Finite Group Databasebeta

← #11883991

Subgroups — #11883991

Order 1152.

1152 conjugacy classes of subgroups.

The subgroup lattice has 932 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
3C2×#63798C211yesmaximal, characteristic, complemented
4#10594621C211yesmaximal, characteristic, complemented
5#10592511C211yesmaximal, characteristic, complemented
6C3×#4819C211yesmaximal, characteristic, complemented
7C3×#4806C211yesmaximal, characteristic, complemented
8#10591652C211yesmaximal, characteristic, complemented
9#10591619C211yesmaximal, characteristic, complemented
10#10590944C211yesmaximal, characteristic, complemented
11#10590907C211yesmaximal, characteristic, complemented
12#10590799C211yesmaximal, characteristic, complemented
13#10590617C211yesmaximal, characteristic, complemented
14#10590499C211yesmaximal, characteristic, complemented
15#10590478C211yesmaximal, characteristic, complemented
16#80553—31nomaximal
17#80060—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic, complemented
19C2×#3802C2211yescharacteristic
20C2×D3×D12—21no—
21C2×D3×D12C2211yescharacteristic
22C2×#3796C2211yescharacteristic, complemented
23#64155C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic, complemented
25C2×#3743C2211yescharacteristic, complemented
26#64104C2211yescharacteristic
27C3×#947C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic, complemented
30C2×C3×D24C2211yescharacteristic
31C2×C3×#204C2211yescharacteristic, complemented
32C3×#895C2211yescharacteristic
33C3×#893C2211yescharacteristic
34D3×#215—24no—
35#63923—21no—
36#63922—21no—
37#63911C2211yescharacteristic
38#63908C2211yescharacteristic, complemented
39#63907—21no—
40#63906—21no—
41#63906—21no—
42C4×#626C2211yescharacteristic
43#63887—21no—
44#63879—21no—
45Dic3×Dic6C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic
48C2×#3714C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50C2×D3×C3⋊C8C2211yescharacteristic, complemented
51#63798—24no—
52C32×#103C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63#5817—31no—
64C22×#215—31no—
65C2×#914—31no—
66C2×D3×SD16—31no—
67C2×#911—31no—
68#5677—31no—
69#5609—31no—
70D4×D12—31no—
71C3×#463—31no—
72C3×#448—31no—
73#5176—31no—
74#5169—31no—
75#5169—31no—
76#5163—31no—
77#5156—31no—
78#5058—31no—
79#5038—31no—
80#5018—31no—
81#4848—31no—
82#4836—31no—
83#4819D311yescharacteristic, complemented
84#4817—31no—
85#4812—31no—
86#4812—31no—
87#4812—61no—
88#4810—31no—
89#4806D311yescharacteristic, complemented
90#4781—31no—
91#4775—31no—
92#4732—31no—
93#4730—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C3×D3×Q8—22no—
101C3×D3×Q8—41no—
102C2×C3×D12—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C2×C3×Dic6C2311yescharacteristic
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626D411yescharacteristic
116C2×#625—21no—
117C2×#625—21no—
118C2×D3×Dic3—21no—
119#3802—22no—
120#3802—41no—
121D3×D12—22no—
122D3×D12—44no—
123D3×D12—41no—
124#3796—22no—
125#3796—41no—
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128#3755—22no—
129#3752—21no—
130#3752—21no—
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132#3750—21no—
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134#3743—22no—
135C3×#215—22no—
136C3×#215—41no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×C4×Dic3C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C3×D24—22no—
145C3×#204—22no—
146Dic3⋊Dic3—21no—
147Dic3⋊Dic3D411yescharacteristic
