Finite Group Databasebeta

← #11889148

Subgroups — #11889148

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#10596188C211yesmaximal, characteristic
2#10593947C211yesmaximal, characteristic, complemented
3C3×#5075C211yesmaximal, characteristic, complemented
4C3×#5071C211yesmaximal, characteristic, complemented
5#10591467C211yesmaximal, characteristic, complemented
6#10591467C211yesmaximal, characteristic, complemented
7#10591465C211yesmaximal, characteristic, complemented
8#10591464C211yesmaximal, characteristic, complemented
9#10591426C211yesmaximal, characteristic, complemented
10#10591425C211yesmaximal, characteristic, complemented
11#10591417C211yesmaximal, characteristic, complemented
12#10591416C211yesmaximal, characteristic, complemented
13#10590362C211yesmaximal, characteristic, complemented
14#10590328C211yesmaximal, characteristic, complemented
15#10590308C211yesmaximal, characteristic, complemented
16#81725—31nomaximal
17#80397—31nomaximal
18C2×D4×C3⋊D3—21no—
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×D4×C3⋊D3C2211yescharacteristic
21C32×#127C2211yescharacteristic
22#64147—21no—
23#64147C2211yescharacteristic
24#64147C2211yescharacteristic
25#64146—21no—
26#64146—21no—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic, complemented
30C2×C3×#214C2211yescharacteristic, complemented
31C3×#870C2211yescharacteristic, complemented
32C3×C4×Dic6C2211yescharacteristic, complemented
33#63900C2211yescharacteristic, complemented
34#63897—21no—
35#63871C2211yescharacteristic, complemented
36#63871C2211yescharacteristic, complemented
37#63868—21no—
38#63849C2211yescharacteristic, complemented
39#63845—21no—
40#63836—21no—
41C2×#3717C2211yescharacteristic
42C2×#3712C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic, complemented
44C3×#832C2211yescharacteristic, complemented
45C3×#832C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51C3×#803C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60#63557C2211yescharacteristic, complemented
61#5717—31no—
62#5717—31no—
63#5717—61no—
64#5694—31no—
65#5581—31no—
66C3×#490—31no—
67C3×#460—31no—
68#5174—31no—
69#5171—31no—
70#5169—31no—
71#5169—31no—
72#5075D311yescharacteristic, complemented
73#5071D311yescharacteristic, complemented
74#5066—31no—
75#5026—31no—
76#4847—31no—
77#4836—31no—
78#4784—31no—
79#4780—31no—
80#4779—31no—
81#4778—31no—
82#4776—31no—
83#4776—31no—
84#4774—31no—
85#4774—31no—
86#4770—31no—
87#4770—31no—
88D3×#102—31no—
89D3×#102—31no—
90#4710—31no—
91#4706—31no—
92C23×C3⋊D3—21no—
93C23×C3⋊D3—21no—
94C2×C32×D4—21no—
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C2×#638—21no—
100C2×#638—21no—
101C2×#638—21no—
102D4×C3⋊D3—22no—
103D4×C3⋊D3—22no—
104D4×C3⋊D3—41no—
105D4×C3⋊D3—41no—
106D4×C3⋊D3—44no—
107C2×C4⋊(C3⋊D3)D411yescharacteristic
108C2×C4⋊(C3⋊D3)C2311yescharacteristic
109C2×C4×C3⋊D3—21no—
110C2×C4×C3⋊D3C2311yescharacteristic
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#624—21no—
114C32×C42C2311yescharacteristic
115#3757—21no—
116#3757—21no—
117#3752—21no—
118#3752D411yescharacteristic
119#3752D411yescharacteristic
120C4⋊(C3⋊Dic3)D411yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C3×#214—41no—
