Finite Group Databasebeta

← #14667516

Subgroups — #14667516

Order 2816.

292 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 63 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#13081577C211yesmaximal, characteristic
2#13070658C211yesmaximal, characteristic
3#13068107C211yesmaximal, characteristic, complemented
4#13066668C211yesmaximal, characteristic, complemented
5#13066599C211yesmaximal, characteristic, complemented
6#13066584C211yesmaximal, characteristic
7C11×#2245C211yesmaximal, characteristic, complemented
8#10623221—21no—
9C11×#499C2211yescharacteristic
10C11×#494C2211yescharacteristic
11C2×#66892—21no—
12#10622707—21no—
13#10622679—21no—
14#10622504—21no—
15#10622503—21no—
16#10622482—21no—
17#10622469—21no—
18C4×D88C2211yescharacteristic
19#10622292C2211yescharacteristic
20C11×#358—21no—
21C11×#358—21no—
22C11×#346C2211yescharacteristic
23#10622202—21no—
24#10622185—21no—
25C4⋊(C11⋊C16)C2211yescharacteristic
26#10622095C2211yescharacteristic
27C2×C11×Q16—21no—
28C2×C11×Q16—21no—
29C11×C4⋊Q8—21no—
30C11×#125—21no—
31C2×D88D411yescharacteristic
32#66950—41no—
33#66949—41no—
34#66949—41no—
35#66946—21no—
36#66946—21no—
37C4⋊C4×D11—41no—
38#66943—21no—
39#66941—21no—
40C4×D44—21no—
41C4×Dic22D411yescharacteristic
42C2×C11×C16—21no—
43C11×#107D411yescharacteristic
44C11×#107D411yescharacteristic
45C11×#106—21no—
46C4×C8×C11C2311yescharacteristic
47#66892—42no—
48#66885—21no—
49#66882D411yescharacteristic
50#66879—21no—
51Dic11⋊C8—21no—
52C2×C11⋊C16—21no—
53#66874—41no—
54#66873—21no—
55#66873—21no—
56#66872—21no—
57#66872—41no—
58#66871—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D411yescharacteristic
61#12362—111nomaximal, Sylow
62C2×Q8×C11—41no—
63C2×D44—21no—
64C2×C4×D11—41no—
65C2×C4×D11—41no—
66C2×C4×D11—41no—
67C2×Dic22—41no—
68C2×Dic22D811yescharacteristic
69C11×Q16—42no—
70C11×Q16—41no—
71C11×Q16—41no—
72C2×C8×C11C2×D411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C42×C11C2×D411yescharacteristic
81(C2×D11)⋊C4—41no—
82(C2×D11)⋊C4—41no—
83(C2×D11)⋊C4—41no—
84C4⋊Dic11—21no—
85C4⋊Dic11—41no—
86C4⋊Dic11D811yescharacteristic
87Dic11⋊C4—21no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90C4×Dic11—21no—
91C2×C11⋊C8—21no—
92C2×C11⋊C8—41no—
93D88—21no—
94D88SD1612yes—
95C11×C16—41no—
96C11⋊C16—41no—
97#3389—111no—
98#2245D1111yescharacteristic, complemented
99#2208—111no—
100#1690—111no—
101#1363—111no—
102#1338—111no—
103#1333—111no—
104C22×D11—41no—
105Q8×C11—81no—
106Q8×C11—81no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—81no—
110C2×C4×C11#12011yescharacteristic
111C2×C4×C11C2×D811yescharacteristic
112C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—41no—
116D44—22no—
117D44—41no—
118C4×D11—82no—
119C4×D11—161no—
120C4×D11—161no—
121Dic22—41no—
122Dic22—161no—
123C8×C11—21no—
124C8×C11C2×SD1611yescharacteristic
125C8×C11#13711yescharacteristic
126C11⋊C8—41no—
127C11⋊C8—81no—
128#554—221no—
129C2×SD32—221no—
130#501—221no—
131#499C2×D1111yescharacteristic
132#494C2×D1111yescharacteristic
133#478—221no—
134#478—221no—
135#475—221no—
136#474—221no—
137#446—111no—
138#442—221no—
139C4×D8—111no—
