Finite Group Databasebeta

← #11887110

Subgroups — #11887110

Order 1152.

1018 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595074C211yesmaximal, characteristic
2#10594988C211yesmaximal, characteristic, complemented
3#10592430C211yesmaximal, characteristic, complemented
4C3×#4735C211yesmaximal, characteristic, complemented
5C3×#67⋊C8C211yesmaximal, characteristic, complemented
6#10591175C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8#10590946C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590879C211yesmaximal, characteristic, complemented
11#10590878C211yesmaximal, characteristic, complemented
12#10590830C211yesmaximal, characteristic, complemented
13#10590759C211yesmaximal, characteristic, complemented
14#10590758C211yesmaximal, characteristic, complemented
15#10590677C211yesmaximal, characteristic, complemented
16#81342—31nomaximal
17#79439—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3811—21no—
20C2×D3×D12C2211yescharacteristic
21#64133C2211yescharacteristic, complemented
22C2×#3744C2211yescharacteristic
23C2×#3744C2211yescharacteristic, complemented
24C3×#930C2211yescharacteristic
25C3×C4×#67C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
27C22×C3×C3⋊C8C2211yescharacteristic, complemented
28C2×C3×D3×C8C2211yescharacteristic, complemented
29#63981—21no—
30Dic3×#67—21no—
31#63964—21no—
32#63923—21no—
33#63918C2211yescharacteristic, complemented
34#63911C2211yescharacteristic
35#63910—21no—
36#63909C2211yescharacteristic
37#63899—21no—
38#63894C2211yescharacteristic
39D3×C4⋊Dic3C2211yescharacteristic, complemented
40#63857C2211yescharacteristic, complemented
41#63846—21no—
42#63844C2211yescharacteristic, complemented
43C2×#3716C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
50C3×#817C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#5609—31no—
62D4×D12—31no—
63#5543—31no—
64#5511—31no—
65C3×#481—31no—
66C3×C8×D4—31no—
67#5114—31no—
68#5114—31no—
69C2×#821—31no—
70C2×#821—31no—
71#5041—31no—
72C2×#809—31no—
73#4870—31no—
74#4864—31no—
75#4863—31no—
76#4852—31no—
77#4848—31no—
78#4842—31no—
79#4776—31no—
80D3×#102—31no—
81#4762—31no—
82#4760—31no—
83#4735—31no—
84#4735D311yescharacteristic, complemented
85#4731—31no—
86#4731—31no—
87#4731—31no—
88#4731—61no—
89#67⋊C8D311yescharacteristic, complemented
90#4694—31no—
91C4×#204—31no—
92C23×C3⋊D3—21no—
93C22×D32—21no—
94C22×C32×C4C2311yescharacteristic
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106#3811—44no—
107C2×#627—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#624—21no—
113C2×D3×Dic3—21no—
114D3×D12—22no—
115D3×D12—41no—
116C2×C32×C8C2311yescharacteristic
117C2×C32×C8C2311yescharacteristic
118#3757—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121#3744—22no—
122#3744—41no—
123C3×#217D411yescharacteristic
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×D3×C8—41no—
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141#3722—21no—
142(C2×D3)⋊Dic3—21no—
143Dic32—21no—
144#3716—41no—
145#3295—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—61no—
148C2×D3×D4—61no—
149C22×D12—31no—
150C22×D12—31no—
151C22×D12—31no—
152C22×D12—61no—
153C22×C3×C8—31no—
154C22×C3×C8—31no—
155C3×#121—31no—
156C3×C4×D4—31no—
157C2×C3×C4⋊C4—31no—
158#940—31no—
159#937—61no—
160D4×Dic3—61no—
161C2×#214—31no—
162#930—31no—
