Finite Group Databasebeta

← #27187303

Subgroups — #27187303

Order 12928.

292 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C2×#15692322C211yesmaximal, characteristic
2C2×C4×#11717581C211yesmaximal, characteristic
3#20266043C212yesmaximal
4#20266043C212yesmaximal
5C2×#15692220C211yesmaximal, characteristic
6C22×#11717581C2212yes—
7C22×#11717581C2212yes—
8#15692322—22no—
9C4×#11717581—22no—
10C22×Dic202C411yescharacteristic
11#15692220—22no—
12#15692220—22no—
13C2×#13108053C411yescharacteristic
14C2×#13108053C411yescharacteristic
15C2×C4×Dic101C2211yescharacteristic
16C2×C4×Dic101C2211yescharacteristic
17C2×C4×Dic101C2211yescharacteristic
18C2×C4⋊C4×C101C411yescharacteristic
19C2×#11717581—22no—
20C2×#11717581—22no—
21C2×#11717581—22no—
22C2×#11717581—24no—
23C2×#11717581Q814yescomplemented
24C2×Dic202—22no—
25C2×Dic202—22no—
26C2×Dic202C814yescomplemented
27C22×Dic101C2×C411yescharacteristic
28C22×Dic101C2×C411yescharacteristic
29C22×Dic101C2×C411yescharacteristic
30C22×Dic101C2311yescharacteristic
31#13108053—22no—
32#13108053—22no—
33C4×Dic101—21no—
34C4×Dic101—21no—
35C4×Dic101—21no—
36C4×Dic101—21no—
37C4×Dic101D412yes—
38C4×Dic101D412yes—
39C22×C4×C101C2×C411yescharacteristic
40C22×C4×C101C2×C411yescharacteristic
41C22×C4×C101C2×C411yescharacteristic
42C4⋊C4×C101—22no—
43C23×C101C22×C411yescharacteristic
44C2×C4×C101—21no—
45C2×C4×C101—21no—
46C2×C4×C101—22no—
47C2×C4×C101—21no—
48C2×C4×C101—22no—
49C2×C4×C101C22⋊C412yes—
50C2×C4×C101C2×C812yes—
51C2×Dic101—21no—
52C2×Dic101—21no—
53C2×Dic101—21no—
54C2×Dic101—22no—
55C2×Dic101C22⋊C412yes—
56C2×Dic101C2×C812yes—
57C2×Dic101C2×C812yes—
58C2×Dic101M1612yes—
59C2×Dic101C2×D411yescharacteristic
60C2×Dic101C2×D411yescharacteristic
61C2×Dic101C2×Q812yes—
62C2×Dic101#4112yes—
63Dic202—28no—
64#11717581—24no—
65#11717581—42no—
66C22×C101C2×C22⋊C411yescharacteristic
67C22×C101C4×Q812yes—
68C22×C101C22×C811yescharacteristic
69C22×C101C2×M1611yescharacteristic
70C22×C101#13112yes—
71C4×C101—22no—
72C4×C101—22no—
73C4×C101—41no—
74Dic101—22no—
75Dic101—41no—
76Dic101C22⋊C814yes—
77Dic101C22⋊Q812yes—
78Dic101#12411yescharacteristic
79Dic101C4⋊Q811yescharacteristic
80C2×C101#39111yescharacteristic
81C2×C101C2×C22⋊C811yescharacteristic
82C2×C101#40811yescharacteristic
83C2×C101C8×Q812yes—
84C2×C101#44612yes—
85#1984—1011nomaximal, Sylow
86C101#198411yescharacteristic, complemented, Sylow
87C2×C4×Q8—1011no—
88C2×C4⋊C8—1011no—
89C2×C4×C8—1011no—
90#336—1012no—
91#336—1012no—
92C22×Q8—1011no—
93C22×C8—1012no—
94C22×C8—1012no—
95C4×Q8—2022no—
96C4×Q8—2022no—
97C2×C4⋊C4—1011no—
98C2×C4⋊C4—1011no—
99C2×C4⋊C4#8793811yescharacteristic
100C2×C42—1011no—
101C2×C42—1011no—
102C2×C42—1011no—
103C4⋊C8—2022no—
104C4×C8—2022no—
105C2×Q8—1014no—
106C2×Q8—2022no—
107C2×Q8—2022no—
108C22×C4—1011no—
109C22×C4—1011no—
110C22×C4—1011no—
111C22×C4—1011no—
112C22×C4C2×#8793811yescharacteristic
113C22×C4C2×#8793811yescharacteristic
114C22×C4C2×#8793811yescharacteristic
115C2×C8—1014no—
116C2×C8—2022no—
117C2×C8—2024no—
118C2×C8—2022no—
119C2×C8—2022no—
120C4⋊C4—22no—
121C4⋊C4—2022no—
122C4⋊C4—2022no—
123C42—1012no—
124C42—1012no—
125C42—2021no—
126C42—2021no—
127C42—2021no—
128C42—2021no—
129C23C22×#8793811yescharacteristic
130Q8—2028no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—22no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—1011no—
137C2×C4—1011no—
138C2×C4—1012no—
139C2×C4—1012no—
140C2×C4—1012no—
141C2×C4—1012no—
142C2×C4—1012no—
143C2×C4—1012no—
144C2×C4—2021no—
145C2×C4—2022no—
146C2×C4—2021no—
147C2×C4—2021no—
148C2×C4C22⋊#8793812yes—
149C2×C4D101⋊C812yes—
150C8—4042no—
151C8—2024no—
152C22C2×C22⋊#8793811yescharacteristic
153C22Q8×#8793812yes—
154C22C2×D101⋊C811yescharacteristic
155C22D101⋊M1611yescharacteristic
156C22#1569234212yes—
157C4—22no—
158C4—22no—
159C4—41no—
160C4—1011no—
161C4—1012no—
162C4—1011no—
163C4—1014no—
164C4—4041no—
165C4—2022no—
166C2(C2×#87938)⋊Q811yescharacteristic
167C2D101⋊(C22⋊C8)11yescharacteristic
168C2#2026615011yescharacteristic
169C2#2026622612yes—
170C2#2026622912yes—
subgroupG/H
center, FrattiniC23C22×#87938
commutatorC22×C101C22×C8
FittingC2×C4⋊C4×C101C4
socle, prime radicalC23×C101C22×C4
cosocleC22×Dic101C23
hypercenterC2×C4⋊C4#87938
hypocenterC101#1984
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
23. C2×#11717581Q8semidirect
26. C2×Dic202C8semidirect
86. C101#1984semidirect

Maximal subgroups

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

subgroupindex
C2×#156923222
C2×C4×#117175812
#202660432
C2×#156922202
#1984101