Finite Group Databasebeta

← C2×#13067658 #14726008

Subgroups — C2×#13067658 #14726008

Order 2816.

984 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622657C212yesmaximal
2C2×#10622599C211yesmaximal, characteristic
3#13067658C218yesmaximal, direct product factor
4C2×#10622176C212yesmaximal
5C2×#10622166C211yesmaximal, characteristic
6C2×C11×#544C211yesmaximal, characteristic
7C11×#544—24no—
8C11×#544—22no—
9C11×#544C2214yes—
10C2×C11×C4⋊Q8—22no—
11C2×C11×#125—22no—
12C2×C11×C22⋊Q8—21no—
13C2×C11×C22⋊Q8C2212yes—
14C2×C11×#117—21no—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C2×#66899—22no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95—21no—
20C2×C11⋊#95C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2212yes—
22#10622657—24no—
23#10622657C2218yes—
24#10622599—22no—
25#10622599C2214yes—
26C2×#66871—22no—
27#10622176C2218yes—
28#10622166C2214yes—
29C22×Q8×C11—21no—
30C22×Q8×C11D412yes—
31C23×C4×C11D411yescharacteristic
32C23×C4×C11D411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C23×Dic11—21no—
35C23×Dic11—21no—
36C11×C4⋊Q8—28no—
37C11×C4⋊Q8—28no—
38C11×#125—28no—
39C11×#125—28no—
40C11×C22⋊Q8—24no—
41C11×C22⋊Q8—24no—
42C11×C22⋊Q8—22no—
43C11×C22⋊Q8—22no—
44C11×C22⋊Q8D414yes—
45C11×C22⋊Q8C2314yes—
46C11×#117—24no—
47C11×#117—24no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4D412yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C22⋊C4—22no—
59C2×C42×C11—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11C2312yes—
64C22×C11⋊C8—22no—
65#66899—28no—
66C11⋊#95—24no—
67C11⋊#95—24no—
68C11⋊#95—21no—
69C11⋊#95C2312yes—
70C22⋊(C11⋊C8)—22no—
71C22⋊(C11⋊C8)C2314yes—
72#66871—28no—
73C2×#1617—111nomaximal, Sylow
74C24×C11C2×D411yescharacteristic
75C2×Q8×C11—24no—
76C2×Q8×C11—22no—
77C2×Q8×C11—44no—
78C2×Q8×C11—82no—
79C2×Q8×C11C2×D414yes—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11Q1614yes—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2411yescharacteristic
96C22×Dic11—22no—
97C22×Dic11—22no—
98C22×Dic11—42no—
99C22×Dic11—44no—
100C22×Dic11—42no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103C22×Dic11—42no—
104C11×C4⋊C4—24no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—28no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4C2×D414yes—
114C11×C22⋊C4—24no—
115C11×C22⋊C4—24no—
116C42×C11—28no—
117C4⋊Dic11—24no—
118C4⋊Dic11—42no—
119C2×C11⋊C8—24no—
120C2×C11⋊C8—44no—
121C2×#544D1111yescharacteristic
122C2×#484—112no—
123C2×#400—111no—
124#1617—118no—
125C2×#328—112no—
126C2×#324—111no—
127C23×C11—22no—
128C23×C11—22no—
129C23×C11#12011yescharacteristic
130C23×C11#12011yescharacteristic
131C23×C11C2×Q1612yes—
132C23×C11#13712yes—
133C23×C11C22×D411yescharacteristic
134Q8×C11—44no—
135Q8×C11—82no—
136Q8×C11—84no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—24no—
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—22no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—41no—
148C2×C4×C11—44no—
149C2×C4×C11—42no—
150C2×C4×C11—44no—
151C2×C4×C11—42no—
152C2×C4×C11—81no—
153C2×C4×C11#12012yes—
154C2×C4×C11C2×Q1614yes—
155C2×C4×C11C22×D412yes—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—44no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—84no—
162C2×Dic11—82no—
163C2×Dic11—82no—
164C11⋊C8—44no—
165#544—24no—
166#544—22no—
167#544C2×D1114yes—
168C2×C4⋊Q8—22no—
169C2×#125—22no—
170C2×C22⋊Q8—21no—
171C2×C22⋊Q8C2×D1112yes—
172C2×#117—21no—
173C22×C4⋊C4—111no—
174C22×C4⋊C4C2×D1111yescharacteristic
175#484—118no—
176#484—224no—
177C2×#107—222no—
178C2×#103—222no—
179C2×C22⋊C8—112no—
180#400—114no—
181#400—222no—
182C2×#95—111no—
183C2×#95—221no—
184C2×#95—221no—
185#328—118no—
186#324—114no—
187C22×C11—24no—
