Finite Group Databasebeta

← #14908603

Subgroups — #14908603

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622719C211yesmaximal, characteristic
2#13070821C214yesmaximal, complemented
3#13070816C212yesmaximal, complemented
4#13070811C212yesmaximal, complemented
5#13070402C212yesmaximal, complemented
6#13070336C212yesmaximal, complemented
7#13070227C211yesmaximal, characteristic
8C2×C11×#467C211yesmaximal, characteristic
9C22×C11×Q16C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C2×C11×C22⋊Q8—21no—
12C2×#66979—21no—
13C11×#467—21no—
14C11×#467—21no—
15C11×#467C2212yes—
16C11×#467C2212yes—
17C2×C11×#107C2211yescharacteristic
18C2×C11×#103—21no—
19#10622719—21no—
20#10622719—21no—
21#10622719C2212yes—
22#10622719C2212yes—
23C2×#66882C2211yescharacteristic
24C2×#66882C2211yescharacteristic
25C2×#66881—21no—
26C2×#66876C2212yes—
27#10622202C2214yescomplemented
28#10622202C2214yescomplemented
29C22⋊(C11⋊C16)C2212yes—
30C22⋊(C11⋊C16)C2212yes—
31#10622128C2214yescomplemented
32#10622127C2214yescomplemented
33C22×Q8×C11—21no—
34C23×C4×C11D411yescharacteristic
35C2×C11×Q16—21no—
36C2×C11×Q16—24no—
37C2×C11×Q16C2312yes—
38C22×C8×C11—24no—
39C22×C8×C11D411yescharacteristic
40C22×C8×C11D411yescharacteristic
41C22×C8×C11D411yescharacteristic
42C22×C8×C11C2311yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C11×C22⋊Q8—22no—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—41no—
48C11×C22⋊Q8—41no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—41no—
51C2×C11×C22⋊C4—41no—
52C2×C22⋊Dic11—41no—
53#66979—22no—
54#66979—22no—
55#66979—41no—
56#66979—41no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4×Dic11—41no—
60C11×#107—21no—
61C11×#107C2312yes—
62C11×#103—22no—
63C11×#103—22no—
64#66882—21no—
65#66882—21no—
66#66882C2312yes—
67#66882C2312yes—
68#66881—22no—
69#66881—22no—
70#66876—24no—
71C2×C11⋊C16C2314yes—
72#33649—111nomaximal, Sylow
73C24×C11D811yescharacteristic
74C2×Q8×C11—22no—
75C2×Q8×C11—41no—
76C2×Q8×C11—42no—
77C2×Q8×C11—42no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11D811yescharacteristic
83C22×C4×C11D811yescharacteristic
84C22×C4×C11D811yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×Dic11—41no—
89C22×Dic11—41no—
90C11×Q16—24no—
91C11×Q16—42no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11#4114yes—
101C2×C8×C11C2411yescharacteristic
102C11×C4⋊C4—22no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—42no—
105C11×C4⋊C4—42no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—42no—
108C22⋊Dic11—42no—
109C22⋊Dic11—42no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4×Dic11—42no—
115C4×Dic11—42no—
116C11⋊C16—24no—
117C2×#467D1111yescharacteristic
118C2×#427—111no—
119#2237—114no—
120#2236—112no—
121#2235—112no—
122#2159—112no—
123#2141—112no—
124#2112—111no—
125C23×C11—22no—
126C23×C11—22no—
127C23×C11—41no—
128C23×C11C2×D811yescharacteristic
129C23×C11C2×D811yescharacteristic
130C23×C11C2×D811yescharacteristic
131Q8×C11—42no—
132Q8×C11—42no—
133Q8×C11—82no—
134C2×C4×C11—22no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—82no—
144C2×C4×C11—82no—
145C2×C4×C11#12312yes—
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11#13712yes—
150C2×C4×C11C22×D411yescharacteristic
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—82no—
154C2×Dic11—82no—
155C8×C11—21no—
156C8×C11—21no—
157C8×C11#12312yes—
158C8×C11C2×#4112yes—
159C22×Q16C2×D1111yescharacteristic
160C23×C8C2×D1111yescharacteristic
161C2×C22⋊Q8—21no—
162C2×#117—221no—
163C2×M32—112no—
164#467—21no—
165#467—21no—
166#467C2×D1112yes—
167#467C2×D1112yes—
168#427—112no—
169#427—112no—
170#427—221no—
171#427—221no—
172C2×#107—111no—
173C2×#107—111no—
174C2×#107C2×D1111yescharacteristic
175C2×#106—221no—
176C2×#103—21no—
177#367—114no—
178#366—114no—
