Finite Group Databasebeta

← #14648284

Subgroups — #14648284

Order 2816.

356 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 97 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#13077717C211yesmaximal, characteristic
2#13069592C211yesmaximal, characteristic
3#13067407C211yesmaximal, characteristic
4#13067280C211yesmaximal, characteristic
5#13066448C211yesmaximal, characteristic
6#13066448C211yesmaximal, characteristic
7C11×#1574C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C42×Dic11C2211yescharacteristic
13#10622538C2211yescharacteristic
14#10622538C2211yescharacteristic
15#10622444—21no—
16#10622443—21no—
17#10622333—22no—
18#10622292—21no—
19C8×Dic22—21no—
20C11×#335—21no—
21C11×#334—21no—
22#10622193—22no—
23#10622124C411yescharacteristic, complemented
24#10622124C411yescharacteristic, complemented
25#10622120C411yescharacteristic, complemented
26#10622120C411yescharacteristic, complemented
27#10622118—21no—
28#10622117—21no—
29C2×C11×M16—21no—
30C2×C42×C11C2311yescharacteristic
31#66979D412yes—
32#66977—21no—
33#66977—21no—
34C2×C4×Dic11—21no—
35C2×C4×Dic11—21no—
36C2×C4×Dic11—21no—
37#66923Q812yes—
38#66922C2×C411yescharacteristic
39#66922C2×C411yescharacteristic
40C4×Dic22—21no—
41C4×Dic22—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8—21no—
44C11×C4⋊C8C2×C411yescharacteristic
45C11×C4⋊C8C2×C411yescharacteristic
46C11×C4⋊C8D411yescharacteristic
47C11×C4⋊C8D411yescharacteristic
48C11×C22⋊C8—21no—
49C11×C22⋊C8—21no—
50C4×C8×C11—21no—
51C4×C8×C11—21no—
52C22⋊(C11⋊C8)—21no—
53C22⋊(C11⋊C8)—21no—
54#66879—22no—
55Dic11⋊C8—22no—
56Dic11⋊C8—22no—
57C8×Dic11—22no—
58C4⋊(C11⋊C8)C2×C411yescharacteristic
59C4⋊(C11⋊C8)C2×C411yescharacteristic
60C4⋊(C11⋊C8)D411yescharacteristic
61C4⋊(C11⋊C8)D411yescharacteristic
62C4×C11⋊C8—21no—
63C4×C11⋊C8—21no—
64#8936—111nomaximal, Sylow
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C22×Dic11—41no—
69C2×Dic22—21no—
70C2×Dic22—21no—
71C11×M16—42no—
72C2×C8×C11—21no—
73C2×C8×C11—21no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11—41no—
77C42×C11C22×C411yescharacteristic
78C42×C11C2×D411yescharacteristic
79C42×C11C2×D411yescharacteristic
80C42×C11C2×Q811yescharacteristic
81C22⋊Dic11—22no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11C4⋊C412yes—
85C4⋊Dic11C4⋊C412yes—
86Dic11⋊C4—22no—
87Dic11⋊C4—22no—
88C4×Dic11—22no—
89C4×Dic11—22no—
90C4×Dic11—22no—
91C4×Dic11—22no—
92C4×Dic11—41no—
93C4×Dic11—41no—
94C4×Dic11—41no—
95C2×C11⋊C8—21no—
96C2×C11⋊C8—21no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—21no—
99#2986—111no—
100#1994—111no—
101#1574—111no—
102#1574D1111yescharacteristic
103#1544—111no—
104#1276—111no—
105#1276—111no—
106C23×C11#12311yescharacteristic
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11C2×C4⋊C411yescharacteristic
114C2×C4×C11C4×D411yescharacteristic
115C2×C4×C11C4×D411yescharacteristic
116C2×C4×C11#12011yescharacteristic
117C2×C4×C11C22⋊Q811yescharacteristic
118C2×C4×C11C22⋊Q811yescharacteristic
119C2×Dic11—22no—
120C2×Dic11—22no—
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124Dic22—41no—
125Dic22—41no—
126Dic22—41no—
127Dic22—41no—
128C8×C11—41no—
129C8×C11—41no—
130C8×C11—41no—
131C8×C11—41no—
132C8×C11—81no—
133C11⋊C8—41no—
134C11⋊C8—41no—
135C11⋊C8—41no—
136C11⋊C8—41no—
137#533—111no—
138#446—221no—
139#446—221no—
140C8×Q8—221no—
141C8×Q8—221no—
142#433—222no—
143#431—111no—
144#431—111no—
145#431C2×D1111yescharacteristic
146#431C2×D1111yescharacteristic
147#423C2×D1111yescharacteristic
