Finite Group Databasebeta

← C2×#10590342 #11861066

Subgroups — C2×#10590342 #11861066

Order 1152.

1013 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63829C211yesmaximal, characteristic
2C2×#63817C211yesmaximal, characteristic, complemented
3C2×#63814C211yesmaximal, characteristic, complemented
4C2×#63632C211yesmaximal, characteristic, complemented
5C2×C3×#805C211yesmaximal, characteristic, complemented
6C2×C3×#803C211yesmaximal, characteristic, complemented
7C2×#63577C211yesmaximal, characteristic, complemented
8#10590342C218yesmaximal, direct product factor
9C2×#4823—31nomaximal
10C2×#4717—31nomaximal
11C2×#3828C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×#3719C411yescharacteristic, complemented
19C2×#3717C411yescharacteristic, complemented
20#63829C414yescomplemented
21#63829C2214yes—
22C2×#3716C411yescharacteristic, complemented
23C2×#3714C411yescharacteristic, complemented
24C2×#3712—21no—
25C2×#3711—21no—
26#63817—22no—
27#63817C2214yescomplemented
28C2×#3710—21no—
29#63814—22no—
30#63814C2214yescomplemented
31C2×D3×C3⋊C8—21no—
32#63632C2214yescomplemented
33C3×#805C2214yescomplemented
34C3×#803C2214yescomplemented
35#63577C2214yescomplemented
36C2×#950—31no—
37C2×#948—31no—
38C2×#907—31no—
39C2×#904—31no—
40C2×#901—31no—
41C2×#901—31no—
42C2×C3×#104—31no—
43C2×C3×#97—31no—
44C2×#822—31no—
45C2×#819—31no—
46C2×#805—31no—
47C2×#805—31no—
48C2×#805—61no—
49C2×#805D311yescharacteristic, complemented
50C2×#803D311yescharacteristic, complemented
51#4823—38no—
52#4717—38no—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C2×#638—21no—
56#3828—21no—
57#3828—21no—
58#3828C2×C412yes—
59#3828C2312yes—
60C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
61C2×C4×C3⋊D3—21no—
62C2×#634C2×C411yescharacteristic
63C2×C3×#67—21no—
64C3×#235—21no—
65C3×#235—21no—
66C3×#235C2×C412yes—
67C3×#235C2312yes—
68C2×C3×D12C2×C411yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6C2×C411yescharacteristic
71C32×C42—21no—
72C32×C42C2312yes—
73#3748—21no—
74#3748C2312yes—
75C2×C3⋊(C3⋊C8)—21no—
76C3×#208—21no—
77C3×#208C2312yes—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8C2×C411yescharacteristic
80C2×C3×C3⋊C8C2×C411yescharacteristic
81C2×C3×C3⋊C8C2×C412yes—
82C2×C3×C3⋊C8D411yescharacteristic
83C2×C3×C3⋊C8D412yes—
84C2×C3×C3⋊C8D411yescharacteristic
85C2×C3×C3⋊C8C2312yes—
86C2×C3×C3⋊C8C2312yes—
87#3719C2×C414yescomplemented
88#3717C2×C414yescomplemented
89#3716C2×C414yescomplemented
90#3714C2×C414yescomplemented
91#3712—24no—
92#3711—24no—
93#3710—24no—
94D3×C3⋊C8—24no—
95C2×#444—91noSylow
96C2×C3×#41—31no—
97C2×#235—31no—
98C2×#235—31no—
99C2×#235—61no—
100C2×#235C2×D311yescharacteristic
101C2×C3×M16—31no—
102C22×C3×C8—31no—
103C22×C3×C8—31no—
104C2×C3×C42—21no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C2×D311yescharacteristic
107#950—34no—
108#950—34no—
109#948—34no—
110#948—62no—
111C2×#216—31no—
112C2×#215—31no—
113C2×#214—31no—
114C2×#213—31no—
115C2×#208—31no—
116C2×#208—31no—
117C2×#208—61no—
118C2×#208—61no—
119C2×#208C2×D311yescharacteristic
120C22×C3⋊C8—61no—
121C22×C3⋊C8C2×D311yescharacteristic
122C22×C3⋊C8C2×D311yescharacteristic
123#907—34no—
124#907—62no—
125C2×Dic12—31no—
126#904—34no—
127#904—34no—
128C2×D24—31no—
