Finite Group Databasebeta

← #353×D277 #47984823

Subgroups — #353×D277 #47984823

Order 35456.

368 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 57 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#127×D277C211yesmaximal, characteristic
2#99×D277C212yesmaximal, complemented
3#31799795C211yesmaximal, characteristic, complemented
4#31799794C212yesmaximal, complemented
5#353×C277C211yesmaximal, characteristic, complemented
6C2×D4×D277—22no—
7C2×D4×D277C411yescharacteristic, complemented
8C2×D4×D277C2211yescharacteristic
9#22579877C411yescharacteristic, complemented
10#22579876—22no—
11#22579876C411yescharacteristic, complemented
12#22579876C2211yescharacteristic
13C22⋊C4×D277—22no—
14C42×D277C411yescharacteristic, complemented
15#22579795C2212yescomplemented
16#22579794—22no—
17#127×C277C2211yescharacteristic
18#99×C277C2212yescomplemented
19C23×D277—21no—
20C23×D277D412yes—
21C2×D1108—22no—
22C2×D1108C2×C411yescharacteristic
23C2×D1108C2×C411yescharacteristic, complemented
24C2×C22⋊D277—22no—
25C2×C22⋊D277—21no—
26C2×C22⋊D277—22no—
27C2×C22⋊D277D412yes—
28D4×D277—41no—
29D4×D277—41no—
30D4×D277—48no—
31D4×D277—41no—
32D4×D277—41no—
33C2×C4×D277—21no—
34C2×C4×D277—42no—
35C2×C4×D277C2×C411yescharacteristic
36C22⋊Dic277—22no—
37#17984540—42no—
38C4×Dic277—21no—
39C4×Dic277C2×C411yescharacteristic, complemented
40C2×D4×C277—22no—
41C2×D4×C277C2×C411yescharacteristic, complemented
42C2×D4×C277C2311yescharacteristic
43C22⋊C4×C277—22no—
44C42×C277C2×C411yescharacteristic, complemented
45C22×D277—22no—
46C22×D277—22no—
47C22×D277—21no—
48C22×D277—44no—
49C22×D277—44no—
50C22×D277—41no—
51C22×D277—41no—
52C22×D277C22⋊C411yescharacteristic
53C22×D277C22⋊C412yes—
54D1108—41no—
55D1108—41no—
56D1108—44no—
57C22⋊D277—42no—
58C22⋊D277—44no—
59C22⋊D277—44no—
60C22⋊D277—42no—
61C2×Dic277—21no—
62C2×Dic277—42no—
63C2×Dic277C22⋊C411yescharacteristic
64C4×D277—24no—
65C4×D277—21no—
66C4×D277—21no—
67C4×D277—84no—
68C23×C277—21no—
69C23×C277C2×D412yes—
70D4×C277—41no—
71D4×C277—41no—
72D4×C277—44no—
73C2×C4×C277—21no—
74C2×C4×C277—42no—
75C2×C4×C277C22×C411yescharacteristic
76C22×C277—22no—
77C22×C277—42no—
78C22×C277—42no—
79C22×C277—41no—
80C22×C277C2×C22⋊C411yescharacteristic
81C2×D277—22no—
82C2×D277—22no—
83C2×D277—44no—
84C2×D277—42no—
85C2×D277—42no—
86C2×D277—41no—
87C2×D277—82no—
88C2×D277—82no—
89C2×D277—82no—
90C2×D277#9911yescharacteristic
91C2×D277#9911yescharacteristic
92C4×C277—22no—
93C4×C277—21no—
94C4×C277—82no—
95Dic277—22no—
96Dic277—21no—
97Dic277—82no—
98C2×C277—21no—
99C2×C277—42no—
100C2×C277—81no—
101C2×C277C2×#9911yescharacteristic
102D277—21no—
103D277—42no—
104D277—81no—
105D277#35312yesdirect product factor
106C277C2×#35311yescharacteristic, complemented, Sylow
107C2×#353—2771nomaximal, Sylow
108C2×#127—2771no—
109C2×#99—2772no—
