Finite Group Databasebeta

← #11884035

Subgroups — #11884035

Order 1152.

1186 conjugacy classes of subgroups.

The subgroup lattice has 943 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595074C211yesmaximal, characteristic, complemented
2#10594899C211yesmaximal, characteristic, complemented
3C2×#63825C211yesmaximal, characteristic, complemented
4C2×D3×#204C211yesmaximal, characteristic, complemented
5#10592430C211yesmaximal, characteristic, complemented
6C3×#4734C211yesmaximal, characteristic, complemented
7C3×#4728C211yesmaximal, characteristic, complemented
8#10591176C211yesmaximal, characteristic, complemented
9#10590951C211yesmaximal, characteristic, complemented
10#10590944C211yesmaximal, characteristic, complemented
11#10590883C211yesmaximal, characteristic, complemented
12#10590860C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590799C211yesmaximal, characteristic, complemented
15#10590795C211yesmaximal, characteristic, complemented
16#80121—31nomaximal
17#79494—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic, complemented
20C2×#3811—21no—
21C2×D3×D12C2211yescharacteristic
22C2×D3×Dic6C2211yescharacteristic, complemented
23#64133C2211yescharacteristic, complemented
24C2×#3744C2211yescharacteristic
25C2×#3744C2211yescharacteristic, complemented
26C3×#930C2211yescharacteristic
27C3×C4×#67C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic, complemented
29C2×C3×D24C2211yescharacteristic, complemented
30C2×C3×#204C2211yescharacteristic, complemented
31C2×C3×D3×C8C2211yescharacteristic, complemented
32#63981—21no—
33#63970—21no—
34#63959—21no—
35#63923—21no—
36#63911C2211yescharacteristic
37#63910—21no—
38#63909C2211yescharacteristic
39#63908C2211yescharacteristic, complemented
40#63894C2211yescharacteristic
41#63879—21no—
42#63860C2211yescharacteristic, complemented
43#63851—21no—
44Dic3×Dic6C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic
46C2×#3717C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic, complemented
48#63825—24no—
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic, complemented
51D3×#204—24no—
52C32×C22⋊C8C2211yescharacteristic, complemented
53#63648C2211yescharacteristic
54#63648C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58C3×#815C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63#5831—31no—
64C2×#949—31no—
65C2×D3×SD16—31no—
66C2×#908—31no—
67C22×#204—31no—
68#5609—31no—
69#5552—31no—
70D4×D12—31no—
71C3×#449—31no—
72C3×#435—31no—
73#5163—31no—
74#5156—31no—
75#5154—31no—
76#5134—31no—
77#5115—31no—
78#5042—31no—
79#4848—31no—
80#4844—31no—
81#4817—31no—
82#4806—31no—
83#4787—31no—
84#4775—31no—
85#4738—31no—
86#4734D311yescharacteristic, complemented
87#4732—31no—
88#4731—31no—
89#4731—31no—
90#4731—61no—
91#4728D311yescharacteristic, complemented
92#4712—31no—
93#4710—31no—
94C23×C3⋊D3—21no—
95C22×D32—21no—
96C22×C32×C4C2311yescharacteristic
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)—41no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67D411yescharacteristic
106C3×#235—22no—
107C3×#235—41no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113#3811—44no—
114C2×#627—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#625—21no—
120C2×#624—21no—
121C2×D3×Dic3—21no—
122D3×D12—22no—
123D3×D12—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128#3757—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3750—21no—
131#3744—22no—
132#3744—41no—
133C3×#217D411yescharacteristic
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4D411yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C3×#208—22no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24—41no—
143C3×#204—22no—
144C3×D3×C8—22no—
