Finite Group Databasebeta

← #14719934

Subgroups — #14719934

Order 2816.

948 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#13077645C212yesmaximal, complemented
2#13066980C214yesmaximal, complemented
3#13066964C214yesmaximal, complemented
4#13066960C212yesmaximal, complemented
5#13066950C212yesmaximal, complemented
6C2×C11×#542C211yesmaximal, characteristic
7C11×#542—28no—
8C2×C11×C4⋊Q8C411yescharacteristic
9C2×C11×#126C412yes—
10C2×C11×#124C411yescharacteristic
11C2×C11×#124C412yes—
12C2×C11×#123C2212yes—
13C2×C11×C22⋊Q8C411yescharacteristic
14C2×C11×C22⋊Q8C2212yes—
15C2×C11×#121C411yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19#10622820C2214yes—
20C2×C22⋊(C11⋊C8)C2214yes—
21#10622624—28no—
22#10622539C2214yes—
23#10622166C2214yes—
24#10622166C2218yes—
25#10622163C2214yes—
26C22×Q8×C11C2×C411yescharacteristic
27C22×Q8×C11C2×C412yes—
28C22×D4×C11C2×C412yes—
29C22×D4×C11C2×C411yescharacteristic
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2312yes—
32C11×C4⋊Q8—24no—
33C11×#126—28no—
34C11×#124—24no—
35C11×#124—28no—
36C11×#123—24no—
37C11×#123—24no—
38C11×C22⋊Q8—24no—
39C11×C22⋊Q8—24no—
40C11×C22⋊Q8—24no—
41C11×#121—24no—
42C4×Q8×C11—24no—
43C4×D4×C11D418yes—
44C11×#117—24no—
45C2×C11×C4⋊C4C2×C411yescharacteristic
46C2×C11×C4⋊C4C2×C411yescharacteristic
47C2×C11×C4⋊C4C2×C412yes—
48C2×C11×C4⋊C4C2×C412yes—
49C2×C11×C4⋊C4C2×C411yescharacteristic
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C22⋊C4C2×C411yescharacteristic
53C2×C11×C22⋊C4C2×C412yes—
54C2×C11×C22⋊C4C2×C412yes—
55C2×C11×C22⋊C4C2×C412yes—
56C2×C11×C22⋊C4C2×C412yes—
57C2×C11×C22⋊C4C2×C412yes—
58C2×C11×C22⋊C4C2311yescharacteristic
59C2×C42×C11C2×C411yescharacteristic
60C2×C42×C11C2×C412yes—
61C2×C42×C11C2311yescharacteristic
62C2×#4318—24no—
63C22×C11⋊C8—24no—
64C22⋊(C11⋊C8)—24no—
65C22⋊(C11⋊C8)—24no—
66C22⋊(C11⋊C8)C2318yes—
67C4⋊(C11⋊C8)—24no—
68#66867—24no—
69#17407—111nomaximal, Sylow
70C24×C11C22×C411yescharacteristic
71C24×C11C22×C412yes—
72C2×Q8×C11—22no—
73C2×Q8×C11—24no—
74C2×Q8×C11—42no—
75C2×Q8×C11—82no—
76C2×D4×C11—24no—
77C2×D4×C11—42no—
78C2×D4×C11—82no—
79C2×D4×C11C22⋊C414yes—
80C22×C4×C11—22no—
81C22×C4×C11—42no—
82C22×C4×C11—82no—
83C22×C4×C11C22×C412yes—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C22×C412yes—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C22×C412yes—
91C22×C4×C11C2×D414yes—
92C22×C4×C11C2×D414yes—
93C22×C4×C11C2411yescharacteristic
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4C22⋊C414yes—
102C11×C22⋊C4—24no—
103C11×C22⋊C4—24no—
104C11×C22⋊C4—24no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—24no—
107C11×C22⋊C4—22no—
108C11×C22⋊C4C22⋊C418yes—
