Finite Group Databasebeta

← C2×#10593841 #11857784

Subgroups — C2×#10593841 #11857784

Order 1152.

1682 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic
2C2×#64286C211yesmaximal, characteristic, complemented
3C22×#3787C211yesmaximal, characteristic, complemented
4#10593841C218yesmaximal, direct product factor
5C2×#63784C212yesmaximal, complemented
6C2×#63782C212yesmaximal, complemented
7C2×C32×#41C411yescharacteristic, complemented
8#41×C3⋊D3—22no—
9#41×C3⋊D3—22no—
10#41×C3⋊D3C414yescomplemented
11#41×C3⋊D3C2214yes—
12C2×#3832C411yescharacteristic, complemented
13C2×Q8×C3⋊D3C2211yescharacteristic
14C2×#3830—21no—
15C2×#3830C411yescharacteristic, complemented
16C2×D4×C3⋊D3—21no—
17C2×D4×C3⋊D3C2211yescharacteristic
18C2×#3828—21no—
19C2×#3828C411yescharacteristic, complemented
20C22×C4×C3⋊D3—21no—
21C22×C4×C3⋊D3C2211yescharacteristic
22C2×C22⋊#157—21no—
23C22×#622—21no—
24#64286—22no—
25#64286C2214yescomplemented
26C2×C4⋊#157C2212yes—
27C2×C4×#157—21no—
28C2×#3787—22no—
29C2×#3787—21no—
30C2×#3787C2212yes—
31C2×#3787C2214yescomplemented
32#63784C2218yescomplemented
33#63782C2218yescomplemented
34C2×D3×#41—62no—
35C23×C3⋊D3—21no—
36C23×C3⋊D3D411yescharacteristic
37C22×#157—22no—
38C32×#41—22no—
39C32×#41C2×C414yescomplemented
40C2×C32×Q8C2×C411yescharacteristic
41C2×C32×D4—21no—
42C2×C32×D4C2×C411yescharacteristic
43C22×C32×C4—21no—
44C22×C32×C4C2×C411yescharacteristic
45C2×#638—21no—
46C2×#638—21no—
47C2×#638—21no—
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3D411yescharacteristic
50#3832—22no—
51#3832C2×C414yescomplemented
52Q8×C3⋊D3—21no—
53Q8×C3⋊D3—21no—
54Q8×C3⋊D3C2×C412yes—
55Q8×C3⋊D3C2312yes—
56#3830—24no—
57#3830—24no—
58#3830—22no—
59#3830C2×C414yescomplemented
60D4×C3⋊D3—24no—
61D4×C3⋊D3—24no—
62D4×C3⋊D3—21no—
63D4×C3⋊D3—21no—
64D4×C3⋊D3C2×C412yes—
65D4×C3⋊D3C2312yes—
66#3828—22no—
67#3828—24no—
68#3828—24no—
69#3828C2×C414yescomplemented
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
72C2×C4×C3⋊D3—21no—
73C2×C4×C3⋊D3—21no—
74C2×C4×C3⋊D3—21no—
75C2×C4×C3⋊D3—24no—
76C2×C4×C3⋊D3—24no—
77C2×C4×C3⋊D3C2×C411yescharacteristic
78C2×C4×C3⋊D3C2×C412yes—
79C2×C4×C3⋊D3D411yescharacteristic
80C2×C4×C3⋊D3D412yes—
81C2×C4×C3⋊D3D411yescharacteristic
82C2×C4×C3⋊D3D412yes—
83C2×C4×C3⋊D3C2311yescharacteristic
84C2×C4×C3⋊D3C2312yes—
85C2×#634—21no—
86C2×#634C2×C411yescharacteristic
87C22⋊#157—24no—
88C2×#622—22no—
89C2×#622—24no—
90C4⋊#157—22no—
91C4⋊#157C2314yes—
92C4×#157—24no—
93#3787—22no—
94#3787—24no—
95#3787C2314yes—
96C2×#416—91nomaximal, Sylow
97C2×C3×#41—22no—
98D3×#41—68no—
99D3×#41—68no—
100D3×#41—68no—
101D3×#41—68no—
102C2×#239—62no—
103C2×D3×Q8—62no—
104C2×#237—62no—
105C2×#237—64no—
106C2×D3×D4—62no—
107C2×D3×D4—64no—
108C2×#235—62no—
109C2×#235—64no—
110C22×C4×D3—62no—
111C22×C4×D3—64no—
