Finite Group Databasebeta

← #14807392

Subgroups — #14807392

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×#10623262C211yesmaximal, characteristic
2C2×#10622705C211yesmaximal, characteristic, complemented
3C2×#10622316C211yesmaximal, characteristic, complemented
4#13074385C211yesmaximal, characteristic
5#13069625C214yesmaximal
6#13069580C211yesmaximal, characteristic, complemented
7#13068955C214yesmaximal, complemented
8#13068385C211yesmaximal, characteristic
9C11×#1960C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999C2212yes—
12C2×Q8×Dic11C2212yes—
13C22×#4326C2214yes—
14#10623262—24no—
15#10623262—24no—
16C2×#66951—22no—
17C2×#66950C2212yes—
18C2×#66942—22no—
19C2×#66925C2211yescharacteristic
20C2×#66923C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C11×#103C2214yes—
23C2×C11×#97C2211yescharacteristic
24C11×#382C2211yescharacteristic
25C2×(C2×D11)⋊C8C2212yes—
26C2×#66880C2214yes—
27#10622705—24no—
28#10622587C2212yes—
29C2×C4×C11⋊C8C2211yescharacteristic
30#10622316—24no—
31#10622287—22no—
32#10622274—22no—
33#10622188C2212yes—
34#10622167C2214yes—
35C22×Q8×C11C2312yes—
36C22×C4×D11C2311yescharacteristic
37C22×Dic22C2312yes—
38C22×C8×C11C2312yes—
39C11×C4⋊Q8—22no—
40C11×C4⋊Q8D414yes—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4C2312yes—
43C2×C42×C11C2311yescharacteristic
44#66999—24no—
45#66999—24no—
46Q8×Dic11—24no—
47Q8×Dic11—24no—
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⋊Dic11—22no—
57C2×C4⋊Dic11C2312yes—
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4D412yes—
61C2×C4×Dic11—22no—
62C2×C4×Dic11C2311yescharacteristic
63C22×C11⋊C8C2312yes—
64#66951—216no—
65#66950—44no—
66#66942—216no—
67#66925—22no—
68#66925—22no—
69#66923—22no—
70#66923D414yes—
71#66922—22no—
72#66922—22no—
73C11×#103—44no—
74C11×#97—22no—
75C11×#95—22no—
76C11⋊#95—24no—
77(C2×D11)⋊C8—24no—
78#66880—28no—
79C4×C11⋊C8—22no—
80#25609—111nomaximal, Sylow
81C23×D11C2×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×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—22no—
100C2×Dic22—24no—
101C2×Dic22—24no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C11×C4⋊C4—28no—
106C11×C4⋊C4—24no—
107C42×C11C2×D412yes—
108C42×C11C2×D412yes—
109#4326—416no—
110(C2×D11)⋊C4—28no—
111(C2×D11)⋊C4—24no—
112(C2×D11)⋊C4—44no—
113C4⋊Dic11—28no—
114C4⋊Dic11—22no—
115C4⋊Dic11—44no—
116C4⋊Dic11—44no—
117C4⋊Dic11C2×D414yes—
118Dic11⋊C4—28no—
119Dic11⋊C4—28no—
120Dic11⋊C4—24no—
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×#491—111no—
130#2621—111no—
131#2001—114no—
132#1991—111no—
133#1960D1111yescharacteristic, complemented
134#1878—114no—
135#1750—111no—
136C23×C11C22×D411yescharacteristic
137C22×D11—21no—
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—24no—
141Q8×C11—28no—
142Q8×C11—44no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—44no—
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—44no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C4×D11—42no—
165C4×D11—42no—
166Dic22—44no—
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—111no—
177C2×#125—222no—
178C2×C22⋊Q8—112no—
179C2×C22⋊Q8—112no—
180C2×C4×Q8—112no—
181C2×#117—111no—
182#494—224no—
183#491—224no—
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#382C2×D1111yescharacteristic
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—41no—
209Dic11—42no—
210Dic11—44no—
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—222no—
222C4⋊Q8—222no—
223C4⋊Q8D4414yes—
224#126—2216no—
225#125—114no—
226#125—2216no—
227#125—222no—
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—112no—
237C2×C4⋊C4—112no—
238C2×C4⋊C4—222no—
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—44no—
251#103—228no—
252C22⋊C8—224no—
253#97—22no—
254C4×C8—222no—
255#95—22no—
256#95—224no—
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—222no—
267C2×Q8—222no—
268C2×Q8—224no—
269C2×Q8—224no—
270C2×Q8C2×D4414yes—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—112no—
274C22×C4—111no—
275C22×C4—222no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—222no—
279C22×C4—222no—
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—24no—
292C4⋊C4—114no—
293C4⋊C4—228no—
294C4⋊C4—228no—
295C4⋊C4—224no—
296C4⋊C4—228no—
297C4⋊C4—222no—
298C4⋊C4—444no—
299C4⋊C4—444no—
300C22⋊C4—228no—
301C22⋊C4—224no—
302C22⋊C4—444no—
303C42—228no—
304C42—221no—
305C42—221no—
306C42C2×D4412yes—
307C42D4×D1112yes—
308C11#2560911yescharacteristic, complemented, Sylow
309C23—221no—
310C23—221no—
311C23—224no—
312C23—221no—
313C23C2×D4×D1111yescharacteristic
314Q8—28no—
315Q8—44no—
316Q8—444no—
317Q8—444no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—44no—
324C2×C4—221no—
325C2×C4—222no—
326C2×C4—224no—
327C2×C4—221no—
328C2×C4—224no—
329C2×C4—221no—
330C2×C4—444no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—442no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4#6693514yes—
337C2×C4C22×D4411yescharacteristic
338C2×C4C2×D4×D1111yescharacteristic
339C2×C4#6703712yes—
340C2×C4#41×D1112yes—
341C8—42no—
342C8—224no—
343C22—441no—
344C22—442no—
345C22—442no—
346C22—442no—
347C22C2×#6693511yescharacteristic
348C22#1062319911yescharacteristic
349C22#1062324611yescharacteristic
350C22#1062331014yes—
351C4—24no—
352C4—44no—
353C4—82no—
354C4—441no—
355C4—442no—
356C4—444no—
357C4—882no—
358C4#1062308512yes—
359C4#1062313012yes—
360C2—881no—
361C2#1307223411yescharacteristic
362C2#1307791212yes—
363C2#1307927412yes—
364C2#1307969412yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1960C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1960D11
hypocenterC11#25609
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
2. C2×#10622705C2semidirect
3. C2×#10622316C2semidirect
6. #13069580C2semidirect
7. #13068955C2semidirect
9. C11×#1960C2semidirect
133. #1960D11semidirect
308. C11#25609semidirect

Maximal subgroups

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

subgroupindex
C2×#106232622
C2×#106227052
C2×#106223162
#130743852
#130696252
#130695802
#130689552
#130683852
C11×#19602
#2560911