Finite Group Databasebeta

← C2×#13067395 #14722839

Subgroups — C2×#13067395 #14722839

Order 2816.

670 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622448C211yesmaximal, characteristic
2C2×#10622446C211yesmaximal, characteristic
3C2×#10622298C211yesmaximal, characteristic
4#13067395C218yesmaximal, direct product factor
5C2×#10622096C211yesmaximal, characteristic, complemented
6C2×#10622118C211yesmaximal, characteristic, complemented
7C2×#10622118C211yesmaximal, characteristic, complemented
8C2×C11×#335C211yesmaximal, characteristic, complemented
9C2×C42×D11C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C2×(C2×D11)⋊C8—21no—
14C2×(C2×D11)⋊C8—21no—
15C2×(C2×D11)⋊C8C411yescharacteristic
16C2×(C2×D11)⋊C8C411yescharacteristic
17C2×#66879—21no—
18C2×Dic11⋊C8C411yescharacteristic
19C2×Dic11⋊C8C411yescharacteristic
20C2×C8×Dic11—21no—
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24#10622448—22no—
25#10622448C2214yes—
26#10622446—22no—
27#10622446C2214yes—
28#10622298C414yes—
29#10622298C2214yes—
30C11×#335C2214yescomplemented
31#10622118C2214yescomplemented
32#10622118C2214yescomplemented
33#10622096C2214yescomplemented
34C22×C4×D11C2×C411yescharacteristic
35C22×C4×D11D411yescharacteristic
36C22×C4×D11Q811yescharacteristic
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C22×C8×C11C2×C411yescharacteristic
40C22×C8×C11C2×C411yescharacteristic
41C2×C42×C11C2311yescharacteristic
42C2×C4×Dic11C2×C411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C2×C4×Dic11Q811yescharacteristic
45C22×C11⋊C8—21no—
46C22×C11⋊C8—21no—
47C22×C11⋊C8C2×C411yescharacteristic
48C22×C11⋊C8C2×C411yescharacteristic
49C42×D11C2×C412yes—
50C42×D11D412yes—
51C42×D11Q812yes—
52C42×D11C2312yes—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8C2312yes—
56C11×C4⋊C8C2312yes—
57C4×C8×C11C2×C412yes—
58C4×C8×C11C2312yes—
59(C2×D11)⋊C8—24no—
60(C2×D11)⋊C8—24no—
61(C2×D11)⋊C8C2×C414yes—
62(C2×D11)⋊C8C2×C414yes—
63#66879—24no—
64Dic11⋊C8C2×C414yes—
65Dic11⋊C8C2×C414yes—
66C8×Dic11—24no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)C2312yes—
70C4⋊(C11⋊C8)C2312yes—
71C4×C11⋊C8C2×C412yes—
72C4×C11⋊C8C2312yes—
73C2×#1572—111nomaximal, Sylow
74C23×D11C4⋊C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×Q811yescharacteristic
78C22×Dic11C4⋊C411yescharacteristic
79C22×Dic11C4⋊C411yescharacteristic
80C22×Dic11C4⋊C411yescharacteristic
81C2×C4×D11—22no—
82C2×C4×D11—22no—
83C2×C4×D11—22no—
84C2×C4×D11—22no—
85C2×C4×D11—42no—
86C2×C4×D11C4⋊C412yes—
87C2×C4×D11C4⋊C412yes—
88C2×C4×D11C4⋊C412yes—
89C2×C4×D11C22×C412yes—
90C2×C4×D11C2×D412yes—
91C2×C4×D11C2×Q812yes—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—42no—
97C2×C8×C11—42no—
98C2×C8×C11C22×C412yes—
99C2×C8×C11C22×C412yes—
100C42×C11C22×C411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×Q811yescharacteristic
103C42×C11C2411yescharacteristic
104C4×Dic11C4⋊C412yes—
105C4×Dic11C4⋊C412yes—
106C4×Dic11C4⋊C412yes—
107C4×Dic11C22×C412yes—
108C4×Dic11C2×D412yes—