123C3×#214—41no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
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—
138#3722—21no—
139#3722—21no—
140#3722—21no—
141Dic32—21no—
142#3717—22no—
143#3712—41no—
144#3710—41no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×D3×D4—61no—
152C2×D3×D4—61no—
153C2×D3×D4—61no—
154C2×D3×D4—62no—
155C2×C3×SD16—31no—
156C2×C3×SD16—31no—
157C3×#127—21no—
158C3×#127C2×D311yescharacteristic
159C3×#127C2×D311yescharacteristic
160C3×#125—31no—
161C3×C4×Q8—31no—
162#946—31no—
163#946—31no—
164C2×#215—31no—
165#938—31no—
166#938—31no—
167#938—31no—
168#938—31no—
169#938—61no—
170#938—61no—
171#938—61no—
172#938—61no—
173#938—62no—
174#937—61no—
175#937—61no—
176#937—61no—
177#937—61no—
178#937—62no—
179#937—62no—
180C2×#214C2×D311yescharacteristic, complemented
181C2×#214C2×D311yescharacteristic, complemented
182C2×#204—31no—
183C2×ΓL(1,𝔽25)—31no—
184C2×ΓL(1,𝔽25)—31no—
185C2×D3×C8—31no—
186C2×D3×C8—31no—
187#898—61no—
188#897—31no—
189#897—31no—
190#894—61no—
191#894—61no—
192#892—31no—
193#892—31no—
194#892—61no—
195D3×C4⋊C4—31no—
196D3×C4⋊C4—31no—
197#890—61no—
198#889—61no—
199#876—61no—
200C4×D12—31no—
201C4×D12—31no—
202C4×D12—31no—
203C4×D12—31no—
204C4×D12—61no—
205C4×D12—61no—
206#872—61no—
207#870C2×D311yescharacteristic, complemented
208C4×Dic6C2×D311yescharacteristic, complemented
209C3×C4⋊C8—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#97—31no—
217#835—31no—
218#832C2×D311yescharacteristic, complemented
219#832C2×D311yescharacteristic, complemented
220#832C2×D311yescharacteristic, complemented
221#832C2×D311yescharacteristic, complemented
222#832C2×D311yescharacteristic, complemented
223#832C2×D311yescharacteristic, complemented
224#821—31no—
225#821—31no—
226#821—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8—31no—
229(C2×D3)⋊C8—31no—
230(C2×D3)⋊C8—31no—
231#818—31no—
232#818—31no—
233#817—31no—
234#816—31no—
235#809—31no—
236#809—31no—
237#809—31no—
238#808—31no—
239#807—31no—
240#807—31no—
241C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
242#803C2×D311yescharacteristic, complemented
243C23×C32—21no—
244C23×C32—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—42no—
247C22×C3⋊D3—42no—
248C22×C3⋊D3—42no—
249C22×C3⋊D3—42no—
250C22×C3⋊D3—81no—
251C22×C3⋊D3—81no—
252C22×C3⋊D3C2×D411yescharacteristic
253C22×C3⋊D3C2×D411yescharacteristic
254C32×D4—21no—
255C32×D4—21no—
256C32×D4—21no—
257C32×D4—21no—
258C32×D4—42no—
259C32×D4—81no—
260C2×C32×C4C2×D411yescharacteristic
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2411yescharacteristic
263#638—42no—
264#638—42no—
265#638—42no—
266#638—42no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3C2×D411yescharacteristic
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4⋊(C3⋊D3)—22no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)#4112yes—
273C4×C3⋊D3—21no—
274C4×C3⋊D3—21no—
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—31no—
292#482—91no—
293#480—91no—
294#478—91no—
295#468—91no—
296#465—91no—
297#460—31no—
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—61no—
307C23×D3—61no—
308C23×D3—62no—
309C23×D3—62no—
310C2×C3×Q8—31no—
311C2×C3×D4—22no—
