Finite Group Databasebeta

← #27186463

Subgroups — #27186463

Order 12928.

246 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 68 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
3Q8⋊#11717581C212yesmaximal, complemented
4D4⋊#11717581C212yesmaximal, complemented
5#41×Dic101C211yesmaximal, characteristic
6#15692322—21no—
7C4⋊#11717581C2212yes—
8C22⋊#11717581—21no—
9C22⋊#11717581—21no—
10#15692310—21no—
11C4×#11717581C2212yes—
12Q8×Dic101C411yescharacteristic
13Q8×Dic101C2211yescharacteristic
14D4×Dic101—21no—
15D4×Dic101—21no—
16D4×Dic101C411yescharacteristic
17D4×Dic101C2211yescharacteristic
18#15692214—21no—
19#15692214C411yescharacteristic
20C2×C4×Dic101—21no—
21C2×C4×Dic101C2211yescharacteristic
22C2×#41×C101C411yescharacteristic
23C2×#11717581—22no—
24C2×#11717581—22no—
25C22×Dic101—21no—
26C22×Dic101—21no—
27C22×Dic101D411yescharacteristic
28C22×Dic101D411yescharacteristic
29C4⋊Dic101—21no—
30C4⋊Dic101—21no—
31C4⋊Dic101C2×C411yescharacteristic
32C4⋊Dic101C2×C411yescharacteristic
33C22⋊Dic101—21no—
34C22⋊Dic101—21no—
35C22⋊Dic101—21no—
36C4×Dic101—21no—
37C4×Dic101—21no—
38C4×Dic101—21no—
39C4×Dic101C2×C411yescharacteristic
40C4×Dic101D411yescharacteristic
41C4×Dic101D411yescharacteristic
42C4×Dic101C2311yescharacteristic
43#41×C101—22no—
44#41×C101—22no—
45C2×Q8×C101C2×C411yescharacteristic
46C2×D4×C101—21no—
47C2×D4×C101C2×C411yescharacteristic
48C22×C4×C101—21no—
49C22×C4×C101C2×C411yescharacteristic
50C23×C101—21no—
51C23×C101C22⋊C411yescharacteristic
52Q8×C101—21no—
53Q8×C101M1612yes—
54D4×C101—24no—
55D4×C101—21no—
56D4×C101M1612yes—
57C2×C4×C101—24no—
58C2×C4×C101—21no—
59C2×C4×C101—21no—
60C2×C4×C101—21no—
61C2×C4×C101C22⋊C411yescharacteristic
62C2×C4×C101C22×C411yescharacteristic
63C2×Dic101—22no—
64C2×Dic101—21no—
65C2×Dic101—21no—
66C2×Dic101—41no—
67C2×Dic101—42no—
68C2×Dic101—42no—
69C2×Dic101C22⋊C411yescharacteristic
70C2×Dic101C22⋊C411yescharacteristic
71C2×Dic101C2×D411yescharacteristic
72C2×Dic101C2×D411yescharacteristic
73#11717581—42no—
74#11717581—42no—
75C22×C101—21no—
76C22×C101—22no—
77C22×C101—21no—
78C22×C101—21no—
79C22×C101—41no—
80C22×C101—41no—
81C22×C101C2×C22⋊C411yescharacteristic
82C4×C101—21no—
83C4×C101—22no—
84C4×C101C2×M1611yescharacteristic
85C4×C101C2×M1611yescharacteristic
86Dic101—21no—
87Dic101—21no—
88Dic101—21no—
89Dic101—41no—
90Dic101—41no—
91Dic101#13512yes—
92C2×C101—41no—
93C2×C101—42no—
94C2×C101#40711yescharacteristic
95C2×C101#41611yescharacteristic
96C2×C101#42111yescharacteristic
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#8793811yescharacteristic
105C4×Q8—1011no—
106C4×Q8—1011no—
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—22no—
122#41—22no—
123C2×Q8C2×#8793811yescharacteristic
124C2×D4—21no—
125C2×D4C2×#8793811yescharacteristic
126C22×C4—21no—
127C22×C4—1011no—
128C22×C4—1011no—
129C22×C4—2021no—
130C22×C4—2021no—
131C22×C4C2×#8793811yescharacteristic
132C2×C8—2022no—
133C2×C8—2022no—
134C4⋊C4—1011no—
135C4⋊C4—1011no—
136C4⋊C4—2021no—
137C4⋊C4—2021no—
138C22⋊C4—2021no—
139C22⋊C4—2021no—
140C22⋊C4—2021no—
141C42—1011no—
142C42—1011no—
143C42—1011no—
144C42—1011no—
145C42—2021no—
146C42—2021no—
147C42—2021no—
148C23—21no—
149C23C22⋊#8793811yescharacteristic
150Q8—21no—
151Q8#1310808312yes—
152D4—24no—
153D4—21no—
154D4#1310808312yes—
155C2×C4—24no—
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—2022no—
167C2×C4—2021no—
168C2×C4—2021no—
169C2×C4C22⋊#8793811yescharacteristic
170C2×C4C22×#8793811yescharacteristic
171C8—4042no—
172C8—4042no—
173C22—21no—
174C22—22no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22C2×C22⋊#8793811yescharacteristic
180C4—21no—
181C4—22no—
182C4—1012no—
183C4—4041no—
184C4—4041no—
185C4—2021no—
186C4—2021no—
187C4—2021no—
188C4C2×#1310808311yescharacteristic
189C4C2×#1310808311yescharacteristic
190C2—41no—
191C2—42no—
192C2#2026614711yescharacteristic
193C2#2026616711yescharacteristic
194C2#2026617411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting, prime radicalC2×#41×C101C4
socleC22×C101C2×C22⋊C4
cosocleC4×Dic101C23
hypercenterC2×#41#87938
hypocenterC101#1488
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #20266198C2semidirect
2. #20266194C2semidirect
3. Q8⋊#11717581C2semidirect
4. D4⋊#11717581C2semidirect
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
Q8⋊#117175812
D4⋊#117175812
#41×Dic1012
#1488101