112C23×C32—21no—
113C23×C32C22⋊C411yescharacteristic
114C22×C3⋊D3—21no—
115C22×C3⋊D3—22no—
116C22×C3⋊D3—22no—
117C22×C3⋊D3—24no—
118C22×C3⋊D3—44no—
119C22×C3⋊D3C22⋊C411yescharacteristic
120C22×C3⋊D3C22⋊C412yes—
121C22×C3⋊D3C2×D412yes—
122C22×C3⋊D3C2×D411yescharacteristic
123C2×#157—24no—
124C2×#157—44no—
125C32×Q8—21no—
126C32×Q8C22×C412yes—
127C32×D4—24no—
128C32×D4—21no—
129C32×D4C22×C412yes—
130C2×C32×C4—21no—
131C2×C32×C4—24no—
132C2×C32×C4C22⋊C411yescharacteristic
133C2×C32×C4C22⋊C412yes—
134C2×C32×C4C22×C411yescharacteristic
135C2×C32×C4C22×C412yes—
136#638—24no—
137#638—24no—
138#638—22no—
139#638—22no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—24no—
142C2×C3⋊Dic3C22⋊C411yescharacteristic
143C2×C3⋊Dic3C22⋊C412yes—
144C2×C3⋊Dic3C2×D411yescharacteristic
145C2×C3⋊Dic3C2×D412yes—
146C4⋊(C3⋊D3)—24no—
147C4⋊(C3⋊D3)—21no—
148C4⋊(C3⋊D3)C22×C412yes—
149C4×C3⋊D3—22no—
150C4×C3⋊D3—22no—
151C4×C3⋊D3—24no—
152C4×C3⋊D3—24no—
153C4×C3⋊D3C22⋊C412yes—
154C4×C3⋊D3C22⋊C412yes—
155C4×C3⋊D3C22⋊C412yes—
156C4×C3⋊D3C22×C411yescharacteristic
157C4×C3⋊D3C22×C412yes—
158C4×C3⋊D3C2×D412yes—
159C4×C3⋊D3C2×D411yescharacteristic
160C4×C3⋊D3C2×D412yes—
161C4×C3⋊D3C2×D411yescharacteristic
162C4×C3⋊D3C2411yescharacteristic
163#634—21no—
164#634—22no—
165#634—22no—
166#634C22×C412yes—
167#622—24no—
168C22×#41—91no—
169C23×C8—91no—
170C2×#117—91no—
171#416—98no—
172C2×#103—92no—
173C2×#102—92no—
174C23×D3—62no—
175C23×D3—64no—
176C3×#41—28no—
177C3×#41—28no—
178C2×C3×Q8—22no—
179C2×C3×D4—24no—
180C2×C3×D4—22no—
181C22×C3×C4—24no—
182C22×C3×C4—22no—
183C2×#67—64no—
184C2×#67—64no—
185C2×#67—64no—
186C22×Dic3—62no—
187C22×Dic3—64no—
188#239—68no—
189#239—68no—
190D3×Q8—64no—
191D3×Q8—64no—
192D3×Q8—64no—
193D3×Q8—64no—
194#237—68no—
195#237—68no—
196#237—616no—
197#237—616no—
198D3×D4—64no—
199D3×D4—64no—
200D3×D4—64no—
201D3×D4—64no—
202D3×D4—616no—
203D3×D4—616no—
204#235—68no—
205#235—616no—
206#235—616no—
207#235—68no—
208C2×D12—62no—
209C2×D12—64no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—64no—
215C2×C4×D3—64no—
216C2×C4×D3—64no—
217C2×C4×D3—64no—
218C2×C4×D3—64no—
219C2×C4×D3—64no—
220C2×C4×D3—64no—
221C2×C4×D3—616no—
222C2×C4×D3—616no—
223C2×Dic6—62no—
224C2×Dic6—64no—
225C22×C32—22no—
226C22×C32—22no—
227C22×C32—42no—
228C22×C32C2×C22⋊C412yes—
229C22×C32C2×C22⋊C411yescharacteristic
230C2×C3⋊D3—22no—
231C2×C3⋊D3—22no—
232C2×C3⋊D3—24no—
233C2×C3⋊D3—24no—
234C2×C3⋊D3—42no—
235C2×C3⋊D3—44no—
236C2×C3⋊D3—44no—
237C2×C3⋊D3C2×C22⋊C412yes—
238C2×C3⋊D3C2×C22⋊C411yescharacteristic
239C2×C3⋊D3#13514yes—
240C2×C3⋊D3C22×D411yescharacteristic
241#157—44no—
242C32×C4—22no—
243C32×C4C2×C22⋊C411yescharacteristic
244C32×C4C2×C22⋊C412yes—
245C32×C4C23×C411yescharacteristic
246C3⋊Dic3—22no—
247C3⋊Dic3C2×C22⋊C411yescharacteristic
