Finite Group Databasebeta

← C2×#13067484 #14723317

Subgroups — C2×#13067484 #14723317

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622444C211yesmaximal, characteristic
2C2×Q8×C11⋊C8C211yesmaximal, characteristic
3C2×C4×#4326C211yesmaximal, characteristic
4#13067484C218yesmaximal, direct product factor
5C2×#10622118C211yesmaximal, characteristic
6C2×#10622094C211yesmaximal, characteristic
7C2×#10622093C211yesmaximal, characteristic
8C2×C11×Q8⋊C8C211yesmaximal, characteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C22×#4326C411yescharacteristic
11C2×C4×Dic22C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66899C411yescharacteristic
15C2×#66879—21no—
16C2×Dic11⋊C8—21no—
17C4×#4326C414yes—
18C4×#4326C2214yes—
19Q8×C11⋊C8—22no—
20Q8×C11⋊C8C2214yes—
21C2×#66874C411yescharacteristic
22C2×#66871C411yescharacteristic
23C2×C4⋊(C11⋊C8)—21no—
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C2×C4×C11⋊C8—21no—
26C2×C4×C11⋊C8C2211yescharacteristic
27C2×C4×C11⋊C8C2211yescharacteristic
28#10622444—22no—
29#10622444C2214yes—
30C11×Q8⋊C8C2214yes—
31#10622118C2214yes—
32#10622094C2214yes—
33#10622093C2214yes—
34C22×Q8×C11C2×C411yescharacteristic
35C22×Dic22C2×C411yescharacteristic
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11C2×C412yes—
41C4×Q8×C11C2312yes—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4C2×C411yescharacteristic
44C2×C42×C11—21no—
45C2×C42×C11C2311yescharacteristic
46C2×#4326—24no—
47C2×#4326C2×C414yes—
48C2×C4⋊Dic11C2×C411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11—21no—
51C22×C11⋊C8—21no—
52C22×C11⋊C8C2×C411yescharacteristic
53C22×C11⋊C8C2×C411yescharacteristic
54C22×C11⋊C8D411yescharacteristic
55C22×C11⋊C8D411yescharacteristic
56C4×Dic22—21no—
57C4×Dic22—21no—
58C4×Dic22C2×C412yes—
59C4×Dic22C2312yes—
60C11×C4⋊C8—21no—
61C11×C4⋊C8C2312yes—
62C4×C8×C11—21no—
63C4×C8×C11C2312yes—
64#66899C2×C414yes—
65#66879—24no—
66Dic11⋊C8—24no—
67#66874C2×C414yes—
68#66871C2×C414yes—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—24no—
71C4⋊(C11⋊C8)C2312yes—
72C4×C11⋊C8—24no—
73C4×C11⋊C8C2×C412yes—
74C4×C11⋊C8D412yes—
75C4×C11⋊C8C2312yes—
76C4×C11⋊C8C2312yes—
77C2×#1587—111nomaximal, Sylow
78C2×Q8×C11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11M1614yes—
81C2×Q8×C11C22×C412yes—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×Dic11—21no—
88C22×Dic11—21no—
89C2×Dic22—21no—
90C2×Dic22—22no—
91C2×Dic22—22no—
92C2×Dic22C22×C412yes—
93C2×C8×C11—24no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—42no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4C22×C412yes—
101C42×C11—22no—
102C42×C11—22no—
103C42×C11C22×C411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C42×C11C2411yescharacteristic
107#4326—28no—
108C4⋊Dic11—21no—
109C4⋊Dic11C22×C412yes—
110Dic11⋊C4—22no—
111Dic11⋊C4—22no—
112C4×Dic11—22no—
113C4×Dic11—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—42no—
120C2×C11⋊C8C22×C412yes—
121C2×C11⋊C8C22×C412yes—
122C2×C11⋊C8C2×D412yes—
123C2×C11⋊C8C2×D412yes—
124C2×#446—111no—
125C2×C8×Q8—111no—
126C2×C4×Q16—111no—
127#1587—118no—
128C2×#334—111no—
129C2×Q8⋊C8—111no—
130C2×Q8⋊C8D1111yescharacteristic
131C2×#322—111no—
132C23×C11C4×D411yescharacteristic
133Q8×C11—22no—
134Q8×C11—24no—
135Q8×C11C2×M1614yes—
136C2×C4×C11—22no—
137C2×C4×C11—24no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—42no—
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C2×M1612yes—
145C2×C4×C11#13112yes—
146C2×C4×C11#13712yes—
147C2×C4×C11#13712yes—
148C2×C4×C11C23×C411yescharacteristic
149C2×C4×C11C22×D411yescharacteristic
150C2×C4×C11C2×#4111yescharacteristic
151C2×Dic11—22no—
152C2×Dic11—22no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155Dic22—22no—
156Dic22—22no—
157Dic22—42no—
158C8×C11—24no—
159C8×C11—42no—
160C11⋊C8—22no—
161C11⋊C8—22no—
162C11⋊C8—22no—
163C11⋊C8—22no—
164C11⋊C8—42no—
165C22×Q16—111no—
166C2×C4×Q8—111no—
167C2×C4×Q8C2×D1111yescharacteristic
168#446—114no—
169#446—222no—
170C8×Q8—114no—
171C8×Q8—222no—
172C4×Q16—114no—
173C4×Q16—114no—
174C2×#107—111no—
175C2×C4⋊C8—111no—
176C2×C4⋊C8—221no—
177C2×C4⋊C8—221no—
178C2×C4⋊C8C2×D1111yescharacteristic