312C2×C3×D4—22no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—21no—
316C2×C3×D4—21no—
317C2×C3×D4—21no—
318C2×C3×D4—21no—
319C2×C3×D4C22×D311yescharacteristic
320C2×C3×D4C22×D311yescharacteristic
321C2×C3×D4C22×D311yescharacteristic
322C2×C3×D4C22×D311yescharacteristic
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—62no—
332C2×#67—62no—
333C2×#67—62no—
334C2×#67—62no—
335D3×D4—62no—
336D3×D4—62no—
337D3×D4—62no—
338D3×D4—62no—
339D3×D4—122no—
340D3×D4—122no—
341D3×D4—121no—
342D3×D4—121no—
343D3×D4—121no—
344D3×D4—121no—
345D3×D4—122no—
346D3×D4—122no—
347D3×D4—124no—
348D3×D4—124no—
349D3×D4—128no—
350C2×D12—31no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—61no—
355C2×D12—61no—
356C2×C4×D3—31no—
357C2×C4×D3—31no—
358C2×C4×D3—31no—
359C2×C4×D3—31no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3—62no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×Dic6C22×D311yescharacteristic
368C3×SD16—121no—
369C3×SD16—121no—
370C2×C3×C8—31no—
371C2×C3×C8—31no—
372C2×C3×C8—31no—
373C2×C3×C8—31no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—61no—
378C3×C4⋊C4—61no—
379C3×C4⋊C4—61no—
380C3×C42—21no—
381C3×C42—61no—
382C3×C42C22×D311yescharacteristic
383C3×C42C22×D311yescharacteristic
384#217—61no—
385#217—61no—
386#217—61no—
387#217—61no—
388#217—62no—
389#217—62no—
390#215—62no—
391#214—41no—
392#214—41no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
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—61no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408C4⋊Dic3—31no—
409C4⋊Dic3—31no—
410C4⋊Dic3—31no—
411C4⋊Dic3—31no—
412C4⋊Dic3—61no—
413C4⋊Dic3—61no—
414C4⋊Dic3—61no—
415C4⋊Dic3—61no—
416C4⋊Dic3C22×D311yescharacteristic
417C4⋊Dic3C22×D311yescharacteristic
418C4⋊Dic3C22×D311yescharacteristic
419Dic3⋊C4—21no—
420Dic3⋊C4—21no—
421Dic3⋊C4—21no—
422Dic3⋊C4—61no—
423Dic3⋊C4—61no—
424Dic3⋊C4—61no—
425Dic3⋊C4—61no—
426C4×Dic3—21no—
427C4×Dic3—61no—
428C4×Dic3—61no—
429C2×C3⋊C8C22×D311yescharacteristic
430C2×C3⋊C8C22×D311yescharacteristic
431C2×C3⋊C8C22×D311yescharacteristic
432C2×C3⋊C8C22×D311yescharacteristic
433#204—62no—
434ΓL(1,𝔽25)—121no—
435ΓL(1,𝔽25)—121no—
436D3×C8—121no—
437D3×C8—121no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32—41no—
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—21no—
449C2×C3⋊D3—21no—
450C2×C3⋊D3—21no—
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—21no—
458C32×C4C2×#4111yescharacteristic
459C32×C4H(5,𝔽2)11yescharacteristic
460C3⋊Dic3—21no—
461C3⋊Dic3—21no—
462C3⋊Dic3—41no—
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—31no—
472C2×SD16—91no—
473C2×M16—91no—
474C22×C8—91no—
475#127D3211yescharacteristic
476#126—181no—
477#125—31no—
478#125—181no—
479#123—181no—
480C22⋊Q8—91no—
481C22⋊Q8—91no—
482#121—91no—
483#121—91no—
484#121—181no—
485#120—181no—
486#120—181no—
487C4×Q8—31no—
488C4×D4—91no—
489C4×D4—91no—
490#117—91no—
491#117—181no—
492C2×C4⋊C4—91no—
493#107—91no—
494#107—91no—
495#106—91no—
496C4⋊C8—31no—
497#103—91no—
498#102—31no—
499#102—31no—
500#102—31no—
501#102—31no—
502#102—31no—
503#102—31no—
504#102—91no—
505#102—91no—
506#102—91no—
507C22⋊C8—91no—
508C22⋊C8—91no—
509#97—31no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C22×D3—31no—
