Finite Group Databasebeta

← C2×#13068193 #14736348

Subgroups — C2×#13068193 #14736348

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622706C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic
3C2×#10622625C211yesmaximal, characteristic
4#13068193C218yesmaximal, direct product factor
5C2×#10622118C211yesmaximal, characteristic, complemented
6C2×#10622184C211yesmaximal, characteristic, complemented
7C2×#10622124C211yesmaximal, characteristic, complemented
8C2×C11×#476C211yesmaximal, characteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4318—21no—
12C2×#66922C2211yescharacteristic
13C11×#476—22no—
14C11×#476C2214yes—
15C2×C11×#106—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#102—21no—
18C2×#66896—21no—
19C2×C22⋊(C11⋊C8)—21no—
20#10622706—22no—
21#10622706C2214yescomplemented
22#10622625—22no—
23#10622625C2214yes—
24#10622620—22no—
25#10622620C2214yes—
26C2×#66874—21no—
27C2×#66874—21no—
28C2×#66871—21no—
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622184C2214yescomplemented
33#10622124C2214yescomplemented
34#10622118C2214yescomplemented
35C22×Q8×C11—21no—
36C22×D4×C11D411yescharacteristic
37C23×C4×C11—21no—
38C22×Dic22—21no—
39C22×C8×C11—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8C2312yes—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11D412yes—
47C4×D4×C11C2312yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C42×C11C2311yescharacteristic
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×#4318—24no—
56C2×#4318—44no—
57C22×C11⋊C8—21no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8D411yescharacteristic
60C22×C11⋊C8D411yescharacteristic
61#66922—21no—
62#66922—21no—
63#66922—21no—
64#66922C2312yes—
65C11×#106—24no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8C2312yes—
68C11×#102—24no—
69#66896—24no—
70C22⋊(C11⋊C8)—24no—
71#66874—24no—
72#66874—24no—
73#66871—24no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)C2312yes—
77C4⋊(C11⋊C8)C2312yes—
78C4×C11⋊C8D412yes—
79C4×C11⋊C8C2312yes—
80C2×#1703—111nomaximal, Sylow
81C24×C11—21no—
82C2×Q8×C11—22no—
83C2×Q8×C11—41no—
84C2×Q8×C11—82no—
85C2×D4×C11—21no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11C2×D412yes—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×Dic11—41no—
99C2×Dic22—22no—
100C2×Dic22—41no—
101C2×Dic22—42no—
102C2×Dic22—42no—
103C2×C8×C11—22no—
104C2×C8×C11—42no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4C2×D412yes—
111C11×C22⋊C4—22no—
112C11×C22⋊C4—22no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C42×C11C2411yescharacteristic
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121#4318—48no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—42no—
127C2×C11⋊C8—42no—
128C2×C11⋊C8C2×D412yes—
129C2×C11⋊C8C2×D412yes—
130C2×#487—111no—
131C2×#476D1111yescharacteristic
132C2×#474—111no—
133C2×#436—111no—
134#1703—118no—
135C2×#334—111no—
136C2×#333—111no—
137C2×#332—111no—
138C23×C11—22no—
139C23×C11—42no—
140C23×C11—42no—
141C23×C11—42no—
142C23×C11#12111yescharacteristic
143Q8×C11—82no—
144Q8×C11—82no—
145D4×C11—22no—
146D4×C11—22no—
147D4×C11—42no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—44no—
154C2×C4×C11—42no—
155C2×C4×C11—82no—
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#13512yes—
160C2×C4×C11AGL(1,ℤ/8)12yes—
161C2×C4×C11#13712yes—
162C2×C4×C11#13712yes—
163C2×C4×C11C22×D411yescharacteristic
164C2×C4×C11C22×D411yescharacteristic
165C2×C4×C11C2×#4111yescharacteristic
166C2×Dic11—42no—
167C2×Dic11—82no—
168Dic22—42no—
169Dic22—42no—
170Dic22—82no—
171C8×C11—42no—
172C11⋊C8—22no—
173C11⋊C8—22no—
174C11⋊C8—42no—
175C11⋊C8—42no—
176C22×M16—221no—
177C2×C4⋊Q8—111no—
178C2×C4⋊Q8C2×D1111yescharacteristic
179C2×C4×D4C2×D1111yescharacteristic
180#487—114no—
181#487—222no—
182#476—22no—
183#476C2×D1114yes—
184#474—114no—
185#474—222no—
186#436—114no—
187#436—222no—
188C2×#107—221no—
189C2×#106—21no—
190C2×C4⋊C8—111no—
191C2×C4⋊C8—111no—
192C2×C4⋊C8C2×D1111yescharacteristic
193C2×#103—221no—
194C2×#103—221no—
195C2×#102—21no—
196C2×#102—221no—
197C2×C22⋊C8—221no—
198C2×C4×C8—111no—
199#334—114no—
200#333—114no—
201#332—114no—
202C22×C11—42no—
203C22×C11—42no—
204C22×C11—42no—
205C22×C11—84no—
