Finite Group Databasebeta

← C2×#10591009 #11858159

Subgroups — C2×#10591009 #11858159

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic
2C2×M16×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×#63874C211yesmaximal, characteristic, complemented
4C2×C3×#825C212yesmaximal, complemented
5C2×#63569C212yesmaximal, complemented
6#10591009C218yesmaximal, direct product factor
7C2×#4821—32nomaximal
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C3×#235C2212yes—
10C2×#3811—21no—
11C2×#3805—21no—
12#64306—22no—
13#64306—22no—
14#64306C414yescomplemented
15#64306C2214yes—
16C2×#3802C411yescharacteristic, complemented
17C2×C4×D32—21no—
18C2×#3798—21no—
19C2×#3797C411yescharacteristic, complemented
20C2×#3796C412yescomplemented
21C2×C32×M16C2211yescharacteristic, complemented
22C2×#3748C2211yescharacteristic, complemented
23M16×C3⋊D3—22no—
24M16×C3⋊D3C2214yescomplemented
25C2×#3743—21no—
26C2×C8×C3⋊D3—21no—
27C2×C3×C4×Dic3C2212yescomplemented
28C2×#3724—21no—
29C2×#3722—21no—
30#63874—22no—
31#63874C2214yescomplemented
32C3×#825C2218yescomplemented
33#63569C2218yescomplemented
34C2×D3×#41—32no—
35C2×D3×M16—32no—
36C2×D3×M16—61no—
37C2×#872—32no—
38C2×C3×#104—32no—
39C2×#837—32no—
40C2×#825D312yescomplemented
41C2×#805—32no—
42#4821—316no—
43C23×C3⋊D3D411yescharacteristic
44C22×D32—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C2×C4×C3⋊D3C2×C411yescharacteristic
48C2×C4×C3⋊D3C2×C411yescharacteristic
49C2×C4×C3⋊D3C2×C412yes—
50C2×C4×C3⋊D3D412yes—
51C2×C4×C3⋊D3D411yescharacteristic
52C2×C4×C3⋊D3D411yescharacteristic
53C2×C4×C3⋊D3D412yes—
54C2×C4×C3⋊D3C2312yes—
55C2×C3×#67—22no—
56C22×C3×Dic3—22no—
57C3×#235—22no—
58C3×#235—22no—
59C3×#235C2×C414yes—
60C3×#235C2314yes—
61C2×C3×D12C2×C412yes—
62C2×C3×C4×D3—22no—
63C2×C3×Dic6C2×C412yes—
64#3811—24no—
65#3811—24no—
66C2×#627—21no—
67C2×#626—22no—
68C2×#625—21no—
69C2×#624—21no—
70#3805—24no—
71#3805—24no—
72C2×D3×Dic3—22no—
73#3802—22no—
74#3802C2×C414yescomplemented
75C4×D32—24no—
76C4×D32—24no—
77#3798—24no—
78#3798—24no—
79#3797—22no—
80#3797C2×C414yescomplemented
81#3796—24no—
82#3796C2×C418yescomplemented
83C32×M16—21no—
84C32×M16C2312yescomplemented
85C2×C32×C8—21no—
86#3748—21no—
87#3748C2312yescomplemented
88C2×C3⋊(C3⋊C8)—21no—
89#3743—24no—
90C8×C3⋊D3—24no—
91C3×C4×Dic3—22no—
92C3×C4×Dic3C2314yescomplemented
93#3724—24no—
94#3722—24no—
95C2×#421—91noSylow
96C2×C3×#41—32no—
97D3×#41—38no—
98D3×#41—38no—
99D3×#41—64no—
100D3×#41—64no—
101C2×#239—32no—
102C2×D3×Q8—32no—
103C2×#237—32no—
