Finite Group Databasebeta

← #14674133

Subgroups — #14674133

Order 2816.

318 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 79 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#13070301C212yesmaximal
2#13066789C214yesmaximal, complemented
3C11×#3135C211yesmaximal, characteristic
4C11×#533C411yescharacteristic
5C11×#532C2211yescharacteristic
6C11×#491C2212yes—
7C11×#490C412yes—
8C11×#489—22no—
9C11×#416—22no—
10C2×C11×#97C411yescharacteristic
11#10622850—22no—
12#10622186C2214yes—
13#10622180—22no—
14C2×C11×#41D412yes—
15C22×C8×C11—21no—
16C11×C4⋊Q8—21no—
17C11×C4⋊Q8C2311yescharacteristic
18C11×#127C2×C411yescharacteristic
19C11×#125C2×C412yes—
20C11×#124D412yes—
21C11×C22⋊Q8—41no—
22C11×#121—41no—
23C4×Q8×C11—41no—
24C4×D4×C11—41no—
25C11×#117—21no—
26C2×C42×C11C2×C411yescharacteristic
27C2×#4318—42no—
28C11×#103—24no—
29C11×#102—24no—
30C11×#97—21no—
31C11×#97C2×C412yes—
32#66900—24no—
33#66897—42no—
34#13598—111nomaximal, Sylow
35C11×#41—42no—
36C11×#41—42no—
37C2×Q8×C11—41no—
38C2×Q8×C11C2×D412yes—
39C2×D4×C11—22no—
40C2×D4×C11—41no—
41C2×D4×C11C22⋊C412yes—
42C22×C4×C11—21no—
43C22×C4×C11—22no—
44C22×C4×C11C22⋊C411yescharacteristic
45C2×C8×C11—22no—
46C2×C8×C11—41no—
47C2×C8×C11—41no—
48C11×C4⋊C4—22no—
49C11×C4⋊C4—41no—
50C11×C4⋊C4—41no—
51C11×C4⋊C4—42no—
52C11×C22⋊C4—42no—
53C11×C22⋊C4—41no—
54C42×C11—21no—
55C42×C11—41no—
56C42×C11C22⋊C411yescharacteristic
57C42×C11C22×C411yescharacteristic
58#4318—44no—
59#4318—82no—
60C2×C11⋊C8—82no—
61#3135D1111yescharacteristic
62#2132—112no—
63#1413—114no—
64C23×C11—22no—
65C23×C11#9911yescharacteristic
66Q8×C11—42no—
67Q8×C11—82no—
68D4×C11—42no—
69D4×C11—82no—
70D4×C11—82no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—42no—
77C2×C4×C11—42no—
78C2×C4×C11—42no—
79C2×C4×C11—81no—
80C2×C4×C11#9911yescharacteristic
81C2×C4×C11C2×C22⋊C411yescharacteristic
82C8×C11—42no—
83C11⋊C8—84no—
84#533Dic1111yescharacteristic
85#532C2×D1111yescharacteristic
86#491C2×D1112yes—
87#490Dic1112yes—
88#489—22no—
89#416—22no—
90#413—222no—
91C2×#97Dic1111yescharacteristic
92#356—114no—
93#355—222no—
94C22×C11—21no—
95C22×C11—41no—
96C22×C11—42no—
97C22×C11—82no—
98C22×C11C2×#9911yescharacteristic
99C4×C11—21no—
100C4×C11—41no—
101C4×C11—41no—
102C4×C11—42no—
103C4×C11—82no—
104C4×C11#35411yescharacteristic
105C4×C11#35411yescharacteristic
106C2×#41C22⋊D1112yes—
107C2×M16—442no—
108C22×C8—21no—
109C4⋊Q8—21no—
110C4⋊Q8C22×D1111yescharacteristic
111#127C2×Dic1111yescharacteristic
112#125C2×Dic1112yes—
113#124C22⋊D1112yes—
114C22⋊Q8—41no—
115#121—41no—
116C4×Q8—41no—
117C4×D4—41no—
118#117—21no—
119C2×C42C2×Dic1111yescharacteristic
120#103—24no—
121#102—24no—
122#101—224no—
123#100—442no—
124#97—21no—
125#97C2×Dic1112yes—
126C2×C11—21no—
127C2×C11—41no—
128C2×C11—82no—
129C2×C11C2×#35411yescharacteristic
130#41—42no—
131#41—42no—
132C2×Q8—41no—
133C2×Q8C2×C22⋊D1112yes—
134C2×D4—22no—
135C2×D4—41no—
136C2×D4C22⋊Dic1112yes—
137C22×C4—21no—
138C22×C4—22no—
139C22×C4C22⋊Dic1111yescharacteristic
140M16—444no—
141M16—882no—
142C2×C8—22no—
143C2×C8—41no—
144C2×C8—41no—
145C2×C8—882no—
146C4⋊C4—22no—
147C4⋊C4—41no—
148C4⋊C4—42no—
149C4⋊C4—41no—
150C22⋊C4—42no—
151C22⋊C4—41no—
152C42—21no—
153C42—41no—
154C42C22⋊Dic1111yescharacteristic
155C42C22×Dic1111yescharacteristic
156C11#1359811yescharacteristic, complemented, Sylow
157C23—22no—
158C23#6689811yescharacteristic
159Q8—42no—
160Q8—82no—
161D4—42no—
162D4—82no—
163D4—82no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—81no—
173C2×C4#6689811yescharacteristic
174C2×C4C2×C22⋊Dic1111yescharacteristic
175C8—42no—
176C8—884no—
177C22—21no—
178C22—41no—
179C22—42no—
180C22—82no—
181C22C2×#6689811yescharacteristic
182C4—21no—
183C4—41no—
184C4—41no—
185C4—42no—
186C4—82no—
187C4#1062217911yescharacteristic
188C4#1062217911yescharacteristic
189C2—21no—
190C2—41no—
191C2—82no—
192C2C2×#1062217911yescharacteristic
subgroupG/H
centerC4#10622179
commutatorC42×C11C22×C4
FrattiniC4⋊Q8C22×D11
FittingC11×#3135C2
socleC2×C11C2×#354
prime radicalC11×#532C22
cosocleC11×C4⋊Q8C23
hypercenter#3135D11
hypocenterC11#13598
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #3135

Complements

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

NH ≅ G/Ntype
2. #13066789C2semidirect
156. C11#13598semidirect

Maximal subgroups

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

subgroupindex
#130703012
#130667892
C11×#31352
#1359811