Finite Group Databasebeta

← #14667149

Subgroups — #14667149

Order 2816.

318 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 59 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#13070828C212yesmaximal, complemented
2#13070191C211yesmaximal, characteristic, complemented
3#13066601C212yesmaximal, complemented
4#13066567C211yesmaximal, characteristic, complemented
5C11×#3253C211yesmaximal, characteristic
6C11×#532—21no—
7C11×#476—22no—
8C11×#469—21no—
9C11×#469C2212yes—
10C11×#459—22no—
11C11×#423C2211yescharacteristic
12#10622738C2211yescharacteristic
13#10622201—22no—
14#10622197—21no—
15#10622195C2211yescharacteristic
16#10622191C2212yes—
17#10622161—21no—
18#10622125—22no—
19C2×C11×#41—41no—
20C2×C11×D8—21no—
21C2×C11×D8D412yes—
22C2×C11×M16D411yescharacteristic
23C2×C11×M16C2311yescharacteristic
24C11×C4⋊Q8—21no—
25C11×#127—21no—
26C11×#124—41no—
27C11×#121—22no—
28C11×#121—41no—
29C4×D4×C11—22no—
30C4×D4×C11—41no—
31C2×C42×C11D411yescharacteristic
32#66979—21no—
33C2×#4318—21no—
34C11×#106—21no—
35C11×#106D412yes—
36C11×C4⋊C8—22no—
37C11×#102—22no—
38C11×#102—22no—
39#66883—22no—
40#66876—22no—
41#12307—111nomaximal, Sylow
42C11×#41—84no—
43C2×Q8×C11—41no—
44C2×D4×C11—22no—
45C2×D4×C11—41no—
46C2×D4×C11—41no—
47C2×D4×C11—42no—
48C22×C4×C11—21no—
49C22×C4×C11—42no—
50C22×C4×C11C2×D411yescharacteristic
51C11×D8—42no—
52C11×D8—81no—
53C11×M16—41no—
54C11×M16—41no—
55C2×C8×C11—21no—
56C2×C8×C11C2×D412yes—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—41no—
59C11×C22⋊C4—42no—
60C11×C22⋊C4—42no—
61C42×C11—21no—
62C42×C11SD1611yescharacteristic
63C42×C11SD1611yescharacteristic
64C22⋊Dic11—41no—
65C4⋊Dic11—41no—
66C4×Dic11—41no—
67#4318—41no—
68#4318—41no—
69C2×C11⋊C8—41no—
70C11⋊C16—42no—
71#3253D1111yescharacteristic
72#2238—112no—
73#2102—111no—
74#1339—112no—
75#1327—111no—
76C23×C11—42no—
77C23×C11AGL(1,ℤ/8)11yescharacteristic
78Q8×C11—82no—
79D4×C11—42no—
80D4×C11—42no—
81D4×C11—82no—
82D4×C11—82no—
83D4×C11—84no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—42no—
89C2×C4×C11—42no—
90C2×C4×C11—84no—
91C2×C4×C11#12011yescharacteristic
92C2×C4×C11C2×SD1611yescharacteristic
93C2×Dic11—81no—
94C8×C11—22no—
95C8×C11—41no—
96C11⋊C8—81no—
97#532—21no—
98#476—22no—
99#469—21no—
100#469C2×D1112yes—
101#459—22no—
102#430—111no—
103#423C2×D1111yescharacteristic
104#365—222no—
105#361—222no—
106#349—112no—
107#344—221no—
108#339—221no—
109H(3,ℤ/4)—111no—
110C22×C11—21no—
111C22×C11—41no—
112C22×C11—82no—
113C22×C11—82no—
114C22×C11—82no—
115C22×C11#45011yescharacteristic
116C4×C11—22no—
117C4×C11—21no—
118C4×C11—41no—
119C4×C11—82no—
120C4×C11#45411yescharacteristic
121C4×C11#45811yescharacteristic
122Dic11—161no—
123C2×#41—41no—
124C2×D8—21no—
125C2×D8C22⋊D1112yes—
126C2×M16—221no—
127C2×M16C22⋊D1111yescharacteristic
128C2×M16C22×D1111yescharacteristic
129C4⋊Q8—21no—
130#127—21no—
131#124—41no—
132#121—22no—
133#121—41no—
134C4×D4—22no—
135C4×D4—41no—
136#117—221no—
137C2×C42C22⋊D1111yescharacteristic
138M32—222no—
139#108—222no—
140#106—21no—
141#106C22⋊D1112yes—
142C4⋊C8—22no—
143#102—22no—
144#102—22no—
145C2×C11—21no—
146C2×C11—41no—
147C2×C11—162no—
148C2×C11#161611yescharacteristic
149#41—84no—
150C2×Q8—41no—
151C2×D4—22no—
152C2×D4—41no—
153C2×D4—41no—
154C2×D4—42no—
155C22×C4—21no—
156C22×C4—42no—
157C22×C4C2×C22⋊D1111yescharacteristic
158D8—42no—
159D8—81no—
160M16—41no—
161M16—41no—
162M16—441no—
163M16—441no—
164C2×C8—21no—
165C2×C8—441no—
166C2×C8C2×C22⋊D1112yes—
167C4⋊C4—22no—
168C4⋊C4—41no—
169C4⋊C4—441no—
170C22⋊C4—42no—
171C22⋊C4—42no—
172C22⋊C4—441no—
173C42—21no—
174C42—441no—
175C42#432411yescharacteristic
176C42#432411yescharacteristic
177C16—442no—
178C11#1230711yescharacteristic, complemented, Sylow
179C23—42no—
180C23#6698511yescharacteristic
181Q8—82no—
182D4—42no—
183D4—42no—
184D4—82no—
185D4—82no—
186D4—84no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—84no—
194C2×C4—881no—
195C2×C4C2×#432411yescharacteristic
196C2×C4#6700611yescharacteristic
197C8—22no—
198C8—41no—
199C8—881no—
200C22—21no—
201C22—41no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22#1062283111yescharacteristic
206C4—22no—
207C4—21no—
208C4—41no—
209C4—82no—
210C4—1761no—
211C4#1062285611yescharacteristic
212C4#1062285811yescharacteristic
213C2—21no—
214C2—41no—
215C2—162no—
216C2#1306765311yescharacteristic
subgroupG/H
centerC2#13067653
commutator, cosocleC2×C11×M16C23
FrattiniC2×M16C22×D11
Fitting, prime radicalC11×#3253C2
socleC2×C11#1616
hypercenter#3253D11
hypocenterC11#12307
LCSG ▷ C2×C11×M16 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #13070828C2semidirect
2. #13070191C2semidirect
3. #13066601C2semidirect
4. #13066567C2semidirect
178. C11#12307semidirect

Maximal subgroups

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

subgroupindex
#130708282
#130701912
#130666012
#130665672
C11×#32532
#1230711