Finite Group Databasebeta

← #14763535

Subgroups — #14763535

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622539C211yesmaximal, characteristic
2#13071023C211yesmaximal, characteristic
3#13069590C212yesmaximal, complemented
4#13069437C212yesmaximal, complemented
5#13068929C214yesmaximal
6#13068621C214yesmaximal, complemented
7C2×C11×#533C211yesmaximal, characteristic
8C11×#533—24no—
9C11×#533C418yescomplemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#125—21no—
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8C2212yes—
15C2×C4×Q8×C11—21no—
16C2×C4×Q8×C11C2212yes—
17C2×C11×#117—21no—
18C22×C42×C11C2211yescharacteristic
19C2×#66979C2212yes—
20C2×#66899C2218yes—
21#10622825—21no—
22#10622825—21no—
23C2×C22⋊(C11⋊C8)C2212yes—
24#10622549C2212yes—
25#10622548C2212yes—
26C4×C4⋊Dic11—21no—
27C4×C4⋊Dic11—21no—
28#10622539—24no—
29C2×C4⋊(C11⋊C8)C2212yes—
30C2×#66867C2212yes—
31#10622167C2218yes—
32C22×Q8×C11—21no—
33C22×Q8×C11C2312yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C11×C4⋊Q8—22no—
38C11×C4⋊Q8—22no—
39C11×C4⋊Q8C2×C414yes—
40C11×C4⋊Q8C2×C414yes—
41C11×#125—28no—
42C11×C22⋊Q8—28no—
43C11×C22⋊Q8—24no—
44C11×C22⋊Q8C2×C418yes—
45C4×Q8×C11—28no—
46C4×Q8×C11—24no—
47C4×Q8×C11C2×C418yes—
48C11×#117—28no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—22no—
56C2×C42×C11—22no—
57C2×C42×C11C2×C414yes—
58C2×C42×C11D411yescharacteristic
59C2×C42×C11D411yescharacteristic
60C2×C42×C11D414yes—
61C2×C42×C11C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11—22no—
64#66979—44no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11C2314yes—
68C2×C4×Dic11—22no—
69C22×C11⋊C8C2314yes—
70#66899—48no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C22⋊(C11⋊C8)—24no—
74C4⋊(C11⋊C8)—24no—
75#66867—24no—
76#21870—111nomaximal, Sylow
77C24×C11C2×D411yescharacteristic
78C2×Q8×C11—24no—
79C2×Q8×C11—22no—
80C2×Q8×C11—24no—
81C2×Q8×C11—24no—
82C2×Q8×C11—44no—
83C2×Q8×C11C22×C414yes—
84C22×C4×C11—24no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—42no—
90C22×C4×C11C22⋊C414yes—
91C22×C4×C11C22⋊C414yes—
92C22×C4×C11C22×C412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—24no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—28no—
105C11×C4⋊C4—28no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4C22×C414yes—
108C11×C22⋊C4—28no—
109C42×C11—28no—
110C42×C11C22⋊C414yes—
111C42×C11C22⋊C414yes—
112C42×C11C22×C412yes—
113C42×C11C22×C412yes—
114C42×C11C2×D412yes—
115C42×C11C2×D412yes—
116C22⋊Dic11—44no—
117C4⋊Dic11—28no—
118C4⋊Dic11—44no—
119C4⋊Dic11—44no—
120C4×Dic11—44no—
121C2×C11⋊C8—24no—
122C2×C11⋊C8—24no—
123C2×C11⋊C8—24no—
124C2×#533D1111yescharacteristic
125C2×#432—111no—
126#2285—111no—
127#1993—112no—
128#1960—112no—
129#1873—114no—
130#1803—114no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—22no—
134C23×C11—22no—
135C23×C11C2×C22⋊C412yes—
136C23×C11C22×D411yescharacteristic
137Q8×C11—28no—
138Q8×C11—48no—
139Q8×C11—44no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—24no—
146C2×C4×C11—24no—
147C2×C4×C11—28no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—44no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—44no—
154C2×C4×C11C2×C22⋊C412yes—
155C2×C4×C11C2×C22⋊C412yes—
156C2×C4×C11C2×C22⋊C412yes—
157C2×C4×C11C2×C22⋊C412yes—
158C2×C4×C11C2×C22⋊C412yes—
159C2×C4×C11#13714yes—
160C2×C4×C11C23×C411yescharacteristic
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11H(5,𝔽2)12yes—
163C2×C4×C112−1+412yes—
164C2×Dic11—44no—
165C2×Dic11—44no—
166C2×Dic11—44no—
167C11⋊C8—44no—
168#533—24no—
169#533Dic1118yescomplemented
170C2×C4⋊Q8C2×D1111yescharacteristic
171C2×C4⋊Q8C2×D1111yescharacteristic
172C2×#125—21no—
173C2×C22⋊Q8—21no—
174C2×C22⋊Q8C2×D1112yes—
175C2×C4×Q8—21no—
176C2×C4×Q8C2×D1112yes—
177C2×#117—21no—
178C2×#117—112no—
179C22×C42C2×D1111yescharacteristic
180#432—224no—
181C2×C4⋊C8—112no—
182C2×#103—118no—
183C2×C22⋊C8—112no—
184C2×#97—112no—
185#384—112no—
186#382—112no—
187#380—221no—
188#380—221no—
189C4×C4⋊C4—221no—
190C4×C4⋊C4—221no—
191#340—118no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11—42no—
