Finite Group Databasebeta

← #11889139

Subgroups — #11889139

Order 1152.

1114 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596080C211yesmaximal, characteristic
2#10594970C211yesmaximal, characteristic, complemented
3C3×#5042C211yesmaximal, characteristic, complemented
4C3×#5035C211yesmaximal, characteristic, complemented
5#10591480C211yesmaximal, characteristic, complemented
6#10591467C211yesmaximal, characteristic, complemented
7#10591444C211yesmaximal, characteristic, complemented
8#10591416C211yesmaximal, characteristic, complemented
9#10591183C211yesmaximal, characteristic, complemented
10#10591149C211yesmaximal, characteristic, complemented
11#10591096C211yesmaximal, characteristic, complemented
12#10590523C211yesmaximal, characteristic, complemented
13#10590484C211yesmaximal, characteristic, complemented
14#10590442C211yesmaximal, characteristic, complemented
15#10590435C211yesmaximal, characteristic, complemented
16#81383—31nomaximal
17#80821—31nomaximal
18C2×D4×C3⋊D3—21no—
19C2×D4×C3⋊D3C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C32×#121C2211yescharacteristic
22#64149C2211yescharacteristic
23#64146—21no—
24C4×#638C2211yescharacteristic
25#64104C2211yescharacteristic
26#64102C2211yescharacteristic
27#64093—21no—
28#64091—21no—
29C2×C3×#214C2211yescharacteristic, complemented
30C3×#926C2211yescharacteristic, complemented
31C3×#924C2211yescharacteristic, complemented
32C2×C3×#208C2211yescharacteristic, complemented
33#63975—21no—
34#63956—21no—
35#63900C2211yescharacteristic, complemented
36#63872C2211yescharacteristic, complemented
37#63871C2211yescharacteristic, complemented
38#63867—21no—
39#63843C2211yescharacteristic, complemented
40#63836—21no—
41C2×#3717C2211yescharacteristic
42C2×#3717C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic, complemented
44C3×#832C2211yescharacteristic, complemented
45C3×#832C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic, complemented
48C3×#810C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52#63572C2211yescharacteristic, complemented
53#63564C2211yescharacteristic
54#63564C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61#5639—31no—
62#5609—31no—
63#5609—31no—
64#5609—61no—
65#5529—31no—
66C3×#482—31no—
67C3×#468—31no—
68#5169—31no—
69#5163—31no—
70#5131—31no—
71#5127—31no—
72#5046—31no—
73#5042D311yescharacteristic, complemented
74#5035D311yescharacteristic, complemented
75#5001—31no—
76#4891—31no—
77#4889—31no—
78#4882—31no—
79#4882—31no—
80#4871—31no—
81#4864—31no—
82#4817—31no—
83#4807—31no—
84#4776—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4764—31no—
88#4764—31no—
89#4762—31no—
90#4731—31no—
91#4728—31no—
92C23×C3⋊D3—21no—
93C23×C3⋊D3—21no—
94C2×C32×D4—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#638—21no—
98C2×#638—21no—
99C2×#638—21no—
100C2×#638D411yescharacteristic
101D4×C3⋊D3—22no—
102D4×C3⋊D3—41no—
103D4×C3⋊D3—44no—
104C2×C4⋊(C3⋊D3)—22no—
105C2×C4⋊(C3⋊D3)—21no—
106C2×C4⋊(C3⋊D3)—21no—
107C2×C4⋊(C3⋊D3)—41no—
108C2×C4⋊(C3⋊D3)C2311yescharacteristic
109C2×C4⋊(C3⋊D3)C2311yescharacteristic
110C2×C4×C3⋊D3—21no—
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#624—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116#3757D411yescharacteristic
117#3752—21no—
118#3752—21no—
119#3752D411yescharacteristic
120#3750D411yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122C3×#217—21no—
123C3×#217—21no—
124C3×#214—41no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×#208—41no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141Dic32—21no—