145Dic3⋊Dic3—21no—
146#3722—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3717—22no—
153#3717D414yescomplemented
154#3716—22no—
155#3714—22no—
156#3714—22no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C2×D3×Q8—31no—
160C2×D3×D4—31no—
161C2×D3×D4—61no—
162C2×D3×D4—61no—
163C2×#235C2×D311yescharacteristic, complemented
164C22×D12—31no—
165C22×D12—31no—
166C22×D12—31no—
167C22×D12—61no—
168C22×Dic6—31no—
169C2×C3×SD16—31no—
170C2×C3×D8—31no—
171C2×C3×M16—31no—
172C22×C3×C8—31no—
173C3×#121—31no—
174C3×C4×D4—31no—
175#949—64no—
176Q8×Dic3—31no—
177C2×#215—31no—
178C2×#215—31no—
179#940—31no—
180#939—61no—
181#938—31no—
182#938—61no—
183#937—61no—
184#936—31no—
185#936—61no—
186C2×#214—31no—
187C2×#213—31no—
188C2×#213—31no—
189#930—31no—
190#930—31no—
191#930C2×D311yescharacteristic
192C4×#67—61no—
193C4×#67C2×D311yescharacteristic
194#924—31no—
195#924—31no—
196#924—61no—
197#924—61no—
198C2×#208C2×D311yescharacteristic, complemented
199D3×SD16—64no—
200#908—64no—
201C2×D24—31no—
202C2×D24—31no—
203C2×D24C2×D311yescharacteristic, complemented
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—31no—
209C2×#204—31no—
210C2×#204—31no—
211C2×#204—61no—
212C2×#204—61no—
213C2×#204—64no—
214C2×#204C2×D311yescharacteristic, complemented
215C2×D3×C8C2×D311yescharacteristic, complemented
216#896—61no—
217#895—31no—
218#895—61no—
219#893—31no—
220#885—61no—
221#884—61no—
222#882—61no—
223#882—61no—
224#882—61no—
225#67⋊C4—61no—
226#875—31no—
227#874—31no—
228C4×D12—31no—
229C4×Dic6—31no—
230C3×C4⋊C8—31no—
231C3×#103—31no—
232C3×#102—31no—
233C3×C22⋊C8—21no—
234C3×C22⋊C8—31no—
235C3×C22⋊C8C2×D311yescharacteristic, complemented
236C3×C22⋊C8C2×D311yescharacteristic, complemented
237C3×#97—31no—
238#832—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—31no—
243#821—31no—
244#821—61no—
245#821—61no—
246#821C2×D311yescharacteristic, complemented
247(C2×D3)⋊C8C2×D311yescharacteristic, complemented
248#818—31no—
249#816—31no—
250#816C2×D311yescharacteristic, complemented
251#815C2×D311yescharacteristic, complemented
252Dic3⋊C8C2×D311yescharacteristic, complemented
253#810—31no—
254#807—31no—
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3—42no—
260C22×C3⋊D3—81no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3C2×D411yescharacteristic
264C2×D32—42no—
265C2×D32—42no—
266C2×D32—81no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—42no—
277C4⋊(C3⋊D3)C2×D412yes—
278#634—21no—
279#634—21no—
280C3×#67—22no—
281C3×#67—42no—
282C3×#67—42no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—21no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—42no—
295C3×Dic6—21no—
296C3×Dic6C2×D412yescomplemented
297#627—42no—
298#626—42no—
299#626—42no—
300#626—42no—
301#626—81no—
302#625—42no—
303#624—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C32×C8—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
313#496—91no—
314#468—91no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—31no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—31no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C23×D3—121no—
329C3×#41—62no—
330C3×#41—121no—
331C2×C3×Q8—31no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C22×C3×C4—21no—
338C22×C3×C4—31no—
339C22×C3×C4—61no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67D1211yescharacteristic
351C22×Dic3—61no—
352D3×Q8—62no—
353D3×Q8—121no—
354D3×D4—62no—
355D3×D4—121no—
356D3×D4—124no—
357D3×D4—124no—
358#235—22no—
359#235—41no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—31no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—62no—
367C2×D12—62no—
368C2×D12—62no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—122no—
376C2×D12—121no—
