Finite Group Databasebeta

← #14673248

Subgroups — #14673248

Order 2816.

434 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 73 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#13070308C212yesmaximal, complemented
2#13069164C212yesmaximal, complemented
3#13068835C211yesmaximal, characteristic, complemented
4#13066739C211yesmaximal, characteristic, complemented
5C11×#3199C211yesmaximal, characteristic
6C11×#535C2212yes—
7#10623350C2211yescharacteristic
8C11×#482—22no—
9C11×#469—21no—
10C11×#466—21no—
11C11×#447—22no—
12C11×#408C2211yescharacteristic
13#10622850C2212yes—
14#10622850C2211yescharacteristic
15C2×#66897—22no—
16#10622737—21no—
17#10622190—21no—
18#10622180—24no—
19#10622171—22no—
20C2×C11×#41C2311yescharacteristic
21C22×D4×C11D412yes—
22C2×C11×D8—21no—
23C2×C11×D8—21no—
24C2×C11×M16D411yescharacteristic
25C22×C8×C11D411yescharacteristic
26C11×#127—22no—
27C11×#124—22no—
28C11×#121—22no—
29C11×#121—22no—
30C11×#120—22no—
31C11×#120—22no—
32C11×#117D412yes—
33#67001—42no—
34C2×#4318—21no—
35C2×#4318—21no—
36C2×#4318—22no—
37C2×#4318—22no—
38C11×#107—21no—
39C11×#106—21no—
40C11×#102—22no—
41C11×#102—22no—
42C11×C22⋊C8—22no—
43#66900—22no—
44#66900D412yes—
45#66897—21no—
46#66897—22no—
47#66897—44no—
48#66886—42no—
49#13429—111nomaximal, Sylow
50C24×C11—22no—
51C11×#41—41no—
52C11×#41—41no—
53C2×Q8×C11C2×D411yescharacteristic
54C2×D4×C11—22no—
55C2×D4×C11—22no—
56C2×D4×C11—42no—
57C2×D4×C11—42no—
58C2×D4×C11—42no—
59C2×D4×C11—42no—
60C2×D4×C11#4111yescharacteristic
61C2×D4×C11#4112yes—
62C22×C4×C11C2×D412yes—
63C22×C4×C11C2×D411yescharacteristic
64C11×D8—81no—
65C11×D8—81no—
66C11×M16—41no—
67C2×C8×C11—21no—
68C2×C8×C11—21no—
69C2×C8×C11—41no—
70C11×C4⋊C4—22no—
71C11×C22⋊C4—22no—
72C11×C22⋊C4—42no—
73C11×C22⋊C4—42no—
74C42×C11—22no—
75#4318—22no—
76#4318—24no—
77#4318—22no—
78#4318—41no—
79#4318—42no—
80#4318—41no—
81#4318—42no—
82C2×C11⋊C8—41no—
83C2×C11⋊C8—41no—
84C2×C11⋊C8—42no—
85C2×C11⋊C8—42no—
86#3199D1111yescharacteristic
87#2134—112no—
88#1914—112no—
89#1858—111no—
90#1392—111no—
91C23×C11—44no—
92C23×C11—42no—
93C23×C11—162no—
94C23×C11#12312yes—
95C23×C11#12411yescharacteristic
96Q8×C11—41no—
97D4×C11—42no—
98D4×C11—41no—
99D4×C11—42no—
100D4×C11—42no—
101D4×C11—82no—
102D4×C11—162no—
103D4×C11—162no—
104C2×C4×C11—21no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—21no—
108C2×C4×C11—42no—
109C2×C4×C11#12011yescharacteristic
110C2×C4×C11#12111yescharacteristic
111C2×C4×C11#12112yes—
112C8×C11—41no—
113C8×C11—41no—
114C11⋊C8—42no—
115C11⋊C8—42no—
116C11⋊C8—82no—
117#568—111no—
118#535C2×D1112yes—
119#482—22no—
120#469—21no—
121#466—21no—
122#447—22no—
123#430—221no—
124#413—111no—
125#413—112no—
126C2×#100—222no—
127#408C2×D1111yescharacteristic
128#355—224no—
129#344—222no—
130#341—221no—
131C22×C11—22no—
132C22×C11—21no—
133C22×C11—41no—