142#3717—22no—
143#3717—41no—
144#3710—41no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—61no—
149C2×D3×D4—61no—
150C2×D3×D4—61no—
151C2×D3×D4—62no—
152C22×D12—31no—
153C22×D12—31no—
154C22×D12—61no—
155C2×C3×SD16—31no—
156C2×C3×M16—31no—
157C3×C22⋊Q8—31no—
158C3×#121—21no—
159C3×#121C2×D311yescharacteristic
160C3×#121C2×D311yescharacteristic
161C3×#117—31no—
162#946—31no—
163Q8×Dic3—31no—
164C2×#215—31no—
165C2×#215—31no—
166#940—31no—
167#940—31no—
168#940—61no—
169#937—61no—
170#937—61no—
171#937—62no—
172C2×#214C2×D311yescharacteristic, complemented
173C4×#67—31no—
174C4×#67—31no—
175C4×#67—61no—
176#926C2×D311yescharacteristic, complemented
177#924C2×D311yescharacteristic, complemented
178C2×#208C2×D311yescharacteristic, complemented
179C2×#204—31no—
180C2×#204—31no—
181C2×D3×C8—31no—
182C2×D3×C8—31no—
183#897—31no—
184#895—31no—
185#895—31no—
186#895—61no—
187#893—31no—
188#893—31no—
189#893—61no—
190#892—61no—
191D3×C4⋊C4—31no—
192D3×C4⋊C4—31no—
193#890—31no—
194#890—31no—
195#889—61no—
196#887—31no—
197#884—61no—
198#884—61no—
199#884—62no—
200#883—61no—
201#883—61no—
202#882—61no—
203#882—61no—
204#882—62no—
205#879—61no—
206#879—61no—
207#872—61no—
208#870—61no—
209C3×#107—31no—
210C3×#107—31no—
211C3×#106—31no—
212C3×#103—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×C22⋊C8—31no—
217#832C2×D311yescharacteristic, complemented
218#832C2×D311yescharacteristic, complemented
219#832C2×D311yescharacteristic, complemented
220#830C2×D311yescharacteristic, complemented
221#821—31no—
222#821—31no—
223#821—31no—
224#821—31no—
225#821—31no—
226#821—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8—31no—
229#815—31no—
230#815—31no—
231Dic3⋊C8—31no—
232Dic3⋊C8—31no—
233#810C2×D311yescharacteristic, complemented
234#809—31no—
235#809—31no—
236#809—31no—
237#809—31no—
238#809—31no—
239#809—31no—
240#808C2×D311yescharacteristic, complemented
241#807C2×D311yescharacteristic, complemented
242#807C2×D311yescharacteristic, complemented
243C23×C32—21no—
244C23×C32C2×D411yescharacteristic
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—42no—
248C22×C3⋊D3—42no—
249C22×C3⋊D3—42no—
250C22×C3⋊D3—42no—
251C22×C3⋊D3—81no—
252C22×C3⋊D3—81no—
253C22×C3⋊D3C2×D411yescharacteristic
254C32×D4—21no—
255C32×D4—21no—
256C32×D4—42no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4C2×D411yescharacteristic
261C2×C32×C4C2411yescharacteristic
262#638—22no—
263#638—42no—
264#638—42no—
265#638—81no—
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—42no—
273C4⋊(C3⋊D3)—42no—
274C4⋊(C3⋊D3)#4112yes—
275C4×C3⋊D3—21no—
276C4×C3⋊D3—21no—
277C4×C3⋊D3—42no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C3×Dic6—21no—
283C3×Dic6—21no—
284#624—42no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288C3×C3⋊C8—21no—
289#552—91no—
290D42—91no—
291#490—91no—
292#482—31no—
293#480—91no—
294#478—91no—
295#468—31no—
296#465—91no—
297#460—91no—
298#450—91no—
299#450—91no—
300#440—91no—
301#435—91no—
302#418—91no—
303C2×#102—91no—
304C23×D3—61no—
305C23×D3—61no—
306C23×D3—62no—
307C23×D3—62no—
308C23×D3—61no—
309C23×D3—61no—
310C2×C3×Q8—31no—
311C2×C3×D4—22no—
312C2×C3×D4—21no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C22×C3×C4—21no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C2×#67—31no—
321C2×#67—31no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—62no—
330C2×#67—62no—
331C2×#67—62no—
332D3×D4—62no—
333D3×D4—62no—
334D3×D4—122no—
335D3×D4—121no—
336D3×D4—121no—
