Finite Group Databasebeta

← #11883983

Subgroups — #11883983

Order 1152.

1152 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#625C211yesmaximal, characteristic, complemented
2C2×#63932C211yesmaximal, characteristic, complemented
3C2×D3×#214C211yesmaximal, characteristic, complemented
4#10594525C211yesmaximal, characteristic, complemented
5#10592456C211yesmaximal, characteristic, complemented
6C3×#4776C211yesmaximal, characteristic, complemented
7C3×#4773C211yesmaximal, characteristic, complemented
8#10591476C211yesmaximal, characteristic, complemented
9#10590962C211yesmaximal, characteristic, complemented
10#10590887C211yesmaximal, characteristic, complemented
11#10590822C211yesmaximal, characteristic, complemented
12#10590725C211yesmaximal, characteristic, complemented
13#10590553C211yesmaximal, characteristic, complemented
14#10590503C211yesmaximal, characteristic, complemented
15#10590499C211yesmaximal, characteristic, complemented
16#80156—31nomaximal
17#80025—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×#625—21no—
21C2×#3795C2211yescharacteristic, complemented
22C2×D3×Dic6C2211yescharacteristic, complemented
23D4×C3⋊Dic3C2211yescharacteristic
24C2×#3754C2211yescharacteristic
25#64096C2211yescharacteristic, complemented
26C2×C3×#214C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C2×C3×D24C2211yescharacteristic, complemented
29C2×C3×#204C2211yescharacteristic, complemented
30C3×#897C2211yescharacteristic, complemented
31C3×#895C2211yescharacteristic, complemented
32#63980—21no—
33#63976—21no—
34#63976—21no—
35#63932—24no—
36D3×#214—24no—
37#63915—21no—
38#63914C2211yescharacteristic
39#63908C2211yescharacteristic
40#63908C2211yescharacteristic
41C4×#625C2211yescharacteristic
42#63899—21no—
43#63898—21no—
44#63885—21no—
45#63863C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50C2×#3711C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic
53#63643C2211yescharacteristic, complemented
54#63642C2211yescharacteristic, complemented
55#63634C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60#63572C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63D4×#67—31no—
64D4×#67—31no—
65C22×#214—31no—
66C2×#932—31no—
67C2×D3×SD16—31no—
68C2×#911—31no—
69#5633—31no—
70#5598—31no—
71C3×#450—31no—
72C3×#447—31no—
73#5176—31no—
74#5170—31no—
75#5165—31no—
76#5158—31no—
77#5154—31no—
78#5153—31no—
79#5049—31no—
80#5038—31no—
81#4780—31no—
82#4776D311yescharacteristic, complemented
83#4775—31no—
84#4773D311yescharacteristic, complemented
85#4762—31no—
86#4762—31no—
87#4757—31no—
88#4757—31no—
89#4757—61no—
90#4738—31no—
91#4734—31no—
92#4730—31no—
93#4728—31no—
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C3⋊Dic3—21no—
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×D3×D4—22no—
102C3×D3×D4—22no—
103C3×D3×D4—41no—
104C3×D3×D4—41no—
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#627—21no—
113C2×#625—21no—
114C2×#625—21no—
115C2×#625—21no—
116C2×#625—21no—
117C2×#625—21no—
118C2×#625—44no—
119C2×#625D411yescharacteristic
120C2×D3×Dic3—21no—
121C2×D3×Dic3—21no—
122#3795—22no—
123#3795—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128#3757—21no—
129#3754D414yescomplemented
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131#3750—21no—
132C4×C3⋊Dic3—21no—
133C4×C3⋊Dic3C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C3×#214—22no—
136C3×#213—22no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3—21no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24—41no—
143C3×#204—41no—
144#3724D411yescharacteristic
