Finite Group Databasebeta

← #14807396

Subgroups — #14807396

Order 2816.

1052 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1052 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623228C211yesmaximal, characteristic
2C2×#10622705C211yesmaximal, characteristic, complemented
3#13074383C211yesmaximal, characteristic
4#13069625C214yesmaximal
5#13069582C211yesmaximal, characteristic, complemented
6#13069436C211yesmaximal, characteristic, complemented
7#13068954C214yesmaximal, complemented
8#13068385C211yesmaximal, characteristic
9C2×C11×#491C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#125C2211yescharacteristic
12C2×#66999C2212yes—
13C22×#4326C2214yes—
14#10623228—24no—
15#10623228—24no—
16C2×#66951—22no—
17C2×#66950C2212yes—
18C2×#66943—22no—
19C2×#66940C2212yes—
20C2×#66925C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C11×#491—24no—
23C2×C11×#103C2214yes—
24C2×C11×#97C2211yescharacteristic
25#10622843C2212yes—
26C2×(C2×D11)⋊C8C2212yes—
27C2×#66880C2214yes—
28#10622705—24no—
29#10622606—22no—
30#10622593—22no—
31#10622549C2211yescharacteristic
32C2×C4×C11⋊C8C2211yescharacteristic
33#10622188C2212yes—
34#10622167C2214yes—
35C22×Q8×C11C2312yes—
36C22×C4×D11C2311yescharacteristic
37C22×Dic22C2312yes—
38C22×C8×C11C2312yes—
39C11×C4⋊Q8—22no—
40C11×C4⋊Q8—22no—
41C11×#125—22no—
42C11×#125D414yes—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4C2312yes—
46C2×C42×C11C2311yescharacteristic
47#66999—44no—
48C2×#4326—28no—
49C2×#4326—28no—
50C2×#4326—44no—
51C2×(C2×D11)⋊C4—22no—
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4D412yes—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11C2312yes—
57C2×Dic11⋊C4—22no—
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4D412yes—
60C2×C4×Dic11—22no—
61C2×C4×Dic11C2311yescharacteristic
62C22×C11⋊C8C2312yes—
63#66951—216no—
64#66950—24no—
65#66950—24no—
66#66943—216no—
67#66940—24no—
68#66940—24no—
69#66925—22no—
70#66925—22no—
71#66922—22no—
72#66922D414yes—
73C11×#103—28no—
74C11×#97—22no—
75C11⋊#95—22no—
76C11⋊#95—24no—
77(C2×D11)⋊C8—24no—
78#66880—44no—
79C4×C11⋊C8—22no—
80#25609—111nomaximal, Sylow
81C23×D11C2×D411yescharacteristic
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11—24no—
85C2×Q8×C11—24no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2411yescharacteristic
90C22×Dic11—22no—
91C22×Dic11—22no—
92C22×Dic11C2×D412yes—
93C22×Dic11C2×D411yescharacteristic
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×C4×D11—22no—
97C2×C4×D11—22no—
98C2×Dic22—22no—
99C2×Dic22—24no—
100C2×Dic22—24no—
101C2×Dic22C2×D414yes—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C11×C4⋊C4—28no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—44no—
108C11×C4⋊C4C2×D414yes—
109C42×C11C2×D412yes—
110C42×C11C2×D412yes—
111#4326—416no—
112(C2×D11)⋊C4—28no—
113(C2×D11)⋊C4—24no—
114(C2×D11)⋊C4—44no—
115C4⋊Dic11—28no—
116C4⋊Dic11—28no—
117C4⋊Dic11—24no—
118Dic11⋊C4—28no—
119Dic11⋊C4—24no—
120Dic11⋊C4—44no—
121C4×Dic11—28no—
122C4×Dic11—21no—
123C4×Dic11—21no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8#4114yes—
127C2×#541—111no—
128C2×#494—111no—
129C2×#491D1111yescharacteristic, complemented
130#2621—111no—
131#2001—114no—
132#1991—111no—
133#1960—111no—
134#1878—114no—
135#1750—111no—
136C23×C11C22×D411yescharacteristic
137C22×D11—21no—
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—24no—
141Q8×C11—44no—
142Q8×C11—44no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—44no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11#12014yes—
150C2×C4×C11C22×D411yescharacteristic
151C2×C4×C11C22×D411yescharacteristic
152C2×C4×C11C2×#4112yes—
153C2×C4×C11H(5,𝔽2)12yes—
154C2×Dic11—22no—
155C2×Dic11—24no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—24no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—44no—
164C4×D11—42no—
165C4×D11—42no—
166Dic22—28no—
167Dic22—44no—
168C8×C11—42no—
169C11⋊C8—24no—
170C22×Q16—114no—
171#541—224no—
172#541—224no—
173C2×C4⋊Q8—111no—
174C2×C4⋊Q8C2×D1111yescharacteristic
175C2×#126—222no—
