Finite Group Databasebeta

← #14675389

Subgroups — #14675389

Order 2816.

1606 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622843C212yesmaximal
2#13066850C214yesmaximal
3#13066848C212yesmaximal
4C4×C11⋊#95C212yesmaximal
5#95×Dic11C214yesmaximal
6C2×C11×#391C211yesmaximal, characteristic
7C23×Q8×C11C2211yescharacteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C22×C4⋊Dic11C2212yes—
11C22×C4×Dic11C2212yes—
12C22×C4×Dic11C2214yes—
13C22×C4×Dic11C2212yes—
14C11×#391C418yescomplemented
15C2×C11×#95C2214yes—
16#10622843C4116yescomplemented
17C2×C11⋊#95C2214yes—
18C2×C11⋊#95C2212yes—
19C2×C11⋊#95C2212yes—
20C2×C11⋊#95C2214yes—
21C2×C11⋊#95C2214yes—
22C2×C11⋊#95C2212yes—
23C22×Q8×C11—41no—
24C22×Q8×C11—42no—
25C22×Q8×C11—41no—
26C22×Q8×C11C2×C418yes—
27C22×Q8×C11C2×C414yes—
28C23×C4×C11C2312yes—
29C23×C4×C11C2312yes—
30C23×C4×C11C2311yescharacteristic
31C23×C4×C11C2312yes—
32C23×Dic11C2314yes—
33C23×Dic11C2314yes—
34C2×C11×C4⋊C4—41no—
35C2×C11×C4⋊C4—41no—
36C2×C11×C4⋊C4C2×C414yes—
37C2×C42×C11—42no—
38C2×C42×C11C2×C414yes—
39C2×C4⋊Dic11—42no—
40C2×C4⋊Dic11—42no—
41C2×C4⋊Dic11C2×C418yes—
42C2×C4×Dic11—28no—
43C2×C4×Dic11—28no—
44C2×C4×Dic11—28no—
45C2×C4×Dic11—42no—
46C2×C4×Dic11—42no—
47C2×C4×Dic11—44no—
48C2×C4×Dic11—42no—
49C2×C4×Dic11C2×C418yes—
50C11×#95C2×C4116yes—
51C11⋊#95—24no—
52C11⋊#95—28no—
53C11⋊#95—42no—
54C11⋊#95C2×C4116yes—
55C11⋊#95C2×C4116yes—
56C11⋊#95Q818yescomplemented
57#13826—111nomaximal, Sylow
58C24×C11C2411yescharacteristic
59C2×Q8×C11—48no—
60C2×Q8×C11—48no—
61C2×Q8×C11—44no—
62C2×Q8×C11—44no—
63C2×Q8×C11C42116yescomplemented
64C22×C4×C11—24no—
65C22×C4×C11—24no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—24no—
74C22×C4×C11—24no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11C22×C414yes—
78C22×C4×C11C22×C414yes—
79C22×C4×C11C22×C414yes—
80C22×C4×C11C22×C414yes—
81C22×C4×C11C22×C414yes—
82C22×C4×C11C22×C412yes—
83C22×C4×C11C22×C414yes—
84C22×C4×C11C2×Q814yes—
85C22×C4×C11#4114yes—
86C22×Dic11—24no—
87C22×Dic11—24no—
88C22×Dic11—24no—
89C22×Dic11—24no—
90C22×Dic11—24no—
91C22×Dic11—24no—
92C22×Dic11—24no—
93C22×Dic11—24no—
94C22×Dic11—24no—
95C22×Dic11—24no—
96C22×Dic11C22×C418yes—
97C22×Dic11C22×C418yes—
98C22×Dic11C2×Q818yes—
99C22×Dic11#4118yes—
100C11×C4⋊C4—44no—
101C42×C11—44no—
102C4⋊Dic11—48no—
103C4×Dic11—48no—
104C4×Dic11—416no—
105C4×Dic11—48no—
106C2×#391—112no—
107C2×#391D1111yescharacteristic
108#1436—114no—
109#1436—112no—
110C4×#95—112no—
111C4×#95—114no—
112C23×C11C23×C412yes—
113C23×C11C23×C411yescharacteristic
114C23×C11C22×Q812yes—
115C23×C11C2×#4112yes—
116C23×C11C2×#4114yes—