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150(C2×D3)⋊Dic3D411yescharacteristic
151#3716—22no—
152#3716—22no—
153#3715—22no—
154#3713—22no—
155#3711—22no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C22×C3×D4—31no—
159C22×C3×D4—31no—
160C22×#67—61no—
161C22×#67—61no—
162C2×D3×Q8—31no—
163C2×#237—31no—
164C2×D3×D4C2×D311yescharacteristic
165C2×D3×D4C2×D311yescharacteristic
166C2×#235—31no—
167C22×Dic6—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×D8—31no—
171C2×C3×D8—31no—
172C3×C22⋊Q8—31no—
173C3×#121—31no—
174#953—61no—
175#953—61no—
176#947—31no—
177C2×#215—31no—
178#940—31no—
179#940—31no—
180#939—61no—
181#939—61no—
182#939—61no—
183#938—31no—
184#938—31no—
185#937—61no—
186#937—61no—
187#936—31no—
188D4×Dic3—31no—
189D4×Dic3—31no—
190D4×Dic3—61no—
191D4×Dic3—61no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—31no—
197C2×#214—61no—
198C2×#214—64no—
199C2×#214C2×D311yescharacteristic
200#932—64no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213C2×D311yescharacteristic
204#930—31no—
205#930—31no—
206C4×#67—31no—
207C4×#67—31no—
208C2×#208—31no—
209C22×C3⋊C8—31no—
210D3×SD16—64no—
211#911—64no—
212C2×D24C2×D311yescharacteristic, complemented
213C2×#204—31no—
214C2×#204—31no—
215C2×#204C2×D311yescharacteristic, complemented
216C2×ΓL(1,𝔽25)—31no—
217C2×D3×C8—31no—
218#897C2×D311yescharacteristic, complemented
219#896—61no—
220#895C2×D311yescharacteristic, complemented
221#893—61no—
222#887—31no—
223#887—31no—
224#887—61no—
225#885—61no—
226#885—61no—
227#884—61no—
228#878—61no—
229C3×#102—21no—
230C3×#102—31no—
231C3×#102—31no—
232C3×#102C2×D311yescharacteristic
233C3×#102C2×D311yescharacteristic
234C3×C22⋊C8—31no—
235C3×C22⋊C8—31no—
236#835—31no—
237#832—31no—
238#821—31no—
239(C2×D3)⋊C8C2×D311yescharacteristic, complemented
240(C2×D3)⋊C8C2×D311yescharacteristic, complemented
241#816—31no—
242#816—31no—
243#816—31no—
244#816—61no—
245#815—31no—
246#815—31no—
247#815—61no—
248Dic3⋊C8—31no—
249Dic3⋊C8—31no—
250#809C2×D311yescharacteristic, complemented
251#809C2×D311yescharacteristic, complemented
252#807—31no—
253#807—31no—
254#807—61no—
255C23×C32—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—42no—
263C22×C3×D3—81no—
264C22×C3×D3—81no—
265C22×C3×D3C2×D411yescharacteristic
266C22×C3×D3C2×D411yescharacteristic
267C32×D4—21no—
268C32×D4C2×D412yes—
269C2×C32×C4—21no—
270C2×C32×C4C2411yescharacteristic
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—42no—
274C2×C3⋊Dic3C2×D411yescharacteristic
275C2×C3⋊Dic3C2×D411yescharacteristic
276#634—21no—
277#634C2×D412yescomplemented
278C3×#67—42no—
279C3×#67—42no—
280C2×C3×Dic3—21no—
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—21no—
289C3×D12—42no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296#627—42no—
297#625—22no—
298#625—42no—
299#625—42no—
300#625—42no—
301#625—42no—
302#625—81no—
303D3×Dic3—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—91no—
317#460—91no—
318#450—31no—
319#449—91no—
320#448—91no—
321#447—31no—
322#440—91no—
323#435—91no—
324C24×C3—61no—
325C24×C3—61no—
326C23×D3—21no—
327C23×D3—21no—
328C2×C3×Q8—31no—
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—62no—
337C2×C3×D4—62no—
338C2×C3×D4—121no—
339C2×C3×D4—121no—
340C2×C3×D4C22×D311yescharacteristic
341C2×C3×D4C22×D311yescharacteristic
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C2×#67—21no—
345C2×#67—21no—
346C2×#67—31no—
347C2×#67—31no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—124no—
359C2×#67—124no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3—61no—
