Finite Group Databasebeta

← #11887114

Subgroups — #11887114

Order 1152.

1038 conjugacy classes of subgroups.

The subgroup lattice has 871 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595982C211yesmaximal, characteristic, complemented
2#10595069C211yesmaximal, characteristic
3C3×#4968C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5#10591175C211yesmaximal, characteristic, complemented
6#10591172C211yesmaximal, characteristic, complemented
7#10591148C211yesmaximal, characteristic, complemented
8#10590597C211yesmaximal, characteristic, complemented
9#10590593C211yesmaximal, characteristic, complemented
10#10590553C211yesmaximal, characteristic, complemented
11#10590552C211yesmaximal, characteristic, complemented
12#10590511C211yesmaximal, characteristic, complemented
13#10590507C211yesmaximal, characteristic, complemented
14#10590472C211yesmaximal, characteristic, complemented
15#10590460C211yesmaximal, characteristic, complemented
16#81342—31nomaximal
17#78758—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic, complemented
22C4×#638—21no—
23C4×#638C2211yescharacteristic
24#64133—21no—
25#64133C2211yescharacteristic, complemented
26#64106C2211yescharacteristic, complemented
27#64105—21no—
28C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
29#64098—21no—
30#64097C2211yescharacteristic, complemented
31#64096C2211yescharacteristic, complemented
32C3×#930C2211yescharacteristic
33C22×C3×C3⋊C8C2211yescharacteristic, complemented
34#63976—21no—
35#63922—21no—
36#63916C2211yescharacteristic
37#63914C2211yescharacteristic
38#63898C2211yescharacteristic
39#63885—21no—
40C2×#3716C2211yescharacteristic
41C2×#3716C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic, complemented
44C3×#830C2211yescharacteristic, complemented
45C3×#809C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#809C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic, complemented
50C3×#809C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52C3×#808C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61D4×#67—31no—
62#5609—31no—
63#5511—31no—
64#5511—31no—
65#5511—61no—
66C3×#481—31no—
67C2×C3×#102—31no—
68#5218—31no—
69#5114—31no—
70C8×#67—31no—
71#5041—31no—
72#4968D311yescharacteristic, complemented
73C2×#809D311yescharacteristic, complemented
74#4870—31no—
75#4864—31no—
76#4863—31no—
77#4852—31no—
78#4778—31no—
79#4777—31no—
80#4776—31no—
81#4776—31no—
82D3×#102—31no—
83D3×#102—31no—
84#4762—31no—
85#4762—31no—
86#4761—31no—
87#4760—31no—
88#4760—31no—
89#4758—31no—
90#4731—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C22×C32×C4—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638D411yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634—21no—
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×D12—22no—
103C2×C3×D12—21no—
104C2×C3×D12—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108D3×#67—44no—
109C2×#626—21no—
110C2×#625—21no—
111C2×#625—21no—
112C2×#625—21no—
113C2×D3×Dic3—21no—
114#3802—22no—
115#3802—41no—
116C32×C4⋊C4—21no—
117C32×C4⋊C4C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3757—21no—
120#3757D411yescharacteristic
121#3752—21no—
122#3752D411yescharacteristic
123C4⋊(C3⋊Dic3)—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126#3750—21no—
127#3750—21no—
128#3750—21no—
129#3750D411yescharacteristic
130C4×C3⋊Dic3—21no—
131C4×C3⋊Dic3C2311yescharacteristic