163#930C2×D311yescharacteristic
164C4×#67—61no—
165C4×#67C2×D311yescharacteristic
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3C2×D311yescharacteristic, complemented
168#924—31no—
169#924—31no—
170#924—31no—
171#924—61no—
172#924—61no—
173C22×C3⋊C8C2×D311yescharacteristic, complemented
174C2×#204—31no—
175C2×#204—31no—
176C2×#204—31no—
177C2×#204—31no—
178C2×#204—31no—
179C2×#204—61no—
180C2×#204—61no—
181C2×D3×C8C2×D311yescharacteristic, complemented
182#897—31no—
183#896—61no—
184#895—31no—
185#895—61no—
186#893—31no—
187D3×C4⋊C4—31no—
188#890—61no—
189#889—61no—
190#888—31no—
191#887—31no—
192#884—61no—
193#882—61no—
194#882—61no—
195#882—61no—
196#878—61no—
197#878—61no—
198#874—31no—
199C4×D12—31no—
200#869—31no—
201C4×Dic6—31no—
202C3×#106—31no—
203C3×#106—31no—
204C3×C4⋊C8—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C22⋊C8—21no—
208C3×C22⋊C8—31no—
209C3×C22⋊C8C2×D311yescharacteristic, complemented
210C3×C22⋊C8C2×D311yescharacteristic, complemented
211C3×C4×C8—31no—
212#832—31no—
213#821—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—61no—
223#821—61no—
224#821C2×D311yescharacteristic, complemented
225#821C2×D311yescharacteristic, complemented
226(C2×D3)⋊C8C2×D311yescharacteristic, complemented
227#817—31no—
228#817C2×D311yescharacteristic, complemented
229#817C2×D311yescharacteristic, complemented
230#816—31no—
231Dic3⋊C8C2×D311yescharacteristic, complemented
232C8×Dic3C2×D311yescharacteristic, complemented
233#810—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#809—31no—
238#808—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3—42no—
244C22×C3⋊D3—81no—
245C22×C3×D3—21no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—42no—
260C4⋊(C3⋊D3)#4112yes—
261#634—21no—
262#634—21no—
263C3×#67—42no—
264C3×#67SD1614yescomplemented
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—81no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276#627—81no—
277#626—42no—
278#626—42no—
279#626—42no—
280#626—81no—
281#624—42no—
282D3×Dic3—81no—
283C32×C8—21no—
284C32×C8—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287#554—91no—
288D42—91no—
289#486—91no—
290#481—31no—
291#481—91no—
292#476—91no—
293#465—91no—
294#465—91no—
295#460—91no—
296#450—91no—
297#450—91no—
298C4×SD16—91no—
299C8×D4—31no—
300C2×#102—91no—
301C2×#102—91no—
302C23×D3—61no—
303C23×D3—61no—
304C23×D3—61no—
305C23×D3—61no—
306C23×D3—121no—
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—61no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C2×#67—21no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67D1211yescharacteristic
321C22×Dic3—21no—
322C22×Dic3—61no—
323D3×D4—62no—
324D3×D4—121no—
325D3×D4—124no—
326D3×D4—124no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—31no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—62no—
334C2×D12—62no—
335C2×D12—62no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12—61no—
340C2×D12—61no—
341C2×D12—61no—
342C2×D12—122no—
343C2×D12—121no—
344C2×D12—121no—
345C2×D12—121no—
346C2×D12—121no—
347C2×D12—122no—
348C2×D12C22×D311yescharacteristic
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3C22×D311yescharacteristic
353C2×Dic6—31no—
354C2×Dic6—31no—
355C2×Dic6—61no—
356C2×Dic6—61no—
357C2×Dic6—61no—
358C2×C3×C8—21no—
359C2×C3×C8—21no—
360C2×C3×C8—31no—
