Finite Group Databasebeta

← #14669262

Subgroups — #14669262

Order 2816.

1206 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 147 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×#10622179C214yesmaximal, complemented
2#13068531C212yesmaximal
3C22×C11×#124C211yesmaximal, characteristic
4C23×Q8×C11C411yescharacteristic, complemented
5C23×D4×C11C2211yescharacteristic
6C2×C11×#124—22no—
7C2×C11×#124—28no—
8C2×C11×#124C412yescomplemented
9C2×C11×#124C2212yes—
10C22×C11×C22⋊C4—22no—
11C22×C42×C11C411yescharacteristic, complemented
12#10622860—22no—
13C2×#66898—22no—
14C2×#66898C2214yes—
15#10622179—28no—
16C25×C11D412yes—
17C22×Q8×C11—24no—
18C22×Q8×C11—21no—
19C22×Q8×C11—42no—
20C22×Q8×C11—42no—
21C22×Q8×C11C2×C412yes—
22C22×D4×C11—24no—
23C22×D4×C11—42no—
24C22×D4×C11—42no—
25C22×D4×C11C2×C411yescharacteristic
26C22×D4×C11D412yes—
27C22×D4×C11C2311yescharacteristic
28C23×C4×C11—21no—
29C23×C4×C11—21no—
30C23×C4×C11C2×C411yescharacteristic
31C11×#124—216no—
32C11×#124—24no—
33C11×#124—24no—
34C11×#124—24no—
35C11×#124D418yes—
36C2×C11×C22⋊C4—216no—
37C2×C11×C22⋊C4—24no—
38C2×C11×C22⋊C4—24no—
39C2×C42×C11—21no—
40C2×C42×C11—24no—
41C2×C42×C11C2×C412yes—
42C2×C22⋊Dic11—24no—
43C2×C22⋊Dic11—44no—
44#66898—28no—
45#66898—44no—
46#12694—111nomaximal, Sylow
47C24×C11—24no—
48C24×C11—24no—
49C24×C11—42no—
50C24×C11—48no—
51C24×C11C22⋊C411yescharacteristic
52C24×C11C22⋊C412yes—
53C24×C11C2×D412yes—
54C2×Q8×C11—24no—
55C2×Q8×C11—22no—
56C2×Q8×C11—416no—
57C2×Q8×C11—42no—
58C2×Q8×C11—42no—
59C2×Q8×C11—42no—
60C2×Q8×C11—42no—
61C2×Q8×C11C22⋊C414yescomplemented
62C2×D4×C11—24no—
63C2×D4×C11—24no—
64C2×D4×C11—22no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C2×D4×C11—42no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—416no—
71C2×D4×C11C2×D414yes—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—24no—
76C22×C4×C11—24no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—44no—
80C22×C4×C11—42no—
81C22×C4×C11—42no—
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22×C411yescharacteristic
84C22×Dic11—44no—
85C11×C22⋊C4—216no—
86C11×C22⋊C4—216no—
87C42×C11—24no—
88C42×C11—22no—
89C42×C11C22⋊C414yescomplemented
90C22⋊Dic11—44no—
91C22⋊Dic11—44no—
92C22⋊Dic11—88no—
93C22×#124D1111yescharacteristic
94C2×#354—114no—
95#1781—112no—
96C23×C11—24no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—22no—
100C23×C11—22no—
101C23×C11—22no—
102C23×C11—22no—
103C23×C11—22no—
104C23×C11—48no—
105C23×C11—44no—
106C23×C11—44no—
107C23×C11—416no—
108C23×C11—48no—
109C23×C11—84no—
110C23×C11—88no—
111C23×C11#9912yes—
112C23×C11C2×C22⋊C411yescharacteristic
113C23×C11#12014yes—
114Q8×C11—44no—
115Q8×C11—48no—
116Q8×C11—44no—
117D4×C11—44no—
118D4×C11—48no—
119D4×C11—44no—
120C2×C4×C11—28no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—24no—
126C2×C4×C11—24no—
127C2×C4×C11—48no—
128C2×C4×C11—44no—
129C2×C4×C11—48no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11#9912yes—
133C2×C4×C11C2×C22⋊C412yes—
134C2×Dic11—84no—
135C2×Dic11—88no—
136C23×Q8Dic1111yescharacteristic, complemented
137C23×D4C2×D1111yescharacteristic
138C2×#124—22no—
139C2×#124—28no—
140C2×#124Dic1112yescomplemented
141C2×#124C2×D1112yes—
142C22×C22⋊C4—22no—
143C22×C42Dic1111yescharacteristic, complemented
144C2×#99—114no—
145C2×#99—222no—
146#379—222no—
147#354—228no—
148C22×C11—24no—
149C22×C11—24no—
150C22×C11—22no—
151C22×C11—22no—
152C22×C11—22no—
153C22×C11—24no—
154C22×C11—44no—
155C22×C11—44no—
156C22×C11—44no—
157C22×C11—44no—
158C22×C11—42no—
159C22×C11—82no—
160C22×C11—816no—
161C22×C11—82no—
162C22×C11#35414yescomplemented
163C22×C11#37911yescharacteristic
