Finite Group Databasebeta

← #47984835

Subgroups — #47984835

Order 35456.

286 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 55 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#31800570C211yesmaximal, characteristic
2#99×D277C212yesmaximal, complemented
3#31799797C211yesmaximal, characteristic, complemented
4#31799794C212yesmaximal, complemented
5#354×C277C211yesmaximal, characteristic, complemented
6C2×#17984564C411yescharacteristic, complemented
7C2×D4×D277C2211yescharacteristic
8#22579877C411yescharacteristic, complemented
9#22579876C2211yescharacteristic
10#22579869C411yescharacteristic, complemented
11#22579853—22no—
12#22579850—22no—
13#22579837C411yescharacteristic, complemented
14C22⋊C4×D277—22no—
15#22579795C2212yes—
16#22579794—22no—
17#124×C277C2211yescharacteristic
18#99×C277C2212yes—
19C23×D277D412yes—
20#17984564—42no—
21C2×D1108—21no—
22C2×D1108—22no—
23C2×D1108C2×C411yescharacteristic
24C2×D1108C2×C411yescharacteristic, complemented
25C2×C22⋊D277—22no—
26C2×C22⋊D277D412yes—
27D4×D277—42no—
28C2×C4×D277—21no—
29C2×C4×D277—42no—
30C2×C4×D277C2×C411yescharacteristic
31#17984542—21no—
32C22⋊Dic277—22no—
33#17984540—21no—
34#17984540—22no—
35#17984540—42no—
36C4×Dic277C2×C411yescharacteristic, complemented
37C2×Q8×C277C2×C411yescharacteristic, complemented
38C2×D4×C277C2311yescharacteristic
39C22⋊C4×C277—22no—
40C22⋊C4×C277—22no—
41C42×C277C2×C411yescharacteristic, complemented
42C22×D277—22no—
43C22×D277—22no—
44C22×D277—21no—
45C22×D277—82no—
46C22×D277C22⋊C412yes—
47C22×D277C22⋊C411yescharacteristic
48D1108—41no—
49D1108—41no—
50D1108—42no—
51D1108—82no—
52C22⋊D277—42no—
53C22⋊D277—82no—
54C2×Dic277—21no—
55C2×Dic277—42no—
56C2×Dic277C22⋊C411yescharacteristic
57C4×D277—22no—
58C4×D277—42no—
59C4×D277—84no—
60C23×C277C2×D412yes—
61Q8×C277—41no—
62D4×C277—41no—
63C2×C4×C277—21no—
64C2×C4×C277—21no—
65C2×C4×C277—42no—
66C2×C4×C277C22×C411yescharacteristic
67C22×C277—22no—
68C22×C277—42no—
69C22×C277C2×C22⋊C411yescharacteristic
70C2×D277—22no—
71C2×D277—41no—
72C2×D277—44no—
73C2×D277—42no—
74C2×D277—42no—
75C2×D277—41no—
76C2×D277—82no—
77C2×D277#9912yes—
78C4×C277—21no—
79C4×C277—41no—
80C4×C277—41no—
81C4×C277—82no—
82Dic277—21no—
83Dic277—41no—
84Dic277—82no—
85C2×C277—21no—
86C2×C277—42no—
87C2×C277C2×#9911yescharacteristic
88D277—22no—
89D277—42no—
90D277—81no—
91C277#212711yescharacteristic, complemented, Sylow
92#2127—2771nomaximal, Sylow
93#535—2771no—
94C2×#99—2772no—
95#354—2771no—
96#354D27711yescharacteristic, complemented
97#353—2772no—
98C2×#41—2771no—
99C22×D4—2771no—
100#127—2771no—
101#127—2771no—
102#124—2771no—
103#124C2×D27711yescharacteristic
104#121—5542no—
105#120—5542no—
106#117—2771no—
107C2×C22⋊C4—5542no—
108#99—2772no—
109#99—5542no—
110#99C2×D27712yes—
111C24—2772no—
112#41—11082no—
113C2×Q8C4×D27711yescharacteristic, complemented
114C2×D4—2772no—
115C2×D4—2771no—
116C2×D4—2771no—
117C2×D4—5541no—
118C2×D4—5542no—
119C2×D4—5542no—
120C2×D4—11082no—
121C2×D4C22×D27711yescharacteristic
122C22×C4—2771no—
123C22×C4—5541no—
124C22×C4—11082no—
125C4⋊C4—5541no—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C22⋊C4—5541no—
129C22⋊C4—5542no—
130C22⋊C4—5542no—
131C22⋊C4—11082no—
132C42—2771no—
133C42C4×D27711yescharacteristic, complemented
134C23—2771no—
135C23—2772no—
136C23—5542no—
137C23—5542no—
138C23—5541no—
139C23—22162no—
140C23D4×D27712yes—
141Q8—41no—
142D4—41no—
143D4—11081no—
144D4—11081no—
145D4—11082no—
146D4—11082no—
147D4—22162no—
148D4—22162no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—2771no—
153C2×C4—5542no—
154C2×C4—5541no—
155C2×C4—11082no—
156C2×C4—11082no—
157C2×C4—22164no—
158C2×C4C2×C4×D27711yescharacteristic
159C22—22no—
160C22—42no—
161C22—2772no—
162C22—5542no—
163C22—11081no—
164C22—11082no—
165C22—11082no—
166C22—11084no—
167C22—11081no—
168C22—22162no—
169C22C22⋊C4×D27711yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—5541no—
175C4—11081no—
176C4—22162no—
177C2—21no—
178C2—42no—
179C2—5542no—
180C2—11082no—
181C2—22161no—
182C2#99×D27711yescharacteristic
subgroupG/H
centerC2#99×D277
commutatorC2×C4×C277C22×C4
FrattiniC2×D4C22×D277
Fitting#354×C277C2
socleC2×C277C2×#99
prime radical#31800570C2
cosocleC2×D4×C277C23
hypercenter#354D277
hypocenterC277#2127
LCSG ▷ C2×C4×C277 ▷ C22×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #99×D277C2semidirect
3. #31799797C2semidirect
4. #31799794C2semidirect
5. #354×C277C2semidirect
6. C2×#17984564C4semidirect
8. #22579877C4semidirect
10. #22579869C4semidirect
13. #22579837C4semidirect
24. C2×D1108C2×C4semidirect
36. C4×Dic277C2×C4semidirect
37. C2×Q8×C277C2×C4semidirect
41. C42×C277C2×C4semidirect
91. C277#2127semidirect
96. #354D277semidirect
113. C2×Q8C4×D277semidirect
133. C42C4×D277semidirect

Maximal subgroups

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

subgroupindex
#318005702
#99×D2772
#317997972
#317997942
#354×C2772
#2127277