Finite Group Databasebeta

← D101⋊#353 #27187398

Subgroups — D101⋊#353 #27187398

Order 12928.

368 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 54 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⋊#99C212yesmaximal, complemented
2#20266082C212yesmaximal, complemented
3#20266081C212yesmaximal, complemented
4#127×D101C211yesmaximal, characteristic
5C2×C22⋊#87938—22no—
6#15692314C2214yescomplemented
7#15692313—22no—
8C2×D4×D101—22no—
9C2×D4×D101C411yescharacteristic, complemented
10C2×D4×D101C2211yescharacteristic
11#15692252C2211yescharacteristic
12#15692251—22no—
13#15692251C411yescharacteristic, complemented
14#15692251C2211yescharacteristic
15C42×D101C411yescharacteristic, complemented
16#127×C101C411yescharacteristic, complemented
17C22×#87938—42no—
18C22⋊#87938—24no—
19C22⋊#87938—42no—
20C23×D101—21no—
21C23×D101D412yes—
22C2×D404—22no—
23C2×D404C2×C411yescharacteristic, complemented
24C2×D404C2311yescharacteristic
25C2×C22⋊D101—22no—
26C2×C22⋊D101—22no—
27C2×C22⋊D101—21no—
28C2×C22⋊D101D412yes—
29D4×D101—41no—
30D4×D101—41no—
31D4×D101—41no—
32D4×D101—41no—
33D4×D101—48no—
34C2×C4×D101—21no—
35C2×C4×D101C2×C411yescharacteristic
36C4×Dic101—21no—
37C4×Dic101C2×C411yescharacteristic, complemented
38C2×D4×C101—22no—
39C2×D4×C101C2×C411yescharacteristic
40C2×D4×C101C2×C411yescharacteristic, complemented
41C42×C101C2×C411yescharacteristic, complemented
42C23×C101—21no—
43C23×C101C22⋊C412yes—
44C22×D101—22no—
45C22×D101—22no—
46C22×D101—21no—
47C22×D101—44no—
48C22×D101—44no—
49C22×D101—41no—
50C22×D101—41no—
51C22×D101C22⋊C411yescharacteristic
52C22×D101C2×D412yes—
53C2×#87938—44no—
54C2×#87938—84no—
55D4×C101—41no—
56D4×C101—41no—
57D4×C101—44no—
58C2×C4×C101—21no—
59C2×C4×C101C22×C411yescharacteristic
60C22⋊D101—42no—
61C22⋊D101—44no—
62C22⋊D101—44no—
63C22⋊D101—42no—
64C2×Dic101—21no—
65C2×Dic101C22⋊C411yescharacteristic
66D404—41no—
67D404—41no—
68D404—44no—
69C4×D101—24no—
70C4×D101—21no—
71C4×D101—21no—
72C22×C101—22no—
73C22×C101—42no—
74C22×C101—42no—
75C22×C101—41no—
76C22×C101C2×C22⋊C411yescharacteristic
77C2×D101—22no—
78C2×D101—22no—
79C2×D101—44no—
80C2×D101—42no—
81C2×D101—42no—
82C2×D101—41no—
83C2×D101—82no—
84C2×D101—82no—
85C2×D101—82no—
86C2×D101#9911yescharacteristic
87C2×D101#9911yescharacteristic
88#87938—84no—
89C4×C101—22no—
90C4×C101—21no—
91Dic101—22no—
92Dic101—21no—
93C2×C101—21no—
94C2×C101—42no—
95C2×C101—81no—
96C2×C101C2×#9911yescharacteristic
97D101—21no—
98D101—42no—
99D101—81no—
100D101#35312yescomplemented
101C2×#353—1011nomaximal, Sylow
102C101C2×#35311yescharacteristic, complemented, Sylow
103C2×#127—1011no—
104C2×#99—1012no—
105#353—1012no—
106#353—1012no—
107C22×D4—1011no—
108C22×D4—1011no—
109C22×D4—2022no—
110#127—1011no—
111#127—1011no—
112#127—1011no—
113#127—2022no—
114#127#8793811yescharacteristic, complemented
115C2×C22⋊C4—2022no—
116C2×C42—1011no—
117#99—1014no—
118#99—2022no—
119C24—1012no—
120C24—2021no—
121C2×D4—22no—
122C2×D4—1012no—
123C2×D4—1011no—
124C2×D4—1011no—
125C2×D4—4041no—
126C2×D4—4041no—
127C2×D4—4048no—
128C2×D4—4041no—
129C2×D4—4041no—
130C2×D4—2022no—
131C2×D4—2021no—
132C2×D4—2022no—
133C2×D4—2022no—
134C2×D4C2×#8793811yescharacteristic
135C2×D4C2×#8793811yescharacteristic, complemented
136C22×C4—1011no—
137C22×C4—4042no—
138C22×C4—2021no—
139C22⋊C4—4042no—
140C22⋊C4—2024no—
141C42—1011no—
142C42—2021no—
143C42C2×#8793811yescharacteristic, complemented
144C23—21no—
145C23—1011no—
146C23—1012no—
147C23—4041no—
148C23—4041no—
149C23—4044no—
150C23—4044no—
151C23—2022no—
152C23—2022no—
153C23—2021no—
154C23C22⋊#8793812yes—
155D4—41no—
156D4—41no—
157D4—44no—
158D4—4041no—
159D4—4044no—
160D4—4041no—
161D4—4042no—
162D4—4044no—
163D4—4044no—
164D4—4042no—
165C2×C4—21no—
166C2×C4—8084no—
167C2×C4—1011no—
168C2×C4—4044no—
169C2×C4—2021no—
170C2×C4—2021no—
171C2×C4—2024no—
172C2×C4—2021no—
173C2×C4C22×#8793811yescharacteristic
174C22—22no—
175C22—42no—
176C22—42no—
177C22—41no—
178C22—8082no—
179C22—8082no—
180C22—8082no—
181C22—1011no—
182C22—1011no—
183C22—4042no—
184C22—4042no—
185C22—4044no—
186C22—4041no—
187C22—2022no—
188C22—2022no—
189C22C2×C22⋊#8793811yescharacteristic
190C4—22no—
191C4—21no—
192C4—8084no—
193C4—2022no—
194C4—2021no—
195C2—21no—
196C2—42no—
197C2—81no—
198C2—8081no—
199C2—1012no—
200C2—4042no—
201C2—2021no—
202C2D101⋊#9911yescharacteristic
subgroupG/H
centerC2D101⋊#99
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#127×C101C4
socleC2×C101C2×#99
prime radical#127×D101C2
cosocleC2×D404C23
hypercenter#127#87938
hypocenterC101C2×#353
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. D101⋊#99C2semidirect
2. #20266082C2semidirect
3. #20266081C2semidirect
6. #15692314C22semidirect
9. C2×D4×D101C4semidirect
13. #15692251C4semidirect
15. C42×D101C4semidirect
16. #127×C101C4semidirect
23. C2×D404C2×C4semidirect
37. C4×Dic101C2×C4semidirect
40. C2×D4×C101C2×C4semidirect
41. C42×C101C2×C4semidirect
100. D101#353semidirect
102. C101C2×#353semidirect
114. #127#87938semidirect
135. C2×D4C2×#87938semidirect
143. C42C2×#87938semidirect

Maximal subgroups

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

subgroupindex
D101⋊#992
#202660822
#202660812
#127×D1012
C2×#353101