Finite Group Databasebeta

← #47981682

Subgroups — #47981682

Order 35456.

346 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 77 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×#22579854C211yesmaximal, characteristic
2#31799966C211yesmaximal, characteristic, complemented
3#31799735C214yesmaximal, complemented
4C4×C22⋊C4×C277C211yesmaximal, characteristic, complemented
5C22×D1108C411yescharacteristic, complemented
6C22×C22⋊D277—21no—
7C2×#17984547—21no—
8#22579854—21no—
9#22579854—21no—
10#22579854C412yescomplemented
11#22579854C2212yes—
12C2×C4⋊Dic277C411yescharacteristic, complemented
13C2×#17984540—21no—
14C22⋊#14555660—21no—
15C22⋊#14555660C2212yescomplemented
16C23×C4×C277C2211yescharacteristic
17C2×C22⋊C4×C277—21no—
18C2×C42×C277—21no—
19#95×C277C2212yescomplemented
20C23×D277—21no—
21C2×D1108—21no—
22C2×D1108—42no—
23C2×D1108C2×C412yes—
24C2×C22⋊D277—22no—
25C2×C22⋊D277—22no—
26C2×C22⋊D277—44no—
27C22×Dic277—21no—
28#17984547—42no—
29C2×#14555660—22no—
30C4⋊Dic277—21no—
31C4⋊Dic277C2×C412yes—
32#17984540—22no—
33#17984540—22no—
34C24×C277D411yescharacteristic
35C22×C4×C277—22no—
36C22×C4×C277—42no—
37C22×C4×C277C2×C411yescharacteristic
38C22×C4×C277C2×C411yescharacteristic
39C22×C4×C277D411yescharacteristic
40C22×C4×C277D411yescharacteristic
41C22×C4×C277D411yescharacteristic
42C22×C4×C277C2311yescharacteristic
43C22⋊C4×C277—24no—
44C42×C277—42no—
45C22×D277—22no—
46C22×D277—42no—
47C22×D277—42no—
48C22×D277—42no—
49D1108—42no—
50D1108—42no—
51C22⋊D277—44no—
52C22⋊D277—44no—
53C2×Dic277—22no—
54C2×Dic277—42no—
55#14555660—42no—
56C23×C277—22no—
57C23×C277—22no—
58C23×C277—41no—
59C23×C277C22⋊C411yescharacteristic
60C23×C277C22⋊C411yescharacteristic
61C23×C277C2×D411yescharacteristic
62C2×C4×C277—22no—
63C2×C4×C277—22no—
64C2×C4×C277—22no—
65C2×C4×C277—24no—
66C2×C4×C277—41no—
67C2×C4×C277—41no—
68C2×C4×C277—41no—
69C2×C4×C277—42no—
70C2×C4×C277—42no—
71C2×C4×C277C22⋊C411yescharacteristic
72C2×C4×C277C22⋊C411yescharacteristic
73C2×C4×C277C22×C411yescharacteristic
74C2×C4×C277C2×D411yescharacteristic
75C22×C277—21no—
76C22×C277—21no—
77C22×C277—21no—
78C22×C277—21no—
79C22×C277—21no—
80C22×C277—21no—
81C22×C277—21no—
82C22×C277—44no—
83C22×C277#10412yes—
84C22×C277C2×C22⋊C411yescharacteristic
85C22×C277AGL(1,ℤ/8)12yes—
86C2×D277—42no—
87C2×D277—42no—
88C2×D277—42no—
89C2×D277—84no—
90C4×C277—21no—
91C4×C277—21no—
92C4×C277—21no—
93C4×C277—44no—
94C4×C277#9912yes—
95Dic277—42no—
96C2×C277—22no—
97C2×C277—22no—
98C2×C277—41no—
99C2×C277C2×#9911yescharacteristic
100C2×C277#41811yescharacteristic
101C2×C277C2×#10411yescharacteristic
102D277—82no—
103C277#150711yescharacteristic, complemented, Sylow
104#1507—2771nomaximal, Sylow
105C2×#121—2771no—
106#407—2771no—
107C4×C22⋊C4D27711yescharacteristic, complemented
108#327—2774no—
109C22×D4—2771no—
110C22×D4—5541no—
111C23×C4C2×D27711yescharacteristic
112C2×M16—5541no—
113#121—2772no—
114#121—2772no—
115#121—5541no—
116#121—5541no—
117C2×C4⋊C4—2771no—
118C2×C22⋊C4—21no—
119C2×C22⋊C4—5541no—
120C2×C42—21no—
121C22⋊C8—2772no—
122C22⋊C8—5541no—
123#95C2×D27712yescomplemented
124C24—5541no—
125C24C22⋊D27711yescharacteristic
126C2×D4—2772no—
127C2×D4—5542no—
128C2×D4—5542no—
129C2×D4—5541no—
130C2×D4—11082no—
131C2×D4—11084no—
132C22×C4—22no—
133C22×C4—42no—
134C22×C4—5541no—
135C22×C4C4×D27711yescharacteristic
136C22×C4C4×D27711yescharacteristic
137C22×C4C22⋊D27711yescharacteristic
138C22×C4D110811yescharacteristic
139C22×C4D110811yescharacteristic
140C22×C4C22×D27711yescharacteristic
141M16—11082no—
142C2×C8—5542no—
143C4⋊C4—2772no—
144C4⋊C4—5541no—
145C22⋊C4—24no—
146C22⋊C4—5542no—
147C22⋊C4—5542no—
148C42—42no—
149C23—22no—
150C23—22no—
151C23—41no—
152C23—5542no—
153C23—11082no—
154C23—11082no—
155C23—11082no—
156C23#1798454011yescharacteristic
157C23#1798454011yescharacteristic
158C23C2×C22⋊D27711yescharacteristic
159D4—11082no—
160D4—11084no—
161D4—11084no—
162D4—11082no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—24no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—5542no—
173C2×C4—11082no—
174C2×C4#1798454011yescharacteristic
175C2×C4#1798454011yescharacteristic
176C2×C4C2×C4×D27711yescharacteristic
177C2×C4C2×D110811yescharacteristic
178C8—11082no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—44no—
187C22—11082no—
188C22—11082no—
189C22—11082no—
190C22—22164no—
191C22#2257980812yes—
192C22C2×#1798454011yescharacteristic
193C22#2257990512yes—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—44no—
198C4—11082no—
199C4#2257979412yes—
200C2—22no—
201C2—22no—
202C2—41no—
203C2—22162no—
204C2C2×#2257979411yescharacteristic
205C2#3180000611yescharacteristic
206C2C2×#2257980811yescharacteristic
subgroupG/H
centerC22C2×#17984540
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
FittingC4×C22⋊C4×C277C2
socleC22×C277C2×C22⋊C4
prime radicalC2×#22579854C2
cosocleC22×C4×C277C23
hypercenterC4×C22⋊C4D277
hypocenterC277#1507
LCSG ▷ C2×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #31799966C2semidirect
3. #31799735C2semidirect
4. C4×C22⋊C4×C277C2semidirect
5. C22×D1108C4semidirect
10. #22579854C4semidirect
12. C2×C4⋊Dic277C4semidirect
15. C22⋊#14555660C22semidirect
19. #95×C277C22semidirect
103. C277#1507semidirect
107. C4×C22⋊C4D277semidirect
123. #95C2×D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225798542
#317999662
#317997352
C4×C22⋊C4×C2772
#1507277