Finite Group Databasebeta

← C2×#10593840 #11857904

Subgroups — C2×#10593840 #11857904

Order 1152.

1706 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic
2C22×C4⋊#157C211yesmaximal, characteristic, complemented
3C2×#64283C211yesmaximal, characteristic, complemented
4#10593840C218yesmaximal, direct product factor
5C2×#63784C212yesmaximal, complemented
6C2×#63782C212yesmaximal, complemented
7C23×#157—21no—
8C2×C32×#41C411yescharacteristic, complemented
9#41×C3⋊D3—22no—
10#41×C3⋊D3—22no—
11#41×C3⋊D3C414yescomplemented
12#41×C3⋊D3C2214yes—
13C2×#3832C411yescharacteristic, complemented
14C2×Q8×C3⋊D3C2211yescharacteristic
15C2×#3830—21no—
16C2×#3830C411yescharacteristic, complemented
17C2×D4×C3⋊D3—21no—
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3828—21no—
20C2×#3828C411yescharacteristic, complemented
21C22×C4×C3⋊D3—21no—
22C22×C4×C3⋊D3C2211yescharacteristic
23C2×#3792—21no—
24C2×C4⋊#157—21no—
25C2×C4⋊#157—22no—
26C2×C4⋊#157C2212yes—
27C2×C4⋊#157C2214yescomplemented
28#64283—22no—
29#64283C2214yescomplemented
30C2×#3788—21no—
31C2×#3787C2212yes—
32#63784C2218yescomplemented
33#63782C2218yescomplemented
34C2×D3×#41—62no—
35C23×C3⋊D3—21no—
36C23×C3⋊D3D411yescharacteristic
37C22×#157—22no—
38C22×#157—24no—
39C22×#157—44no—
40C32×#41—22no—
41C32×#41C2×C414yescomplemented
42C2×C32×Q8C2×C411yescharacteristic, complemented
43C2×C32×D4—21no—
44C2×C32×D4C2×C411yescharacteristic, complemented
45C22×C32×C4—21no—
46C22×C32×C4C2×C411yescharacteristic
47C2×#638—21no—
48C2×#638—21no—
49C2×#638—21no—
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3D411yescharacteristic
52#3832—22no—
53#3832C2×C414yescomplemented
54Q8×C3⋊D3—21no—
55Q8×C3⋊D3—21no—
56Q8×C3⋊D3C2×C412yescomplemented
57Q8×C3⋊D3C2312yes—
58#3830—24no—
59#3830—24no—
60#3830—22no—
61#3830C2×C414yescomplemented
62D4×C3⋊D3—24no—
63D4×C3⋊D3—24no—
64D4×C3⋊D3—21no—
65D4×C3⋊D3—21no—
66D4×C3⋊D3C2×C412yescomplemented
67D4×C3⋊D3C2312yes—
68#3828—22no—
69#3828—24no—
70#3828—24no—
71#3828C2×C414yescomplemented
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
74C2×C4×C3⋊D3—21no—
75C2×C4×C3⋊D3—21no—
76C2×C4×C3⋊D3—21no—
77C2×C4×C3⋊D3—24no—
78C2×C4×C3⋊D3—24no—
79C2×C4×C3⋊D3C2×C411yescharacteristic
80C2×C4×C3⋊D3C2×C412yes—
81C2×C4×C3⋊D3D411yescharacteristic
82C2×C4×C3⋊D3D412yes—
83C2×C4×C3⋊D3D411yescharacteristic
84C2×C4×C3⋊D3D412yes—
85C2×C4×C3⋊D3C2311yescharacteristic
86C2×C4×C3⋊D3C2312yes—
