Finite Group Databasebeta

← #11883985

Subgroups — #11883985

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
1D4×#626C211yesmaximal, characteristic, complemented
2C2×#63937C211yesmaximal, characteristic, complemented
3C2×D3×#214C211yesmaximal, characteristic, complemented
4#10594382C211yesmaximal, characteristic, complemented
5#10592475C211yesmaximal, characteristic, complemented
6C3×#4773C211yesmaximal, characteristic, complemented
7C3×#4757C211yesmaximal, characteristic, complemented
8#10591468C211yesmaximal, characteristic, complemented
9#10590963C211yesmaximal, characteristic, complemented
10#10590951C211yesmaximal, characteristic, complemented
11#10590883C211yesmaximal, characteristic, complemented
12#10590728C211yesmaximal, characteristic, complemented
13#10590576C211yesmaximal, characteristic, complemented
14#10590549C211yesmaximal, characteristic, complemented
15#10590506C211yesmaximal, characteristic, complemented
16#80025—31nomaximal
17#79794—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×#626—21no—
21C2×#3796C2211yescharacteristic, complemented
22C2×D3×Dic6C2211yescharacteristic, complemented
23C2×#3754C2211yescharacteristic
24C2×#3744C2211yescharacteristic, complemented
25#64106C2211yescharacteristic, complemented
26C3×D4×Dic3C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C2×C3×D24C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic, complemented
31C3×#887C2211yescharacteristic, complemented
32#63981—21no—
33#63978—21no—
34#63977—21no—
35#63937—24no—
36D3×#214—24no—
37#63916C2211yescharacteristic
38#63911C2211yescharacteristic
39#63909C2211yescharacteristic
40C4×#626C2211yescharacteristic
41#63893—21no—
42Dic3×D12—21no—
43#63886—21no—
44#63860C2211yescharacteristic, complemented
45#63852—21no—
46C2×#3717C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3712C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic
53#63647C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63D4×#67—31no—
64C22×#214—31no—
65C2×#914—31no—
66C2×D3×SD16—31no—
67C2×#911—31no—
68#5598—31no—
69#5576—31no—
70D4×D12—31no—
71C3×#447—31no—
72C3×#440—31no—
73#5158—31no—
74#5154—31no—
75#5153—31no—
76#5038—31no—
77#5027—31no—
78#5016—31no—
79#4886—31no—
80#4883—31no—
81#4810—31no—
82#4806—31no—
83#4780—31no—
84#4776—31no—
85#4776—31no—
86#4776—61no—
87#4773D311yescharacteristic, complemented
88#4762—31no—
89#4757D311yescharacteristic, complemented
90#4738—31no—
91#4730—31no—
92#4712—31no—
93#4706—31no—
94C23×C3⋊D3—21no—
95C23×C3×D3—21no—
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98D4×C3⋊D3—22no—
99D4×C3⋊D3—41no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C22×C3×Dic3—21no—
105C3×D3×D4—22no—
106C3×D3×D4—41no—
107C2×C3×D12—21no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#627—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—44no—
119C2×#626D411yescharacteristic
120C2×D3×Dic3—21no—
121C2×D3×Dic3—21no—
122#3796—22no—
123#3796—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128#3754—22no—
129#3752—21no—
130C4⋊(C3⋊Dic3)—21no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132#3744—41no—
133C3×#217—21no—
134C3×#214D414yescomplemented
135C3×#213—22no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D24—41no—
144Dic3⋊Dic3D411yescharacteristic
145#3722—21no—
146#3722D411yescharacteristic
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151#3717—22no—
152#3716—22no—
153#3715—22no—
154#3714—22no—
155#3712—22no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C22×C3×D4—31no—
159C22×#67—61no—
160C2×#239—31no—
161C2×D3×Q8—31no—
162C2×#237—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—61no—
166C2×D3×D4C2×D311yescharacteristic
167C22×D12—61no—
168C22×Dic6—31no—
169C2×C3×SD16—31no—
170C2×C3×D8—31no—
171C2×C3×D8—31no—
172C3×#121—31no—
173C3×C4×Q8—31no—
174C3×C4×D4—31no—
175#953—61no—
176C2×#215—31no—
177C2×#215—31no—
178#940—31no—
179#939—61no—
180#939—61no—
181#938—31no—
182#937—61no—
183#936—31no—
184D4×Dic3—61no—
185D4×Dic3C2×D311yescharacteristic
186C2×#214—31no—
187C2×#214—31no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214—61no—
