Finite Group Databasebeta

← #27187135

Subgroups — #27187135

Order 12928.

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

normal subgroups only

This group has 332 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#20266255C211yesmaximal, characteristic, complemented
2#20266175C212yesmaximal, complemented
3#20266157C211yesmaximal, characteristic, complemented
4#20266048C212yesmaximal, complemented
5#20265725C211yesmaximal, characteristic
6#15692342—24no—
7D101⋊M16C2212yes—
8C2×#13108083—22no—
9#15692334C2212yes—
10#15692319—24no—
11#15692313—22no—
12C2×#13108073C2211yescharacteristic
13C2×#13108073C2211yescharacteristic
14#15692255C411yescharacteristic, complemented
15#15692242C411yescharacteristic, complemented
16#15692242C411yescharacteristic, complemented
17#15692226—22no—
18D4×Dic101—22no—
19C42×D101C2211yescharacteristic
20#127×C101C411yescharacteristic, complemented
21#13108084D414yescomplemented
22#13108083—24no—
23#13108083—22no—
24D101⋊C8—22no—
25C2×#11717581—24no—
26C4⋊#87938—22no—
27C22⋊#87938—22no—
28C4×#87938—22no—
29#13108073—22no—
30#13108073—22no—
31#13108073—22no—
32#13108073—22no—
33C2×Dic202C2×C411yescharacteristic
34C2×Dic202C2×C411yescharacteristic
35C2×C22⋊D101—21no—
36C2×C22⋊D101D412yes—
37C22×Dic101—21no—
38C22×Dic101D412yes—
39C2×C4×D101—21no—
40C2×C4×D101C2311yescharacteristic
41C4⋊Dic101—22no—
42C22⋊Dic101—22no—
43C22⋊Dic101—22no—
44C4×Dic101—21no—
45C4×Dic101C2×C411yescharacteristic
46C2×D4×C101—22no—
47C2×D4×C101C2×C411yescharacteristic
48C2×D4×C101C2×C411yescharacteristic
49C42×C101C2×C411yescharacteristic
50C23×C101—21no—
51C23×C101C22⋊C412yes—
52C22×D101C2×D411yescharacteristic
53C2×#87938—42no—
54D4×C101—22no—
55D4×C101—22no—
56D4×C101—44no—
57C2×C4×C101—21no—
58C2×C4×C101C22×C411yescharacteristic
59C22⋊D101—24no—
60C22⋊D101—42no—
61C2×Dic101—22no—
62C2×Dic101—22no—
63C2×Dic101—21no—
64C2×Dic101—21no—
65C2×Dic101—41no—
66C2×Dic101—41no—
67C2×Dic101C22⋊C412yes—
68C2×Dic101C2×D411yescharacteristic
69C4×D101—42no—
70C4×D101C2×D412yes—
71C4×D101#4112yes—
72Dic202—22no—
73Dic202—22no—
74#11717581—24no—
75C22×C101—22no—
76C22×C101—42no—
77C22×C101—42no—
78C22×C101—41no—
79C22×C101C2×C22⋊C411yescharacteristic
80C2×D101—41no—
81C2×D101#12112yes—
82#87938—82no—
83C4×C101—22no—
84C4×C101C4×D412yes—
85Dic101—22no—
86Dic101—41no—
87Dic101—41no—
88Dic101#12011yescharacteristic
89Dic101#12311yescharacteristic
90C2×C101—21no—
91C2×C101—42no—
92C2×C101—81no—
93C2×C101#38611yescharacteristic
94D101—22no—
95#1884—1011nomaximal, Sylow
96C101#188411yescharacteristic, complemented, Sylow
97#568—1011no—
98#532—1011no—
99#421—1012no—
100#410—1011no—
101#339—1012no—
102C2×#41—1011no—
103C2×#41—1011no—
104#131—2024no—
105C2×M16—1012no—
106C2×M16—2022no—
107C4⋊Q8—1011no—
108#127#8793811yescharacteristic, complemented
109#124—1011no—
110#124—1011no—
111#121—2022no—
112C4×D4—2022no—
113#117—1012no—
114C2×C42—1011no—
115#104—2024no—
116#99—2022no—
117#41—2022no—
118#41—2022no—
119#41—2022no—
120#41—2022no—
121C2×Q8—1011no—
122C2×Q8—1011no—
123C2×D4—22no—
124C2×D4—1012no—
125C2×D4—2021no—
126C2×D4C2×#8793811yescharacteristic
127C2×D4C2×#8793811yescharacteristic
128C22×C4—1011no—
129C22×C4—1012no—
130C22×C4—2021no—
131C22×C4—2021no—
132M16—1014no—
133M16—2022no—
134M16—2024no—
135C2×C8—2022no—
136C2×C8—2024no—
137C4⋊C4—2022no—
138C4⋊C4—2022no—
139C22⋊C4—2022no—
140C22⋊C4—2022no—
141C22⋊C4—2022no—
142C42—1011no—
143C42—2021no—
144C42—2022no—
145C42C2×#8793811yescharacteristic
146C23—21no—
147C23—1011no—
148C23C22⋊#8793812yes—
149Q8—2022no—
150Q8—2022no—
151D4—22no—
152D4—22no—
153D4—44no—
154D4—4042no—
155D4—2024no—
156C2×C4—21no—
157C2×C4—1011no—
158C2×C4—1012no—
159C2×C4—1012no—
160C2×C4—1012no—
161C2×C4—4042no—
162C2×C4—4042no—
163C2×C4—4041no—
164C2×C4—4041no—
165C2×C4—2022no—
166C2×C4—2022no—
167C2×C4—2021no—
168C2×C4—2021no—
169C2×C4C22×#8793811yescharacteristic
170C8—2024no—
171C22—22no—
172C22—42no—
173C22—42no—
174C22—41no—
175C22—1012no—
176C22—4041no—
177C22C2×C22⋊#8793811yescharacteristic
178C4—22no—
179C4—8082no—
180C4—1011no—
181C4—1011no—
182C4—4041no—
183C4—4041no—
184C4—2022no—
185C4D4×#8793812yes—
186C2—21no—
187C2—42no—
188C2—81no—
189C2—2022no—
190C2#2026612511yescharacteristic
subgroupG/H
centerC2#20266125
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#127×C101C4
socleC2×C101#386
prime radical#20265725C2
cosocleC2×C4×D101C23
hypercenter#127#87938
hypocenterC101#1884
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #20266255C2semidirect
2. #20266175C2semidirect
3. #20266157C2semidirect
4. #20266048C2semidirect
14. #15692255C4semidirect
15. #15692242C4semidirect
16. #15692242C4semidirect
20. #127×C101C4semidirect
21. #13108084D4semidirect
96. C101#1884semidirect
108. #127#87938semidirect

Maximal subgroups

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

subgroupindex
#202662552
#202661752
#202661572
#202660482
#202657252
#1884101