Finite Group Databasebeta

← #14726905

Subgroups — #14726905

Order 2816.

890 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 890 conjugacy classes of subgroups — too many to draw. Only its 187 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
1#13082426C211yesmaximal, characteristic
2#13078655C212yesmaximal
3#13067657C214yesmaximal
4#13067589C214yesmaximal
5#13067179C212yesmaximal
6#13066940C211yesmaximal, characteristic
7C11×#2581C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10#10623343—21no—
11#10623101—22no—
12#10623100—24no—
13Q8×Dic22—22no—
14#10623031—21no—
15#10623031C2214yes—
16#10623001—22no—
17#10623001C2212yes—
18C11×#400C2212yes—
19C11×#395C2212yes—
20C11×#391—21no—
21C11×#389—21no—
22C11×#387—22no—
23C11×#382C2211yescharacteristic
24#10622841C2214yes—
25#10622644—22no—
26C4×#4326—24no—
27#10622634—22no—
28#10622583C2214yes—
29#10622538C2212yes—
30#10622166C2214yes—
31#10622090C2218yes—
32C22×Q8×C11D411yescharacteristic
33C22×Q8×C11C2311yescharacteristic
34C4×Q8×C11—22no—
35C4×Q8×C11—22no—
36C4×Q8×C11—22no—
37C4×Q8×C11—22no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C4⋊C4C2311yescharacteristic
43C2×C11×C4⋊C4C2312yes—
44C2×C42×C11—21no—
45C2×C42×C11D412yes—
46C2×C42×C11C2311yescharacteristic
47Q8×Dic11—24no—
48Q8×Dic11—24no—
49C2×#4326—24no—
50#66979—24no—
51#66979—22no—
52#66977—22no—
53#66977—24no—
54#66977C2314yes—
55#66943—24no—
56#66943—28no—
57#66941—24no—
58#66941—28no—
59#66923—24no—
60#66923—22no—
61#66922—22no—
62#66922—22no—
63#66922D412yes—
64#66922D412yes—
65C4×Dic22—24no—
66C4×Dic22—24no—
67C4×Dic22—22no—
68C4×Dic22D414yes—
69C11×#95—21no—
70C11×#95—22no—
71C11×#95—22no—
72C11×#95—22no—
73C11×#95C2312yes—
74#66899—24no—
75C22⋊(C11⋊C8)C2314yes—
76#66874—24no—
77#66871—24no—
78C4⋊(C11⋊C8)—22no—
79C4×C11⋊C8—22no—
80#18221—111nomaximal, Sylow
81C2×Q8×C11—22no—
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11—42no—
85C2×Q8×C11Q1614yescomplemented
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2411yescharacteristic
94C2×Dic22—24no—
95C2×Dic22—22no—
96C2×Dic22C2×D414yes—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—44no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—42no—
104C42×C11—22no—
105C42×C11—22no—
106C42×C11—42no—
107C42×C11C2×D412yes—
108C42×C11C2×D412yes—
109C22⋊Dic11—24no—
110#4326—48no—
111C4⋊Dic11—24no—
112C4⋊Dic11—24no—
113C4⋊Dic11—24no—
114C4⋊Dic11—22no—
115C4⋊Dic11—22no—
116C4⋊Dic11—22no—
117C4⋊Dic11C2×D414yes—
118Dic11⋊C4—28no—
119Dic11⋊C4—24no—
120Dic11⋊C4—24no—
121C4×Dic11—28no—
122C4×Dic11—24no—
123C2×C11⋊C8—24no—
124#3502—111no—
125#3104—112no—
126#2581D1111yescharacteristic
127#1617—114no—
128#1605—114no—
129#1518—112no—
130#1461—111no—
131C23×C11C22×D411yescharacteristic
132Q8×C11—28no—
133Q8×C11—24no—
134Q8×C11—42no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12012yes—
152C2×C4×C11C2×Q1614yes—
153C2×C4×C11C2×Q1612yes—
154C2×C4×C11#13712yes—
155C2×C4×C11C22×D412yes—
156C2×Dic11—24no—
157C2×Dic11—24no—
158Dic22—44no—
159Dic22—44no—
160Dic22—84no—
161C11⋊C8—44no—
162Q82—222no—
163#557—224no—
164#557—222no—
165#544—114no—
166#544—221no—
167#533—112no—
168#533—222no—
169#519—221no—
170C2×C4×Q8C2×D1111yescharacteristic
171C2×C4×Q8C2×D1111yescharacteristic
172#484—114no—
173#477—222no—
174#462—222no—
175#451—114no—
176C4×Q16—224no—
177#431—112no—
178#400C2×D1112yes—
179#395C2×D1112yes—
180#391—21no—
181#389—21no—
182#387—22no—
183#382C2×D1111yescharacteristic
184#328—118no—
