Finite Group Databasebeta

← #11883987

Subgroups — #11883987

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#10595401C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic, complemented
3#10595297C211yesmaximal, characteristic, complemented
4C2×#63937C211yesmaximal, characteristic, complemented
5#10592868C211yesmaximal, characteristic, complemented
6C3×#5176C211yesmaximal, characteristic, complemented
7C3×#5170C211yesmaximal, characteristic, complemented
8#10591590C211yesmaximal, characteristic, complemented
9#10591568C211yesmaximal, characteristic, complemented
10#10591498C211yesmaximal, characteristic, complemented
11#10591438C211yesmaximal, characteristic, complemented
12#10590963C211yesmaximal, characteristic, complemented
13#10590944C211yesmaximal, characteristic, complemented
14#10590795C211yesmaximal, characteristic, complemented
15#10590728C211yesmaximal, characteristic, complemented
16#81857—31nomaximal
17#80060—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×#3811—21no—
21C2×D3×D12C2211yescharacteristic
22C2×#3796C2211yescharacteristic, complemented
23C2×C32×SD16C2211yescharacteristic, complemented
24#64155C2211yescharacteristic, complemented
25C2×#3755C2211yescharacteristic
26C3×#947C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C3×#940C2211yescharacteristic
29C3×#938C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic, complemented
31C2×C3×#213C2211yescharacteristic, complemented
32C2×C3×D24C2211yescharacteristic, complemented
33#63983—21no—
34#63981—21no—
35#63958—21no—
36D3×#215—24no—
37#63937—24no—
38#63916C2211yescharacteristic
39#63908C2211yescharacteristic, complemented
40#63907—21no—
41#63906—21no—
42C4×#626C2211yescharacteristic
43#63894C2211yescharacteristic
44#63887—21no—
45#63879—21no—
46Dic3×Dic6C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3712C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63648C2211yescharacteristic
54#63647C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58C3×#815C2211yescharacteristic, complemented
59#63575C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#5817—31no—
64C22×#215—31no—
65C2×#914—31no—
66C2×D3×SD16—31no—
67C2×#911—31no—
68#5717—31no—
69#5677—31no—
70#5609—31no—
71C3×#496—31no—
72C3×#448—31no—
73#5176D311yescharacteristic, complemented
74#5174—31no—
75#5170D311yescharacteristic, complemented
76#5169—31no—
77#5169—31no—
78#5169—61no—
79#5163—31no—
80#5158—31no—
81#5157—31no—
82#5156—31no—
83#5075—31no—
84#5057—31no—
85#5038—31no—
86#4819—31no—
87#4817—31no—
88#4812—31no—
89#4810—31no—
90#4732—31no—
91#4730—31no—
92#4710—31no—
93#4706—31no—
94C23×C3⋊D3—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99D4×C3⋊D3—22no—
100D4×C3⋊D3—41no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C3×D3×Q8—22no—
107C3×D3×Q8—41no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6—21no—
113C2×C3×Dic6C2311yescharacteristic
114#3811—44no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626D411yescharacteristic
119C2×#625—21no—
120C2×#624—21no—
121C2×D3×Dic3—21no—
122D3×D12—22no—
123D3×D12—41no—
124#3796—22no—
125#3796—41no—
126C32×SD16—41no—
127C2×C32×C8C2311yescharacteristic
128#3755—22no—
129#3752—21no—
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131#3750—21no—
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C3×#217—21no—
134C3×#215—22no—
135C3×#214—22no—
136C3×#213—22no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3C2311yescharacteristic
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D24—41no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3D411yescharacteristic
146#3722—21no—
147#3722D411yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151Dic32—21no—
152#3717D414yescomplemented
