Finite Group Databasebeta

← #11887009

Subgroups — #11887009

Order 1152.

1087 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595074C211yesmaximal, characteristic, complemented
2#10594906C211yesmaximal, characteristic, complemented
3#10592431C211yesmaximal, characteristic, complemented
4C3×#4736C211yesmaximal, characteristic, complemented
5C3×#67⋊C8C211yesmaximal, characteristic, complemented
6#10591164C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8#10590947C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590878C211yesmaximal, characteristic, complemented
11#10590832C211yesmaximal, characteristic, complemented
12#10590765C211yesmaximal, characteristic, complemented
13#10590764C211yesmaximal, characteristic, complemented
14#10590763C211yesmaximal, characteristic, complemented
15#10590679C211yesmaximal, characteristic, complemented
16#81302—31nomaximal
17#79438—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3811—21no—
20C2×#3804—21no—
21C2×D3×D12C2211yescharacteristic
22#64139C2211yescharacteristic, complemented
23C2×#3745C2211yescharacteristic
24C2×#3745C2211yescharacteristic, complemented
25C3×#930C2211yescharacteristic
26C3×C4×#67C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
28C22×C3×C3⋊C8C2211yescharacteristic, complemented
29C2×C3×D3×C8C2211yescharacteristic, complemented
30#63981—21no—
31#63966—21no—
32#63923—21no—
33#63918C2211yescharacteristic, complemented
34#63911C2211yescharacteristic
35#63910—21no—
36#63909C2211yescharacteristic
37#63909C2211yescharacteristic, complemented
38#63895—21no—
39#63894C2211yescharacteristic
40#63894C2211yescharacteristic, complemented
41#63890—21no—
42D3×C4⋊Dic3C2211yescharacteristic, complemented
43C2×#3714C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
50C3×#818C2211yescharacteristic, complemented
51C3×#818C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#5609—31no—
62#5555—31no—
63D4×D12—31no—
64#5507—31no—
65C3×#480—31no—
66C3×C8×D4—31no—
67#5115—31no—
68#5115—31no—
69C2×#821—31no—
70C2×#821—31no—
71#5038—31no—
72C2×#809—31no—
73#4890—31no—
74#4883—31no—
75#4882—31no—
76#4872—31no—
77#4846—31no—
78#4843—31no—
79#4786—31no—
80#4773—31no—
81D3×#102—31no—
82#4760—31no—
83#4736—31no—
84#4736D311yescharacteristic, complemented
85#4732—31no—
86#4732—31no—
87#4732—31no—
88#4732—61no—
89#67⋊C8D311yescharacteristic, complemented
90#4694—31no—
91C4×D24—31no—
92C23×C3⋊D3—21no—
93C22×D32—21no—
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)—41no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67D411yescharacteristic
104C22×C3×Dic3—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107#3811—44no—
108C2×#627—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#624—21no—
115C2×#624—21no—
116#3804—44no—
117C2×D3×Dic3—21no—
118D3×D12—22no—
119D3×D12—41no—
120C2×C32×C8C2311yescharacteristic
121C2×C32×C8C2311yescharacteristic
122#3752—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3745—22no—
125#3745—41no—
126C3×#217D411yescharacteristic
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8—41no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×D3×C8—41no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141#3722—21no—
142#3722—21no—
143#3722—21no—
144#3722—21no—
145#3714—41no—
146#3294—91noSylow
147C2×#237—61no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C2×D3×D4—61no—
151C2×#235—61no—
152C22×D12—31no—
153C22×D12—31no—
154C22×D12—31no—
155C22×D12—61no—
156C22×C3×C8—31no—
157C22×C3×C8—31no—
158C3×#121—31no—
159C3×C4×D4—31no—
160C2×C3×C4⋊C4—31no—
161#940—31no—