129C2×#204—31no—
130C2×#204—31no—
131#901—34no—
132#901—34no—
133#901—62no—
134#901—62no—
135C2×ΓL(1,𝔽25)—61no—
136C2×ΓL(1,𝔽25)—61no—
137C2×ΓL(1,𝔽25)—61no—
138C2×D3×C8—61no—
139C2×D3×C8—61no—
140C2×D3×C8—61no—
141C3×#104—34no—
142C3×#97—34no—
143#822—34no—
144#819—34no—
145#805—34no—
146#805—34no—
147#805—64no—
148#805C2×D314yescomplemented
149#803C2×D314yescomplemented
150C23×C32#4111yescharacteristic
151C22×C3⋊D3—21no—
152C22×C3×D3—21no—
153C2×C32×C4—22no—
154C2×C32×C4—42no—
155C2×C32×C4C22×C411yescharacteristic
156C2×C32×C4C22×C411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4#4111yescharacteristic
160C2×C32×C4C2411yescharacteristic
161#638—22no—
162#638—22no—
163C2×C3⋊Dic3—21no—
164C4⋊(C3⋊D3)—21no—
165C4⋊(C3⋊D3)C22×C412yes—
166C4×C3⋊D3—22no—
167C4×C3⋊D3—22no—
168#634—21no—
169#634C22×C412yes—
170C3×#67—22no—
171C3×#67—22no—
172C2×C3×Dic3—21no—
173C3×D12—21no—
174C3×D12C22×C412yes—
175C3×C4×D3—22no—
176C3×C4×D3—22no—
177C3×Dic6—21no—
178C3×Dic6C22×C412yes—
179C3⋊(C3⋊C8)—22no—
180C3×C3⋊C8—22no—
181C3×C3⋊C8C22×C412yes—
182C3×C3⋊C8C22×C412yes—
183C3×C3⋊C8C2×D412yes—
184C3×C3⋊C8C2×D412yes—
185C2×#135—91no—
186C2×#131—91no—
187C2×#131—91no—
188#444—98no—
189C2×#108—91no—
190C2×#104—31no—
191C2×#104—91no—
192C2×#97—31no—
193C3×#41—32no—
194C3×#41—32no—
195C3×#41—61no—
196C3×#41—61no—
197C2×C3×Q8—31no—
198C2×C3×D4—31no—
199C2×C3×D4—61no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—41no—
204C22×C3×C4—61no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C2×#67—21no—
208C2×#67—61no—
209C2×#67—61no—
210C2×#67—121no—
211#235—21no—
212#235—21no—
213#235—32no—
214#235—32no—
215#235—32no—
216#235—32no—
217#235—62no—
218#235—62no—
219#235—61no—
220#235—61no—
221#235—61no—
222#235—61no—
223#235—121no—
224#235—121no—
225#235C4×D312yes—
226#235C22×D312yes—
227C2×D12—31no—
228C2×D12—31no—
229C2×D12—61no—
230C2×D12C4×D311yescharacteristic
231C2×C4×D3—21no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×C4×D3—121no—
235C2×Dic6—31no—
236C2×Dic6—31no—
237C2×Dic6—61no—
238C2×Dic6C4×D311yescharacteristic
239C3×M16—32no—
240C3×M16—61no—
241C2×C3×C8—31no—
242C2×C3×C8—31no—
243C2×C3×C8—32no—
244C2×C3×C8—31no—
245C2×C3×C8—31no—
246C2×C3×C8—32no—
247C2×C3×C8—32no—
248C2×C3×C8—32no—
249C2×C3×C8—61no—
250C3×C42—21no—
251C3×C42—21no—
252C3×C42—22no—
253C3×C42—41no—
254C3×C42C22×D312yes—
255C3×C42C22×D312yes—
256#216—34no—
257#215—34no—
258#214—34no—
259#213—34no—
260#208—21no—
261#208—32no—
262#208—32no—
263#208—62no—
264#208—61no—
265#208—61no—
266#208—64no—
267#208—121no—
268#208C22×D312yes—
269C2×C3⋊C8—21no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—64no—
273C2×C3⋊C8—121no—
274C2×C3⋊C8C4×D311yescharacteristic
275C2×C3⋊C8C4×D311yescharacteristic
276C2×C3⋊C8C4×D312yes—
277C2×C3⋊C8D1211yescharacteristic
278C2×C3⋊C8D1211yescharacteristic
279C2×C3⋊C8D1212yes—
280C2×C3⋊C8C22×D312yes—
281C2×C3⋊C8C22×D312yes—
282Dic12—34no—
283D24—34no—
284#204—34no—
285#204—34no—
286ΓL(1,𝔽25)—64no—
287ΓL(1,𝔽25)—64no—
288ΓL(1,𝔽25)—64no—
289D3×C8—64no—
290D3×C8—64no—
291D3×C8—64no—
292C22×C32—22no—
293C22×C32C4×D411yescharacteristic
294C22×C32C4×D411yescharacteristic
295C22×C32C2×#4111yescharacteristic
296C2×C3⋊D3—22no—
297C2×C3⋊D3—42no—
298C2×C3×D3—22no—
299C2×C3×D3—42no—