87C2×#634—21no—
88C2×#634C2×C411yescharacteristic, complemented
89#3792—24no—
90C2×#622—22no—
91C4⋊#157—22no—
92C4⋊#157—24no—
93C4⋊#157C2314yes—
94#3788—24no—
95#3787—22no—
96#3787C2314yes—
97C2×#417—91nomaximal, Sylow
98C2×C3×#41—22no—
99D3×#41—68no—
100D3×#41—68no—
101D3×#41—68no—
102D3×#41—68no—
103C2×#239—62no—
104C2×D3×Q8—62no—
105C2×#237—62no—
106C2×#237—64no—
107C2×D3×D4—62no—
108C2×D3×D4—64no—
109C2×#235—62no—
110C2×#235—64no—
111C22×C4×D3—62no—
112C22×C4×D3—64no—
113C23×C32—21no—
114C23×C32C22⋊C411yescharacteristic
115C22×C3⋊D3—21no—
116C22×C3⋊D3—22no—
117C22×C3⋊D3—22no—
118C22×C3⋊D3—22no—
119C22×C3⋊D3—22no—
120C22×C3⋊D3—42no—
121C22×C3⋊D3—42no—
122C22×C3⋊D3C22⋊C411yescharacteristic
123C22×C3⋊D3C22⋊C412yes—
124C22×C3⋊D3C2×D412yes—
125C22×C3⋊D3C2×D411yescharacteristic
126C2×#157—24no—
127C2×#157—48no—
128C2×#157—44no—
129C32×Q8—21no—
130C32×Q8C22×C412yescomplemented
131C32×D4—24no—
132C32×D4—21no—
133C32×D4C22×C412yescomplemented
134C2×C32×C4—21no—
135C2×C32×C4—24no—
136C2×C32×C4C22⋊C411yescharacteristic
137C2×C32×C4C22⋊C412yes—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C22×C412yes—
140#638—24no—
141#638—24no—
142#638—22no—
143#638—22no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—24no—
146C2×C3⋊Dic3C22⋊C411yescharacteristic
147C2×C3⋊Dic3C22⋊C412yes—
148C2×C3⋊Dic3C2×D411yescharacteristic
149C2×C3⋊Dic3C2×D412yes—
150C4⋊(C3⋊D3)—24no—
151C4⋊(C3⋊D3)—21no—
152C4⋊(C3⋊D3)C22×C412yescomplemented
153C4×C3⋊D3—22no—
154C4×C3⋊D3—22no—
155C4×C3⋊D3—24no—
156C4×C3⋊D3—24no—
157C4×C3⋊D3C22⋊C412yes—
158C4×C3⋊D3C22⋊C412yes—
159C4×C3⋊D3C22⋊C412yes—
160C4×C3⋊D3C22×C411yescharacteristic
161C4×C3⋊D3C22×C412yes—
162C4×C3⋊D3C2×D412yes—
163C4×C3⋊D3C2×D411yescharacteristic
164C4×C3⋊D3C2×D411yescharacteristic
165C4×C3⋊D3C2×D412yes—
166C4×C3⋊D3C2411yescharacteristic
167#634—21no—
168#634—22no—
169#634—22no—
170#634C22×C412yescomplemented
171#622—24no—
172C22×#41—91no—
173C22×M16—91no—
174C22×C4⋊C4—91no—
175#417—98no—
176C2×#103—92no—
177C2×#102—92no—
178C23×D3—62no—
179C23×D3—64no—
180C3×#41—28no—
181C3×#41—28no—
182C2×C3×Q8—22no—
183C2×C3×D4—24no—
184C2×C3×D4—22no—
185C22×C3×C4—24no—
186C22×C3×C4—22no—
187C2×#67—64no—
188C2×#67—64no—
189C2×#67—64no—
190C22×Dic3—62no—
191C22×Dic3—64no—
192#239—68no—
193#239—68no—
194D3×Q8—64no—
195D3×Q8—64no—
196D3×Q8—64no—
197D3×Q8—64no—
198#237—68no—
199#237—68no—
200#237—616no—
201#237—616no—
202D3×D4—64no—
203D3×D4—64no—
