Finite Group Databasebeta

← #14667504

Subgroups — #14667504

Order 2816.

308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081572C211yesmaximal, characteristic, complemented
2#13070857C211yesmaximal, characteristic, complemented
3#13068097C211yesmaximal, characteristic, complemented
4#13066667C211yesmaximal, characteristic, complemented
5#13066597C211yesmaximal, characteristic, complemented
6#13066583C211yesmaximal, characteristic, complemented
7C11×#2206C211yesmaximal, characteristic
8#10623070—21no—
9C2×C11×D16—21no—
10C11×#493C2211yescharacteristic
11C4×C11×D8C2211yescharacteristic
12#10622765—21no—
13#10622688—21no—
14#10622622—21no—
15#10622489—21no—
16#10622379—21no—
17#10622372—21no—
18#10622296C2211yescharacteristic
19#10622292C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C11×#357—21no—
22#10622200—21no—
23#10622200—21no—
24#10622182—21no—
25#10622099C2211yescharacteristic
26#10622095C2211yescharacteristic
27C2×C11×D8—21no—
28C2×C11×D8—21no—
29C2×C11×D8D411yescharacteristic
30C11×#127—21no—
31C4×D4×C11—21no—
32D4×Dic11—21no—
33D4×Dic11—21no—
34C2×#4324—41no—
35#66977—41no—
36C2×Dic11⋊C4—41no—
37#66943—21no—
38#66941—21no—
39#66931—41no—
40#66931—41no—
41#66923—21no—
42C4×Dic22D411yescharacteristic
43C11×D16—42no—
44C2×C11×C16—21no—
45C11×#107D411yescharacteristic
46C11×#102—21no—
47C4×C8×C11C2311yescharacteristic
48#66896—21no—
49#66896—21no—
50#66896—41no—
51#66882D411yescharacteristic
52#66882D411yescharacteristic
53#66881—21no—
54#66879—21no—
55Dic11⋊C8—21no—
56C2×C11⋊C16—21no—
57#66872—21no—
58#66871—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D411yescharacteristic
61#12360—111nomaximal, Sylow
62C2×D4×C11—21no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C22×C4×C11—41no—
67C22×Dic11—41no—
68C22×Dic11—41no—
69C2×Dic22—41no—
70C2×Dic22D811yescharacteristic
71C11×D8—21no—
72C11×D8—42no—
73C11×D8—41no—
74C11×D8—41no—
75C11×D8SD1612yescomplemented
76C2×C8×C11C2×D411yescharacteristic
77C2×C8×C11C2×D411yescharacteristic
78C11×C4⋊C4—21no—
79C11×C22⋊C4—41no—
80C42×C11C2×D411yescharacteristic
81C22⋊Dic11—41no—
82C22⋊Dic11—41no—
83#4324—82no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—41no—
87C4⋊Dic11D811yescharacteristic
88Dic11⋊C4—21no—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93C4×Dic11—21no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—41no—
96C11×C16—41no—
97C11⋊C16—41no—
98#3389—111no—
99#2244—111no—
100#2206D1111yescharacteristic
101#1688—111no—
102#1363—111no—
103#1338—111no—
104#1333—111no—
105C23×C11—41no—
106C23×C11—81no—
107D4×C11—22no—
108D4×C11—41no—
109D4×C11—81no—
110D4×C11—81no—
111D4×C11—81no—
112D4×C11—81no—
113D4×C11—161no—
114C2×C4×C11—41no—
115C2×C4×C11—161no—
116C2×C4×C11#12011yescharacteristic
117C2×C4×C11C2×D811yescharacteristic
118C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—41no—
122C2×Dic11—41no—
123C2×Dic11—82no—
124C2×Dic11—161no—
125Dic22—41no—
126Dic22—161no—
127C8×C11—21no—
128C8×C11C2×SD1611yescharacteristic
129C8×C11#13711yescharacteristic
130C11⋊C8—41no—
131C11⋊C8—81no—
132#554—221no—
133C2×D16—21no—
134#501—221no—
135#499—111no—
136#493C2×D1111yescharacteristic
137#478—221no—
138#478—221no—
139#474—221no—
140#460—221no—
141#446—111no—
142#442—221no—
143C4×D8C2×D1111yescharacteristic
144C4⋊C16C2×D1111yescharacteristic
