Finite Group Databasebeta

← #14667505

Subgroups — #14667505

Order 2816.

308 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 71 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#13070859C211yesmaximal, characteristic, complemented
2#13070651C211yesmaximal, characteristic
3#13068100C211yesmaximal, characteristic, complemented
4#13066668C211yesmaximal, characteristic, complemented
5#13066598C211yesmaximal, characteristic, complemented
6#13066583C211yesmaximal, characteristic, complemented
7C11×#3389C211yesmaximal, characteristic, complemented
8C11×#554—21no—
9C11×#501—21no—
10C11×#499C2211yescharacteristic
11C11×#478—21no—
12C11×#478—21no—
13C11×#474—21no—
14C11×#446C2211yescharacteristic
15C11×#442—21no—
16C4×C11×D8C2211yescharacteristic
17C2×#66890—21no—
18#10622640—21no—
19#10622308C2211yescharacteristic
20#10622129—21no—
21#10622129—21no—
22#10622129—21no—
23#10622123—21no—
24C4⋊(C11⋊C16)C2211yescharacteristic
25#10622099C2211yescharacteristic
26#10622095C2211yescharacteristic
27C2×C11×D8D411yescharacteristic
28C11×C4⋊Q8—21no—
29C11×#125—21no—
30C11×#125—21no—
31C11×C22⋊Q8—41no—
32C11×C22⋊Q8—41no—
33C11×C22⋊Q8—41no—
34C4×Q8×C11D411yescharacteristic
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C2×C11×C4⋊C4—41no—
39C2×#4325—41no—
40C2×D88—21no—
41C2×D88—21no—
42#66927—21no—
43C11×#107—21no—
44C11×#107D411yescharacteristic
45C11×#107D411yescharacteristic
46C11×#107D411yescharacteristic
47C11×#106—21no—
48C11×#106—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8D411yescharacteristic
51C11×#102—21no—
52C11×#102—21no—
53C11×#102—21no—
54C11×#97—21no—
55C4×C8×C11C2311yescharacteristic
56#66890—42no—
57C2×C11⋊C16—21no—
58C2×C11⋊C16—21no—
59#66873—41no—
60C4⋊(C11⋊C8)—21no—
61#12360—111nomaximal, Sylow
62C2×Q8×C11—41no—
63C2×Q8×C11D811yescharacteristic
64C2×D4×C11—21no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C2×D44—41no—
69C2×D44—41no—
70C2×D44—41no—
71C11×D8—21no—
72C11×D8SD1612yescomplemented
73C2×C8×C11—21no—
74C2×C8×C11C2×D411yescharacteristic
75C2×C8×C11C2×D411yescharacteristic
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4D811yescharacteristic
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C42×C11—21no—
90C42×C11C2×D411yescharacteristic
91#4325—82no—
92C2×C11⋊C8—41no—
93D88—42no—
94D88—41no—
95D88—41no—
96C11⋊C16—41no—
97C11⋊C16—41no—
98#3389D1111yescharacteristic, complemented
99#2244—111no—
100#2206—111no—
101#1688—111no—
102#1363—111no—
103#1338—111no—
104#1333—111no—
105C23×C11—41no—
106C22×D11—81no—
107Q8×C11—41no—
108Q8×C11—161no—
109D4×C11—22no—
110D4×C11—41no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—82no—
117C2×C4×C11—161no—
118C2×C4×C11—161no—
119C2×C4×C11#12011yescharacteristic
120C2×C4×C11C2×D811yescharacteristic
121C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
122D44—81no—
123D44—81no—
124D44—81no—
125D44—81no—
126D44—161no—
127C8×C11—21no—
128C8×C11—41no—
129C8×C11C2×SD1611yescharacteristic
130C8×C11#13711yescharacteristic
131C11⋊C8—81no—
132#554—21no—
133C2×D16—221no—
134#501—21no—
135#499C2×D1111yescharacteristic
136#493—111no—
137#478—21no—
138#478—21no—
139#474—21no—
140#460—221no—
141#446C2×D1111yescharacteristic
142#442—21no—
143C4×D8C2×D1111yescharacteristic
144C4⋊C16—111no—
145#357—221no—