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C2×C3×C3⋊C8—41no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141#3716—22no—
142#3716—41no—
143#3716—41no—
144#3710—41no—
145#3295—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C22×D12C2×D311yescharacteristic
152C22×C3×C8—31no—
153C3×#121—31no—
154C2×C3×C4⋊C4—21no—
155C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
156C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
157#953—61no—
158#940—31no—
159#940—31no—
160#939—61no—
161#938—31no—
162#937—61no—
163#937—61no—
164D4×Dic3—31no—
165C2×#214—31no—
166C2×#214—31no—
167C2×#214—31no—
168#930C2×D311yescharacteristic
169C4×#67—31no—
170C4×#67—31no—
171C4×#67—61no—
172C4×#67—61no—
173C4×#67—61no—
174C4×#67—62no—
175#924—31no—
176#924—31no—
177#924—61no—
178#924—61no—
179#924—61no—
180#924—62no—
181C22×C3⋊C8C2×D311yescharacteristic, complemented
182C2×#204—31no—
183C2×#204—31no—
184C2×#204—31no—
185C2×D3×C8—31no—
186C2×D3×C8—31no—
187#897—31no—
188#897—31no—
189#897—61no—
190#896—61no—
191#896—61no—
192#896—62no—
193#895—31no—
194#893—31no—
195D3×C4⋊C4—31no—
196D3×C4⋊C4—31no—
197D3×C4⋊C4—61no—
198#889—61no—
199#889—61no—
200#889—62no—
201#888—31no—
202#888—31no—
203#888—61no—
204#887—31no—
205#887—31no—
206#887—61no—
207#884—61no—
208#882—61no—
209C3×#106—31no—
210C3×#106—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×C22⋊C8—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#830C2×D311yescharacteristic, complemented
222#821—31no—
223#821—31no—
224#821—31no—
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—31no—
227#817—31no—
228#816—31no—
229Dic3⋊C8—31no—
230Dic3⋊C8—31no—
231C8×Dic3—31no—
232C8×Dic3—31no—
233#810—31no—
234#809C2×D311yescharacteristic
235#809C2×D311yescharacteristic
236#809C2×D311yescharacteristic, complemented
237#809C2×D311yescharacteristic, complemented
238#809C2×D311yescharacteristic, complemented
239#809C2×D311yescharacteristic, complemented
240#808—31no—
241#808C2×D311yescharacteristic, complemented
242#808C2×D311yescharacteristic, complemented
243C23×C32C2×D411yescharacteristic
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—42no—
249C22×C3×D3—42no—
250C22×C3×D3—81no—
251C2×D32—42no—
252C2×D32—42no—
253C2×D32—81no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—81no—
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261#638SD1614yescomplemented
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3C2×D411yescharacteristic
265C2×C3⋊Dic3C2×D411yescharacteristic
266C2×C3⋊Dic3C2×D411yescharacteristic
267C4×C3⋊D3—21no—
268C4×C3⋊D3—21no—
269C4×C3⋊D3—81no—
270#634—21no—
271#634—21no—
272#634—81no—
273C3×#67—42no—
274C2×C3×Dic3—21no—
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—42no—
281C3×D12#4112yes—
282#626—42no—
283#625—42no—
284#625—42no—
285#625—81no—
286D3×Dic3—42no—
287C3×C3⋊C8—21no—
288C3×C3⋊C8—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291#554—91no—
292D42—91no—
293#486—91no—
294#481—31no—
295#481—91no—
296#476—91no—
297#465—91no—
298#465—91no—
299#460—91no—
300#450—91no—
301#450—91no—
302C4×SD16—91no—
303C8×D4—91no—
304C2×#102—31no—
305C2×#102—91no—
306C24×C3—61no—
307C23×D3—21no—
308C23×D3—61no—
309C23×D3—61no—
310C2×C3×D4—31no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—62no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C2×C3×D4—121no—
317C22×C3×C4—22no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C2×#67—21no—
324C2×#67—31no—