363C22×Dic3—61no—
364C22×Dic3—121no—
365D3×Q8—62no—
366D3×Q8—121no—
367#237—62no—
368#237—121no—
369D3×D4—22no—
370D3×D4—22no—
371D3×D4—41no—
372D3×D4—41no—
373#235—62no—
374#235—121no—
375C2×D12—21no—
376C2×D12C22×D311yescharacteristic
377C2×D12C22×D311yescharacteristic
378C2×D12C22×D311yescharacteristic
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3C22×D311yescharacteristic
382C2×C4×D3C22×D311yescharacteristic
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—61no—
386C2×Dic6—62no—
387C2×Dic6—61no—
388C2×Dic6—61no—
389C2×Dic6—121no—
390C2×Dic6C22×D311yescharacteristic
391C3×SD16—62no—
392C3×SD16—121no—
393C3×D8—62no—
394C3×D8—121no—
395C2×C3×C8—21no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C3×C4⋊C4—21no—
401C3×C4⋊C4—61no—
402C3×C4⋊C4C22×D311yescharacteristic
403C3×C4⋊C4C22×D311yescharacteristic
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406#217—31no—
407#217—31no—
408#217—61no—
409#217—61no—
410#217—61no—
411#217—61no—
412#217—61no—
413#217—61no—
414#217—121no—
415#215—62no—
416#214—22no—
417#214—34no—
418#214—34no—
419#214—64no—
420#214—62no—
421#214—62no—
422#214—62no—
423#213—22no—
424#213—62no—
425#213—62no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434C4⋊Dic3—21no—
435C4⋊Dic3—31no—
436C4⋊Dic3—31no—
437C4⋊Dic3—61no—
438Dic3⋊C4—31no—
439Dic3⋊C4—31no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4—121no—
443C4×Dic3—31no—
444C4×Dic3—31no—
445C4×Dic3—61no—
446C4×Dic3—61no—
447C4×Dic3—61no—
448C4×Dic3—121no—
449#208—62no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—61no—
453C2×C3⋊C8—62no—
454C2×C3⋊C8C22×D311yescharacteristic
455C2×C3⋊C8C22×D311yescharacteristic
456D24—41no—
457#204—41no—
458#204—62no—
459#204—62no—
460ΓL(1,𝔽25)—62no—
461D3×C8—62no—
462C22×C32—22no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32C22×D411yescharacteristic
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
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—84no—
481C2×C3×D3—84no—
482C2×C3×D3AGL(1,ℤ/8)12yescomplemented
483C32×C4—41no—
484C32×C4C22×D411yescharacteristic
485C32×C4H(5,𝔽2)11yescharacteristic
486C3⋊Dic3—22no—
487C3⋊Dic3—21no—
488C3⋊Dic3—21no—
489C3⋊Dic3—41no—
490C3×Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—41no—
493C2×#41—91no—
494C22×Q8—91no—
495C22×D4—31no—
496C22×D4—31no—
497C22×D4—181no—
498AGL(1,ℤ/8)—184no—
499C2×SD16—31no—
500C2×SD16—31no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—184no—
506C2×D8—31no—
507C2×D8—31no—
508C2×D8—91no—
509C2×M16—91no—
510C22×C8—91no—
511#127—91no—
512#124—91no—
513#124—181no—
514C22⋊Q8—31no—
515C22⋊Q8—181no—
516#121—31no—
517#121—91no—
518#121—91no—
519#121—181no—
520#121—181no—
521#120—181no—
522#120—181no—
523C4×Q8—91no—
524C4×D4—91no—
525C4×D4—91no—
526C4×D4—181no—
527#107—91no—
528C4⋊C8—91no—
529#103—91no—
530#103—91no—
531#102—31no—
532#102—31no—
533#102—91no—
534#102D3211yescharacteristic
535C22⋊C8—31no—
536C22⋊C8—31no—
537#97—91no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—31no—
541C23×C3—31no—
542C23×C3—41no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—122no—
547C23×C3—122no—
548C23×C3—122no—
549C23×C3—122no—
550C23×C3—241no—
551C23×C3—241no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—42no—
556C22×D3—42no—
557C22×D3—42no—
558C22×D3—42no—
559C22×D3—81no—
560C22×D3—81no—
561C22×D3D3×D411yescharacteristic
562C22×D3D3×D411yescharacteristic
563C3×Q8—61no—
564C3×Q8—61no—
565C3×D4—21no—
566C3×D4—21no—
567C3×D4—22no—
568C3×D4—41no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—61no—