104C2×#237—62no—
105C2×D3×D4—32no—
106C2×D3×D4—62no—
107C2×#235—62no—
108C2×#235C2×D312yes—
109C22×C4×D3—32no—
110C22×C4×D3—61no—
111C22×C4×D3—62no—
112C2×C3×M16—21no—
113C2×C3×M16C2×D312yescomplemented
114C2×C3×C42—32no—
115C2×(C2×D3)⋊C4—62no—
116C2×Dic3⋊C4—62no—
117C2×C4×Dic3C2×D312yescomplemented
118C2×#208—32no—
119C2×#208—61no—
120D3×M16—38no—
121D3×M16—64no—
122D3×M16—64no—
123D3×M16—64no—
124C2×ΓL(1,𝔽25)—62no—
125C2×ΓL(1,𝔽25)—62no—
126C2×D3×C8—62no—
127C2×D3×C8—62no—
128#872—38no—
129#872—64no—
130C3×#104—38no—
131#837—38no—
132#825C2×D318yescomplemented
133#805—38no—
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—42no—
136C22×C3⋊D3C22⋊C411yescharacteristic
137C22×C3⋊D3C22⋊C411yescharacteristic
138C22×C3⋊D3C22⋊C412yes—
139C22×C3⋊D3C2×D412yes—
140C22×C3×D3—22no—
141C2×D32—24no—
142C2×D32—44no—
143C2×C32×C4C22×C411yescharacteristic
144C2×C32×C4C22×C411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3C22⋊C411yescharacteristic
150C2×C3⋊Dic3C22⋊C412yes—
151C2×C3⋊Dic3C22⋊C411yescharacteristic
152C2×C3⋊Dic3C2×D412yes—
153C4×C3⋊D3C22⋊C412yes—
154C4×C3⋊D3C22⋊C412yes—
155C4×C3⋊D3C22⋊C412yes—
156C4×C3⋊D3C22⋊C412yes—
157C4×C3⋊D3C22×C412yes—
158C4×C3⋊D3C22×C412yes—
159C4×C3⋊D3C2×D412yes—
160C4×C3⋊D3C2×D412yes—
161C3×#67—24no—
162C3×#67—24no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—24no—
165C2×C3×Dic3—44no—
166C3×D12—22no—
167C3×D12C22×C414yes—
168C3×C4×D3—24no—
169C3×C4×D3—24no—
170C3×Dic6—22no—
171C3×Dic6C22×C414yes—
172#627—24no—
173#626—28no—
174#625—24no—
175#624—24no—
176D3×Dic3—28no—
177C32×C8—22no—
178C3⋊(C3⋊C8)—22no—
179C22×#41—91no—
180C22×M16—91no—
181C2×#117—91no—
182#421—98no—
183C2×#104—32no—
184C2×#104—92no—
185C23×D3—32no—
186C23×D3—61no—
187C23×D3—62no—
188C3×#41—34no—
189C3×#41—34no—
190C3×#41—62no—
191C3×#41—62no—
192C2×C3×Q8—32no—
193C2×C3×D4—32no—
194C2×C3×D4—62no—
195C22×C3×C4—21no—
196C22×C3×C4—62no—
197C22×C3×C4—62no—
198C22×C3×C4C22×D312yes—
199C2×#67—22no—
200C2×#67—62no—
201C2×#67—62no—
202C22×Dic3—22no—
203C22×Dic3—32no—
204C22×Dic3—61no—
205C22×Dic3—62no—
206#239—38no—
207#239—64no—
208D3×Q8—38no—
209D3×Q8—64no—
210#237—38no—
211#237—64no—
212#237—68no—
213#237—68no—
214D3×D4—38no—
215D3×D4—64no—
216D3×D4—68no—
217D3×D4—68no—
218#235—22no—
219#235—22no—
220#235—68no—
221#235—68no—
222#235C4×D314yes—
223#235C22×D314yes—
224C2×D12—62no—
225C2×D12C4×D312yes—
226C2×C4×D3—22no—
227C2×C4×D3—32no—
228C2×C4×D3—32no—
229C2×C4×D3—34no—
230C2×C4×D3—34no—
231C2×C4×D3—32no—
232C2×C4×D3—32no—
233C2×C4×D3—34no—
