Finite Group Databasebeta

← #14647118

Subgroups — #14647118

Order 2816.

680 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊Dic11C211yesmaximal, characteristic
2C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
3#13066455C214yesmaximal, complemented
4C11×#1797C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C22×C4⋊Dic11C411yescharacteristic
7C22×C4⋊Dic11C411yescharacteristic
8C22×C4×Dic11—21no—
9C2×C11×C4⋊C8C2212yes—
10C2×C11×C22⋊C8—21no—
11C2×C11⋊#95—21no—
12C2×C22⋊(C11⋊C8)—21no—
13C4×C4⋊Dic11—21no—
14C4×C4⋊Dic11—21no—
15C4×C4⋊Dic11C412yes—
16C4×C4⋊Dic11C2212yes—
17C2×C4×C11⋊C8C2212yes—
18C11×#336—21no—
19#10622162—21no—
20C23×C4×C11C2×C411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11—21no—
24C23×Dic11—21no—
25C22×C8×C11—22no—
26C2×C42×C11—24no—
27C2×C42×C11C2×C411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11C2311yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—22no—
34C2×C4⋊Dic11—24no—
35C2×C4⋊Dic11C814yescomplemented
36C2×C4⋊Dic11C2×C412yes—
37C2×C4⋊Dic11C2×C412yes—
38C2×C4×Dic11—22no—
39C2×C4×Dic11—22no—
40C2×C4×Dic11—42no—
41C2×C4×Dic11—42no—
42C22×C11⋊C8—22no—
43C11×C4⋊C8—24no—
44C11×C22⋊C8—42no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C22⋊(C11⋊C8)—24no—
48C4×C11⋊C8—24no—
49#8706—111nomaximal, Sylow
50C24×C11C22⋊C411yescharacteristic
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—41no—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C2×C812yes—
62C22×C4×C11M1612yes—
63C22×C4×C11D812yes—
64C22×C4×C11SD1612yes—
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—24no—
69C22×Dic11—24no—
70C22×Dic11—22no—
71C22×Dic11—22no—
72C22×Dic11—42no—
73C22×Dic11—42no—
74C22×Dic11—42no—
75C22×Dic11—42no—
76C2×C8×C11—42no—
77C2×C8×C11—42no—
78C2×C8×C11—42no—
79C42×C11—22no—
80C42×C11—22no—
81C42×C11—22no—
82C42×C11#4114yes—
83C4⋊Dic11—24no—
84C4⋊Dic11—24no—
85C4⋊Dic11—22no—
86C4⋊Dic11—22no—
87C4⋊Dic11C2×C814yes—
88C4⋊Dic11M1614yes—
89C4×Dic11—44no—
90C4×Dic11—42no—
91C4×Dic11—42no—
92C2×C11⋊C8—24no—
93C2×C11⋊C8—42no—
94C2×C11⋊C8—42no—
95C2×C4×C4⋊C4—111no—
96#1797D1111yescharacteristic
97C4×C22⋊C8—111no—
98#1279—114no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11C22⋊C812yes—
104C23×C11#10212yes—
105C23×C11#10412yes—
106C23×C11C2×C22⋊C411yescharacteristic
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—24no—
114C2×C4×C11—24no—
115C2×C4×C11—24no—
116C2×C4×C11—24no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—44no—
121C2×C4×C11C22⋊C812yes—
122C2×C4×C11#10212yes—
123C2×C4×C11#11712yes—
124C2×C4×C11#12312yes—
125C2×C4×C11#12312yes—
126C2×C4×C11C22×C811yescharacteristic
127C2×C4×C11C2×M1611yescharacteristic
128C2×C4×C11C2×M1612yes—
129C2×C4×C11C2×D811yescharacteristic
130C2×C4×C11C2×SD1611yescharacteristic
131C2×C4×C11#13712yes—
132C2×Dic11—24no—
133C2×Dic11—24no—
134C2×Dic11—48no—
135C2×Dic11—48no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C8×C11—82no—
141C11⋊C8—44no—
142C22×C4⋊C4—111no—
143C22×C4⋊C4—111no—
144C22×C42—221no—
145C22×C42C2×D1111yescharacteristic
146C2×C4⋊C8C2×D1112yes—
147C2×C22⋊C8—21no—
148C2×C22⋊C8—221no—
149C2×C4×C8—112no—
150C4×C4⋊C4—112no—
151C4×C4⋊C4—112no—
152C4×C4⋊C4—221no—
153C4×C4⋊C4—221no—
154C2×#95—221no—
155#336—21no—
156#336—221no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—22no—
160C22×C11—22no—
161C22×C11—22no—
162C22×C11—22no—
163C22×C11D4⋊C814yes—
164C22×C11#38111yescharacteristic
165C22×C11C2×C22⋊C811yescharacteristic
166C22×C11#40711yescharacteristic
167C22×C11C2×#10211yescharacteristic
168C22×C11#41911yescharacteristic
169C22×C11C2×#10411yescharacteristic
170C22×C11#42111yescharacteristic
171C4×C11—22no—
172C4×C11—22no—
173C4×C11—22no—
