Finite Group Databasebeta

← #47984299

Subgroups — #47984299

Order 35456.

430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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#31800564C211yesmaximal, characteristic
2C2×#22579864C212yesmaximal, complemented
3C2×#22579794C212yesmaximal, complemented
4#31799863C211yesmaximal, characteristic, complemented
5#342×C277C211yesmaximal, characteristic, complemented
6C22×C22⋊D277C2212yes—
7C23×Dic277C2211yescharacteristic
8#22579864—22no—
9#22579864—24no—
10#22579864—24no—
11#22579854—22no—
12#22579850—22no—
13C2×C4⋊Dic277—22no—
14C2×C22⋊Dic277C2211yescharacteristic
15C2×#17984540—22no—
16#22579794—24no—
17#22579787—22no—
18C2×C22⋊C4×C277C2211yescharacteristic
19C2×C22⋊C4×C277C2212yes—
20C23×D277D412yes—
21C2×D1108—22no—
22C2×C22⋊D277—22no—
23C2×C22⋊D277—22no—
24C2×C22⋊D277—22no—
25C2×C22⋊D277—22no—
26C2×C22⋊D277—22no—
27C2×C22⋊D277—22no—
28C22×Dic277—21no—
29C22×Dic277—22no—
30C22×Dic277—22no—
31C22×Dic277—21no—
32C22×Dic277—21no—
33C22×Dic277D412yes—
34C22×Dic277D412yescomplemented
35C4⋊Dic277—28no—
36C4⋊Dic277—22no—
37C22⋊Dic277—22no—
38#17984540—28no—
39#17984540—24no—
40C24×C277C2311yescharacteristic
41C22×C4×C277—22no—
42C22×C4×C277D412yes—
43C22⋊C4×C277—22no—
44C22⋊C4×C277—22no—
45C22⋊C4×C277D414yescomplemented
46C22×D277—22no—
47C22×D277—22no—
48C22×D277—22no—
49C22×D277—44no—
50D1108—82no—
51C22⋊D277—42no—
52C22⋊D277—42no—
53C22⋊D277—42no—
54C22⋊D277—42no—
55C2×Dic277—24no—
56C2×Dic277—22no—
57C2×Dic277—22no—
58C2×Dic277—22no—
59C2×Dic277—22no—
60C2×Dic277—41no—
61C2×Dic277—42no—
62C2×Dic277—41no—
63C2×Dic277—42no—
64C2×Dic277—41no—
65C23×C277—42no—
66C23×C277C2×D412yes—
67C23×C277C2×D411yescharacteristic
68C23×C277C2×D411yescharacteristic
69C23×C277C2×D412yes—
70C23×C277#4111yescharacteristic
71C2×C4×C277—22no—
72C2×C4×C277—24no—
73C2×C4×C277—44no—
74C2×C4×C277—42no—
75C22×C277—22no—
76C22×C277—24no—
77C22×C277—41no—
78C22×C277—42no—
79C22×C277—41no—
80C22×C277#12012yes—
81C22×C277#12011yescharacteristic
82C22×C277#12111yescharacteristic
83C22×C277#12112yes—
84C22×C277#12711yescharacteristic
85C2×D277—44no—
86C2×D277—42no—
87C2×D277—44no—
88C2×D277—82no—
89C4×C277—44no—
90C4×C277—42no—
91Dic277—42no—
92Dic277—42no—
93Dic277—81no—
94C2×C277—21no—
95C2×C277—22no—
96C2×C277—22no—
97C2×C277—21no—
98C2×C277#39211yescharacteristic
99C2×C277#45812yes—
100D277—82no—
101C277#202211yescharacteristic, complemented, Sylow
102#2022—2771nomaximal, Sylow
103#534—2771no—
104C2×#123—2772no—
105C2×#99—2772no—
106#381—2771no—
107#342D27711yescharacteristic, complemented
108C22×D4—2772no—
109C23×C4—2771no—
110#123—5544no—
111#123—5542no—
112#123—5544no—
113#121—5542no—
114#120—5542no—
115C2×C4⋊C4—5542no—
116C2×C22⋊C4—2771no—
117C2×C22⋊C4—5542no—
118C2×C22⋊C4C2×D27711yescharacteristic
119C2×C22⋊C4C2×D27712yes—
120#99—5544no—
121#95—5542no—
122C24—2772no—
123C24C22×D27711yescharacteristic
124C2×D4—5542no—
125C2×D4—5542no—
126C2×D4—5542no—
127C2×D4—5542no—
128C2×D4—5542no—
129C2×D4—5542no—
130C2×D4—5542no—
131C22×C4—22no—
132C22×C4—2772no—
133C22×C4—2772no—
134C22×C4—5542no—
135C22×C4—5541no—
136C22×C4—5542no—
137C22×C4—5541no—
138C22×C4—5541no—
139C22×C4D110812yes—
140C4⋊C4—5548no—
141C4⋊C4—5542no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—5548no—
145C22⋊C4—5544no—
146C22⋊C4—5542no—
147C22⋊C4D110814yescomplemented
148C23—42no—
149C23—5542no—
150C23—5542no—
151C23—5542no—
152C23—11084no—
153C23D4×D27712yes—
154C23D4×D27711yescharacteristic
155C23C2×D110811yescharacteristic
156C23C2×D110812yes—
157C23#1798456411yescharacteristic
158D4—11082no—
159D4—11082no—
160D4—11082no—
161D4—11082no—
162D4—22162no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—44no—
166C2×C4—42no—
167C2×C4—5544no—
168C2×C4—5542no—
169C2×C4—5542no—
170C2×C4—5542no—
171C2×C4—5542no—
172C2×C4—11081no—
173C2×C4—11082no—
174C2×C4—11081no—
175C2×C4—11082no—
176C2×C4—11081no—
177C22—22no—
178C22—24no—
179C22—41no—
180C22—42no—
181C22—41no—
182C22—11084no—
183C22—11082no—
184C22—11084no—
185C22—22162no—
186C22#2257985012yes—
187C22#2257985011yescharacteristic
188C22#2257985511yescharacteristic
189C22#2257985512yes—
190C22#2257987711yescharacteristic
191C4—44no—
192C4—42no—
193C4—11082no—
194C4—11082no—
195C4—22161no—
196C2—22no—
197C2—21no—
198C2—22no—
199C2—21no—
200C2—22162no—
201C2#3179991211yescharacteristic
202C2#3180019312yes—
subgroupG/H
centerC22#22579850
commutator, cosocleC24×C277C23
FrattiniC24C22×D277
Fitting#342×C277C2
socleC22×C277#120
prime radical#31800564C2
hypercenter#342D277
hypocenterC277#2022
LCSG ▷ C24×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#22579864C2semidirect
3. C2×#22579794C2semidirect
4. #31799863C2semidirect
5. #342×C277C2semidirect
34. C22×Dic277D4semidirect
45. C22⋊C4×C277D4semidirect
101. C277#2022semidirect
107. #342D277semidirect
147. C22⋊C4D1108semidirect

Maximal subgroups

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

subgroupindex
#318005642
C2×#225798642
C2×#225797942
#317998632
#342×C2772
#2022277