361C2×C3×C8—31no—
362C2×C3×C8—121no—
363C2×C3×C8—121no—
364C2×C3×C8C22×D311yescharacteristic
365C2×C3×C8C22×D311yescharacteristic
366C2×C3×C8C22×D311yescharacteristic
367C2×C3×C8C22×D311yescharacteristic
368C3×C4⋊C4—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—61no—
373C3×C22⋊C4—31no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—61no—
376C3×C42—31no—
377#217—61no—
378#217—61no—
379#217—61no—
380#217—121no—
381#217D1211yescharacteristic
382#214—121no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4D1211yescharacteristic
390C4⋊Dic3—21no—
391C4⋊Dic3—31no—
392C4⋊Dic3—31no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399C4⋊Dic3C22×D311yescharacteristic
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—121no—
408Dic3⋊C4D1211yescharacteristic
409C4×Dic3—61no—
410C4×Dic3—61no—
411C4×Dic3C22×D311yescharacteristic
412C2×C3⋊C8—41no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415#204—62no—
416#204—62no—
417#204—122no—
418#204—121no—
419#204—121no—
420#204—122no—
421#204—121no—
422D3×C8—41no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32C2×SD1612yes—
426C22×C32C22×D411yescharacteristic
427C2×C3⋊D3—22no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3—41no—
432C2×C3⋊D3—41no—
433C2×C3⋊D3—84no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3C2×SD1612yes—
440D32—84no—
441C32×C4—21no—
442C32×C4C2×#4111yescharacteristic
443C32×C4H(5,𝔽2)11yescharacteristic
444C3⋊Dic3—41no—
445C3⋊Dic3—41no—
446C3×Dic3—21no—
447C3×Dic3—21no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C3×Dic3C2×SD1612yes—
452C22×D4—91no—
453C22×D4—91no—
454C22×D4—181no—
455C2×SD16—91no—
456C2×SD16—91no—
457C2×SD16—91no—
458C22×C8—31no—
459C22×C8—31no—
460C4⋊Q8—91no—
461#127—91no—
462#125—181no—
463C22⋊Q8—91no—
464C22⋊Q8—91no—
465C22⋊Q8—181no—
466C22⋊Q8—181no—
467#121—31no—
468#121—91no—
469#121—181no—
470#120—181no—
471#120—181no—
472C4×Q8—91no—
473C4×D4—31no—
474C4×D4—91no—
475C4×D4—181no—
476C2×C4⋊C4—31no—
477C2×C4⋊C4—91no—
478#106—31no—
479#106—31no—
480#106—91no—
481C4⋊C8—31no—
482#103—91no—
483#102—31no—
484#102—31no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490#102—91no—
491#102—91no—
492C22⋊C8—31no—
493C22⋊C8D3211yescharacteristic, complemented
494C4×C8—31no—
495C23×C3—21no—
496C23×C3—31no—
497C23×C3—61no—
498C23×C3C2×D1211yescharacteristic
499C23×C3D3×D411yescharacteristic
500C22×D3—21no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—121no—
506C22×D3—121no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—124no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—122no—
516C22×D3—242no—
517C22×D3—241no—
518C22×D3—241no—
519C22×D3—241no—
520C22×D3—241no—
521C22×D3—242no—
522C22×D3C2×D1211yescharacteristic
523C3×D4—34no—
524C3×D4—61no—
525C3×D4—61no—
526C3×D4—122no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—31no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—241no—
544C2×C3×C4C2×D1211yescharacteristic
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4C23×D311yescharacteristic
547C2×C3×C4C23×D311yescharacteristic
548#67—42no—
549#67—122no—
550#67—122no—
551#67—122no—
552#67—241no—
553#67#20414yescomplemented
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—81no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—241no—
565C2×Dic3C2×D1211yescharacteristic