174C4×C11—41no—
175C4×C11#43112yes—
176C4×C11#43212yes—
177C4×C11#48012yes—
178C4×C11#48312yes—
179Dic11—44no—
180Dic11—44no—
181C23×C4—221no—
182C23×C4—221no—
183C23×C4C4×D1111yescharacteristic
184C23×C4D4411yescharacteristic
185C23×C4C22⋊D1111yescharacteristic
186C22×C8—22no—
187C22×C8—222no—
188C2×C4⋊C4—114no—
189C2×C4⋊C4—112no—
190C2×C4⋊C4—112no—
191C2×C4⋊C4—224no—
192C2×C4⋊C4—222no—
193C2×C4⋊C4—221no—
194C2×C4⋊C4—221no—
195C2×C42—24no—
196C2×C42—222no—
197C2×C42—222no—
198C2×C42—442no—
199C2×C42—442no—
200C2×C42C4×D1111yescharacteristic
201C2×C42D4411yescharacteristic
202C2×C42C22⋊D1111yescharacteristic
203C2×C42C22×D1111yescharacteristic
204C4⋊C8—24no—
205C22⋊C8—42no—
206C22⋊C8—224no—
207C4×C8—224no—
208#95—222no—
209#95—222no—
210C2×C11—24no—
211C2×C11C2×D4⋊C811yescharacteristic
212C2×C11#147911yescharacteristic
213C2×C11#148611yescharacteristic
214C2×C11#149111yescharacteristic
215C2×C11#181711yescharacteristic
216C2×C11#182311yescharacteristic
217C2×C11#182611yescharacteristic
218C24(C2×D11)⋊C411yescharacteristic
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—41no—
226C22×C4—224no—
227C22×C4—224no—
228C22×C4—222no—
229C22×C4—222no—
230C22×C4—442no—
231C22×C4—442no—
232C22×C4—442no—
233C22×C4—442no—
234C22×C4C8×D1112yes—
235C22×C4#431312yes—
236C22×C4(C2×D11)⋊C411yescharacteristic
237C22×C4(C2×D11)⋊C411yescharacteristic
238C22×C4(C2×D11)⋊C411yescharacteristic
239C22×C4#432312yes—
240C22×C4#432512yes—
241C22×C4C2×C4×D1111yescharacteristic
242C22×C4C2×D4411yescharacteristic
243C22×C4C2×C22⋊D1111yescharacteristic
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—224no—
248C2×C8—442no—
249C2×C8—442no—
250C4⋊C4—114no—
251C4⋊C4—114no—
252C4⋊C4—224no—
253C4⋊C4—224no—
254C4⋊C4—222no—
255C4⋊C4—222no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—444no—
260C42—442no—
261C42—442no—
262C42#434114yes—
263C11#870611yescharacteristic, complemented, Sylow
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#6687312yes—
269C23(C2×D11)⋊C812yes—
270C23#6688912yes—
271C23C2×(C2×D11)⋊C411yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—24no—
281C2×C4—24no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—44no—
286C2×C4—224no—
287C2×C4—224no—
288C2×C4—448no—
289C2×C4—442no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4—448no—
294C2×C4#6687312yes—
295C2×C4(C2×D11)⋊C812yes—
296C2×C4#6693012yes—
297C2×C4#6693912yes—
298C2×C4C2×C8×D1111yescharacteristic
299C2×C4C2×#431311yescharacteristic
300C2×C4M16×D1112yes—
301C2×C4C2×#432311yescharacteristic
302C2×C4#6698812yes—
303C2×C4C2×#432511yescharacteristic
304C2×C4#6700412yes—
305C8—82no—
306C8—444no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22#1062212114yes—
314C22#1062255611yescharacteristic
315C22C2×#6687311yescharacteristic
316C22#1062261711yescharacteristic
317C22C2×(C2×D11)⋊C811yescharacteristic
318C22#1062273911yescharacteristic
319C22C2×#6688911yescharacteristic
320C22#1062275211yescharacteristic
321C4—22no—
322C4—22no—
323C4—22no—
324C4—41no—
325C4—444no—
326C4—444no—
327C4#1062233112yes—
328C4#1062233212yes—
329C4#1062264612yes—
330C4#1062265612yes—
331C2—24no—
332C2C2×#1062212111yescharacteristic
333C2#1306701011yescharacteristic
334C2#1306704011yescharacteristic
335C2#1306706211yescharacteristic
336C2#1306868211yescharacteristic
337C2#1306870011yescharacteristic
338C2#1306871311yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1797D11
hypocenterC11#8706
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #13066455C2semidirect
35. C2×C4⋊Dic11C8semidirect
263. C11#8706semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊Dic112
C4×C22⋊(C11⋊C8)2
#130664552
C11×#17972
#870611