377C2×D12—121no—
378C2×D12—121no—
379C2×D12—121no—
380C2×D12—122no—
381C2×D12C22×D311yescharacteristic
382C2×D12C22×D311yescharacteristic
383C2×C4×D3—21no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3C22×D311yescharacteristic
388C2×Dic6—31no—
389C2×Dic6—31no—
390C2×Dic6—61no—
391C2×Dic6—62no—
392C2×Dic6—61no—
393C2×Dic6—61no—
394C2×Dic6—121no—
395C2×Dic6C22×D311yescharacteristic
396C3×SD16—62no—
397C3×D8—121no—
398C3×M16—62no—
399C2×C3×C8—21no—
400C2×C3×C8—21no—
401C2×C3×C8—31no—
402C2×C3×C8—31no—
403C2×C3×C8—62no—
404C2×C3×C8C22×D311yescharacteristic
405C2×C3×C8C22×D311yescharacteristic
406C2×C3×C8C22×D311yescharacteristic
407C2×C3×C8C22×D311yescharacteristic
408C3×C4⋊C4—31no—
409C3×C4⋊C4—31no—
410C3×C22⋊C4—31no—
411C3×C22⋊C4—31no—
412C3×C22⋊C4—61no—
413C3×C42—31no—
414#217—61no—
415#217—61no—
416#217—61no—
417#217—61no—
418#217—61no—
419#217—121no—
420#217D1211yescharacteristic
421#215—34no—
422#215—62no—
423#214—62no—
424#213—62no—
425#213—62no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4D1211yescharacteristic
435C4⋊Dic3—31no—
436C4⋊Dic3—31no—
437C4⋊Dic3—61no—
438C4⋊Dic3—61no—
439C4⋊Dic3C22×D311yescharacteristic
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443Dic3⋊C4—121no—
444Dic3⋊C4D1211yescharacteristic
445C4×Dic3—61no—
446C4×Dic3—61no—
447C4×Dic3C22×D311yescharacteristic
448#208—22no—
449C2×C3⋊C8C22×D311yescharacteristic
450C2×C3⋊C8C22×D311yescharacteristic
451D24—41no—
452D24—62no—
453D24—62no—
454#204—22no—
455#204—34no—
456#204—62no—
457#204—62no—
458#204—62no—
459#204—62no—
460#204—122no—
461#204—121no—
462#204—121no—
463#204—122no—
464D3×C8—22no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—21no—
468C22×C32C22×D411yescharacteristic
469C2×C3⋊D3—22no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—84no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3AGL(1,ℤ/8)12yescomplemented
485D32—84no—
486C32×C4—21no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—41no—
490C3⋊Dic3—41no—
491C3×Dic3—22no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—41no—
496C2×#41—31no—
497C22×Q8—91no—
498C22×D4—91no—
499C22×D4—91no—
500C22×D4—181no—
501AGL(1,ℤ/8)—184no—
502C2×SD16—31no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—184no—
509C2×D8—31no—
510C2×D8—91no—
511C2×D8—91no—
512C2×M16—31no—
513C22×C8—31no—
514#127—91no—
515#124—91no—
516#124—181no—
517C22⋊Q8—91no—
518C22⋊Q8—181no—
519#121—31no—
520#121—91no—
521#121—91no—
522#121—181no—
523#121—181no—
524#120—181no—
525#120—181no—
526C4×Q8—91no—
527C4×D4—31no—
528C4×D4—91no—
529C4×D4—181no—
530#107—91no—
531C4⋊C8—31no—
532#103—31no—
533#103—91no—
534#102—31no—
535#102—91no—
536#102—91no—
537#102—91no—
538C22⋊C8—31no—
539C22⋊C8D3211yescharacteristic, complemented
540#97—31no—
541C23×C3—21no—
542C23×C3—31no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3C2×D1211yescharacteristic
546C23×C3D3×D411yescharacteristic
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—121no—
554C22×D3—121no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—124no—
563C22×D3—122no—
564C22×D3—242no—
565C22×D3—241no—
566C22×D3—241no—
567C22×D3—241no—
568C22×D3—241no—
569C22×D3—242no—
570C22×D3C2×D1211yescharacteristic
571C3×Q8—32no—
572C3×Q8—61no—
573C3×D4—62no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—61no—
577C3×D4—61no—
578C3×D4—122no—
579C3×D4—122no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—31no—
587C2×C3×C4—31no—
588C2×C3×C4—31no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—122no—
596C2×C3×C4C2×D1211yescharacteristic
597C2×C3×C4D3×D411yescharacteristic
598C2×C3×C4C23×D311yescharacteristic
599C2×C3×C4C23×D311yescharacteristic
600#67—22no—
601#67—42no—
602#67—42no—
603#67—122no—
604#67—122no—