300C32×C4—42no—
301C32×C4C4×D411yescharacteristic
302C32×C4C4×D411yescharacteristic
303C32×C4C23×C411yescharacteristic
304C32×C4C22×D411yescharacteristic
305C3⋊Dic3—22no—
306C3×Dic3—22no—
307C2×#41—31no—
308C2×#41—91no—
309#135—94no—
310#135—94no—
311C2×Q16—91no—
312C2×SD16—91no—
313C2×SD16—91no—
314C2×D8—91no—
315#131—94no—
316#131—94no—
317#131—182no—
318#131—182no—
319C2×M16—31no—
320C2×M16—91no—
321C2×M16—181no—
322C2×M16—181no—
323C22×C8—31no—
324C22×C8—31no—
325C22×C8—181no—
326C22×C8—181no—
327C2×C42D3211yescharacteristic
328#108—94no—
329#104—34no—
330#104—94no—
331#97—34no—
332C23×C3—21no—
333C23×C3—61no—
334C23×C3#23511yescharacteristic
335C23×C3#23711yescharacteristic
336C22×D3—21no—
337C22×D3—61no—
338C22×D3—61no—
339C22×D3—121no—
340C3×Q8—32no—
341C3×Q8—61no—
342C3×D4—32no—
343C3×D4—62no—
344C3×D4—62no—
345C3×D4—61no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—42no—
357C2×C3×C4—44no—
358C2×C3×C4—61no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4C2×C4×D311yescharacteristic
362C2×C3×C4C2×C4×D311yescharacteristic
363C2×C3×C4C2×C4×D311yescharacteristic
364C2×C3×C4C2×C4×D311yescharacteristic
365C2×C3×C4C2×D1211yescharacteristic
366C2×C3×C4C2×D1211yescharacteristic
367C2×C3×C4#23511yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4#23711yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373#67—22no—
374#67—22no—
375#67—62no—
376#67—62no—
377#67—62no—
378#67—62no—
379#67—122no—
380#67—122no—
381C2×Dic3—21no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—121no—
385D12—21no—
386D12—32no—
387D12—32no—
388D12—62no—
389D12—61no—
390D12—61no—
391D12—121no—
392D12C2×C4×D312yes—
393C4×D3—22no—
394C4×D3—22no—
395C4×D3—62no—
396C4×D3—62no—
397C4×D3—62no—
398C4×D3—62no—
399C4×D3—122no—
400C4×D3—122no—
401Dic6—21no—
402Dic6—32no—
403Dic6—32no—
404Dic6—62no—
405Dic6—61no—
406Dic6—61no—
407Dic6—121no—
408Dic6C2×C4×D312yes—
409C3×C8—32no—
410C3×C8—32no—
411C3×C8—32no—
412C3×C8—32no—
413C3×C8—62no—
414C3⋊C8—22no—
415C3⋊C8—62no—
416C3⋊C8—62no—
417C3⋊C8—122no—
418C3⋊C8C2×C4×D312yes—
419C3⋊C8C2×C4×D312yes—
420C3⋊C8C2×D1212yes—
421C3⋊C8C2×D1212yes—
422C2×C32—21no—
423C2×C32—21no—
424C2×C32#44412yescomplemented
425C2×C32C2×C4×D411yescharacteristic
426C3⋊D3—42no—
427C3×D3—42no—
428#41—32no—
429#41—32no—
430#41—61no—
431#41—61no—
432#41—92no—
433#41—92no—
434#41—181no—
435#41—181no—
436C2×Q8—31no—
437C2×Q8—91no—
438C2×D4—31no—
439C2×D4—61no—
440C2×D4—91no—
441C2×D4—181no—
442C22×C4—21no—
443C22×C4—61no—
444C22×C4—181no—
445C22×C4C2×D3211yescharacteristic
446Q16—94no—
447SD16—94no—
448SD16—94no—
449D8—94no—
450M16—32no—
451M16—61no—
452M16—92no—
453M16—184no—
454M16—184no—
455M16—181no—
456C2×C8—32no—
457C2×C8—32no—
458C2×C8—31no—
459C2×C8—31no—
460C2×C8—32no—
461C2×C8—32no—
462C2×C8—31no—
463C2×C8—31no—
464C2×C8—61no—
465C2×C8—184no—
466C2×C8—184no—
467C2×C8—181no—
468C42—21no—
469C42C2×D3212yes—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—42no—
476C22×C3—62no—
477C22×C3—122no—
478C22×C3C4×D1211yescharacteristic
479C22×C3C4×D1211yescharacteristic
480C22×C3#67⋊C411yescharacteristic
481C22×C3#67⋊C411yescharacteristic
482C22×C3C2×#23511yescharacteristic
483C22×C3C2×#23711yescharacteristic
484C2×D3—22no—
485C2×D3—42no—
486C2×D3—62no—