117C23×C11H(5,𝔽2)11yescharacteristic
118C23×C11H(5,𝔽2)12yes—
119C23×C11H(5,𝔽2)11yescharacteristic
120Q8×C11—416no—
121C2×C4×C11—24no—
122C2×C4×C11—24no—
123C2×C4×C11—24no—
124C2×C4×C11—24no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—24no—
128C2×C4×C11—24no—
129C2×C4×C11—24no—
130C2×C4×C11—24no—
131C2×C4×C11—24no—
132C2×C4×C11—24no—
133C2×C4×C11—28no—
134C2×C4×C11—28no—
135C2×C4×C11—28no—
136C2×C4×C11—24no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—44no—
140C2×C4×C11C2×C4214yes—
141C2×C4×C11C2×C4218yes—
142C2×C4×C11C4×Q818yes—
143C2×Dic11—28no—
144C2×Dic11—28no—
145C2×Dic11—28no—
146C2×Dic11—28no—
147C2×Dic11—28no—
148C2×Dic11—28no—
149C2×Dic11—28no—
150C2×Dic11—28no—
151C2×Dic11—28no—
152C2×Dic11—44no—
153C2×Dic11—44no—
154C2×Dic11—44no—
155C2×Dic11—44no—
156C2×Dic11C4×Q8116yes—
157C23×Q8C2×D1111yescharacteristic
158C22×C4⋊C4—112no—
159C22×C4⋊C4C2×D1111yescharacteristic
160C22×C42—112no—
161C22×C42—112no—
162C22×C42—114no—
163C22×C42C2×D1111yescharacteristic
164#391—1116no—
165#391Dic1118yescomplemented
166C2×#95—112no—
167C2×#95—114no—
168C2×#95—114no—
169C2×#95—114no—
170C2×#95—112no—
171C2×#95—112no—
172C2×#95C2×D1114yes—
173C22×C11C22×C4211yescharacteristic
174C22×C11C2×C4×Q812yes—
175C22×C11C2×C4×Q814yes—
176C22×C11C4×#4112yes—
177C22×C11C4×#4114yes—
178C22×C11#51812yes—
179C22×C11#51812yes—
180C22×C11#51811yescharacteristic
181C22×C11#51811yescharacteristic
182C22×C11#55114yes—
183C22×C11#55112yes—
184C22×C11#55412yes—
185C22×C11#55414yes—
186C22×C11#55511yescharacteristic
187C22×C11#55512yes—
188C22×C11Q8211yescharacteristic
189C4×C11—28no—
190C4×C11—28no—
191C4×C11—24no—
192C4×C11—44no—
193Dic11—216no—
194Dic11—48no—
195C22×Q8—42no—
196C22×Q8—41no—
197C22×Q8—41no—
198C22×Q8C4×D1118yes—
199C22×Q8C2×Dic1114yes—
200C23×C4—114no—
201C23×C4—114no—
202C23×C4C22×D1112yes—
203C23×C4C22×D1112yes—
204C23×C4C22×D1111yescharacteristic
205C23×C4C22×D1112yes—
206C2×C4⋊C4—41no—
207C2×C4⋊C4—41no—
208C2×C4⋊C4—118no—
209C2×C4⋊C4—442no—
210C2×C4⋊C4—442no—
211C2×C4⋊C4C2×Dic1114yes—
212C2×C42—42no—
213C2×C42—118no—
214C2×C42—228no—
215C2×C42—228no—
216C2×C42—228no—
217C2×C42—442no—
218C2×C42—442no—
219C2×C42—444no—
220C2×C42—442no—
221C2×C42C2×Dic1114yes—
222#95—1116no—
223#95—1116no—
224#95—118no—
225#95—228no—
226#95—224no—
227#95—442no—
228#95C2×Dic11116yes—
229C2×C11C42×Q812yes—
230C2×C11#227311yescharacteristic
231C2×C11#236814yes—
232C2×C11#236812yes—
233C2×C11#236912yes—
234C2×C11#236911yescharacteristic
235C2×C11#237212yes—
236C2×C11#237211yescharacteristic
237C24C23×D1111yescharacteristic
238C2×Q8—48no—
239C2×Q8—48no—
240C2×Q8—44no—
241C2×Q8—44no—
