Finite Group Databasebeta

← #14647103

Subgroups — #14647103

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊Dic11C211yesmaximal, characteristic
2#13068684C211yesmaximal, characteristic
3#13066458C214yesmaximal
4C11×#1817C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C22×C4⋊Dic11C411yescharacteristic
7C22×C4⋊Dic11C411yescharacteristic
8C22×C4×Dic11C412yes—
9C2×C11×C22⋊C8C2212yes—
10C2×C11⋊#95C2212yes—
11C2×C22⋊(C11⋊C8)C2212yes—
12C4×C4⋊Dic11—21no—
13C4×C4⋊Dic11—21no—
14C4×C4⋊Dic11—21no—
15C4×C4⋊Dic11—21no—
16C11×#336—21no—
17C11×#336—21no—
18#10622162—21no—
19#10622162—21no—
20C23×C4×C11C2×C411yescharacteristic
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11C2311yescharacteristic
23C23×Dic11C2×C412yes—
24C23×Dic11C2×C412yes—
25C22×C8×C11—22no—
26C2×C42×C11—24no—
27C2×C42×C11D411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—22no—
36C2×C4⋊Dic11—24no—
37C2×C4⋊Dic11C814yescomplemented
38C2×C4×Dic11—22no—
39C2×C4×Dic11—22no—
40C2×C4×Dic11—44no—
41C22×C11⋊C8—22no—
42C11×C22⋊C8—24no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45C22⋊(C11⋊C8)—24no—
46#8701—111nomaximal, Sylow
47C24×C11C22×C411yescharacteristic
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—41no—
54C22×C4×C11—41no—
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C2×C812yes—
60C22×C4×C11M1612yes—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11#4114yes—
64C22×Dic11—22no—
65C22×Dic11—22no—
66C22×Dic11—22no—
67C22×Dic11—22no—
68C22×Dic11—42no—
69C22×Dic11—42no—
70C22×Dic11—42no—
71C22×Dic11—42no—
72C22×Dic11C2×C814yes—
73C22×Dic11M1614yes—
74C2×C8×C11—42no—
75C2×C8×C11—42no—
76C2×C8×C11—42no—
77C42×C11—22no—
78C42×C11—22no—
79C42×C11—22no—
80C42×C11—22no—
81C4⋊Dic11—24no—
82C4⋊Dic11—24no—
83C4⋊Dic11—24no—
84C4⋊Dic11—24no—
85C4×Dic11—44no—
86C4×Dic11—44no—
87C2×C11⋊C8—42no—
88C2×C11⋊C8—42no—
89C2×C11⋊C8—42no—
90C2×C4×C4⋊C4—111no—
91#1817—111no—
92#1817D1111yescharacteristic
93#1280—114no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11C2×C22⋊C411yescharacteristic
99C23×C11#11712yes—
100C23×C11C22×C811yescharacteristic
101C23×C11C2×M1611yescharacteristic
102C23×C11C2×M1612yes—
103C2×C4×C11—28no—
104C2×C4×C11—21no—
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—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—24no—
117C2×C4×C11—24no—
118C2×C4×C11—44no—
119C2×C4×C11C22⋊C812yes—
120C2×C4×C11C22⋊C812yes—
121C2×C4×C11#10012yes—
122C2×C4×C11#10112yes—
123C2×C4×C11#12312yes—
124C2×C4×C11#12312yes—
125C2×Dic11—24no—
126C2×Dic11—24no—
127C2×Dic11—44no—
128C2×Dic11—44no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—44no—
134C2×Dic11—44no—
135C8×C11—82no—
136C11⋊C8—82no—
137C22×C4⋊C4—111no—
138C22×C4⋊C4—111no—
139C22×C42—112no—
140C22×C42C2×D1111yescharacteristic
141C2×C22⋊C8—112no—
142C2×C22⋊C8C2×D1112yes—
143C4×C4⋊C4—221no—
144C4×C4⋊C4—221no—
145C4×C4⋊C4—221no—
146C4×C4⋊C4—221no—
147C2×#95—112no—
148#336—21no—
149#336—21no—
150#336—221no—
151#336—221no—
152C22×C11—22no—
153C22×C11—22no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—22no—
159C22×C11—22no—
160C22×C11#38111yescharacteristic
161C22×C11C2×C22⋊C811yescharacteristic
162C22×C11#40711yescharacteristic
163C22×C11#41011yescharacteristic
164C22×C11#41011yescharacteristic
165C22×C11C2×#10011yescharacteristic
166C22×C11C2×#10111yescharacteristic
167C22×C11#43112yes—
168C22×C11#43212yes—
169C4×C11—22no—
170C4×C11—22no—
171C4×C11—22no—
172C4×C11—22no—
173C4×C11—22no—
174C4×C11—22no—
175Dic11—44no—
176Dic11—44no—
177C23×C4—112no—