191C2×#214—64no—
192C2×#214C2×D311yescharacteristic
193C2×#213—31no—
194C2×#213C2×D311yescharacteristic
195#930—31no—
196#930—61no—
197C4×#67—31no—
198C22×C3⋊C8—31no—
199#914—64no—
200D3×SD16—64no—
201#911—64no—
202C2×D24—31no—
203C2×D24C2×D311yescharacteristic, complemented
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—61no—
209C2×ΓL(1,𝔽25)—31no—
210C2×ΓL(1,𝔽25)—31no—
211C2×D3×C8—31no—
212#897—31no—
213#897—31no—
214#897—61no—
215#897—61no—
216#895—31no—
217#895—31no—
218#895—61no—
219#895C2×D311yescharacteristic, complemented
220#887C2×D311yescharacteristic, complemented
221#885—61no—
222#882—61no—
223#882—61no—
224#878—61no—
225#875—31no—
226#875—61no—
227#874—31no—
228C4×D12—31no—
229C4×D12—61no—
230C3×#107—31no—
231C3×#103—31no—
232C3×#102—21no—
233C3×#102—31no—
234C3×#102C2×D311yescharacteristic
235C3×#102C2×D311yescharacteristic
236C3×C22⋊C8—31no—
237C3×#97—31no—
238#832—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—61no—
242(C2×D3)⋊C8C2×D311yescharacteristic, complemented
243#816—31no—
244#816C2×D311yescharacteristic, complemented
245#815C2×D311yescharacteristic, complemented
246Dic3⋊C8—31no—
247#810—31no—
248#809—31no—
249#809—31no—
250#809—31no—
251#809—61no—
252#809C2×D311yescharacteristic, complemented
253#807C2×D311yescharacteristic, complemented
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×D3—42no—
264C22×C3×D3—42no—
265C22×C3×D3—81no—
266C22×C3×D3C2×D411yescharacteristic
267C32×D4—21no—
268C32×D4C2×D412yes—
269C2×C32×C4—21no—
270C2×C32×C4C2411yescharacteristic
271#638—42no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3C2×D411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4×C3⋊D3—21no—
277C4×C3⋊D3—21no—
278#634—21no—
279#634—21no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—42no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—42no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×Dic6—21no—
295C3×Dic6C2×D412yescomplemented
296#627—42no—
297#626—22no—
298#626—42no—
299#626—42no—
300#626—42no—
301#626—42no—
302#626—81no—
303D3×Dic3—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—91no—
314#468—91no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—31no—
322#440—31no—
323#435—91no—
324C24×C3—61no—
325C23×D3—21no—
326C23×D3—61no—
327C23×D3—61no—
328C23×D3—121no—
329C2×C3×Q8—31no—
330C2×C3×D4—21no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—62no—
336C2×C3×D4—121no—
337C2×C3×D4C22×D311yescharacteristic
338C2×C3×D4C22×D311yescharacteristic
339C22×C3×C4—31no—
340C22×C3×C4—61no—
341C2×#67—21no—
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—121no—
351C2×#67—124no—
352C22×Dic3—21no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355#239—62no—
356#239—121no—
357D3×Q8—62no—
358D3×Q8—121no—
359#237—62no—
360#237—121no—
361D3×D4—22no—
362D3×D4—41no—
363D3×D4—62no—
364D3×D4—62no—
365D3×D4—122no—
366D3×D4—121no—
367D3×D4—121no—
368D3×D4—122no—
369C2×D12—21no—
370C2×D12—31no—
371C2×D12—31no—
372C2×D12—31no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—124no—
380C2×D12C22×D311yescharacteristic
381C2×D12C22×D311yescharacteristic
382C2×C4×D3—31no—
383C2×C4×D3—31no—
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—34no—
397C3×D8—62no—
398C3×D8—121no—
399C2×C3×C8—21no—
400C2×C3×C8—31no—
401C2×C3×C8—31no—
402C2×C3×C8C22×D311yescharacteristic
403C2×C3×C8C22×D311yescharacteristic
404C3×C4⋊C4—21no—
405C3×C4⋊C4—31no—
406C3×C4⋊C4—61no—
407C3×C4⋊C4C22×D311yescharacteristic
408C3×C4⋊C4C22×D311yescharacteristic
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411C3×C42—31no—
412C3×C42—61no—
413#217—21no—
414#217—31no—
415#217—61no—
416#217—61no—
417#217—61no—
418#215—62no—
419#215—62no—
420#214—62no—
421#214—62no—
422#214—62no—
423#214—62no—
424#214—122no—
425#214D1214yescomplemented
426#213—22no—
427#213—62no—
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—61no—
439(C2×D3)⋊C4—121no—
440C4⋊Dic3—31no—
441C4⋊Dic3—61no—
442C4⋊Dic3—61no—
443C4⋊Dic3—121no—
444C4⋊Dic3C22×D311yescharacteristic
445Dic3⋊C4—21no—
446Dic3⋊C4—31no—
447C4×Dic3—21no—
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—41no—
456D24—62no—