242C2×Q8C4×Dic11116yescomplemented
243C22×C4—24no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—118no—
257C22×C4—118no—
258C22×C4—118no—
259C22×C4—118no—
260C22×C4—224no—
261C22×C4—224no—
262C22×C4—224no—
263C22×C4—224no—
264C22×C4—224no—
265C22×C4—224no—
266C22×C4—224no—
267C22×C4—224no—
268C22×C4—224no—
269C22×C4—224no—
270C22×C4C2×C4×D1114yes—
271C22×C4C2×C4×D1114yes—
272C22×C4C2×C4×D1114yes—
273C22×C4Q8×D1114yes—
274C22×C4#434314yes—
275C22×C4C22×Dic1114yes—
276C22×C4C22×Dic1114yes—
277C22×C4C22×Dic1112yes—
278C22×C4C22×Dic1114yes—
279C4⋊C4—44no—
280C4⋊C4—448no—
281C42—44no—
282C42—448no—
283C42—4416no—
284C42—448no—
285C11#1382611yescharacteristic, complemented, Sylow
286C23C22×C4×D1112yes—
287C23#6703711yescharacteristic
288C23#6703711yescharacteristic
289C23#6703712yes—
290C23C2×Q8×D1112yes—
291C23C2×#434312yes—
292C23#41×D1114yes—
293C23C23×Dic1111yescharacteristic
294Q8—416no—
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—24no—
307C2×C4—28no—
308C2×C4—28no—
309C2×C4—24no—
310C2×C4—28no—
311C2×C4—44no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—1116no—
315C2×C4—228no—
316C2×C4—228no—
317C2×C4—228no—
318C2×C4—228no—
319C2×C4—228no—
320C2×C4—228no—
321C2×C4—228no—
322C2×C4—228no—
323C2×C4—228no—
324C2×C4—444no—
325C2×C4—444no—
326C2×C4—444no—
327C2×C4—444no—
328C2×C4C2×C4×Dic1114yes—
329C2×C4C2×C4×Dic1118yes—
330C2×C4Q8×Dic1118yes—
331C22#1062301712yes—
332C22#1062301712yes—
333C22C4×Q8×D1114yes—
334C22C4×#434314yes—
335C22#1062316714yes—
336C22#1062316814yes—
337C22#1062320112yes—
338C22#1062321012yes—
339C22#1062325311yescharacteristic
340C22#1062326112yes—
341C22#1062326511yescharacteristic
342C22C22×C4×Dic1111yescharacteristic
343C22#1062332911yescharacteristic
344C22#1062332911yescharacteristic
345C22C2×Q8×Dic1112yes—
346C22#41×Dic1112yes—
347C4—28no—
348C4—28no—
349C4—24no—
350C4—44no—
351C4—2216no—
352C4—448no—
353C2C4×Q8×Dic1112yes—
354C2#1307096911yescharacteristic
355C2#1307169514yes—
356C2#1307170112yes—
357C2#1307170412yes—
358C2#1307170611yescharacteristic
359C2#1307172712yes—
360C2#1307172811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C11×#391C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#391D11
hypocenterC11#13826
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
14. C11×#391C4semidirect
16. #10622843C4semidirect
56. C11⋊#95Q8semidirect
63. C2×Q8×C11C42semidirect
165. #391Dic11semidirect
242. C2×Q8C4×Dic11semidirect
285. C11#13826semidirect

Maximal subgroups

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

subgroupindex
C2×#106228432
#130668502
#130668482
C4×C11⋊#952
#95×Dic112
C2×C11×#3912
#1382611