Finite Group Databasebeta

← #27186448

Subgroups — #27186448

Order 12928.

234 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 62 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
1D101⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C4×#13108084C211yesmaximal, characteristic, complemented
3Q8⋊#11717581C212yesmaximal, complemented
4D4⋊#11717581C212yesmaximal, complemented
5#20265706C211yesmaximal, characteristic
6C2×#13108084—21no—
7C2×D101⋊C8—21no—
8#15692322—21no—
9C4⋊#11717581C2212yes—
10#15692310—21no—
11C4×#11717581C2212yes—
12#15692248—21no—
13#15692247C411yescharacteristic
14#15692237—21no—
15#15692231C411yescharacteristic
16#15692226C411yescharacteristic
17Q8×Dic101C2211yescharacteristic
18D4×Dic101C2211yescharacteristic
19#15692215—21no—
20#15692211—21no—
21C42×D101C2211yescharacteristic
22#124×C101C411yescharacteristic
23#13108084—24no—
24D101⋊C8—42no—
25C2×#11717581—22no—
26C2×#11717581—22no—
27C2×C22⋊D101—21no—
28C22×Dic101—21no—
29C2×C4×D101C2×C411yescharacteristic
30C2×C4×D101D411yescharacteristic
31C2×C4×D101D411yescharacteristic
32C4⋊Dic101—21no—
33C4⋊Dic101C2×C411yescharacteristic
34C4⋊Dic101C2×C411yescharacteristic
35#13108053—21no—
36#13108053—21no—
37#13108053—21no—
38C22⋊Dic101—21no—
39C22⋊Dic101—21no—
40#13108051—21no—
41C4×Dic101—21no—
42C4×Dic101D411yescharacteristic
43C4×Dic101D411yescharacteristic
44C4×Dic101C2311yescharacteristic
45C2×Q8×C101C2×C411yescharacteristic
46C2×D4×C101C2×C411yescharacteristic
47C22⋊C4×C101—21no—
48C22⋊C4×C101—21no—
49C42×C101C2×C411yescharacteristic
50C23×C101—21no—
51C22×D101C22⋊C411yescharacteristic
52Q8×C101—22no—
53D4×C101—22no—
54C2×C4×C101—21no—
55C2×C4×C101C22⋊C411yescharacteristic
56C2×C4×C101C22⋊C411yescharacteristic
57C2×C4×C101C22×C411yescharacteristic
58C22⋊D101—42no—
59C2×Dic101—21no—
60C2×Dic101—21no—
61C2×Dic101—41no—
62C2×Dic101—41no—
63C2×Dic101C22⋊C411yescharacteristic
64C2×Dic101C2×D411yescharacteristic
65C2×Dic101C2×D411yescharacteristic
66C4×D101—22no—
67C4×D101—22no—
68C4×D101—21no—
69C4×D101—21no—
70#11717581—24no—
71#11717581—42no—
72C22×C101—41no—
73C22×C101—41no—
74C22×C101—41no—
75C22×C101C2×C22⋊C411yescharacteristic
76C2×D101—21no—
77C2×D101—21no—
78C2×D101#10412yes—
79C4×C101—21no—
80C4×C101—21no—
81C4×C101—41no—
82C4×C101#13112yes—
83Dic101—21no—
84Dic101—21no—
85Dic101—41no—
86Dic101—41no—
87Dic101AGL(1,ℤ/8)11yescharacteristic
88Dic101#13711yescharacteristic
89C2×C101—81no—
90C2×C101#40811yescharacteristic
91C2×C101#41711yescharacteristic
92C2×C101C2×#10411yescharacteristic
93D101—22no—
94#1483—1011nomaximal, Sylow
95C101#148311yescharacteristic, complemented, Sylow
96#529—1011no—
97C2×C4⋊C8—1011no—
98C4×M16—1011no—
99Q8⋊C8—1012no—
100D4⋊C8—1012no—
101C2×M16—2021no—
102C22×C8—2021no—
103#126—2021no—
104#125—1011no—
105#124#8793811yescharacteristic
106#123—2021no—
107C22⋊Q8—1011no—
108#121—1011no—
109C4×Q8—1011no—
110C4×D4—1011no—
111C4×D4—2021no—
112#117—2021no—
113C2×C42—1011no—
114C4⋊C8—1012no—
115C4⋊C8—2021no—
116#97—2021no—
117C4×C8—1012no—
118C2×Q8C2×#8793811yescharacteristic
119C2×D4—2021no—
120C2×D4C2×#8793811yescharacteristic
121C22×C4—1011no—
122C22×C4—1011no—
123C22×C4—1011no—
124C22×C4—2021no—
125M16—2024no—
126C2×C8—4042no—
127C2×C8—2022no—
128C2×C8—2022no—
129C4⋊C4—1011no—
130C4⋊C4—1011no—
131C4⋊C4—2021no—
132C4⋊C4—2021no—
133C4⋊C4—2021no—
134C4⋊C4—2021no—
135C22⋊C4—21no—
136C22⋊C4—21no—
137C22⋊C4—2021no—
138C22⋊C4—2021no—
139C22⋊C4—2021no—
140C42—1011no—
141C42—1011no—
142C42—1011no—
143C42—2021no—
144C42C2×#8793811yescharacteristic
145C23—21no—
146C23—1011no—
147Q8—22no—
148D4—22no—
149D4—4042no—
150C2×C4—21no—
151C2×C4—1011no—
152C2×C4—1011no—
153C2×C4—1011no—
154C2×C4—4041no—
155C2×C4—4041no—
156C2×C4—2021no—
157C2×C4—2021no—
158C2×C4—2022no—
159C2×C4—2021no—
160C2×C4—2021no—
161C2×C4—2022no—
162C2×C4C22⋊#8793811yescharacteristic
163C2×C4C22⋊#8793811yescharacteristic
164C2×C4C22×#8793811yescharacteristic
165C8—4042no—
166C8—2024no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22—1012no—
171C22—2021no—
172C22—2021no—
173C22C2×C22⋊#8793811yescharacteristic
174C4—21no—
175C4—21no—
176C4—41no—
177C4—1011no—
178C4—1011no—
179C4—4041no—
180C4—4041no—
181C4—2021no—
182C4—2021no—
183C4#1569234212yes—
184C2—81no—
185C2—2022no—
186C2#2026615111yescharacteristic
187C2#2026616811yescharacteristic
188C2D101⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#124×C101C4
socleC22×C101C2×C22⋊C4
prime radical#15692226C4
cosocleC4×Dic101C23
hypercenter#124#87938
hypocenterC101#1483
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. D101⋊(C4⋊C8)C2semidirect
2. C4×#13108084C2semidirect
3. Q8⋊#11717581C2semidirect
4. D4⋊#11717581C2semidirect
95. C101#1483semidirect

Maximal subgroups

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

subgroupindex
D101⋊(C4⋊C8)2
C4×#131080842
Q8⋊#117175812
D4⋊#117175812
#202657062
#1483101