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151Dic32—21no—
152#3717—22no—
153#3715D414yescomplemented
154#3714—41no—
155#3713—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—
166C22×D12—31no—
167C22×D12—61no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×D8—31no—
172C3×#124—31no—
173C3×#121—31no—
174C3×C4×D4—31no—
175#947—61no—
176#947C2×D311yescharacteristic, complemented
177#946—31no—
178#946—31no—
179#946—61no—
180#946—61no—
181Q8×Dic3—31no—
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—61no—
187C2×#215—64no—
188C2×#215C2×D311yescharacteristic
189C2×#215C2×D311yescharacteristic, complemented
190#940—31no—
191#938—31no—
192#937—61no—
193C2×#214—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—31no—
197#930—31no—
198#930—61no—
199#930—61no—
200C4×#67—31no—
201C4×#67—61no—
202C22×C3⋊C8—31no—
203#914—64no—
204D3×SD16—64no—
205#911—64no—
206C2×D24—31no—
207C2×D24C2×D311yescharacteristic
208C2×#204—31no—
209C2×#204C2×D311yescharacteristic, complemented
210C2×ΓL(1,𝔽25)—31no—
211C2×ΓL(1,𝔽25)—31no—
212C2×ΓL(1,𝔽25)—61no—
213C2×D3×C8—31no—
214#895—31no—
215#895—31no—
216#895—61no—
217#895C2×D311yescharacteristic
218#893C2×D311yescharacteristic
219#885—61no—
220#884—61no—
221#884—61no—
222#882—61no—
223#882—61no—
224#882—61no—
225#67⋊C4—61no—
226#878—61no—
227#874—31no—
228C4×D12—31no—
229C4×Dic6—31no—
230C3×C4⋊C8—31no—
231C3×#103—21no—
232C3×#103—31no—
233C3×#103C2×D311yescharacteristic, complemented
234C3×#103C2×D311yescharacteristic, complemented
235C3×#102—31no—
236C3×C22⋊C8—31no—
237#832—31no—
238#832—31no—
239#821—31no—
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)⋊C8C2×D311yescharacteristic, complemented
247#815—31no—
248Dic3⋊C8C2×D311yescharacteristic, complemented
249#810C2×D311yescharacteristic, complemented
250#809C2×D311yescharacteristic, complemented
251#807—31no—
252#807—31no—
253#807—61no—
254#803—31no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C2×D32—81no—
267C32×Q8—21no—
268C32×Q8—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4C2411yescharacteristic
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3C2×D411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—42no—
277C4×C3⋊D3—21no—
278C4×C3⋊D3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—42no—
289C3×D12C2×D412yes—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×C4×D3—42no—
294C3×Dic6—21no—
295C3×Dic6—42no—
296C3×Dic6C2×D412yescomplemented
297#626—22no—
298#626—42no—
299#626—42no—
300#626—42no—
301#626—81no—
302#625—42no—
303#625—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C3⋊(C3⋊C8)C2×D412yescomplemented
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
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—31no—
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—
328C2×C3×Q8—21no—
329C2×C3×Q8—31no—
330C2×C3×Q8—61no—
331C2×C3×Q8—62no—
332C2×C3×Q8—121no—
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×Q8C22×D311yescharacteristic
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—61no—
339C22×C3×C4—31no—
340C22×C3×C4—61no—
341C22×C3×C4—61no—
342C2×#67—31no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C22×Dic3—61no—
352#239—62no—
353#239—121no—
354D3×Q8—22no—
355D3×Q8—41no—
356#237—62no—
357#237—121no—
358D3×D4—62no—
359D3×D4—62no—
360D3×D4—62no—
361D3×D4—121no—
362D3×D4—124no—
363D3×D4—121no—
364D3×D4—121no—
365C2×D12—21no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—61no—