337D3×D4—122no—
338D3×D4—124no—
339D3×D4—124no—
340D3×D4—128no—
341C2×D12—31no—
342C2×D12—31no—
343C2×D12—31no—
344C2×D12—31no—
345C2×D12—61no—
346C2×D12—61no—
347C2×D12—62no—
348C2×D12—62no—
349C2×D12—61no—
350C2×D12—61no—
351C2×D12—62no—
352C2×D12—62no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—122no—
356C2×D12—121no—
357C2×D12—121no—
358C2×D12—122no—
359C2×C4×D3—31no—
360C2×C4×D3—31no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—62no—
367C2×Dic6C22×D311yescharacteristic
368C3×SD16—121no—
369C3×M16—121no—
370C2×C3×C8—31no—
371C2×C3×C8—31no—
372C2×C3×C8—31no—
373C2×C3×C8—31no—
374C3×C4⋊C4—21no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4—61no—
379C3×C4⋊C4C22×D311yescharacteristic
380C3×C4⋊C4C22×D311yescharacteristic
381C3×C22⋊C4—22no—
382C3×C22⋊C4—21no—
383C3×C22⋊C4—21no—
384C3×C22⋊C4—61no—
385C3×C22⋊C4—61no—
386C3×C42—61no—
387#217—21no—
388#217—21no—
389#217—31no—
390#217—31no—
391#217—61no—
392#215—62no—
393#215—121no—
394#214—41no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406C4⋊Dic3—61no—
407C4⋊Dic3—61no—
408C4⋊Dic3—61no—
409C4⋊Dic3—61no—
410C4⋊Dic3C22×D311yescharacteristic
411C4⋊Dic3C22×D311yescharacteristic
412C4⋊Dic3C22×D311yescharacteristic
413Dic3⋊C4—21no—
414Dic3⋊C4—31no—
415Dic3⋊C4—31no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420Dic3⋊C4—61no—
421Dic3⋊C4—61no—
422Dic3⋊C4—61no—
423C4×Dic3—21no—
424C4×Dic3—31no—
425C4×Dic3—31no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C4×Dic3—61no—
429#208—41no—
430C2×C3⋊C8C22×D311yescharacteristic
431C2×C3⋊C8C22×D311yescharacteristic
432C2×C3⋊C8C22×D311yescharacteristic
433C2×C3⋊C8C22×D311yescharacteristic
434#204—62no—
435#204—121no—
436D3×C8—121no—
437D3×C8—121no—
438C22×C32—21no—
439C22×C32—21no—
440C22×C32—21no—
441C22×C32—41no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32C22×D411yescharacteristic
445C2×C3⋊D3—22no—
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3⋊D3—41no—
449C2×C3⋊D3—41no—
450C2×C3⋊D3—41no—
451C2×C3⋊D3—41no—
452C2×C3⋊D3—41no—
453C2×C3⋊D3—84no—
454C2×C3⋊D3—84no—
455C2×C3⋊D3AGL(1,ℤ/8)12yes—
456C32×C4—21no—
457C32×C4—41no—
458C32×C4C2×#4111yescharacteristic
459C32×C4H(5,𝔽2)11yescharacteristic
460C3⋊Dic3—21no—
461C3⋊Dic3—21no—
462C3⋊Dic3—21no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C22×D4—91no—
468C22×D4—91no—
469C22×D4—181no—
470C2×SD16—31no—
471C2×SD16—91no—
472C2×SD16—91no—
473C2×M16—31no—
474C22×C8—91no—
475#127—91no—
476#126—181no—
477#125—91no—
478#125—181no—
479#123—181no—
480C22⋊Q8—31no—
481C22⋊Q8—91no—
482#121—91no—
483#121—181no—
484#121D3211yescharacteristic
485#120—181no—
486#120—181no—
487C4×Q8—91no—
488C4×D4—91no—
489C4×D4—91no—
490#117—31no—
491#117—181no—
492C2×C4⋊C4—91no—
493#107—31no—
494#107—31no—
495#106—31no—
496C4⋊C8—91no—
497#103—31no—
498#102—31no—
499#102—31no—
500#102—31no—
501#102—91no—
502#102—91no—
503#102—91no—
504#102—91no—
505#102—91no—
506#102—91no—
507C22⋊C8—31no—
508C22⋊C8—91no—
509#97—91no—
510C23×C3—22no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3D3×D411yescharacteristic
515C23×C3D3×D411yescharacteristic
516C22×D3—31no—
517C22×D3—31no—
518C22×D3—61no—
519C22×D3—62no—
520C22×D3—61no—
521C22×D3—61no—
522C22×D3—62no—
523C22×D3—61no—
524C22×D3—61no—
525C22×D3—122no—
526C22×D3—122no—
527C22×D3—122no—
528C22×D3—122no—
529C22×D3—122no—
530C22×D3—122no—
531C22×D3—124no—
532C22×D3—124no—
533C22×D3—124no—
534C22×D3—124no—
535C22×D3—122no—
536C22×D3—122no—
537C22×D3—241no—
538C22×D3—241no—
539C22×D3—241no—
540C22×D3—241no—