179#358—114no—
180#358—114no—
181C22⋊C16—112no—
182C22⋊C16—112no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—44no—
191C22×C11#48012yes—
192C22×C11#51012yes—
193C22×C11C22×D811yescharacteristic
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—82no—
197C4×C11—82no—
198C4×C11#48012yes—
199C4×C11C2×#12311yescharacteristic
200C4×C11C2×#13711yescharacteristic
201Dic11—82no—
202Dic11—82no—
203C22×Q8—21no—
204C23×C4C22⋊D1111yescharacteristic
205C2×Q16—24no—
206C2×Q16—21no—
207C2×Q16C22×D1112yes—
208C22×C8—24no—
209C22×C8C22⋊D1111yescharacteristic
210C22×C8C22⋊D1111yescharacteristic
211C22×C8C22⋊D1111yescharacteristic
212C22×C8C22×D1111yescharacteristic
213C22×C8C22×D1111yescharacteristic
214C22×C8C22×D1111yescharacteristic
215C22⋊Q8—22no—
216C22⋊Q8—22no—
217C22⋊Q8—41no—
218C22⋊Q8—41no—
219#117—222no—
220#117—222no—
221#117—441no—
222#117—441no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—41no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C22⋊C4—41no—
228C2×C22⋊C4—441no—
229C2×C42—441no—
230M32—224no—
231C2×C16—114no—
232#107—21no—
233#107—112no—
234#107—112no—
235#107—221no—
236#107—221no—
237#107C22×D1112yes—
238#106—222no—
239#106—222no—
240#103—22no—
241#103—22no—
242C2×C11—22no—
243C2×C11—22no—
244C2×C11—41no—
245C2×C11C2×#48011yescharacteristic
246C2×C11C2×#51011yescharacteristic
247C2×C11#341411yescharacteristic
248C24#432311yescharacteristic
249C2×Q8—22no—
250C2×Q8—41no—
251C2×Q8—42no—
252C2×Q8—42no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—441no—
258C22×C4—441no—
259C22×C4#432311yescharacteristic
260C22×C4#432311yescharacteristic
261C22×C4#432311yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265Q16—24no—
266Q16—42no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8#434114yes—
273C2×C8C2×C22⋊D1111yescharacteristic
274C2×C8C2×C22⋊D1111yescharacteristic
275C2×C8C2×C22⋊D1111yescharacteristic
276C2×C8C23×D1111yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—222no—
282C4⋊C4—222no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—442no—
288C22⋊C4—442no—
289C42—442no—
290C42—442no—
291C16—224no—
292C11#3364911yescharacteristic, complemented, Sylow
293C23—22no—
294C23—22no—
295C23—41no—
296C23C2×#432311yescharacteristic
297C23C2×#432311yescharacteristic
298C23C2×#432311yescharacteristic
299Q8—42no—
300Q8—42no—
301Q8—82no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4—442no—
314C2×C4—442no—
315C2×C4—882no—
316C2×C4—882no—
317C2×C4C2×#432311yescharacteristic
318C2×C4C2×#432311yescharacteristic
319C2×C4C2×#432311yescharacteristic
320C2×C4#6698812yes—
321C2×C4#6700412yes—
322C2×C4C22×C22⋊D1111yescharacteristic
323C8—21no—
324C8—21no—
325C8#6698812yes—
326C8C2×#434112yes—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—44no—
335C22#1062264612yes—
336C22#1062279212yes—
337C22C22×#432311yescharacteristic
338C4—21no—
339C4—21no—
340C4—82no—
341C4—82no—
342C4—882no—
343C4—882no—
344C4#1062264612yes—
345C4C2×#6698811yescharacteristic
346C4C2×#6700411yescharacteristic
347C2—22no—
348C2—22no—
349C2—41no—
350C2C2×#1062264611yescharacteristic
351C2C2×#1062279211yescharacteristic
352C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#467C2
socleC22×C11C22×D8
prime radicalC24×C11D8
hypercenterC2×#467D11
hypocenterC11#33649
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
2. #13070821C2semidirect
3. #13070816C2semidirect
4. #13070811C2semidirect
5. #13070402C2semidirect
6. #13070336C2semidirect
27. #10622202C22semidirect
28. #10622202C22semidirect
31. #10622128C22semidirect
32. #10622127C22semidirect
292. C11#33649semidirect

Maximal subgroups

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

subgroupindex
C2×#106227192
#130708212
#130708162
#130708112
#130704022
#130703362
#130702272
C2×C11×#4672
#3364911