Finite Group Databasebeta

← #14719946

Subgroups — #14719946

Order 2816.

912 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077701C212yesmaximal, complemented
2#13066985C214yesmaximal, complemented
3#13066968C214yesmaximal, complemented
4#13066957C212yesmaximal, complemented
5#13066950C212yesmaximal, complemented
6C2×C11×#542C211yesmaximal, characteristic
7C11×#542—28no—
8C2×C11×C4⋊Q8C411yescharacteristic
9C2×C11×#126C2212yes—
10C2×C11×#124C411yescharacteristic
11C2×C11×#124C2212yes—
12C2×C11×#123C412yes—
13C2×C11×C22⋊Q8C412yes—
14C2×C11×C22⋊Q8C411yescharacteristic
15C2×C11×#121C411yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19#10622637—28no—
20#10622539C2214yes—
21#10622539C2214yes—
22#10622538C2214yes—
23#10622166C2214yes—
24#10622163C2214yes—
25#10622163C2218yes—
26C22×Q8×C11C2×C412yes—
27C22×Q8×C11C2×C411yescharacteristic
28C22×D4×C11C2×C411yescharacteristic
29C22×D4×C11C2×C412yes—
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C412yes—
32C11×C4⋊Q8—24no—
33C11×#126—24no—
34C11×#126—24no—
35C11×#124—24no—
36C11×#124—24no—
37C11×#124—24no—
38C11×#123—28no—
39C11×C22⋊Q8—24no—
40C11×C22⋊Q8—28no—
41C11×#121—24no—
42C4×Q8×C11D418yes—
43C4×D4×C11—24no—
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⋊C4C2×C412yes—
51C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
58C2×C11×C22⋊C4C2312yes—
59C2×C42×C11C2×C411yescharacteristic
60C2×C42×C11C2312yes—
61C2×C42×C11C2311yescharacteristic
62C22⋊(C11⋊C8)C2318yes—
63C4⋊(C11⋊C8)—24no—
64C4⋊(C11⋊C8)—24no—
65C4⋊(C11⋊C8)—24no—
66#66867—24no—
67#66867—24no—
68C4×C11⋊C8—24no—
69#17409—111nomaximal, Sylow
70C24×C11C22×C411yescharacteristic
71C24×C11C22×C412yes—
72C2×Q8×C11—24no—
73C2×Q8×C11—42no—
74C2×Q8×C11—82no—
75C2×Q8×C11C22⋊C414yes—
76C2×D4×C11—22no—
77C2×D4×C11—24no—
78C2×D4×C11—42no—
79C2×D4×C11—82no—
80C22×C4×C11—22no—
81C22×C4×C11—24no—
82C22×C4×C11—42no—
83C22×C4×C11—82no—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C22×C412yes—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C22×C412yes—
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C22×C412yes—
92C22×C4×C11C2411yescharacteristic
93C11×C4⋊C4—22no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—24no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4C22⋊C414yes—
99C11×C4⋊C4C22⋊C418yes—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—24no—
102C11×C22⋊C4—24no—
103C11×C22⋊C4—24no—
104C11×C22⋊C4—24no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—22no—
107C11×C22⋊C4—22no—
108C42×C11—22no—
109C42×C11C2×D414yes—
110C42×C11C2×D414yes—
111C42×C11C2×D414yes—
112C2×C11⋊C8—28no—
113C2×#542D1111yescharacteristic
114#2983—112no—
115#1473—114no—
116#1469—114no—
117#1466—112no—
118#1464—112no—
119C23×C11—21no—
120C23×C11—22no—
121C23×C11—22no—
122C23×C11—24no—
123C23×C11—42no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—42no—
127C23×C11C23×C411yescharacteristic
128Q8×C11—44no—
129Q8×C11—84no—
130D4×C11—44no—
131D4×C11—84no—
132C2×C4×C11—22no—
133C2×C4×C11—24no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—44no—
143C2×C4×C11—42no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—84no—
147C2×C4×C11C2×C22⋊C412yes—
148C2×C4×C11C2×C22⋊C414yes—
149C2×C4×C11C2×C22⋊C412yes—
150C2×C4×C11C2×C22⋊C414yes—
151C2×C4×C11C22×D412yes—
152C11⋊C8—48no—
153#542—28no—
154C2×C4⋊Q8Dic1111yescharacteristic
155C2×#126C2×D1112yes—
156C2×#124Dic1111yescharacteristic
157C2×#124C2×D1112yes—
158C2×#123Dic1112yes—
159C2×C22⋊Q8Dic1112yes—
160C2×C22⋊Q8Dic1111yescharacteristic
161C2×#121Dic1111yescharacteristic
162C2×C4×Q8C2×D1111yescharacteristic
163C2×C4×D4C2×D1111yescharacteristic
164C2×#117C2×D1111yescharacteristic
165#446—228no—
166#432—114no—
167#432—114no—
168#431—114no—
169#324—114no—
170#323—114no—
171#323—118no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—41no—
175C22×C11—42no—
176C22×C11—41no—
