Finite Group Databasebeta

← #14647170

Subgroups — #14647170

Order 2816.

554 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 131 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×#10622549C211yesmaximal, characteristic
2#13068378C211yesmaximal, characteristic
3#13066498C214yesmaximal, complemented
4C11×#1749C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C22×C4⋊Dic11C411yescharacteristic
7C22×C4⋊Dic11C411yescharacteristic
8C2×C11×C22⋊C8—21no—
9C2×C11×#97C2212yes—
10C2×C11⋊#95—21no—
11C2×C11⋊#95—21no—
12C2×C22⋊(C11⋊C8)—21no—
13#10622549—21no—
14#10622549—21no—
15#10622549C412yes—
16#10622549C2212yes—
17C2×#66867C2212yes—
18C11×#336—21no—
19#10622162—21no—
20C23×C4×C11C2×C411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11—21no—
24C23×Dic11—21no—
25C22×C8×C11—22no—
26C2×C42×C11—24no—
27C2×C42×C11C2×C411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11C2311yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—42no—
34C2×C4⋊Dic11—42no—
35C2×C4⋊Dic11C2×C412yes—
36C2×C4⋊Dic11C2×C412yes—
37C22×C11⋊C8—22no—
38C11×C22⋊C8—24no—
39C11×#97—24no—
40C11⋊#95—22no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43C11⋊#95—22no—
44C22⋊(C11⋊C8)—24no—
45#66867—24no—
46#8718—111nomaximal, Sylow
47C24×C11C22⋊C411yescharacteristic
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—41no—
56C22×C4×C11—41no—
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—22no—
64C22×Dic11—22no—
65C22×Dic11—42no—
66C22×Dic11—42no—
67C22×Dic11—42no—
68C22×Dic11—42no—
69C22×Dic11—42no—
70C22×Dic11—42no—
71C2×C8×C11—24no—
72C2×C8×C11—42no—
73C2×C8×C11—42no—
74C42×C11—22no—
75C42×C11—22no—
76C42×C11—22no—
77C42×C11#4114yes—
78C4⋊Dic11—42no—
79C4⋊Dic11—42no—
80C4⋊Dic11—42no—
81C4⋊Dic11—42no—
82C2×C11⋊C8—24no—
83C2×C11⋊C8—42no—
84C2×C11⋊C8—42no—
85C2×#382—111no—
86#1749—111no—
87#1749D1111yescharacteristic
88#1295—114no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11#10012yes—
94C23×C11#10412yes—
95C23×C11#10412yes—
96C23×C11C2×C22⋊C411yescharacteristic
97C2×C4×C11—28no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—44no—
113C2×C4×C11—44no—
114C2×C4×C11#10112yes—
115C2×C4×C11#11712yes—
116C2×C4×C11#12312yes—
117C2×C4×C11#12312yes—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—84no—
125C2×Dic11—84no—
126C8×C11—44no—
127C11⋊C8—44no—
128C22×C4⋊C4—111no—
129C22×C4⋊C4—111no—
130C22×C42C2×D1111yescharacteristic
131C2×C22⋊C8—21no—
132C2×C22⋊C8—221no—
133C2×#97—112no—
134C2×#97C2×D1112yes—
135#382—112no—
136#382—112no—
137#382—221no—
138#382—221no—
139C2×#95—221no—
140C2×#95—221no—
141#336—21no—
142#336—221no—
143C22×C11—22no—
144C22×C11—22no—
145C22×C11—22no—
146C22×C11—22no—
147C22×C11—22no—
148C22×C11—22no—
149C22×C11#32914yes—
150C22×C11#38111yescharacteristic
151C22×C11C2×#10011yescharacteristic
152C22×C11C2×#10111yescharacteristic
153C22×C11C2×#10411yescharacteristic
154C22×C11C2×#10411yescharacteristic
155C22×C11#42111yescharacteristic
156C22×C11#42111yescharacteristic
157C4×C11—22no—
158C4×C11—22no—
159C4×C11—22no—
160C4×C11—22no—
161C4×C11—41no—
162C4×C11—41no—
163Dic11—82no—
164Dic11—82no—