153#3715—22no—
154#3714—22no—
155#3712—22no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C22×C3×Q8—31no—
159C2×#239—31no—
160C2×D3×Q8C2×D311yescharacteristic, complemented
161C2×#237—31no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—61no—
166C2×D3×D4—61no—
167C2×D3×D4—61no—
168C22×D12—31no—
169C2×C3×SD16—21no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16C2×D311yescharacteristic, complemented
173C2×C3×SD16C2×D311yescharacteristic, complemented
174C2×C3×D8—31no—
175C2×C3×D8—31no—
176C3×#127—31no—
177C3×#124—31no—
178C3×#121—31no—
179#947—61no—
180#947C2×D311yescharacteristic, complemented
181#946—31no—
182#946—31no—
183#946—61no—
184#946—61no—
185Q8×Dic3—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—61no—
191C2×#215—64no—
192C2×#215C2×D311yescharacteristic, complemented
193#940C2×D311yescharacteristic
194#938—31no—
195#938—31no—
196#938—61no—
197#938C2×D311yescharacteristic
198#937—61no—
199#937—61no—
200#937—61no—
201C2×#214—31no—
202C2×#214C2×D311yescharacteristic, complemented
203C2×#213—31no—
204C2×#213C2×D311yescharacteristic, complemented
205#930—31no—
206#930—61no—
207C4×#67—31no—
208C4×#67—61no—
209C22×C3⋊C8—31no—
210#914—64no—
211D3×SD16—64no—
212#911—64no—
213C2×D24—31no—
214C2×D24C2×D311yescharacteristic, complemented
215C2×#204—31no—
216C2×ΓL(1,𝔽25)—31no—
217C2×ΓL(1,𝔽25)—31no—
218C2×D3×C8—31no—
219#895—31no—
220#893—31no—
221#885—61no—
222#884—61no—
223#884—61no—
224#882—61no—
225#67⋊C4—61no—
226#878—61no—
227C4×D12—31no—
228C4×D12—31no—
229C4×Dic6—31no—
230C3×#103—31no—
231C3×#103—31no—
232C3×C22⋊C8—31no—
233C3×#97—31no—
234#835C2×D311yescharacteristic, complemented
235#832—31no—
236#832—31no—
237#832—31no—
238#832—31no—
239#832—61no—
240#821—31no—
241#821—31no—
242#821—31no—
243#821—61no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—61no—
247(C2×D3)⋊C8C2×D311yescharacteristic, complemented
248#818—31no—
249#816C2×D311yescharacteristic, complemented
250#815C2×D311yescharacteristic, complemented
251Dic3⋊C8—31no—
252#809—31no—
253#807—31no—
254C4⋊(C3⋊C8)—31no—
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—42no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3—81no—
260C22×C3⋊D3C2×D411yescharacteristic
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3C2×D411yescharacteristic
264C2×D32—42no—
265C2×D32—42no—
266C2×D32—81no—
267C32×Q8—21no—
268C32×Q8—21no—
269C32×D4—21no—
270C32×D4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C2411yescharacteristic
273#638—42no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3C2×D411yescharacteristic
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)C2×D412yes—
278C4×C3⋊D3—21no—
279C4×C3⋊D3—21no—
280C3×#67—42no—
281C3×#67—42no—
282C3×#67—81no—
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×Dic6—42no—
297C3×Dic6C2×D412yescomplemented
298#626—22no—
299#626—42no—
300#626—42no—
301#626—42no—
302#625—42no—
303#624—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C3⋊(C3⋊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—31no—
314#468—91no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—31no—
321#447—91no—
322#440—91no—
323#435—91no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C23×D3—121no—
329C2×C3×Q8—21no—
330C2×C3×Q8—31no—
331C2×C3×Q8—61no—
332C2×C3×Q8—62no—
333C2×C3×Q8—121no—
334C2×C3×Q8C22×D311yescharacteristic
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×D4—21no—
337C2×C3×D4—31no—
338C2×C3×D4—31no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4C22×D311yescharacteristic
343C2×C3×D4C22×D311yescharacteristic
344C22×C3×C4—31no—
345C22×C3×C4—61no—
346C2×#67—21no—
347C2×#67—21no—
348C2×#67—21no—
349C2×#67—31no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—121no—