541C22×D3—242no—
542C22×D3—242no—
543C3×Q8—61no—
544C3×Q8—61no—
545C3×D4—21no—
546C3×D4—21no—
547C3×D4—21no—
548C3×D4—21no—
549C3×D4—41no—
550C3×D4—41no—
551C3×D4—44no—
552C3×D4—42no—
553C3×D4—42no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—22no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4D3×D411yescharacteristic
570C2×C3×C4D3×D411yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573#67—62no—
574#67—62no—
575#67—64no—
576#67—122no—
577#67—122no—
578#67—124no—
579#67—122no—
580#67—122no—
581#67—124no—
582#67—241no—
583#67—241no—
584#67—242no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598D12—32no—
599D12—32no—
600D12—62no—
601D12—62no—
602D12—61no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—61no—
608D12—121no—
609D12—121no—
610D12—122no—
611D12—122no—
612D12—122no—
613D12—122no—
614D12—124no—
615D12—124no—
616C4×D3—61no—
617C4×D3—61no—
618C4×D3—61no—
619C4×D3—61no—
620C4×D3—121no—
621C4×D3—121no—
622C4×D3—122no—
623C4×D3—122no—
624C4×D3—124no—
625C4×D3—122no—
626C4×D3—122no—
627Dic6—21no—
628Dic6—21no—
629C3×C8—61no—
630C3×C8—61no—
631C3×C8—61no—
632C3×C8—61no—
633C3⋊C8—21no—
634C3⋊C8—21no—
635C3⋊C8—21no—
636C3⋊C8—21no—
637C2×C32—41no—
638C2×C32—81no—
639C2×C32#54611yescharacteristic
640C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
641C2×C32#57711yescharacteristic
642C3⋊D3—22no—
643C3⋊D3—42no—
644C3⋊D3—81no—
645C24—181no—
646C24—181no—
647C2×Q8—31no—
648C2×D4—21no—
649C2×D4—91no—
650C2×D4—91no—
651C2×D4—91no—
652C2×D4—182no—
653C2×D4—181no—
654C2×D4—181no—
655C2×D4—181no—
656C2×D4—181no—
657C2×D4—182no—
658C2×D4—181no—
659C2×D4—361no—
660C2×D4—361no—
661C2×D4—364no—
662C2×D4C2×D3211yescharacteristic
663C22×C4—91no—
664C22×C4—181no—
665C22×C4—181no—
666C22×C4C2×D3211yescharacteristic
667SD16—121no—
668SD16—182no—
669SD16—361no—
670M16—121no—
671C2×C8—31no—
672C2×C8—31no—
673C2×C8—31no—
674C2×C8—31no—
675C2×C8—361no—
676C4⋊C4—31no—
677C4⋊C4—31no—
678C4⋊C4—31no—
679C4⋊C4—61no—
680C4⋊C4—91no—
681C4⋊C4—181no—
682C4⋊C4—181no—
683C4⋊C4—181no—
684C4⋊C4—181no—
685C4⋊C4—181no—
686C4⋊C4C2×D3211yescharacteristic
687C22⋊C4—21no—
688C22⋊C4—61no—
689C22⋊C4—61no—
690C22⋊C4—91no—
691C22⋊C4—91no—
692C22⋊C4—181no—
693C22⋊C4—181no—
694C22⋊C4—181no—
695C42—61no—
696C42—91no—
697C42—181no—
698C22×C3—22no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3C2×D3×D411yescharacteristic
718C22×C3C2×D3×D411yescharacteristic
719C2×D3—32no—
720C2×D3—32no—
721C2×D3—62no—
722C2×D3—61no—
723C2×D3—61no—
724C2×D3—61no—
725C2×D3—61no—
726C2×D3—64no—
727C2×D3—62no—
728C2×D3—62no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—122no—
732C2×D3—122no—
733C2×D3—121no—
734C2×D3—121no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—122no—
738C2×D3—122no—
739C2×D3—122no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—244no—
747C2×D3—244no—
748C2×D3—248no—
749C2×D3—248no—
750C2×D3—244no—
751C2×D3—244no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—41no—
757C3×C4—42no—
758C3×C4—41no—
759C3×C4—41no—
760C3×C4—121no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4#100411yescharacteristic
765C3×C4D3×#4111yescharacteristic
766C3×C4D3×#4111yescharacteristic
767C3×C4#100911yescharacteristic
768Dic3—41no—
769Dic3—41no—
770Dic3—41no—
771Dic3—41no—
772Dic3—62no—
773Dic3—61no—
774Dic3—61no—
775Dic3—61no—
776Dic3—61no—
777Dic3—61no—
778Dic3—61no—
779Dic3—121no—
780Dic3—121no—
781C32#331011yescharacteristic, complemented, Sylow
782C23—21no—
783C23—91no—
784C23—181no—
785C23—181no—
786C23—362no—
787C23—362no—
