Finite Group Databasebeta

← #14807389

Subgroups — #14807389

Order 2816.

1052 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622705C211yesmaximal, characteristic, complemented
2C2×#10622682C211yesmaximal, characteristic, complemented
3#13074382C211yesmaximal, characteristic
4#13069624C214yesmaximal
5#13069582C211yesmaximal, characteristic, complemented
6#13069437C211yesmaximal, characteristic, complemented
7#13068957C214yesmaximal, complemented
8#13068382C211yesmaximal, characteristic
9C2×C11×#541C211yesmaximal, characteristic
10C11×#541—24no—
11C11×#541—24no—
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#126—22no—
14C2×C11×#125—22no—
15C2×C11×#125C2211yescharacteristic
16C2×C11×C22⋊Q8C2212yes—
17C2×C4×Q8×C11C2212yes—
18C2×C11×#117C2211yescharacteristic
19C22×#4326C2214yes—
20C2×#66977C2212yes—
21C2×#66922C2211yescharacteristic
22C2×#66899C2214yes—
23C2×C22⋊(C11⋊C8)C2212yes—
24#10622705—24no—
25#10622682—24no—
26#10622596—22no—
27C2×#66874C2214yes—
28#10622566—22no—
29#10622549C2211yescharacteristic
30#10622542C2212yes—
31C2×#66867C2211yescharacteristic
32C2×C4×C11⋊C8C2211yescharacteristic
33#10622167C2214yes—
34#10622162C2212yes—
35C22×Q8×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C22×Dic22C2312yes—
38C11×C4⋊Q8—22no—
39C11×C4⋊Q8D414yes—
40C11×#126—216no—
41C11×#125—216no—
42C11×#125—22no—
43C11×#125D414yes—
44C11×C22⋊Q8—24no—
45C11×C22⋊Q8—24no—
46C4×Q8×C11—24no—
47C4×Q8×C11—24no—
48C11×#117—22no—
49C11×#117—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4D412yes—
58C2×C42×C11—22no—
59C2×C42×C11C2311yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—22no—
62C2×#4326—28no—
63C2×#4326—28no—
64C2×#4326—44no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11C2312yes—
67#66977—44no—
68C2×Dic11⋊C4—22no—
69C22×C11⋊C8C2312yes—
70C22×C11⋊C8C2312yes—
71#66922—22no—
72#66922—22no—
73#66899—44no—
74C11⋊#95—24no—
75C11⋊#95—22no—
76C22⋊(C11⋊C8)—24no—
77#66874—28no—
78#66867—22no—
79C4×C11⋊C8—22no—
80#25609—111nomaximal, Sylow
81C24×C11C2×D411yescharacteristic
82C2×Q8×C11—22no—
83C2×Q8×C11—24no—
84C2×Q8×C11—24no—
85C2×Q8×C11C2×D414yes—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2411yescharacteristic
96C22×Dic11—22no—
97C22×Dic11—22no—
98C2×Dic22—22no—
99C2×Dic22—22no—
100C2×Dic22—24no—
101C2×Dic22—24no—
102C11×C4⋊C4—28no—
103C11×C4⋊C4—28no—
104C11×C4⋊C4—28no—
105C11×C4⋊C4—28no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4C2×D414yes—
109C11×C22⋊C4—28no—
110C11×C22⋊C4—24no—
111C42×C11—28no—
112C42×C11—21no—
113C42×C11—21no—
114C42×C11C2×D412yes—
115C42×C11C2×D412yes—
116C22⋊Dic11—44no—
117#4326—416no—
118C4⋊Dic11—24no—
119C4⋊Dic11—44no—
120Dic11⋊C4—44no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8#4114yes—
127C2×#541D1111yescharacteristic
128C2×#494—111no—
129C2×#491—111no—
130#2621—111no—
131#2001—114no—
132#1991—111no—
133#1960—111no—
134#1878—114no—
135#1750—111no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—24no—
140C23×C11C22×D411yescharacteristic
141Q8×C11—28no—
142Q8×C11—44no—
143C2×C4×C11—24no—
144C2×C4×C11—22no—
145C2×C4×C11—24no—
146C2×C4×C11—24no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—24no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—44no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11#12014yes—
157C2×C4×C11C22×D411yescharacteristic
158C2×C4×C11C22×D411yescharacteristic
159C2×C4×C11C2×#4112yes—
160C2×C4×C11H(5,𝔽2)12yes—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—44no—
166Dic22—44no—
167Dic22—44no—
168C11⋊C8—24no—
169C11⋊C8—42no—
170C22×Q16—114no—
171#541—24no—
172#541—24no—
173C2×C4⋊Q8—111no—
174C2×C4⋊Q8C2×D1111yescharacteristic
175C2×#126—22no—
176C2×#125—22no—
177C2×#125C2×D1111yescharacteristic
178C2×C22⋊Q8—112no—
179C2×C22⋊Q8C2×D1112yes—
180C2×C4×Q8C2×D1112yes—
181C2×#117C2×D1111yescharacteristic
182#494—224no—
183#491—224no—