109C42×C11—22no—
110C42×C11—24no—
111C42×C11C2×D414yes—
112#4318—84no—
113C2×C11⋊C8—28no—
114C2×C11⋊C8—84no—
115C2×#542D1111yescharacteristic
116#2973—112no—
117#1472—114no—
118#1468—114no—
119#1467—112no—
120#1464—112no—
121C23×C11—24no—
122C23×C11—21no—
123C23×C11—22no—
124C23×C11—42no—
125C23×C11—42no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11C2×C22⋊C414yes—
129C23×C11C23×C411yescharacteristic
130Q8×C11—44no—
131Q8×C11—84no—
132D4×C11—44no—
133D4×C11—84no—
134C2×C4×C11—22no—
135C2×C4×C11—21no—
136C2×C4×C11—22no—
137C2×C4×C11—21no—
138C2×C4×C11—22no—
139C2×C4×C11—21no—
140C2×C4×C11—22no—
141C2×C4×C11—24no—
142C2×C4×C11—44no—
143C2×C4×C11—44no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—41no—
147C2×C4×C11—44no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11C2×C22⋊C412yes—
152C2×C4×C11C2×C22⋊C412yes—
153C2×C4×C11C2×C22⋊C414yes—
154C2×C4×C11C22×D412yes—
155C11⋊C8—48no—
156#542—28no—
157C2×C4⋊Q8Dic1111yescharacteristic
158C2×#126Dic1112yes—
159C2×#124Dic1111yescharacteristic
160C2×#124Dic1112yes—
161C2×#123C2×D1112yes—
162C2×C22⋊Q8Dic1111yescharacteristic
163C2×C22⋊Q8C2×D1112yes—
164C2×#121Dic1111yescharacteristic
165C2×C4×Q8C2×D1111yescharacteristic
166C2×C4×D4C2×D1111yescharacteristic
167C2×#117C2×D1111yescharacteristic
168#435—228no—
169#432—114no—
170#407—114no—
171C2×C22⋊C8—114no—
172#324—114no—
173#324—118no—
174#323—114no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—24no—
178C22×C11—24no—
179C22×C11—24no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—84no—
184C22×C11—82no—
185C22×C11C22×C22⋊C411yescharacteristic
186C22×C11#56812yes—
187C4×C11—22no—
188C4×C11—22no—
189C4×C11—24no—
190C4×C11—22no—
191C4×C11—41no—
192C4×C11—42no—
193C4×C11—42no—
194C4×C11—41no—
195C4×C11—41no—
196C22×Q8C2×Dic1111yescharacteristic
197C22×Q8C2×Dic1112yes—
198C22×D4C2×Dic1112yes—
199C22×D4C2×Dic1111yescharacteristic
200C23×C4C2×Dic1111yescharacteristic
201C23×C4C22×D1112yes—
202C2×M16—224no—
203C22×C8—224no—
204C4⋊Q8—24no—
205#126—28no—
206#124—24no—
207#124—28no—
208#123—24no—
209#123—24no—
210C22⋊Q8—24no—
211C22⋊Q8—24no—
212C22⋊Q8—24no—
213#121—24no—
214C4×Q8—24no—
215C4×D4C22⋊D1118yes—
216#117—24no—
217C2×C4⋊C4C2×Dic1111yescharacteristic
218C2×C4⋊C4C2×Dic1111yescharacteristic
219C2×C4⋊C4C2×Dic1112yes—
220C2×C4⋊C4C2×Dic1112yes—
221C2×C4⋊C4C2×Dic1111yescharacteristic
222C2×C4⋊C4C22×D1111yescharacteristic
223C2×C4⋊C4C22×D1112yes—
224C2×C22⋊C4C2×Dic1111yescharacteristic
225C2×C22⋊C4C2×Dic1112yes—
226C2×C22⋊C4C2×Dic1112yes—
227C2×C22⋊C4C2×Dic1112yes—
228C2×C22⋊C4C2×Dic1112yes—
229C2×C22⋊C4C2×Dic1112yes—
230C2×C22⋊C4C22×D1111yescharacteristic
