Finite Group Databasebeta

← #27186617

Subgroups — #27186617

Order 12928.

200 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 54 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#20266198C211yesmaximal, characteristic, complemented
2#20266197C211yesmaximal, characteristic, complemented
3#20266034C212yesmaximal, complemented
4#20266032C212yesmaximal, complemented
5#20265708C211yesmaximal, characteristic
6#15692322—21no—
7C4⋊#11717581—21no—
8C22⋊#11717581—21no—
9C22⋊#11717581—21no—
10#15692310C2212yes—
11#15692310C2212yes—
12#15692248—21no—
13#15692246C2211yescharacteristic
14#15692242C2211yescharacteristic
15#15692236—21no—
16#15692234C411yescharacteristic
17#15692220C411yescharacteristic
18D4×Dic101—21no—
19D4×Dic101C411yescharacteristic
20#15692211—21no—
21C2×C4×Dic101C2211yescharacteristic
22#121×C101C411yescharacteristic
23C2×#11717581—22no—
24C2×#11717581—22no—
25C2×Dic202C2×C411yescharacteristic
26C22×Dic101—21no—
27C22×Dic101D411yescharacteristic
28C22×Dic101D411yescharacteristic
29C4⋊Dic101—21no—
30C4⋊Dic101C2×C411yescharacteristic
31#13108053—21no—
32#13108053—21no—
33#13108053—21no—
34C22⋊Dic101—21no—
35C22⋊Dic101—21no—
36C22⋊Dic101—21no—
37C22⋊Dic101—21no—
38C4×Dic101—21no—
39C4×Dic101C2×C411yescharacteristic
40C4×Dic101D411yescharacteristic
41C4×Dic101D411yescharacteristic
42C4×Dic101C2311yescharacteristic
43C2×D4×C101—21no—
44C2×D4×C101C2×C411yescharacteristic
45C22×C4×C101C2×C411yescharacteristic
46C4⋊C4×C101C2×C411yescharacteristic
47C22⋊C4×C101—21no—
48C23×C101—21no—
49C23×C101C22⋊C411yescharacteristic
50D4×C101—41no—
51D4×C101—42no—
52C2×C4×C101—21no—
53C2×C4×C101—41no—
54C2×C4×C101C22⋊C411yescharacteristic
55C2×C4×C101C22×C411yescharacteristic
56C2×Dic101—21no—
57C2×Dic101—21no—
58C2×Dic101—41no—
59C2×Dic101—41no—
60C2×Dic101—42no—
61C2×Dic101C22⋊C411yescharacteristic
62C2×Dic101C22⋊C411yescharacteristic
63C2×Dic101C2×D411yescharacteristic
64C2×Dic101C2×D411yescharacteristic
65Dic202—41no—
66#11717581—42no—
67#11717581—42no—
68C22×C101—21no—
69C22×C101—21no—
70C22×C101—21no—
71C22×C101—41no—
72C22×C101—41no—
73C22×C101—41no—
74C22×C101C2×C22⋊C411yescharacteristic
75C4×C101—21no—
76C4×C101—21no—
77C4×C101—41no—
78Dic101—21no—
79Dic101—21no—
80Dic101—21no—
81Dic101—21no—
82Dic101—41no—
83Dic101—41no—
84C2×C101—41no—
85C2×C101—81no—
86C2×C101#41311yescharacteristic
87C2×C101#42111yescharacteristic
88C2×C101#42111yescharacteristic
89#1535—1011nomaximal, Sylow
90C101#153511yescharacteristic, complemented, Sylow
91#529—1011no—
92#432—1011no—
93#432—1011no—
94#330—1012no—
95#329—1012no—
96#126—2021no—
97#125—1011no—
98#124—1011no—
99#123—2021no—
100C22⋊Q8—1011no—
101#121#8793811yescharacteristic
102C4×Q8—1011no—
103C4×D4—1011no—
104C4×D4—2021no—
105#117—2021no—
106C2×C42—1011no—
107C4⋊C8—2021no—
108C4⋊C8—2021no—
109C22⋊C8—2021no—
110C22⋊C8—2021no—
111#97—1012no—
112#97—1012no—
113C2×Q8—1011no—
114C2×D4—21no—
115C2×D4C2×#8793811yescharacteristic
116C22×C4—1011no—
117C22×C4—1011no—
118C22×C4—2021no—
119C22×C4C2×#8793811yescharacteristic
120C2×C8—2022no—
121C2×C8—2022no—
122C4⋊C4—1011no—
123C4⋊C4—2021no—
124C4⋊C4—2021no—
125C4⋊C4—2021no—
126C4⋊C4—2021no—
127C4⋊C4C2×#8793811yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—2021no—
130C22⋊C4—2021no—
131C22⋊C4—2021no—
132C22⋊C4—2021no—
133C42—1011no—
134C42—1011no—
135C42—1011no—
136C42—1011no—
137C42—2021no—
138C23—21no—
139C23C22⋊#8793811yescharacteristic
140Q8—4041no—
141D4—41no—
142D4—42no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—1011no—
146C2×C4—1011no—
147C2×C4—1011no—
148C2×C4—1011no—
149C2×C4—4042no—
150C2×C4—4041no—
151C2×C4—4041no—
152C2×C4—2021no—
153C2×C4—2021no—
154C2×C4C22⋊#8793811yescharacteristic
155C2×C4C22×#8793811yescharacteristic
156C8—4042no—
157C8—4042no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—41no—
162C22—41no—
163C22—41no—
164C22C2×C22⋊#8793811yescharacteristic
165C4—21no—
166C4—21no—
167C4—41no—
168C4—4041no—
169C4—4041no—
170C4—2021no—
171C4—2021no—
172C4—2021no—
173C4—2021no—
174C2—41no—
175C2—81no—
176C2#2026616411yescharacteristic
177C2#2026617411yescharacteristic
178C2#2026617511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting, prime radical#121×C101C4
socleC22×C101C2×C22⋊C4
cosocleC4×Dic101C23
hypercenter#121#87938
hypocenterC101#1535
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #20266198C2semidirect
2. #20266197C2semidirect
3. #20266034C2semidirect
4. #20266032C2semidirect
90. C101#1535semidirect

Maximal subgroups

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

subgroupindex
#202661982
#202661972
#202660342
#202660322
#202657082
#1535101