Finite Group Databasebeta

← #14674121

Subgroups — #14674121

Order 2816.

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

normal subgroups only

This group has 326 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#13070281C212yesmaximal
2#13066787C214yesmaximal, complemented
3C11×#3135C211yesmaximal, characteristic
4C11×#533C411yescharacteristic, complemented
5C11×#532C2211yescharacteristic
6C11×#491C412yescomplemented
7C11×#490C2212yes—
8C11×#489—22no—
9C11×#416—22no—
10C2×C11×#97C411yescharacteristic, complemented
11#10622853—22no—
12#10622183C2214yes—
13#10622179—22no—
14C2×C11×#41D412yes—
15C22×C8×C11—21no—
16C11×C4⋊Q8—21no—
17C11×C4⋊Q8C2×C411yescharacteristic
18C11×#127C2311yescharacteristic
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
27#66979—42no—
28C11×#103—24no—
29C11×#102—24no—
30C11×#97—21no—
31C11×#97C2×C412yes—
32#66898—24no—
33#66898—42no—
34#13594—111nomaximal, Sylow
35C11×#41—42no—
36C11×#41—42no—
37C2×Q8×C11—41no—
38C2×Q8×C11C22⋊C412yes—
39C2×D4×C11—22no—
40C2×D4×C11—41no—
41C2×D4×C11C2×D412yes—
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
58C22⋊Dic11—44no—
59C4⋊Dic11—82no—
60C4×Dic11—82no—
61#3135D1111yescharacteristic
62#2126—112no—
63#1412—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—21no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
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
82C2×Dic11—84no—
83C8×C11—42no—
84#533Dic1111yescharacteristic, complemented
85#532C2×D1111yescharacteristic
86#491Dic1112yescomplemented
87#490C2×D1112yes—
88#489—22no—
89#416—22no—
90#410—222no—
91C2×#97Dic1111yescharacteristic, complemented
92#354—222no—
93#353—114no—
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
106Dic11—164no—
107C2×#41C22⋊D1112yes—
108C22×C8—21no—
109C4⋊Q8—21no—
110C4⋊Q8C2×Dic1111yescharacteristic
111#127C22×D1111yescharacteristic
112#125C2×Dic1112yes—
113#124C22⋊D1112yes—
114C22⋊Q8—41no—
115#121—41no—
116C4×Q8—41no—
117C4×D4—41no—
118#117—21no—
119#117—442no—
120C2×C42C2×Dic1111yescharacteristic
121#103—24no—
122#102—24no—
123#99—224no—
124#99—442no—
125#97—21no—
126#97C2×Dic1112yes—
127C2×C11—21no—
128C2×C11—41no—
129C2×C11—82no—
130C2×C11C2×#35411yescharacteristic
131#41—42no—
132#41—42no—
133C2×Q8—41no—
134C2×Q8C22⋊Dic1112yes—
135C2×D4—22no—
136C2×D4—41no—
137C2×D4C2×C22⋊D1112yes—
138C22×C4—21no—
139C22×C4—22no—
140C22×C4C22⋊Dic1111yescharacteristic
141C2×C8—22no—
142C2×C8—41no—
143C2×C8—41no—
144C4⋊C4—22no—
145C4⋊C4—41no—
146C4⋊C4—42no—
147C4⋊C4—41no—
148C4⋊C4—882no—
149C22⋊C4—42no—
150C22⋊C4—41no—
151C22⋊C4—444no—
152C42—21no—
153C42—41no—
154C42—882no—
155C42C22⋊Dic1111yescharacteristic
156C42C22×Dic1111yescharacteristic
157C11#1359411yescharacteristic, complemented, Sylow
158C23—22no—
159C23#6689811yescharacteristic
160Q8—42no—
161Q8—82no—
162D4—42no—
163D4—82no—
164D4—82no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—81no—
174C2×C4—884no—
175C2×C4#6689811yescharacteristic
176C2×C4C2×C22⋊Dic1111yescharacteristic
177C8—42no—
178C22—21no—
179C22—41no—
180C22—42no—
181C22—82no—
182C22C2×#6689811yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—42no—
187C4—82no—
188C4—1764no—
189C4#1062217911yescharacteristic
190C4#1062217911yescharacteristic
191C2—21no—
192C2—41no—
193C2—82no—
194C2C2×#1062217911yescharacteristic
subgroupG/H
centerC4#10622179
commutatorC42×C11C22×C4
Frattini#127C22×D11
FittingC11×#3135C2
socleC2×C11C2×#354
prime radicalC11×#532C22
cosocleC11×#127C23
hypercenter#3135D11
hypocenterC11#13594
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. #13066787C2semidirect
4. C11×#533C4semidirect
6. C11×#491C4semidirect
10. C2×C11×#97C4semidirect
84. #533Dic11semidirect
86. #491Dic11semidirect
91. C2×#97Dic11semidirect
157. C11#13594semidirect

Maximal subgroups

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

subgroupindex
#130702812
#130667872
C11×#31352
#1359411