Finite Group Databasebeta

← #14664385

Subgroups — #14664385

Order 2816.

462 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 87 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#13072933C211yesmaximal, characteristic
2#13066957C211yesmaximal, characteristic
3#13066639C214yesmaximal, complemented
4C4×C11×#99C211yesmaximal, characteristic
5C2×C4×D4×C11C2211yescharacteristic
6C22×C4⋊Dic11C411yescharacteristic, complemented
7C2×C11×#99—21no—
8C4×C11×C22⋊C4—21no—
9#10622833—21no—
10#10622825—21no—
11#10622825C411yescharacteristic, complemented
12#10622599C412yescomplemented
13#10622562C2212yes—
14#10622559—21no—
15#10622541—21no—
16#10622539—21no—
17C11×#342C2212yes—
18#10622163—21no—
19#10622163C2212yes—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11—21no—
24C4×D4×C11—41no—
25C4×D4×C11—41no—
26C2×C11×C4⋊C4C2×C411yescharacteristic
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4D411yescharacteristic
29C2×C11×C22⋊C4C2311yescharacteristic
30C2×C42×C11—41no—
31C2×C42×C11D411yescharacteristic
32C2×C22⋊Dic11—21no—
33C2×C22⋊Dic11—22no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—41no—
37C2×C4⋊Dic11—41no—
38C2×C4⋊Dic11C2×C412yes—
39C2×Dic11⋊C4—22no—
40C11×#99—24no—
41C11×#95—41no—
42C11⋊#95—22no—
43C11⋊#95—22no—
44C11⋊#95C2×C412yes—
45C22⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—41no—
47#66867—41no—
48#11786—111nomaximal, Sylow
49C24×C11C22⋊C411yescharacteristic
50C24×C11C2×D411yescharacteristic
51C2×D4×C11—22no—
52C2×D4×C11—22no—
53C2×D4×C11—41no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—42no—
59C22×C4×C11—42no—
60C22×C4×C11—42no—
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—22no—
67C22×Dic11—22no—
68C22×Dic11—42no—
69C22×Dic11—82no—
70C11×C4⋊C4—41no—
71C11×C22⋊C4—24no—
72C11×C22⋊C4—41no—
73C11×C22⋊C4—41no—
74C11×C22⋊C4—42no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—82no—
78C22⋊Dic11—42no—
79C22⋊Dic11—82no—
80C4⋊Dic11—42no—
81C4⋊Dic11—42no—
82C4⋊Dic11—41no—
83C4⋊Dic11—41no—
84Dic11⋊C4—82no—
85C2×C11⋊C8—42no—
86#2487—111no—
87C4×#99D1111yescharacteristic
88#1466—111no—
89#1352—114no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—41no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11#10412yes—
99C23×C11C2×C22⋊C411yescharacteristic
100C23×C11#13712yes—
101D4×C11—44no—
102C2×C4×C11—22no—
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—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—44no—
116C2×C4×C11—81no—
117C2×C4×C11—82no—
118C2×C4×C11—82no—
119C2×C4×C11#9911yescharacteristic
120C2×C4×C11#9911yescharacteristic
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—84no—
128C11⋊C8—82no—
129C2×C4×D4C2×D1111yescharacteristic
130C22×C4⋊C4—111no—
131#432—221no—
132C2×#99—21no—
133#400—112no—
134#399—112no—
135#389—221no—
136#386—221no—
137#385—221no—
138#380—111no—
139#380—221no—
140C4×C22⋊C4—21no—
141#342C2×D1112yes—
142#323—112no—
143#323—221no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—22no—
147C22×C11—22no—
148C22×C11—42no—
149C22×C11—42no—
150C22×C11—42no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—81no—
156C22×C11C2×#9911yescharacteristic
157C22×C11#41911yescharacteristic