325C2×#67—31no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—124no—
335C22×Dic3—61no—
336D3×D4—62no—
337D3×D4—62no—
338D3×D4—121no—
339D3×D4—121no—
340D3×D4—124no—
341C2×D12—22no—
342C2×D12—21no—
343C2×D12—41no—
344C2×D12—61no—
345C2×D12C22×D311yescharacteristic
346C2×D12C22×D311yescharacteristic
347C2×D12C22×D311yescharacteristic
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—62no—
355C2×Dic6—31no—
356C2×Dic6—31no—
357C2×Dic6—61no—
358C2×Dic6—61no—
359C2×Dic6—61no—
360C2×Dic6—62no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C2×C3×C8—121no—
366C3×C4⋊C4—22no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4C22×D311yescharacteristic
373C3×C4⋊C4C22×D311yescharacteristic
374C3×C4⋊C4C22×D311yescharacteristic
375C3×C4⋊C4C22×D311yescharacteristic
376C3×C22⋊C4—61no—
377#217—31no—
378#217—31no—
379#217—61no—
380#217—61no—
381#217—61no—
382#217—62no—
383#217—61no—
384#217—61no—
385#214—62no—
386#214—121no—
387#214—121no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—31no—
390(C2×D3)⋊C4—31no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—62no—
397C4⋊Dic3—31no—
398C4⋊Dic3—31no—
399C4⋊Dic3—61no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3—62no—
403C4⋊Dic3C22×D311yescharacteristic
404Dic3⋊C4—31no—
405Dic3⋊C4—31no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—62no—
414Dic3⋊C4—62no—
415Dic3⋊C4—62no—
416Dic3⋊C4—62no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—62no—
425C2×C3⋊C8—41no—
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428C2×C3⋊C8C22×D311yescharacteristic
429C2×C3⋊C8C22×D311yescharacteristic
430#204—62no—
431#204—121no—
432#204—121no—
433D3×C8—121no—
434D3×C8—121no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32C2×SD1612yes—
438C22×C32C22×D411yescharacteristic
439C2×C3⋊D3—21no—
440C2×C3⋊D3—21no—
441C2×C3⋊D3C2×SD1612yes—
442C2×C3×D3—22no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—84no—
452D32—84no—
453C32×C4—21no—
454C32×C4—41no—
455C32×C4—41no—
456C32×C4C2×#4111yescharacteristic
457C32×C4H(5,𝔽2)11yescharacteristic
458C3⋊Dic3—21no—
459C3⋊Dic3—21no—
460C3⋊Dic3—41no—
461C3⋊Dic3—41no—
462C3⋊Dic3C2×SD1612yes—
463C3×Dic3—41no—
464C22×D4—31no—
465C22×D4—91no—
466C22×D4—181no—
467C2×SD16—91no—
468C2×SD16—91no—
469C2×SD16—91no—
470C22×C8—31no—
471C22×C8—91no—
472C4⋊Q8—91no—
473#127—91no—
474#125—181no—
475C22⋊Q8—91no—
476C22⋊Q8—91no—
477C22⋊Q8—181no—
478C22⋊Q8—181no—
479#121—31no—
480#121—91no—
481#121—181no—
482#120—181no—
483#120—181no—
484C4×Q8—91no—
485C4×D4—91no—
486C4×D4—91no—
487C4×D4—181no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4D3211yescharacteristic, complemented
490#106—31no—
491#106—31no—
492#106—91no—
493C4⋊C8—91no—
494#103—91no—
495#102—31no—
496#102—31no—
497#102—31no—
498#102—31no—
499#102—31no—
500#102—31no—
501#102—91no—
502#102—91no—
503#102—91no—
504C22⋊C8—31no—
505C22⋊C8—91no—
506C4×C8—91no—
507C23×C3—21no—
508C23×C3—61no—
509C23×C3—61no—
510C23×C3—61no—
511C23×C3—122no—
512C23×C3—122no—
513C23×C3—241no—
514C23×C3D3×D411yescharacteristic
515C23×C3D3×D411yescharacteristic
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—31no—
520C22×D3—31no—
521C22×D3—42no—
522C22×D3—42no—
523C22×D3—61no—
524C22×D3—81no—
525C22×D3—122no—
526C22×D3—122no—
527C22×D3—122no—
528C22×D3—122no—
529C22×D3—241no—
530C22×D3—241no—
531C3×D4—32no—
532C3×D4—61no—
533C3×D4—61no—
534C3×D4—61no—
535C3×D4—61no—
536C3×D4—61no—
537C3×D4—122no—
538C3×D4—122no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—61no—
