Finite Group Databasebeta

← #14652619

Subgroups — #14652619

Order 2816.

640 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×#10622541C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3C2×#10622107C214yesmaximal
4C11×#1749C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C22×C4⋊Dic11C411yescharacteristic
7C22×C4⋊Dic11C411yescharacteristic
8C22×Dic11⋊C4C2212yes—
9C2×C11×C22⋊C8C2212yes—
10C2×C11×#97—21no—
11C2×C11⋊#95C412yes—
12C2×C22⋊(C11⋊C8)C2212yes—
13#10622541—21no—
14#10622541—21no—
15#10622541—21no—
16#10622541—21no—
17C2×C4⋊(C11⋊C8)—21no—
18C11×#336—21no—
19#10622162—21no—
20#10622107—28no—
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C23×Dic11C2×C412yes—
25C23×Dic11C2×C412yes—
26C22×C8×C11—22no—
27C2×C42×C11—42no—
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—24no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—42no—
38C2×Dic11⋊C4—22no—
39C2×Dic11⋊C4—22no—
40C2×Dic11⋊C4—24no—
41C2×Dic11⋊C4—24no—
42C22×C11⋊C8—22no—
43C11×C22⋊C8—22no—
44C11×C22⋊C8D414yes—
45C11×#97—42no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C22⋊(C11⋊C8)—24no—
49C4⋊(C11⋊C8)—42no—
50#9654—111nomaximal, Sylow
51C24×C11C22×C411yescharacteristic
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×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D412yes—
67C22×C4×C11#4112yes—
68C22×Dic11—22no—
69C22×Dic11—22no—
70C22×Dic11—24no—
71C22×Dic11—24no—
72C22×Dic11—22no—
73C22×Dic11—24no—
74C22×Dic11—42no—
75C22×Dic11—42no—
76C22×Dic11M1614yes—
77C2×C8×C11—24no—
78C2×C8×C11—42no—
79C2×C8×C11—42no—
80C42×C11—22no—
81C42×C11—22no—
82C42×C11—41no—
83C42×C11—41no—
84C4⋊Dic11—24no—
85C4⋊Dic11—24no—
86C4⋊Dic11—42no—
87C4⋊Dic11—42no—
88Dic11⋊C4—44no—
89Dic11⋊C4—42no—
90Dic11⋊C4—42no—
91C2×C11⋊C8—42no—
92C2×C11⋊C8—42no—
93C2×C11⋊C8—42no—
94C2×#389—111no—
95#1797—111no—
96#1749D1111yescharacteristic
97C2×#324—114no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11C2×C22⋊C411yescharacteristic
103C23×C11C4×D412yes—
104C23×C11C2×M1612yes—
105C23×C11#13112yes—
106C2×C4×C11—28no—
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—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—44no—
123C2×C4×C11#9912yes—
124C2×C4×C11#10112yes—
125C2×C4×C11#10112yes—
126C2×C4×C11#12112yes—
127C2×C4×C11#12411yescharacteristic
128C2×C4×C11#12711yescharacteristic
129C2×Dic11—24no—
130C2×Dic11—28no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—44no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11—84no—
138C8×C11—44no—
139C11⋊C8—82no—
140C22×C4⋊C4—112no—
141C22×C4⋊C4—111no—
142C22×C4⋊C4—111no—
143C22×C42C2×D1111yescharacteristic
144C2×C4⋊C8—221no—
145C2×C22⋊C8—112no—
146C2×C22⋊C8C2×D1112yes—
147C2×#97—21no—
148#389—221no—
149#389—221no—
150#389—221no—
151#389—221no—
152C2×#95—112no—
153#336—21no—
154#336—221no—
155#324—228no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—22no—
160C22×C11—22no—
161C22×C11—22no—
162C22×C11#39011yescharacteristic
163C22×C11#40711yescharacteristic
164C22×C11#40811yescharacteristic
165C22×C11C2×#9911yescharacteristic
166C22×C11#41011yescharacteristic
167C22×C11C2×#10111yescharacteristic
168C22×C11C2×#10111yescharacteristic
169C22×C11#43514yes—
170C4×C11—22no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—22no—
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—41no—
177Dic11—44no—
178Dic11—82no—
179C23×C4—112no—
180C23×C4—112no—
