Finite Group Databasebeta

← #14644749

Subgroups — #14644749

Order 2816.

528 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068469C211yesmaximal, characteristic
2C4×C4⋊(C11⋊C8)C211yesmaximal, characteristic
3C2×#10622185C212yesmaximal
4#13066499C212yesmaximal
5C4×C11×C4⋊Q8C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C4×Q8×C11—21no—
8C11×#391—21no—
9C11×#389—21no—
10C11×#389C412yes—
11C11×#384C2211yescharacteristic
12C4×C11×C4⋊C4—21no—
13C4×C11×C4⋊C4C412yes—
14C43×C11C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2212yes—
16C2×C4⋊(C11⋊C8)C2212yes—
17C2×#66867—21no—
18C2×C4×C11⋊C8—21no—
19#10622185C418yescomplemented
20#10622162—21no—
21#10622162—21no—
22C22×Q8×C11—21no—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8C2×C414yes—
25C4×Q8×C11—42no—
26C4×Q8×C11—42no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4C2×C412yes—
32C2×C11×C4⋊C4C2×C412yes—
33C2×C42×C11—22no—
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C42×C11C2311yescharacteristic
41C22×C11⋊C8—22no—
42C22×C11⋊C8—22no—
43C11×#95—22no—
44C11×#95—22no—
45C4⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)C2×C414yes—
48C4⋊(C11⋊C8)C2×C414yes—
49#66867—42no—
50C4×C11⋊C8—42no—
51#8236—111nomaximal, Sylow
52C2×Q8×C11—24no—
53C2×Q8×C11—41no—
54C2×Q8×C11—41no—
55C2×Q8×C11—42no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C11×C4⋊C4—22no—
66C11×C4⋊C4—24no—
67C11×C4⋊C4—42no—
68C11×C4⋊C4—44no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4C4214yes—
74C42×C11—22no—
75C42×C11—22no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—22no—
79C42×C11—41no—
80C42×C11—44no—
81C42×C11D812yes—
82C42×C11SD1612yes—
83C42×C11C22×C412yes—
84C42×C11#4112yes—
85C2×C11⋊C8—24no—
86C2×C11⋊C8—24no—
87C2×C11⋊C8—42no—
88C2×C11⋊C8—42no—
89C2×C11⋊C8—42no—
90C2×C11⋊C8—42no—
91C4×C4⋊Q8D1111yescharacteristic
92#1767—111no—
93C4×C4⋊C8—111no—
94C2×#332—112no—
95#1296—112no—
96C23×C11C2×C22⋊C411yescharacteristic
97Q8×C11—44no—
98Q8×C11—44no—
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—24no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11#10112yes—
117C2×C4×C11#10212yes—
118C2×C4×C11#10212yes—
119C2×C4×C11C2×C4211yescharacteristic
120C2×C4×C11#11711yescharacteristic
121C2×C4×C11C4×D412yes—
122C2×C4×C11C4×D412yes—
123C2×C4×C11C2×D811yescharacteristic
124C2×C4×C11C2×SD1611yescharacteristic
125C2×C4×C11#13512yes—
126C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C11#13712yes—
128C2×C4×C11#13711yescharacteristic
129C11⋊C8—44no—
130C11⋊C8—44no—
131C2×C4⋊Q8C2×D1111yescharacteristic
132C2×C4×Q8—21no—
133C2×C4⋊C8—112no—
134C2×C4⋊C8—112no—
135C2×#97—221no—
136C2×C4×C8—221no—
137#391—21no—
138#389—21no—
139#389Dic1112yes—
140#384C2×D1111yescharacteristic
141C4×C4⋊C4—21no—
142C4×C4⋊C4Dic1112yes—
143C43C2×D1111yescharacteristic
144#336—221no—
145#336—221no—
146#332—118no—
147C22×C11C4×C22⋊C411yescharacteristic
148C22×C11C2×#10111yescharacteristic
149C22×C11#41311yescharacteristic
150C22×C11C2×#10211yescharacteristic
151C22×C11#41611yescharacteristic
152C22×C11#41711yescharacteristic
153C22×C11#41911yescharacteristic
154C4×C11—22no—
155C4×C11—22no—
156C4×C11—22no—
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—41no—
160C4×C11—44no—
161C4×C11—82no—
162C4×C11C4×D812yes—
163C4×C11C4×SD1612yes—
164C4×C11#44012yes—
165C4×C11#44112yes—
166C22×Q8—21no—