162#937—61no—
163C2×#213—31no—
164#930—31no—
165#930—31no—
166#930—31no—
167#930—31no—
168#930—61no—
169#930C2×D311yescharacteristic
170#929—61no—
171C4×#67C2×D311yescharacteristic
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3C2×D311yescharacteristic, complemented
174C22×C3⋊C8C2×D311yescharacteristic, complemented
175C2×D24—31no—
176C2×D24—31no—
177C2×D24—31no—
178C2×D24—31no—
179C2×D24—31no—
180C2×D24—61no—
181C2×D24—61no—
182C2×D3×C8C2×D311yescharacteristic, complemented
183#897—61no—
184#896—61no—
185#895—31no—
186#895—31no—
187#895—61no—
188#894—61no—
189#893—31no—
190#893—31no—
191D3×C4⋊C4—31no—
192#888—31no—
193#886—61no—
194#886—61no—
195#884—61no—
196#882—61no—
197#882—61no—
198#882—61no—
199#874—31no—
200C4×D12—31no—
201C4×D12—31no—
202#869—31no—
203C3×#107—31no—
204C3×#107—31no—
205C3×C4⋊C8—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×C22⋊C8—21no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8C2×D311yescharacteristic, complemented
211C3×C22⋊C8C2×D311yescharacteristic, complemented
212C3×C4×C8—31no—
213#832—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—31no—
223#821—31no—
224#821—61no—
225#821—61no—
226#821C2×D311yescharacteristic, complemented
227#821C2×D311yescharacteristic, complemented
228(C2×D3)⋊C8C2×D311yescharacteristic, complemented
229#818—31no—
230#818C2×D311yescharacteristic, complemented
231#818C2×D311yescharacteristic, complemented
232Dic3⋊C8C2×D311yescharacteristic, complemented
233C8×Dic3C2×D311yescharacteristic, complemented
234#809—31no—
235#809—31no—
236#809—31no—
237#809—31no—
238#809—31no—
239#807—31no—
240C23×C32C2×D411yescharacteristic
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—42no—
245C22×C3⋊D3—42no—
246C22×C3⋊D3—81no—
247C22×C3×D3—21no—
248C22×C3×D3C2×D411yescharacteristic
249C2×D32—42no—
250C2×D32—42no—
251C2×D32—81no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256#638—42no—
257C2×C3⋊Dic3—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)—21no—
263C4⋊(C3⋊D3)—42no—
264C4⋊(C3⋊D3)#4112yescomplemented
265C3×#67—42no—
266C3×#67D814yescomplemented
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—42no—
271C2×C3×Dic3C2×D411yescharacteristic
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C3×D12—21no—
275C3×D12—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278#627—42no—
279#626—42no—
280#626—42no—
281#626—42no—
282#626—42no—
283#626—81no—
284#624—42no—
285#624—42no—
286D3×Dic3—42no—
287C32×C8—21no—
288C32×C8—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291#547—91no—
292D42—91no—
293#486—91no—
294#480—31no—
295#480—91no—
296#474—91no—
297#466—91no—
298#466—91no—
299#459—91no—
300#447—91no—
301#447—91no—
302C4×D8—91no—
303C8×D4—31no—
304C2×#102—91no—
305C2×#102—91no—
306C23×D3—61no—
307C23×D3—61no—
308C23×D3—61no—
309C23×D3—61no—
310C23×D3—121no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—61no—
314C22×C3×C4—21no—
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C2×#67—21no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—121no—
328C2×#67D1211yescharacteristic
329C22×Dic3—21no—
330C22×Dic3—61no—
331#237—124no—
332D3×D4—62no—
333D3×D4—121no—
334D3×D4—124no—
335D3×D4—124no—
336#235—124no—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—31no—
340C2×D12—31no—
341C2×D12—31no—
342C2×D12—31no—
343C2×D12—61no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—62no—
347C2×D12—62no—
348C2×D12—62no—
349C2×D12—61no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—122no—
357C2×D12—121no—
358C2×D12—121no—
359C2×D12—121no—
360C2×D12—121no—
361C2×D12—122no—
