Finite Group Databasebeta

← C2×#13068114 #14736293

Subgroups — C2×#13068114 #14736293

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622692C211yesmaximal, characteristic, complemented
2C2×#10622455C211yesmaximal, characteristic
3C2×#10622696C211yesmaximal, characteristic
4C2×#10622451C211yesmaximal, characteristic
5#13068114C218yesmaximal, direct product factor
6C2×#10622117C211yesmaximal, characteristic, complemented
7C2×#10622119C211yesmaximal, characteristic, complemented
8C2×C11×#332C211yesmaximal, characteristic, complemented
9C2×C11×C4⋊Q8C2211yescharacteristic
10C22×#4325—21no—
11C22×#4313—21no—
12C2×C4×D44C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×#66899—21no—
17C2×#66885—21no—
18C2×(C2×D11)⋊C8—21no—
19C2×#66881—21no—
20#10622696—22no—
21#10622696C2214yes—
22#10622692—22no—
23#10622692C2214yescomplemented
24C2×#66872—21no—
25C2×#66872—21no—
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27C2×C4×C11⋊C8C2211yescharacteristic
28#10622455—22no—
29#10622455C2214yes—
30#10622451—22no—
31#10622451C2214yes—
32C11×#332C2214yescomplemented
33#10622119C2214yescomplemented
34#10622117C2214yescomplemented
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×#4313—24no—
58C2×#4313—44no—
59C4×D44—21no—
60C4×D44—21no—
61C4×D44D412yes—
62C4×D44C2312yes—
63#66922—21no—
64#66922—21no—
65#66922—21no—
66#66922C2312yes—
67C11×C4⋊C8—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2312yes—
70C11×C4⋊C8C2312yes—
71#66899—24no—
72#66885—24no—
73(C2×D11)⋊C8—24no—
74#66881—24no—
75#66872—24no—
76#66872—24no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)C2312yes—
79C4×C11⋊C8D412yes—
80C4×C11⋊C8C2312yes—
81C2×#1691—111nomaximal, Sylow
82C23×D11—21no—
83C2×Q8×C11—22no—
84C2×Q8×C11—41no—
85C2×Q8×C11—42no—
86C2×Q8×C11—42no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×Dic11—21no—
92C22×Dic11—41no—
93C2×D44—21no—
94C2×D44—22no—
95C2×D44—22no—
96C2×D44C2×D412yes—
97C2×C4×D11—22no—
98C2×C4×D11—22no—
99C2×C4×D11—42no—
100C2×C4×D11—42no—
101C2×Dic22—22no—
102C2×Dic22—41no—
103C2×Dic22—82no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—42no—
107C2×C8×C11—42no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115C42×C11C2411yescharacteristic
116#4325—48no—
117(C2×D11)⋊C4—22no—
118(C2×D11)⋊C4—22no—
119C4⋊Dic11—21no—
120C4⋊Dic11—22no—
121C4⋊Dic11—22no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124C4⋊Dic11C2×D412yes—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—42no—
128C2×C11⋊C8SD1614yescomplemented
129C2×C11⋊C8C2×D412yes—
130C2×C11⋊C8C2×D412yes—
131#4313—48no—
132C2×#498—111no—
133C2×#476—111no—
134C2×#461—111no—
135C2×#436—111no—
136#1691—118no—
137C2×#335—111no—
138C2×#333—111no—
139C2×#332D1111yescharacteristic, complemented
140C23×C11#12111yescharacteristic
141C22×D11—22no—
142C22×D11—42no—
143C22×D11—42no—
144C22×D11—42no—
145Q8×C11—42no—
146Q8×C11—42no—
147Q8×C11—82no—
148C2×C4×C11—22no—
149C2×C4×C11—42no—
150C2×C4×C11—82no—
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11C2×SD1612yes—
155C2×C4×C11AGL(1,ℤ/8)12yes—
156C2×C4×C11#13712yes—
157C2×C4×C11#13712yes—
158C2×C4×C11C22×D411yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C2×C4×C11C2×#4111yescharacteristic
161C2×Dic11—22no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11—82no—
165D44—22no—
166D44—22no—
167D44—42no—
168C4×D11—42no—
169C4×D11—42no—
170C4×D11—44no—
171Dic22—82no—
172Dic22—82no—
173C8×C11—42no—
174C8×C11—42no—
175C11⋊C8—22no—
176C11⋊C8—42no—
177C11⋊C8C2×SD1614yescomplemented
178C22×SD16—221no—
179C22×M16—221no—
180C2×C4⋊Q8—111no—
181C2×C4⋊Q8C2×D1111yescharacteristic
182C2×C4×D4—111no—
183#498—114no—
184#498—222no—
185#476—114no—
186#476—222no—
187#461—114no—
188#461—222no—
189#436—114no—
190#436—222no—
191C2×#106—221no—
192C2×#106—221no—
193C2×#106—221no—
194C2×C4⋊C8—111no—
195C2×C4⋊C8C2×D1111yescharacteristic
196C2×C4⋊C8C2×D1111yescharacteristic
197C2×#103—221no—
198C2×#102—221no—
199C2×C22⋊C8—221no—
200C2×C4×C8—111no—
201#335—114no—
202#333—114no—
203#332C2×D1114yescomplemented
204C22×C11#46112yes—
205C22×C11#46812yes—
206C22×C11#47112yes—
207C22×C11C2×#12111yescharacteristic
208C2×D11—42no—
209C2×D11—42no—
210C2×D11—42no—
211C2×D11—84no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—82no—