566C2×Dic3C2×D1211yescharacteristic
567C2×Dic3C2×D1211yescharacteristic
568D12—21no—
569D12—21no—
570D12—32no—
571D12—32no—
572D12—62no—
573D12—62no—
574D12—61no—
575D12—61no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—61no—
580D12—121no—
581D12—121no—
582D12—122no—
583D12—122no—
584D12—122no—
585D12—124no—
586D12—122no—
587D12—122no—
588D12—241no—
589C4×D3—21no—
590C4×D3—21no—
591C4×D3—122no—
592C4×D3—122no—
593C4×D3—241no—
594Dic6—61no—
595Dic6—61no—
596Dic6—61no—
597Dic6—61no—
598Dic6—121no—
599Dic6—121no—
600Dic6—241no—
601Dic6—241no—
602C3×C8—21no—
603C3×C8—21no—
604C3×C8—21no—
605C3×C8—21no—
606C3×C8—41no—
607C3×C8—41no—
608C3×C8—61no—
609C3×C8—61no—
610C3⋊C8—21no—
611C3⋊C8—21no—
612C2×C32—22no—
613C2×C32#54611yescharacteristic
614C2×C32C22×SD1611yescharacteristic
615C2×C32#57611yescharacteristic
616C3⋊D3—42no—
617C3⋊D3—81no—
618C3×D3—22no—
619C3×D3—81no—
620C24—181no—
621C24—181no—
622C2×Q8—91no—
623C2×Q8—181no—
624C2×D4—31no—
625C2×D4—31no—
626C2×D4—61no—
627C2×D4—91no—
628C2×D4—91no—
629C2×D4—182no—
630C2×D4—181no—
631C2×D4—181no—
632C2×D4—181no—
633C2×D4—182no—
634C2×D4—181no—
635C2×D4—181no—
636C2×D4—361no—
637C2×D4—361no—
638C2×D4—364no—
639C22×C4—31no—
640C22×C4—61no—
641C22×C4—181no—
642C22×C4—181no—
643C22×C4C2×D3211yescharacteristic
644SD16—182no—
645SD16—361no—
646SD16—361no—
647C2×C8—31no—
648C2×C8—31no—
649C2×C8—121no—
650C2×C8—121no—
651C2×C8C2×D3211yescharacteristic
652C2×C8C2×D3211yescharacteristic
653C4⋊C4—31no—
654C4⋊C4—31no—
655C4⋊C4—31no—
656C4⋊C4—31no—
657C4⋊C4—61no—
658C4⋊C4—91no—
659C4⋊C4—181no—
660C4⋊C4—181no—
661C4⋊C4—181no—
662C4⋊C4—181no—
663C4⋊C4—181no—
664C22⋊C4—31no—
665C22⋊C4—31no—
666C22⋊C4—61no—
667C22⋊C4—181no—
668C22⋊C4—181no—
669C22⋊C4—181no—
670C22⋊C4—181no—
671C42—31no—
672C42—181no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—22no—
679C22×C3—32no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3C2×#20412yes—
688C22×C3D3×SD1612yes—
689C22×C3C22×D1211yescharacteristic
690C22×C3C2×D3×D411yescharacteristic
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—62no—
697C2×D3—62no—
698C2×D3—122no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—122no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—241no—
711C2×D3—241no—
712C2×D3—241no—
713C2×D3—241no—
714C2×D3—244no—
715C2×D3—244no—
716C2×D3—244no—
717C2×D3—244no—
718C2×D3—248no—
719C2×D3C2×#20412yes—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—32no—
725C3×C4—41no—
726C3×C4—61no—
727C3×C4—61no—
728C3×C4—121no—
729C3×C4—121no—
730C3×C4—121no—
731C3×C4#100411yescharacteristic
732C3×C4D3×#4111yescharacteristic
733C3×C4D3×#4111yescharacteristic
734C3×C4#100911yescharacteristic
735Dic3—21no—
736Dic3—21no—
737Dic3—41no—
738Dic3—41no—
739Dic3—41no—
740Dic3—121no—
741Dic3—121no—
742Dic3—121no—
743Dic3—121no—
744Dic3—241no—
745Dic3—241no—
746Dic3C2×#20412yes—
747C32#329511yescharacteristic, complemented, Sylow
748C23—31no—
749C23—61no—
750C23—181no—
751C23—181no—
752C23—362no—
753C23—362no—
754C23—362no—
755C23—362no—
756C23—721no—
757C23—721no—
758C23D3×D1211yescharacteristic
759Q8—181no—
760Q8—181no—
761Q8—721no—
762D4—34no—
763D4—61no—
764D4—61no—
765D4—92no—
766D4—122no—
767D4—181no—
768D4—181no—
769D4—181no—
770D4—362no—
771D4—362no—
772D4—362no—
773D4—362no—
