Finite Group Databasebeta

← #27186461

Subgroups — #27186461

Order 12928.

248 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 76 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#20266196C211yesmaximal, characteristic
2#20266181C211yesmaximal, characteristic
3#20266027C212yesmaximal, complemented
4Q8⋊#11717581C212yesmaximal, complemented
5C4×Q8×D101C211yesmaximal, characteristic
6C2×#13108084—21no—
7C4⋊#11717581—21no—
8C4⋊#11717581—21no—
9C4⋊#11717581C2212yes—
10#15692312—21no—
11C4×#11717581C2212yes—
12C2×Q8×D101C411yescharacteristic
13Q8×Dic101C2211yescharacteristic
14C4×Dic202—21no—
15C4×Dic202C411yescharacteristic
16#15692220—21no—
17#15692220C2211yescharacteristic
18C4⋊C4×D101—21no—
19C4⋊C4×D101C411yescharacteristic
20C42×D101—21no—
21C42×D101C2211yescharacteristic
22C4×Q8×C101C411yescharacteristic
23#13108084—42no—
24C2×#11717581—22no—
25C2×#11717581—22no—
26C2×Dic202—21no—
27C2×Dic202C2×C411yescharacteristic
28Q8×D101—22no—
29Q8×D101—22no—
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#13108053—21no—
38#13108053—21no—
39#13108053—21no—
40C4×Dic101—21no—
41C4×Dic101—21no—
42C4×Dic101—21no—
43C4×Dic101D411yescharacteristic
44C4×Dic101D411yescharacteristic
45C4×Dic101C2311yescharacteristic
46C2×Q8×C101C2×C411yescharacteristic
47C4⋊C4×C101—21no—
48C4⋊C4×C101C2×C411yescharacteristic
49C42×C101—21no—
50C42×C101C2×C411yescharacteristic
51C22×D101C22⋊C411yescharacteristic
52Q8×C101—21no—
53Q8×C101M1612yescomplemented
54C2×C4×C101—21no—
55C2×C4×C101—21no—
56C2×C4×C101C22⋊C411yescharacteristic
57C2×C4×C101C22⋊C411yescharacteristic
58C2×C4×C101C22×C411yescharacteristic
59C2×Dic101—21no—
60C2×Dic101—21no—
61C2×Dic101C22⋊C411yescharacteristic
62C2×Dic101C2×D411yescharacteristic
63C2×Dic101C2×D411yescharacteristic
64C4×D101—24no—
65C4×D101—21no—
66C4×D101—21no—
67C4×D101—41no—
68C4×D101—42no—
69C4×D101SD1612yes—
70C4×D101Q1612yes—
71Dic202—24no—
72Dic202—21no—
73Dic202M1612yescomplemented
74#11717581—42no—
75#11717581—42no—
76C22×C101C2×C22⋊C411yescharacteristic
77C2×D101—21no—
78C2×D101—21no—
79C2×D101#10312yes—
80C4×C101—22no—
81C4×C101—21no—
82C4×C101—41no—
83C4×C101#10312yes—
84C4×C101C2×M1611yescharacteristic
85C4×C101C2×M1611yescharacteristic
86Dic101—21no—
87Dic101—22no—
88Dic101—21no—
89Dic101—41no—
90Dic101C2×SD1611yescharacteristic
91Dic101C2×Q1611yescharacteristic
92C2×C101#40711yescharacteristic
93C2×C101C2×#10311yescharacteristic
94C2×C101#42111yescharacteristic
95D101—22no—
96#1487—1011nomaximal, Sylow
97C101#148711yescharacteristic, complemented, Sylow
98C2×C4×Q8—1011no—
99#431—1011no—
100#423—1011no—
101Q8⋊C8—1012no—
102Q8⋊C8—1012no—
103C22×Q8—1011no—
104C2×M16—2021no—
105C4×Q8—1011no—
106C4×Q8—1011no—
107C4×Q8—1011no—
108C4×Q8—2021no—
109C4×Q8—2021no—
110C4×Q8#8793811yescharacteristic
111C2×C4⋊C4—1011no—
112C2×C4⋊C4—2021no—
113C2×C42—1011no—
114C2×C42—2021no—
115C4⋊C8—1012no—
116C4⋊C8—2021no—
117C4⋊C8—2021no—
118C22⋊C8—2021no—
119C4×C8—1012no—
120C2×Q8—1011no—
121C2×Q8—2021no—
122C2×Q8—2022no—
123C2×Q8—2022no—
124C2×Q8C2×#8793811yescharacteristic
125C22×C4—1011no—
126C22×C4—1011no—
127C22×C4—1011no—
128C22×C4—2021no—
129C22×C4—2021no—
130M16—4042no—
131C2×C8—2022no—
132C2×C8—2022no—
133C4⋊C4—21no—
134C4⋊C4—1011no—
135C4⋊C4—2021no—
136C4⋊C4—2021no—
137C4⋊C4—2021no—
138C4⋊C4—2021no—
139C4⋊C4C2×#8793811yescharacteristic
140C42—21no—
141C42—1011no—
142C42—1011no—
143C42—1011no—
144C42—2021no—
145C42—2021no—
146C42—2021no—
147C42C2×#8793811yescharacteristic
148C23—1011no—
149Q8—21no—
150Q8—1012no—
151Q8—2024no—
152Q8—2021no—
153Q8#1310808412yescomplemented
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—1011no—
157C2×C4—1012no—
158C2×C4—1012no—
159C2×C4—1011no—
160C2×C4—1011no—
161C2×C4—4041no—
162C2×C4—4042no—
163C2×C4—2024no—
164C2×C4—2021no—
165C2×C4—2021no—
166C2×C4—2021no—
167C2×C4—2021no—
168C2×C4C22⋊#8793811yescharacteristic
169C2×C4C22⋊#8793811yescharacteristic
170C2×C4C22×#8793811yescharacteristic
171C8—4042no—
172C8—4042no—
173C22—1012no—
174C22—2021no—
175C22—2021no—
176C22C2×C22⋊#8793811yescharacteristic
177C4—22no—
178C4—21no—
179C4—41no—
180C4—1011no—
181C4—1011no—
182C4—4041no—
183C4—2021no—
184C4—2022no—
185C4—2021no—
186C4#1569231812yes—
187C4D101⋊M1611yescharacteristic
188C4C2×#1310808411yescharacteristic
189C2—2022no—
190C2#2026614811yescharacteristic
191C2C2×#1569231811yescharacteristic
192C2#2026617411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4×Q8×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×D101C22⋊C4
cosocleC4×Dic101C23
hypercenterC4×Q8#87938
hypocenterC101#1487
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
3. #20266027C2semidirect
4. Q8⋊#11717581C2semidirect
53. Q8×C101M16semidirect
73. Dic202M16semidirect
97. C101#1487semidirect
153. Q8#13108084semidirect

Maximal subgroups

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

subgroupindex
#202661962
#202661812
#202660272
Q8⋊#117175812
C4×Q8×D1012
#1487101