109C4×Dic11C2×Q812yes—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—42no—
115C2×C11⋊C8—42no—
116C2×C11⋊C8C22×C412yes—
117C2×C11⋊C8C22×C412yes—
118C2×#432—111no—
119C2×#431—111no—
120C2×#431—111no—
121#1572—118no—
122C2×#335—111no—
123C2×#335D1111yescharacteristic, complemented
124C2×#334—111no—
125C2×#334—111no—
126C23×C11C2×C4⋊C411yescharacteristic
127C22×D11—22no—
128C22×D11—22no—
129C22×D11—22no—
130C22×D11C2×C4⋊C412yes—
131C2×C4×C11—22no—
132C2×C4×C11C2×C4⋊C411yescharacteristic
133C2×C4×C11C2×C4⋊C411yescharacteristic
134C2×C4×C11C2×C4⋊C411yescharacteristic
135C2×C4×C11#13112yes—
136C2×C4×C11#13112yes—
137C2×C4×C11#13512yes—
138C2×C4×C11#13512yes—
139C2×C4×C11C23×C411yescharacteristic
140C2×C4×C11C22×D411yescharacteristic
141C2×C4×C11C22×Q811yescharacteristic
142C2×Dic11—22no—
143C2×Dic11—22no—
144C2×Dic11—22no—
145C2×Dic11C2×C4⋊C412yes—
146C2×Dic11C2×C4⋊C412yes—
147C2×Dic11C2×C4⋊C412yes—
148C4×D11—22no—
149C4×D11—22no—
150C4×D11—22no—
151C4×D11—22no—
152C4×D11—24no—
153C4×D11—24no—
154C4×D11—42no—
155C4×D11—42no—
156C8×C11—22no—
157C8×C11—22no—
158C8×C11—42no—
159C8×C11—42no—
160C11⋊C8—22no—
161C11⋊C8—22no—
162C11⋊C8—42no—
163C11⋊C8—42no—
164C22×C42—111no—
165#432—114no—
166#432—222no—
167#431—114no—
168#431—114no—
169#431—114no—
170#431—222no—
171C2×C4⋊C8—111no—
172C2×C4⋊C8—111no—
173C2×C4⋊C8—111no—
174C2×C4⋊C8—111no—
175C2×C4⋊C8C2×D1111yescharacteristic
176C2×C4⋊C8C2×D1111yescharacteristic
177C2×C22⋊C8—111no—
178C2×C22⋊C8—111no—
179C2×C22⋊C8—221no—
180C2×C22⋊C8—221no—
181C2×#97—221no—
182C2×C4×C8—111no—
183C2×C4×C8—221no—
184C2×C4×C8C2×D1111yescharacteristic
185#335—114no—
186#335C2×D1114yescomplemented
187#334—114no—
188#334—114no—
189C22×C11#42412yes—
190C22×C11#42712yes—
191C22×C11#43012yes—
192C22×C11C22×C4⋊C411yescharacteristic
193C2×D11—22no—
194C2×D11—22no—
195C2×D11—22no—
196C2×D11—44no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11#42412yes—
200C4×C11#42712yes—
201C4×C11C2×#13111yescharacteristic
202C4×C11C2×#13111yescharacteristic
203C4×C11C2×#13511yescharacteristic
204C4×C11C2×#13511yescharacteristic
205Dic11—22no—
206Dic11—22no—
207Dic11—22no—
208C23×C4—111no—
209C23×C4—111no—
210C23×C4—111no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—111no—
214C22×C8—111no—
215C22×C8—221no—
216C22×C8—221no—
217C22×C8C4×D1111yescharacteristic
218C22×C8C4×D1111yescharacteristic
219C2×C42—111no—
220C2×C42—111no—
221C2×C42—111no—
222C2×C42—112no—
223C2×C42—112no—
224C2×C42—112no—
225C2×C42—112no—
226C2×C42C22×D1111yescharacteristic
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—114no—
230C4⋊C8—114no—
231C4⋊C8—112no—
232C4⋊C8—112no—
233C4⋊C8—221no—
234C4⋊C8—221no—
235C4⋊C8C22×D1112yes—
236C4⋊C8C22×D1112yes—
237C22⋊C8—114no—
238C22⋊C8—114no—
239C22⋊C8—224no—
240C22⋊C8—224no—
241#97—224no—
242C4×C8—112no—
243C4×C8—112no—
244C4×C8—224no—
245C4×C8C4×D1112yes—
246C4×C8C22×D1112yes—
247C2×C11#157214yescomplemented
248C2×C11C2×#42411yescharacteristic
249C2×C11C2×#42711yescharacteristic