110#353—2771no—
111#353—2772no—
112#353D27711yescharacteristic, direct product factor
113C22×D4—2771no—
114C22×D4—2771no—
115C22×D4—5542no—
116#127—2771no—
117#127—2771no—
118#127—2771no—
119#127—5542no—
120#127C2×D27711yescharacteristic
121C2×C22⋊C4—5542no—
122C2×C42—2771no—
123#99—2772no—
124#99—5542no—
125#99C2×D27712yescomplemented
126C24—2772no—
127C24—5541no—
128C2×D4—22no—
129C2×D4—2772no—
130C2×D4—2771no—
131C2×D4—2771no—
132C2×D4—5542no—
133C2×D4—5541no—
134C2×D4—5542no—
135C2×D4—5542no—
136C2×D4—11081no—
137C2×D4—11081no—
138C2×D4—11081no—
139C2×D4—11081no—
140C2×D4—11088no—
141C2×D4C4×D27711yescharacteristic, complemented
142C2×D4C22×D27711yescharacteristic
143C22×C4—2771no—
144C22×C4—5541no—
145C22×C4—11082no—
146C22⋊C4—22no—
147C22⋊C4—5542no—
148C22⋊C4—11082no—
149C42—2771no—
150C42—5541no—
151C42C4×D27711yescharacteristic, complemented
152C23—21no—
153C23—2771no—
154C23—2772no—
155C23—5542no—
156C23—5542no—
157C23—5541no—
158C23—11081no—
159C23—11081no—
160C23—11084no—
161C23—11084no—
162C23D4×D27712yes—
163D4—41no—
164D4—41no—
165D4—44no—
166D4—11081no—
167D4—11081no—
168D4—11084no—
169D4—11082no—
170D4—11084no—
171D4—11084no—
172D4—11082no—
173C2×C4—21no—
174C2×C4—42no—
175C2×C4—2771no—
176C2×C4—5541no—
177C2×C4—5541no—
178C2×C4—5544no—
179C2×C4—5541no—
180C2×C4—11082no—
181C2×C4—22164no—
182C2×C4C2×C4×D27711yescharacteristic
183C22—22no—
184C22—42no—
185C22—42no—
186C22—41no—
187C22—2771no—
188C22—2771no—
189C22—5542no—
190C22—5542no—
191C22—11082no—
192C22—11082no—
193C22—11084no—
194C22—11081no—
195C22—22162no—
196C22—22162no—
197C22—22162no—
198C22C22⋊C4×D27711yescharacteristic
199C4—22no—
200C4—21no—
201C4—82no—
202C4—5542no—
203C4—5541no—
204C4—22162no—
205C2—21no—
206C2—42no—
207C2—81no—
208C2—2772no—
209C2—5541no—
210C2—11082no—
211C2—22161no—
212C2#99×D27711yescharacteristic
subgroupG/H
centerC2#99×D277
commutatorC2×C4×C277C22×C4
FrattiniC2×D4C22×D277
Fitting#353×C277C2
socleC2×C277C2×#99
prime radical#127×D277C2
cosocleC2×D4×C277C23
hypercenter#353D277
hypocenterC277C2×#353
LCSG ▷ C2×C4×C277 ▷ C22×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #99×D277C2semidirect
3. #31799795C2semidirect
4. #31799794C2semidirect
5. #353×C277C2semidirect
7. C2×D4×D277C4semidirect
9. #22579877C4semidirect
11. #22579876C4semidirect
14. C42×D277C4semidirect
15. #22579795C22semidirect
18. #99×C277C22semidirect
23. C2×D1108C2×C4semidirect
39. C4×Dic277C2×C4semidirect
41. C2×D4×C277C2×C4semidirect
44. C42×C277C2×C4semidirect
105. D277#353direct (N × H)
106. C277C2×#353semidirect
112. #353D277direct (N × H)
125. #99C2×D277semidirect
141. C2×D4C4×D277semidirect
151. C42C4×D277semidirect

Maximal subgroups

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

subgroupindex
#127×D2772
#99×D2772
#317997952
#317997942
#353×C2772
C2×#353277