Finite Group Databasebeta

← #14645539

Subgroups — #14645539

Order 2816.

738 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 147 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×Q8×Dic22C211yesmaximal, characteristic
2#13068612C211yesmaximal, characteristic
3#13067300C212yesmaximal
4#13067046C212yesmaximal
5C11×#1461C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×Q8×Dic11—21no—
8Q8×Dic22—24no—
9Q8×Dic22—24no—
10C2×#66941—21no—
11C2×#66941—22no—
12C2×#66922C412yes—
13C2×#66922C2211yescharacteristic
14C2×C4×Dic22C412yes—
15C2×C4×Dic22C2211yescharacteristic
16C11×#431C2212yes—
17C2×#66900—21no—
18#10622537C2212yes—
19C11×#324—22no—
20#10622168—21no—
21#10622120—24no—
22#10622094—24no—
23C22×Q8×C11D411yescharacteristic
24C22×Dic22—22no—
25C22×Dic22—21no—
26C22×Dic22C2×C411yescharacteristic
27C4×Q8×C11—22no—
28C4×Q8×C11—22no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C4⋊C4D412yes—
31C2×C42×C11C2×C412yes—
32C2×C42×C11C2311yescharacteristic
33Q8×Dic11—28no—
34C2×C4⋊Dic11—22no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11C2×C412yes—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×Dic11⋊C4—22no—
39C2×Dic11⋊C4—21no—
40C2×C4×Dic11—22no—
41C2×C4×Dic11—21no—
42C2×#4318—22no—
43#66941—216no—
44#66941—28no—
45#66922—22no—
46#66922—24no—
47#66922—24no—
48#66922D414yes—
49C4×Dic22—24no—
50C4×Dic22—22no—
51C4×Dic22—24no—
52C4×Dic22D414yes—
53C11×C4⋊C8—22no—
54C11×C22⋊C8—22no—
55C4×C8×C11—22no—
56#66900—42no—
57C4⋊(C11⋊C8)—22no—
58C4⋊(C11⋊C8)—22no—
59#8396—111nomaximal, Sylow
60C2×Q8×C11—22no—
61C2×Q8×C11—22no—
62C2×Q8×C11SD1612yes—
63C2×Q8×C11Q1612yes—
64C22×C4×C11C22⋊C412yes—
65C22×C4×C11C22⋊C412yes—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—22no—
71C22×Dic11—21no—
72C2×Dic22—24no—
73C2×Dic22—28no—
74C2×Dic22—21no—
75C2×Dic22—24no—
76C2×Dic22—82no—
77C2×Dic22—84no—
78C2×Dic22C22⋊C412yes—
79C2×C8×C11—42no—
80C11×C4⋊C4—24no—
81C11×C4⋊C4—22no—
82C42×C11—22no—
83C42×C11—22no—
84C42×C11C2×D412yes—
85C42×C11C2×D412yes—
86C4⋊Dic11—28no—
87C4⋊Dic11—21no—
88C4⋊Dic11—22no—
89C4⋊Dic11—24no—
90C4⋊Dic11C22⋊C414yes—
91C4⋊Dic11C22⋊C412yes—
92Dic11⋊C4—28no—
93Dic11⋊C4—24no—
94C4×Dic11—28no—
95C4×Dic11—24no—
96#4318—42no—
97#4318—42no—
98C2×C11⋊C8—42no—
99C2×Q82—111no—
100#1801—111no—
101#1549—112no—
102#1487—112no—
103#1461D1111yescharacteristic
104C23×C11C2×C22⋊C411yescharacteristic
105Q8×C11—24no—
106Q8×C11—24no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—41no—
112C2×C4×C11—42no—
113C2×C4×C11#10314yes—
114C2×C4×C11C2×C22⋊C411yescharacteristic
115C2×C4×C11C2×C22⋊C411yescharacteristic
116C2×C4×C11#12012yes—
117C2×C4×C11#12012yes—
118C2×C4×C11C2×SD1611yescharacteristic
119C2×C4×C11C2×Q1611yescharacteristic
120C2×C4×C11#13712yes—
121C2×Dic11—24no—
122C2×Dic11—22no—
123C2×Dic11—24no—
124C2×Dic11—22no—
125C2×Dic11—44no—
126C2×Dic11—42no—
127Dic22—24no—
128Dic22—22no—
129Dic22—84no—
130Dic22—88no—
131Dic22#10114yescomplemented
132C8×C11—82no—
133C11⋊C8—82no—
134Q82—224no—
135Q82—224no—
136C2×C4⋊Q8—111no—
137C2×C4⋊Q8—112no—
138C2×C4⋊Q8—221no—
139C2×C4⋊Q8—222no—
140C2×C4×Q8—111no—
141C2×C4×Q8—112no—
142C2×C4×Q8—221no—
143C2×C4×Q8C2×D1111yescharacteristic
144#431C2×D1112yes—
145#423—112no—
146C2×#101—221no—
147#343—221no—