206C22×C11#46312yes—
207C22×C11#47012yes—
208C22×C11#47112yes—
209C22×C11C2×#12111yescharacteristic
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—42no—
213C4×C11—82no—
214C4×C11#46312yes—
215C4×C11#47012yes—
216C4×C11C2×#13511yescharacteristic
217C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
218C4×C11C2×#13711yescharacteristic
219C4×C11C2×#13711yescharacteristic
220Dic11—82no—
221C22×Q8—21no—
222C22×Q8—221no—
223C22×D4C22⋊D1111yescharacteristic
224C23×C4—21no—
225C2×M16—224no—
226C2×M16—444no—
227C22×C8—21no—
228C22×C8—111no—
229C22×C8—111no—
230C22×C8—221no—
231C22×C8—221no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—112no—
236C4⋊Q8—221no—
237C4⋊Q8—221no—
238C4⋊Q8—221no—
239C4⋊Q8C22×D1112yes—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4C22⋊D1112yes—
243C4×D4C22×D1112yes—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4C22⋊D1111yescharacteristic
249C2×C22⋊C4—21no—
250C2×C42C22×D1111yescharacteristic
251#107—224no—
252#106—24no—
253C4⋊C8—21no—
254C4⋊C8—112no—
255C4⋊C8—112no—
256C4⋊C8—221no—
257C4⋊C8—221no—
258C4⋊C8C22×D1112yes—
259#103—224no—
260#103—224no—
261#102—24no—
262#102—224no—
263C22⋊C8—224no—
264C4×C8—112no—
265C4×C8—112no—
266C2×C11—82no—
267C2×C11#170314yescomplemented
268C2×C11C2×#46311yescharacteristic
269C2×C11C2×#47011yescharacteristic
270C2×C11C2×#47111yescharacteristic
271C24—21no—
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—82no—
275C2×Q8—222no—
276C2×Q8—441no—
277C2×Q8—442no—
278C2×Q8—442no—
279C2×D4—21no—
280C2×D4—22no—
281C2×D4—22no—
282C2×D4C2×C22⋊D1112yes—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—41no—
289C22×C4—441no—
290C22×C4D4×D1111yescharacteristic
291C22×C4#434111yescharacteristic
292C22×C4C2×C22⋊D1111yescharacteristic
293M16—448no—
294C2×C8—22no—
295C2×C8—42no—
296C2×C8—112no—
297C2×C8—112no—
298C2×C8—222no—
299C2×C8—222no—
300C2×C8—222no—
301C2×C8—222no—
302C2×C8—442no—
303C2×C8—442no—
304C4⋊C4—21no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—222no—
310C4⋊C4—222no—
311C4⋊C4—441no—
312C4⋊C4—441no—
313C4⋊C4C2×C22⋊D1112yes—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C42D4×D1111yescharacteristic
317C42#434111yescharacteristic
318C42C2×C22⋊D1111yescharacteristic
319C42C23×D1111yescharacteristic
320C11C2×#170311yescharacteristic, complemented, Sylow
321C23—22no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23#6699211yescharacteristic
326Q8—82no—
327Q8—82no—
328Q8—442no—
329Q8—442no—
330Q8—882no—
331D4—22no—
332D4—22no—
333D4—42no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—82no—
342C2×C4—442no—
343C2×C4—882no—
344C2×C4#6696712yes—
345C2×C4#6696912yes—
346C2×C4#6699211yescharacteristic
347C2×C4#6699211yescharacteristic
348C2×C4#6699211yescharacteristic
349C2×C4#6699512yes—
350C2×C4#6700412yes—
351C2×C4C2×D4×D1111yescharacteristic
352C2×C4C2×#434111yescharacteristic
353C2×C4C22×C22⋊D1111yescharacteristic
354C8—42no—
355C8—222no—
356C8—222no—
357C8—442no—
358C8—442no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—84no—
363C22#1062266512yes—
364C22#1062277812yes—
365C22#1062281312yes—
366C22C2×#6699211yescharacteristic
367C4—21no—
368C4—21no—
369C4—42no—
370C4—82no—
371C4—882no—
372C4#1062266512yes—
373C4#1062277812yes—
374C4C2×#6696711yescharacteristic
375C4C2×#6696911yescharacteristic
376C4C2×#6699511yescharacteristic
377C4C2×#6700411yescharacteristic
378C2—82no—
379C2#1306819314yesdirect product factor
380C2C2×#1062277811yescharacteristic
381C2C2×#1062266511yescharacteristic
382C2C2×#1062281311yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#476C2
socleC23×C11#121
prime radicalC22×D4×C11D4
hypercenterC2×#476D11
hypocenterC11C2×#1703
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10622706C2semidirect
4. #13068193C2direct (N × H)
5. C2×#10622118C2semidirect
6. C2×#10622184C2semidirect
7. C2×#10622124C2semidirect
21. #10622706C22semidirect
32. #10622184C22semidirect
33. #10622124C22semidirect
34. #10622118C22semidirect
267. C2×C11#1703semidirect
320. C11C2×#1703semidirect
379. C2#13068193direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227062
C2×#106226202
C2×#106226252
#130681932
C2×#106221182
C2×#106221842
C2×#106221242
C2×C11×#4762
C2×#170311