176C2×#125—222no—
177C2×#125C2×D1111yescharacteristic
178C2×C22⋊Q8—112no—
179C2×C22⋊Q8—112no—
180C2×C4×Q8—112no—
181C2×#117—111no—
182#494—224no—
183#491—24no—
184C2×#103—114no—
185C2×#103C2×D1114yes—
186C2×C22⋊C8—112no—
187C2×#97C2×D1111yescharacteristic
188C2×C4×C8—111no—
189#398—222no—
190#397—222no—
191#391—112no—
192#382—111no—
193#340—114no—
194#336—112no—
195C22×C11C2×#12011yescharacteristic
196C22×C11#53211yescharacteristic
197C22×C11#53511yescharacteristic
198C22×C11#57814yes—
199C2×D11—42no—
200C2×D11—41no—
201C2×D11—42no—
202C2×D11—42no—
203C4×C11—24no—
204C4×C11—44no—
205C4×C11—82no—
206C4×C11#54612yes—
207C4×C11#55012yes—
208Dic11—44no—
209Dic11—41no—
210Dic11—42no—
211Dic11—82no—
212C22×Q8—112no—
213C22×Q8C22×D1112yes—
214C23×C4—111no—
215C2×Q16—228no—
216C2×Q16—228no—
217C2×Q16—444no—
218C22×C8—112no—
219C22×C8C22×D1112yes—
220C4⋊Q8—22no—
221C4⋊Q8—22no—
222C4⋊Q8—114no—
223C4⋊Q8—222no—
224#126—2216no—
225#125—22no—
226#125—2216no—
227#125C22⋊D1114yes—
228C22⋊Q8—224no—
229C22⋊Q8—224no—
230C22⋊Q8—444no—
231C4×Q8—224no—
232C4×Q8—224no—
233#117—222no—
234#117—222no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—112no—
238C2×C4⋊C4—112no—
239C2×C4⋊C4—222no—
240C2×C4⋊C4—222no—
241C2×C4⋊C4—222no—
242C2×C4⋊C4—222no—
243C2×C4⋊C4C22×D1112yes—
244C2×C22⋊C4—112no—
245C2×C22⋊C4—222no—
246C2×C22⋊C4—222no—
247C2×C42—111no—
248C2×C42—222no—
249C2×C42C22×D1111yescharacteristic
250#103—28no—
251#103—444no—
252C22⋊C8—224no—
253#97—22no—
254C4×C8—222no—
255#95—224no—
256#95—222no—
257C2×C11#243111yescharacteristic
258C2×C11#301112yes—
259C2×C11#317712yes—
260C2×C11#322312yes—
261D11—81no—
262C24—111no—
263C2×Q8—22no—
264C2×Q8—24no—
265C2×Q8—24no—
266C2×Q8—22no—
267C2×Q8—114no—
268C2×Q8—222no—
269C2×Q8—224no—
270C2×Q8—224no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—112no—
274C22×C4—111no—
275C22×C4—222no—
276C22×C4—221no—
277C22×C4—222no—
278C22×C4—222no—
279C22×C4—221no—
280C22×C4—222no—
281C22×C4D4×D1112yes—
282C22×C4C23×D1111yescharacteristic
283Q16—4416no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—114no—
288C2×C8—222no—
289C2×C8—222no—
290C4⋊C4—28no—
291C4⋊C4—22no—
292C4⋊C4—44no—
293C4⋊C4—228no—
294C4⋊C4—228no—
295C4⋊C4—224no—
296C4⋊C4—228no—
297C4⋊C4—224no—
298C4⋊C4—444no—
299C4⋊C4C2×C22⋊D1114yes—
300C22⋊C4—228no—
301C22⋊C4—224no—
302C22⋊C4—444no—
303C42—228no—
304C42—221no—
305C42—221no—
306C42D4×D1112yes—
307C42C2×C22⋊D1112yes—
308C11#2560911yescharacteristic, complemented, Sylow
309C23—224no—
310C23—221no—
311C23—221no—
312C23—221no—
313C23C2×D4×D1111yescharacteristic
314Q8—44no—
315Q8—44no—
316Q8—228no—
317Q8—444no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—224no—
325C2×C4—222no—
326C2×C4—224no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—442no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—442no—
334C2×C4—444no—
335C2×C4—442no—
336C2×C4#6699014yes—
337C2×C4C2×D4×D1111yescharacteristic
338C2×C4#41×D1112yes—
339C2×C4#6704212yes—
340C2×C4C22×C22⋊D1111yescharacteristic
341C8—42no—
342C8—224no—
343C22—441no—
344C22—442no—
345C22—442no—
346C22—442no—
347C22#1062319911yescharacteristic
348C22#1062320511yescharacteristic
349C22#1062331014yes—
350C22C2×#6699011yescharacteristic
351C4—24no—
352C4—44no—
353C4—82no—
354C4—441no—
355C4—444no—
356C4—442no—
357C4—882no—
358C4#1062320712yes—
359C4#1062336512yes—
360C2—881no—
361C2#1307223811yescharacteristic
362C2#1307791012yes—
363C2#1307927412yes—
364C2#1307970012yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#491C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#491D11
hypocenterC11#25609
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
2. C2×#10622705C2semidirect
5. #13069582C2semidirect
6. #13069436C2semidirect
7. #13068954C2semidirect
9. C2×C11×#491C2semidirect
129. C2×#491D11semidirect
308. C11#25609semidirect

Maximal subgroups

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

subgroupindex
C2×#106232282
C2×#106227052
#130743832
#130696252
#130695822
#130694362
#130689542
#130683852
C2×C11×#4912
#2560911