164C22×C11C2×#9911yescharacteristic
165C22×C11C2×#9911yescharacteristic
166C4×C11—22no—
167C4×C11—22no—
168C4×C11—44no—
169C4×C11—44no—
170Dic11—164no—
171C25C22⋊D1112yes—
172C22×Q8—24no—
173C22×Q8—21no—
174C22×Q8—42no—
175C22×Q8—42no—
176C22×Q8C2×Dic1112yes—
177C22×D4—24no—
178C22×D4—42no—
179C22×D4—42no—
180C22×D4C2×Dic1111yescharacteristic
181C22×D4C22⋊D1112yes—
182C22×D4C22×D1111yescharacteristic
183C23×C4—21no—
184C23×C4—21no—
185C23×C4C2×Dic1111yescharacteristic
186#124—216no—
187#124—24no—
188#124—24no—
189#124—24no—
190#124C22⋊D1118yes—
191C2×C22⋊C4—216no—
192C2×C22⋊C4—24no—
193C2×C22⋊C4—24no—
194C2×C22⋊C4—224no—
195C2×C22⋊C4—444no—
196C2×C42—21no—
197C2×C42—24no—
198C2×C42C2×Dic1112yes—
199#99—228no—
200#99—444no—
201C2×C11—21no—
202C2×C11—24no—
203C2×C11—21no—
204C2×C11—44no—
205C2×C11—82no—
206C2×C11#178111yescharacteristic
207C2×C11C2×#35412yes—
208C24—24no—
209C24—24no—
210C24—42no—
211C24—48no—
212C24C22⋊Dic1112yes—
213C24C22⋊Dic1111yescharacteristic
214C24C2×C22⋊D1112yes—
215C2×Q8—24no—
216C2×Q8—22no—
217C2×Q8—416no—
218C2×Q8—42no—
219C2×Q8—42no—
220C2×Q8—42no—
221C2×Q8—42no—
222C2×Q8C22⋊Dic1114yescomplemented
223C2×D4—24no—
224C2×D4—24no—
225C2×D4—22no—
226C2×D4—41no—
227C2×D4—41no—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4—42no—
231C2×D4—416no—
232C2×D4C2×C22⋊D1114yes—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—24no—
237C22×C4—24no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—42no—
241C22×C4—44no—
242C22×C4—42no—
243C22×C4—444no—
244C22×C4C22⋊Dic1111yescharacteristic
245C22×C4C22×Dic1111yescharacteristic
246C22⋊C4—216no—
247C22⋊C4—216no—
248C22⋊C4—444no—
249C22⋊C4—444no—
250C22⋊C4—888no—
251C42—24no—
252C42—22no—
253C42C22⋊Dic1114yescomplemented
254C11#1269411yescharacteristic, complemented, Sylow
255C23—21no—
256C23—21no—
257C23—24no—
258C23—22no—
259C23—22no—
260C23—22no—
261C23—22no—
262C23—22no—
263C23—48no—
264C23—44no—
265C23—44no—
266C23—416no—
267C23—48no—
268C23—84no—
269C23—88no—
270C23#6689812yes—
271C23C2×C22⋊Dic1111yescharacteristic
272C23#6700614yes—
273Q8—44no—
274Q8—48no—
275Q8—44no—
276D4—44no—
277D4—48no—
278D4—44no—
279C2×C4—28no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—24no—
285C2×C4—24no—
286C2×C4—48no—
287C2×C4—44no—
288C2×C4—48no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—884no—
292C2×C4—888no—
293C2×C4#6689812yes—
294C2×C4C2×C22⋊Dic1112yes—
295C22—24no—
296C22—24no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—24no—
301C22—44no—
302C22—44no—
303C22—44no—
304C22—44no—
305C22—42no—
306C22—82no—
307C22—816no—
308C22—82no—
309C22#1062217914yescomplemented
310C22C2×#6689811yescharacteristic
311C22C2×#6689811yescharacteristic
312C22#1062286011yescharacteristic
313C4—22no—
314C4—22no—
315C4—44no—
316C4—44no—
317C4—1764no—
318C2—21no—
319C2—21no—
320C2—24no—
321C2—44no—
322C2—82no—
323C2#1306853111yescharacteristic
324C2C2×#1062217912yes—
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC22×C11×#124C2
socleC22×C11C2×#99
prime radicalC23×D4×C11C22
cosocleC22×D4×C11C23
hypercenterC22×#124D11
hypocenterC11#12694
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C2×#10622179C2semidirect
4. C23×Q8×C11C4semidirect
8. C2×C11×#124C4semidirect
11. C22×C42×C11C4semidirect
61. C2×Q8×C11C22⋊C4semidirect
89. C42×C11C22⋊C4semidirect
136. C23×Q8Dic11semidirect
140. C2×#124Dic11semidirect
143. C22×C42Dic11semidirect
162. C22×C11#354semidirect
222. C2×Q8C22⋊Dic11semidirect
253. C42C22⋊Dic11semidirect
254. C11#12694semidirect
309. C22#10622179semidirect

Maximal subgroups

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

subgroupindex
C2×#106221792
#130685312
C22×C11×#1242
#1269411