370C2×D12—62no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—121no—
378C2×D12—121no—
379C2×D12—124no—
380C2×D12C22×D311yescharacteristic
381C2×D12C22×D311yescharacteristic
382C2×D12C22×D311yescharacteristic
383C2×C4×D3—21no—
384C2×C4×D3—21no—
385C2×C4×D3—31no—
386C2×C4×D3—31no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3C22×D311yescharacteristic
390C2×Dic6—21no—
391C2×Dic6C22×D311yescharacteristic
392C3×SD16—62no—
393C3×SD16—62no—
394C3×SD16—121no—
395C3×D8—62no—
396C2×C3×C8—21no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C22×D311yescharacteristic
401C3×C4⋊C4—21no—
402C3×C4⋊C4C22×D311yescharacteristic
403C3×C4⋊C4C22×D311yescharacteristic
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C42—31no—
409#217—31no—
410#217—61no—
411#215—22no—
412#215—34no—
413#215—41no—
414#215—62no—
415#215—62no—
416#215—62no—
417#215—122no—
418#214—34no—
419#213—62no—
420#213—62no—
421#213—121no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—31no—
427(C2×D3)⋊C4—31no—
428(C2×D3)⋊C4—31no—
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)⋊C4—121no—
435(C2×D3)⋊C4—121no—
436C4⋊Dic3—31no—
437C4⋊Dic3—31no—
438C4⋊Dic3—31no—
439C4⋊Dic3—61no—
440C4⋊Dic3—61no—
441Dic3⋊C4—31no—
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444Dic3⋊C4—61no—
445Dic3⋊C4—121no—
446C4×Dic3—61no—
447C4×Dic3—61no—
448C4×Dic3C22×D311yescharacteristic
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8—62no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455D24—22no—
456D24—121no—
457#204—22no—
458#204—62no—
459ΓL(1,𝔽25)—62no—
460ΓL(1,𝔽25)—62no—
461ΓL(1,𝔽25)—122no—
462D3×C8—62no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—22no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3AGL(1,ℤ/8)12yescomplemented
482D32—84no—
483D32—84no—
484C32×C4—41no—
485C32×C4—41no—
486C32×C4C22×D411yescharacteristic
487C32×C4H(5,𝔽2)11yescharacteristic
488C3⋊Dic3—21no—
489C3⋊Dic3—41no—
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C2×#41—91no—
495C22×Q8—31no—
496C22×D4—91no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—31no—
502C2×SD16—31no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—184no—
507C2×D8—31no—
508C2×D8—91no—
509C2×D8—91no—
510C2×M16—91no—
511C22×C8—91no—
512#127—91no—
513#124—31no—
514#124—181no—
515C22⋊Q8—91no—
516C22⋊Q8—181no—
517#121—31no—
518#121—91no—
519#121—91no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—91no—
525C4×D4—31no—
526C4×D4—91no—
527C4×D4—181no—
528#107—91no—
529C4⋊C8—31no—
530#103—31no—
531#103D3211yescharacteristic, complemented
532#102—31no—
533#102—91no—
534#102—91no—
535#102—91no—
536C22⋊C8—31no—
537C22⋊C8—91no—
538#97—91no—
539C23×C3—31no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—31no—
547C22×D3—31no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—121no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—241no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3D3×D411yescharacteristic
565C3×Q8—21no—
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—32no—
570C3×Q8—41no—
571C3×Q8—41no—
572C3×Q8—61no—
573C3×Q8—122no—
574C3×D4—32no—
575C3×D4—61no—
576C3×D4—61no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—122no—
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—122no—
595C2×C3×C4—122no—
596C2×C3×C4C23×D311yescharacteristic
597C2×C3×C4C23×D311yescharacteristic
598#67—62no—
599#67—122no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—122no—
605#67—122no—
606#67—241no—
