Finite Group Databasebeta

← #14647124

Subgroups — #14647124

Order 2816.

680 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic
2C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
3#13066457C214yesmaximal, complemented
4C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
5C22×C11×C4⋊C4C411yescharacteristic
6C22×C11×C4⋊C4C411yescharacteristic
7C22×C42×C11—21no—
8C22×C42×C11C2211yescharacteristic
9C4×C11×C4⋊C4—21no—
10C4×C11×C4⋊C4—21no—
11C4×C11×C4⋊C4C412yes—
12C4×C11×C4⋊C4C2212yes—
13C2×C11×#95—21no—
14C2×C22⋊(C11⋊C8)—21no—
15C2×C22⋊(C11⋊C8)—21no—
16C2×C4⋊(C11⋊C8)C2212yes—
17C2×C4×C11⋊C8C2212yes—
18#10622162—21no—
19#10622162—21no—
20C23×C4×C11—21no—
21C23×C4×C11—21no—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—24no—
29C2×C11×C4⋊C4C814yescomplemented
30C2×C11×C4⋊C4C2×C412yes—
31C2×C11×C4⋊C4C2×C412yes—
32C2×C42×C11—24no—
33C2×C42×C11—22no—
34C2×C42×C11—22no—
35C2×C42×C11—44no—
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11C2311yescharacteristic
40C22×C11⋊C8—22no—
41C22×C11⋊C8—22no—
42C11×#95—22no—
43C11×#95—22no—
44C22⋊(C11⋊C8)—24no—
45C22⋊(C11⋊C8)—42no—
46C4⋊(C11⋊C8)—24no—
47C4×C11⋊C8—24no—
48#8707—111nomaximal, Sylow
49C24×C11C22⋊C411yescharacteristic
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—24no—
55C22×C4×C11—24no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—41no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C2×C812yes—
69C22×C4×C11M1612yes—
70C22×C4×C11SD1612yes—
71C22×C4×C11Q1612yes—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C11×C4⋊C4—24no—
76C11×C4⋊C4—24no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4C2×C814yes—
80C11×C4⋊C4M1614yes—
81C42×C11—22no—
82C42×C11—22no—
83C42×C11—22no—
84C42×C11—44no—
85C42×C11—44no—
86C42×C11#4114yes—
87C2×C11⋊C8—24no—
88C2×C11⋊C8—42no—
89C2×C11⋊C8—42no—
90C2×C11⋊C8—42no—
91C2×C11⋊C8—42no—
92C2×C11⋊C8—42no—
93C2×C4×C4⋊C4D1111yescharacteristic
94#1797—111no—
95C4×C22⋊C8—111no—
96#1279—114no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11C22⋊C812yes—
102C23×C11#10312yes—
103C23×C11#10412yes—
104C23×C11C2×C22⋊C411yescharacteristic
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—24no—
112C2×C4×C11—24no—
113C2×C4×C11—24no—
114C2×C4×C11—24no—
115C2×C4×C11—21no—
116C2×C4×C11—24no—
117C2×C4×C11—24no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—44no—
121C2×C4×C11—48no—
122C2×C4×C11—48no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11C22⋊C812yes—
128C2×C4×C11#10312yes—
129C2×C4×C11#11712yes—
130C2×C4×C11#12312yes—
131C2×C4×C11#12312yes—
132C2×C4×C11C22×C811yescharacteristic
133C2×C4×C11C2×M1612yes—
134C2×C4×C11C2×M1611yescharacteristic
135C2×C4×C11C2×SD1611yescharacteristic
136C2×C4×C11C2×Q1611yescharacteristic
137C2×C4×C11AGL(1,ℤ/8)12yes—
138C11⋊C8—44no—
139C11⋊C8—82no—
140C22×C4⋊C4Dic1111yescharacteristic
141C22×C4⋊C4Dic1111yescharacteristic
142C22×C42—21no—
143C22×C42C2×D1111yescharacteristic
144C2×C4⋊C8—112no—
145C2×C22⋊C8—221no—
146C2×C22⋊C8—221no—
147C2×C4×C8—112no—
148C4×C4⋊C4—21no—
149C4×C4⋊C4—21no—
150C4×C4⋊C4Dic1112yes—
151C4×C4⋊C4C2×D1112yes—
152C2×#95—21no—
153#336—221no—
154#336—221no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—22no—
160C22×C11—22no—
161C22×C11Q8⋊C814yes—
162C22×C11#38111yescharacteristic
163C22×C11C2×C22⋊C811yescharacteristic
164C22×C11#40711yescharacteristic
165C22×C11C2×#10311yescharacteristic
166C22×C11#41811yescharacteristic
167C22×C11C2×#10411yescharacteristic
168C22×C11#42111yescharacteristic
169C4×C11—22no—
170C4×C11—22no—
171C4×C11—22no—
172C4×C11—41no—
173C4×C11—44no—
174C4×C11—44no—
175C4×C11#43112yes—
176C4×C11#43212yes—
177C4×C11#48112yes—
