Finite Group Databasebeta

← #14723666

Subgroups — #14723666

Order 2816.

618 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
1#13078651C211yesmaximal, characteristic
2C2×C8×Dic22C211yesmaximal, characteristic
3#13067464C214yesmaximal, complemented
4C8×#4326C214yesmaximal, complemented
5#13067392C211yesmaximal, characteristic
6#13067044C211yesmaximal, characteristic
7#13067019C211yesmaximal, characteristic
8#13066899C211yesmaximal, characteristic
9C11×#2960C211yesmaximal, characteristic
10C11×#533C2211yescharacteristic
11C2×C4×Dic22C2211yescharacteristic
12C11×#446—21no—
13C11×#446C2212yes—
14C8×Q8×C11—21no—
15C8×Q8×C11C2212yes—
16C11×#424—21no—
17C11×#423C2211yescharacteristic
18C11×#405—21no—
19C2×C4×C8×C11C2211yescharacteristic
20C2×Dic11⋊C8—21no—
21C2×C8×Dic11—21no—
22#10622704C412yes—
23#10622703C412yes—
24#10622663C412yes—
25#10622657C412yes—
26C4×#4326C2214yes—
27#10622538C2211yescharacteristic
28#10622538C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C8×Dic22—21no—
31C8×Dic22—21no—
32C8×Dic22C2212yes—
33C8×Dic22C2212yes—
34Q8⋊(C11⋊C8)C2214yes—
35#10622122C2214yes—
36#10622117C2214yes—
37#10622093C2212yes—
38C8×C11⋊C8C2212yes—
39C22×Dic22C2×C411yescharacteristic
40C2×C11×M16—21no—
41C22×C8×C11D411yescharacteristic
42C22×C8×C11D411yescharacteristic
43C11×C4⋊Q8C2×C411yescharacteristic
44C11×C4⋊Q8C2×C411yescharacteristic
45C11×#125—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8C2×C412yes—
48C4×Q8×C11—21no—
49C4×Q8×C11C2312yes—
50C11×#117—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4326C2×C414yes—
53C2×C4⋊Dic11C2×C411yescharacteristic
54C2×Dic11⋊C4—21no—
55C2×C4×Dic11—21no—
56C22×C11⋊C8—21no—
57C4×Dic22—21no—
58C4×Dic22—21no—
59C4×Dic22C2×C412yes—
60C4×Dic22C2312yes—
61C11×C4⋊C8—22no—
62C11×C4⋊C8—22no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8C2312yes—
65C11×#97—22no—
66C4×C8×C11—22no—
67C4×C8×C11D411yescharacteristic
68C4×C8×C11D411yescharacteristic
69C4×C8×C11C2311yescharacteristic
70C4×C8×C11C2311yescharacteristic
71#66899C2×C414yes—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)C2×C412yes—
74Dic11⋊C8—22no—
75Dic11⋊C8—22no—
76C8×Dic11—22no—
77C8×Dic11—22no—
78#66874C2×C414yes—
79#66871C2×C414yes—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)C2×C412yes—
83C4⋊(C11⋊C8)C2312yes—
84C4×C11⋊C8C2312yes—
85C4×C11⋊C8C2312yes—
86#17903—111nomaximal, Sylow
87C2×Q8×C11—21no—
88C2×Q8×C11C22×C412yes—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×Dic11—21no—
93C22×Dic11—21no—
94C2×Dic22—24no—
95C2×Dic22—21no—
96C2×Dic22C22×C412yes—
97C11×M16—42no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11Q1614yescomplemented
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11C2×D411yescharacteristic
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4C22×C412yes—
111C11×C22⋊C4—22no—
112C42×C11—22no—
113C42×C11C22×C411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C42×C11C2411yescharacteristic
117#4326—28no—
118C4⋊Dic11—21no—
119C4⋊Dic11C22×C412yes—
120Dic11⋊C4—22no—
121Dic11⋊C4—22no—
122C4×Dic11—22no—
123C4×Dic11—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—42no—
127C2×C11⋊C8C22×C414yes—
128#3104—111no—
129#2960D1111yescharacteristic
130C2×C8×Q8—111no—
131#1584—114no—
132C8×Q16—114no—
133#1571—111no—
134#1487—111no—
135#1481—111no—
136#1450—111no—
137C23×C11C4×D411yescharacteristic
138Q8×C11—24no—
139Q8×C11—42no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11C2×Q1612yes—
148C2×C4×C11#13512yes—
149C2×C4×C11C23×C411yescharacteristic
150C2×C4×C11C22×D411yescharacteristic
151C2×C4×C11C2×#4111yescharacteristic
152C2×Dic11—24no—
153C2×Dic11—22no—
154C2×Dic11—22no—
155C2×Dic11—42no—
156Dic22—24no—
157Dic22—22no—
158Dic22#13114yes—
159C8×C11—21no—
160C8×C11—21no—
161C8×C11—42no—
162C8×C11C2×Q1612yes—
163C8×C11C2×Q1612yes—
164C11⋊C8—24no—
165C11⋊C8—42no—
166C11⋊C8—42no—
167#533C2×D1111yescharacteristic
168C2×C4×Q8—111no—
169#484—112no—
170#477—112no—
171#462—112no—
172#451—112no—
173#446—21no—
174#446C2×D1112yes—
175C8×Q8—21no—
176C8×Q8—112no—
177C8×Q8—112no—
178C8×Q8—221no—
179C8×Q8—221no—
180C8×Q8C2×D1112yes—
181C4×Q16—114no—
182#431—111no—
183#431—111no—
184#424—21no—
185#423C2×D1111yescharacteristic