177C22×C11—42no—
178C22×C11—42no—
179C22×C11—41no—
180C22×C11—82no—
181C22×C11—84no—
182C22×C11C22×C22⋊C411yescharacteristic
183C22×C11#56812yes—
184C4×C11—22no—
185C4×C11—24no—
186C4×C11—22no—
187C4×C11—22no—
188C4×C11—24no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—42no—
192C4×C11—41no—
193C22×Q8C2×Dic1112yes—
194C22×Q8C2×Dic1111yescharacteristic
195C22×D4C2×Dic1111yescharacteristic
196C22×D4C2×Dic1112yes—
197C23×C4C2×Dic1111yescharacteristic
198C23×C4C2×Dic1112yes—
199C4⋊Q8—24no—
200#126—24no—
201#126—24no—
202#124—24no—
203#124—24no—
204#124—24no—
205#123—28no—
206C22⋊Q8—24no—
207C22⋊Q8—28no—
208#121—24no—
209C4×Q8C22⋊D1118yes—
210C4×D4—24no—
211#117—24no—
212C2×C4⋊C4C2×Dic1111yescharacteristic
213C2×C4⋊C4C2×Dic1111yescharacteristic
214C2×C4⋊C4C2×Dic1112yes—
215C2×C4⋊C4C2×Dic1112yes—
216C2×C4⋊C4C2×Dic1111yescharacteristic
217C2×C4⋊C4C2×Dic1112yes—
218C2×C4⋊C4C22×D1111yescharacteristic
219C2×C22⋊C4C2×Dic1111yescharacteristic
220C2×C22⋊C4C2×Dic1112yes—
221C2×C22⋊C4C2×Dic1112yes—
222C2×C22⋊C4C2×Dic1112yes—
223C2×C22⋊C4C2×Dic1112yes—
224C2×C22⋊C4C22×D1111yescharacteristic
225C2×C22⋊C4C22×D1112yes—
226C2×C42C2×Dic1111yescharacteristic
227C2×C42C22×D1111yescharacteristic
228C2×C42C22×D1112yes—
229C4⋊C8—224no—
230C4⋊C8—224no—
231C4⋊C8—224no—
232C22⋊C8—118no—
233#97—224no—
234#97—224no—
235C4×C8—224no—
236C2×C11—22no—
237C2×C11—81no—
238C2×C11—82no—
239C2×C11#287911yescharacteristic
240C2×C11#288411yescharacteristic
241C2×C11#288811yescharacteristic
242C24C22×Dic1111yescharacteristic
243C24C22×Dic1112yes—
244C2×Q8—24no—
245C2×Q8—42no—
246C2×Q8—82no—
247C2×Q8C22⋊Dic1114yes—
248C2×D4—22no—
249C2×D4—24no—
250C2×D4—42no—
251C2×D4—82no—
252C22×C4—22no—
253C22×C4—24no—
254C22×C4—42no—
255C22×C4—82no—
256C22×C4C22×Dic1111yescharacteristic
257C22×C4C22×Dic1111yescharacteristic
258C22×C4C22×Dic1112yes—
259C22×C4C22×Dic1111yescharacteristic
260C22×C4C22×Dic1111yescharacteristic
261C22×C4C22×Dic1112yes—
262C22×C4C22×Dic1111yescharacteristic
263C22×C4C22×Dic1112yes—
264C22×C4C23×D1111yescharacteristic
265C2×C8—228no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—24no—
269C4⋊C4—24no—
270C4⋊C4—22no—
271C4⋊C4C22⋊Dic1114yes—
272C4⋊C4C22⋊Dic1118yes—
273C22⋊C4—22no—
274C22⋊C4—24no—
275C22⋊C4—24no—
276C22⋊C4—24no—
277C22⋊C4—24no—
278C22⋊C4—22no—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C42—22no—
282C42C2×C22⋊D1114yes—
283C42C2×C22⋊D1114yes—
284C42C2×C22⋊D1114yes—
285C11#1740911yescharacteristic, complemented, Sylow
286C23—21no—
287C23—22no—
288C23—22no—
289C23—24no—
290C23—42no—
291C23—41no—
292C23—41no—
293C23—42no—
294C23C23×Dic1111yescharacteristic
295Q8—44no—
296Q8—84no—
297D4—44no—
298D4—84no—
299C2×C4—22no—
300C2×C4—24no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—44no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—84no—
314C2×C4C2×C22⋊Dic1112yes—
315C2×C4C2×C22⋊Dic1114yes—
316C2×C4C2×C22⋊Dic1112yes—
317C2×C4C2×C22⋊Dic1114yes—
318C2×C4C22×C22⋊D1112yes—
319C8—448no—
320C22—21no—
321C22—21no—
322C22—41no—
323C22—42no—
324C22—41no—
325C22—42no—
326C22—42no—
327C22—41no—
328C22—82no—
329C22—84no—
330C22#1062335012yes—
331C22C22×C22⋊Dic1111yescharacteristic
332C4—22no—
333C4—24no—
334C4—22no—
335C4—22no—
336C4—24no—
337C4—41no—
338C4—41no—
339C4—42no—
340C4—41no—
341C2—22no—
342C2—81no—
343C2—82no—
344C2#1307706111yescharacteristic
345C2#1307708011yescharacteristic
346C2#1307709511yescharacteristic
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#17409
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. #13077701C2semidirect
2. #13066985C2semidirect
3. #13066968C2semidirect
4. #13066957C2semidirect
5. #13066950C2semidirect
285. C11#17409semidirect

Maximal subgroups

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

subgroupindex
#130777012
#130669852
#130669682
#130669572
#130669502
C2×C11×#5422
#1740911