178C23×C4—112no—
179C23×C4C4×D1111yescharacteristic
180C23×C4C4×D1111yescharacteristic
181C23×C4C22×D1111yescharacteristic
182C22×C8—22no—
183C22×C8—222no—
184C2×C4⋊C4—114no—
185C2×C4⋊C4—224no—
186C2×C4⋊C4—222no—
187C2×C4⋊C4—221no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—221no—
191C2×C42—24no—
192C2×C42—222no—
193C2×C42—222no—
194C2×C42—444no—
195C2×C42D4411yescharacteristic
196C2×C42D4411yescharacteristic
197C2×C42C22⋊D1111yescharacteristic
198C2×C42C22⋊D1111yescharacteristic
199C22⋊C8—24no—
200C22⋊C8—224no—
201#95—222no—
202#95—222no—
203C2×C11—22no—
204C2×C11—22no—
205C2×C11#146011yescharacteristic
206C2×C11#146111yescharacteristic
207C2×C11#146611yescharacteristic
208C2×C11#146711yescharacteristic
209C2×C11#181711yescharacteristic
210C2×C11#182011yescharacteristic
211C2×C11#182111yescharacteristic
212C24C2×C4×D1111yescharacteristic
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—114no—
221C22×C4—114no—
222C22×C4—222no—
223C22×C4—222no—
224C22×C4—222no—
225C22×C4—222no—
226C22×C4—442no—
227C22×C4—442no—
228C22×C4—442no—
229C22×C4—442no—
230C22×C4C8×D1112yes—
231C22×C4#431312yes—
232C22×C4(C2×D11)⋊C411yescharacteristic
233C22×C4(C2×D11)⋊C411yescharacteristic
234C22×C4(C2×D11)⋊C411yescharacteristic
235C22×C4(C2×D11)⋊C411yescharacteristic
236C22×C4C2×D4411yescharacteristic
237C22×C4#434114yes—
238C22×C4C2×C22⋊D1111yescharacteristic
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—442no—
243C2×C8—442no—
244C2×C8—442no—
245C4⋊C4—224no—
246C4⋊C4—224no—
247C4⋊C4—224no—
248C4⋊C4—224no—
249C42—22no—
250C42—22no—
251C42—22no—
252C42—22no—
253C42—444no—
254C42—444no—
255C11#870111yescharacteristic, complemented, Sylow
256C23—21no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23#6693012yes—
261C23C2×C8×D1111yescharacteristic
262C23C2×#431311yescharacteristic
263C23M16×D1112yes—
264C23C2×(C2×D11)⋊C411yescharacteristic
265C2×C4—28no—
266C2×C4—21no—
267C2×C4—21no—
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—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—44no—
281C2×C4—224no—
282C2×C4—224no—
283C2×C4—444no—
284C2×C4—444no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—444no—
290C2×C4—444no—
291C2×C4(C2×D11)⋊C812yes—
292C2×C4(C2×D11)⋊C812yes—
293C2×C4#6688712yes—
294C2×C4#6688812yes—
295C2×C4#6693912yes—
296C2×C4#6698812yes—
297C8—82no—
298C8—882no—
299C22—22no—
300C22—22no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—22no—
306C22—22no—
307C22#1062233112yes—
308C22#1062233212yes—
309C22#1062255611yescharacteristic
310C22#1062261911yescharacteristic
311C22#1062261911yescharacteristic
312C22C2×(C2×D11)⋊C811yescharacteristic
313C22#1062273911yescharacteristic
314C22C2×#6688711yescharacteristic
315C22C2×#6688811yescharacteristic
316C4—22no—
317C4—22no—
318C4—22no—
319C4—22no—
320C4—22no—
321C4—22no—
322C4—444no—
323C4—444no—
324C2—22no—
325C2—22no—
326C2#1306693611yescharacteristic
327C2#1306693911yescharacteristic
328C2#1306695611yescharacteristic
329C2#1306695911yescharacteristic
330C2#1306868211yescharacteristic
331C2#1306869111yescharacteristic
332C2#1306869411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC23×C11C22×C8
FrattiniC23×C4C22×D11
FittingC11×#1817C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22×C4
cosocleC23×C4×C11C23
hypercenter#1817D11
hypocenterC11#8701
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
37. C2×C4⋊Dic11C8semidirect
255. C11#8701semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊Dic112
#130686842
#130664582
C11×#18172
#870111