Finite Group Databasebeta

← #47984858

Subgroups — #47984858

Order 35456.

262 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 65 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#31800566C211yesmaximal, characteristic
2#31799986C211yesmaximal, characteristic, complemented
3#31799798C214yesmaximal, complemented
4#413×C277C211yesmaximal, characteristic, complemented
5C22×D1108C411yescharacteristic
6C2×#17984547—21no—
7#22579876C412yes—
8#22579869C2212yes—
9#22579854—21no—
10#22579854—21no—
11#22579848—21no—
12#22579848—21no—
13#22579839C411yescharacteristic
14#22579799C2212yescomplemented
15#22579797—21no—
16C2×#41×C277C2211yescharacteristic
17C2×M16×C277—21no—
18#101×C277C2212yescomplemented
19#100×C277—21no—
20C23×D277—21no—
21C2×D1108—21no—
22C2×D1108—41no—
23C2×D1108—41no—
24C2×D1108C2×C412yes—
25C2×C22⋊D277—22no—
26C2×C22⋊D277—22no—
27#17984547—22no—
28#17984547—41no—
29C2×#14555660—41no—
30C4⋊Dic277—21no—
31C22⋊Dic277—21no—
32#17984540—22no—
33#17984540—22no—
34C4×Dic277C2×C412yes—
35#41×C277—41no—
36#41×C277—41no—
37C2×Q8×C277C2311yescharacteristic
38C2×D4×C277C2×C411yescharacteristic
39C2×D4×C277D411yescharacteristic
40C2×D4×C277D411yescharacteristic
41C22×C4×C277C2×C411yescharacteristic
42C22×C4×C277D411yescharacteristic
43C22×C4×C277D411yescharacteristic
44M16×C277—22no—
45M16×C277—41no—
46C2×C8×C277—41no—
47C22×D277—22no—
48C22×D277—42no—
49C22×D277—82no—
50D1108—42no—
51D1108—41no—
52D1108—41no—
53C22⋊D277—82no—
54C22⋊D277—82no—
55C2×Dic277—22no—
56#14555660—42no—
57C23×C277C22⋊C411yescharacteristic
58C23×C277C22⋊C411yescharacteristic
59C23×C277C22⋊C411yescharacteristic
60Q8×C277—41no—
61D4×C277—41no—
62D4×C277—41no—
63D4×C277—41no—
64C2×C4×C277—21no—
65C2×C4×C277—21no—
66C2×C4×C277—21no—
67C2×C4×C277—21no—
68C2×C4×C277—21no—
69C2×C4×C277—21no—
70C2×C4×C277C22⋊C411yescharacteristic
71C2×C4×C277C22×C411yescharacteristic
72C2×C4×C277C2×D411yescharacteristic
73C2×C4×C277C2×D411yescharacteristic
74C8×C277—42no—
75C22×C277—21no—
76C22×C277—21no—
77C22×C277—21no—
78C22×C277—41no—
79C22×C277—41no—
80C22×C277—41no—
81C22×C277C2×C22⋊C411yescharacteristic
82C2×D277—42no—
83C2×D277—42no—
84C2×D277—42no—
85C2×D277—84no—
86C4×C277—21no—
87C4×C277—21no—
88C4×C277—21no—
89C4×C277#9911yescharacteristic
90C4×C277#9911yescharacteristic
91Dic277—42no—
92C2×C277—21no—
93C2×C277—41no—
94C2×C277—41no—
95C2×C277—41no—
96C2×C277C2×#9911yescharacteristic
97D277—82no—
98C277#213411yescharacteristic, complemented, Sylow
99#2134—2771nomaximal, Sylow
100#535—2771no—
101#413—2771no—
102#413D27711yescharacteristic, complemented
103#355—2774no—
104C2×#41C2×D27711yescharacteristic
105C22×D4—2771no—
106C2×M16—21no—
107C2×M16—5541no—
108#127—2772no—
109#124—2772no—
110#121—5541no—
111#121—5541no—
112#120—5541no—
113#120—5541no—
114#117—2771no—
115#101—2772no—
116#101C2×D27712yescomplemented
117#100—21no—
118#100—5541no—
119C24—5541no—
120#41—41no—
121#41—41no—
122C2×Q8C22×D27711yescharacteristic
123C2×D4—2772no—
124C2×D4—5542no—
125C2×D4—5542no—
126C2×D4—5541no—
127C2×D4—11081no—
128C2×D4—11081no—
129C2×D4C4×D27711yescharacteristic
130C2×D4C22⋊D27711yescharacteristic
131C2×D4D110811yescharacteristic
132C22×C4C4×D27711yescharacteristic
133C22×C4C22⋊D27711yescharacteristic
134C22×C4D110811yescharacteristic
135M16—22no—
136M16—41no—
137M16—5542no—
138M16—11081no—
139C2×C8—41no—
140C2×C8—11081no—
141C4⋊C4—5541no—
142C22⋊C4—5541no—
143C22⋊C4—5542no—
144C22⋊C4—5542no—
145C42—2772no—
146C23—5542no—
147C23—11082no—
148C23—22162no—
149C23#1798454011yescharacteristic
150C23#1798454011yescharacteristic
151C23#1798454011yescharacteristic
152Q8—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—11082no—
157D4—11081no—
158D4—11081no—
159D4—22162no—
160D4—22162no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—5542no—
168C2×C4#1798454011yescharacteristic
169C2×C4C2×C4×D27711yescharacteristic
170C2×C4C2×C22⋊D27711yescharacteristic
171C2×C4C2×D110811yescharacteristic
172C8—42no—
173C8—11082no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22—11082no—
181C22—11082no—
182C22—11082no—
183C22—22164no—
184C22C2×#1798454011yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—11082no—
189C4#2257979411yescharacteristic
190C4#2257979411yescharacteristic
191C2—21no—
192C2—41no—
193C2—41no—
194C2—41no—
195C2—22162no—
196C2C2×#2257979411yescharacteristic
subgroupG/H
centerC2C2×#22579794
commutatorC2×C4×C277C22×C4
FrattiniC2×Q8C22×D277
Fitting#413×C277C2
socleC2×C277C2×#99
prime radical#31800566C2
cosocleC2×Q8×C277C23
hypercenter#413D277
hypocenterC277#2134
LCSG ▷ C2×C4×C277 ▷ C22×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #31799986C2semidirect
3. #31799798C2semidirect
4. #413×C277C2semidirect
14. #22579799C22semidirect
18. #101×C277C22semidirect
98. C277#2134semidirect
102. #413D277semidirect
116. #101C2×D277semidirect

Maximal subgroups

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

subgroupindex
#318005662
#317999862
#317997982
#413×C2772
#2134277