788C23—362no—
789C23—362no—
790C23—721no—
791C23—721no—
792C23#381111yescharacteristic
793Q8—61no—
794Q8—61no—
795D4—21no—
796D4—21no—
797D4—42no—
798D4—92no—
799D4—182no—
800D4—181no—
801D4—181no—
802D4—181no—
803D4—362no—
804D4—362no—
805D4—362no—
806D4—362no—
807D4—721no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—91no—
816C2×C4—91no—
817C2×C4—91no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—362no—
821C2×C4—362no—
822C2×C4#381111yescharacteristic
823C2×C4C22×D3211yescharacteristic
824C8—61no—
825C8—61no—
826C8—61no—
827C8—61no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—42no—
832C2×C3—41no—
833C2×C3—41no—
834C2×C3—82no—
835C2×C3—81no—
836C2×C3—81no—
837C2×C3#561011yescharacteristic
838C2×C3#565411yescharacteristic
839C2×C3#577011yescharacteristic
840C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
841C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
842C2×C3#577811yescharacteristic
843D3—62no—
844D3—62no—
845D3—122no—
846D3—124no—
847D3—122no—
848D3—122no—
849D3—242no—
850D3—241no—
851D3—241no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—92no—
859C22—181no—
860C22—181no—
861C22—182no—
862C22—361no—
863C22—361no—
864C22—361no—
865C22—361no—
866C22—361no—
867C22—724no—
868C22—724no—
869C22C2×#381111yescharacteristic
870C4—21no—
871C4—41no—
872C4—121no—
873C4—121no—
874C4—121no—
875C4—121no—
876C4—181no—
877C4—181no—
878C4—181no—
879C4#6431211yescharacteristic
880C4#6431411yescharacteristic
881C3—21no—
882C3#8082111yescharacteristic, complemented
883C3#8138311yescharacteristic, complemented
884C2—41no—
885C2—81no—
886C2—182no—
887C2—362no—
888C2—721no—
889C2#1059510011yescharacteristic
890C2#1059516311yescharacteristic
891C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radical#10596080C2
hypercenter#121D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10594970C2semidirect
3. C3×#5042C2semidirect
4. C3×#5035C2semidirect
5. #10591480C2semidirect
6. #10591467C2semidirect
7. #10591444C2semidirect
8. #10591416C2semidirect
9. #10591183C2semidirect
10. #10591149C2semidirect
11. #10591096C2semidirect
12. #10590523C2semidirect
13. #10590484C2semidirect
14. #10590442C2semidirect
15. #10590435C2semidirect
29. C2×C3×#214C22semidirect
30. C3×#926C22semidirect
31. C3×#924C22semidirect
32. C2×C3×#208C22semidirect
35. #63900C22semidirect
36. #63872C22semidirect
37. #63871C22semidirect
39. #63843C22semidirect
42. C2×#3717C22semidirect
43. C2×#3710C22semidirect
44. C3×#832C22semidirect
45. C3×#832C22semidirect
46. C3×#832C22semidirect
47. C3×#830C22semidirect
48. C3×#810C22semidirect
49. C3×#808C22semidirect
50. C3×#807C22semidirect
51. C3×#807C22semidirect
52. #63572C22semidirect
56. #63564C22semidirect
57. #63564C22semidirect
58. #63564C22semidirect
59. #63557C22semidirect
60. #63555C22semidirect
73. #5042D3semidirect
74. #5035D3semidirect
172. C2×#214C2×D3semidirect
176. #926C2×D3semidirect
177. #924C2×D3semidirect
178. C2×#208C2×D3semidirect
217. #832C2×D3semidirect
218. #832C2×D3semidirect
219. #832C2×D3semidirect
220. #830C2×D3semidirect
233. #810C2×D3semidirect
240. #808C2×D3semidirect
241. #807C2×D3semidirect
242. #807C2×D3semidirect
781. C32#3310semidirect
882. C3#80821semidirect
883. C3#81383semidirect

Maximal subgroups

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

subgroupindex
#105960802
#105949702
C3×#50422
C3×#50352
#105914802
#105914672
#105914442
#105914162
#105911832
#105911492
#105910962
#105905232
#105904842
#105904422
#105904352
#813833
#808213