Finite Group Databasebeta

← #14726906

Subgroups — #14726906

Order 2816.

890 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 890 conjugacy classes of subgroups — too many to draw. Only its 203 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#13078651C212yesmaximal
2#13073978C211yesmaximal, characteristic
3#13067658C214yesmaximal
4#13067590C214yesmaximal
5#13067180C212yesmaximal
6#13066940C211yesmaximal, characteristic
7C11×#3502C211yesmaximal, characteristic
8Q82×C11—22no—
9C11×#557—22no—
10C11×#557—24no—
11C11×#544—21no—
12C11×#544C2214yes—
13C11×#533—22no—
14C11×#533C2212yes—
15C11×#519—21no—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18#10622843—21no—
19#10622704—22no—
20#10622703—22no—
21#10622663C2214yes—
22#10622657C2214yes—
23C4×#4326—24no—
24#10622599C2212yes—
25#10622592C2212yes—
26#10622586—21no—
27#10622549C2211yescharacteristic
28#10622546—22no—
29#10622538C2212yes—
30#10622176C2218yes—
31#10622166C2214yes—
32C22×Q8×C11D411yescharacteristic
33C22×Dic22C2311yescharacteristic
34C11×C4⋊Q8—22no—
35C11×C4⋊Q8—22no—
36C11×C4⋊Q8—24no—
37C11×C4⋊Q8—28no—
38C11×C4⋊Q8D412yes—
39C11×C4⋊Q8D412yes—
40C11×#125—24no—
41C11×#125—24no—
42C11×#125—28no—
43C11×#125—22no—
44C11×C22⋊Q8—22no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8C2314yes—
47C4×Q8×C11—24no—
48C4×Q8×C11—24no—
49C4×Q8×C11—24no—
50C4×Q8×C11—24no—
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×Q8×C11D414yes—
55C11×#117—24no—
56C11×#117—22no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4C2312yes—
59C2×C42×C11D412yes—
60C2×C42×C11C2311yescharacteristic
61C2×#4326—24no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11—21no—
67C4×Dic22—22no—
68C4×Dic22—22no—
69#66899—24no—
70C11⋊#95—21no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95—22no—
74C11⋊#95C2312yes—
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—24no—
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11Q1614yescomplemented
86C2×Q8×C11C2×D414yes—
87C22×C4×C11C2×D412yes—
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2411yescharacteristic
92C22×Dic11—21no—
93C22×Dic11—22no—
94C22×Dic11—21no—
95C2×Dic22—22no—
96C2×Dic22—42no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—28no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4C2×D414yes—
109C11×C22⋊C4—24no—
110C42×C11—28no—
111C42×C11—22no—
112C42×C11—22no—
113C42×C11—24no—
114C42×C11C2×D412yes—
115C42×C11C2×D412yes—
116#4326—48no—
117C4⋊Dic11—22no—
118C4⋊Dic11—42no—
119Dic11⋊C4—44no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122C4×Dic11—42no—
123C2×C11⋊C8—24no—
124#3502D1111yescharacteristic
125#3104—112no—
126#2581—111no—
127#1617—114no—
128#1605—114no—
129#1518—112no—
130#1461—111no—
131C23×C11C22×D411yescharacteristic
132Q8×C11—28no—
133Q8×C11—44no—
134Q8×C11—44no—
135Q8×C11—84no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—22no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12012yes—
147C2×C4×C11C2×Q1614yes—
148C2×C4×C11C2×Q1612yes—
149C2×C4×C11#13712yes—
150C2×C4×C11C22×D412yes—
151C2×Dic11—22no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—42no—
157C2×Dic11—41no—
158C2×Dic11—42no—
159Dic22—24no—
160Dic22—42no—
161C11⋊C8—44no—
162Q82—22no—
163#557—22no—
164#557—24no—
165#544—21no—
166#544C2×D1114yes—
167#533—22no—