554C2×C3×C4—81no—
555C2×C3×C4—81no—
556C2×C3×C4—82no—
557C2×C3×C4D3×D411yescharacteristic
558C2×C3×C4D3×D411yescharacteristic
559C2×C3×C4C23×D311yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561#67—34no—
562#67—34no—
563#67—42no—
564#67—64no—
565#67—122no—
566#67—122no—
567#67—122no—
568#67—122no—
569#67—122no—
570#67—241no—
571#67—241no—
572C2×Dic3—21no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—62no—
583C2×Dic3—62no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—122no—
589D12—21no—
590D12—21no—
591D12—21no—
592D12—21no—
593D12—21no—
594D12—42no—
595D12—122no—
596D12#23512yes—
597C4×D3—61no—
598C4×D3—61no—
599C4×D3—61no—
600C4×D3—61no—
601C4×D3—121no—
602C4×D3—121no—
603C4×D3—122no—
604C4×D3—241no—
605C4×D3—241no—
606C4×D3—242no—
607Dic6—61no—
608Dic6—61no—
609Dic6—61no—
610Dic6—61no—
611Dic6—121no—
612Dic6—121no—
613Dic6—241no—
614Dic6—241no—
615Dic6—242no—
616C3×C8—61no—
617C3×C8—61no—
618C3×C8—61no—
619C3×C8—61no—
620C3⋊C8—21no—
621C3⋊C8—21no—
622C3⋊C8—21no—
623C3⋊C8—21no—
624C2×C32—22no—
625C2×C32#54611yescharacteristic
626C2×C32C22×SD1611yescharacteristic
627C2×C32#57611yescharacteristic
628C3⋊D3—22no—
629C3×D3—42no—
630C3×D3—81no—
631C3×D3—81no—
632C24—61no—
633C24—181no—
634C2×Q8—91no—
635C2×Q8—181no—
636C2×D4—31no—
637C2×D4—31no—
638C2×D4—31no—
639C2×D4—62no—
640C2×D4—61no—
641C2×D4—61no—
642C2×D4—91no—
643C2×D4—121no—
644C2×D4—181no—
645C2×D4—181no—
646C2×D4—181no—
647C2×D4—181no—
648C2×D4—182no—
649C2×D4—361no—
650C2×D4—364no—
651C22×C4—21no—
652C22×C4—91no—
653C22×C4—181no—
654C22×C4—181no—
655C22×C4C2×D3211yescharacteristic
656SD16—182no—
657SD16—361no—
658SD16—361no—
659C2×C8—31no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—31no—
663C2×C8—121no—
664C2×C8—361no—
665C4⋊C4—21no—
666C4⋊C4—31no—
667C4⋊C4—91no—
668C4⋊C4—91no—
669C4⋊C4—181no—
670C4⋊C4—181no—
671C4⋊C4—181no—
672C4⋊C4—181no—
673C4⋊C4—181no—
674C4⋊C4C2×D3211yescharacteristic
675C4⋊C4C2×D3211yescharacteristic
676C22⋊C4—61no—
677C22⋊C4—91no—
678C22⋊C4—91no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C22⋊C4—181no—
683C42—91no—
684C42—181no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—22no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—62no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3—244no—
703C22×C3D3×SD1612yes—
704C22×C3D3×SD1612yes—
705C22×C3C2×D3×D411yescharacteristic
706C22×C3C2×D3×D411yescharacteristic
707C2×D3—22no—
708C2×D3—32no—
709C2×D3—32no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—41no—
718C2×D3—62no—
719C2×D3—61no—
720C2×D3—61no—
721C2×D3—61no—
722C2×D3—61no—
723C2×D3—84no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—244no—
727C2×D3—244no—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—41no—
733C3×C4—42no—
734C3×C4—42no—
735C3×C4—41no—
736C3×C4—41no—
737C3×C4—41no—
738C3×C4—41no—
739C3×C4—121no—
740C3×C4C2×#23511yescharacteristic
741C3×C4#100411yescharacteristic
742C3×C4D3×#4111yescharacteristic
743C3×C4#100911yescharacteristic
744Dic3—32no—
745Dic3—32no—
746Dic3—41no—
747Dic3—62no—
748Dic3—61no—
749Dic3—61no—
750Dic3—61no—
751Dic3—61no—
752Dic3—121no—
753Dic3—121no—
754Dic3—122no—
755Dic3—122no—
756Dic3—121no—
757Dic3—121no—
758Dic3—121no—
759Dic3—121no—
760C32#329511yescharacteristic, complemented, Sylow
761C23—61no—
762C23—61no—
763C23—61no—
764C23—91no—
765C23—122no—
766C23—122no—
767C23—241no—
768C23—362no—
769C23—362no—
770C23—721no—
771C23#381111yescharacteristic