487C2×D3—62no—
488C2×D3—122no—
489C2×D3—122no—
490C2×D3—122no—
491C2×D3—242no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—42no—
497C3×C4—42no—
498C3×C4—44no—
499C3×C4—62no—
500C3×C4C4×D1211yescharacteristic
501C3×C4C4×D1211yescharacteristic
502C3×C4#67⋊C411yescharacteristic
503C3×C4#67⋊C411yescharacteristic
504C3×C4C22×C4×D311yescharacteristic
505C3×C4C22×C4×D311yescharacteristic
506C3×C4C22×D1211yescharacteristic
507C3×C4C2×D3×D411yescharacteristic
508Dic3—22no—
509Dic3—62no—
510Dic3—62no—
511Dic3—122no—
512C32C2×#44411yescharacteristic, complemented, Sylow
513C23—61no—
514C23—181no—
515C23#380411yescharacteristic
516Q8—32no—
517Q8—61no—
518Q8—92no—
519Q8—181no—
520D4—32no—
521D4—62no—
522D4—62no—
523D4—61no—
524D4—92no—
525D4—182no—
526D4—182no—
527D4—181no—
528C2×C4—22no—
529C2×C4—42no—
530C2×C4—61no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—181no—
534C2×C4—182no—
535C2×C4—182no—
536C2×C4C4×D3211yescharacteristic
537C2×C4C4×D3211yescharacteristic
538C2×C4D3×D1211yescharacteristic
539C2×C4D3×D1211yescharacteristic
540C2×C4#380411yescharacteristic
541C2×C4C22×D3211yescharacteristic
542C8—32no—
543C8—32no—
544C8—32no—
545C8—32no—
546C8—62no—
547C8—182no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—22no—
554C2×C3—41no—
555C2×C3—41no—
556C2×C3—122no—
557C2×C3#471712yescomplemented
558C2×C3#482312yescomplemented
559C2×C3C2×C4×D1211yescharacteristic
560C2×C3C2×#67⋊C411yescharacteristic
561D3—42no—
562D3—122no—
563D3—122no—
564D3—242no—
565C22—22no—
566C22—62no—
567C22—122no—
568C22—182no—
569C22—362no—
570C22#6388011yescharacteristic
571C22#6388011yescharacteristic
572C22C2×#380411yescharacteristic
573C4—42no—
574C4—62no—
575C4—182no—
576C4#6388011yescharacteristic
577C4#6388011yescharacteristic
578C4C2×C4×D3211yescharacteristic
579C4C2×D3×D1211yescharacteristic
580C3—21no—
581C3C2×#471711yescharacteristic, complemented
582C3C2×#482311yescharacteristic, complemented
583C2—21no—
584C2—21no—
585C2—122no—
586C2—362no—
587C2#1059034212yesdirect product factor
588C2C2×#6388011yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C4×D4
prime radicalC2×#63829C2
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C2×#444
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#63817C2semidirect
3. C2×#63814C2semidirect
4. C2×#63632C2semidirect
5. C2×C3×#805C2semidirect
6. C2×C3×#803C2semidirect
7. C2×#63577C2semidirect
8. #10590342C2direct (N × H)
18. C2×#3719C4semidirect
19. C2×#3717C4semidirect
20. #63829C4semidirect
22. C2×#3716C4semidirect
23. C2×#3714C4semidirect
27. #63817C22semidirect
30. #63814C22semidirect
32. #63632C22semidirect
33. C3×#805C22semidirect
34. C3×#803C22semidirect
35. #63577C22semidirect
49. C2×#805D3semidirect
50. C2×#803D3semidirect
87. #3719C2×C4semidirect
88. #3717C2×C4semidirect
89. #3716C2×C4semidirect
90. #3714C2×C4semidirect
148. #805C2×D3semidirect
149. #803C2×D3semidirect
424. C2×C32#444semidirect
512. C32C2×#444semidirect
557. C2×C3#4717semidirect
558. C2×C3#4823semidirect
581. C3C2×#4717semidirect
582. C3C2×#4823semidirect
587. C2#10590342direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638292
C2×#638172
C2×#638142
C2×#636322
C2×C3×#8052
C2×C3×#8032
C2×#635772
#105903422
C2×#48233
C2×#47173