204D3×D4—64no—
205D3×D4—64no—
206D3×D4—616no—
207D3×D4—616no—
208#235—68no—
209#235—616no—
210#235—616no—
211#235—68no—
212C2×D12—62no—
213C2×D12—64no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—64no—
219C2×C4×D3—64no—
220C2×C4×D3—64no—
221C2×C4×D3—64no—
222C2×C4×D3—64no—
223C2×C4×D3—64no—
224C2×C4×D3—64no—
225C2×C4×D3—616no—
226C2×C4×D3—616no—
227C2×Dic6—62no—
228C2×Dic6—64no—
229C22×C32—22no—
230C22×C32—22no—
231C22×C32—42no—
232C22×C32C2×C22⋊C412yes—
233C22×C32C2×C22⋊C411yescharacteristic
234C2×C3⋊D3—22no—
235C2×C3⋊D3—22no—
236C2×C3⋊D3—22no—
237C2×C3⋊D3—22no—
238C2×C3⋊D3—24no—
239C2×C3⋊D3—42no—
240C2×C3⋊D3—42no—
241C2×C3⋊D3—42no—
242C2×C3⋊D3—44no—
243C2×C3⋊D3C2×C22⋊C412yes—
244C2×C3⋊D3C2×C22⋊C411yescharacteristic
245C2×C3⋊D3AGL(1,ℤ/8)12yes—
246C2×C3⋊D3#13712yes—
247C2×C3⋊D3C22×D411yescharacteristic
248#157—44no—
249C32×C4—22no—
250C32×C4C2×C22⋊C411yescharacteristic
251C32×C4C2×C22⋊C412yes—
252C32×C4C23×C411yescharacteristic
253C3⋊Dic3—22no—
254C3⋊Dic3C2×C22⋊C411yescharacteristic
255C3⋊Dic3C2×C22⋊C412yes—
256C3⋊Dic3C22×D411yescharacteristic
257C2×#41—94no—
258C2×#41—94no—
259C2×#41—91no—
260C2×#41—91no—
261C2×#41—91no—
262C2×#41—181no—
263C2×#41—181no—
264C2×#41—182no—
265C2×#41—182no—
266C2×#41#15711yescharacteristic, complemented
267C22×Q8—91no—
268C22×D4—91no—
269C22×D4—181no—
270C23×C4—91no—
271C23×C4—181no—
272C23×C4—181no—
273C2×M16—94no—
274C2×M16—181no—
275C2×M16—182no—
276C2×M16—181no—
277C22×C8—92no—
278C2×C4⋊C4—92no—
279C2×C4⋊C4—94no—
280C2×C4⋊C4—181no—
281C2×C4⋊C4—182no—
282#103—98no—
283#102—98no—
284C23×C3—24no—
285C23×C3—22no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—64no—
289C22×D3—64no—
290C22×D3—64no—
291C22×D3—68no—
292C22×D3—68no—
293C22×D3—124no—
294C22×D3—124no—
295C22×D3—128no—
296C22×D3—128no—
297C3×Q8—24no—
298C3×Q8—24no—
299C3×D4—216no—
300C3×D4—24no—
301C3×D4—24no—
302C2×C3×C4—24no—
303C2×C3×C4—216no—
304C2×C3×C4—22no—
305C2×C3×C4—24no—
306C2×C3×C4—22no—
307C2×C3×C4—24no—
308#67—68no—
309#67—68no—
310#67—616no—
311#67—616no—
312C2×Dic3—62no—
313C2×Dic3—64no—
314C2×Dic3—62no—
315C2×Dic3—64no—
316C2×Dic3—64no—
317C2×Dic3—616no—
318D12—64no—
319D12—616no—
320D12—64no—
321C4×D3—64no—
322C4×D3—64no—
323C4×D3—64no—
324C4×D3—62no—
325C4×D3—64no—
326C4×D3—64no—
327C4×D3—64no—
328C4×D3—62no—
329C4×D3—62no—
330C4×D3—62no—
331C4×D3—616no—
332C4×D3—68no—
333C4×D3—68no—
334C4×D3—616no—
335Dic6—64no—