362C2×D12C22×D311yescharacteristic
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3C22×D311yescharacteristic
369C2×Dic6—61no—
370C2×Dic6—61no—
371C2×C3×C8—21no—
372C2×C3×C8—21no—
373C2×C3×C8—31no—
374C2×C3×C8—31no—
375C2×C3×C8—121no—
376C2×C3×C8—121no—
377C2×C3×C8C22×D311yescharacteristic
378C2×C3×C8C22×D311yescharacteristic
379C2×C3×C8C22×D311yescharacteristic
380C2×C3×C8C22×D311yescharacteristic
381C3×C4⋊C4—31no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—61no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—61no—
389C3×C42—31no—
390#217D1211yescharacteristic
391#213—121no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
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—121no—
404(C2×D3)⋊C4D1211yescharacteristic
405C4⋊Dic3—21no—
406C4⋊Dic3—31no—
407C4⋊Dic3—31no—
408C4⋊Dic3—61no—
409C4⋊Dic3—61no—
410C4⋊Dic3—61no—
411C4⋊Dic3C22×D311yescharacteristic
412C4⋊Dic3C22×D311yescharacteristic
413C4⋊Dic3C22×D311yescharacteristic
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4D1211yescharacteristic
417C4×Dic3C22×D311yescharacteristic
418C2×C3⋊C8—41no—
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421D24—62no—
422D24—62no—
423D24—122no—
424D24—121no—
425D24—121no—
426D24—122no—
427D24—121no—
428D3×C8—41no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32C2×D812yes—
432C22×C32C22×D411yescharacteristic
433C2×C3⋊D3—22no—
434C2×C3⋊D3—41no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3⋊D3—41no—
438C2×C3⋊D3—41no—
439C2×C3⋊D3—41no—
440C2×C3⋊D3—41no—
441C2×C3⋊D3—41no—
442C2×C3⋊D3—84no—
443C2×C3×D3—21no—
444C2×C3×D3—21no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3C2×D812yes—
449D32—84no—
450C32×C4—21no—
451C32×C4C2×#4111yescharacteristic
452C32×C4H(5,𝔽2)11yescharacteristic
453C3⋊Dic3—41no—
454C3×Dic3—21no—
455C3×Dic3—21no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C3×Dic3C2×D812yes—
460C2×#41—181no—
461C22×D4—91no—
462C22×D4—91no—
463C22×D4—181no—
464C2×D8—91no—
465C2×D8—91no—
466C2×D8—91no—
467C22×C8—31no—
468C22×C8—31no—
469C4⋊Q8—91no—
470#127—91no—
471#123—181no—
472#123—181no—
473C22⋊Q8—181no—
474#121—31no—
475#121—91no—
476#121—91no—
477#121—91no—
478#121—181no—
479#120—181no—
480#120—181no—
481C4×D4—31no—
482C4×D4—91no—
483C4×D4—91no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—91no—
486#107—31no—
487#107—31no—
488#107—91no—
489C4⋊C8—31no—
490#102—31no—
491#102—31no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496#102—91no—
497#102—91no—
498#102—91no—
499#102—91no—
500C22⋊C8—31no—
501C22⋊C8D3211yescharacteristic, complemented
502C4×C8—31no—
503C23×C3—21no—
504C23×C3—31no—
505C23×C3—61no—
506C23×C3C2×D1211yescharacteristic
507C23×C3D3×D411yescharacteristic
508C22×D3—21no—
509C22×D3—61no—
510C22×D3—61no—
511C22×D3—61no—
512C22×D3—61no—
513C22×D3—61no—
514C22×D3—61no—
515C22×D3—121no—
516C22×D3—121no—
517C22×D3—121no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—124no—
524C22×D3—122no—
525C22×D3—122no—
526C22×D3—122no—
527C22×D3—242no—
528C22×D3—241no—
529C22×D3—241no—
530C22×D3—241no—
531C22×D3—241no—
532C22×D3—242no—
533C22×D3C2×D1211yescharacteristic
534C3×D4—34no—
535C3×D4—61no—
536C3×D4—61no—
537C3×D4—122no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—31no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—122no—
555C2×C3×C4C2×D1211yescharacteristic
556C2×C3×C4D3×D411yescharacteristic
557C2×C3×C4C23×D311yescharacteristic
558C2×C3×C4C23×D311yescharacteristic
559#67—42no—
560#67—122no—
561#67—122no—
562#67—122no—
563#67—122no—
564#67—122no—
565#67—122no—
566#67—242no—