250C2×C11C2×#43011yescharacteristic
251D11—42no—
252C24—111no—
253C22×C4—111no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—112no—
257C22×C4—112no—
258C22×C4—112no—
259C22×C4—112no—
260C22×C4—112no—
261C22×C4—112no—
262C22×C4—222no—
263C22×C4—222no—
264C22×C4—222no—
265C22×C4—222no—
266C22×C4—442no—
267C22×C4C2×C4×D1111yescharacteristic
268C22×C4D4×D1111yescharacteristic
269C22×C4Q8×D1111yescharacteristic
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—42no—
275C2×C8—42no—
276C2×C8—112no—
277C2×C8—112no—
278C2×C8—222no—
279C2×C8—222no—
280C2×C8—222no—
281C2×C8—222no—
282C2×C8—442no—
283C2×C8—442no—
284C2×C8C2×C4×D1112yes—
285C2×C8C2×C4×D1112yes—
286C42—112no—
287C42—112no—
288C42—112no—
289C42—112no—
290C42—112no—
291C42—112no—
292C42C2×C4×D1111yescharacteristic
293C42D4×D1111yescharacteristic
294C42Q8×D1111yescharacteristic
295C42C23×D1111yescharacteristic
296C11C2×#157211yescharacteristic, complemented, Sylow
297C23—112no—
298C23—222no—
299C23—222no—
300C23—222no—
301C23C4⋊C4×D1111yescharacteristic
302C2×C4—22no—
303C2×C4—112no—
304C2×C4—112no—
305C2×C4—112no—
306C2×C4—222no—
307C2×C4—222no—
308C2×C4—222no—
309C2×C4—224no—
310C2×C4—222no—
311C2×C4—222no—
312C2×C4—222no—
313C2×C4—222no—
314C2×C4—224no—
315C2×C4—442no—
316C2×C4—442no—
317C2×C4C4⋊C4×D1111yescharacteristic
318C2×C4C4⋊C4×D1111yescharacteristic
319C2×C4C4⋊C4×D1111yescharacteristic
320C2×C4#6695412yes—
321C2×C4#6696012yes—
322C2×C4#6696512yes—
323C2×C4#6697212yes—
324C2×C4C22×C4×D1111yescharacteristic
325C2×C4C2×D4×D1111yescharacteristic
326C2×C4C2×Q8×D1111yescharacteristic
327C8—22no—
328C8—22no—
329C8—42no—
330C8—42no—
331C8—222no—
332C8—222no—
333C8—442no—
334C8—442no—
335C22—222no—
336C22—222no—
337C22—222no—
338C22—444no—
339C22#1062245212yes—
340C22#1062249312yes—
341C22#1062250612yes—
342C22C2×C4⋊C4×D1111yescharacteristic
343C4—21no—
344C4—21no—
345C4—222no—
346C4—222no—
347C4—222no—
348C4#1062245212yes—
349C4#1062249312yes—
350C4C2×#6695411yescharacteristic
351C4C2×#6696011yescharacteristic
352C4C2×#6696511yescharacteristic
353C4C2×#6697211yescharacteristic
354C2—442no—
355C2#1306739514yesdirect product factor
356C2C2×#1062245211yescharacteristic
357C2C2×#1062249311yescharacteristic
358C2C2×#1062250611yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×#335C2
socleC23×C11C2×C4⋊C4
prime radicalC23×D11C4⋊C4
cosocleC42×C11C24
hypercenterC2×#335D11
hypocenterC11C2×#1572
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
4. #13067395C2direct (N × H)
5. C2×#10622096C2semidirect
6. C2×#10622118C2semidirect
7. C2×#10622118C2semidirect
8. C2×C11×#335C2semidirect
30. C11×#335C22semidirect
31. #10622118C22semidirect
32. #10622118C22semidirect
33. #10622096C22semidirect
123. C2×#335D11semidirect
186. #335C2×D11semidirect
247. C2×C11#1572semidirect
296. C11C2×#1572semidirect
355. C2#13067395direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106224482
C2×#106224462
C2×#106222982
#130673952
C2×#106220962
C2×#106221182
C2×C11×#3352
C2×#157211