Finite Group Databasebeta

← #27186466

Subgroups — #27186466

Order 12928.

246 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 66 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#20266199C211yesmaximal, characteristic, complemented
2#20266196C211yesmaximal, characteristic, complemented
3Q8⋊#11717581C212yesmaximal, complemented
4#20266025C212yesmaximal, complemented
5C4×#13108075C211yesmaximal, characteristic
6C4⋊#11717581—21no—
7C4⋊#11717581C2212yes—
8#15692312—21no—
9#15692312—21no—
10#15692310—21no—
11C4×#11717581C2212yes—
12C2×#13108075C411yescharacteristic
13Q8×Dic101C2211yescharacteristic
14C4×D404—21no—
15C4×D404C411yescharacteristic
16#15692217—21no—
17#15692217C2211yescharacteristic
18#15692213—21no—
19#15692213C411yescharacteristic
20C42×D101—21no—
21C42×D101C2211yescharacteristic
22C4×Q8×C101C411yescharacteristic
23C2×#11717581—22no—
24C2×#11717581—22no—
25#13108075—22no—
26#13108075—22no—
27C2×D404—21no—
28C2×D404C2×C411yescharacteristic
29C2×C4×D101—21no—
30C2×C4×D101—21no—
31C2×C4×D101—21no—
32C2×C4×D101C2×C411yescharacteristic
33C2×C4×D101D411yescharacteristic
34C2×C4×D101D411yescharacteristic
35C4⋊Dic101—21no—
36C4⋊Dic101C2×C411yescharacteristic
37#13108051—21no—
38#13108051—21no—
39#13108051—21no—
40C4×Dic101—21no—
41C4×Dic101—21no—
42C4×Dic101D411yescharacteristic
43C4×Dic101D411yescharacteristic
44C4×Dic101C2311yescharacteristic
45C2×Q8×C101C2×C411yescharacteristic
46C4⋊C4×C101—21no—
47C4⋊C4×C101C2×C411yescharacteristic
48C42×C101—21no—
49C42×C101C2×C411yescharacteristic
50C22×D101—21no—
51C22×D101C22⋊C411yescharacteristic
52Q8×C101—21no—
53Q8×C101M1612yes—
54C2×C4×C101—21no—
55C2×C4×C101—21no—
56C2×C4×C101C22⋊C411yescharacteristic
57C2×C4×C101C22⋊C411yescharacteristic
58C2×C4×C101C22×C411yescharacteristic
59C2×Dic101—21no—
60C2×Dic101C22⋊C411yescharacteristic
61C2×Dic101C2×D411yescharacteristic
62C2×Dic101C2×D411yescharacteristic
63D404—24no—
64D404—21no—
65D404M1612yes—
66C4×D101—24no—
67C4×D101—21no—
68C4×D101—21no—
69C4×D101—22no—
70C4×D101—41no—
71C4×D101—42no—
72C4×D101—42no—
73#11717581—42no—
74#11717581—42no—
75C22×C101C2×C22⋊C411yescharacteristic
76C2×D101—21no—
77C2×D101—22no—
78C2×D101—21no—
79C2×D101—21no—
80C2×D101—41no—
81C2×D101—41no—
82C4×C101—22no—
83C4×C101—21no—
84C4×C101—21no—
85C4×C101—41no—
86C4×C101C2×M1611yescharacteristic
87C4×C101C2×M1611yescharacteristic
88Dic101—21no—
89Dic101—21no—
90Dic101—41no—
91Dic101#13512yes—
92C2×C101#40711yescharacteristic
93C2×C101#41611yescharacteristic
94C2×C101#42111yescharacteristic
95D101—41no—
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#8793811yescharacteristic
107C4×D4—1011no—
108C4×D4—1011no—
109C4×D4—2021no—
110C4×D4—2021no—
111#117—1011no—
112#117—2021no—
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×Q8C2×#8793811yescharacteristic
124C2×D4—1011no—
125C2×D4—2021no—
126C22×C4—1011no—
127C22×C4—1011no—
128C22×C4—1011no—
129C22×C4—2021no—
130C22×C4—2021no—
131C22×C4—2021no—
132C2×C8—2022no—
133C2×C8—2022no—
134C4⋊C4—21no—
135C4⋊C4—1011no—
136C4⋊C4—2021no—
137C4⋊C4C2×#8793811yescharacteristic
138C22⋊C4—2021no—
139C22⋊C4—2021no—
140C22⋊C4—2021no—
141C42—21no—
142C42—1011no—
143C42—1011no—
144C42—1011no—
145C42—2021no—
146C42—2021no—
147C42C2×#8793811yescharacteristic
148C23—1011no—
149C23—2021no—
150Q8—21no—
151Q8#1310808412yes—
152D4—1012no—
153D4—2024no—
154D4—2021no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—1011no—
158C2×C4—1011no—
159C2×C4—1011no—
160C2×C4—4042no—
161C2×C4—4041no—
162C2×C4—4042no—
163C2×C4—2022no—
164C2×C4—2024no—
165C2×C4—2021no—
166C2×C4—2021no—
167C2×C4—2021no—
168C2×C4C22⋊#8793811yescharacteristic
169C2×C4C22⋊#8793811yescharacteristic
170C2×C4C22×#8793811yescharacteristic
171C8—4042no—
172C8—4042no—
173C22—4041no—
174C22—4041no—
175C22—2022no—
176C22—2021no—
177C22—2021no—
178C22—2021no—
179C22C2×C22⋊#8793811yescharacteristic
180C4—22no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—1012no—
185C4—4041no—
186C4—2021no—
187C4—2021no—
188C4D101⋊M1611yescharacteristic
189C4C2×#1310808411yescharacteristic
190C2—4042no—
191C2—4041no—
192C2#2026614811yescharacteristic
193C2#2026616711yescharacteristic
194C2#2026617611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4×Q8×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC2×#13108075C4
cosocleC4×Dic101C23
hypercenterC4×Q8#87938
hypocenterC101#1488
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #20266199C2semidirect
2. #20266196C2semidirect
3. Q8⋊#11717581C2semidirect
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
#202661992
#202661962
Q8⋊#117175812
#202660252
C4×#131080752
#1488101