134C22×C11—42no—
135C22×C11—82no—
136C22×C11—82no—
137C22×C11—82no—
138C22×C11—164no—
139C22×C11#39411yescharacteristic
140C4×C11—22no—
141C4×C11—21no—
142C4×C11—82no—
143C4×C11B(4,𝔽2)11yescharacteristic
144C4×C11#45811yescharacteristic
145C2×#41C22×D1111yescharacteristic
146C22×D4C22⋊D1112yes—
147C2×D8—21no—
148C2×D8—21no—
149#131—442no—
150C2×M16—221no—
151C2×M16—222no—
152C2×M16—221no—
153C2×M16—222no—
154C2×M16C22⋊D1111yescharacteristic
155C22×C8C22⋊D1111yescharacteristic
156#127—22no—
157#124—22no—
158#121—22no—
159#121—22no—
160#120—22no—
161#120—22no—
162#117C22⋊D1112yes—
163#108—442no—
164#107—21no—
165#106—21no—
166#102—22no—
167#102—22no—
168#101—112no—
169#101—222no—
170#100—221no—
171#100—222no—
172#100—444no—
173C22⋊C8—22no—
174C2×C11—21no—
175C2×C11—41no—
176C2×C11—42no—
177C2×C11—162no—
178C2×C11#204411yescharacteristic
179C24—22no—
180#41—41no—
181#41—41no—
182C2×Q8D4×D1111yescharacteristic
183C2×D4—22no—
184C2×D4—22no—
185C2×D4—42no—
186C2×D4—42no—
187C2×D4—42no—
188C2×D4—42no—
189C2×D4#434111yescharacteristic
190C2×D4#434112yes—
191C22×C4C2×C22⋊D1111yescharacteristic
192C22×C4C2×C22⋊D1112yes—
193D8—81no—
194D8—81no—
195M16—41no—
196M16—224no—
197M16—222no—
198M16—222no—
199M16—441no—
200M16—441no—
201M16—442no—
202M16—442no—
203C2×C8—21no—
204C2×C8—21no—
205C2×C8—41no—
206C2×C8—441no—
207C2×C8—441no—
208C2×C8—442no—
209C2×C8—442no—
210C4⋊C4—22no—
211C22⋊C4—22no—
212C22⋊C4—42no—
213C22⋊C4—42no—
214C42—22no—
215C11#1342911yescharacteristic, complemented, Sylow
216C23—44no—
217C23—42no—
218C23—162no—
219C23#6698812yes—
220C23#6698911yescharacteristic
221Q8—41no—
222D4—41no—
223D4—42no—
224D4—42no—
225D4—42no—
226D4—82no—
227D4—162no—
228D4—162no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—42no—
234C2×C4#6699111yescharacteristic
235C2×C4#6699212yes—
236C2×C4#6700611yescharacteristic
237C8—41no—
238C8—41no—
239C8—442no—
240C8—442no—
241C8—882no—
242C22—22no—
243C22—21no—
244C22—41no—
245C22—42no—
246C22—82no—
247C22—82no—
248C22—82no—
249C22—164no—
250C22#1062283511yescharacteristic
251C4—21no—
252C4—22no—
253C4—82no—
254C4#1062285611yescharacteristic
255C4#1062285711yescharacteristic
256C2—21no—
257C2—42no—
258C2—41no—
259C2—162no—
260C2#1306986411yescharacteristic
subgroupG/H
centerC2#13069864
commutator, cosocleC2×C11×#41C23
FrattiniC2×#41C22×D11
Fitting, prime radicalC11×#3199C2
socleC2×C11#2044
hypercenter#3199D11
hypocenterC11#13429
LCSG ▷ C2×C11×#41 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #3199

Complements

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

NH ≅ G/Ntype
1. #13070308C2semidirect
2. #13069164C2semidirect
3. #13068835C2semidirect
4. #13066739C2semidirect
215. C11#13429semidirect

Maximal subgroups

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

subgroupindex
#130703082
#130691642
#130688352
#130667392
C11×#31992
#1342911