457#204—62no—
458#204—62no—
459#204—121no—
460#204—121no—
461#204—122no—
462ΓL(1,𝔽25)—62no—
463ΓL(1,𝔽25)—62no—
464D3×C8—62no—
465C22×C32—22no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32C22×D411yescharacteristic
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—21no—
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×D3—84no—
485C2×C3×D3AGL(1,ℤ/8)12yescomplemented
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—91no—
498C22×D4—31no—
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—31no—
511C2×D8—91no—
512C2×M16—91no—
513C22×C8—91no—
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—31no—
527C4×D4—31no—
528C4×D4—91no—
529C4×D4—181no—
530#107—31no—
531C4⋊C8—91no—
532#103—31no—
533#103—91no—
534#102—31no—
535#102—91no—
536#102—91no—
537#102D3211yescharacteristic
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—
547C23×C3—122no—
548C23×C3—122no—
549C23×C3—241no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—31no—
553C22×D3—31no—
554C22×D3—42no—
555C22×D3—42no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—81no—
560C22×D3—121no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—122no—
565C22×D3—124no—
566C22×D3—242no—
567C22×D3—241no—
568C22×D3—241no—
569C22×D3—242no—
570C22×D3D3×D411yescharacteristic
571C3×Q8—32no—
572C3×Q8—61no—
573C3×D4—21no—
574C3×D4—21no—
575C3×D4—22no—
576C3×D4—41no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—61no—
581C3×D4—122no—
582C3×D4—122no—
583C3×D4C2×D1212yes—
584C3×D4D3×D412yes—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—31no—
589C2×C3×C4—31no—
590C2×C3×C4—31no—
591C2×C3×C4—41no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—122no—
597C2×C3×C4C23×D311yescharacteristic
598C2×C3×C4C23×D311yescharacteristic
599#67—42no—
600#67—62no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—122no—
605#67—122no—
606#67—122no—
607#67—124no—
608#67—241no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—31no—
612C2×Dic3—31no—
613C2×Dic3—42no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—121no—
618C2×Dic3—122no—
619C2×Dic3—122no—
620C2×Dic3D3×D411yescharacteristic
621C2×Dic3D3×D411yescharacteristic
622C2×Dic3D3×D411yescharacteristic
623D12—21no—
624D12—21no—
625D12—21no—
626D12—21no—
627D12—42no—
628D12—62no—
629D12—62no—
630D12—61no—
631D12—61no—
632D12—61no—
633D12—61no—
634D12—121no—
635D12—122no—
636D12—122no—
637D12—122no—
638D12—122no—
639D12—241no—
640C4×D3—21no—
641C4×D3—21no—
642C4×D3—61no—
643C4×D3—61no—
644C4×D3—61no—
645C4×D3—61no—
646C4×D3—121no—
647C4×D3—121no—
648C4×D3—122no—
649C4×D3—122no—
650Dic6—21no—
651Dic6—61no—
652Dic6—61no—
653Dic6—61no—
654Dic6—61no—
655Dic6—121no—
656Dic6—121no—
657Dic6—122no—
658Dic6—122no—
659Dic6C2×D1212yescomplemented
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⋊C8C2×D1212yescomplemented
670C2×C32—42no—
671C2×C32D4211yescharacteristic
672C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
673C2×C32#57711yescharacteristic
674C3⋊D3—41no—
675C3⋊D3—81no—
676C3×D3—22no—
677C3×D3—81no—
678C3×D3—81no—
679C24—61no—
680C24—181no—
681#41—182no—
682#41—361no—
683C2×Q8—31no—
684C2×Q8—91no—
685C2×Q8—181no—
686C2×Q8—182no—
687C2×Q8—361no—
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—61no—
691C2×D4—61no—
692C2×D4—62no—
693C2×D4—91no—
694C2×D4—91no—
695C2×D4—121no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—181no—
701C2×D4—181no—
702C2×D4—182no—
703C2×D4—364no—
704C2×D4—361no—
705C2×D4C2×D3211yescharacteristic
706C22×C4—31no—
707C22×C4—61no—
708C22×C4—91no—
709C22×C4—181no—
710C22×C4—181no—
711SD16—34no—
712SD16—182no—
713SD16—182no—
714SD16—182no—
715SD16—182no—
716SD16—361no—
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—61no—
728C4⋊C4—91no—
729C4⋊C4—181no—
730C4⋊C4C2×D3211yescharacteristic
731C22⋊C4—61no—
732C22⋊C4—61no—
733C22⋊C4—91no—
734C22⋊C4—91no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C22⋊C4—181no—
740C42—31no—
741C42—61no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—21no—
745C22×C3—32no—
746C22×C3—42no—
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×C3—244no—
762C22×C3C2×D3×D411yescharacteristic
