Finite Group Databasebeta

← #27171090

Subgroups — #27171090

Order 12928.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#15692303C211yesmaximal, characteristic
2C2×#15692183C212yesmaximal, complemented
3#20265176C212yesmaximal, complemented
4C2×#15692174C211yesmaximal, characteristic, complemented
5#391×C101C211yesmaximal, characteristic, complemented
6#15692303—24no—
7#15692303—22no—
8#15692303C414yescomplemented
9C2×#13108075—22no—
10C2×#13108074—22no—
11C2×#13108074C2212yes—
12C2×Q8×D101—22no—
13C2×#13108058C2212yes—
14#15692183—24no—
15#15692178—22no—
16#15692175—22no—
17#15692174—22no—
18C22×Q8×C101C2211yescharacteristic
19C2×C4⋊C4×C101C2211yescharacteristic
20C2×C42×C101C2211yescharacteristic
21#95×C101—22no—
22#13108075—28no—
23#13108075—28no—
24#13108074—28no—
25#13108074—28no—
26#13108074—22no—
27#13108074—22no—
28#13108074C2×C414yes—
29#13108074D414yes—
30C2×Dic202—22no—
31C2×Dic202D412yes—
32Q8×D101—28no—
33Q8×D101—28no—
34C2×D404—22no—
35C2×D404D412yes—
36C2×C22⋊D101—22no—
37C2×C4×D101—24no—
38C2×C4×D101—22no—
39#13108058—22no—
40#13108058—22no—
41C2×#11717579—22no—
42C2×Q8×C101—22no—
43C2×Q8×C101—22no—
44C2×Q8×C101C2×C412yes—
45C2×Q8×C101D412yes—
46C22×C4×C101—21no—
47C22×C4×C101—21no—
48C22×C4×C101D412yes—
49C22×C4×C101C2311yescharacteristic
50C4⋊C4×C101—22no—
51C42×C101—22no—
52C23×C101C2×D411yescharacteristic
53C22×D101—22no—
54Q8×C101—24no—
55Q8×C101—24no—
56C2×C4×C101—22no—
57C2×C4×C101—22no—
58C2×C4×C101—22no—
59C2×C4×C101—41no—
60C2×C4×C101—41no—
61C2×C4×C101—42no—
62C2×C4×C101—41no—
63C2×C4×C101C22⋊C414yes—
64C2×C4×C101C22×C411yescharacteristic
65C2×C4×C101C2×D412yes—
66C2×C4×C101C2×D412yes—
67C2×C4×C101C2×D411yescharacteristic
68C22⋊D101—24no—
69C22⋊D101—24no—
70C2×Dic101—22no—
71D404—28no—
72D404—22no—
73D404C22⋊C414yes—
74C4×D101—216no—
75C4×D101—24no—
76C4×D101—24no—
77Dic202—28no—
78Dic202—22no—
79Dic202C22⋊C414yes—
80#11717579—42no—
81C22×C101—21no—
82C22×C101—21no—
83C22×C101C2×C22⋊C411yescharacteristic
84C22×C101#12011yescharacteristic
85C22×C101#12011yescharacteristic
86C2×D101—24no—
87C2×D101—42no—
88C2×D101—42no—
89C4×C101—24no—
90C4×C101—42no—
91C4×C101—81no—
92C4×C101C2×C22⋊C412yes—
93C4×C101#12012yes—
94Dic101—24no—
95C2×C101—21no—
96C2×C101—21no—
97C2×C101#37911yescharacteristic
98C2×C101#45411yescharacteristic
99C2×C101#45611yescharacteristic
100D101—44no—
101#1793—1011nomaximal, Sylow
102C101#179311yescharacteristic, complemented, Sylow
103C2×2−1+4—1011no—
104C2×#104—1012no—
105#417—1012no—
106C2×#101—1011no—
107#391D10111yescharacteristic, complemented
1082−1+4—1014no—
1092−1+4—2024no—
1102−1+4—2022no—
111C2×#41—1012no—
112C2×#41—2022no—
113C2×#41—2022no—
114C22×Q8—2022no—
115C22×Q8C2×D10111yescharacteristic
116C2×M16—1012no—
117C2×C4⋊C4C2×D10111yescharacteristic
118C2×C42C2×D10111yescharacteristic
119#104—2024no—
120#103—2022no—
121#102—2022no—
122#101—2022no—
123#95—22no—
124#41—1014no—
125#41—1014no—
126#41—2028no—
127#41—2028no—
128#41—2028no—
129#41—2028no—
130#41—2022no—
131#41—2022no—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—1012no—
135C2×Q8—2022no—
136C2×Q8—2028no—
137C2×Q8—2028no—
138C2×Q8C4×D10112yes—
139C2×Q8D40412yes—
140C2×D4—1012no—
141C2×D4—2022no—
142C2×D4—2022no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—2024no—
146C22×C4—2022no—
147C22×C4C22⋊D10112yes—
148C22×C4C22×D10111yescharacteristic
149M16—2022no—
150M16—2022no—
151C2×C8—2022no—
152C4⋊C4—22no—
153C42—22no—
154C23—2022no—
155C23C2×C22⋊D10111yescharacteristic
156Q8—24no—
157Q8—24no—
158Q8—1014no—
159Q8—2028no—
160Q8—2022no—
161D4—1014no—
162D4—2028no—
163D4—2024no—
164D4—2024no—
165D4—2022no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—20216no—
174C2×C4—2022no—
175C2×C4—2024no—
176C2×C4—2024no—
177C2×C4#1310805114yes—
178C2×C4C2×C4×D10111yescharacteristic
179C2×C4D4×D10112yes—
180C2×C4D4×D10112yes—
181C2×C4C2×D40411yescharacteristic
182C8—4042no—
183C22—21no—
184C22—21no—
185C22—4042no—
186C22—4042no—
187C22—2024no—
188C22C2×#1310805111yescharacteristic
189C22#1569222311yescharacteristic
190C22#1569222311yescharacteristic
191C4—24no—
192C4—42no—
193C4—81no—
194C4—2024no—
195C4C22⋊C4×D10112yes—
196C4#1569222512yes—
197C2—21no—
198C2—21no—
199C2—4044no—
200C2#2026503211yescharacteristic
201C2#2026534911yescharacteristic
202C2#2026535911yescharacteristic
subgroupG/H
centerC22#15692223
commutatorC2×C4×C101C22×C4
FrattiniC22×C4C22×D101
Fitting#391×C101C2
socleC22×C101#120
prime radicalC2×#15692303C2
cosocleC22×C4×C101C23
hypercenter#391D101
hypocenterC101#1793
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#15692183C2semidirect
3. #20265176C2semidirect
4. C2×#15692174C2semidirect
5. #391×C101C2semidirect
8. #15692303C4semidirect
102. C101#1793semidirect
107. #391D101semidirect

Maximal subgroups

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

subgroupindex
C2×#156923032
C2×#156921832
#202651762
C2×#156921742
#391×C1012
#1793101