Finite Group Databasebeta

← C2×#13068128 #14736301

Subgroups — C2×#13068128 #14736301

Order 2816.

758 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622691C211yesmaximal, characteristic, complemented
2C2×#10622454C211yesmaximal, characteristic
3C2×#10622696C211yesmaximal, characteristic
4C2×#10622451C211yesmaximal, characteristic
5#13068128C218yesmaximal, direct product factor
6C2×#10622118C211yesmaximal, characteristic, complemented
7C2×#10622124C211yesmaximal, characteristic, complemented
8C2×C11×#332C211yesmaximal, characteristic, complemented
9C2×C11×C4⋊Q8C2211yescharacteristic
10C22×#4325—21no—
11C22×#4314—21no—
12C22×#4313—21no—
13C2×C4×D44C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×#66899—21no—
18C2×(C2×D11)⋊C8—21no—
19C2×#66880—21no—
20#10622696—22no—
21#10622696C2214yes—
22#10622691—22no—
23#10622691C2214yescomplemented
24C2×#66871—21no—
25C2×#66871—21no—
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27C2×C4×C11⋊C8C2211yescharacteristic
28#10622454—22no—
29#10622454C2214yes—
30#10622451—22no—
31#10622451C2214yes—
32C11×#332C2214yescomplemented
33#10622124C2214yescomplemented
34#10622118C2214yescomplemented
35C22×Q8×C11—21no—
36C22×D44D411yescharacteristic
37C22×C4×D11—21no—
38C22×Dic22—21no—
39C22×C8×C11—21no—
40C22×C8×C11—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8C2312yes—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4325—24no—
49C2×#4325—44no—
50C2×(C2×D11)⋊C4—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11D411yescharacteristic
54C22×C11⋊C8—21no—
55C22×C11⋊C8D411yescharacteristic
56C22×C11⋊C8D411yescharacteristic
57C2×#4314—24no—
58C2×#4314—44no—
59C2×#4313—24no—
60C2×#4313—44no—
61C4×D44—21no—
62C4×D44—21no—
63C4×D44D412yes—
64C4×D44C2312yes—
65#66922—21no—
66#66922—21no—
67#66922—21no—
68#66922C2312yes—
69C11×C4⋊C8—21no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8C2312yes—
72C11×C4⋊C8C2312yes—
73#66899—24no—
74(C2×D11)⋊C8—24no—
75#66880—24no—
76#66871—24no—
77#66871—24no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)C2312yes—
80C4×C11⋊C8D412yes—
81C4×C11⋊C8C2312yes—
82C2×#1693—111nomaximal, Sylow
83C23×D11—21no—
84C2×Q8×C11—22no—
85C2×Q8×C11—41no—
86C2×Q8×C11—42no—
87C2×Q8×C11—42no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×Dic11—21no—
93C22×Dic11—41no—
94C2×D44—21no—
95C2×D44—22no—
96C2×D44—22no—
97C2×D44C2×D412yes—
98C2×C4×D11—22no—
99C2×C4×D11—22no—
100C2×C4×D11—42no—
101C2×C4×D11—42no—
102C2×Dic22—22no—
103C2×Dic22—41no—
104C2×Dic22—42no—
105C2×Dic22—42no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—42no—
109C2×C8×C11—42no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C42×C11C2411yescharacteristic
118#4325—48no—
119(C2×D11)⋊C4—22no—
120(C2×D11)⋊C4—22no—
121C4⋊Dic11—21no—
122C4⋊Dic11—22no—
123C4⋊Dic11—22no—
124C4⋊Dic11—41no—
125C4⋊Dic11—41no—
126C4⋊Dic11C2×D412yes—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—42no—
130C2×C11⋊C8SD1614yescomplemented
131C2×C11⋊C8C2×D412yes—
132C2×C11⋊C8C2×D412yes—
133#4314—48no—
134#4313—48no—
135C2×#500—111no—
136C2×#461—111no—
137C2×#461—111no—
138C2×#436—111no—
139#1693—118no—
140C2×#334—111no—
141C2×#332—111no—
142C2×#332D1111yescharacteristic, complemented
143C23×C11#12111yescharacteristic
144C22×D11—22no—
145C22×D11—42no—
146C22×D11—42no—
147C22×D11—42no—
148Q8×C11—42no—
149Q8×C11—42no—
150Q8×C11—82no—
151C2×C4×C11—22no—
152C2×C4×C11—42no—
153C2×C4×C11—82no—
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11C2×SD1612yes—
158C2×C4×C11AGL(1,ℤ/8)12yes—
159C2×C4×C11AGL(1,ℤ/8)12yes—
160C2×C4×C11#13712yes—
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C2×#4111yescharacteristic
164C2×Dic11—22no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—82no—
168D44—22no—
169D44—22no—
170D44—42no—
171C4×D11—42no—
172C4×D11—42no—
173C4×D11—44no—
174Dic22—42no—
175Dic22—42no—
176Dic22—82no—
177C8×C11—42no—
178C8×C11—42no—
179C11⋊C8—22no—
180C11⋊C8—42no—
181C11⋊C8C2×SD1614yescomplemented
182C22×SD16—221no—
183C22×SD16—221no—
184C22×M16—221no—
185C2×C4⋊Q8—111no—
186C2×C4⋊Q8C2×D1111yescharacteristic
187C2×C4×D4—111no—
188#500—114no—
189#500—222no—
190#461—114no—
191#461—114no—
192#461—222no—
193#461—222no—
194#436—114no—
195#436—222no—
196C2×#107—221no—
197C2×#107—221no—
198C2×C4⋊C8—111no—
199C2×C4⋊C8C2×D1111yescharacteristic
200C2×C4⋊C8C2×D1111yescharacteristic
201C2×#103—221no—
202C2×#103—221no—
203C2×C22⋊C8—221no—
204C2×C4×C8—111no—
205#334—114no—
206#332—114no—
207#332C2×D1114yescomplemented
208C22×C11#46112yes—
