Finite Group Databasebeta

← #27186465

Subgroups — #27186465

Order 12928.

246 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 64 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#20266194C211yesmaximal, characteristic, complemented
3#20266027C212yesmaximal, complemented
4#20266025C212yesmaximal, complemented
5#20265645C211yesmaximal, characteristic
6#15692322—21no—
7C4⋊#11717581C2212yes—
8C22⋊#11717581—21no—
9C22⋊#11717581—21no—
10#15692310—21no—
11C4×#11717581C2212yes—
12C2×#13108074C411yescharacteristic
13#15692220C411yescharacteristic
14#15692220C2211yescharacteristic
15#15692217C411yescharacteristic
16#15692217C2211yescharacteristic
17#15692215—21no—
18#15692215—21no—
19#15692212—21no—
20C2×C4×Dic101C2211yescharacteristic
21C42×D101—21no—
22#117×C101C411yescharacteristic
23C2×#11717581—22no—
24C2×#11717581—22no—
25#13108074—22no—
26#13108074—22no—
27C2×Dic202C2×C411yescharacteristic
28C2×D404C2×C411yescharacteristic
29C2×C22⋊D101—21no—
30C22×Dic101D411yescharacteristic
31C22×Dic101D411yescharacteristic
32C2×C4×D101—21no—
33C2×C4×D101—21no—
34C2×C4×D101—21no—
35#13108053—21no—
36#13108053—21no—
37#13108051—21no—
38#13108051—21no—
39C4×Dic101—21no—
40C4×Dic101—21no—
41C4×Dic101C2×C411yescharacteristic
42C4×Dic101D411yescharacteristic
43C4×Dic101D411yescharacteristic
44C4×Dic101C2311yescharacteristic
45C22×C4×C101C2×C411yescharacteristic
46C4⋊C4×C101C2×C411yescharacteristic
47C4⋊C4×C101C2×C411yescharacteristic
48C22⋊C4×C101—21no—
49C42×C101—21no—
50C23×C101C22⋊C411yescharacteristic
51C22×D101—21no—
52C2×C4×C101—21no—
53C2×C4×C101—21no—
54C2×C4×C101—21no—
55C2×C4×C101—21no—
56C2×C4×C101C22⋊C411yescharacteristic
57C2×C4×C101C22×C411yescharacteristic
58C22⋊D101—24no—
59C2×Dic101—21no—
60C2×Dic101—22no—
61C2×Dic101—41no—
62C2×Dic101C22⋊C411yescharacteristic
63C2×Dic101C22⋊C411yescharacteristic
64C2×Dic101C2×D411yescharacteristic
65C2×Dic101C2×D411yescharacteristic
66D404—21no—
67D404M1612yes—
68C4×D101—24no—
69C4×D101—42no—
70C4×D101—42no—
71Dic202—21no—
72Dic202M1612yes—
73#11717581—42no—
74#11717581—42no—
75C22×C101—21no—
76C22×C101—21no—
77C22×C101—21no—
78C22×C101C2×C22⋊C411yescharacteristic
79C2×D101—22no—
80C2×D101—41no—
81C2×D101—41no—
82C4×C101—21no—
83C4×C101—41no—
84C4×C101—41no—
85C4×C101C2×M1611yescharacteristic
86C4×C101C2×M1611yescharacteristic
87Dic101—22no—
88Dic101—21no—
89Dic101—21no—
90Dic101—21no—
91Dic101#13512yes—
92C2×C101—41no—
93C2×C101#40711yescharacteristic
94C2×C101#41611yescharacteristic
95C2×C101#42111yescharacteristic
96D101—42no—
97#1488—1011nomaximal, Sylow
98C101#148811yescharacteristic, complemented, Sylow
99C4×#41—1011no—
100#432—1011no—
101#431—1011no—
102Q8⋊C8—1012no—
103D4⋊C8—1012no—
104C2×#41—1011no—
105C4×Q8—1011no—
106C4×Q8—1011no—
107C4×D4—1011no—
108C4×D4—1011no—
109C4×D4—2021no—
110C4×D4—2021no—
111#117—2021no—
112#117#8793811yescharacteristic
113C2×C42—1011no—
114C2×C42—2021no—
115C4⋊C8—1012no—
116C4⋊C8—2021no—
117C22⋊C8—2021no—
118C22⋊C8—2021no—
119#97—2021no—
120C4×C8—1012no—
121#41—2022no—
122#41—2022no—
123C2×Q8—1011no—
124C2×D4—1011no—
125C2×D4—2021no—
126C22×C4—1011no—
127C22×C4—1011no—
128C22×C4—2021no—
129C22×C4—2021no—
130C22×C4—2021no—
131C22×C4C2×#8793811yescharacteristic
132C2×C8—2022no—
133C2×C8—2022no—
134C4⋊C4—2021no—
135C4⋊C4—2021no—
136C4⋊C4C2×#8793811yescharacteristic
137C4⋊C4C2×#8793811yescharacteristic
138C22⋊C4—21no—
139C22⋊C4—2021no—
140C22⋊C4—2021no—
141C42—21no—
142C42—1011no—
143C42—1011no—
144C42—1011no—
145C42—1011no—
146C42—2021no—
147C42—2021no—
148C23—2021no—
149C23C22⋊#8793811yescharacteristic
150Q8—1012no—
151Q8—2021no—
152D4—1012no—
153D4—2024no—
154D4—2021no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—1011no—
160C2×C4—1011no—
161C2×C4—1011no—
162C2×C4—1011no—
163C2×C4—4042no—
164C2×C4—4042no—
165C2×C4—4041no—
166C2×C4—2024no—
167C2×C4—2022no—
168C2×C4—2021no—
169C2×C4C22⋊#8793811yescharacteristic
170C2×C4C22×#8793811yescharacteristic
171C8—4042no—
172C8—4042no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—4041no—
177C22—4041no—
178C22—2022no—
179C22C2×C22⋊#8793811yescharacteristic
180C4—21no—
181C4—41no—
182C4—41no—
183C4—1012no—
184C4—2022no—
185C4—2021no—
186C4—2021no—
187C4—2021no—
188C4D101⋊M1611yescharacteristic
189C4D101⋊M1611yescharacteristic
190C2—41no—
191C2—4042no—
192C2#2026614911yescharacteristic
193C2#2026616711yescharacteristic
194C2#2026617411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#117×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC2×#13108074C4
cosocleC4×Dic101C23
hypercenter#117#87938
hypocenterC101#1488
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #20266198C2semidirect
2. #20266194C2semidirect
3. #20266027C2semidirect
4. #20266025C2semidirect
98. C101#1488semidirect

Maximal subgroups

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

subgroupindex
#202661982
#202661942
#202660272
#202660252
#202656452
#1488101