607C2×Dic3—21no—
608C2×Dic3—31no—
609C2×Dic3—31no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—121no—
614C2×Dic3—122no—
615C2×Dic3D3×D411yescharacteristic
616C2×Dic3D3×D411yescharacteristic
617C2×Dic3D3×D411yescharacteristic
618D12—21no—
619D12—21no—
620D12—21no—
621D12—21no—
622D12—21no—
623D12—42no—
624D12—62no—
625D12—61no—
626D12—61no—
627D12—61no—
628D12—61no—
629D12—121no—
630D12—121no—
631D12—122no—
632D12—122no—
633D12—122no—
634D12—122no—
635D12—122no—
636D12—242no—
637D12—241no—
638D12D3×D412yes—
639C4×D3—21no—
640C4×D3—21no—
641C4×D3—42no—
642C4×D3—42no—
643C4×D3—61no—
644C4×D3—61no—
645C4×D3—61no—
646C4×D3—61no—
647C4×D3—121no—
648C4×D3—121no—
649C4×D3—122no—
650Dic6—21no—
651Dic6—42no—
652Dic6D3×D412yescomplemented
653C3×C8—21no—
654C3×C8—21no—
655C3×C8—41no—
656C3×C8—61no—
657C3×C8—61no—
658C3⋊C8—21no—
659C3⋊C8—21no—
660C3⋊C8—32no—
661C3⋊C8—32no—
662C3⋊C8—62no—
663C2×C32D4211yescharacteristic
664C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
665C2×C32#57711yescharacteristic
666C3⋊D3—41no—
667C3⋊D3—81no—
668C3×D3—22no—
669C3×D3—42no—
670C3×D3—81no—
671C3×D3—81no—
672C24—181no—
673C24—181no—
674#41—182no—
675#41—361no—
676C2×Q8—31no—
677C2×Q8—61no—
678C2×Q8—62no—
679C2×Q8—121no—
680C2×Q8C2×D3211yescharacteristic
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—61no—
685C2×D4—91no—
686C2×D4—91no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—182no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—182no—
695C2×D4—181no—
696C2×D4—361no—
697C2×D4—364no—
698C2×D4—361no—
699C22×C4—31no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—91no—
703C22×C4—181no—
704SD16—62no—
705SD16—62no—
706SD16—94no—
707SD16—121no—
708SD16—182no—
709SD16—182no—
710D8—62no—
711D8—182no—
712D8—361no—
713M16—182no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—91no—
717C2×C8—182no—
718C2×C8C2×D3211yescharacteristic
719C4⋊C4—91no—
720C4⋊C4—91no—
721C4⋊C4—181no—
722C4⋊C4—181no—
723C4⋊C4C2×D3211yescharacteristic
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—61no—
728C22⋊C4—91no—
729C22⋊C4—91no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C42—31no—
734C42—181no—
735C22×C3—21no—
736C22×C3—32no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—62no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3C2×D3×D411yescharacteristic
749C22×C3C2×D3×D411yescharacteristic
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—22no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—241no—
777C2×D3—241no—
778C2×D3—241no—
779C2×D3—244no—
780C2×D3—244no—
781C2×D3—244no—
782C2×D3—244no—
783C2×D3#91412yescomplemented
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—41no—
787C3×C4—41no—
788C3×C4—41no—
789C3×C4—41no—
790C3×C4—61no—
791C3×C4—61no—
792C3×C4—62no—
793C3×C4—61no—
794C3×C4—81no—
795C3×C4—81no—
796C3×C4C2×D3×D411yescharacteristic
797C3×C4C2×D3×D411yescharacteristic
798C3×C4#100411yescharacteristic
799C3×C4#100911yescharacteristic
800Dic3—21no—
801Dic3—21no—
802Dic3—22no—
803Dic3—21no—
804Dic3—61no—
805Dic3—61no—
806Dic3—121no—
807Dic3—121no—
808Dic3—121no—
809Dic3—241no—
810C32#326511yescharacteristic, complemented, Sylow
811C23—31no—
812C23—61no—
813C23—61no—
814C23—61no—
815C23—91no—
816C23—181no—
817C23—362no—
818C23—362no—
819C23—362no—
820C23—362no—
821C23—721no—
822C23—721no—
823Q8—21no—
824Q8—21no—
825Q8—32no—
826Q8—61no—
827Q8—122no—
828D4—32no—
829D4—61no—
830D4—61no—
831D4—61no—
832D4—61no—