188C22×C11—24no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11#45112yes—
194C22×C11#45112yes—
195C22×C11#45412yes—
196C22×C11#45812yes—
197C22×C11C2×#12011yescharacteristic
198C22×C11C22×Q1611yescharacteristic
199C22×C11C2×#13711yescharacteristic
200C4×C11—24no—
201C4×C11—22no—
202C4×C11—22no—
203C4×C11—44no—
204C4×C11—42no—
205C4×C11—44no—
206Dic11—82no—
207Dic11—82no—
208C22×Q8—21no—
209C22×Q8C22⋊D1112yes—
210C23×C4—221no—
211C23×C4—221no—
212C23×C4C22⋊D1111yescharacteristic
213C23×C4C22⋊D1111yescharacteristic
214C23×C4C22×D1111yescharacteristic
215C22×C8—222no—
216C4⋊Q8—28no—
217C4⋊Q8—28no—
218#125—28no—
219#125—28no—
220C22⋊Q8—24no—
221C22⋊Q8—24no—
222C22⋊Q8—22no—
223C22⋊Q8—22no—
224C22⋊Q8C22⋊D1114yes—
225C22⋊Q8C22×D1114yes—
226#117—24no—
227#117—24no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—112no—
236C2×C4⋊C4—222no—
237C2×C4⋊C4—222no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4C22⋊D1112yes—
240C2×C4⋊C4C22⋊D1112yes—
241C2×C4⋊C4C22×D1112yes—
242C2×C22⋊C4—22no—
243C2×C42—22no—
244#107—228no—
245#103—228no—
246C22⋊C8—114no—
247C22⋊C8—222no—
248#95—112no—
249#95—221no—
250#95—224no—
251#95—224no—
252C2×C11—21no—
253C2×C11—21no—
254C2×C11—22no—
255C2×C11#161714yescomplemented
256C2×C11C2×#45111yescharacteristic
257C2×C11C2×#45411yescharacteristic
258C2×C11C2×#45811yescharacteristic
259C24C2×C22⋊D1111yescharacteristic
260C2×Q8—24no—
261C2×Q8—22no—
262C2×Q8—44no—
263C2×Q8—82no—
264C2×Q8C2×C22⋊D1114yes—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—222no—
275C22×C4—222no—
276C22×C4—442no—
277C22×C4—442no—
278C22×C4—444no—
279C22×C4—442no—
280C22×C4—441no—
281C22×C4—441no—
282C22×C4#432614yes—
283C22×C4C2×C22⋊D1112yes—
284C22×C4C2×C22⋊D1112yes—
285C22×C4C2×C22⋊D1112yes—
286C22×C4C2×C22⋊D1111yescharacteristic
287C22×C4C2×C22⋊D1112yes—
288C22×C4C23×D1111yescharacteristic
289C2×C8—224no—
290C2×C8—444no—
291C4⋊C4—24no—
292C4⋊C4—24no—
293C4⋊C4—24no—
294C4⋊C4—28no—
295C4⋊C4—24no—
296C4⋊C4—24no—
297C4⋊C4—22no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—224no—
301C4⋊C4—442no—
302C4⋊C4C2×C22⋊D1114yes—
303C22⋊C4—24no—
304C22⋊C4—24no—
305C42—28no—
306C11C2×#161711yescharacteristic, complemented, Sylow
307C23—22no—
308C23—22no—
309C23#6699512yes—
310C23C2×#432612yes—
311C23#6700611yescharacteristic
312C23#6700611yescharacteristic
313C23C22×C22⋊D1111yescharacteristic
314Q8—44no—
315Q8—82no—
316Q8—84no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—22no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—442no—
334C2×C4—442no—
335C2×C4—444no—
336C2×C4—442no—
337C2×C4—442no—
338C2×C4—884no—
339C2×C4—882no—
340C2×C4—882no—
341C2×C4C2×#432614yes—
342C2×C4#6700612yes—
343C2×C4C22×C22⋊D1112yes—
344C8—444no—
345C22—24no—
346C22—24no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22#1062284112yes—
352C22#1062284112yes—
353C22#1062285612yes—
354C22#1062285812yes—
355C22C2×#6699511yescharacteristic
356C22C22×#432611yescharacteristic
357C22C2×#6700611yescharacteristic
358C4—24no—
359C4—22no—
360C4—22no—
361C4—44no—
362C4—42no—
363C4—44no—
364C4—882no—
365C4—882no—
366C2—21no—
367C2—21no—
368C2—22no—
369C2#1306765814yesdirect product factor
370C2C2×#1062284111yescharacteristic
371C2C2×#1062285811yescharacteristic
372C2C2×#1062285611yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#544C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenterC2×#544D11
hypocenterC11C2×#1617
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #13067658C2direct (N × H)
255. C2×C11#1617semidirect
306. C11C2×#1617semidirect
369. C2#13067658direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226572
C2×#106225992
#130676582
C2×#106221762
C2×#106221662
C2×C11×#5442
C2×#161711