Finite Group Databasebeta

← #47984298

Subgroups — #47984298

Order 35456.

430 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 73 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×#22579863C212yesmaximal, complemented
3C2×#22579794C212yesmaximal, complemented
4#31799769C211yesmaximal, characteristic, complemented
5#381×C277C211yesmaximal, characteristic, complemented
6C22×C22⋊D277C2212yes—
7#22579864—22no—
8#22579863—24no—
9#22579863—24no—
10#22579854—22no—
11#22579850—22no—
12C2×#17984542—22no—
13C2×C22⋊Dic277C2212yes—
14C2×#17984540—22no—
15#22579794—24no—
16C23×C4×C277C2211yescharacteristic
17C2×C22⋊C4×C277C2211yescharacteristic
18C2×C22⋊C4×C277C2211yescharacteristic
19#95×C277—22no—
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—22no—
29C22×Dic277D412yes—
30C4⋊Dic277—22no—
31#17984542—28no—
32C22⋊Dic277—22no—
33C22⋊Dic277D414yescomplemented
34#17984540—28no—
35#17984540—24no—
36C24×C277C2311yescharacteristic
37C22×C4×C277—21no—
38C22×C4×C277—22no—
39C22×C4×C277—22no—
40C22×C4×C277—21no—
41C22×C4×C277—21no—
42C22×C4×C277D412yes—
43C22×C4×C277D412yescomplemented
44C22⋊C4×C277—22no—
45C22⋊C4×C277—22no—
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—44no—
60C23×C277—42no—
61C23×C277C2×D412yes—
62C23×C277C2×D412yes—
63C23×C277C2×D411yescharacteristic
64C23×C277C2×D411yescharacteristic
65C23×C277#4111yescharacteristic
66C2×C4×C277—22no—
67C2×C4×C277—24no—
68C2×C4×C277—22no—
69C2×C4×C277—41no—
70C2×C4×C277—42no—
71C2×C4×C277—41no—
72C2×C4×C277—42no—
73C2×C4×C277—42no—
74C2×C4×C277—41no—
75C22×C277—22no—
76C22×C277—24no—
77C22×C277—42no—
78C22×C277—41no—
79C22×C277—41no—
80C22×C277#12011yescharacteristic
81C22×C277#12012yes—
82C22×C277#12112yes—
83C22×C277#12111yescharacteristic
84C22×C277#12711yescharacteristic
85C2×D277—44no—
86C2×D277—42no—
87C2×D277—44no—
88C2×D277—82no—
89C4×C277—42no—
90C4×C277—42no—
91C4×C277—81no—
92Dic277—44no—
93Dic277—42no—
94C2×C277—22no—
95C2×C277—21no—
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#381D27711yescharacteristic, complemented
107#342—2771no—
108C22×D4—2772no—
109C23×C4C2×D27711yescharacteristic
110#123—5542no—
111#123—5544no—
112#123—5544no—
113#121—5542no—
114#120—5542no—
115C2×C4⋊C4—5542no—
116C2×C22⋊C4—2772no—
117C2×C22⋊C4—5542no—
118C2×C22⋊C4C2×D27711yescharacteristic
119C2×C22⋊C4C2×D27711yescharacteristic
120#99—5544no—
121#95—22no—
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—22no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—2772no—
137C22×C4—5542no—
138C22×C4C22⋊D27712yes—
139C22×C4D110812yescomplemented
140C4⋊C4—5548no—
141C4⋊C4—5542no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—2774no—
145C22⋊C4—5548no—
146C22⋊C4—5544no—
147C22⋊C4—5542no—
148C23—42no—
149C23—5542no—
150C23—5542no—
151C23—5542no—
152C23—11084no—
153C23D4×D27712yes—
154C23D4×D27712yes—
155C23C2×C22⋊D27711yescharacteristic
156C23C2×D110811yescharacteristic
157C23#1798456311yescharacteristic
158D4—11082no—
159D4—11082no—
160D4—11082no—
161D4—11082no—
162D4—22162no—
163C2×C4—22no—
164C2×C4—24no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—42no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—5542no—
173C2×C4—5544no—
174C2×C4—5542no—
175C2×C4—5542no—
176C2×C4—11084no—
177C22—22no—
178C22—24no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—11084no—
183C22—11082no—
184C22—11084no—
185C22—22162no—
186C22#2257984811yescharacteristic
187C22#2257985012yes—
188C22#2257985312yes—
189C22#2257985411yescharacteristic
190C22#2257987611yescharacteristic
191C4—42no—
192C4—42no—
193C4—81no—
194C4—11084no—
195C4—11082no—
196C2—21no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—22162no—
201C2#3179991111yescharacteristic
202C2#3180019112yes—
subgroupG/H
centerC22#22579848
commutator, cosocleC24×C277C23
FrattiniC24C22×D277
Fitting#381×C277C2
socleC22×C277#120
prime radical#31800564C2
hypercenter#381D277
hypocenterC277#2022
LCSG ▷ C24×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#22579863C2semidirect
3. C2×#22579794C2semidirect
4. #31799769C2semidirect
5. #381×C277C2semidirect
33. C22⋊Dic277D4semidirect
43. C22×C4×C277D4semidirect
101. C277#2022semidirect
106. #381D277semidirect
139. C22×C4D1108semidirect

Maximal subgroups

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

subgroupindex
#318005642
C2×#225798632
C2×#225797942
#317997692
#381×C2772
#2022277