158C22×C11C2×#10411yescharacteristic
159C4×C11—21no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—84no—
165C4×C11#35212yes—
166Dic11—82no—
167Dic11—82no—
168C22×D4C22⋊D1111yescharacteristic
169C23×C4—221no—
170C23×C4C4×D1111yescharacteristic
171C23×C4C22⋊D1111yescharacteristic
172C4×D4—41no—
173C4×D4—41no—
174C2×C4⋊C4—112no—
175C2×C4⋊C4—221no—
176C2×C4⋊C4—221no—
177C2×C4⋊C4—222no—
178C2×C4⋊C4—441no—
179C2×C4⋊C4—441no—
180C2×C4⋊C4C4×D1111yescharacteristic
181C2×C22⋊C4—22no—
182C2×C22⋊C4—221no—
183C2×C22⋊C4—222no—
184C2×C22⋊C4D4411yescharacteristic
185C2×C22⋊C4C22×D1111yescharacteristic
186C2×C42—41no—
187C2×C42D4411yescharacteristic
188C4⋊C8—441no—
189#99—24no—
190C22⋊C8—222no—
191#97—441no—
192#95—41no—
193#95—112no—
194#95—222no—
195#95—222no—
196C2×C11—21no—
197C2×C11—21no—
198C2×C11—42no—
199C2×C11—42no—
200C2×C11#150811yescharacteristic
201C2×C11C2×#35211yescharacteristic
202C2×C11#212811yescharacteristic
203C24(C2×D11)⋊C411yescharacteristic
204C24C2×C22⋊D1111yescharacteristic
205C2×D4—22no—
206C2×D4—22no—
207C2×D4—41no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—222no—
216C22×C4—222no—
217C22×C4—442no—
218C22×C4—882no—
219C22×C4(C2×D11)⋊C411yescharacteristic
220C22×C4(C2×D11)⋊C411yescharacteristic
221C22×C4(C2×D11)⋊C411yescharacteristic
222C22×C4C2×C4×D1111yescharacteristic
223C22×C4C2×D4411yescharacteristic
224C2×C8—442no—
225C4⋊C4—41no—
226C4⋊C4—442no—
227C4⋊C4—442no—
228C4⋊C4—441no—
229C4⋊C4—441no—
230C4⋊C4—882no—
231C22⋊C4—24no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C22⋊C4—42no—
235C22⋊C4—442no—
236C22⋊C4—882no—
237C42—21no—
238C42—21no—
239C42—82no—
240C11#1178611yescharacteristic, complemented, Sylow
241C23—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23—41no—
246C23—41no—
247C23—41no—
248C23—41no—
249C23#6686912yes—
250C23C2×(C2×D11)⋊C411yescharacteristic
251C23#6700412yes—
252D4—44no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—44no—
267C2×C4—81no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—442no—
271C2×C4—442no—
272C2×C4—442no—
273C2×C4—442no—
274C2×C4—442no—
275C2×C4—442no—
276C2×C4—884no—
277C2×C4#6687011yescharacteristic
278C2×C4#6687011yescharacteristic
279C8—882no—
280C22—21no—
281C22—21no—
282C22—22no—
283C22—22no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—81no—
292C22C2×#6686911yescharacteristic
293C22C2×#6687011yescharacteristic
294C22#1062261711yescharacteristic
295C4—21no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—84no—
301C4—882no—
302C4—882no—
303C4#1062211012yes—
304C2—21no—
305C2—21no—
306C2—42no—
307C2—42no—
308C2#1306713511yescharacteristic
309C2C2×#1062211011yescharacteristic
310C2#1307028711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC4×C11×#99C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenterC4×#99D11
hypocenterC11#11786
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #13066639C2semidirect
6. C22×C4⋊Dic11C4semidirect
11. #10622825C4semidirect
12. #10622599C4semidirect
240. C11#11786semidirect

Maximal subgroups

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

subgroupindex
#130729332
#130669572
#130666392
C4×C11×#992
#1178611