358C22×Dic3—61no—
359#239—62no—
360#239—121no—
361D3×Q8—22no—
362D3×Q8—41no—
363#237—62no—
364#237—121no—
365D3×D4—62no—
366D3×D4—62no—
367D3×D4—62no—
368D3×D4—122no—
369D3×D4—121no—
370D3×D4—121no—
371D3×D4—121no—
372D3×D4—124no—
373D3×D4—124no—
374D3×D4—122no—
375C2×D12—31no—
376C2×D12—31no—
377C2×D12—31no—
378C2×D12—61no—
379C2×D12—62no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12—121no—
384C2×D12C22×D311yescharacteristic
385C2×D12C22×D311yescharacteristic
386C2×C4×D3—21no—
387C2×C4×D3—31no—
388C2×C4×D3—31no—
389C2×C4×D3—61no—
390C2×C4×D3—61no—
391C2×C4×D3—61no—
392C2×C4×D3—61no—
393C2×C4×D3C22×D311yescharacteristic
394C2×Dic6—21no—
395C2×Dic6C22×D311yescharacteristic
396C3×SD16—41no—
397C3×SD16—41no—
398C3×SD16—42no—
399C3×SD16—62no—
400C3×SD16—62no—
401C3×D8—62no—
402C3×D8—121no—
403C2×C3×C8—21no—
404C2×C3×C8—31no—
405C2×C3×C8—31no—
406C2×C3×C8C22×D311yescharacteristic
407C2×C3×C8C22×D311yescharacteristic
408C3×C4⋊C4—31no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C42—31no—
413#217—21no—
414#217—31no—
415#217—61no—
416#217—61no—
417#215—22no—
418#215—34no—
419#215—62no—
420#215—62no—
421#215—62no—
422#215—122no—
423#214—22no—
424#214—62no—
425#213—22no—
426#213—62no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—31no—
431(C2×D3)⋊C4—31no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—121no—
439C4⋊Dic3—31no—
440C4⋊Dic3—31no—
441C4⋊Dic3—31no—
442C4⋊Dic3—61no—
443C4⋊Dic3—61no—
444C4⋊Dic3C22×D311yescharacteristic
445Dic3⋊C4—31no—
446Dic3⋊C4—61no—
447Dic3⋊C4—61no—
448Dic3⋊C4—61no—
449Dic3⋊C4—121no—
450C4×Dic3—61no—
451C4×Dic3—61no—
452C4×Dic3C22×D311yescharacteristic
453C2×C3⋊C8—31no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—61no—
456C2×C3⋊C8—62no—
457C2×C3⋊C8C22×D311yescharacteristic
458C2×C3⋊C8C22×D311yescharacteristic
459D24—41no—
460D24—62no—
461#204—34no—
462ΓL(1,𝔽25)—62no—
463ΓL(1,𝔽25)—62no—
464D3×C8—62no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32C22×D411yescharacteristic
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—22no—
472C2×C3⋊D3—21no—
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—41no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—21no—
490C3⋊Dic3—41no—
491C3×Dic3—22no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—41no—
496C2×#41—91no—
497C22×Q8—31no—
498C22×D4—91no—
499C22×D4—91no—
500C22×D4—181no—
501AGL(1,ℤ/8)—184no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×SD16—184no—
508C2×SD16D3211yescharacteristic, complemented
509C2×D8—31no—
510C2×D8—31no—
511C2×D8—91no—
512C2×M16—91no—
513C22×C8—91no—
514#127—31no—
515#124—31no—
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—91no—
528C4×D4—91no—
529C4×D4—181no—
530#107—91no—
531C4⋊C8—91no—
532#103—31no—
533#103—31no—
534#102—91no—
535#102—91no—
536#102—91no—
537#102—91no—
538C22⋊C8—31no—
539C22⋊C8—91no—
540#97—31no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—31no—
544C23×C3—41no—
545C23×C3—61no—
546C23×C3—61no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—31no—
550C22×D3—31no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—61no—
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×D3D3×D411yescharacteristic
571C3×Q8—21no—
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—21no—
575C3×Q8—32no—
576C3×Q8—41no—
577C3×Q8—41no—
578C3×Q8—61no—
579C3×Q8—122no—
580C3×D4—22no—
581C3×D4—21no—
582C3×D4—21no—
583C3×D4—21no—
584C3×D4—21no—
585C3×D4—41no—
586C3×D4—61no—
587C3×D4—61no—
588C3×D4—61no—
589C3×D4—61no—
590C3×D4—122no—
591C3×D4—122no—
592C3×D4—241no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—31no—
597C2×C3×C4—31no—
598C2×C3×C4—31no—
599C2×C3×C4—41no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—122no—