574C3×D4—61no—
575C3×D4—122no—
576C3×D4—122no—
577C3×D4—122no—
578C3×D4D3×D412yes—
579C3×D4D3×D412yes—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—41no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4C23×D311yescharacteristic
592C2×C3×C4C23×D311yescharacteristic
593#67—42no—
594#67—42no—
595#67—62no—
596#67—62no—
597#67—122no—
598#67—122no—
599#67—122no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—122no—
605#67—241no—
606#67—241no—
607C2×Dic3—21no—
608C2×Dic3—31no—
609C2×Dic3—31no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—121no—
619C2×Dic3—121no—
620C2×Dic3—122no—
621C2×Dic3—122no—
622C2×Dic3—122no—
623C2×Dic3—122no—
624C2×Dic3—242no—
625C2×Dic3D3×D411yescharacteristic
626C2×Dic3D3×D411yescharacteristic
627D12—21no—
628D12—21no—
629D12—21no—
630D12—21no—
631D12—21no—
632D12—21no—
633D12—42no—
634C4×D3—21no—
635C4×D3—21no—
636C4×D3—21no—
637C4×D3—21no—
638C4×D3—122no—
639C4×D3—122no—
640Dic6—21no—
641Dic6—21no—
642Dic6—32no—
643Dic6—32no—
644Dic6—62no—
645Dic6—61no—
646Dic6—61no—
647Dic6—121no—
648Dic6—122no—
649Dic6—122no—
650C3×C8—21no—
651C3×C8—21no—
652C3×C8—41no—
653C3×C8—61no—
654C3×C8—61no—
655C3⋊C8—21no—
656C3⋊C8—21no—
657C3⋊C8—32no—
658C3⋊C8—32no—
659C3⋊C8—62no—
660C2×C32—42no—
661C2×C32D4211yescharacteristic
662C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
663C2×C32#57711yescharacteristic
664C3×D3—22no—
665C3×D3—41no—
666C3×D3—81no—
667C3×D3—81no—
668C3×D3—81no—
669C24—61no—
670C24—61no—
671#41—182no—
672#41—361no—
673C2×Q8—31no—
674C2×Q8—91no—
675C2×Q8—181no—
676C2×Q8—182no—
677C2×Q8—361no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—31no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—62no—
685C2×D4—62no—
686C2×D4—91no—
687C2×D4—121no—
688C2×D4—121no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—364no—
695C2×D4C2×D3211yescharacteristic
696C22×C4—31no—
697C22×C4—31no—
698C22×C4—181no—
699C22×C4—181no—
700C22×C4—181no—
701SD16—62no—
702SD16—94no—
703SD16—121no—
704SD16—182no—
705SD16—182no—
706SD16—182no—
707D8—62no—
708D8—121no—
709D8—182no—
710M16—182no—
711C2×C8—31no—
712C2×C8—31no—
713C2×C8—91no—
714C2×C8—182no—
715C2×C8C2×D3211yescharacteristic
716C4⋊C4—61no—
717C4⋊C4—91no—
718C4⋊C4—91no—
719C4⋊C4—181no—
720C4⋊C4C2×D3211yescharacteristic
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—91no—
724C22⋊C4—91no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C42—91no—
731C42—181no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—21no—
735C22×C3—32no—
736C22×C3—42no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—244no—
758C22×C3—244no—
759C22×C3C2×D3×D411yescharacteristic
760C22×C3C2×D3×D411yescharacteristic
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—21no—
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—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—84no—
776C2×D3—84no—
777C2×D3#91112yescomplemented
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—41no—
781C3×C4—41no—
782C3×C4—61no—
783C3×C4—61no—
784C3×C4—81no—
785C3×C4—121no—
786C3×C4C2×D3×D411yescharacteristic
787C3×C4C2×D3×D411yescharacteristic
788C3×C4#100411yescharacteristic
789C3×C4#100411yescharacteristic
790Dic3—21no—
791Dic3—21no—
792Dic3—41no—
793Dic3—61no—
794Dic3—61no—
795Dic3—61no—
796Dic3—61no—
797Dic3—62no—
798Dic3—62no—
799Dic3—122no—
800Dic3—121no—
801Dic3—121no—
802Dic3—121no—
803Dic3—121no—
804Dic3—241no—
805C32#326511yescharacteristic, complemented, Sylow
806C23—21no—
807C23—31no—
808C23—31no—
809C23—61no—
810C23—61no—
811C23—61no—
812C23—122no—