148C43—111no—
149#339—222no—
150#335—21no—
151#335—221no—
152#334—21no—
153#334—221no—
154#332—111no—
155#332—111no—
156#332—111no—
157#332—111no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11#38511yescharacteristic
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11#44311yescharacteristic
166C4×C11#44311yescharacteristic
167C4×C11#44411yescharacteristic
168C4×C11#44411yescharacteristic
169C4×C11#45411yescharacteristic
170C4×C11#45611yescharacteristic
171Dic11—44no—
172Dic11—42no—
173Dic11—42no—
174C2×M16—21no—
175C4⋊Q8—111no—
176C4⋊Q8—111no—
177#125—112no—
178C22⋊Q8—221no—
179C22⋊Q8—221no—
180C4×Q8—221no—
181C4×Q8—221no—
182#117—112no—
183C2×C42—221no—
184C2×C42—221no—
185C2×C42—221no—
186C2×C42C22×D1111yescharacteristic
187C4⋊C8—21no—
188C4⋊C8—21no—
189C4⋊C8—111no—
190C4⋊C8—111no—
191C4⋊C8—111no—
192C4⋊C8—111no—
193C4⋊C8—222no—
194C4⋊C8—222no—
195C4⋊C8C4×D1111yescharacteristic
196C4⋊C8C4×D1111yescharacteristic
197C4⋊C8C22⋊D1111yescharacteristic
198C4⋊C8C22⋊D1111yescharacteristic
199C22⋊C8—21no—
200C22⋊C8—21no—
201C22⋊C8—221no—
202C22⋊C8—221no—
203#97—222no—
204C4×C8—21no—
205C4×C8—21no—
206C4×C8—222no—
207C4×C8—221no—
208C4×C8—221no—
209C2×C11—41no—
210C2×C11#185711yescharacteristic
211C2×C11#186611yescharacteristic
212C2×C11#186611yescharacteristic
213C2×Q8—221no—
214C2×Q8—221no—
215C22×C4—441no—
216C22×C4#433911yescharacteristic
217C22×C4D4×D1111yescharacteristic
218C22×C4#434311yescharacteristic
219M16—42no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—41no—
225C2×C8—221no—
226C2×C8—221no—
227C2×C8—221no—
228C2×C8—221no—
229C4⋊C4—112no—
230C4⋊C4—112no—
231C4⋊C4—221no—
232C4⋊C4—222no—
233C4⋊C4—221no—
234C4⋊C4—222no—
235C22⋊C4—222no—
236C42—222no—
237C42—222no—
238C42—222no—
239C42—222no—
240C42—441no—
241C42—441no—
242C42—441no—
243C42C2×C4×D1111yescharacteristic
244C42D4×D1111yescharacteristic
245C42Q8×D1111yescharacteristic
246C42C2×C22⋊D1111yescharacteristic
247C11#893611yescharacteristic, complemented, Sylow
248C23#6694711yescharacteristic
249Q8—441no—
250Q8—441no—
251Q8—441no—
252Q8—441no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—222no—
260C2×C4—222no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4—442no—
264C2×C4C4⋊C4×D1111yescharacteristic
265C2×C4#6694611yescharacteristic
266C2×C4#6694911yescharacteristic
267C2×C4C4×C22⋊D1111yescharacteristic
268C2×C4#6699011yescharacteristic
269C2×C4#6699911yescharacteristic
270C8—41no—
271C8—41no—
272C8—41no—
273C8—41no—
274C8—81no—
275C8—441no—
276C8—441no—
277C8—441no—
278C8—441no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22#1062260211yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—444no—
287C4—442no—
288C4—442no—
289C4#1062250711yescharacteristic
290C4#1062250811yescharacteristic
291C4#1062275711yescharacteristic
292C4#1062275811yescharacteristic
293C4#1062281411yescharacteristic
294C4#1062281811yescharacteristic
295C2—41no—
296C2#1306882911yescharacteristic
297C2#1306888811yescharacteristic
298C2#1306889011yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1574C2
socleC22×C11#385
prime radicalC23×C11#123
cosocleC2×C42×C11C23
hypercenter#1574D11
hypocenterC11#8936
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
23. #10622124C4semidirect
24. #10622124C4semidirect
25. #10622120C4semidirect
26. #10622120C4semidirect
247. C11#8936semidirect

Maximal subgroups

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

subgroupindex
#130777172
#130695922
#130674072
#130672802
#130664482
C11×#15742
#893611