Finite Group Databasebeta

← #14737651

Subgroups — #14737651

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079202C211yesmaximal, characteristic
2#13078746C212yesmaximal
3#13068046C214yesmaximal, complemented
4#13068010C212yesmaximal, complemented
5#13067986C212yesmaximal, complemented
6#13067379C211yesmaximal, characteristic
7#13067314C212yesmaximal
8C2×C8×Q8×C11C211yesmaximal, characteristic
9C2×C4×Q8×C11C2211yescharacteristic
10#10623001C2212yes—
11C8×Q8×C11—21no—
12C8×Q8×C11—21no—
13C8×Q8×C11C2212yes—
14C8×Q8×C11C2212yes—
15C2×C11×C4⋊C8—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C4×C8×C11—21no—
18C2×C4×C8×C11C2211yescharacteristic
19#10622841—22no—
20#10622729—21no—
21#10622729—21no—
22#10622644C2214yes—
23#10622643—24no—
24#10622633C2214yes—
25#10622584—22no—
26#10622539C2212yes—
27#10622312C2211yescharacteristic
28C4×Dic44—21no—
29C4×Dic44—21no—
30#10622295C2211yescharacteristic
31#10622294C2212yes—
32#10622124C2214yes—
33#10622120C2214yes—
34#10622096C2212yes—
35#10622095C2212yes—
36C22×Q8×C11D411yescharacteristic
37C22×C8×C11—21no—
38C22×C8×C11D411yescharacteristic
39C22×C8×C11D411yescharacteristic
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11D412yes—
43C4×Q8×C11C2312yes—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C42×C11—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4326—24no—
49#66979—22no—
50#66977—22no—
51#66977—22no—
52C2×Dic44—21no—
53C2×Dic44—21no—
54#66923—22no—
55#66922C2312yes—
56#66922C2312yes—
57C4×Dic22—22no—
58C4×Dic22—22no—
59C11×C4⋊C8—22no—
60C11×C4⋊C8—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8C2312yes—
63C4×C8×C11—22no—
64C4×C8×C11—22no—
65C4×C8×C11D411yescharacteristic
66C4×C8×C11D411yescharacteristic
67C4×C8×C11C2311yescharacteristic
68C4×C8×C11C2311yescharacteristic
69#66899—24no—
70C22⋊(C11⋊C8)—22no—
71#66882—21no—
72#66882—21no—
73#66880—22no—
74#66880—22no—
75#66874—24no—
76#66872—24no—
77C4⋊(C11⋊C8)C2314yes—
78#66867—22no—
79#19265—111nomaximal, Sylow
80C2×Q8×C11—24no—
81C2×Q8×C11—21no—
82C2×Q8×C11C2×D412yes—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C2×Dic22—22no—
89C2×Dic22—22no—
90C2×C8×C11—22no—
91C2×C8×C11—22no—
92C2×C8×C11—41no—
93C2×C8×C11—42no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C11×C4⋊C4—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4C2×D412yes—
102C42×C11—22no—
103C42×C11—22no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11C2411yescharacteristic
108C22⋊Dic11—42no—
109#4326—48no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—22no—
113C4⋊Dic11—22no—
114Dic11⋊C4—42no—
115Dic11⋊C4—42no—
116C4×Dic11—42no—
117C2×C11⋊C8—24no—
118Dic44—42no—
119Dic44—42no—
120#3170—111no—
121#3113—112no—
122C2×C8×Q8D1111yescharacteristic
123#1680—114no—
124#1674—112no—
125#1670—112no—
126#1568—111no—
127#1552—112no—
128C23×C11#12111yescharacteristic
129Q8×C11—24no—
130Q8×C11—22no—
131Q8×C11#13514yes—
132C2×C4×C11—24no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—22no—
139C2×C4×C11—42no—
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11C22×D411yescharacteristic
144C2×C4×C11C22×D411yescharacteristic
145C2×C4×C11C2×#4111yescharacteristic
146C2×Dic11—42no—
147C2×Dic11—42no—
148Dic22—44no—
149Dic22—42no—
150Dic22—42no—
151C8×C11—21no—
152C8×C11—21no—
153C8×C11—21no—
154C8×C11—42no—
155C8×C11#13712yes—
156C11⋊C8—44no—
157#533—112no—
158C2×C4×Q8C2×D1111yescharacteristic
159#500—111no—
160#494—111no—
161#487—112no—
162#483—222no—
163#475—114no—
164#467—221no—
165#467—221no—
166#462—114no—
167#451—222no—
168C8×Q8—21no—
169C8×Q8—21no—
170C8×Q8C2×D1112yes—
171C8×Q8C2×D1112yes—
172#441—224no—
173C4×Q16—221no—
174C4×Q16—221no—
175#432—112no—
176C2×C4⋊C8—21no—
177C2×C4⋊C8C2×D1111yescharacteristic