248C3⋊Dic3C2×C22⋊C412yes—
249C3⋊Dic3C22×D411yescharacteristic
250C2×#41—94no—
251C2×#41—94no—
252C2×#41—91no—
253C2×#41—91no—
254C2×#41—91no—
255C2×#41—181no—
256C2×#41—181no—
257C2×#41—182no—
258C2×#41—182no—
259C2×#41#15711yescharacteristic, complemented
260C22×Q8—91no—
261C22×D4—91no—
262C22×D4—181no—
263C23×C4—91no—
264C23×C4—181no—
265C22×C8—92no—
266C22×C8—94no—
267C22×C8—182no—
268C22×C8—181no—
269C22×C8—181no—
270#117—94no—
271#117—182no—
272C2×C4⋊C4—92no—
273C2×C22⋊C4—181no—
274C2×C42—181no—
275#103—98no—
276#102—98no—
277C23×C3—24no—
278C23×C3—22no—
279C22×D3—62no—
280C22×D3—62no—
281C22×D3—64no—
282C22×D3—64no—
283C22×D3—64no—
284C22×D3—68no—
285C22×D3—68no—
286C22×D3—128no—
287C22×D3—1216no—
288C3×Q8—24no—
289C3×Q8—24no—
290C3×D4—216no—
291C3×D4—24no—
292C3×D4—24no—
293C2×C3×C4—24no—
294C2×C3×C4—216no—
295C2×C3×C4—22no—
296C2×C3×C4—24no—
297C2×C3×C4—24no—
298C2×C3×C4—22no—
299#67—68no—
300#67—68no—
301#67—616no—
302#67—616no—
303C2×Dic3—62no—
304C2×Dic3—64no—
305C2×Dic3—62no—
306C2×Dic3—64no—
307C2×Dic3—64no—
308C2×Dic3—616no—
309D12—64no—
310D12—616no—
311D12—64no—
312C4×D3—64no—
313C4×D3—64no—
314C4×D3—64no—
315C4×D3—62no—
316C4×D3—64no—
317C4×D3—64no—
318C4×D3—64no—
319C4×D3—62no—
320C4×D3—62no—
321C4×D3—62no—
322C4×D3—616no—
323C4×D3—68no—
324C4×D3—68no—
325C4×D3—616no—
326Dic6—64no—
327Dic6—68no—
328Dic6—68no—
329Dic6—64no—
330C2×C32—22no—
331C2×C32—42no—
332C2×C32#41612yescomplemented
333C2×C32C22×C22⋊C411yescharacteristic
334C3⋊D3—22no—
335C3⋊D3—42no—
336C3⋊D3#41612yescomplemented
337C3⋊D3C2×#13512yes—
338C24—91no—
339C24—181no—
340#41—22no—
341#41—94no—
342#41—94no—
343#41—94no—
344#41—184no—
345#41—184no—
346#41—184no—
347#41—184no—
348#41—182no—
349#41—182no—
350#41—182no—
351#41C2×#15714yescomplemented
352C2×Q8—92no—
353C2×Q8—92no—
354C2×Q8—91no—
355C2×Q8—181no—
356C2×Q8—181no—
357C2×Q8—181no—
358C2×Q8C2×#15711yescharacteristic
359C2×D4—21no—
360C2×D4—92no—
361C2×D4—92no—
362C2×D4—91no—
363C2×D4—181no—
364C2×D4—181no—
365C2×D4—181no—
366C2×D4—181no—
367C2×D4—184no—
368C2×D4—184no—
369C2×D4—181no—
370C2×D4—181no—
371C2×D4C2×#15711yescharacteristic
372C22×C4—21no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4—92no—
376C22×C4—91no—
377C22×C4—92no—
378C22×C4—92no—
379C22×C4—92no—
380C22×C4—91no—
381C22×C4—91no—
382C22×C4—181no—
383C22×C4—184no—
384C22×C4—184no—
385C22×C4—181no—
386C22×C4—181no—
387C22×C4—181no—
388C22×C4—182no—
389C22×C4C2×#15711yescharacteristic
390C2×C8—94no—
391C2×C8—182no—
392C2×C8—184no—
393C2×C8—182no—
394C2×C8—184no—
395C4⋊C4—94no—
396C4⋊C4—182no—
397C22⋊C4—184no—
398C42—184no—
399C22×C3—28no—
400C22×C3—22no—
401C22×C3—24no—
402C22×C3—44no—
403C22×C3—48no—
404C2×D3—62no—
405C2×D3—62no—
406C2×D3—68no—
407C2×D3—64no—
408C2×D3—68no—
409C2×D3—128no—
410C2×D3—128no—
411C2×D3—124no—
