Finite Group Databasebeta

← C2×#13068029 #14736146

Subgroups — C2×#13068029 #14736146

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622704C211yesmaximal, characteristic, complemented
2C2×#10622688C211yesmaximal, characteristic
3C2×C8×Dic22C211yesmaximal, characteristic, complemented
4#13068029C218yesmaximal, direct product factor
5C2×#10622095C211yesmaximal, characteristic, complemented
6C2×#10622184C211yesmaximal, characteristic, complemented
7C2×#10622182C211yesmaximal, characteristic
8C2×C11×#486C211yesmaximal, characteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C22×#4324—21no—
12C2×C4×Dic22C2211yescharacteristic
13C11×#486—22no—
14C11×#486C2214yes—
15C2×C11×#102—21no—
16C2×C11×#102—21no—
17C2×C4×C8×C11C2211yescharacteristic
18C2×#66896—21no—
19C2×Dic11⋊C8—21no—
20C2×C8×Dic11—21no—
21#10622704—22no—
22#10622704C2214yescomplemented
23#10622688—22no—
24#10622688C2214yes—
25C2×#66874—21no—
26C2×#66871—21no—
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C8×Dic22—22no—
31C8×Dic22C2214yescomplemented
32#10622184C2214yescomplemented
33#10622182C2214yes—
34#10622095C2214yescomplemented
35C22×Q8×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×Dic22D411yescharacteristic
40C22×C8×C11D411yescharacteristic
41C22×C8×C11D411yescharacteristic
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8C2312yes—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127—21no—
49C11×#127C2312yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4324—24no—
54C2×#4324—44no—
55C2×C4⋊Dic11D411yescharacteristic
56C2×Dic11⋊C4—21no—
57C2×C4×Dic11—21no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8—21no—
60C22×C11⋊C8—21no—
61C4×Dic22—21no—
62C4×Dic22—21no—
63C4×Dic22D412yes—
64C4×Dic22C2312yes—
65C11×#102—24no—
66C11×#102—24no—
67C4×C8×C11D412yes—
68C4×C8×C11C2312yes—
69#66896—24no—
70Dic11⋊C8—24no—
71C8×Dic11—24no—
72#66874—24no—
73#66871—24no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)C2312yes—
78C4⋊(C11⋊C8)C2312yes—
79C4⋊(C11⋊C8)C2312yes—
80C2×#1678—111nomaximal, Sylow
81C24×C11—41no—
82C2×Q8×C11—22no—
83C2×Q8×C11—41no—
84C2×Q8×C11—82no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—42no—
92C2×D4×C11—42no—
93C2×D4×C11—42no—
94C2×D4×C11—42no—
95C2×D4×C11—82no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C22×Dic11—21no—
101C22×Dic11—21no—
102C2×Dic22—21no—
103C2×Dic22—22no—
104C2×Dic22SD1614yes—
105C2×Dic22C2×D412yes—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11C2×D412yes—
109C2×C8×C11C2×D412yes—
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#4324—48no—
119C4⋊Dic11—21no—
120C4⋊Dic11C2×D412yes—
121Dic11⋊C4—22no—
122Dic11⋊C4—22no—
123C4×Dic11—22no—
124C4×Dic11—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—42no—
129C2×C11⋊C8—42no—
130C2×C11⋊C8—42no—
131C2×#486D1111yescharacteristic
132C2×#477—111no—
133C2×#460—111no—
134C2×C8×Q8—111no—
135#1678—118no—
136C2×#334—111no—
137C2×#333—111no—
138C2×#331—111no—
139C23×C11—42no—
140C23×C11—82no—
141C23×C11—82no—
142C23×C11—82no—
143C23×C11#12111yescharacteristic
144Q8×C11—82no—
145Q8×C11—82no—
146D4×C11—42no—
147D4×C11—42no—
148D4×C11—42no—
149D4×C11—42no—
150D4×C11—82no—
151D4×C11—82no—
152D4×C11—82no—
153D4×C11—82no—
154C2×C4×C11—22no—
155C2×C4×C11—42no—
156C2×C4×C11—82no—
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11C2×SD1612yes—
161C2×C4×C11#13512yes—
162C2×C4×C11#13512yes—
163C2×C4×C11#13712yes—
164C2×C4×C11C22×D411yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C2×#4111yescharacteristic
167C2×Dic11—22no—
168C2×Dic11—24no—
169C2×Dic11—22no—
170C2×Dic11—42no—
171Dic22—22no—
172Dic22—24no—
173Dic22C2×SD1614yes—
174C8×C11—22no—
175C8×C11—22no—
176C11⋊C8—42no—
177C11⋊C8—42no—
178C11⋊C8—42no—
179C22×SD16—221no—
180C2×C4⋊Q8C2×D1111yescharacteristic
181C2×#127C2×D1111yescharacteristic
182C2×C4×Q8—111no—
183#486—22no—
184#486C2×D1114yes—
185#477—114no—
186#477—222no—
187#460—114no—
188#460—222no—
189C8×Q8—114no—
190C8×Q8—222no—
191C2×#107—221no—
192C2×C4⋊C8—111no—
193C2×C4⋊C8—111no—
194C2×C4⋊C8—111no—
195C2×C4⋊C8—221no—
196C2×#103—221no—
197C2×#102—21no—
198C2×#102—21no—
199C2×#102—221no—
200C2×C4×C8—221no—
201C2×C4×C8C2×D1111yescharacteristic
202#334—114no—
203#333—114no—
204#331—114no—
205C22×C11—82no—
206C22×C11—82no—
207C22×C11—82no—