178C2×C4×C8—21no—
179C2×C4×C8C2×D1111yescharacteristic
180#335—112no—
181#334—112no—
182#332—114no—
183#332—114no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11#47312yes—
187C22×C11C2×#12111yescharacteristic
188C4×C11—21no—
189C4×C11—24no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—42no—
194C4×C11C2×#13512yes—
195C4×C11C2×#13711yescharacteristic
196C4×C11#57511yescharacteristic
197Dic11—82no—
198Dic11—82no—
199C22×Q8D4411yescharacteristic
200C2×Q16—224no—
201C2×Q16—221no—
202C2×Q16—221no—
203C22×C8—21no—
204C22×C8C22⋊D1111yescharacteristic
205C22×C8C22⋊D1111yescharacteristic
206C4⋊Q8—112no—
207C4⋊Q8—112no—
208#125—222no—
209C22⋊Q8—222no—
210C22⋊Q8—222no—
211C4×Q8—21no—
212C4×Q8—21no—
213C4×Q8—222no—
214C4×Q8—222no—
215C4×Q8D4412yes—
216C4×Q8C22×D1112yes—
217#117—222no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4D4411yescharacteristic
220C2×C42—21no—
221C2×C42C22×D1111yescharacteristic
222#107—221no—
223#107—221no—
224#106—224no—
225C4⋊C8—22no—
226C4⋊C8—22no—
227C4⋊C8—21no—
228C4⋊C8—114no—
229C4⋊C8C22×D1112yes—
230#103—224no—
231#103—222no—
232#103—222no—
233#103—224no—
234C22⋊C8—222no—
235#97—222no—
236C4×C8—22no—
237C4×C8—22no—
238C4×C8C22⋊D1111yescharacteristic
239C4×C8C22⋊D1111yescharacteristic
240C4×C8C22×D1111yescharacteristic
241C4×C8C22×D1111yescharacteristic
242C2×C11—22no—
243C2×C11#303711yescharacteristic
244C2×C11#305011yescharacteristic
245C2×C11C2×#47311yescharacteristic
246C2×Q8—24no—
247C2×Q8—21no—
248C2×Q8—222no—
249C2×Q8—222no—
250C2×Q8C2×D4412yes—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4C2×D4411yescharacteristic
254C22×C4#433911yescharacteristic
255C22×C4C2×C22⋊D1111yescharacteristic
256Q16—442no—
257Q16—448no—
258Q16—442no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—42no—
263C2×C8—224no—
264C2×C8C2×C22⋊D1111yescharacteristic
265C2×C8C2×C22⋊D1111yescharacteristic
266C2×C8C2×C22⋊D1111yescharacteristic
267C2×C8C2×C22⋊D1111yescharacteristic
268C4⋊C4—22no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—222no—
272C4⋊C4—222no—
273C4⋊C4—222no—
274C4⋊C4—222no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C4⋊C4C2×D4412yes—
278C22⋊C4—442no—
279C42—22no—
280C42—22no—
281C42—442no—
282C42C2×D4411yescharacteristic
283C42#433911yescharacteristic
284C42C2×C22⋊D1111yescharacteristic
285C42C23×D1111yescharacteristic
286C11#1926511yescharacteristic, complemented, Sylow
287C23#6698311yescharacteristic
288Q8—24no—
289Q8—22no—
290Q8—444no—
291Q8—442no—
292Q8—442no—
293Q8#6695714yes—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—42no—
302C2×C4—442no—
303C2×C4—442no—
304C2×C4#6698311yescharacteristic
305C2×C4#6698311yescharacteristic
306C2×C4#6698311yescharacteristic
307C2×C4C22×D4411yescharacteristic
308C2×C4C2×#433911yescharacteristic
309C2×C4C22×C22⋊D1111yescharacteristic
310C8—21no—
311C8—21no—
312C8—21no—
313C8—42no—
314C8—444no—
315C8#6699512yes—
316C22—21no—
317C22—21no—
318C22#1062275612yes—
319C22C2×#6698311yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—24no—
324C4—21no—
325C4—42no—
326C4—882no—
327C4—882no—
328C4C2×#6695712yes—
329C4C2×#6699511yescharacteristic
330C4#1062335311yescharacteristic
331C2—22no—
332C2#1307808811yescharacteristic
333C2#1307819711yescharacteristic
334C2C2×#1062275611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C8×Q8×C11C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenterC2×C8×Q8D11
hypocenterC11#19265
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
3. #13068046C2semidirect
4. #13068010C2semidirect
5. #13067986C2semidirect
286. C11#19265semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130787462
#130680462
#130680102
#130679862
#130673792
#130673142
C2×C8×Q8×C112
#1926511