605C2×C3×C4C23×D311yescharacteristic
606C2×C3×C4C23×D311yescharacteristic
607#67—42no—
608#67—42no—
609#67—62no—
610#67—81no—
611#67—122no—
612#67—122no—
613#67—122no—
614#67—122no—
615#67—122no—
616#67—122no—
617#67—124no—
618#67—122no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—31no—
622C2×Dic3—31no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—121no—
627C2×Dic3—122no—
628C2×Dic3D3×D411yescharacteristic
629C2×Dic3D3×D411yescharacteristic
630C2×Dic3D3×D411yescharacteristic
631D12—21no—
632D12—21no—
633D12—21no—
634D12—21no—
635D12—32no—
636D12—32no—
637D12—62no—
638D12—62no—
639D12—61no—
640D12—61no—
641D12—121no—
642D12—122no—
643D12—122no—
644D12—122no—
645C4×D3—21no—
646C4×D3—21no—
647C4×D3—42no—
648C4×D3—61no—
649C4×D3—61no—
650C4×D3—61no—
651C4×D3—61no—
652C4×D3—121no—
653C4×D3—121no—
654C4×D3—122no—
655C4×D3—122no—
656C4×D3—122no—
657Dic6—21no—
658Dic6—42no—
659Dic6D3×D412yescomplemented
660C3×C8—21no—
661C3×C8—21no—
662C3×C8—32no—
663C3×C8—41no—
664C3×C8—61no—
665C3⋊C8—21no—
666C3⋊C8—61no—
667C3⋊C8—61no—
668C3⋊C8—121no—
669C3⋊C8D3×D412yescomplemented
670C2×C32—81no—
671C2×C32D4211yescharacteristic
672C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
673C2×C32#57711yescharacteristic
674C3⋊D3—41no—
675C3⋊D3—42no—
676C3×D3—22no—
677C3×D3—81no—
678C3×D3—81no—
679C24—181no—
680C24—181no—
681#41—182no—
682#41—361no—
683C2×Q8—31no—
684C2×Q8—61no—
685C2×Q8—62no—
686C2×Q8—121no—
687C2×Q8C2×D3211yescharacteristic
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—61no—
691C2×D4—61no—
692C2×D4—61no—
693C2×D4—91no—
694C2×D4—91no—
695C2×D4—181no—
696C2×D4—182no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—182no—
701C2×D4—181no—
702C2×D4—361no—
703C2×D4—361no—
704C2×D4—364no—
705C2×D4C2×D3211yescharacteristic
706C22×C4—31no—
707C22×C4—61no—
708C22×C4—91no—
709C22×C4—181no—
710C22×C4—181no—
711SD16—41no—
712SD16—62no—
713SD16—62no—
714SD16—94no—
715SD16—182no—
716SD16—182no—
717D8—62no—
718D8—121no—
719D8—182no—
720M16—182no—
721C2×C8—31no—
722C2×C8—31no—
723C2×C8—91no—
724C2×C8—182no—
725C2×C8C2×D3211yescharacteristic
726C4⋊C4—31no—
727C4⋊C4—91no—
728C4⋊C4—91no—
729C4⋊C4—181no—
730C4⋊C4—181no—
731C22⋊C4—61no—
732C22⋊C4—61no—
733C22⋊C4—61no—
734C22⋊C4—91no—
735C22⋊C4—91no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C22⋊C4—181no—
740C42—31no—
741C42—181no—
742C22×C3—21no—
743C22×C3—32no—
744C22×C3—42no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—61no—
752C22×C3—61no—
753C22×C3—81no—
754C22×C3—81no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3C2×D3×D411yescharacteristic
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—61no—
773C2×D3—62no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—61no—
778C2×D3—61no—
779C2×D3—62no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—122no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—241no—
788C2×D3—241no—
789C2×D3—244no—
790C2×D3—244no—
791C2×D3—244no—
792C2×D3—244no—
793C2×D3—248no—
794C2×D3#91412yescomplemented
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—62no—
800C3×C4—61no—
801C3×C4—61no—
802C3×C4—61no—
803C3×C4—81no—
804C3×C4—121no—
805C3×C4C2×D3×D411yescharacteristic
806C3×C4C2×D3×D411yescharacteristic
807C3×C4#100411yescharacteristic
808C3×C4#100411yescharacteristic
809Dic3—21no—
810Dic3—21no—
811Dic3—22no—
812Dic3—21no—
813Dic3—41no—
814Dic3—61no—
815Dic3—61no—
816Dic3—121no—
817Dic3—121no—
818Dic3—121no—
819Dic3—241no—
820C32#326511yescharacteristic, complemented, Sylow
821C23—21no—
822C23—31no—
823C23—61no—
824C23—61no—
825C23—91no—
826C23—181no—
827C23—362no—
828C23—362no—
829C23—362no—
830C23—362no—
831C23—721no—
832C23—721no—
833Q8—21no—
834Q8—21no—
835Q8—32no—
836Q8—61no—