140C4⋊C16—111no—
141#358—21no—
142#358—21no—
143#358—221no—
144#346C2×D1111yescharacteristic
145#334—111no—
146#332—221no—
147C22×C11#44711yescharacteristic
148C2×D11—42no—
149C2×D11—81no—
150C2×D11—81no—
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—81no—
154C4×C11—81no—
155C4×C11—161no—
156C4×C11#44811yescharacteristic
157C4×C11#45411yescharacteristic
158Dic11—41no—
159Dic11—41no—
160Dic11—81no—
161C2×Q16—21no—
162C2×Q16—21no—
163C2×D8—111no—
164C4⋊Q8—21no—
165C4⋊Q8—221no—
166#125—21no—
167#125—221no—
168C22⋊Q8—441no—
169C22⋊Q8—441no—
170C22⋊Q8—441no—
171C4×Q8—111no—
172C4×D4—221no—
173C4×D4—221no—
174C4×D4—221no—
175C2×C4⋊C4—441no—
176SD32—442no—
177C2×C16—21no—
178C2×C16—221no—
179#107—111no—
180#107—221no—
181#107C22⋊D1111yescharacteristic
182#107C22⋊D1111yescharacteristic
183#106—21no—
184#106—221no—
185#106—441no—
186C4⋊C8—111no—
187C4⋊C8—221no—
188C4⋊C8—221no—
189#103—441no—
190#102—221no—
191#102—221no—
192#102—221no—
193#97—221no—
194C4×C8C22×D1111yescharacteristic
195C2×C11#162711yescharacteristic
196C2×C11#219111yescharacteristic
197C2×C11#219411yescharacteristic
198D11—82no—
199C2×Q8—41no—
200C2×Q8—111no—
201C2×Q8—441no—
202C2×D4—221no—
203C22×C4—441no—
204C22×C4—441no—
205C22×C4—441no—
206Q16—42no—
207Q16—41no—
208Q16—41no—
209D8—112no—
210D8—221no—
211C2×C8—221no—
212C2×C8—441no—
213C2×C8D4×D1111yescharacteristic
214C2×C8C2×C22⋊D1111yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—111no—
222C4⋊C4—221no—
223C4⋊C4—221no—
224C4⋊C4—441no—
225C4⋊C4—441no—
226C4⋊C4—441no—
227C22⋊C4—441no—
228C22⋊C4—441no—
229C22⋊C4—441no—
230C42—221no—
231C42D4×D1111yescharacteristic
232C16—41no—
233C16—441no—
234C11#1236211yescharacteristic, complemented, Sylow
235C23—441no—
236Q8—81no—
237Q8—81no—
238Q8—441no—
239Q8—1761no—
240D4—222no—
241D4—441no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—81no—
245C2×C4—221no—
246C2×C4—221no—
247C2×C4—441no—
248C2×C4—882no—
249C2×C4—1761no—
250C2×C4—1761no—
251C2×C4D8×D1111yescharacteristic
252C2×C4#6696411yescharacteristic
253C2×C4#6699011yescharacteristic
254C8—21no—
255C8—441no—
256C8—881no—
257C8SD16×D1111yescharacteristic
258C8#6696811yescharacteristic
259C22—442no—
260C22—881no—
261C22—881no—
262C22#1062276911yescharacteristic
263C4—21no—
264C4—21no—
265C4—81no—
266C4—81no—
267C4—161no—
268C4—441no—
269C4—441no—
270C4—881no—
271C4#1062267511yescharacteristic
272C4#1062278311yescharacteristic
273C2—882no—
274C2#1306771611yescharacteristic
275C2#1307056511yescharacteristic
276C2#1307058411yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2245C2
socleC22×C11#447
prime radicalC2×D88D4
hypercenter#2245D11
hypocenterC11#12362
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2245

Complements

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

NH ≅ G/Ntype
3. #13068107C2semidirect
4. #13066668C2semidirect
5. #13066599C2semidirect
7. C11×#2245C2semidirect
98. #2245D11semidirect
234. C11#12362semidirect

Maximal subgroups

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

subgroupindex
#130815772
#130706582
#130681072
#130666682
#130665992
#130665842
C11×#22452
#1236211