178C4×C11#48412yes—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4C2×Dic1111yescharacteristic
182C23×C4C22⋊D1111yescharacteristic
183C23×C4C22⋊D1111yescharacteristic
184C22×C8—222no—
185C22×C8—222no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—24no—
190C2×C4⋊C4C11⋊C814yescomplemented
191C2×C4⋊C4C2×Dic1112yes—
192C2×C4⋊C4C2×Dic1112yes—
193C2×C42—24no—
194C2×C42—22no—
195C2×C42—22no—
196C2×C42—44no—
197C2×C42C2×Dic1111yescharacteristic
198C2×C42C22⋊D1111yescharacteristic
199C2×C42C22⋊D1111yescharacteristic
200C2×C42C22×D1111yescharacteristic
201C4⋊C8—224no—
202C22⋊C8—224no—
203C22⋊C8—442no—
204C4×C8—224no—
205#95—22no—
206#95—22no—
207C2×C11—24no—
208C2×C11C2×Q8⋊C811yescharacteristic
209C2×C11#147811yescharacteristic
210C2×C11#148711yescharacteristic
211C2×C11#149011yescharacteristic
212C2×C11#181711yescharacteristic
213C2×C11#182411yescharacteristic
214C2×C11#182611yescharacteristic
215C24C22⋊Dic1111yescharacteristic
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—24no—
221C22×C4—24no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—41no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4C2×C11⋊C812yes—
232C22×C4#431812yes—
233C22×C4#432512yes—
234C22×C4#432612yes—
235C22×C4C22⋊Dic1111yescharacteristic
236C22×C4C22⋊Dic1111yescharacteristic
237C22×C4C22⋊Dic1111yescharacteristic
238C22×C4C22×Dic1111yescharacteristic
239C22×C4C2×C22⋊D1111yescharacteristic
240C22×C4C2×C22⋊D1111yescharacteristic
241C2×C8—224no—
242C2×C8—442no—
243C2×C8—442no—
244C2×C8—442no—
245C2×C8—442no—
246C2×C8—442no—
247C4⋊C4—24no—
248C4⋊C4—24no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4C2×C11⋊C814yes—
252C4⋊C4#431814yes—
253C42—22no—
254C42—22no—
255C42—22no—
256C42—44no—
257C42—44no—
258C42#433914yes—
259C11#870711yescharacteristic, complemented, Sylow
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23C22⋊(C11⋊C8)12yes—
265C23#6689912yes—
266C23#6690112yes—
267C23C2×C22⋊Dic1111yescharacteristic
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—24no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—44no—
284C2×C4—48no—
285C2×C4—48no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4C22⋊(C11⋊C8)12yes—
291C2×C4#6689912yes—
292C2×C4C22×C11⋊C811yescharacteristic
293C2×C4C2×#431812yes—
294C2×C4C2×#431811yescharacteristic
295C2×C4#6697912yes—
296C2×C4#6698212yes—
297C2×C4#6698212yes—
298C2×C4#6698512yes—
299C2×C4C2×#432511yescharacteristic
300C2×C4C2×#432611yescharacteristic
301C8—444no—
302C8—882no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22—22no—
309C22Q8⋊(C11⋊C8)14yes—
310C22C2×C22⋊(C11⋊C8)11yescharacteristic
311C22#1062282011yescharacteristic
312C22#1062282411yescharacteristic
313C22#1062282811yescharacteristic
314C22C2×#6689911yescharacteristic
315C22C2×#6690111yescharacteristic
316C22#1062284911yescharacteristic
317C4—22no—
318C4—22no—
319C4—22no—
320C4—44no—
321C4—41no—
322C4—44no—
323C4#1062253812yes—
324C4#1062253912yes—
325C4#1062258112yes—
326C4#1062258312yes—
327C2—24no—
328C2C2×Q8⋊(C11⋊C8)11yescharacteristic
329C2#1306700711yescharacteristic
330C2#1306704511yescharacteristic
331C2#1306705911yescharacteristic
332C2#1306868411yescharacteristic
333C2#1306870611yescharacteristic
334C2#1306871511yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC2×C4×C11×C4⋊C4C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#8707
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13066457C2semidirect
29. C2×C11×C4⋊C4C8semidirect
190. C2×C4⋊C4C11⋊C8semidirect
259. C11#8707semidirect

Maximal subgroups

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

subgroupindex
#130685962
C4×C22⋊(C11⋊C8)2
#130664572
C2×C4×C11×C4⋊C42
#870711