517C22×D3—31no—
518C22×D3—31no—
519C22×D3—31no—
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—21no—
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—41no—
554C3×D4—41no—
555C3×D4—41no—
556C3×D4—41no—
557C3×D4—44no—
558C3×D4—42no—
559C3×D4—42no—
560C3×D4—81no—
561C3×D4—81no—
562C3×D4—82no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4D3×D411yescharacteristic
571C2×C3×C4D3×D411yescharacteristic
572C2×C3×C4D3×D411yescharacteristic
573C2×C3×C4D3×D411yescharacteristic
574C2×C3×C4C23×D311yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576#67—122no—
577#67—122no—
578#67—122no—
579#67—122no—
580#67—122no—
581#67—122no—
582#67—124no—
583#67—124no—
584#67—124no—
585#67—124no—
586#67—122no—
587#67—122no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—62no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601D12—32no—
602D12—32no—
603D12—62no—
604D12—62no—
605D12—62no—
606D12—64no—
607D12—62no—
608D12—61no—
609D12—61no—
610C4×D3—61no—
611C4×D3—61no—
612C4×D3—61no—
613C4×D3—61no—
614C4×D3—61no—
615C4×D3—61no—
616C4×D3—61no—
617C4×D3—61no—
618C4×D3—121no—
619C4×D3—121no—
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—81no—
638C2×C32—81no—
639C2×C32#54611yescharacteristic
640C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
641C2×C32#57711yescharacteristic
642C3⋊D3—22no—
643C3⋊D3—41no—
644C3⋊D3—42no—
645C24—181no—
646C24—181no—
647C2×Q8—31no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—91no—
651C2×D4—91no—
652C2×D4—181no—
653C2×D4—181no—
654C2×D4—182no—
655C2×D4—182no—
656C2×D4—181no—
657C2×D4—181no—
658C2×D4—361no—
659C2×D4—361no—
660C2×D4—364no—
661C2×D4C2×D3211yescharacteristic
662C2×D4C2×D3211yescharacteristic
663C22×C4—91no—
664C22×C4—91no—
665C22×C4—181no—
666C22×C4—181no—
667SD16—121no—
668SD16—121no—
669SD16—182no—
670M16—361no—
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—61no—
681C4⋊C4—61no—
682C4⋊C4—91no—
683C4⋊C4—91no—
684C4⋊C4—181no—
685C4⋊C4—181no—
686C4⋊C4—181no—
687C22⋊C4—91no—
688C22⋊C4—91no—
689C22⋊C4—181no—
690C22⋊C4—181no—
691C22⋊C4—181no—
692C22⋊C4—181no—
693C22⋊C4—181no—
694C22⋊C4—181no—
695C42—61no—
696C42—181no—
697C42C2×D3211yescharacteristic
698C22×C3—21no—
699C22×C3—42no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
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—62no—
727C2×D3—64no—
728C2×D3—61no—
729C2×D3—62no—
730C2×D3—61no—
731C2×D3—61no—
732C2×D3—61no—
733C2×D3—61no—
734C2×D3—61no—
735C2×D3—62no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—122no—
741C2×D3—122no—
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—22no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—21no—
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—61no—
773Dic3—61no—
774Dic3—61no—
775Dic3—61no—
776Dic3—121no—
777Dic3—121no—
778Dic3—122no—
779Dic3—121no—
780Dic3—121no—
781C32#331011yescharacteristic, complemented, Sylow
782C23—21no—
783C23—21no—
784C23—91no—
785C23—91no—
786C23—181no—
787C23—362no—
788C23—362no—
789C23—362no—
790C23—362no—
791C23—721no—
792C23—721no—
793Q8—61no—
794Q8—61no—
795D4—21no—
796D4—21no—
797D4—21no—
798D4—21no—
799D4—42no—
800D4—81no—
801D4—92no—
802D4—182no—
803D4—181no—
804D4—362no—
805D4—362no—
806D4—362no—
