Finite Group Databasebeta

← #14738374

Subgroups — #14738374

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079810C212yesmaximal
2#13079202C211yesmaximal, characteristic, complemented
3#13068139C212yesmaximal, complemented
4#13068105C212yesmaximal, complemented
5#13068067C214yesmaximal, complemented
6#13067379C211yesmaximal, characteristic, complemented
7#13067344C212yesmaximal, complemented
8C11×#2931C211yesmaximal, characteristic
9C2×C11×#131—21no—
10C11×#532C2211yescharacteristic
11#10623001C2212yes—
12C11×#436—21no—
13C11×#436C2212yes—
14C8×D4×C11—21no—
15C8×D4×C11C2212yes—
16C11×#423C2211yescharacteristic
17C11×#408—21no—
18C2×C4×C8×C11C2211yescharacteristic
19#10622729—21no—
20#10622729—21no—
21#10622693—22no—
22#10622684—22no—
23#10622648—24no—
24#10622621C2214yes—
25#10622620C2214yes—
26#10622539C2212yes—
27#10622312C2211yescharacteristic
28C4×Dic44—21no—
29C4×Dic44—21no—
30#10622295C2211yescharacteristic
31#10622294C2212yes—
32#10622120C2214yes—
33#10622119C2214yes—
34#10622096C2212yes—
35#10622095C2212yes—
36C2×C11×#41—21no—
37C11×#131—44no—
38C2×C11×M16—21no—
39C2×C11×M16—22no—
40C22×C8×C11—22no—
41C22×C8×C11D411yescharacteristic
42C22×C8×C11D411yescharacteristic
43C11×C4⋊Q8D411yescharacteristic
44C11×#127D411yescharacteristic
45C11×#124—21no—
46C11×#121—21no—
47C11×#121D412yes—
48C4×D4×C11—21no—
49C4×D4×C11C2312yes—
50C2×C42×C11C2311yescharacteristic
51#66979—22no—
52#66977—22no—
53#66977—22no—
54C2×Dic44—21no—
55C2×Dic44—21no—
56#66923—22no—
57#66922C2312yes—
58#66922C2312yes—
59C4×Dic22—22no—
60C4×Dic22—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8C2312yes—
63C11×C22⋊C8—22no—
64C11×C22⋊C8—22no—
65C4×C8×C11D411yescharacteristic
66C4×C8×C11D411yescharacteristic
67C4×C8×C11C2311yescharacteristic
68C4×C8×C11C2311yescharacteristic
69#66896—24no—
70#66896—24no—
71C22⋊(C11⋊C8)—22no—
72#66882—21no—
73#66882—21no—
74#66880—22no—
75#66880—22no—
76#66872—24no—
77#66871—24no—
78C4⋊(C11⋊C8)C2314yes—
79#66867—22no—
80#19336—111nomaximal, Sylow
81C11×#41—42no—
82C11×#41—42no—
83C2×Q8×C11—21no—
84C2×D4×C11—22no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11C2×D412yes—
88C22×C4×C11—22no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C2×Dic22—22no—
93C2×Dic22—22no—
94C11×M16—42no—
95C11×M16—44no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C2×C8×C11—44no—
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C11×C4⋊C4—21no—
105C11×C4⋊C4C2×D412yes—
106C11×C22⋊C4—22no—
107C11×C22⋊C4—22no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111C42×C11C2411yescharacteristic
112C22⋊Dic11—42no—
113C4⋊Dic11—22no—
114C4⋊Dic11—22no—
115C4⋊Dic11—22no—
116C4⋊Dic11—22no—
117Dic11⋊C4—42no—
118Dic11⋊C4—42no—
119C4×Dic11—42no—
120C2×C11⋊C8—24no—
121Dic44—42no—
122Dic44—42no—
123#3235—112no—
124#3170—111no—
125#2931D1111yescharacteristic
126#1695—112no—
127#1689—112no—
128#1683—114no—
129#1568—111no—
130#1559—112no—
131C23×C11—22no—
132C23×C11#12111yescharacteristic
133Q8×C11—42no—
134D4×C11—24no—
135D4×C11—42no—
136D4×C11—42no—
137D4×C11—44no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C2×C4×C11C22×D411yescharacteristic
150C2×C4×C11C2×#4111yescharacteristic
151C2×Dic11—42no—
152C2×Dic11—42no—
153Dic22—42no—
154Dic22—42no—
155Dic22—82no—
156C8×C11—21no—
157C8×C11—21no—
158C8×C11—21no—
159C8×C11—42no—
160C8×C11AGL(1,ℤ/8)12yes—
161C11⋊C8—44no—
162C2×#131—21no—
163#533—112no—
164#532C2×D1111yescharacteristic
165#501—222no—
166#500—111no—
167#494—111no—
168#490—222no—
169#487—112no—
170#482—224no—
171#476—114no—
172#474—114no—
173#467—221no—
174#467—221no—
175C4×Q16—221no—
176C4×Q16—221no—
177#436—21no—
178#436C2×D1112yes—
179C8×D4—21no—
180C8×D4C2×D1112yes—
181#432—112no—
182#423C2×D1111yescharacteristic
183#408—21no—
184C2×C4×C8C2×D1111yescharacteristic
185#335—112no—
186#334—112no—
187#333—114no—