837Q8—122no—
838D4—21no—
839D4—21no—
840D4—61no—
841D4—61no—
842D4—61no—
843D4—61no—
844D4—92no—
845D4—122no—
846D4—122no—
847D4—182no—
848D4—181no—
849D4—241no—
850D4—362no—
851D4—362no—
852D4—362no—
853D4—362no—
854D4—362no—
855C2×C4—21no—
856C2×C4—31no—
857C2×C4—31no—
858C2×C4—31no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—91no—
864C2×C4—122no—
865C2×C4—181no—
866C2×C4—181no—
867C2×C4—181no—
868C2×C4—362no—
869C2×C4—362no—
870C2×C4C22×D3211yescharacteristic
871C8—21no—
872C8—32no—
873C8—61no—
874C8—181no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—62no—
879C2×C3—82no—
880C2×C3—81no—
881C2×C3—81no—
882C2×C3—241no—
883C2×C3—241no—
884C2×C3#559011yescharacteristic
885C2×C3#571711yescharacteristic
886C2×C3C2×#91411yescharacteristic
887C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
888C2×C3#577511yescharacteristic
889C2×C3#577811yescharacteristic
890D3—22no—
891D3—81no—
892D3—81no—
893D3—122no—
894D3—121no—
895D3—122no—
896D3—121no—
897D3—122no—
898D3—242no—
899C22—32no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—61no—
904C22—61no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—181no—
912C22—181no—
913C22—181no—
914C22—182no—
915C22—361no—
916C22—361no—
917C22—724no—
918C22—724no—
919C22D32×D411yescharacteristic
920C4—41no—
921C4—61no—
922C4—61no—
923C4—61no—
924C4—62no—
925C4—121no—
926C4—181no—
927C4—361no—
928C4D32×D411yescharacteristic
929C4#6433011yescharacteristic
930C3—21no—
931C3#8006011yescharacteristic, complemented
932C3#8185711yescharacteristic, complemented
933C2—62no—
934C2—81no—
935C2—241no—
936C2—241no—
937C2—361no—
938C2—362no—
939C2D3×#91411yescharacteristic
940C2#1059475411yescharacteristic
941C2#1059529511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10595401C2semidirect
2. C2×D3×#215C2semidirect
3. #10595297C2semidirect
4. C2×#63937C2semidirect
5. #10592868C2semidirect
6. C3×#5176C2semidirect
7. C3×#5170C2semidirect
8. #10591590C2semidirect
9. #10591568C2semidirect
10. #10591498C2semidirect
11. #10591438C2semidirect
12. #10590963C2semidirect
13. #10590944C2semidirect
14. #10590795C2semidirect
15. #10590728C2semidirect
19. C2×C3×D3×Q8C22semidirect
22. C2×#3796C22semidirect
23. C2×C32×SD16C22semidirect
24. #64155C22semidirect
26. C3×#947C22semidirect
27. C2×C3×#215C22semidirect
30. C2×C3×#214C22semidirect
31. C2×C3×#213C22semidirect
32. C2×C3×D24C22semidirect
39. #63908C22semidirect
46. Dic3×Dic6C22semidirect
48. C2×#3715C22semidirect
50. C2×#3712C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63659C22semidirect
54. #63647C22semidirect
55. C3×#835C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#816C22semidirect
58. C3×#815C22semidirect
59. #63575C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
73. #5176D3semidirect
75. #5170D3semidirect
152. #3717D4semidirect
160. C2×D3×Q8C2×D3semidirect
172. C2×C3×SD16C2×D3semidirect
173. C2×C3×SD16C2×D3semidirect
180. #947C2×D3semidirect
192. C2×#215C2×D3semidirect
202. C2×#214C2×D3semidirect
204. C2×#213C2×D3semidirect
214. C2×D24C2×D3semidirect
234. #835C2×D3semidirect
247. (C2×D3)⋊C8C2×D3semidirect
249. #816C2×D3semidirect
250. #815C2×D3semidirect
297. C3×Dic6C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
484. C2×C3×D3AGL(1,ℤ/8)semidirect
508. C2×SD16D32semidirect
659. Dic6D3×D4semidirect
669. C3⋊C8D3×D4semidirect
794. C2×D3#914semidirect
820. C32#3265semidirect
931. C3#80060semidirect
932. C3#81857semidirect

Maximal subgroups

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

subgroupindex
#105954012
C2×D3×#2152
#105952972
C2×#639372
#105928682
C3×#51762
C3×#51702
#105915902
#105915682
#105914982
#105914382
#105909632
#105909442
#105907952
#105907282
#818573
#800603