185#324—114no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11C2×#12011yescharacteristic
189C22×C11C22×Q1611yescharacteristic
190C22×C11C2×#13711yescharacteristic
191C4×C11—24no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—22no—
195C4×C11—42no—
196C4×C11—42no—
197C4×C11—82no—
198C4×C11—81no—
199C4×C11#45114yes—
200Dic11—44no—
201Dic11—44no—
202C22×Q8C22⋊D1111yescharacteristic
203C22×Q8C22×D1111yescharacteristic
204C2×Q16—224no—
205C4⋊Q8—112no—
206C4⋊Q8—112no—
207C4⋊Q8—222no—
208C4⋊Q8—222no—
209C4⋊Q8—228no—
210C4⋊Q8—224no—
211#125—224no—
212#125—228no—
213#125—224no—
214#125—222no—
215C22⋊Q8—114no—
216C22⋊Q8—222no—
217C22⋊Q8—224no—
218C4×Q8—22no—
219C4×Q8—22no—
220C4×Q8—22no—
221C4×Q8—22no—
222C4×Q8—114no—
223C4×Q8—224no—
224C4×Q8—224no—
225C4×Q8—224no—
226C4×Q8—224no—
227C4×Q8—222no—
228#117—222no—
229#117—224no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4C22⋊D1111yescharacteristic
234C2×C4⋊C4C22×D1111yescharacteristic
235C2×C4⋊C4C22×D1112yes—
236C2×C42—21no—
237C2×C42C22⋊D1112yes—
238C2×C42C22×D1111yescharacteristic
239#107—224no—
240C4⋊C8—222no—
241#103—224no—
242#103—224no—
243C22⋊C8—114no—
244C4×C8—222no—
245#95—21no—
246#95—22no—
247#95—22no—
248#95—22no—
249#95C22×D1112yes—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11C2×#45111yescharacteristic
253C2×C11#302011yescharacteristic
254C2×C11#302511yescharacteristic
255C2×Q8—22no—
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8—42no—
259C2×Q8—114no—
260C2×Q8—224no—
261C2×Q8—222no—
262C2×Q8#432614yescomplemented
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4C2×C22⋊D1112yes—
267C22×C4C2×C22⋊D1112yes—
268C22×C4C2×C22⋊D1111yescharacteristic
269C22×C4C2×C22⋊D1111yescharacteristic
270C22×C4C23×D1111yescharacteristic
271Q16—448no—
272C2×C8—224no—
273C4⋊C4—22no—
274C4⋊C4—24no—
275C4⋊C4—22no—
276C4⋊C4—44no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—114no—
281C4⋊C4—224no—
282C4⋊C4—224no—
283C4⋊C4—224no—
284C4⋊C4—228no—
285C4⋊C4—222no—
286C4⋊C4—222no—
287C4⋊C4—224no—
288C4⋊C4—222no—
289C4⋊C4—224no—
290C22⋊C4—224no—
291C42—22no—
292C42—22no—
293C42—42no—
294C42—228no—
295C42—224no—
296C42D4×D1112yes—
297C42D4×D1112yes—
298C11#1822111yescharacteristic, complemented, Sylow
299C23C22×C22⋊D1111yescharacteristic
300Q8—28no—
301Q8—24no—
302Q8—42no—
303Q8—444no—
304Q8—444no—
305Q8—884no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—224no—
321C2×C4—224no—
322C2×C4#6699011yescharacteristic
323C2×C4#6699011yescharacteristic
324C2×C4#6699012yes—
325C2×C4C2×#432614yes—
326C2×C4C2×#432612yes—
327C2×C4#6700412yes—
328C2×C4C2×D4×D1112yes—
329C8—444no—
330C22—21no—
331C22—21no—
332C22C2×#6699011yescharacteristic
333C22C22×#432611yescharacteristic
334C22C2×#6700411yescharacteristic
335C4—24no—
336C4—21no—
337C4—21no—
338C4—22no—
339C4—42no—
340C4—42no—
341C4—82no—
342C4—81no—
343C4—444no—
344C4—444no—
345C4#1062266314yes—
346C2—21no—
347C2—21no—
348C2C2×#1062266311yescharacteristic
349C2#1307797911yescharacteristic
350C2#1307800711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2581C2
socleC22×C11C2×#120
prime radicalC23×C11C22×D4
hypercenter#2581D11
hypocenterC11#18221
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2581

Complements

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

NH ≅ G/Ntype
85. C2×Q8×C11Q16semidirect
262. C2×Q8#4326semidirect
298. C11#18221semidirect

Maximal subgroups

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

subgroupindex
#130824262
#130786552
#130676572
#130675892
#130671792
#130669402
C11×#25812
#1822111