807D4—362no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—91no—
813C2×C4—91no—
814C2×C4—181no—
815C2×C4—181no—
816C2×C4—181no—
817C2×C4—181no—
818C2×C4—181no—
819C2×C4—362no—
820C2×C4—362no—
821C2×C4#381111yescharacteristic
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—82no—
832C2×C3—82no—
833C2×C3—81no—
834C2×C3—81no—
835C2×C3—81no—
836C2×C3—81no—
837C2×C3#561211yescharacteristic
838C2×C3#567611yescharacteristic
839C2×C3#576211yescharacteristic
840C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
841C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
842C2×C3#577511yescharacteristic
843D3—62no—
844D3—62no—
845D3—122no—
846D3—122no—
847D3—124no—
848D3—121no—
849D3—122no—
850D3—121no—
851D3—122no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—92no—
859C22—181no—
860C22—181no—
861C22—181no—
862C22—181no—
863C22—181no—
864C22—182no—
865C22—361no—
866C22—361no—
867C22—724no—
868C22—724no—
869C22C2×#381111yescharacteristic
870C4—21no—
871C4—21no—
872C4—121no—
873C4—121no—
874C4—121no—
875C4—121no—
876C4—181no—
877C4—181no—
878C4—361no—
879C4#6431211yescharacteristic
880C4#6431411yescharacteristic
881C3—21no—
882C3#8039711yescharacteristic, complemented
883C3#8172511yescharacteristic, complemented
884C2—81no—
885C2—81no—
886C2—182no—
887C2—361no—
888C2—362no—
889C2#1059510011yescharacteristic
890C2#1059511511yescharacteristic
891C2#1059524311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radical#10596188C2
hypercenter#127D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10593947C2semidirect
3. C3×#5075C2semidirect
4. C3×#5071C2semidirect
5. #10591467C2semidirect
6. #10591467C2semidirect
7. #10591465C2semidirect
8. #10591464C2semidirect
9. #10591426C2semidirect
10. #10591425C2semidirect
11. #10591417C2semidirect
12. #10591416C2semidirect
13. #10590362C2semidirect
14. #10590328C2semidirect
15. #10590308C2semidirect
29. C2×C3×#214C22semidirect
30. C2×C3×#214C22semidirect
31. C3×#870C22semidirect
32. C3×C4×Dic6C22semidirect
33. #63900C22semidirect
35. #63871C22semidirect
36. #63871C22semidirect
38. #63849C22semidirect
42. C2×#3712C22semidirect
43. C2×#3710C22semidirect
44. C3×#832C22semidirect
45. C3×#832C22semidirect
46. C3×#832C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
49. C3×#832C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. C3×#803C22semidirect
52. #63575C22semidirect
53. #63575C22semidirect
54. #63573C22semidirect
55. #63566C22semidirect
59. #63557C22semidirect
60. #63557C22semidirect
72. #5075D3semidirect
73. #5071D3semidirect
180. C2×#214C2×D3semidirect
181. C2×#214C2×D3semidirect
207. #870C2×D3semidirect
208. C4×Dic6C2×D3semidirect
218. #832C2×D3semidirect
219. #832C2×D3semidirect
220. #832C2×D3semidirect
221. #832C2×D3semidirect
222. #832C2×D3semidirect
223. #832C2×D3semidirect
241. C4⋊(C3⋊C8)C2×D3semidirect
242. #803C2×D3semidirect
781. C32#3310semidirect
882. C3#80397semidirect
883. C3#81725semidirect

Maximal subgroups

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

subgroupindex
#105961882
#105939472
C3×#50752
C3×#50712
#105914672
#105914652
#105914642
#105914262
#105914252
#105914172
#105914162
#105903622
#105903282
#105903082
#817253
#803973