181C23×C4C4×D1111yescharacteristic
182C23×C4C4×D1111yescharacteristic
183C23×C4C22×D1111yescharacteristic
184C22×C8—22no—
185C22×C8—222no—
186C2×C4⋊C4—224no—
187C2×C4⋊C4—221no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—221no—
191C2×C4⋊C4—224no—
192C2×C4⋊C4—222no—
193C2×C4⋊C4—224no—
194C2×C4⋊C4—222no—
195C2×C4⋊C4—442no—
196C2×C42—42no—
197C2×C42D4411yescharacteristic
198C2×C42D4411yescharacteristic
199C2×C42C22⋊D1111yescharacteristic
200C2×C42C22⋊D1111yescharacteristic
201C4⋊C8—442no—
202C22⋊C8—22no—
203C22⋊C8—224no—
204C22⋊C8D4414yes—
205#97—42no—
206#95—222no—
207#95—222no—
208C2×C11—24no—
209C2×C11#146311yescharacteristic
210C2×C11#146711yescharacteristic
211C2×C11#147011yescharacteristic
212C2×C11#147211yescharacteristic
213C2×C11#195511yescharacteristic
214C2×C11#196411yescharacteristic
215C2×C11#196611yescharacteristic
216C24C2×C4×D1111yescharacteristic
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—114no—
226C22×C4—224no—
227C22×C4—222no—
228C22×C4—224no—
229C22×C4—222no—
230C22×C4—222no—
231C22×C4—224no—
232C22×C4—442no—
233C22×C4—442no—
234C22×C4(C2×D11)⋊C411yescharacteristic
235C22×C4(C2×D11)⋊C411yescharacteristic
236C22×C4(C2×D11)⋊C411yescharacteristic
237C22×C4(C2×D11)⋊C411yescharacteristic
238C22×C4C2×D4411yescharacteristic
239C22×C4C2×D4412yes—
240C22×C4#433912yes—
241C22×C4C2×C22⋊D1111yescharacteristic
242C2×C8—24no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—442no—
246C2×C8—442no—
247C2×C8—442no—
248C4⋊C4—224no—
249C4⋊C4—224no—
250C4⋊C4—442no—
251C4⋊C4—442no—
252C4⋊C4—442no—
253C4⋊C4—442no—
254C4⋊C4—444no—
255C42—22no—
256C42—22no—
257C42—41no—
258C42—41no—
259C11#965411yescharacteristic, complemented, Sylow
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23C4×D4412yes—
265C23M16×D1112yes—
266C23#6696012yes—
267C23C2×(C2×D11)⋊C411yescharacteristic
268C2×C4—28no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—44no—
285C2×C4—224no—
286C2×C4—228no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—444no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4—884no—
294C2×C4#6687012yes—
295C2×C4#6688812yes—
296C2×C4#6688812yes—
297C2×C4#6692711yescharacteristic
298C2×C4#6692811yescharacteristic
299C2×C4#6698312yes—
300C8—44no—
301C8—882no—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22#1062231914yes—
309C22#1062255211yescharacteristic
310C22C2×#6687011yescharacteristic
311C22#1062261911yescharacteristic
312C22#1062273911yescharacteristic
313C22#1062274211yescharacteristic
314C22C2×#6688811yescharacteristic
315C22C2×#6688811yescharacteristic
316C4—22no—
317C4—21no—
318C4—21no—
319C4—22no—
320C4—22no—
321C4—22no—
322C4—41no—
323C4—444no—
324C4—882no—
325C2—24no—
326C2#1306694511yescharacteristic
327C2#1306695911yescharacteristic
328C2#1306697311yescharacteristic
329C2#1306698111yescharacteristic
330C2#1306941411yescharacteristic
331C2#1306945211yescharacteristic
332C2#1306946011yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutator, prime radicalC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1749C2
socleC23×C11C2×C22⋊C4
cosocleC23×C4×C11C23
hypercenter#1749D11
hypocenterC11#9654
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
259. C11#9654semidirect

Maximal subgroups

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

subgroupindex
C2×#106225412
#130685962
C2×#106221072
C11×#17492
#965411