168#533C2×D1112yes—
169#519—21no—
170C2×C4×Q8—111no—
171C2×C4×Q8C2×D1111yescharacteristic
172#484—114no—
173#477—222no—
174#462—222no—
175#451—114no—
176C4×Q16—224no—
177#431—112no—
178#400—112no—
179#395—112no—
180#391—221no—
181#389—221no—
182#387—222no—
183#382—111no—
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—44no—
196C4×C11—42no—
197C4×C11—44no—
198C4×C11#45114yes—
199Dic11—42no—
200Dic11—82no—
201Dic11—81no—
202C22×Q8—111no—
203C22×Q8C22⋊D1111yescharacteristic
204C2×Q16—224no—
205C4⋊Q8—22no—
206C4⋊Q8—22no—
207C4⋊Q8—24no—
208C4⋊Q8—28no—
209C4⋊Q8C22⋊D1112yes—
210C4⋊Q8C22⋊D1112yes—
211#125—24no—
212#125—24no—
213#125—28no—
214#125—22no—
215C22⋊Q8—22no—
216C22⋊Q8—24no—
217C22⋊Q8C22×D1114yes—
218C4×Q8—24no—
219C4×Q8—24no—
220C4×Q8—24no—
221C4×Q8—24no—
222C4×Q8—22no—
223C4×Q8—22no—
224C4×Q8—22no—
225C4×Q8—222no—
226C4×Q8—222no—
227C4×Q8C22⋊D1114yes—
228#117—24no—
229#117—22no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—222no—
234C2×C4⋊C4C22⋊D1111yescharacteristic
235C2×C4⋊C4C22×D1112yes—
236C2×C42—221no—
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—112no—
246#95—221no—
247#95—222no—
248#95—222no—
249#95—222no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11C2×#45111yescharacteristic
253C2×C11#302011yescharacteristic
254C2×C11#302511yescharacteristic
255C2×Q8—24no—
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8—222no—
260C2×Q8—442no—
261C2×Q8#432614yescomplemented
262C2×Q8C2×C22⋊D1114yes—
263C22×C4—221no—
264C22×C4—222no—
265C22×C4—221no—
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—24no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—28no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—24no—
282C4⋊C4—24no—
283C4⋊C4—24no—
284C4⋊C4—222no—
285C4⋊C4—444no—
286C4⋊C4—442no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4C2×C22⋊D1114yes—
290C22⋊C4—24no—
291C42—28no—
292C42—22no—
293C42—22no—
294C42—24no—
295C42—442no—
296C42C2×C22⋊D1112yes—
297C42C2×C22⋊D1112yes—
298C11#1822111yescharacteristic, complemented, Sylow
299C23C22×C22⋊D1111yescharacteristic
300Q8—28no—
301Q8—44no—
302Q8—44no—
303Q8—84no—
304Q8—224no—
305Q8—442no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—222no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4—441no—
322C2×C4#6699512yes—
323C2×C4C2×#432614yes—
324C2×C4C2×#432612yes—
325C2×C4#6700611yescharacteristic
326C2×C4#6700611yescharacteristic
327C2×C4#6700612yes—
328C2×C4C22×C22⋊D1112yes—
329C8—444no—
330C22—21no—
331C22—21no—
332C22C2×#6699511yescharacteristic
333C22C22×#432611yescharacteristic
334C22C2×#6700611yescharacteristic
335C4—24no—
336C4—21no—
337C4—21no—
338C4—22no—
339C4—44no—
340C4—42no—
341C4—44no—
342C4—442no—
343C4—882no—
344C4—881no—
345C4#1062284114yes—
346C2—21no—
347C2—21no—
348C2C2×#1062284111yescharacteristic
349C2#1307798011yescharacteristic
350C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3502C2
socleC22×C11C2×#120
prime radicalC23×C11C22×D4
hypercenter#3502D11
hypocenterC11#18221
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3502

Complements

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

NH ≅ G/Ntype
85. C2×Q8×C11Q16semidirect
261. 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
#130786512
#130739782
#130676582
#130675902
#130671802
#130669402
C11×#35022
#1822111