763C22×C3C2×D3×D411yescharacteristic
764C2×D3—21no—
765C2×D3—21no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—62no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—61no—
778C2×D3—61no—
779C2×D3—84no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—122no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—241no—
790C2×D3—241no—
791C2×D3—244no—
792C2×D3—244no—
793C2×D3—248no—
794C2×D3#91112yescomplemented
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—61no—
800C3×C4—61no—
801C3×C4—61no—
802C3×C4—62no—
803C3×C4—81no—
804C3×C4—121no—
805C3×C4C22×D1211yescharacteristic
806C3×C4C2×D3×D411yescharacteristic
807C3×C4#100411yescharacteristic
808C3×C4#100911yescharacteristic
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—122no—
827C23—122no—
828C23—181no—
829C23—241no—
830C23—362no—
831C23—362no—
832C23—721no—
833Q8—32no—
834Q8—61no—
835Q8—181no—
836Q8—181no—
837Q8—362no—
838D4—21no—
839D4—61no—
840D4—61no—
841D4—61no—
842D4—61no—
843D4—122no—
844D4—122no—
845D4—182no—
846D4—181no—
847D4—181no—
848D4—362no—
849D4—362no—
850D4—362no—
851D4—362no—
852D4—362no—
853D4—721no—
854D4D3×D1212yes—
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—42no—
879C2×C3—42no—
880C2×C3—62no—
881C2×C3—82no—
882C2×C3—241no—
883C2×C3—241no—
884C2×C3D4×D1211yescharacteristic
885C2×C3#559011yescharacteristic
886C2×C3C2×#91111yescharacteristic
887C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
888C2×C3#577511yescharacteristic
889C2×C3#577811yescharacteristic
890D3—22no—
891D3—81no—
892D3—81no—
893D3—122no—
894D3—121no—
895D3—121no—
896D3—242no—
897D3—241no—
898D3—241no—
899C22—22no—
900C22—32no—
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—244no—
915C22—361no—
916C22—361no—
917C22—361no—
918C22—724no—
919C22D32×D411yescharacteristic
920C4—41no—
921C4—61no—
922C4—61no—
923C4—61no—
924C4—62no—
925C4—121no—
926C4—181no—
927C4—361no—
928C4C2×D3×D1211yescharacteristic
929C4#6431411yescharacteristic
930C3—21no—
931C3#7979411yescharacteristic, complemented
932C3#8002511yescharacteristic, complemented
933C2—42no—
934C2—62no—
935C2—241no—
936C2—241no—
937C2—361no—
938C2—721no—
939C2#1059427711yescharacteristic
940C2D3×#91111yescharacteristic
941C2#1059475411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. D4×#626C2semidirect
2. C2×#63937C2semidirect
3. C2×D3×#214C2semidirect
4. #10594382C2semidirect
5. #10592475C2semidirect
6. C3×#4773C2semidirect
7. C3×#4757C2semidirect
8. #10591468C2semidirect
9. #10590963C2semidirect
10. #10590951C2semidirect
11. #10590883C2semidirect
12. #10590728C2semidirect
13. #10590576C2semidirect
14. #10590549C2semidirect
15. #10590506C2semidirect
21. C2×#3796C22semidirect
22. C2×D3×Dic6C22semidirect
24. C2×#3744C22semidirect
25. #64106C22semidirect
29. C2×C3×D24C22semidirect
30. C3×#895C22semidirect
31. C3×#887C22semidirect
44. #63860C22semidirect
46. C2×#3717C22semidirect
47. C2×#3716C22semidirect
48. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3712C22semidirect
51. C2×D3×C3⋊C8C22semidirect
53. #63647C22semidirect
54. #63636C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×#816C22semidirect
57. C3×#815C22semidirect
58. C3×#809C22semidirect
59. C3×#807C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63567C22semidirect
62. #63562C22semidirect
87. #4773D3semidirect
89. #4757D3semidirect
134. C3×#214D4semidirect
203. C2×D24C2×D3semidirect
219. #895C2×D3semidirect
220. #887C2×D3semidirect
242. (C2×D3)⋊C8C2×D3semidirect
244. #816C2×D3semidirect
245. #815C2×D3semidirect
252. #809C2×D3semidirect
253. #807C2×D3semidirect
295. C3×Dic6C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
425. #214D12semidirect
485. C2×C3×D3AGL(1,ℤ/8)semidirect
659. Dic6C2×D12semidirect
669. C3⋊C8C2×D12semidirect
794. C2×D3#911semidirect
820. C32#3265semidirect
931. C3#79794semidirect
932. C3#80025semidirect

Maximal subgroups

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

subgroupindex
D4×#6262
C2×#639372
C2×D3×#2142
#105943822
#105924752
C3×#47732
C3×#47572
#105914682
#105909632
#105909512
#105908832
#105907282
#105905762
#105905492
#105905062
#800253
#797943