Finite Group Databasebeta

← #14763072

Subgroups — #14763072

Order 2816.

1194 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 1194 conjugacy classes of subgroups — too many to draw. Only its 235 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×#10623356C211yesmaximal, characteristic
2#13077251C212yesmaximal, complemented
3#13069462C214yesmaximal, complemented
4#13069458C214yesmaximal, complemented
5#13068544C211yesmaximal, characteristic
6#13068539C212yesmaximal, complemented
7C11×#1785C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C23×Dic22C2211yescharacteristic
10#10623356—28no—
11C2×#66997C2212yes—
12C2×#66989C2212yes—
13C2×#66988C414yes—
14C2×#66979C2211yescharacteristic
15C2×#66977C414yes—
16C2×C11×#101C2212yes—
17C2×C11×#100C2212yes—
18C11×#407C2212yes—
19C2×#66900C2212yes—
20C2×#66897C2212yes—
21#10622820C2212yes—
22C2×#66888C2214yes—
23C2×#66888C2214yes—
24#10622731C2214yes—
25M16×Dic11C2214yes—
26#10622333—28no—
27C2×C11×#41—24no—
28C2×C11×#41—42no—
29C2×C11×#41—42no—
30C22×Q8×C11C2311yescharacteristic
31C22×D4×C11C2×C412yes—
32C22×D4×C11C2311yescharacteristic
33C23×C4×C11C2×C412yes—
34C23×C4×C11C2311yescharacteristic
35C23×Dic11C2×C412yes—
36C22×Dic22—24no—
37C22×Dic22—42no—
38C22×Dic22—42no—
39C22×Dic22C2×C412yes—
40C22×Dic22C2312yes—
41C2×C11×M16C2314yes—
42C2×C22⋊Dic11C2×C418yes—
43C2×C22⋊Dic11C2×C412yes—
44#66997—24no—
45#66997—24no—
46#66989—24no—
47#66989—24no—
48#66988—216no—
49#66979D418yes—
50C2×C4⋊Dic11C2×C412yes—
51#66977—216no—
52C2×Dic11⋊C4C2×C418yes—
53C2×C4×Dic11C2312yes—
54C2×#4318C2314yes—
55C11×#101—42no—
56C11×#100—42no—
57C11×C22⋊C8—24no—
58#66900—42no—
59#66897—42no—
60C22⋊(C11⋊C8)—24no—
61#66888—44no—
62#66888—44no—
63#66879—24no—
64Dic11⋊C8—28no—
65C8×Dic11—24no—
66#21802—111nomaximal, Sylow
67C24×C11C22×C412yes—
68C24×C11C22×C411yescharacteristic
69C11×#41—416no—
70C2×Q8×C11—22no—
71C2×Q8×C11—22no—
72C2×Q8×C11—22no—
73C2×D4×C11—24no—
74C2×D4×C11—22no—
75C2×D4×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11—42no—
78C2×D4×C11—42no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—24no—
82C22×C4×C11—42no—
83C22×C4×C11—42no—
84C22×C4×C11C22×C412yes—
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C2×D414yes—
87C22×C4×C11C2411yescharacteristic
88C22×Dic11—24no—
89C22×Dic11—42no—
90C22×Dic11—42no—
91C22×Dic11C22×C414yes—
92C22×Dic11C22×C414yes—
93C2×Dic22—24no—
94C2×Dic22—22no—
95C2×Dic22—22no—
96C2×Dic22—24no—
97C2×Dic22—24no—
98C2×Dic22—42no—
99C2×Dic22—42no—
100C2×Dic22—416no—
101C11×M16—24no—
102C11×M16—24no—
103C2×C8×C11—24no—
104C22⋊Dic11—216no—
105C22⋊Dic11C22⋊C418yes—
106C4⋊Dic11C22⋊C418yes—
107Dic11⋊C4—216no—
108C4×Dic11C2×D414yes—
109C4×Dic11C2×D414yes—
110#4318—24no—
111#4318—24no—
112C2×C11⋊C8—24no—
113C2×#536—111no—
114#2921—112no—
115#1967—114no—
116#1966—114no—
117#1785—111no—
118#1785D1111yescharacteristic
119#1784—112no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—22no—
123C23×C11—22no—
124C23×C11—22no—
125C23×C11—42no—
126C23×C11—44no—
127C23×C11C2×C22⋊C412yes—
128C23×C11C23×C411yescharacteristic
129Q8×C11—44no—
130D4×C11—48no—
131D4×C11—44no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—28no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—48no—
139C2×C4×C11C2×C22⋊C412yes—
140C2×C4×C11C22×D412yes—
141C2×C4×C11H(5,𝔽2)12yes—
142C2×C4×C11H(5,𝔽2)12yes—
143C2×Dic11—24no—
144C2×Dic11—24no—
145C2×Dic11—24no—
146C2×Dic11—44no—
147C2×Dic11—48no—
148C2×Dic11C2×C22⋊C418yes—
149Dic22—48no—
150Dic22—44no—
151Dic22—44no—
152C8×C11—44no—
153C11⋊C8—44no—
154C22×#41C2×D1111yescharacteristic
155C23×Q8—111no—
156#536—228no—
157C2×C4⋊Q8—112no—
158C2×#124—112no—
159C2×#123—114no—
160C2×C22⋊Q8—114no—
161C2×#117—111no—
162#433—228no—
163#423—114no—
164C2×#101—112no—