165C23×C4—221no—
166C23×C4—221no—
167C23×C4C4×D1111yescharacteristic
168C23×C4D4411yescharacteristic
169C23×C4C22⋊D1111yescharacteristic
170C22×C8—22no—
171C22×C8—222no—
172C2×C4⋊C4—112no—
173C2×C4⋊C4—112no—
174C2×C4⋊C4—221no—
175C2×C4⋊C4—221no—
176C2×C4⋊C4—442no—
177C2×C4⋊C4—442no—
178C2×C42—24no—
179C2×C42C4×D1111yescharacteristic
180C2×C42D4411yescharacteristic
181C2×C42C22⋊D1111yescharacteristic
182C2×C42C22×D1111yescharacteristic
183C22⋊C8—24no—
184C22⋊C8—224no—
185#97—24no—
186#97—224no—
187#95—222no—
188#95—222no—
189#95—222no—
190#95—222no—
191C2×C11—24no—
192C2×C11C2×#32911yescharacteristic
193C2×C11#152811yescharacteristic
194C2×C11#152811yescharacteristic
195C2×C11#153311yescharacteristic
196C2×C11#182111yescharacteristic
197C2×C11#182611yescharacteristic
198C2×C11#182611yescharacteristic
199C24(C2×D11)⋊C411yescharacteristic
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—222no—
210C22×C4—222no—
211C22×C4—442no—
212C22×C4—442no—
213C22×C4—442no—
214C22×C4—442no—
215C22×C4—442no—
216C22×C4—442no—
217C22×C4(C2×D11)⋊C411yescharacteristic
218C22×C4(C2×D11)⋊C411yescharacteristic
219C22×C4(C2×D11)⋊C411yescharacteristic
220C22×C4C2×C4×D1111yescharacteristic
221C22×C4C2×D4411yescharacteristic
222C22×C4C2×C22⋊D1111yescharacteristic
223C2×C8—24no—
224C2×C8—42no—
225C2×C8—42no—
226C2×C8—224no—
227C2×C8—442no—
228C2×C8—442no—
229C4⋊C4—442no—
230C4⋊C4—442no—
231C4⋊C4—442no—
232C4⋊C4—442no—
233C42—22no—
234C42—22no—
235C42—22no—
236C42#434114yes—
237C11#871811yescharacteristic, complemented, Sylow
238C23—21no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23#6686912yes—
243C23#6688712yes—
244C23#6688912yes—
245C23C2×(C2×D11)⋊C411yescharacteristic
246C2×C4—28no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—44no—
262C2×C4—44no—
263C2×C4—442no—
264C2×C4—442no—
265C2×C4—442no—
266C2×C4—442no—
267C2×C4—442no—
268C2×C4—442no—
269C2×C4—884no—
270C2×C4—884no—
271C2×C4#6688812yes—
272C2×C4#6693012yes—
273C2×C4#6693912yes—
274C2×C4#6698812yes—
275C8—44no—
276C8—444no—
277C22—22no—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22#1062210214yes—
284C22C2×#6686911yescharacteristic
285C22#1062255611yescharacteristic
286C22#1062261811yescharacteristic
287C22C2×#6688711yescharacteristic
288C22C2×#6688811yescharacteristic
289C22C2×#6688911yescharacteristic
290C22#1062275211yescharacteristic
291C4—22no—
292C4—22no—
293C4—22no—
294C4—22no—
295C4—41no—
296C4—41no—
297C4—882no—
298C4—882no—
299C2—24no—
300C2C2×#1062210211yescharacteristic
301C2#1306721711yescharacteristic
302C2#1306721911yescharacteristic
303C2#1306723911yescharacteristic
304C2#1306869411yescharacteristic
305C2#1306871311yescharacteristic
306C2#1306871611yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1749C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1749D11
hypocenterC11#8718
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
3. #13066498C2semidirect
237. C11#8718semidirect

Maximal subgroups

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

subgroupindex
C2×#106225492
#130683782
#130664982
C11×#17492
#871811