605#67—122no—
606#67—122no—
607#67—122no—
608#67—241no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—121no—
616C2×Dic3—121no—
617C2×Dic3—122no—
618C2×Dic3C2×D1211yescharacteristic
619C2×Dic3C2×D1211yescharacteristic
620C2×Dic3C2×D1211yescharacteristic
621D12—21no—
622D12—21no—
623D12—21no—
624D12—21no—
625D12—32no—
626D12—32no—
627D12—62no—
628D12—62no—
629D12—61no—
630D12—61no—
631D12—61no—
632D12—61no—
633D12—61no—
634D12—61no—
635D12—121no—
636D12—121no—
637D12—122no—
638D12—122no—
639D12—124no—
640D12—122no—
641D12—122no—
642D12—122no—
643D12—241no—
644C4×D3—21no—
645C4×D3—21no—
646C4×D3—42no—
647C4×D3—122no—
648C4×D3—122no—
649C4×D3—122no—
650Dic6—21no—
651Dic6—61no—
652Dic6—61no—
653Dic6—61no—
654Dic6—61no—
655Dic6—121no—
656Dic6—121no—
657Dic6—122no—
658Dic6—122no—
659Dic6D3×D412yescomplemented
660C3×C8—21no—
661C3×C8—21no—
662C3×C8—21no—
663C3×C8—21no—
664C3×C8—32no—
665C3×C8—41no—
666C3×C8—41no—
667C3×C8—61no—
668C3⋊C8—21no—
669C3⋊C8D3×D412yescomplemented
670C2×C32—41no—
671C2×C32D4211yescharacteristic
672C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
673C2×C32#57711yescharacteristic
674C3⋊D3—42no—
675C3⋊D3—81no—
676C3×D3—22no—
677C3×D3—81no—
678C3×D3—81no—
679C24—181no—
680C24—181no—
681#41—62no—
682#41—121no—
683C2×Q8—31no—
684C2×Q8—91no—
685C2×Q8—181no—
686C2×Q8—182no—
687C2×Q8—361no—
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—31no—
691C2×D4—61no—
692C2×D4—61no—
693C2×D4—91no—
694C2×D4—91no—
695C2×D4—182no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—182no—
700C2×D4—181no—
701C2×D4—181no—
702C2×D4—181no—
703C2×D4—361no—
704C2×D4—361no—
705C2×D4—364no—
706C22×C4—31no—
707C22×C4—61no—
708C22×C4—181no—
709C22×C4—181no—
710C22×C4C2×D3211yescharacteristic
711SD16—62no—
712SD16—94no—
713SD16—182no—
714SD16—182no—
715SD16—182no—
716SD16—361no—
717D8—121no—
718D8—182no—
719D8—182no—
720M16—62no—
721C2×C8—31no—
722C2×C8—31no—
723C2×C8—62no—
724C2×C8C2×D3211yescharacteristic
725C2×C8C2×D3211yescharacteristic
726C4⋊C4—31no—
727C4⋊C4—31no—
728C4⋊C4—91no—
729C4⋊C4—181no—
730C4⋊C4—181no—
731C22⋊C4—31no—
732C22⋊C4—31no—
733C22⋊C4—61no—
734C22⋊C4—181no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C22⋊C4—181no—
740C42—31no—
741C42—181no—
742C22×C3—22no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—32no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—61no—
754C22×C3—61no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3C22×D1211yescharacteristic
762C22×C3C2×D3×D411yescharacteristic
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—62no—
772C2×D3—62no—
773C2×D3—122no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—122no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—241no—
786C2×D3—241no—
787C2×D3—241no—
788C2×D3—241no—
789C2×D3—244no—
790C2×D3—244no—
791C2×D3—244no—
792C2×D3—244no—
793C2×D3—248no—
794C2×D3#90812yescomplemented
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—41no—
800C3×C4—61no—
801C3×C4—61no—
802C3×C4—62no—
803C3×C4—61no—
804C3×C4—121no—
805C3×C4C2×D3×D411yescharacteristic
806C3×C4C2×D3×D411yescharacteristic
807C3×C4#100411yescharacteristic
808C3×C4#100911yescharacteristic
809Dic3—21no—
810Dic3—21no—
811Dic3—21no—
812Dic3—22no—
813Dic3—41no—
814Dic3—121no—
815Dic3—121no—
816Dic3—121no—
817Dic3—121no—
818Dic3—241no—
819Dic3—241no—
820C32#326511yescharacteristic, complemented, Sylow
821C23—31no—
822C23—61no—
823C23—61no—
824C23—181no—
825C23—181no—
826C23—362no—
827C23—362no—
828C23—362no—
829C23—362no—
830C23—721no—
831C23—721no—
832C23D3×D1211yescharacteristic
833Q8—32no—
834Q8—61no—
835Q8—181no—
836Q8—181no—
837Q8—362no—
838D4—62no—
839D4—61no—
840D4—61no—
841D4—61no—
842D4—61no—
843D4—92no—
844D4—122no—