148#332—224no—
149Q8⋊C8—224no—
150#324—22no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11#37911yescharacteristic
154C22×C11C2×#10311yescharacteristic
155C22×C11#41911yescharacteristic
156C4×C11—22no—
157C4×C11—21no—
158C4×C11—24no—
159C4×C11—42no—
160C4×C11C2×#10112yes—
161C4×C11#44812yes—
162C4×C11#45112yes—
163Dic11—24no—
164Dic11—44no—
165Dic11—42no—
166C22×Q8—111no—
167C22×Q8—222no—
168C22×Q8—221no—
169C22×Q8D4411yescharacteristic
170C2×M16—222no—
171C4⋊Q8—114no—
172C4⋊Q8—224no—
173C4⋊Q8—224no—
174C4⋊Q8—2216no—
175C4⋊Q8—228no—
176C4⋊Q8—222no—
177C4×Q8—22no—
178C4×Q8—22no—
179C4×Q8—114no—
180C4×Q8—224no—
181C4×Q8—224no—
182C4×Q8—228no—
183C4×Q8—222no—
184C2×C4⋊C4—111no—
185C2×C4⋊C4—112no—
186C2×C4⋊C4—222no—
187C2×C4⋊C4—222no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4D4411yescharacteristic
191C2×C4⋊C4C22⋊D1112yes—
192C2×C42—222no—
193C2×C42—221no—
194C2×C42C4×D1112yes—
195C2×C42C22×D1111yescharacteristic
196C4⋊C8—22no—
197C4⋊C8—222no—
198C4⋊C8—222no—
199#101—442no—
200C22⋊C8—22no—
201C4×C8—22no—
202C2×C11—21no—
203C2×C11—21no—
204C2×C11#178411yescharacteristic
205C2×C11#178711yescharacteristic
206C2×C11#179511yescharacteristic
207C2×Q8—22no—
208C2×Q8—22no—
209C2×Q8—112no—
210C2×Q8—224no—
211C2×Q8—228no—
212C2×Q8—221no—
213C2×Q8—224no—
214C2×Q8—882no—
215C2×Q8—884no—
216C2×Q8#431412yes—
217C2×Q8Dic4412yes—
218C22×C4—221no—
219C22×C4—222no—
220C22×C4—221no—
221C22×C4(C2×D11)⋊C412yes—
222C22×C4(C2×D11)⋊C412yes—
223C22×C4C2×C4×D1111yescharacteristic
224C22×C4C2×D4411yescharacteristic
225C22×C4C2×C22⋊D1111yescharacteristic
226M16—442no—
227M16—442no—
228C2×C8—42no—
229C2×C8—442no—
230C4⋊C4—22no—
231C4⋊C4—24no—
232C4⋊C4—112no—
233C4⋊C4—114no—
234C4⋊C4—228no—
235C4⋊C4—228no—
236C4⋊C4—221no—
237C4⋊C4—222no—
238C4⋊C4—224no—
239C4⋊C4—224no—
240C42—22no—
241C42—22no—
242C42—228no—
243C42—224no—
244C42D4×D1112yes—
245C42D4×D1112yes—
246C11#839611yescharacteristic, complemented, Sylow
247C23C2×(C2×D11)⋊C411yescharacteristic
248Q8—24no—
249Q8—24no—
250Q8—114no—
251Q8—224no—
252Q8—222no—
253Q8—884no—
254Q8—888no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—224no—
262C2×C4—222no—
263C2×C4—224no—
264C2×C4—222no—
265C2×C4—444no—
266C2×C4—442no—
267C2×C4#6688014yes—
268C2×C4C22⋊C4×D1111yescharacteristic
269C2×C4C22⋊C4×D1111yescharacteristic
270C2×C4#6693512yes—
271C2×C4C2×#431411yescharacteristic
272C2×C4C2×Dic4411yescharacteristic
273C2×C4#6696212yes—
274C2×C4#6699012yes—
275C8—82no—
276C8—882no—
277C22—21no—
278C22—21no—
279C22#1062256811yescharacteristic
280C22C2×#6688011yescharacteristic
281C22#1062273311yescharacteristic
282C4—24no—
283C4—22no—
284C4—21no—
285C4—42no—
286C4—224no—
287C4—444no—
288C4—442no—
289C4#1062235112yes—
290C4#1062235212yes—
291C4D11×#10112yes—
292C2—21no—
293C2—21no—
294C2#1306853811yescharacteristic
295C2#1306855211yescharacteristic
296C2#1306858411yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1461C2
socleC22×C11#379
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1461D11
hypocenterC11#8396
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
131. Dic22#101semidirect
246. C11#8396semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic222
#130686122
#130673002
#130670462
C11×#14612
#839611