145#357—21no—
146#357—221no—
147#357—221no—
148#346—111no—
149#334—111no—
150#331—221no—
151C22×C11—42no—
152C22×C11—81no—
153C22×C11—81no—
154C22×C11—161no—
155C22×C11—161no—
156C22×C11—161no—
157C22×C11#44711yescharacteristic
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—81no—
161C4×C11#44811yescharacteristic
162C4×C11#45411yescharacteristic
163Dic11—41no—
164Dic11—41no—
165Dic11—81no—
166Dic11—81no—
167C2×SD16—441no—
168C2×D8—21no—
169C2×D8—21no—
170C2×D8C22⋊D1111yescharacteristic
171C4⋊Q8—221no—
172#127—21no—
173#125—221no—
174#125—221no—
175C22⋊Q8—441no—
176C22⋊Q8—441no—
177C22⋊Q8—441no—
178C4×Q8—111no—
179C4×D4—21no—
180C4×D4—221no—
181C4×D4—221no—
182C2×C4⋊C4—441no—
183D16—42no—
184C2×C16—21no—
185C2×C16—221no—
186#107—111no—
187#107—111no—
188#107—221no—
189#107C22⋊D1111yescharacteristic
190#106—221no—
191#106—221no—
192C4⋊C8—111no—
193C4⋊C8—221no—
194C4⋊C8—221no—
195#102—21no—
196#102—221no—
197#102—221no—
198#102—441no—
199#97—221no—
200C4×C8C22×D1111yescharacteristic
201C2×C11—82no—
202C2×C11—321no—
203C2×C11#162711yescharacteristic
204C2×C11#219011yescharacteristic
205C2×C11#219211yescharacteristic
206C2×Q8—111no—
207C2×Q8—441no—
208C2×D4—21no—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4—41no—
212C22×C4—41no—
213C22×C4—441no—
214C22×C4—441no—
215SD16—882no—
216D8—21no—
217D8—42no—
218D8—41no—
219D8—41no—
220D8#432412yescomplemented
221C2×C8—221no—
222C2×C8—441no—
223C2×C8D4×D1111yescharacteristic
224C2×C8C2×C22⋊D1111yescharacteristic
225C4⋊C4—21no—
226C4⋊C4—111no—
227C4⋊C4—221no—
228C4⋊C4—221no—
229C4⋊C4—221no—
230C4⋊C4—441no—
231C4⋊C4—441no—
232C4⋊C4—441no—
233C4⋊C4—441no—
234C4⋊C4—441no—
235C22⋊C4—41no—
236C22⋊C4—441no—
237C22⋊C4—441no—
238C42—221no—
239C42D4×D1111yescharacteristic
240C16—41no—
241C16—441no—
242C11#1236011yescharacteristic, complemented, Sylow
243C23—41no—
244C23—81no—
245Q8—441no—
246Q8—1761no—
247D4—22no—
248D4—41no—
249D4—81no—
250D4—81no—
251D4—81no—
252D4—81no—
253D4—161no—
254C2×C4—41no—
255C2×C4—161no—
256C2×C4—221no—
257C2×C4—221no—
258C2×C4—441no—
259C2×C4—441no—
260C2×C4—882no—
261C2×C4—1761no—
262C2×C4D8×D1111yescharacteristic
263C2×C4#6696411yescharacteristic
264C2×C4#6699011yescharacteristic
265C8—21no—
266C8—441no—
267C8—881no—
268C8C2×#432411yescharacteristic
269C8#6700411yescharacteristic
270C22—42no—
271C22—81no—
272C22—81no—
273C22—161no—
274C22—161no—
275C22—161no—
276C22#1062276911yescharacteristic
277C4—21no—
278C4—21no—
279C4—81no—
280C4—441no—
281C4—441no—
282C4—881no—
283C4—881no—
284C4#1062265311yescharacteristic
285C4#1062281411yescharacteristic
286C2—82no—
287C2—321no—
288C2#1306771811yescharacteristic
289C2#1307056011yescharacteristic
290C2#1307057211yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
Fitting, prime radicalC11×#2206C2
socleC22×C11#447
hypercenter#2206D11
hypocenterC11#12360
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #13081572C2semidirect
2. #13070857C2semidirect
3. #13068097C2semidirect
4. #13066667C2semidirect
5. #13066597C2semidirect
6. #13066583C2semidirect
75. C11×D8SD16semidirect
220. D8#4324semidirect
242. C11#12360semidirect

Maximal subgroups

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

subgroupindex
#130815722
#130708572
#130680972
#130666672
#130665972
#130665832
C11×#22062
#1236011