C2×SD16—91no—
452C2×SD16—91no—
453C2×M16—91no—
454C22×C8—91no—
455#127—91no—
456#126—181no—
457#125—91no—
458#125—181no—
459#123—181no—
460C22⋊Q8—91no—
461C22⋊Q8—91no—
462#121—31no—
463#121—31no—
464#121—181no—
465#120—181no—
466#120—181no—
467C4×Q8—91no—
468C4×D4—91no—
469C4×D4—91no—
470#117—31no—
471#117—181no—
472C2×C4⋊C4—31no—
473#107—31no—
474#107D3211yescharacteristic, complemented
475#106—31no—
476C4⋊C8—91no—
477#103—91no—
478#102—31no—
479#102—31no—
480#102—31no—
481#102—31no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487C22⋊C8—31no—
488C22⋊C8—31no—
489#97—91no—
490C23×C3—31no—
491C23×C3—31no—
492C23×C3—61no—
493C23×C3—61no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—121no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—241no—
508C22×D3—241no—
509C22×D3—241no—
510C22×D3—241no—
511C22×D3D3×D411yescharacteristic
512C22×D3D3×D411yescharacteristic
513C3×D4—61no—
514C3×D4—61no—
515C3×D4—61no—
516C3×D4—61no—
517C3×D4—122no—
518C3×D4—122no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—122no—
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—62no—
538#67—62no—
539#67—122no—
540#67—122no—
541#67—122no—
542#67—122no—
543#67—241no—
544#67—241no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—121no—
556C2×Dic3D3×D411yescharacteristic
557C2×Dic3D3×D411yescharacteristic
558D12—21no—
559D12—21no—
560D12—21no—
561D12—21no—
562D12—32no—
563D12—32no—
564D12—42no—
565D12—42no—
566D12—62no—
567D12—61no—
568D12—61no—
569D12—121no—
570D12—122no—
571D12—122no—
572C4×D3—21no—
573C4×D3—21no—
574C4×D3—21no—
575C4×D3—21no—
576C4×D3—42no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—242no—
580Dic6—62no—
581Dic6—61no—
582Dic6—61no—
583Dic6—61no—
584Dic6—61no—
585Dic6—121no—
586C3×C8—22no—
587C3×C8—21no—
588C3×C8—21no—
589C3×C8—61no—
590C3×C8—61no—
591C3⋊C8—21no—
592C3⋊C8—21no—
593C3⋊C8—61no—
594C3⋊C8—61no—
595C3⋊C8—121no—
596C2×C32#54611yescharacteristic
597C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
598C2×C32#57711yescharacteristic
599C3⋊D3—42no—
600C3×D3—22no—
601C3×D3—41no—
602C3×D3—81no—
603C3×D3—81no—
604C24—181no—
605C24—181no—
606C2×Q8—91no—
607C2×D4—31no—
608C2×D4—31no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4—91no—
612C2×D4—91no—
613C2×D4—181no—
614C2×D4—181no—
615C2×D4—182no—
616C2×D4—182no—
617C2×D4—181no—
618C2×D4—181no—
619C2×D4—361no—
620C2×D4—361no—
621C2×D4—364no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—61no—
625C22×C4—181no—
626SD16—182no—
627SD16—361no—
628SD16—361no—
629M16—361no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8—361no—
634C2×C8C2×D3211yescharacteristic
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—61no—
638C4⋊C4—91no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C4⋊C4C2×D3211yescharacteristic
645C4⋊C4C2×D3211yescharacteristic
646C22⋊C4—61no—
647C22⋊C4—61no—
648C22⋊C4—61no—
649C22⋊C4—91no—
650C22⋊C4—91no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C42—61no—
655C42—91no—
656C42—181no—
657C22×C3—21no—
658C22×C3—32no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—61no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3C2×D3×D411yescharacteristic
671C22×C3C2×D3×D411yescharacteristic
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—21no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—62no—
684C2×D3—62no—
685C2×D3—122no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—241no—
691C2×D3—241no—
692C2×D3—244no—
693C2×D3—244no—
694C2×D3—244no—
695C2×D3—244no—
696C2×D3#91112yes—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—61no—
704C3×C4—61no—
705C3×C4—81no—
706C3×C4—81no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4D3×#4111yescharacteristic
710C3×C4D3×#4111yescharacteristic
711C3×C4#100911yescharacteristic