845D4—122no—
846D4—181no—
847D4—181no—
848D4—181no—
849D4—362no—
850D4—362no—
851D4—362no—
852D4—362no—
853D4—362no—
854D4—721no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—31no—
858C2×C4—31no—
859C2×C4—31no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—122no—
865C2×C4—181no—
866C2×C4—181no—
867C2×C4—362no—
868C2×C4—362no—
869C2×C4D3×D1211yescharacteristic
870C2×C4C22×D3211yescharacteristic
871C8—21no—
872C8—21no—
873C8—32no—
874C8—61no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—42no—
879C2×C3—41no—
880C2×C3—41no—
881C2×C3—62no—
882C2×C3—241no—
883C2×C3—241no—
884C2×C3D4×D1211yescharacteristic
885C2×C3#559011yescharacteristic
886C2×C3C2×#90811yescharacteristic
887C2×C3#575111yescharacteristic
888C2×C3#577011yescharacteristic
889C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
890D3—22no—
891D3—81no—
892D3—81no—
893D3—122no—
894D3—122no—
895D3—242no—
896D3—242no—
897D3—241no—
898D3—241no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—32no—
903C22—61no—
904C22—61no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—182no—
912C22—361no—
913C22—361no—
914C22—361no—
915C22—361no—
916C22—361no—
917C22—724no—
918C22—724no—
919C22C2×D3×D1211yescharacteristic
920C4—21no—
921C4—61no—
922C4—61no—
923C4—61no—
924C4—62no—
925C4—121no—
926C4—361no—
927C4—361no—
928C4D32×D411yescharacteristic
929C4#6431411yescharacteristic
930C3—21no—
931C3#7949411yescharacteristic, complemented
932C3#8012111yescharacteristic, complemented
933C2—41no—
934C2—62no—
935C2—241no—
936C2—241no—
937C2—362no—
938C2—721no—
939C2#1059427711yescharacteristic
940C2#1059467911yescharacteristic
941C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3265
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. #10594899C2semidirect
3. C2×#63825C2semidirect
4. C2×D3×#204C2semidirect
5. #10592430C2semidirect
6. C3×#4734C2semidirect
7. C3×#4728C2semidirect
8. #10591176C2semidirect
9. #10590951C2semidirect
10. #10590944C2semidirect
11. #10590883C2semidirect
12. #10590860C2semidirect
13. #10590826C2semidirect
14. #10590799C2semidirect
15. #10590795C2semidirect
19. C2×C3×#235C22semidirect
22. C2×D3×Dic6C22semidirect
23. #64133C22semidirect
25. C2×#3744C22semidirect
28. C2×C3×#208C22semidirect
29. C2×C3×D24C22semidirect
30. C2×C3×#204C22semidirect
31. C2×C3×D3×C8C22semidirect
39. #63908C22semidirect
42. #63860C22semidirect
44. Dic3×Dic6C22semidirect
46. C2×#3717C22semidirect
47. C2×#3716C22semidirect
50. C2×#3714C22semidirect
52. C32×C22⋊C8C22semidirect
54. #63648C22semidirect
55. C3×#821C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#816C22semidirect
58. C3×#815C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. #63575C22semidirect
61. #63567C22semidirect
62. #63563C22semidirect
86. #4734D3semidirect
91. #4728D3semidirect
153. #3717D4semidirect
163. C2×#235C2×D3semidirect
198. C2×#208C2×D3semidirect
203. C2×D24C2×D3semidirect
214. C2×#204C2×D3semidirect
215. C2×D3×C8C2×D3semidirect
235. C3×C22⋊C8C2×D3semidirect
236. C3×C22⋊C8C2×D3semidirect
246. #821C2×D3semidirect
247. (C2×D3)⋊C8C2×D3semidirect
250. #816C2×D3semidirect
251. #815C2×D3semidirect
252. Dic3⋊C8C2×D3semidirect
296. C3×Dic6C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
484. C2×C3×D3AGL(1,ℤ/8)semidirect
539. C22⋊C8D32semidirect
659. Dic6D3×D4semidirect
669. C3⋊C8D3×D4semidirect
794. C2×D3#908semidirect
820. C32#3265semidirect
931. C3#79494semidirect
932. C3#80121semidirect

Maximal subgroups

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

subgroupindex
#105950742
#105948992
C2×#638252
C2×D3×#2042
#105924302
C3×#47342
C3×#47282
#105911762
#105909512
#105909442
#105908832
#105908602
#105908262
#105907992
#105907952
#801213
#794943