567#67—241no—
568#67D2414yescomplemented
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—42no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—121no—
576C2×Dic3—122no—
577C2×Dic3C2×D1211yescharacteristic
578C2×Dic3C2×D1211yescharacteristic
579C2×Dic3C2×D1211yescharacteristic
580D12—21no—
581D12—21no—
582D12—32no—
583D12—32no—
584D12—62no—
585D12—62no—
586D12—61no—
587D12—61no—
588D12—61no—
589D12—61no—
590D12—61no—
591D12—61no—
592D12—61no—
593D12—61no—
594D12—61no—
595D12—61no—
596D12—121no—
597D12—121no—
598D12—121no—
599D12—121no—
600D12—122no—
601D12—122no—
602D12—122no—
603D12—124no—
604D12—122no—
605D12—122no—
606D12—122no—
607D12—241no—
608C4×D3—21no—
609C4×D3—21no—
610C4×D3—122no—
611C4×D3—122no—
612C4×D3—122no—
613C4×D3—122no—
614C4×D3—122no—
615Dic6—122no—
616Dic6—122no—
617C3×C8—21no—
618C3×C8—21no—
619C3×C8—21no—
620C3×C8—21no—
621C3×C8—41no—
622C3×C8—41no—
623C3×C8—61no—
624C3×C8—61no—
625C3⋊C8—21no—
626C3⋊C8—21no—
627C2×C32—22no—
628C2×C32#54611yescharacteristic
629C2×C32C22×D811yescharacteristic
630C2×C32#57711yescharacteristic
631C3⋊D3—42no—
632C3⋊D3—81no—
633C3⋊D3—81no—
634C3×D3—22no—
635C3×D3—81no—
636C24—181no—
637C24—181no—
638#41—364no—
639C2×Q8—181no—
640C2×D4—31no—
641C2×D4—31no—
642C2×D4—61no—
643C2×D4—91no—
644C2×D4—91no—
645C2×D4—91no—
646C2×D4—182no—
647C2×D4—181no—
648C2×D4—181no—
649C2×D4—181no—
650C2×D4—182no—
651C2×D4—181no—
652C2×D4—181no—
653C2×D4—181no—
654C2×D4—181no—
655C2×D4—361no—
656C2×D4—361no—
657C2×D4—364no—
658C22×C4—31no—
659C22×C4—61no—
660C22×C4—181no—
661C22×C4—181no—
662C22×C4—181no—
663C22×C4C2×D3211yescharacteristic
664D8—182no—
665D8—361no—
666D8—361no—
667C2×C8—31no—
668C2×C8—31no—
669C2×C8—121no—
670C2×C8—121no—
671C2×C8C2×D3211yescharacteristic
672C2×C8C2×D3211yescharacteristic
673C4⋊C4—31no—
674C4⋊C4—31no—
675C4⋊C4—31no—
676C4⋊C4—31no—
677C4⋊C4—61no—
678C4⋊C4—91no—
679C4⋊C4—181no—
680C4⋊C4—181no—
681C22⋊C4—31no—
682C22⋊C4—31no—
683C22⋊C4—61no—
684C22⋊C4—181no—
685C22⋊C4—181no—
686C22⋊C4—181no—
687C22⋊C4—181no—
688C22⋊C4—181no—
689C42—31no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—22no—
696C22×C3—32no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—121no—
702C22×C3—121no—
703C22×C3—121no—
704C22×C3C2×D2412yes—
705C22×C3D3×D812yes—
706C22×C3C22×D1211yescharacteristic
707C22×C3C2×D3×D411yescharacteristic
708C2×D3—21no—
709C2×D3—21no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—62no—
714C2×D3—62no—
715C2×D3—122no—
716C2×D3—121no—
717C2×D3—121no—
718C2×D3—121no—
719C2×D3—121no—
720C2×D3—122no—
721C2×D3—121no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3—241no—
734C2×D3—241no—
735C2×D3—241no—
736C2×D3—241no—
737C2×D3—241no—
738C2×D3—241no—
739C2×D3—241no—
740C2×D3—244no—
741C2×D3—244no—
742C2×D3—244no—
743C2×D3—244no—
744C2×D3—248no—
745C2×D3C2×D2412yes—
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—32no—
751C3×C4—41no—
752C3×C4—61no—
753C3×C4—61no—
754C3×C4—121no—
755C3×C4—121no—
756C3×C4—121no—
757C3×C4#100411yescharacteristic
758C3×C4D3×#4111yescharacteristic
759C3×C4D3×#4111yescharacteristic
760C3×C4#100911yescharacteristic
761Dic3—21no—
762Dic3—21no—
763Dic3—41no—
764Dic3—41no—
765Dic3—41no—
766Dic3—121no—
767Dic3—121no—
768Dic3—241no—
769Dic3C2×D2412yes—
770C32#329411yescharacteristic, complemented, Sylow
771C23—31no—
772C23—61no—
773C23—181no—
774C23—181no—
775C23—181no—
776C23—362no—
777C23—362no—
778C23—362no—
779C23—362no—
780C23—721no—
781C23—721no—
782C23D3×D1211yescharacteristic
783Q8—362no—
784D4—34no—
785D4—61no—
786D4—61no—
787D4—92no—
788D4—122no—
