Finite Group Databasebeta

← #14647181

Subgroups — #14647181

Order 2816.

526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 123 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#13071023C211yesmaximal, characteristic
2#13068378C211yesmaximal, characteristic
3#13066498C214yesmaximal, complemented
4C11×#1749C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C2×#66979C412yes—
7C2×C11×C22⋊C8—21no—
8C2×C11×#97C2212yes—
9#10622825—21no—
10#10622825—21no—
11C2×C22⋊(C11⋊C8)—21no—
12#10622549C2212yes—
13#10622548C411yescharacteristic
14#10622548C411yescharacteristic
15C4×C4⋊Dic11—21no—
16C4×C4⋊Dic11—21no—
17C2×#66867C2212yes—
18C11×#336—21no—
19#10622162—21no—
20C23×C4×C11C2×C411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C22×C8×C11—22no—
24C2×C42×C11—24no—
25C2×C42×C11C2×C411yescharacteristic
26C2×C42×C11D411yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C42×C11C2311yescharacteristic
29C2×C22⋊Dic11—22no—
30#66979—44no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11C2×C412yes—
36C2×C4⋊Dic11C2×C412yes—
37C2×C4×Dic11—22no—
38C22×C11⋊C8—22no—
39C11×C22⋊C8—24no—
40C11×#97—24no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43C22⋊(C11⋊C8)—24no—
44#66867—24no—
45#8721—111nomaximal, Sylow
46C24×C11C22⋊C411yescharacteristic
47C22×C4×C11—22no—
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—41no—
55C22×C4×C11—41no—
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22×C411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×Dic11—22no—
63C22×Dic11—22no—
64C2×C8×C11—24no—
65C2×C8×C11—42no—
66C2×C8×C11—42no—
67C42×C11—22no—
68C42×C11—22no—
69C42×C11—22no—
70C42×C11#4114yes—
71C22⋊Dic11—44no—
72C4⋊Dic11—42no—
73C4⋊Dic11—42no—
74C4⋊Dic11—42no—
75C4⋊Dic11—42no—
76C4⋊Dic11—42no—
77C4⋊Dic11—42no—
78C4×Dic11—44no—
79C2×C11⋊C8—24no—
80C2×C11⋊C8—42no—
81C2×C11⋊C8—42no—
82#2285—111no—
83#1749—111no—
84#1749D1111yescharacteristic
85#1295—114no—
86C23×C11—21no—
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11#10112yes—
93C23×C11C2×C22⋊C411yescharacteristic
94C2×C4×C11—28no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
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—44no—
108C2×C4×C11—44no—
109C2×C4×C11#10012yes—
110C2×C4×C11#10412yes—
111C2×C4×C11#10412yes—
112C2×C4×C11#11712yes—
113C2×C4×C11#12312yes—
114C2×C4×C11#12312yes—
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C8×C11—44no—
122C11⋊C8—44no—
123C2×#117—112no—
124C22×C42C2×D1111yescharacteristic
125C2×C22⋊C8—21no—
126C2×C22⋊C8—221no—
127C2×#97—112no—
128C2×#97C2×D1112yes—
129#384—111no—
130#384—111no—
131#382—112no—
132#380—221no—
133#380—221no—
134C4×C4⋊C4—221no—
135C4×C4⋊C4—221no—
136#336—21no—
137#336—221no—
138C22×C11—22no—
139C22×C11—22no—
140C22×C11—22no—
141C22×C11—41no—
142C22×C11—41no—
143C22×C11—41no—
144C22×C11—41no—
145C22×C11#38111yescharacteristic
146C22×C11C2×#10011yescharacteristic
147C22×C11C2×#10111yescharacteristic
148C22×C11C2×#10411yescharacteristic
149C22×C11C2×#10411yescharacteristic
150C22×C11#42111yescharacteristic
151C22×C11#42111yescharacteristic
152C4×C11—22no—
153C4×C11—22no—
154C4×C11—22no—
155C4×C11—22no—
156C4×C11—22no—
157C4×C11—22no—
158Dic11—82no—
159Dic11—82no—
160C23×C4C4×D1111yescharacteristic
161C23×C4D4411yescharacteristic
162C23×C4C22⋊D1111yescharacteristic
163C22×C8—22no—
164C22×C8—222no—
165#117—444no—
166C2×C4⋊C4—112no—
167C2×C4⋊C4—112no—
168C2×C4⋊C4—221no—
169C2×C4⋊C4—221no—
170C2×C4⋊C4—221no—
171C2×C4⋊C4—221no—
172C2×C22⋊C4—222no—
173C2×C42—24no—
174C2×C42—222no—
175C2×C42C4×D1111yescharacteristic
176C2×C42D4411yescharacteristic
177C2×C42C22⋊D1111yescharacteristic
178C2×C42C22×D1111yescharacteristic
179C22⋊C8—24no—
180C22⋊C8—224no—
181#97—24no—
182#97—224no—
183#95—222no—
184#95—222no—
185C2×C11—42no—
186C2×C11#152511yescharacteristic
187C2×C11#153111yescharacteristic
188C2×C11#153111yescharacteristic
189C2×C11#153611yescharacteristic
190C2×C11#182111yescharacteristic
191C2×C11#182611yescharacteristic
192C2×C11#182611yescharacteristic
193C24(C2×D11)⋊C411yescharacteristic
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—222no—
204C22×C4—222no—
205C22×C4(C2×D11)⋊C411yescharacteristic
206C22×C4(C2×D11)⋊C411yescharacteristic
207C22×C4(C2×D11)⋊C411yescharacteristic
208C22×C4C2×C4×D1111yescharacteristic
209C22×C4C2×D4411yescharacteristic
210C22×C4C2×C22⋊D1111yescharacteristic
211C2×C8—24no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—224no—
215C2×C8—442no—
216C2×C8—442no—
217C4⋊C4—442no—
218C4⋊C4—442no—
219C4⋊C4—442no—
220C4⋊C4—442no—
221C4⋊C4—442no—
222C4⋊C4—442no—
223C22⋊C4—444no—
224C42—22no—
225C42—22no—
226C42—22no—
227C42—444no—
228C42#434114yes—
229C11#872111yescharacteristic, complemented, Sylow
230C23—21no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23#6688812yes—
237C23C2×(C2×D11)⋊C411yescharacteristic
238C2×C4—28no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—44no—
252C2×C4—44no—
253C2×C4—442no—
254C2×C4—442no—
255C2×C4—442no—
256C2×C4—442no—
257C2×C4—442no—
258C2×C4—442no—
259C2×C4#6686912yes—
260C2×C4#6688712yes—
261C2×C4#6688912yes—
262C2×C4#6693012yes—
263C2×C4#6693912yes—
264C2×C4#6698812yes—
265C8—44no—
266C8—444no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22C2×#6686911yescharacteristic
275C22#1062255611yescharacteristic
276C22#1062261811yescharacteristic
277C22C2×#6688711yescharacteristic
278C22C2×#6688811yescharacteristic
279C22C2×#6688911yescharacteristic
280C22#1062275211yescharacteristic
281C4—22no—
282C4—22no—
283C4—22no—
284C4—22no—
285C4—22no—
286C4—22no—
287C4—882no—
288C4—882no—
289C2—42no—
290C2#1306720711yescharacteristic
291C2#1306723011yescharacteristic
292C2#1306723211yescharacteristic
293C2#1306725011yescharacteristic
294C2#1306869411yescharacteristic
295C2#1306871311yescharacteristic
296C2#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#8721
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
229. C11#8721semidirect

Maximal subgroups

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

subgroupindex
#130710232
#130683782
#130664982
C11×#17492
#872111