234C2×C4×D3—34no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×C4×D3—62no—
238C2×C4×D3—62no—
239C2×C4×D3—61no—
240C2×C4×D3—61no—
241C2×C4×D3—62no—
242C2×C4×D3—62no—
243C2×C4×D3—68no—
244C2×C4×D3—68no—
245C2×C4×D3—62no—
246C2×C4×D3—62no—
247C2×Dic6—62no—
248C2×Dic6C4×D312yes—
249C3×M16—22no—
250C3×M16—22no—
251C3×M16—22no—
252C3×M16C22×D314yescomplemented
253C2×C3×C8—22no—
254C2×C3×C8—22no—
255C3×C42—34no—
256C3×C42—62no—
257(C2×D3)⋊C4—68no—
258Dic3⋊C4—68no—
259C4×Dic3—22no—
260C4×Dic3C22×D314yescomplemented
261#208—34no—
262#208—62no—
263#208—62no—
264#208—62no—
265C2×C3⋊C8—62no—
266C2×C3⋊C8—62no—
267ΓL(1,𝔽25)—68no—
268ΓL(1,𝔽25)—68no—
269D3×C8—68no—
270D3×C8—68no—
271C22×C32—22no—
272C22×C32C2×C22⋊C411yescharacteristic
273C22×C32C2×C22⋊C411yescharacteristic
274C22×C32C22×D411yescharacteristic
275C2×C3⋊D3—22no—
276C2×C3⋊D3—22no—
277C2×C3⋊D3—42no—
278C2×C3⋊D3—42no—
279C2×C3⋊D3C2×C22⋊C412yes—
280C2×C3⋊D3C2×C22⋊C412yes—
281C2×C3×D3—24no—
282C2×C3×D3—44no—
283D32—48no—
284C32×C4C2×C22⋊C411yescharacteristic
285C32×C4C2×C22⋊C411yescharacteristic
286C32×C4C23×C411yescharacteristic
287C32×C4C22×D411yescharacteristic
288C3⋊Dic3C2×C22⋊C412yes—
289C3⋊Dic3C2×C22⋊C412yes—
290C3×Dic3—24no—
291C3×Dic3—44no—
292C2×#41—32no—
293C2×#41—92no—
294C2×#41—94no—
295C2×#41—94no—
296C2×#41—181no—
297C2×#41—181no—
298C2×#41—182no—
299C2×#41—182no—
300C22×Q8—91no—
301C22×D4—91no—
302C22×D4—181no—
303C23×C4—91no—
304C23×C4—181no—
305C2×M16—91no—
306C2×M16—94no—
307C2×M16—181no—
308C2×M16—182no—
309C2×M16D3211yescharacteristic, complemented
310C22×C8—181no—
311#117—94no—
312#117—182no—
313C2×C4⋊C4—181no—
314C2×C22⋊C4—181no—
315C2×C42—32no—
316#104—38no—
317#104—98no—
318C23×C3—21no—
319C23×C3—62no—
320C23×C3D3×D412yes—
321C22×D3—22no—
322C22×D3—32no—
323C22×D3—32no—
324C22×D3—34no—
325C22×D3—34no—
326C22×D3—61no—
327C22×D3—61no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—68no—
331C22×D3—128no—
332C22×D3—124no—
333C22×D3—124no—
334C3×Q8—34no—
335C3×Q8—62no—
336C3×D4—34no—
337C3×D4—64no—
338C3×D4—64no—
339C3×D4—62no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—62no—
347C2×C3×C4—64no—
348C2×C3×C4—64no—
349C2×C3×C4—64no—
350C2×C3×C4—124no—
351C2×C3×C4C2×C4×D312yes—
352C2×C3×C4C2×C4×D312yes—
353C2×C3×C4D3×D412yes—
354C2×C3×C4D3×D412yes—
355C2×C3×C4D3×D412yes—
356C2×C3×C4C23×D312yes—
357#67—24no—
358#67—24no—
359#67—68no—
360#67—68no—
361C2×Dic3—22no—
362C2×Dic3—24no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—34no—
366C2×Dic3—34no—