772Q8—181no—
773Q8—181no—
774Q8—721no—
775D4—32no—
776D4—61no—
777D4—61no—
778D4—61no—
779D4—61no—
780D4—61no—
781D4—94no—
782D4—122no—
783D4—122no—
784D4—362no—
785D4—362no—
786D4—362no—
787D4—721no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—61no—
793C2×C4—81no—
794C2×C4—91no—
795C2×C4—91no—
796C2×C4—91no—
797C2×C4—181no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4—181no—
801C2×C4—362no—
802C2×C4—721no—
803C2×C4#381111yescharacteristic
804C2×C4C22×D3211yescharacteristic
805C8—61no—
806C8—61no—
807C8—61no—
808C8—61no—
809C2×C3—22no—
810C2×C3—22no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—42no—
815C2×C3—122no—
816C2×C3—241no—
817C2×C3—241no—
818C2×C3#549011yescharacteristic
819C2×C3#565411yescharacteristic
820C2×C3#575711yescharacteristic
821C2×C3C2×D3×SD1611yescharacteristic
822C2×C3C2×D3×SD1611yescharacteristic
823C2×C3#577411yescharacteristic
824D3—42no—
825D3—62no—
826D3—62no—
827D3—81no—
828D3—81no—
829D3—122no—
830C22—21no—
831C22—21no—
832C22—62no—
833C22—92no—
834C22—121no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—181no—
843C22—181no—
844C22—244no—
845C22—724no—
846C22#6394012yes—
847C22C2×#381111yescharacteristic
848C4—21no—
849C4—41no—
850C4—41no—
851C4—92no—
852C4—121no—
853C4—181no—
854C4—181no—
855C4—361no—
856C4—361no—
857C4D3×#23511yescharacteristic
858C4#6430711yescharacteristic
859C3—21no—
860C3#7875811yescharacteristic, complemented
861C3#8134211yescharacteristic, complemented
862C2—22no—
863C2—122no—
864C2—182no—
865C2—241no—
866C2—241no—
867C2#1059507711yescharacteristic
868C2#1059510211yescharacteristic
869C2C2×#6394011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radical#10595069C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595982C2semidirect
3. C3×#4968C2semidirect
4. C2×C3×#809C2semidirect
5. #10591175C2semidirect
6. #10591172C2semidirect
7. #10591148C2semidirect
8. #10590597C2semidirect
9. #10590593C2semidirect
10. #10590553C2semidirect
11. #10590552C2semidirect
12. #10590511C2semidirect
13. #10590507C2semidirect
14. #10590472C2semidirect
15. #10590460C2semidirect
21. C2×C32×C4⋊C4C22semidirect
25. #64133C22semidirect
26. #64106C22semidirect
28. C4⋊C4×C3⋊D3C22semidirect
30. #64097C22semidirect
31. #64096C22semidirect
33. C22×C3×C3⋊C8C22semidirect
41. C2×#3716C22semidirect
42. C2×#3716C22semidirect
43. C2×#3710C22semidirect
44. C3×#830C22semidirect
47. C3×#809C22semidirect
48. C3×#809C22semidirect
49. C3×#809C22semidirect
50. C3×#809C22semidirect
51. C3×#808C22semidirect
52. C3×#808C22semidirect
53. #63573C22semidirect
54. #63572C22semidirect
55. #63567C22semidirect
57. #63563C22semidirect
58. #63563C22semidirect
59. #63557C22semidirect
60. #63553C22semidirect
72. #4968D3semidirect
73. C2×#809D3semidirect
155. C2×C3×C4⋊C4C2×D3semidirect
156. C2×C3×C4⋊C4C2×D3semidirect
181. C22×C3⋊C8C2×D3semidirect
221. #830C2×D3semidirect
236. #809C2×D3semidirect
237. #809C2×D3semidirect
238. #809C2×D3semidirect
239. #809C2×D3semidirect
241. #808C2×D3semidirect
242. #808C2×D3semidirect
261. #638SD16semidirect
489. C2×C4⋊C4D32semidirect
760. C32#3295semidirect
860. C3#78758semidirect
861. C3#81342semidirect

Maximal subgroups

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

subgroupindex
#105959822
#105950692
C3×#49682
C2×C3×#8092
#105911752
#105911722
#105911482
#105905972
#105905932
#105905532
#105905522
#105905112
#105905072
#105904722
#105904602
#813423
#787583