186C2×C4⋊C8—111no—
187C2×C4⋊C8—221no—
188#405—21no—
189C2×C4×C8—221no—
190C2×C4×C8C2×D1111yescharacteristic
191#335—114no—
192Q8⋊C8—114no—
193Q8⋊C8—114no—
194#322—112no—
195C82—112no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11C4×Q1612yes—
199C22×C11C2×C4×D411yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—42no—
204C4×C11—42no—
205C4×C11C4×Q1612yes—
206C4×C11C2×#13112yes—
207C4×C11C22×Q1611yescharacteristic
208C4×C11C2×#13511yescharacteristic
209Dic11—24no—
210Dic11—42no—
211C22×Q8—111no—
212C2×Q16—114no—
213C2×M16—21no—
214C22×C8—221no—
215C22×C8C22⋊D1111yescharacteristic
216C22×C8C22⋊D1111yescharacteristic
217C4⋊Q8C4×D1111yescharacteristic
218C4⋊Q8C4×D1111yescharacteristic
219#125—21no—
220C22⋊Q8—21no—
221C22⋊Q8C4×D1112yes—
222C4×Q8—21no—
223C4×Q8—112no—
224C4×Q8—112no—
225C4×Q8—221no—
226C4×Q8—221no—
227C4×Q8C22×D1112yes—
228#117—21no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—221no—
231C2×C42—221no—
232C2×C42C22×D1111yescharacteristic
233#107—114no—
234C4⋊C8—22no—
235C4⋊C8—22no—
236C4⋊C8—21no—
237C4⋊C8—112no—
238C4⋊C8—112no—
239C4⋊C8—222no—
240C4⋊C8—222no—
241C4⋊C8—221no—
242C4⋊C8—221no—
243C4⋊C8C22×D1112yes—
244#103—114no—
245#103—114no—
246C22⋊C8—112no—
247C22⋊C8—221no—
248#97—22no—
249C4×C8—22no—
250C4×C8—112no—
251C4×C8—112no—
252C4×C8—222no—
253C4×C8—222no—
254C4×C8C22⋊D1111yescharacteristic
255C4×C8C22⋊D1111yescharacteristic
256C4×C8C22×D1111yescharacteristic
257C4×C8C22×D1111yescharacteristic
258C2×C11—22no—
259C2×C11#292911yescharacteristic
260C2×C11C2×C4×Q1611yescharacteristic
261C2×C11#295511yescharacteristic
262C2×Q8—21no—
263C2×Q8—112no—
264C2×Q8—224no—
265C2×Q8—221no—
266C2×Q8C2×C4×D1112yes—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4C2×C4×D1111yescharacteristic
270C22×C4#433911yescharacteristic
271C22×C4C2×C22⋊D1111yescharacteristic
272Q16—228no—
273M16—42no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—114no—
277C2×C8—222no—
278C2×C8—222no—
279C2×C8—442no—
280C2×C8#432614yescomplemented
281C2×C8C2×C22⋊D1111yescharacteristic
282C2×C8C2×C22⋊D1111yescharacteristic
283C2×C8C2×C22⋊D1111yescharacteristic
284C2×C8C2×C22⋊D1111yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—112no—
291C4⋊C4—221no—
292C4⋊C4—222no—
293C4⋊C4—222no—
294C4⋊C4C2×C4×D1112yes—
295C22⋊C4—22no—
296C42—22no—
297C42—222no—
298C42—222no—
299C42C2×C4×D1111yescharacteristic
300C42#433911yescharacteristic
301C42C2×C22⋊D1111yescharacteristic
302C42C23×D1111yescharacteristic
303C11#1790311yescharacteristic, complemented, Sylow
304C23C4×C22⋊D1111yescharacteristic
305Q8—24no—
306Q8—42no—
307Q8—114no—
308Q8—224no—
309Q8—222no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—41no—
314C2×C4—224no—
315C2×C4—222no—
316C2×C4—222no—
317C2×C4—442no—
318C2×C4C4×C22⋊D1111yescharacteristic
319C2×C4C4×C22⋊D1111yescharacteristic
320C2×C4C4×C22⋊D1111yescharacteristic
321C2×C4C2×#432612yes—
322C2×C4#6700312yes—
323C2×C4C22×C4×D1111yescharacteristic
324C2×C4C2×#433911yescharacteristic
325C2×C4C22×C22⋊D1111yescharacteristic
326C8—21no—
327C8—21no—
328C8—42no—
329C8—224no—
330C8—442no—
331C8—442no—
332C8C2×#432612yes—
333C8C2×#432612yes—
334C22—21no—
335C22—21no—
336C22C4×#432612yes—
337C22C2×C4×C22⋊D1111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—42no—
343C4—224no—
344C4—442no—
345C4C4×#432612yes—
346C4D11×#13112yes—
347C4C22×#432611yescharacteristic
348C4C2×#6700311yescharacteristic
349C2—22no—
350C2#1307730811yescharacteristic
351C2C2×C4×#432611yescharacteristic
352C2#1307751711yescharacteristic
subgroupG/H
centerC2×C8C2×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2960C2
socleC22×C11C2×C4×D4
prime radicalC23×C11C4×D4
cosocleC42×C11C24
hypercenter#2960D11
hypocenterC11#17903
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ #2960

Complements

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

NH ≅ G/Ntype
3. #13067464C2semidirect
4. C8×#4326C2semidirect
100. C2×C8×C11Q16semidirect
280. C2×C8#4326semidirect
303. C11#17903semidirect

Maximal subgroups

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

subgroupindex
#130786512
C2×C8×Dic222
#130674642
C8×#43262
#130673922
#130670442
#130670192
#130668992
C11×#29602
#1790311