209C22×C11#46912yes—
210C22×C11#47312yes—
211C22×C11C2×#12111yescharacteristic
212C2×D11—42no—
213C2×D11—42no—
214C2×D11—42no—
215C2×D11—84no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—82no—
219C4×C11#46112yes—
220C4×C11#46912yes—
221C4×C11C22×SD1611yescharacteristic
222C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
223C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
224C4×C11C2×#13711yescharacteristic
225Dic11—42no—
226Dic11—82no—
227C22×Q8—21no—
228C22×Q8—221no—
229C22×D4—111no—
230C23×C4—221no—
231C2×SD16—224no—
232C2×SD16—224no—
233C2×SD16—444no—
234C2×SD16—444no—
235C2×M16—224no—
236C2×M16—444no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—111no—
240C22×C8—111no—
241C22×C8—221no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—112no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248C4⋊Q8—221no—
249C4⋊Q8C22×D1112yes—
250C4×D4—112no—
251C4×D4—112no—
252C4×D4—221no—
253C4×D4—221no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C42C22×D1111yescharacteristic
261#107—224no—
262#107—224no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—112no—
266C4⋊C8—221no—
267C4⋊C8C22×D1112yes—
268C4⋊C8C22×D1112yes—
269#103—224no—
270#103—224no—
271C22⋊C8—224no—
272C4×C8—112no—
273C4×C8—112no—
274C2×C11#169314yescomplemented
275C2×C11C2×#46111yescharacteristic
276C2×C11C2×#46911yescharacteristic
277C2×C11C2×#47311yescharacteristic
278D11—82no—
279C24—221no—
280C2×Q8—22no—
281C2×Q8—41no—
282C2×Q8—42no—
283C2×Q8—42no—
284C2×Q8—222no—
285C2×Q8—441no—
286C2×Q8—442no—
287C2×Q8—442no—
288C2×D4—112no—
289C2×D4—221no—
290C2×D4—222no—
291C2×D4—222no—
292C22×C4—41no—
293C22×C4—221no—
294C22×C4—222no—
295C22×C4—222no—
296C22×C4—442no—
297C22×C4—442no—
298C22×C4—441no—
299C22×C4#433911yescharacteristic
300C22×C4D4×D1111yescharacteristic
301C22×C4D4×D1111yescharacteristic
302SD16—448no—
303SD16—448no—
304M16—448no—
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—114no—
310C2×C8—112no—
311C2×C8—112no—
312C2×C8—222no—
313C2×C8—222no—
314C2×C8—442no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—112no—
320C4⋊C4—221no—
321C4⋊C4—222no—
322C4⋊C4—222no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C22⋊C4—222no—
326C22⋊C4—222no—
327C42#433911yescharacteristic
328C42D4×D1111yescharacteristic
329C42D4×D1111yescharacteristic
330C42C23×D1111yescharacteristic
331C11C2×#169311yescharacteristic, complemented, Sylow
332C23—222no—
333C23—442no—
334C23—442no—
335C23—442no—
336C23#6693711yescharacteristic
337Q8—42no—
338Q8—42no—
339Q8—82no—
340Q8—442no—
341Q8—442no—
342Q8—882no—
343D4—222no—
344D4—222no—
345D4—442no—
346C2×C4—22no—
347C2×C4—42no—
348C2×C4—82no—
349C2×C4—222no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4—442no—
353C2×C4—444no—
354C2×C4—442no—
355C2×C4—882no—
356C2×C4#6693711yescharacteristic
357C2×C4#6693711yescharacteristic
358C2×C4#6693711yescharacteristic
359C2×C4#6696412yes—
360C2×C4SD16×D1112yes—
361C2×C4#6696712yes—
362C2×C4#6697112yes—
363C2×C4C2×#433911yescharacteristic
364C2×C4C2×D4×D1111yescharacteristic
365C2×C4C2×D4×D1111yescharacteristic
366C8—42no—
367C8—42no—
368C8—114no—
369C8—222no—
370C8—442no—
371C22—442no—
372C22—442no—
373C22—442no—
374C22—884no—
375C22#1062236812yes—
376C22#1062239512yes—
377C22#1062243112yes—
378C22C2×#6693711yescharacteristic
379C4—21no—
380C4—21no—
381C4—82no—
382C4—442no—
383C4—882no—
384C4#1062239512yes—
385C4#1062243112yes—
386C4C2×#6696411yescharacteristic
387C4C2×SD16×D1111yescharacteristic
388C4C2×#6696711yescharacteristic
389C4C2×#6697111yescharacteristic
390C2—882no—
391C2#1306812814yesdirect product factor
392C2C2×#1062243111yescharacteristic
393C2C2×#1062239511yescharacteristic
394C2C2×#1062236811yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#332C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenterC2×#332D11
hypocenterC11C2×#1693
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
1. C2×#10622691C2semidirect
5. #13068128C2direct (N × H)
6. C2×#10622118C2semidirect
7. C2×#10622124C2semidirect
8. C2×C11×#332C2semidirect
23. #10622691C22semidirect
32. C11×#332C22semidirect
33. #10622124C22semidirect
34. #10622118C22semidirect
130. C2×C11⋊C8SD16semidirect
142. C2×#332D11semidirect
181. C11⋊C8C2×SD16semidirect
207. #332C2×D11semidirect
274. C2×C11#1693semidirect
331. C11C2×#1693semidirect
391. C2#13068128direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226912
C2×#106224542
C2×#106226962
C2×#106224512
#130681282
C2×#106221182
C2×#106221242
C2×C11×#3322
C2×#169311