789D4—181no—
790D4—181no—
791D4—181no—
792D4—181no—
793D4—181no—
794D4—362no—
795D4—362no—
796D4—362no—
797D4—362no—
798D4—362no—
799D4—362no—
800D4—721no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—31no—
804C2×C4—31no—
805C2×C4—31no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—122no—
812C2×C4—181no—
813C2×C4—362no—
814C2×C4—362no—
815C2×C4—362no—
816C2×C4D3×D1211yescharacteristic
817C2×C4C22×D3211yescharacteristic
818C8—21no—
819C8—21no—
820C8—61no—
821C8—61no—
822C2×C3—22no—
823C2×C3—22no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—42no—
828C2×C3—62no—
829C2×C3—241no—
830C2×C3#555411yescharacteristic
831C2×C3#565411yescharacteristic
832C2×C3C22×D2411yescharacteristic
833C2×C3#575111yescharacteristic
834C2×C3C2×D3×D811yescharacteristic
835C2×C3#577811yescharacteristic
836D3—22no—
837D3—81no—
838D3—122no—
839D3—122no—
840D3—242no—
841D3—242no—
842D3—241no—
843D3—241no—
844D3—241no—
845D3—241no—
846D3—481no—
847C22—21no—
848C22—21no—
849C22—32no—
850C22—61no—
851C22—61no—
852C22—121no—
853C22—121no—
854C22—121no—
855C22—182no—
856C22—361no—
857C22—361no—
858C22—361no—
859C22—361no—
860C22—361no—
861C22—361no—
862C22—361no—
863C22—361no—
864C22—724no—
865C22—724no—
866C22D3×D2412yes—
867C22C2×D3×D1211yescharacteristic
868C4—21no—
869C4—32no—
870C4—61no—
871C4—61no—
872C4—121no—
873C4—121no—
874C4—121no—
875C4—361no—
876C4#6431211yescharacteristic
877C4#6431411yescharacteristic
878C3—21no—
879C3#7943811yescharacteristic, complemented
880C3#8130211yescharacteristic, complemented
881C2—22no—
882C2—62no—
883C2—241no—
884C2—362no—
885C2—721no—
886C2—721no—
887C2#1059429311yescharacteristic
888C2C2×D3×D2411yescharacteristic
889C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10595074C2semidirect
2. #10594906C2semidirect
3. #10592431C2semidirect
4. C3×#4736C2semidirect
5. C3×#67⋊C8C2semidirect
6. #10591164C2semidirect
7. C2×#63564C2semidirect
8. #10590947C2semidirect
9. D3×#821C2semidirect
10. #10590878C2semidirect
11. #10590832C2semidirect
12. #10590765C2semidirect
13. #10590764C2semidirect
14. #10590763C2semidirect
15. #10590679C2semidirect
22. #64139C22semidirect
24. C2×#3745C22semidirect
27. C2×C3×C4⋊Dic3C22semidirect
28. C22×C3×C3⋊C8C22semidirect
29. C2×C3×D3×C8C22semidirect
33. #63918C22semidirect
37. #63909C22semidirect
40. #63894C22semidirect
42. D3×C4⋊Dic3C22semidirect
43. C2×#3714C22semidirect
44. C32×C22⋊C8C22semidirect
46. #63648C22semidirect
47. C3×#821C22semidirect
48. C3×#821C22semidirect
49. C3×(C2×D3)⋊C8C22semidirect
50. C3×#818C22semidirect
51. C3×#818C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63575C22semidirect
57. #63564C22semidirect
58. #63564C22semidirect
59. #63564C22semidirect
60. #63563C22semidirect
84. #4736D3semidirect
89. #67⋊C8D3semidirect
173. C2×C4⋊Dic3C2×D3semidirect
174. C22×C3⋊C8C2×D3semidirect
182. C2×D3×C8C2×D3semidirect
210. C3×C22⋊C8C2×D3semidirect
211. C3×C22⋊C8C2×D3semidirect
226. #821C2×D3semidirect
227. #821C2×D3semidirect
228. (C2×D3)⋊C8C2×D3semidirect
230. #818C2×D3semidirect
231. #818C2×D3semidirect
232. Dic3⋊C8C2×D3semidirect
233. C8×Dic3C2×D3semidirect
264. C4⋊(C3⋊D3)#41semidirect
266. C3×#67D8semidirect
501. C22⋊C8D32semidirect
568. #67D24semidirect
770. C32#3294semidirect
879. C3#79438semidirect
880. C3#81302semidirect

Maximal subgroups

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

subgroupindex
#105950742
#105949062
#105924312
C3×#47362
C3×#67⋊C82
#105911642
C2×#635642
#105909472
D3×#8212
#105908782
#105908322
#105907652
#105907642
#105907632
#105906792
#813023
#794383