165C2×#101—114no—
166C2×#101—114no—
167C2×#101C2×D1112yes—
168C2×#100—112no—
169C2×#100C2×D1112yes—
170#407—112no—
171#407C2×D1112yes—
172C4×M16—114no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—24no—
176C22×C11—42no—
177C22×C11—42no—
178C22×C11—42no—
179C22×C11—44no—
180C22×C11—82no—
181C22×C11—82no—
182C22×C11C22×C22⋊C411yescharacteristic
183C22×C11#51811yescharacteristic
184C22×C11#51811yescharacteristic
185C4×C11—22no—
186C4×C11—42no—
187C4×C11#53514yes—
188Dic11—28no—
189Dic11—44no—
190C2×#41—24no—
191C2×#41—42no—
192C2×#41—42no—
193C22×Q8—112no—
194C22×Q8—112no—
195C22×Q8—224no—
196C22×Q8—442no—
197C22×Q8—442no—
198C22×Q8C22×D1111yescharacteristic
199C22×D4C4×D1112yes—
200C22×D4C22×D1111yescharacteristic
201C23×C4—112no—
202C23×C4C4×D1112yes—
203C23×C4C22×D1111yescharacteristic
204C2×M16—114no—
205C2×M16C22×D1114yes—
206C4⋊Q8—224no—
207C4⋊Q8—224no—
208#124—224no—
209#124—224no—
210#123—2216no—
211C22⋊Q8—2216no—
212#117—118no—
213C2×C4⋊C4—112no—
214C2×C4⋊C4—118no—
215C2×C22⋊C4—112no—
216C2×C22⋊C4—118no—
217C2×C42—112no—
218C4⋊C8—228no—
219#101—42no—
220#101—444no—
221#101—444no—
222#101—442no—
223#100—42no—
224#100—442no—
225C22⋊C8—24no—
226C22⋊C8—224no—
227#97—224no—
228C4×C8—224no—
229C2×C11—21no—
230C2×C11—21no—
231C2×C11—42no—
232C2×C11—82no—
233C2×C11#230911yescharacteristic
234C2×C11#288912yes—
235C24C2×C4×D1112yes—
236C24C2×C4×D1111yescharacteristic
237#41—416no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—224no—
242C2×Q8—222no—
243C2×Q8—222no—
244C2×Q8—224no—
245C2×Q8—224no—
246C2×Q8—442no—
247C2×Q8—442no—
248C2×Q8—4416no—
249C2×D4—24no—
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—42no—
254C2×D4—42no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—114no—
261C22×C4—114no—
262C22×C4—224no—
263C22×C4—442no—
264C22×C4—442no—
265C22×C4C2×C4×D1112yes—
266C22×C4C2×C4×D1111yescharacteristic
267C22×C4D4×D1114yes—
268C22×C4C23×D1111yescharacteristic
269M16—24no—
270M16—24no—
271M16—224no—
272M16—224no—
273C2×C8—24no—
274C2×C8—224no—
275C4⋊C4—118no—
276C4⋊C4—2216no—
277C22⋊C4—118no—
278C22⋊C4—2216no—
279C42—114no—
280C42—114no—
281C11#2180211yescharacteristic, complemented, Sylow
282C23—21no—
283C23—21no—
284C23—22no—
285C23—22no—
286C23—22no—
287C23—42no—
288C23—44no—
289C23C22⋊C4×D1112yes—
290C23C22×C4×D1111yescharacteristic
291Q8—44no—
292Q8—448no—
293Q8—444no—
294Q8—444no—
295D4—48no—
296D4—44no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—28no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—48no—
304C2×C4—118no—
305C2×C4—224no—
306C2×C4—224no—
307C2×C4—224no—
308C2×C4—444no—
309C2×C4—448no—
310C2×C4C22⋊C4×D1112yes—
311C2×C4C2×D4×D1112yes—
312C2×C4#6703712yes—
313C2×C4#6703712yes—
314C8—44no—
315C8—444no—
316C22—22no—
317C22—22no—
318C22—24no—
319C22—42no—
320C22—42no—
321C22—42no—
322C22—44no—
323C22—82no—
324C22—82no—
325C22C2×C22⋊C4×D1111yescharacteristic
326C22#1062301711yescharacteristic
327C22#1062301711yescharacteristic
328C4—22no—
329C4—42no—
330C4—228no—
331C4—444no—
332C4#1062312314yes—
333C2—21no—
334C2—21no—
335C2—42no—
336C2—82no—
337C2#1307119711yescharacteristic
338C2#1307709712yes—
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1785C2
socleC22×C11C22×C22⋊C4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#1785D11
hypocenterC11#21802
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1785

Complements

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

NH ≅ G/Ntype
2. #13077251C2semidirect
3. #13069462C2semidirect
4. #13069458C2semidirect
6. #13068539C2semidirect
281. C11#21802semidirect

Maximal subgroups

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

subgroupindex
C2×#106233562
#130772512
#130694622
#130694582
#130685442
#130685392
C11×#17852
#2180211