188#332—114no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—42no—
193C22×C11—42no—
194C22×C11—42no—
195C22×C11C2×#12111yescharacteristic
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—42no—
201C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
202C4×C11#57511yescharacteristic
203C4×C11#57812yes—
204Dic11—82no—
205Dic11—82no—
206C2×#41—21no—
207C2×Q16—221no—
208C2×Q16—221no—
209#131—44no—
210C2×M16—21no—
211C2×M16—22no—
212C22×C8—22no—
213C22×C8C22⋊D1111yescharacteristic
214C22×C8C22⋊D1111yescharacteristic
215C4⋊Q8—112no—
216C4⋊Q8—112no—
217C4⋊Q8D4411yescharacteristic
218#127D4411yescharacteristic
219#125—222no—
220#124—21no—
221C22⋊Q8—222no—
222C22⋊Q8—222no—
223#121—21no—
224#121D4412yes—
225C4×Q8—222no—
226C4×Q8—222no—
227C4×D4—21no—
228C4×D4C22×D1112yes—
229#117—222no—
230C2×C42C22×D1111yescharacteristic
231#107—221no—
232#107—221no—
233#107—224no—
234#106—224no—
235C4⋊C8—21no—
236C4⋊C8—114no—
237C4⋊C8C22×D1112yes—
238#103—222no—
239#103—222no—
240#102—224no—
241#102—224no—
242C22⋊C8—22no—
243C22⋊C8—22no—
244C22⋊C8—222no—
245#97—222no—
246C4×C8C22⋊D1111yescharacteristic
247C4×C8C22⋊D1111yescharacteristic
248C4×C8C22×D1111yescharacteristic
249C4×C8C22×D1111yescharacteristic
250C2×C11—41no—
251C2×C11—82no—
252C2×C11#303611yescharacteristic
253C2×C11#305911yescharacteristic
254C2×C11#306711yescharacteristic
255#41—42no—
256#41—42no—
257C2×Q8—21no—
258C2×Q8—222no—
259C2×Q8—222no—
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4C2×D4412yes—
264C22×C4—22no—
265C22×C4C2×D4411yescharacteristic
266C22×C4#433911yescharacteristic
267C22×C4C2×C22⋊D1111yescharacteristic
268Q16—442no—
269Q16—442no—
270M16—42no—
271M16—44no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—41no—
275C2×C8—44no—
276C2×C8—224no—
277C2×C8C2×C22⋊D1111yescharacteristic
278C2×C8C2×C22⋊D1111yescharacteristic
279C2×C8C2×C22⋊D1111yescharacteristic
280C2×C8C2×C22⋊D1111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—222no—
283C4⋊C4—222no—
284C4⋊C4—222no—
285C4⋊C4—222no—
286C4⋊C4—442no—
287C4⋊C4—442no—
288C4⋊C4C2×D4412yes—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—442no—
292C42—442no—
293C42C2×D4411yescharacteristic
294C42#433911yescharacteristic
295C42C2×C22⋊D1111yescharacteristic
296C42C23×D1111yescharacteristic
297C11#1933611yescharacteristic, complemented, Sylow
298C23—22no—
299C23#6698311yescharacteristic
300Q8—42no—
301Q8—442no—
302Q8—442no—
303Q8—882no—
304D4—24no—
305D4—42no—
306D4—42no—
307D4—44no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—442no—
316C2×C4—442no—
317C2×C4#6698311yescharacteristic
318C2×C4#6698311yescharacteristic
319C2×C4#6698311yescharacteristic
320C2×C4C22×D4411yescharacteristic
321C2×C4C2×#433911yescharacteristic
322C2×C4C22×C22⋊D1111yescharacteristic
323C8—21no—
324C8—21no—
325C8—21no—
326C8—42no—
327C8—444no—
328C8#6698512yes—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—42no—
333C22—42no—
334C22—42no—
335C22C2×#6698311yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—882no—
342C4—882no—
343C4#1062328412yes—
344C4C2×#6698511yescharacteristic
345C4#1062335311yescharacteristic
346C2—41no—
347C2—82no—
348C2#1307808011yescharacteristic
349C2#1307827111yescharacteristic
350C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2931C2
socleC22×C11C2×#121
prime radicalC11×#532C22
hypercenter#2931D11
hypocenterC11#19336
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2931

Complements

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

NH ≅ G/Ntype
2. #13079202C2semidirect
3. #13068139C2semidirect
4. #13068105C2semidirect
5. #13068067C2semidirect
6. #13067379C2semidirect
7. #13067344C2semidirect
297. C11#19336semidirect

Maximal subgroups

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

subgroupindex
#130798102
#130792022
#130681392
#130681052
#130680672
#130673792
#130673442
C11×#29312
#1933611