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#44711yescharacteristic
155C2×D11—161no—
156C2×D11—161no—
157C2×D11—161no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—81no—
163C4×C11—81no—
164C4×C11—81no—
165C4×C11#44811yescharacteristic
166C4×C11#45411yescharacteristic
167C2×SD16—441no—
168C2×D8—221no—
169C2×D8—221no—
170C2×D8C22⋊D1111yescharacteristic
171C4⋊Q8—21no—
172#127—221no—
173#125—21no—
174#125—21no—
175C22⋊Q8—41no—
176C22⋊Q8—41no—
177C22⋊Q8—41no—
178C4×Q8C22⋊D1111yescharacteristic
179C4×D4—21no—
180C4×D4—21no—
181C4×D4—21no—
182C2×C4⋊C4—41no—
183D16—442no—
184C2×C16—221no—
185C2×C16—221no—
186#107—21no—
187#107C22⋊D1111yescharacteristic
188#107C22⋊D1111yescharacteristic
189#107C22⋊D1111yescharacteristic
190#106—21no—
191#106—21no—
192C4⋊C8—21no—
193C4⋊C8—221no—
194C4⋊C8C22⋊D1111yescharacteristic
195#102—21no—
196#102—21no—
197#102—21no—
198#102—441no—
199#97—21no—
200C4×C8C22×D1111yescharacteristic
201C2×C11—82no—
202C2×C11#162711yescharacteristic
203C2×C11#219011yescharacteristic
204C2×C11#219211yescharacteristic
205D11—321no—
206C2×Q8—41no—
207C2×Q8#432311yescharacteristic
208C2×D4—21no—
209C2×D4—441no—
210C2×D4—441no—
211C2×D4—441no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215SD16—882no—
216D8—21no—
217D8—442no—
218D8—441no—
219D8—441no—
220D8#432512yescomplemented
221C2×C8—21no—
222C2×C8—441no—
223C2×C8C2×C22⋊D1111yescharacteristic
224C2×C8C2×C22⋊D1111yescharacteristic
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4#432311yescharacteristic
235C22⋊C4—41no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C42—21no—
239C42C2×C22⋊D1111yescharacteristic
240C16—441no—
241C16—441no—
242C11#1236011yescharacteristic, complemented, Sylow
243C23—41no—
244C23—881no—
245Q8—41no—
246Q8—161no—
247D4—22no—
248D4—41no—
249D4—881no—
250D4—881no—
251D4—881no—
252D4—881no—
253D4—1761no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—82no—
260C2×C4—161no—
261C2×C4—161no—
262C2×C4C2×#432311yescharacteristic
263C2×C4#6698511yescharacteristic
264C2×C4#6700611yescharacteristic
265C8—21no—
266C8—41no—
267C8—881no—
268C8C2×#432511yescharacteristic
269C8#6699511yescharacteristic
270C22—42no—
271C22—81no—
272C22—81no—
273C22—1761no—
274C22—1761no—
275C22—1761no—
276C22#1062283011yescharacteristic
277C4—21no—
278C4—21no—
279C4—41no—
280C4—41no—
281C4—81no—
282C4—81no—
283C4—81no—
284C4#1062284011yescharacteristic
285C4#1062285811yescharacteristic
286C2—82no—
287C2—3521no—
288C2#1306771911yescharacteristic
289C2#1307056211yescharacteristic
290C2#1307057311yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#3389C2
socleC22×C11#447
prime radical#13070651C2
hypercenter#3389D11
hypocenterC11#12360
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #446 ◁ #3389

Complements

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

NH ≅ G/Ntype
1. #13070859C2semidirect
3. #13068100C2semidirect
4. #13066668C2semidirect
5. #13066598C2semidirect
6. #13066583C2semidirect
7. C11×#3389C2semidirect
72. C11×D8SD16semidirect
98. #3389D11semidirect
220. D8#4325semidirect
242. C11#12360semidirect

Maximal subgroups

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

subgroupindex
#130708592
#130706512
#130681002
#130666682
#130665982
#130665832
C11×#33892
#1236011