367C2×Dic3—44no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—68no—
373D12—22no—
374D12—68no—
375D12C2×C4×D314yes—
376C4×D3—24no—
377C4×D3—24no—
378C4×D3—34no—
379C4×D3—34no—
380C4×D3—34no—
381C4×D3—34no—
382C4×D3—34no—
383C4×D3—34no—
384C4×D3—34no—
385C4×D3—34no—
386C4×D3—62no—
387C4×D3—62no—
388C4×D3—62no—
389C4×D3—62no—
390C4×D3—62no—
391C4×D3—62no—
392C4×D3—62no—
393C4×D3—62no—
394C4×D3—68no—
395C4×D3—68no—
396Dic6—22no—
397Dic6—68no—
398Dic6C2×C4×D314yes—
399C3×C8—24no—
400C3×C8—24no—
401C3⋊C8—64no—
402C3⋊C8—64no—
403C2×C32—21no—
404C2×C32—21no—
405C2×C32#42112yescomplemented
406C2×C32C22×C22⋊C411yescharacteristic
407C3⋊D3—22no—
408C3⋊D3—22no—
409C3×D3—44no—
410C24—91no—
411C24—181no—
412#41—34no—
413#41—34no—
414#41—62no—
415#41—62no—
416#41—98no—
417#41—184no—
418#41—184no—
419#41—184no—
420#41—184no—
421#41—184no—
422C2×Q8—32no—
423C2×Q8—94no—
424C2×Q8—181no—
425C2×Q8—182no—
426C2×D4—32no—
427C2×D4—62no—
428C2×D4—94no—
429C2×D4—182no—
430C2×D4—182no—
431C2×D4—181no—
432C2×D4—184no—
433C2×D4—184no—
434C22×C4—62no—
435C22×C4—62no—
436C22×C4—91no—
437C22×C4—92no—
438C22×C4—91no—
439C22×C4—91no—
440C22×C4—92no—
441C22×C4—92no—
442C22×C4—92no—
443C22×C4—91no—
444C22×C4—91no—
445C22×C4—184no—
446C22×C4—184no—
447C22×C4—181no—
448C22×C4—182no—
449C22×C4C2×D3211yescharacteristic
450M16—21no—
451M16—92no—
452M16—184no—
453M16—181no—
454M16C2×D3212yescomplemented
455C2×C8—21no—
456C2×C8—184no—
457C2×C8—181no—
458C4⋊C4—184no—
459C22⋊C4—184no—
460C42—34no—
461C42—62no—
462C22×C3—24no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—42no—
467C22×C3—64no—
468C22×C3—124no—
469C22×C3D3×C22⋊C412yes—
470C22×C3D3×C22⋊C412yes—
471C22×C3C2×D3×D412yes—
472C2×D3—24no—
473C2×D3—34no—
474C2×D3—34no—
475C2×D3—44no—
476C2×D3—62no—
477C2×D3—62no—
478C2×D3—64no—
479C2×D3—64no—
480C2×D3—64no—
481C2×D3—122no—
482C2×D3—1216no—
483C2×D3—124no—
484C2×D3—124no—
485C2×D3—124no—
486C2×D3—124no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—64no—
492C3×C4—124no—
493C3×C4D3×C22⋊C412yes—
494C3×C4D3×C22⋊C412yes—
495C3×C4C22×C4×D312yes—
496C3×C4C2×D3×D412yes—
497Dic3—24no—
498Dic3—34no—
499Dic3—34no—
500Dic3—44no—
501Dic3—62no—
502Dic3—62no—
503C32C2×#42111yescharacteristic, complemented, Sylow
504C23—62no—
505C23—91no—
506C23—91no—
507C23—92no—
508C23—92no—
509C23—184no—
510C23—362no—
511C23—364no—
512C23#380211yescharacteristic
513Q8—34no—
514Q8—62no—
515Q8—184no—
516D4—34no—
517D4—64no—
518D4—64no—
519D4—62no—
520D4—188no—
521D4—184no—
522C2×C4—62no—
523C2×C4—64no—