712C3×C4#100911yescharacteristic
713Dic3—21no—
714Dic3—21no—
715Dic3—41no—
716Dic3—41no—
717Dic3—61no—
718Dic3—61no—
719Dic3—61no—
720Dic3—61no—
721Dic3—121no—
722Dic3—121no—
723Dic3—122no—
724Dic3—121no—
725Dic3—121no—
726C32#331011yescharacteristic, complemented, Sylow
727C23—31no—
728C23—31no—
729C23—61no—
730C23—61no—
731C23—181no—
732C23—362no—
733C23—362no—
734C23—362no—
735C23—362no—
736C23—721no—
737C23—721no—
738Q8—181no—
739Q8—181no—
740D4—61no—
741D4—61no—
742D4—61no—
743D4—61no—
744D4—92no—
745D4—122no—
746D4—122no—
747D4—182no—
748D4—181no—
749D4—362no—
750D4—362no—
751D4—362no—
752D4—721no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—31no—
756C2×C4—31no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—91no—
764C2×C4—91no—
765C2×C4—122no—
766C2×C4—181no—
767C2×C4—362no—
768C2×C4C22×D3211yescharacteristic
769C8—21no—
770C8—61no—
771C8—61no—
772C8—181no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—62no—
777C2×C3—121no—
778C2×C3—241no—
779C2×C3—241no—
780C2×C3#565411yescharacteristic
781C2×C3#565411yescharacteristic
782C2×C3C2×#91111yescharacteristic
783C2×C3#577011yescharacteristic
784C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
785C2×C3#577811yescharacteristic
786D3—22no—
787D3—41no—
788D3—81no—
789D3—81no—
790D3—122no—
791D3—122no—
792D3—242no—
793C22—32no—
794C22—61no—
795C22—61no—
796C22—61no—
797C22—61no—
798C22—61no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—182no—
806C22—361no—
807C22—361no—
808C22—724no—
809C22—724no—
810C22D32×D411yescharacteristic
811C4—41no—
812C4—41no—
813C4—61no—
814C4—61no—
815C4—121no—
816C4—121no—
817C4—181no—
818C4—181no—
819C4—361no—
820C4#6430611yescharacteristic
821C4#6432011yescharacteristic
822C3—21no—
823C3#8130311yescharacteristic, complemented
824C3#8138311yescharacteristic, complemented
825C2—62no—
826C2—121no—
827C2—241no—
828C2—241no—
829C2—362no—
830C2#1059461611yescharacteristic
831C2D3×#91111yescharacteristic
832C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#10594618C2
hypercenter#107D32
hypocenterC32#3310
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. #10594550C2semidirect
3. #10592588C2semidirect
4. C3×#4885C2semidirect
5. C3×#4882C2semidirect
6. #10590946C2semidirect
7. #10590946C2semidirect
8. #10590888C2semidirect
9. #10590725C2semidirect
10. #10590592C2semidirect
11. D3×#809C2semidirect
12. #10590588C2semidirect
13. #10590578C2semidirect
14. #10590553C2semidirect
15. #10590435C2semidirect
23. #64096C22semidirect
26. C3×#892C22semidirect
27. C3×D3×C4⋊C4C22semidirect
34. #63872C22semidirect
37. #63857C22semidirect
38. #63857C22semidirect
40. C2×#3716C22semidirect
41. C2×#3716C22semidirect
42. C2×#3711C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#107C22semidirect
45. #63642C22semidirect
46. #63637C22semidirect
48. C3×#821C22semidirect
49. C3×#821C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#809C22semidirect
53. C3×#809C22semidirect
54. C3×#808C22semidirect
55. C3×#807C22semidirect
56. #63572C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
76. #4885D3semidirect
77. #4882D3semidirect
185. #892C2×D3semidirect
186. D3×C4⋊C4C2×D3semidirect
203. C3×#107C2×D3semidirect
204. C3×#107C2×D3semidirect
216. #821C2×D3semidirect
217. #821C2×D3semidirect
218. (C2×D3)⋊C8C2×D3semidirect
219. (C2×D3)⋊C8C2×D3semidirect
235. #809C2×D3semidirect
236. #809C2×D3semidirect
237. #808C2×D3semidirect
238. #807C2×D3semidirect
474. #107D32semidirect
726. C32#3310semidirect
823. C3#81303semidirect
824. C3#81383semidirect

Maximal subgroups

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

subgroupindex
#105946182
#105945502
#105925882
C3×#48852
C3×#48822
#105909462
#105908882
#105907252
#105905922
D3×#8092
#105905882
#105905782
#105905532
#105904352
#813833
#813033