215C4×C11#46112yes—
216C4×C11#46812yes—
217C4×C11C22×SD1611yescharacteristic
218C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
219C4×C11C2×#13711yescharacteristic
220C4×C11C2×#13711yescharacteristic
221Dic11—42no—
222Dic11—82no—
223C22×Q8—21no—
224C22×Q8—221no—
225C22×D4—111no—
226C23×C4—221no—
227C2×SD16—224no—
228C2×SD16—444no—
229C2×M16—224no—
230C2×M16—444no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—111no—
234C22×C8—111no—
235C22×C8—221no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—112no—
240C4⋊Q8—221no—
241C4⋊Q8—221no—
242C4⋊Q8—221no—
243C4⋊Q8C22×D1112yes—
244C4×D4—112no—
245C4×D4—112no—
246C4×D4—221no—
247C4×D4—221no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4—221no—
253C2×C22⋊C4—221no—
254C2×C42C22×D1111yescharacteristic
255#106—224no—
256#106—224no—
257#106—224no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—112no—
261C4⋊C8—221no—
262C4⋊C8C22×D1112yes—
263C4⋊C8C22×D1112yes—
264#103—224no—
265#102—224no—
266C22⋊C8—224no—
267C4×C8—112no—
268C4×C8—112no—
269C2×C11#169114yescomplemented
270C2×C11C2×#46111yescharacteristic
271C2×C11C2×#46811yescharacteristic
272C2×C11C2×#47111yescharacteristic
273D11—82no—
274C24—221no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—42no—
278C2×Q8—42no—
279C2×Q8—222no—
280C2×Q8—441no—
281C2×Q8—882no—
282C2×D4—112no—
283C2×D4—221no—
284C2×D4—222no—
285C2×D4—222no—
286C22×C4—41no—
287C22×C4—221no—
288C22×C4—222no—
289C22×C4—222no—
290C22×C4—442no—
291C22×C4—442no—
292C22×C4—441no—
293C22×C4#433911yescharacteristic
294C22×C4D4×D1111yescharacteristic
295C22×C4D4×D1111yescharacteristic
296SD16—448no—
297M16—448no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—42no—
301C2×C8—42no—
302C2×C8—114no—
303C2×C8—112no—
304C2×C8—112no—
305C2×C8—222no—
306C2×C8—222no—
307C2×C8—442no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—112no—
313C4⋊C4—221no—
314C4⋊C4—222no—
315C4⋊C4—222no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C22⋊C4—222no—
319C22⋊C4—222no—
320C42#433911yescharacteristic
321C42D4×D1111yescharacteristic
322C42D4×D1111yescharacteristic
323C42C23×D1111yescharacteristic
324C11C2×#169111yescharacteristic, complemented, Sylow
325C23—222no—
326C23—442no—
327C23—442no—
328C23—442no—
329C23#6693711yescharacteristic
330Q8—42no—
331Q8—42no—
332Q8—82no—
333Q8—882no—
334Q8—882no—
335D4—222no—
336D4—222no—
337D4—442no—
338C2×C4—22no—
339C2×C4—42no—
340C2×C4—82no—
341C2×C4—222no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—444no—
346C2×C4—442no—
347C2×C4—882no—
348C2×C4#6693711yescharacteristic
349C2×C4#6693711yescharacteristic
350C2×C4#6693711yescharacteristic
351C2×C4#6696412yes—
352C2×C4SD16×D1112yes—
353C2×C4#6696812yes—
354C2×C4#6697112yes—
355C2×C4C2×#433911yescharacteristic
356C2×C4C2×D4×D1111yescharacteristic
357C2×C4C2×D4×D1111yescharacteristic
358C8—42no—
359C8—42no—
360C8—114no—
361C8—222no—
362C8—442no—
363C22—442no—
364C22—442no—
365C22—442no—
366C22—884no—
367C22#1062236712yes—
368C22#1062239312yes—
369C22#1062243112yes—
370C22C2×#6693711yescharacteristic
371C4—21no—
372C4—21no—
373C4—82no—
374C4—442no—
375C4—882no—
376C4#1062239312yes—
377C4#1062243112yes—
378C4C2×#6696411yescharacteristic
379C4C2×SD16×D1111yescharacteristic
380C4C2×#6696811yescharacteristic
381C4C2×#6697111yescharacteristic
382C2—882no—
383C2#1306811414yesdirect product factor
384C2C2×#1062243111yescharacteristic
385C2C2×#1062239311yescharacteristic
386C2C2×#1062236711yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#332C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenterC2×#332D11
hypocenterC11C2×#1691
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×#10622692C2semidirect
5. #13068114C2direct (N × H)
6. C2×#10622117C2semidirect
7. C2×#10622119C2semidirect
8. C2×C11×#332C2semidirect
23. #10622692C22semidirect
32. C11×#332C22semidirect
33. #10622119C22semidirect
34. #10622117C22semidirect
128. C2×C11⋊C8SD16semidirect
139. C2×#332D11semidirect
177. C11⋊C8C2×SD16semidirect
203. #332C2×D11semidirect
269. C2×C11#1691semidirect
324. C11C2×#1691semidirect
383. C2#13068114direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226922
C2×#106224552
C2×#106226962
C2×#106224512
#130681142
C2×#106221172
C2×#106221192
C2×C11×#3322
C2×#169111