524C2×C4—64no—
525C2×C4—64no—
526C2×C4—92no—
527C2×C4—91no—
528C2×C4—91no—
529C2×C4—92no—
530C2×C4—92no—
531C2×C4—92no—
532C2×C4—92no—
533C2×C4—92no—
534C2×C4—92no—
535C2×C4—92no—
536C2×C4—92no—
537C2×C4—92no—
538C2×C4—124no—
539C2×C4—184no—
540C2×C4—188no—
541C2×C4C4×D3211yescharacteristic
542C2×C4C4×D3211yescharacteristic
543C2×C4#380211yescharacteristic
544C2×C4#381111yescharacteristic
545C2×C4#381111yescharacteristic
546C2×C4C22×D3211yescharacteristic
547C8—22no—
548C8—182no—
549C2×C3—22no—
550C2×C3—22no—
551C2×C3—22no—
552C2×C3—21no—
553C2×C3—41no—
554C2×C3—41no—
555C2×C3—124no—
556C2×C3#482114yescomplemented
557C2×C3C2×D3×C22⋊C412yes—
558D3—44no—
559D3—64no—
560D3—64no—
561D3—64no—
562D3—122no—
563C22—22no—
564C22—64no—
565C22—92no—
566C22—92no—
567C22—124no—
568C22—182no—
569C22—182no—
570C22—362no—
571C22—362no—
572C22—368no—
573C22#6392111yescharacteristic
574C22#6392111yescharacteristic
575C22C2×#380211yescharacteristic
576C4—64no—
577C4—92no—
578C4—92no—
579C4—124no—
580C4#6392111yescharacteristic
581C4#6392111yescharacteristic
582C4C2×C4×D3211yescharacteristic
583C4C2×#381111yescharacteristic
584C3—21no—
585C3C2×#482112yescomplemented
586C2—21no—
587C2—21no—
588C2—124no—
589C2—182no—
590C2—182no—
591C2#1059100912yesdirect product factor
592C2C2×#6392111yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#64306C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32C2×#421
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×M16×C3⋊D3C2semidirect
3. C2×#63874C2semidirect
4. C2×C3×#825C2semidirect
5. C2×#63569C2semidirect
6. #10591009C2direct (N × H)
14. #64306C4semidirect
16. C2×#3802C4semidirect
19. C2×#3797C4semidirect
20. C2×#3796C4semidirect
21. C2×C32×M16C22semidirect
22. C2×#3748C22semidirect
24. M16×C3⋊D3C22semidirect
27. C2×C3×C4×Dic3C22semidirect
31. #63874C22semidirect
32. C3×#825C22semidirect
33. #63569C22semidirect
40. C2×#825D3semidirect
74. #3802C2×C4semidirect
80. #3797C2×C4semidirect
82. #3796C2×C4semidirect
84. C32×M16C23semidirect
87. #3748C23semidirect
92. C3×C4×Dic3C23semidirect
113. C2×C3×M16C2×D3semidirect
117. C2×C4×Dic3C2×D3semidirect
132. #825C2×D3semidirect
252. C3×M16C22×D3semidirect
260. C4×Dic3C22×D3semidirect
309. C2×M16D32semidirect
405. C2×C32#421semidirect
454. M16C2×D32semidirect
503. C32C2×#421semidirect
556. C2×C3#4821semidirect
585. C3C2×#4821semidirect
591. C2#10591009direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643062
C2×M16×C3⋊D32
C2×#638742
C2×C3×#8252
C2×#635692
#105910092
C2×#48213