167C22×C8—222no—
168C22×C8—222no—
169C4⋊Q8—22no—
170C4⋊Q8C4×D1114yes—
171C4×Q8—42no—
172C4×Q8—42no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4C2×Dic1112yes—
178C2×C4⋊C4C2×Dic1112yes—
179C2×C42—22no—
180C2×C42C2×Dic1111yescharacteristic
181C2×C42C2×Dic1111yescharacteristic
182C2×C42C22⋊D1111yescharacteristic
183C2×C42C22⋊D1111yescharacteristic
184C2×C42C22⋊D1111yescharacteristic
185C2×C42C22⋊D1111yescharacteristic
186C2×C42C22×D1111yescharacteristic
187C4⋊C8—114no—
188C4⋊C8—114no—
189C4⋊C8—222no—
190C4⋊C8—222no—
191#97—442no—
192C4×C8—442no—
193#95—22no—
194#95—22no—
195C2×C11#154611yescharacteristic
196C2×C11#154711yescharacteristic
197C2×C11#155211yescharacteristic
198C2×C11#155411yescharacteristic
199C2×C11C4×#10111yescharacteristic
200C2×C11C4×#10211yescharacteristic
201C2×C11#176311yescharacteristic
202C2×Q8—24no—
203C2×Q8—41no—
204C2×Q8—41no—
205C2×Q8—42no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4C22⋊Dic1111yescharacteristic
209C22×C4C22⋊Dic1111yescharacteristic
210C22×C4C22⋊Dic1111yescharacteristic
211C22×C4C22⋊Dic1111yescharacteristic
212C22×C4C22×Dic1111yescharacteristic
213C22×C4C2×C22⋊D1111yescharacteristic
214C22×C4C2×C22⋊D1111yescharacteristic
215C2×C8—224no—
216C2×C8—224no—
217C2×C8—442no—
218C2×C8—442no—
219C2×C8—442no—
220C2×C8—442no—
221C4⋊C4—22no—
222C4⋊C4—24no—
223C4⋊C4—42no—
224C4⋊C4—44no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4C4×Dic1114yes—
230C42—22no—
231C42—22no—
232C42—21no—
233C42—22no—
234C42—21no—
235C42—41no—
236C42—44no—
237C42#432312yes—
238C42#432412yes—
239C42C2×C4×D1112yes—
240C42#433912yes—
241C11#823611yescharacteristic, complemented, Sylow
242C23C2×C22⋊Dic1111yescharacteristic
243Q8—44no—
244Q8—44no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—24no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4#6689612yes—
263C2×C4#6689612yes—
264C2×C4#6690012yes—
265C2×C4C2×C4×Dic1111yescharacteristic
266C2×C4#6697911yescharacteristic
267C2×C4C4×C22⋊D1112yes—
268C2×C4C4×C22⋊D1112yes—
269C2×C4C2×#432311yescharacteristic
270C2×C4C2×#432411yescharacteristic
271C2×C4#6699512yes—
272C2×C4#6700211yescharacteristic
273C2×C4#6700312yes—
274C2×C4#6700411yescharacteristic
275C8—444no—
276C8—444no—
277C22C4×C22⋊Dic1111yescharacteristic
278C22C2×#6689611yescharacteristic
279C22#1062283811yescharacteristic
280C22C2×#6690011yescharacteristic
281C22#1062284511yescharacteristic
282C22#1062284611yescharacteristic
283C22#1062285011yescharacteristic
284C4—22no—
285C4—22no—
286C4—22no—
287C4—21no—
288C4—21no—
289C4—41no—
290C4—44no—
291C4—82no—
292C4C4×#432312yes—
293C4C4×#432412yes—
294C4#1062263912yes—
295C4#1062264312yes—
296C2#1306728811yescharacteristic
297C2#1306729311yescharacteristic
298C2#1306731611yescharacteristic
299C2#1306732611yescharacteristic
300C2C4×#6690011yescharacteristic
301C2C4×#6689611yescharacteristic
302C2#1306844611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC2×C4×C11C2×C42
FrattiniC2×C42C22×D11
FittingC4×C11×C4⋊Q8C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenterC4×C4⋊Q8D11
hypocenterC11#8236
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
19. #10622185C4semidirect
241. C11#8236semidirect

Maximal subgroups

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

subgroupindex
#130684692
C4×C4⋊(C11⋊C8)2
C2×#106221852
#130664992
C4×C11×C4⋊Q82
#823611