184C2×#103—114no—
185C2×#103—114no—
186C2×C22⋊C8—112no—
187C2×#97—111no—
188C2×C4×C8—111no—
189#398—222no—
190#397—222no—
191#391—112no—
192#382—111no—
193#340—114no—
194#336—112no—
195C22×C11—42no—
196C22×C11—41no—
197C22×C11—42no—
198C22×C11—42no—
199C22×C11C2×#12011yescharacteristic
200C22×C11#53211yescharacteristic
201C22×C11#53511yescharacteristic
202C22×C11#57814yes—
203C4×C11—24no—
204C4×C11—41no—
205C4×C11—44no—
206C4×C11—42no—
207C4×C11—44no—
208C4×C11#54612yes—
209C4×C11#55012yes—
210Dic11—82no—
211Dic11—82no—
212C22×Q8—112no—
213C22×Q8C22×D1112yes—
214C23×C4C22×D1111yescharacteristic
215C2×Q16—228no—
216C2×Q16—228no—
217C2×Q16—444no—
218C22×C8—112no—
219C22×C8—112no—
220C4⋊Q8—22no—
221C4⋊Q8—222no—
222C4⋊Q8—222no—
223C4⋊Q8C22⋊D1114yes—
224#126—216no—
225#125—216no—
226#125—22no—
227#125C22⋊D1114yes—
228C22⋊Q8—24no—
229C22⋊Q8—24no—
230C22⋊Q8—444no—
231C4×Q8—24no—
232C4×Q8—24no—
233#117—22no—
234#117—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—112no—
240C2×C4⋊C4—222no—
241C2×C4⋊C4—222no—
242C2×C4⋊C4C22⋊D1112yes—
243C2×C4⋊C4C22×D1112yes—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—222no—
246C2×C22⋊C4C22⋊D1112yes—
247C2×C42—22no—
248C2×C42C22×D1111yescharacteristic
249C2×C42C22×D1111yescharacteristic
250#103—228no—
251#103—444no—
252C22⋊C8—224no—
253#97—222no—
254C4×C8—222no—
255#95—222no—
256#95—224no—
257C2×C11—81no—
258C2×C11#243111yescharacteristic
259C2×C11#301112yes—
260C2×C11#317712yes—
261C2×C11#322312yes—
262C24C2×C22⋊D1111yescharacteristic
263C2×Q8—22no—
264C2×Q8—24no—
265C2×Q8—24no—
266C2×Q8—224no—
267C2×Q8—224no—
268C2×Q8—222no—
269C2×Q8—222no—
270C2×Q8C2×C22⋊D1114yes—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—222no—
278C22×C4—222no—
279C22×C4C2×C22⋊D1112yes—
280C22×C4C2×C22⋊D1111yescharacteristic
281C22×C4C2×C22⋊D1112yes—
282C22×C4C23×D1111yescharacteristic
283Q16—4416no—
284C2×C8—114no—
285C2×C8—222no—
286C2×C8—222no—
287C2×C8—222no—
288C2×C8—222no—
289C2×C8—222no—
290C4⋊C4—28no—
291C4⋊C4—28no—
292C4⋊C4—28no—
293C4⋊C4—28no—
294C4⋊C4—24no—
295C4⋊C4—22no—
296C4⋊C4—224no—
297C4⋊C4—444no—
298C4⋊C4—444no—
299C4⋊C4C2×C22⋊D1114yes—
300C22⋊C4—28no—
301C22⋊C4—24no—
302C22⋊C4—444no—
303C42—28no—
304C42—21no—
305C42—21no—
306C42C2×C22⋊D1112yes—
307C42C2×C22⋊D1112yes—
308C11#2560911yescharacteristic, complemented, Sylow
309C23—21no—
310C23—21no—
311C23—24no—
312C23—21no—
313C23C22×C22⋊D1111yescharacteristic
314Q8—28no—
315Q8—44no—
316Q8—444no—
317Q8—444no—
318C2×C4—24no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—24no—
322C2×C4—22no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—44no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—442no—
334C2×C4—444no—
335C2×C4—442no—
336C2×C4#6700614yes—
337C2×C4#41×D1112yes—
338C2×C4#6704212yes—
339C2×C4C22×C22⋊D1111yescharacteristic
340C2×C4C22×C22⋊D1111yescharacteristic
341C8—224no—
342C8—442no—
343C22—41no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22#1062336111yescharacteristic
348C22#1062336311yescharacteristic
349C22#1062336914yes—
350C22C2×#6700611yescharacteristic
351C4—24no—
352C4—41no—
353C4—44no—
354C4—42no—
355C4—44no—
356C4—882no—
357C4—882no—
358C4#1062336012yes—
359C4#1062336512yes—
360C2—81no—
361C2#1307223111yescharacteristic
362C2#1307791112yes—
363C2#1307926912yes—
364C2#1307969312yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#541C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#541D11
hypocenterC11#25609
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. C2×#10622705C2semidirect
2. C2×#10622682C2semidirect
5. #13069582C2semidirect
6. #13069437C2semidirect
7. #13068957C2semidirect
308. C11#25609semidirect

Maximal subgroups

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

subgroupindex
C2×#106227052
C2×#106226822
#130743822
#130696242
#130695822
#130694372
#130689572
#130683822
C2×C11×#5412
#2560911