813C23—122no—
814C23—122no—
815C23—122no—
816C23—241no—
817C23—241no—
818Q8—61no—
819Q8—61no—
820Q8—92no—
821Q8—181no—
822Q8—362no—
823D4—21no—
824D4—61no—
825D4—61no—
826D4—61no—
827D4—61no—
828D4—61no—
829D4—61no—
830D4—122no—
831D4—122no—
832D4—122no—
833D4—182no—
834D4—362no—
835D4—362no—
836D4—362no—
837D4—362no—
838D4—721no—
839D4#380212yes—
840C2×C4—21no—
841C2×C4—31no—
842C2×C4—31no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—91no—
849C2×C4—91no—
850C2×C4—181no—
851C2×C4—181no—
852C2×C4—362no—
853C2×C4—362no—
854C2×C4—362no—
855C2×C4C22×D3211yescharacteristic
856C8—21no—
857C8—61no—
858C8—61no—
859C8—92no—
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—42no—
864C2×C3—42no—
865C2×C3—62no—
866C2×C3—82no—
867C2×C3—121no—
868C2×C3—241no—
869C2×C3—241no—
870C2×C3—241no—
871C2×C3#559011yescharacteristic
872C2×C3#559011yescharacteristic
873C2×C3C2×#91111yescharacteristic
874C2×C3#576211yescharacteristic
875C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
876C2×C3#577511yescharacteristic
877D3—22no—
878D3—41no—
879D3—81no—
880D3—81no—
881D3—81no—
882C22—22no—
883C22—32no—
884C22—41no—
885C22—41no—
886C22—61no—
887C22—61no—
888C22—61no—
889C22—61no—
890C22—61no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—244no—
901C22—244no—
902C22D32×D411yescharacteristic
903C4—41no—
904C4—61no—
905C4—61no—
906C4—121no—
907C4—181no—
908C4—181no—
909C4—182no—
910C4—361no—
911C4C2×#380211yescharacteristic
912C4#6431311yescharacteristic
913C3—21no—
914C3#8002511yescharacteristic, complemented
915C3#8015611yescharacteristic, complemented
916C2—42no—
917C2—62no—
918C2—121no—
919C2—241no—
920C2—241no—
921C2—241no—
922C2#1059427111yescharacteristic
923C2D3×#91111yescharacteristic
924C2#1059474911yescharacteristic
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×#625C2semidirect
2. C2×#63932C2semidirect
3. C2×D3×#214C2semidirect
4. #10594525C2semidirect
5. #10592456C2semidirect
6. C3×#4776C2semidirect
7. C3×#4773C2semidirect
8. #10591476C2semidirect
9. #10590962C2semidirect
10. #10590887C2semidirect
11. #10590822C2semidirect
12. #10590725C2semidirect
13. #10590553C2semidirect
14. #10590503C2semidirect
15. #10590499C2semidirect
21. C2×#3795C22semidirect
22. C2×D3×Dic6C22semidirect
25. #64096C22semidirect
28. C2×C3×D24C22semidirect
29. C2×C3×#204C22semidirect
30. C3×#897C22semidirect
31. C3×#895C22semidirect
45. #63863C22semidirect
46. C2×#3716C22semidirect
47. C2×#3716C22semidirect
48. C2×#3715C22semidirect
49. C2×#3713C22semidirect
50. C2×#3711C22semidirect
51. C2×D3×C3⋊C8C22semidirect
53. #63643C22semidirect
54. #63642C22semidirect
55. #63634C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#809C22semidirect
59. C3×#809C22semidirect
60. #63572C22semidirect
61. #63566C22semidirect
62. #63563C22semidirect
82. #4776D3semidirect
84. #4773D3semidirect
129. #3754D4semidirect
212. C2×D24C2×D3semidirect
215. C2×#204C2×D3semidirect
218. #897C2×D3semidirect
220. #895C2×D3semidirect
239. (C2×D3)⋊C8C2×D3semidirect
240. (C2×D3)⋊C8C2×D3semidirect
250. #809C2×D3semidirect
251. #809C2×D3semidirect
277. #634C2×D4semidirect
306. C3⋊(C3⋊C8)C2×D4semidirect
482. C2×C3×D3AGL(1,ℤ/8)semidirect
777. C2×D3#911semidirect
805. C32#3265semidirect
914. C3#80025semidirect
915. C3#80156semidirect

Maximal subgroups

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

subgroupindex
D4×#6252
C2×#639322
C2×D3×#2142
#105945252
#105924562
C3×#47762
C3×#47732
#105914762
#105909622
#105908872
#105908222
#105907252
#105905532
#105905032
#105904992
#801563
#800253