833D4—61no—
834D4—122no—
835D4—182no—
836D4—181no—
837D4—181no—
838D4—362no—
839D4—362no—
840D4—362no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—721no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—31no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—91no—
854C2×C4—122no—
855C2×C4—122no—
856C2×C4—181no—
857C2×C4—181no—
858C2×C4—181no—
859C2×C4—362no—
860C2×C4C22×D3211yescharacteristic
861C8—21no—
862C8—61no—
863C8—61no—
864C8—92no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—62no—
869C2×C3—122no—
870C2×C3—241no—
871C2×C3—241no—
872C2×C3#559011yescharacteristic
873C2×C3#560911yescharacteristic
874C2×C3C2×#91411yescharacteristic
875C2×C3#577011yescharacteristic
876C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
877C2×C3#577811yescharacteristic
878D3—22no—
879D3—42no—
880D3—81no—
881D3—81no—
882D3—121no—
883D3—121no—
884D3—241no—
885D3—241no—
886D3—241no—
887D3—481no—
888C22—32no—
889C22—61no—
890C22—61no—
891C22—62no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—181no—
901C22—181no—
902C22—181no—
903C22—361no—
904C22—361no—
905C22—361no—
906C22—724no—
907C22—724no—
908C22D32×D411yescharacteristic
909C4—41no—
910C4—41no—
911C4—61no—
912C4—61no—
913C4—61no—
914C4—62no—
915C4—181no—
916C4—361no—
917C4#6430711yescharacteristic
918C4D32×D411yescharacteristic
919C3—21no—
920C3#8006011yescharacteristic, complemented
921C3#8055311yescharacteristic, complemented
922C2—62no—
923C2—122no—
924C2—241no—
925C2—241no—
926C2—361no—
927C2—721no—
928C2#1059427511yescharacteristic
929C2D3×#91411yescharacteristic
930C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595401C2semidirect
2. C2×D3×#215C2semidirect
3. C2×#63798C2semidirect
4. #10594621C2semidirect
5. #10592511C2semidirect
6. C3×#4819C2semidirect
7. C3×#4806C2semidirect
8. #10591652C2semidirect
9. #10591619C2semidirect
10. #10590944C2semidirect
11. #10590907C2semidirect
12. #10590799C2semidirect
13. #10590617C2semidirect
14. #10590499C2semidirect
15. #10590478C2semidirect
18. C2×C3×D3×Q8C22semidirect
22. C2×#3796C22semidirect
23. #64155C22semidirect
24. C2×#3755C22semidirect
25. C2×#3743C22semidirect
27. C3×#947C22semidirect
29. C2×C3×#215C22semidirect
31. C2×C3×#204C22semidirect
38. #63908C22semidirect
45. Dic3×Dic6C22semidirect
46. C2×#3717C22semidirect
48. C2×#3714C22semidirect
49. C2×#3713C22semidirect
50. C2×D3×C3⋊C8C22semidirect
52. C32×#103C22semidirect
53. #63648C22semidirect
54. #63634C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#809C22semidirect
60. #63563C22semidirect
61. #63557C22semidirect
62. #63554C22semidirect
83. #4819D3semidirect
89. #4806D3semidirect
153. #3715D4semidirect
160. C2×D3×Q8C2×D3semidirect
176. #947C2×D3semidirect
189. C2×#215C2×D3semidirect
209. C2×#204C2×D3semidirect
233. C3×#103C2×D3semidirect
234. C3×#103C2×D3semidirect
246. (C2×D3)⋊C8C2×D3semidirect
248. Dic3⋊C8C2×D3semidirect
249. #810C2×D3semidirect
250. #809C2×D3semidirect
296. C3×Dic6C2×D4semidirect
306. C3⋊(C3⋊C8)C2×D4semidirect
481. C2×C3×D3AGL(1,ℤ/8)semidirect
531. #103D32semidirect
652. Dic6D3×D4semidirect
783. C2×D3#914semidirect
810. C32#3265semidirect
920. C3#80060semidirect
921. C3#80553semidirect

Maximal subgroups

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

subgroupindex
#105954012
C2×D3×#2152
C2×#637982
#105946212
#105925112
C3×#48192
C3×#48062
#105916522
#105916192
#105909442
#105909072
#105907992
#105906172
#105904992
#105904782
#805533
#800603