Finite Group Databasebeta

← #27183739

Subgroups — #27183739

Order 12928.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#20265877C212yesmaximal, complemented
2#20265579C211yesmaximal, characteristic, complemented
3#20265499C212yesmaximal, complemented
4#20265489C212yesmaximal, complemented
5#20265477C212yesmaximal, complemented
6#20265427C212yesmaximal, complemented
7#20265256C211yesmaximal, characteristic, complemented
8#20265218C212yesmaximal, complemented
9C4×D8×C101C211yesmaximal, characteristic, complemented
10C2×#13108057C2212yes—
11#15692248—22no—
12#15692247C2212yes—
13#15692238—22no—
14#15692228—22no—
15#15692226C2212yes—
16#15692226C2212yes—
17C4×D404C2211yescharacteristic
18C4×C22⋊D101—22no—
19#15692213C2212yes—
20C4⋊C4×D101C2212yes—
21#15692189C2211yescharacteristic
22#15692189C2211yescharacteristic
23#15692188C2212yes—
24#15692187C2212yes—
25#15692186C2212yes—
26C4⋊#11717579C2211yescharacteristic
27#15692176C2212yes—
28#15692176C2212yes—
29#15692167C2212yes—
30C2×D8×C101C2211yescharacteristic
31C4×D4×C101C2212yes—
32#107×C101C2211yescharacteristic
33#102×C101C2212yes—
34C4×C8×C101C2211yescharacteristic
35C2×D404D411yescharacteristic
36C2×C22⋊D101—22no—
37C2×C22⋊D101—22no—
38C2×C4×D101—22no—
39C2×C4×D101C2312yes—
40#13108057—24no—
41C2×#11717579C2312yes—
42C4⋊Dic101D411yescharacteristic
43C4⋊Dic101C2312yes—
44C4⋊Dic101C2312yes—
45#13108053—22no—
46#13108053—22no—
47#13108053—22no—
48C22⋊Dic101—22no—
49C22⋊Dic101—22no—
50#13108051—22no—
51#13108051D412yes—
52C4×Dic101—22no—
53C2×D4×C101C2312yes—
54C22×C4×C101—22no—
55D8×C101—22no—
56C2×C8×C101C2311yescharacteristic
57C2×C8×C101C2311yescharacteristic
58C4⋊C4×C101C2312yes—
59C22⋊C4×C101—22no—
60C42×C101C2311yescharacteristic
61C23×C101—22no—
62C22×D101C2×D412yes—
63D4×C101—22no—
64D4×C101—22no—
65C2×C4×C101—22no—
66C2×C4×C101—82no—
67C2×C4×C101C2×D411yescharacteristic
68C2×C4×C101C2×D411yescharacteristic
69C2×C4×C101C2411yescharacteristic
70C22⋊D101—44no—
71C22⋊D101—82no—
72C2×Dic101—22no—
73C2×Dic101—22no—
74C2×Dic101C2×D412yes—
75D404—41no—
76C4×D101—22no—
77C4×D101—22no—
78C4×D101—82no—
79C8×C101—21no—
80C8×C101#4112yes—
81#11717579—22no—
82C22×C101—42no—
83C22×C101—42no—
84C22×C101—42no—
85C22×C101C22×D411yescharacteristic
86C2×D101—22no—
87C2×D101—22no—
88C2×D101—22no—
89C4×C101—21no—
90C4×C101—21no—
91C4×C101—42no—
92C4×C101C2×#4111yescharacteristic
93C4×C1012−1+411yescharacteristic
94Dic101—22no—
95Dic101—42no—
96Dic101—42no—
97C2×C101—82no—
98C2×C101#54711yescharacteristic
99C2×C101#57511yescharacteristic
100C2×C101#57611yescharacteristic
101D101—42no—
102#3355—1011nomaximal, Sylow
103C101#335511yescharacteristic, complemented, Sylow
104#553—1012no—
105#499—1011no—
106#482—1012no—
107#480—1012no—
108#478—1012no—
109#469—1012no—
110C4×D8D10111yescharacteristic, complemented
111#436—1011no—
112#428—1012no—
113C2×D8C2×D10111yescharacteristic
114C2×M16—1012no—
115#126—2022no—
116#125—1012no—
117#123—2022no—
118#121—1012no—
119#121—1012no—
120#121—2022no—
121C4×D4—1011no—
122C4×D4—2022no—
123C4×D4C2×D10112yes—
124#117—1012no—
125C2×C4⋊C4—1012no—
126#107—1011no—
127#107—1011no—
128#107—1012no—
129#107C2×D10111yescharacteristic
130#106—1012no—
131#106—1012no—
132C4⋊C8—1011no—
133#102—1012no—
134#102—1012no—
135#102C2×D10112yes—
136C22⋊C8—1012no—
137C4×C8C2×D10111yescharacteristic
138C2×D4—1011no—
139C2×D4—2022no—
140C2×D4—2022no—
141C2×D4C22×D10112yes—
142C22×C4—22no—
143C22×C4—1012no—
144C22×C4—2022no—
145D8—22no—
146M16—2024no—
147C2×C8—1012no—
148C2×C8C22×D10111yescharacteristic
149C2×C8C22×D10111yescharacteristic
150C4⋊C4—1011no—
151C4⋊C4—1012no—
152C4⋊C4—1012no—
153C4⋊C4—2022no—
154C4⋊C4—2022no—
155C4⋊C4—2022no—
156C4⋊C4C22×D10112yes—
157C22⋊C4—22no—
158C22⋊C4—1012no—
159C22⋊C4—2022no—
160C22⋊C4—2022no—
161C22⋊C4—2022no—
162C42—2022no—
163C42C22×D10111yescharacteristic
164C23—22no—
165C23—1012no—
166D4—22no—
167D4—22no—
168D4—8082no—
169D4—4041no—
170D4—4044no—
171C2×C4—22no—
172C2×C4—82no—
173C2×C4—8082no—
174C2×C4—1012no—
175C2×C4—2022no—
176C2×C4—2022no—
177C2×C4—2022no—
178C2×C4—2022no—
179C2×C4D4×D10111yescharacteristic
180C2×C4D4×D10111yescharacteristic
181C2×C4C23×D10111yescharacteristic
182C8—21no—
183C8—2022no—
184C8#1310807412yes—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—2022no—
189C22—2022no—
190C22—2022no—
191C22C2×D4×D10111yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—4042no—
196C4—4042no—
197C4—2022no—
198C4C2×#1310807411yescharacteristic
199C4#1569230211yescharacteristic
200C2—82no—
201C2—4042no—
202C2#2026583211yescharacteristic
203C2#2026597411yescharacteristic
204C2#2026597811yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
FittingC4×D8×C101C2
socleC22×C101C22×D4
hypercenterC4×D8D101
hypocenterC101#3355
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #20265877C2semidirect
2. #20265579C2semidirect
3. #20265499C2semidirect
4. #20265489C2semidirect
5. #20265477C2semidirect
6. #20265427C2semidirect
7. #20265256C2semidirect
8. #20265218C2semidirect
9. C4×D8×C101C2semidirect
103. C101#3355semidirect
110. C4×D8D101semidirect

Maximal subgroups

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

subgroupindex
#202658772
#202655792
#202654992
#202654892
#202654772
#202654272
#202652562
#202652182
C4×D8×C1012
#3355101