179C2×#103—111no—
180C2×#103—111no—
181C2×#97—221no—
182C2×C4×C8—111no—
183C2×C4×C8—111no—
184C2×C4×C8—221no—
185C2×C4×C8C2×D1111yescharacteristic
186#334—114no—
187Q8⋊C8—114no—
188Q8⋊C8C2×D1114yes—
189#322—114no—
190C22×C11#43512yes—
191C22×C11#44112yes—
192C22×C11#44312yes—
193C22×C11C2×C4×D411yescharacteristic
194C4×C11—24no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—42no—
198C4×C11#43512yes—
199C4×C11#44112yes—
200C4×C11C22×M1611yescharacteristic
201C4×C11C2×#13111yescharacteristic
202C4×C11C2×#13711yescharacteristic
203C4×C11C2×#13711yescharacteristic
204Dic11—42no—
205Dic11—42no—
206C22×Q8—111no—
207C22×Q8C4×D1111yescharacteristic
208C2×Q16—114no—
209C2×Q16—224no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—111no—
213C22×C8—111no—
214C22×C8—111no—
215C22×C8—111no—
216C22×C8—221no—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×Q8—112no—
220C4×Q8—112no—
221C4×Q8—221no—
222C4×Q8—221no—
223C4×Q8C4×D1112yes—
224C4×Q8C22×D1112yes—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4C4×D1111yescharacteristic
229C2×C42—21no—
230C2×C42—221no—
231C2×C42C22×D1111yescharacteristic
232#107—114no—
233C4⋊C8—21no—
234C4⋊C8—112no—
235C4⋊C8—224no—
236C4⋊C8—224no—
237C4⋊C8—221no—
238C4⋊C8C22×D1112yes—
239#103—114no—
240#103—114no—
241#97—224no—
242C4×C8—21no—
243C4×C8—112no—
244C4×C8—112no—
245C4×C8—112no—
246C4×C8—112no—
247C4×C8—224no—
248C4×C8C22×D1112yes—
249C2×C11#158714yescomplemented
250C2×C11C2×#43511yescharacteristic
251C2×C11C2×#44111yescharacteristic
252C2×C11C2×#44311yescharacteristic
253C2×Q8—21no—
254C2×Q8—22no—
255C2×Q8—112no—
256C2×Q8—221no—
257C2×Q8—222no—
258C2×Q8—222no—
259C2×Q8#431314yes—
260C2×Q8C2×C4×D1112yes—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4C2×C4×D1111yescharacteristic
266C22×C4D4×D1111yescharacteristic
267C22×C4#434111yescharacteristic
268Q16—228no—
269C2×C8—24no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—42no—
273C2×C8—112no—
274C2×C8—112no—
275C2×C8—112no—
276C2×C8—112no—
277C2×C8—222no—
278C2×C8—222no—
279C2×C8—222no—
280C2×C8—222no—
281C2×C8—222no—
282C2×C8—442no—
283C4⋊C4—22no—
284C4⋊C4—21no—
285C4⋊C4—22no—
286C4⋊C4—112no—
287C4⋊C4—221no—
288C4⋊C4—222no—
289C4⋊C4—222no—
290C4⋊C4C2×C4×D1112yes—
291C42—22no—
292C42—22no—
293C42—222no—
294C42—222no—
295C42C2×C4×D1111yescharacteristic
296C42D4×D1111yescharacteristic
297C42#434111yescharacteristic
298C42C23×D1111yescharacteristic
299C11C2×#158711yescharacteristic, complemented, Sylow
300C23(C22⋊D11)⋊C411yescharacteristic
301Q8—22no—
302Q8—24no—
303Q8—222no—
304Q8—222no—
305Q8—442no—
306Q8C2×#431314yes—
307C2×C4—22no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—42no—
312C2×C4—222no—
313C2×C4—222no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4(C22⋊D11)⋊C411yescharacteristic
317C2×C4(C22⋊D11)⋊C411yescharacteristic
318C2×C4(C22⋊D11)⋊C411yescharacteristic
319C2×C4C2×#431312yes—
320C2×C4#6696012yes—
321C2×C4#6696812yes—
322C2×C4#6697112yes—
323C2×C4C22×C4×D1111yescharacteristic
324C2×C4C2×D4×D1111yescharacteristic
325C2×C4C2×#434111yescharacteristic
326C8—24no—
327C8—42no—
328C8—222no—
329C8—222no—
330C8—222no—
331C8—222no—
332C8—442no—
333C22#1062234312yes—
334C22#1062240212yes—
335C22#1062243712yes—
336C22C2×(C22⋊D11)⋊C411yescharacteristic
337C4—24no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—442no—
342C4—442no—
343C4#1062234312yes—
344C4#1062240212yes—
345C4C22×#431311yescharacteristic
346C4C2×#6696011yescharacteristic
347C4C2×#6696811yescharacteristic
348C4C2×#6697111yescharacteristic
349C2#1306748414yesdirect product factor
350C2C2×#1062234311yescharacteristic
351C2C2×#1062240211yescharacteristic
352C2C2×#1062243711yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×Q8⋊C8C2
socle, prime radicalC23×C11C4×D4
cosocleC42×C11C24
hypercenterC2×Q8⋊C8D11
hypocenterC11C2×#1587
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. #13067484C2direct (N × H)
249. C2×C11#1587semidirect
299. C11C2×#1587semidirect
349. C2#13067484direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106224442
C2×Q8×C11⋊C82
C2×C4×#43262
#130674842
C2×#106221182
C2×#106220942
C2×#106220932
C2×C11×Q8⋊C82
C2×#158711