208C22×C11—164no—
209C22×C11#46412yes—
210C22×C11#46512yes—
211C22×C11#47212yes—
212C22×C11C2×#12111yescharacteristic
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—82no—
216C4×C11#46412yes—
217C4×C11#46512yes—
218C4×C11C22×SD1611yescharacteristic
219C4×C11C2×#13511yescharacteristic
220C4×C11C2×#13511yescharacteristic
221C4×C11C2×#13711yescharacteristic
222Dic11—24no—
223Dic11—42no—
224C22×Q8—21no—
225C22×Q8—111no—
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—21no—
229C2×SD16—224no—
230C2×SD16—444no—
231C22×C8—221no—
232C22×C8—221no—
233C22×C8—221no—
234C22×C8C22⋊D1111yescharacteristic
235C22×C8C22⋊D1111yescharacteristic
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8C22×D1112yes—
240#127—21no—
241#127—21no—
242#127—21no—
243#127C22×D1112yes—
244C4×Q8—112no—
245C4×Q8—112no—
246C4×Q8—221no—
247C4×Q8—221no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—221no—
252C2×C42—221no—
253C2×C42C22×D1111yescharacteristic
254#107—224no—
255C4⋊C8—112no—
256C4⋊C8—112no—
257C4⋊C8—112no—
258C4⋊C8—224no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261C4⋊C8—221no—
262#103—224no—
263#102—24no—
264#102—24no—
265#102—224no—
266C4×C8—224no—
267C4×C8C22⋊D1112yes—
268C4×C8C22×D1112yes—
269C2×C11—162no—
270C2×C11#167814yescomplemented
271C2×C11C2×#46411yescharacteristic
272C2×C11C2×#46511yescharacteristic
273C2×C11C2×#47211yescharacteristic
274C24—41no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—82no—
278C2×Q8—114no—
279C2×Q8—112no—
280C2×Q8—222no—
281C2×Q8—221no—
282C2×D4—22no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—82no—
293C22×C4—41no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4D4×D1111yescharacteristic
297C22×C4#434111yescharacteristic
298C22×C4C2×C22⋊D1111yescharacteristic
299SD16—448no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—222no—
303C2×C8—222no—
304C2×C8—222no—
305C2×C8—442no—
306C2×C8—442no—
307C2×C8—442no—
308C2×C8C2×C22⋊D1112yes—
309C2×C8C2×C22⋊D1112yes—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—112no—
315C4⋊C4—221no—
316C4⋊C4—222no—
317C4⋊C4—222no—
318C42—222no—
319C42—222no—
320C42D4×D1111yescharacteristic
321C42#434111yescharacteristic
322C42C2×C22⋊D1111yescharacteristic
323C42C23×D1111yescharacteristic
324C11C2×#167811yescharacteristic, complemented, Sylow
325C23—42no—
326C23—82no—
327C23—82no—
328C23—82no—
329C23#6699111yescharacteristic
330Q8—82no—
331Q8—82no—
332Q8—114no—
333Q8—222no—
334Q8—224no—
335D4—42no—
336D4—42no—
337D4—42no—
338D4—42no—
339D4—82no—
340D4—82no—
341D4—82no—
342D4—82no—
343C2×C4—22no—
344C2×C4—42no—
345C2×C4—82no—
346C2×C4—224no—
347C2×C4—222no—
348C2×C4—222no—
349C2×C4—442no—
350C2×C4SD16×D1112yes—
351C2×C4#6696912yes—
352C2×C4#6699111yescharacteristic
353C2×C4#6699111yescharacteristic
354C2×C4#6699111yescharacteristic
355C2×C4#6700312yes—
356C2×C4#6700412yes—
357C2×C4C2×D4×D1111yescharacteristic
358C2×C4C2×#434111yescharacteristic
359C2×C4C22×C22⋊D1111yescharacteristic
360C8—22no—
361C8—22no—
362C8—442no—
363C8—442no—
364C8—442no—
365C22—82no—
366C22—82no—
367C22—82no—
368C22—164no—
369C22#1062266712yes—
370C22#1062277312yes—
371C22#1062278412yes—
372C22C2×#6699111yescharacteristic
373C4—21no—
374C4—21no—
375C4—82no—
376C4—224no—
377C4—442no—
378C4#1062266712yes—
379C4#1062278412yes—
380C4C2×SD16×D1111yescharacteristic
381C4C2×#6696911yescharacteristic
382C4C2×#6700311yescharacteristic
383C4C2×#6700411yescharacteristic
384C2—162no—
385C2#1306802914yesdirect product factor
386C2C2×#1062266711yescharacteristic
387C2C2×#1062278411yescharacteristic
388C2C2×#1062277311yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#486C2
socleC23×C11#121
prime radicalC2×C11×#127C22
hypercenterC2×#486D11
hypocenterC11C2×#1678
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×#10622704C2semidirect
3. C2×C8×Dic22C2semidirect
4. #13068029C2direct (N × H)
5. C2×#10622095C2semidirect
6. C2×#10622184C2semidirect
22. #10622704C22semidirect
31. C8×Dic22C22semidirect
32. #10622184C22semidirect
34. #10622095C22semidirect
270. C2×C11#1678semidirect
324. C11C2×#1678semidirect
385. C2#13068029direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227042
C2×#106226882
C2×C8×Dic222
#130680292
C2×#106220952
C2×#106221842
C2×#106221822
C2×C11×#4862
C2×#167811