336Dic6—68no—
337Dic6—68no—
338Dic6—64no—
339C2×C32—22no—
340C2×C32—42no—
341C2×C32#41712yescomplemented
342C2×C32C22×C22⋊C411yescharacteristic
343C3⋊D3—22no—
344C3⋊D3—42no—
345C3⋊D3#41712yescomplemented
346C3⋊D3C2×AGL(1,ℤ/8)11yescharacteristic
347C3⋊D3C2×#13711yescharacteristic
348C24—91no—
349C24—181no—
350#41—22no—
351#41—94no—
352#41—94no—
353#41—94no—
354#41—184no—
355#41—184no—
356#41—184no—
357#41—184no—
358#41—182no—
359#41—182no—
360#41—182no—
361#41C2×#15714yescomplemented
362C2×Q8—92no—
363C2×Q8—92no—
364C2×Q8—91no—
365C2×Q8—181no—
366C2×Q8—181no—
367C2×Q8—181no—
368C2×Q8C2×#15711yescharacteristic, complemented
369C2×D4—21no—
370C2×D4—92no—
371C2×D4—92no—
372C2×D4—91no—
373C2×D4—181no—
374C2×D4—181no—
375C2×D4—181no—
376C2×D4—181no—
377C2×D4—184no—
378C2×D4—184no—
379C2×D4—181no—
380C2×D4—181no—
381C2×D4C2×#15711yescharacteristic, complemented
382C22×C4—21no—
383C22×C4—91no—
384C22×C4—91no—
385C22×C4—92no—
386C22×C4—92no—
387C22×C4—91no—
388C22×C4—91no—
389C22×C4—92no—
390C22×C4—92no—
391C22×C4—91no—
392C22×C4—181no—
393C22×C4—184no—
394C22×C4—184no—
395C22×C4—181no—
396C22×C4—181no—
397C22×C4—181no—
398C22×C4—182no—
399C22×C4—184no—
400C22×C4—364no—
401C22×C4C2×#15711yescharacteristic
402M16—184no—
403M16—184no—
404C2×C8—94no—
405C2×C8—182no—
406C2×C8—182no—
407C4⋊C4—94no—
408C4⋊C4—184no—
409C4⋊C4—182no—
410C22×C3—28no—
411C22×C3—24no—
412C22×C3—22no—
413C22×C3—44no—
414C22×C3—48no—
415C2×D3—62no—
416C2×D3—62no—
417C2×D3—64no—
418C2×D3—64no—
419C2×D3—64no—
420C2×D3—68no—
421C2×D3—124no—
422C2×D3—124no—
423C2×D3—128no—
424C2×D3—124no—
425C2×D3—128no—
426C2×D3—128no—
427C2×D3—1216no—
428C2×D3—128no—
429C3×C4—28no—
430C3×C4—22no—
431C3×C4—24no—
432C3×C4—22no—
433Dic3—62no—
434Dic3—62no—
435Dic3—64no—
436Dic3—68no—
437C32C2×#41711yescharacteristic, complemented, Sylow
438C23—21no—
439C23—91no—
440C23—92no—
441C23—92no—
442C23—91no—
443C23—182no—
444C23—182no—
445C23—182no—
446C23—182no—
447C23—181no—
448C23—362no—
449C23—362no—
450C23C22⋊#15711yescharacteristic
451Q8—21no—
452Q8—92no—
453Q8—182no—
454Q8—182no—
455Q8—181no—
456Q8C22×#15712yescomplemented
457D4—24no—
458D4—21no—
459D4—92no—
460D4—184no—
461D4—182no—
462D4—182no—
463D4—184no—
464D4—184no—
465D4—181no—
466D4C22×#15712yescomplemented
467C2×C4—21no—
468C2×C4—24no—
469C2×C4—92no—
470C2×C4—92no—
471C2×C4—91no—
472C2×C4—91no—
473C2×C4—92no—
474C2×C4—91no—
475C2×C4—91no—
476C2×C4—92no—