412C2×D3—1216no—
413C2×D3—1216no—
414C2×D3—128no—
415C3×C4—28no—
416C3×C4—22no—
417C3×C4—24no—
418C3×C4—22no—
419Dic3—62no—
420Dic3—62no—
421Dic3—64no—
422Dic3—68no—
423C32C2×#41611yescharacteristic, complemented, Sylow
424C23—21no—
425C23—91no—
426C23—92no—
427C23—92no—
428C23—91no—
429C23—184no—
430C23—182no—
431C23—182no—
432C23—181no—
433C23—364no—
434C23C22⋊#15711yescharacteristic
435Q8—21no—
436Q8—92no—
437Q8—182no—
438Q8—182no—
439Q8—181no—
440Q8C22×#15712yes—
441D4—24no—
442D4—21no—
443D4—92no—
444D4—184no—
445D4—182no—
446D4—182no—
447D4—184no—
448D4—184no—
449D4—181no—
450D4C22×#15712yes—
451C2×C4—21no—
452C2×C4—24no—
453C2×C4—91no—
454C2×C4—92no—
455C2×C4—91no—
456C2×C4—92no—
457C2×C4—92no—
458C2×C4—91no—
459C2×C4—91no—
460C2×C4—92no—
461C2×C4—92no—
462C2×C4—92no—
463C2×C4—92no—
464C2×C4—91no—
465C2×C4—91no—
466C2×C4—92no—
467C2×C4—184no—
468C2×C4—182no—
469C2×C4—182no—
470C2×C4—184no—
471C2×C4—181no—
472C2×C4—184no—
473C2×C4—184no—
474C2×C4—364no—
475C2×C4C22⋊#15712yes—
476C2×C4C22⋊#15711yescharacteristic
477C2×C4C22×#15711yescharacteristic
478C2×C4C22×#15712yes—
479C8—184no—
480C2×C3—22no—
481C2×C3—24no—
482C2×C3—44no—
483C2×C3—48no—
484D3—64no—
485D3—64no—
486D3—124no—
487D3—128no—
488C22—22no—
489C22—22no—
490C22—42no—
491C22—91no—
492C22—91no—
493C22—94no—
494C22—92no—
495C22—184no—
496C22—184no—
497C22—182no—
498C22—182no—
499C22—364no—
500C22—364no—
501C22—362no—
502C22C2×C22⋊#15712yes—
503C22C2×C22⋊#15711yescharacteristic
504C4—22no—
505C4—91no—
506C4—92no—
507C4—91no—
508C4—182no—
509C4—364no—
510C4C2×C22⋊#15712yes—
511C4C2×C22⋊#15711yescharacteristic
512C4C23×#15711yescharacteristic
513C3—22no—
514C2—22no—
515C2—42no—
516C2—92no—
517C2—92no—
518C2—182no—
519C2—362no—
520C2#1059384112yesdirect product factor
521C2C22×C22⋊#15711yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC32×C4C23×C4
FrattiniC4C23×#157
FittingC2×C32×#41C4
socleC22×C32C2×C22⋊C4
prime radicalC2×#41×C3⋊D3C2
cosocleC4×C3⋊D3C24
hypercenterC2×#41#157
hypocenterC32C2×#416
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#64286C2semidirect
3. C22×#3787C2semidirect
4. #10593841C2direct (N × H)
5. C2×#63784C2semidirect
6. C2×#63782C2semidirect
7. C2×C32×#41C4semidirect
10. #41×C3⋊D3C4semidirect
12. C2×#3832C4semidirect
15. C2×#3830C4semidirect
19. C2×#3828C4semidirect
25. #64286C22semidirect
31. C2×#3787C22semidirect
32. #63784C22semidirect
33. #63782C22semidirect
39. C32×#41C2×C4semidirect
51. #3832C2×C4semidirect
59. #3830C2×C4semidirect
69. #3828C2×C4semidirect
259. C2×#41#157semidirect
332. C2×C32#416semidirect
336. C3⋊D3#416semidirect
351. #41C2×#157semidirect
423. C32C2×#416semidirect
520. C2#10593841direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
C2×#642862
C22×#37872
#105938412
C2×#637842
C2×#637822
C2×#4169