231C2×C42C2×Dic1111yescharacteristic
232C2×C42C2×Dic1112yes—
233C2×C42C22×D1111yescharacteristic
234C4⋊C8—224no—
235C22⋊C8—118no—
236C22⋊C8—224no—
237C22⋊C8—224no—
238#97—224no—
239C2×C11—22no—
240C2×C11—44no—
241C2×C11—81no—
242C2×C11#287911yescharacteristic
243C2×C11#288311yescharacteristic
244C2×C11#288911yescharacteristic
245C24C22×Dic1111yescharacteristic
246C24C22×Dic1112yes—
247C2×Q8—22no—
248C2×Q8—24no—
249C2×Q8—42no—
250C2×Q8—82no—
251C2×D4—24no—
252C2×D4—42no—
253C2×D4—82no—
254C2×D4C22⋊Dic1114yes—
255C22×C4—22no—
256C22×C4—42no—
257C22×C4—82no—
258C22×C4C22×Dic1112yes—
259C22×C4C22×Dic1111yescharacteristic
260C22×C4C22×Dic1111yescharacteristic
261C22×C4C22×Dic1111yescharacteristic
262C22×C4C22×Dic1111yescharacteristic
263C22×C4C22×Dic1112yes—
264C22×C4C22×Dic1111yescharacteristic
265C22×C4C22×Dic1112yes—
266C22×C4C2×C22⋊D1114yes—
267C22×C4C2×C22⋊D1114yes—
268C22×C4C23×D1111yescharacteristic
269M16—884no—
270C2×C8—228no—
271C2×C8—884no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4C22⋊Dic1114yes—
280C22⋊C4—24no—
281C22⋊C4—24no—
282C22⋊C4—24no—
283C22⋊C4—22no—
284C22⋊C4—24no—
285C22⋊C4—22no—
286C22⋊C4C22⋊Dic1118yes—
287C42—22no—
288C42—24no—
289C42C2×C22⋊D1114yes—
290C11#1740711yescharacteristic, complemented, Sylow
291C23—24no—
292C23—21no—
293C23—22no—
294C23—42no—
295C23—42no—
296C23—41no—
297C23—41no—
298C23C2×C22⋊Dic1114yes—
299C23C23×Dic1111yescharacteristic
300Q8—44no—
301Q8—84no—
302D4—44no—
303D4—84no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—44no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4C2×C22⋊Dic1112yes—
322C2×C4C2×C22⋊Dic1112yes—
323C2×C4C2×C22⋊Dic1114yes—
324C2×C4C22×C22⋊D1112yes—
325C8—448no—
326C22—21no—
327C22—21no—
328C22—24no—
329C22—24no—
330C22—24no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—84no—
335C22—82no—
336C22#1062335012yes—
337C22C22×C22⋊Dic1111yescharacteristic
338C4—22no—
339C4—22no—
340C4—24no—
341C4—22no—
342C4—41no—
343C4—42no—
344C4—42no—
345C4—41no—
346C4—41no—
347C2—22no—
348C2—44no—
349C2—81no—
350C2#1307706111yescharacteristic
351C2#1307707711yescharacteristic
352C2#1307709911yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#542C2
socleC22×C11C22×C22⋊C4
prime radicalC2×C11×#121C4
cosocleC22×C4×C11C24
hypercenterC2×#542D11
hypocenterC11#17407
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. #13077645C2semidirect
2. #13066980C2semidirect
3. #13066964C2semidirect
4. #13066960C2semidirect
5. #13066950C2semidirect
290. C11#17407semidirect

Maximal subgroups

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

subgroupindex
#130776452
#130669802
#130669642
#130669602
#130669502
C2×C11×#5422
#1740711