196C22×C11—42no—
197C22×C11C22×C22⋊C411yescharacteristic
198C22×C11#53511yescharacteristic
199C22×C11#53611yescharacteristic
200C22×C11C2×#13712yes—
201C22×C11#57512yes—
202C4×C11—22no—
203C4×C11—22no—
204C4×C11—22no—
205C4×C11—22no—
206C4×C11—44no—
207C4×C11—44no—
208C4×C11#41914yes—
209C4×C11#52012yes—
210C4×C11#53712yes—
211Dic11—84no—
212C22×Q8—21no—
213C22×Q8C22×D1112yes—
214C23×C4C22⋊D1111yescharacteristic
215C23×C4C22⋊D1111yescharacteristic
216C23×C4C22×D1111yescharacteristic
217C22×C8—114no—
218C4⋊Q8—22no—
219C4⋊Q8—22no—
220C4⋊Q8C2×Dic1114yes—
221C4⋊Q8C2×Dic1114yes—
222#125—28no—
223C22⋊Q8—28no—
224C22⋊Q8—24no—
225C22⋊Q8C2×Dic1118yes—
226C4×Q8—28no—
227C4×Q8—24no—
228C4×Q8C2×Dic1118yes—
229#117—28no—
230#117—444no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—114no—
237C2×C4⋊C4—222no—
238C2×C4⋊C4—222no—
239C2×C4⋊C4C22×D1112yes—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—222no—
242C2×C42—22no—
243C2×C42—222no—
244C2×C42C2×Dic1114yes—
245C2×C42C22⋊D1111yescharacteristic
246C2×C42C22⋊D1111yescharacteristic
247C2×C42C22⋊D1114yes—
248C2×C42C22×D1111yescharacteristic
249C2×C42C22×D1111yescharacteristic
250C4⋊C8—224no—
251#103—448no—
252C22⋊C8—224no—
253#97—224no—
254#95—222no—
255#95—222no—
256C2×C11—42no—
257C2×C11#231111yescharacteristic
258C2×C11C2×#41911yescharacteristic
259C2×C11#289611yescharacteristic
260C2×C11#321612yes—
261C2×C11#323712yes—
262C24C2×C22⋊D1111yescharacteristic
263C2×Q8—24no—
264C2×Q8—22no—
265C2×Q8—24no—
266C2×Q8—24no—
267C2×Q8—44no—
268C2×Q8C22×Dic1114yes—
269C22×C4—24no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—42no—
275C22×C4—224no—
276C22×C4C22⋊Dic1114yes—
277C22×C4C22⋊Dic1114yes—
278C22×C4C22×Dic1112yes—
279C22×C4C2×C22⋊D1111yescharacteristic
280C22×C4C2×C22⋊D1111yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
282C22×C4C2×C22⋊D1111yescharacteristic
283C22×C4C2×C22⋊D1112yes—
284C22×C4C2×C22⋊D1111yescharacteristic
285C22×C4C23×D1111yescharacteristic
286C2×C8—224no—
287C2×C8—224no—
288C2×C8—224no—
289C4⋊C4—24no—
290C4⋊C4—24no—
291C4⋊C4—24no—
292C4⋊C4—28no—
293C4⋊C4—28no—
294C4⋊C4—22no—
295C4⋊C4—228no—
296C4⋊C4—444no—
297C4⋊C4—444no—
298C4⋊C4C22×Dic1114yes—
299C22⋊C4—28no—
300C22⋊C4—444no—
301C42—28no—
302C42—444no—
303C42C22⋊Dic1114yes—
304C42C22⋊Dic1114yes—
305C42C22×Dic1112yes—
306C42C22×Dic1112yes—
307C42C2×C22⋊D1112yes—
308C42C2×C22⋊D1112yes—
309C11#2187011yescharacteristic, complemented, Sylow
310C23—22no—
311C23—22no—
312C23—21no—
313C23—21no—
314C23C2×C22⋊Dic1112yes—
315C23C22×C22⋊D1111yescharacteristic
316Q8—28no—
317Q8—48no—
318Q8—44no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—28no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—444no—
334C2×C4—444no—
335C2×C4—444no—
336C2×C4#6699514yes—
337C2×C4C2×C22⋊Dic1112yes—
338C2×C4C2×C22⋊Dic1112yes—
339C2×C4C2×C22⋊Dic1112yes—
340C2×C4C2×C22⋊Dic1112yes—
341C2×C4C2×C22⋊Dic1112yes—
342C2×C4#6704212yes—
343C2×C4#6704312yes—
344C2×C4C23×Dic1111yescharacteristic
345C2×C4C22×C22⋊D1111yescharacteristic
346C8—444no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—42no—
351C22—42no—
352C22C2×#6699512yes—
353C22#1062335312yes—
354C22#1062335611yescharacteristic
355C22#1062336111yescharacteristic
356C22C22×C22⋊Dic1111yescharacteristic
357C4—22no—
358C4—22no—
359C4—22no—
360C4—22no—
361C4—44no—
362C4—44no—
363C4—884no—
364C4#1062283814yes—
365C4#1062335812yes—
366C4#1062336412yes—
367C2—42no—
368C2#1307120811yescharacteristic
369C2C2×#1062283811yescharacteristic
370C2#1307713511yescharacteristic
371C2#1307962312yes—
372C2#1307982612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#533C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#533D11
hypocenterC11#21870
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
3. #13069590C2semidirect
4. #13069437C2semidirect
6. #13068621C2semidirect
9. C11×#533C4semidirect
169. #533Dic11semidirect
309. C11#21870semidirect

Maximal subgroups

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

subgroupindex
C2×#106225392
#130710232
#130695902
#130694372
#130689292
#130686212
C2×C11×#5332
#2187011