774D4—721no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—31no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—181no—
786C2×C4—181no—
787C2×C4—241no—
788C2×C4—362no—
789C2×C4—721no—
790C2×C4D3×D1211yescharacteristic
791C2×C4C22×D3211yescharacteristic
792C8—21no—
793C8—21no—
794C8—61no—
795C8—61no—
796C2×C3—22no—
797C2×C3—22no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—42no—
802C2×C3—62no—
803C2×C3—241no—
804C2×C3#555411yescharacteristic
805C2×C3#565411yescharacteristic
806C2×C3C22×#20411yescharacteristic
807C2×C3#575211yescharacteristic
808C2×C3C2×D3×SD1611yescharacteristic
809C2×C3#577411yescharacteristic
810D3—22no—
811D3—81no—
812D3—122no—
813D3—122no—
814D3—242no—
815D3—242no—
816D3—241no—
817D3—241no—
818C22—21no—
819C22—21no—
820C22—32no—
821C22—61no—
822C22—61no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22—182no—
827C22—361no—
828C22—361no—
829C22—361no—
830C22—361no—
831C22—361no—
832C22—724no—
833C22—724no—
834C22D3×#20412yes—
835C22C2×D3×D1211yescharacteristic
836C4—21no—
837C4—32no—
838C4—61no—
839C4—61no—
840C4—121no—
841C4—121no—
842C4—121no—
843C4—361no—
844C4—361no—
845C4#6431211yescharacteristic
846C4#6431411yescharacteristic
847C3—21no—
848C3#7943911yescharacteristic, complemented
849C3#8134211yescharacteristic, complemented
850C2—22no—
851C2—62no—
852C2—241no—
853C2—362no—
854C2—721no—
855C2#1059429311yescharacteristic
856C2C2×D3×#20411yescharacteristic
857C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595074C2
hypercenterC22⋊C8D32
hypocenterC32#3295
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
2. #10594988C2semidirect
3. #10592430C2semidirect
4. C3×#4735C2semidirect
5. C3×#67⋊C8C2semidirect
6. #10591175C2semidirect
7. C2×#63564C2semidirect
8. #10590946C2semidirect
9. D3×#821C2semidirect
10. #10590879C2semidirect
11. #10590878C2semidirect
12. #10590830C2semidirect
13. #10590759C2semidirect
14. #10590758C2semidirect
15. #10590677C2semidirect
21. #64133C22semidirect
23. C2×#3744C22semidirect
26. C2×C3×C4⋊Dic3C22semidirect
27. C22×C3×C3⋊C8C22semidirect
28. C2×C3×D3×C8C22semidirect
33. #63918C22semidirect
39. D3×C4⋊Dic3C22semidirect
40. #63857C22semidirect
42. #63844C22semidirect
43. C2×#3716C22semidirect
44. C32×C22⋊C8C22semidirect
46. #63648C22semidirect
47. C3×#821C22semidirect
48. C3×#821C22semidirect
49. C3×(C2×D3)⋊C8C22semidirect
50. C3×#817C22semidirect
51. C3×#817C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63573C22semidirect
55. #63567C22semidirect
58. #63564C22semidirect
59. #63564C22semidirect
60. #63563C22semidirect
84. #4735D3semidirect
89. #67⋊C8D3semidirect
167. C2×C4⋊Dic3C2×D3semidirect
173. C22×C3⋊C8C2×D3semidirect
181. C2×D3×C8C2×D3semidirect
209. C3×C22⋊C8C2×D3semidirect
210. C3×C22⋊C8C2×D3semidirect
224. #821C2×D3semidirect
225. #821C2×D3semidirect
226. (C2×D3)⋊C8C2×D3semidirect
228. #817C2×D3semidirect
229. #817C2×D3semidirect
231. Dic3⋊C8C2×D3semidirect
232. C8×Dic3C2×D3semidirect
264. C3×#67SD16semidirect
493. C22⋊C8D32semidirect
553. #67#204semidirect
747. C32#3295semidirect
848. C3#79439semidirect
849. C3#81342semidirect

Maximal subgroups

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

subgroupindex
#105950742
#105949882
#105924302
C3×#47352
C3×#67⋊C82
#105911752
C2×#635642
#105909462
D3×#8212
#105908792
#105908782
#105908302
#105907592
#105907582
#105906772
#813423
#794393