477C2×C4—92no—
478C2×C4—92no—
479C2×C4—92no—
480C2×C4—91no—
481C2×C4—91no—
482C2×C4—92no—
483C2×C4—184no—
484C2×C4—182no—
485C2×C4—182no—
486C2×C4—184no—
487C2×C4—181no—
488C2×C4—184no—
489C2×C4—184no—
490C2×C4—364no—
491C2×C4—368no—
492C2×C4C22⋊#15712yes—
493C2×C4C22⋊#15711yescharacteristic
494C2×C4C22×#15712yes—
495C2×C4C22×#15711yescharacteristic
496C8—184no—
497C2×C3—22no—
498C2×C3—24no—
499C2×C3—44no—
500C2×C3—48no—
501D3—62no—
502D3—62no—
503D3—64no—
504D3—124no—
505D3—128no—
506C22—22no—
507C22—22no—
508C22—42no—
509C22—91no—
510C22—91no—
511C22—92no—
512C22—92no—
513C22—92no—
514C22—182no—
515C22—182no—
516C22—184no—
517C22—182no—
518C22—182no—
519C22—362no—
520C22—362no—
521C22—364no—
522C22—362no—
523C22C2×C22⋊#15712yes—
524C22C2×C22⋊#15711yescharacteristic
525C4—22no—
526C4—91no—
527C4—92no—
528C4—91no—
529C4—182no—
530C4—364no—
531C4C2×C22⋊#15712yes—
532C4C2×C22⋊#15711yescharacteristic
533C4C23×#15711yescharacteristic
534C3—22no—
535C2—22no—
536C2—42no—
537C2—91no—
538C2—91no—
539C2—92no—
540C2—182no—
541C2—362no—
542C2#1059384012yesdirect product factor
543C2C22×C22⋊#15711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#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×#417
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊#157C2semidirect
3. C2×#64283C2semidirect
4. #10593840C2direct (N × H)
5. C2×#63784C2semidirect
6. C2×#63782C2semidirect
8. C2×C32×#41C4semidirect
11. #41×C3⋊D3C4semidirect
13. C2×#3832C4semidirect
16. C2×#3830C4semidirect
20. C2×#3828C4semidirect
27. C2×C4⋊#157C22semidirect
29. #64283C22semidirect
32. #63784C22semidirect
33. #63782C22semidirect
41. C32×#41C2×C4semidirect
42. C2×C32×Q8C2×C4semidirect
44. C2×C32×D4C2×C4semidirect
53. #3832C2×C4semidirect
56. Q8×C3⋊D3C2×C4semidirect
61. #3830C2×C4semidirect
66. D4×C3⋊D3C2×C4semidirect
71. #3828C2×C4semidirect
73. C2×C4⋊(C3⋊D3)C2×C4semidirect
88. C2×#634C2×C4semidirect
130. C32×Q8C22×C4semidirect
133. C32×D4C22×C4semidirect
152. C4⋊(C3⋊D3)C22×C4semidirect
170. #634C22×C4semidirect
266. C2×#41#157semidirect
341. C2×C32#417semidirect
345. C3⋊D3#417semidirect
361. #41C2×#157semidirect
368. C2×Q8C2×#157semidirect
381. C2×D4C2×#157semidirect
437. C32C2×#417semidirect
456. Q8C22×#157semidirect
466. D4C22×#157semidirect
542. C2#10593840direct (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
C22×C4⋊#1572
C2×#642832
#105938402
C2×#637842
C2×#637822
C2×#4179