Finite Group Databasebeta

← #47982242

Subgroups — #47982242

Order 35456.

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

normal subgroups only

This group has 236 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#31800712C211yesmaximal, characteristic, complemented
2#31800375C211yesmaximal, characteristic, complemented
3#31800202C211yesmaximal, characteristic, complemented
4#31800198C211yesmaximal, characteristic
5#31799750C211yesmaximal, characteristic, complemented
6#31799731C211yesmaximal, characteristic, complemented
7Q8⋊C8×C277C211yesmaximal, characteristic, complemented
8C2×#17984552—22no—
9C2×#17984550—21no—
10C2×D2216—21no—
11#22579880C2211yescharacteristic
12#22579877C2211yescharacteristic
13#22579872—21no—
14#22579858—22no—
15#22579856—21no—
16C4×D1108—21no—
17C4×D1108C2211yescharacteristic
18C4⋊C4×D277—21no—
19C4⋊#14555660C2211yescharacteristic
20#22579802—21no—
21#22579800—21no—
22C4×Q8×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4×C8×C277C2211yescharacteristic
25C2×Dic554D412yes—
26C2×D1108—21no—
27C2×D1108—21no—
28C2×D1108—21no—
29C2×D1108D411yescharacteristic
30C2×C4×D277—22no—
31C2×C4×D277—21no—
32#17984552—44no—
33#17984550—42no—
34D2216—42no—
35C2×#14555660—21no—
36C4⋊Dic277—21no—
37C4⋊Dic277—21no—
38C4⋊Dic277D411yescharacteristic
39#17984542—22no—
40#17984542—22no—
41#17984540—22no—
42#17984540—21no—
43C2×Q8×C277D411yescharacteristic
44C2×C8×C277—21no—
45C2×C8×C277—21no—
46C4⋊C4×C277—21no—
47C4⋊C4×C277D411yescharacteristic
48C42×C277—21no—
49C42×C277C2311yescharacteristic
50C22×D277—21no—
51C22×D277—41no—
52Dic554—42no—
53D1108—21no—
54D1108—42no—
55D1108—41no—
56D1108—41no—
57D1108—41no—
58D1108—41no—
59D1108SD1612yescomplemented
60C2×Dic277—21no—
61C2×Dic277—22no—
62C4×D277—41no—
63C4×D277—41no—
64C4×D277—82no—
65#14555660—41no—
66Q8×C277—21no—
67Q8×C277—21no—
68C2×C4×C277—21no—
69C2×C4×C277—21no—
70C2×C4×C277C2×D411yescharacteristic
71C2×C4×C277C2×D411yescharacteristic
72C2×C4×C277C2×D411yescharacteristic
73C8×C277—22no—
74C8×C277—41no—
75C22×C277#12011yescharacteristic
76C2×D277—22no—
77C2×D277—41no—
78C2×D277—41no—
79C2×D277—81no—
80C2×D277—81no—
81C2×D277—81no—
82C4×C277—21no—
83C4×C277—41no—
84C4×C277—41no—
85C4×C277C2×SD1611yescharacteristic
86C4×C277#13511yescharacteristic
87C4×C277AGL(1,ℤ/8)11yescharacteristic
88C4×C277#13711yescharacteristic
89Dic277—41no—
90Dic277—42no—
91C2×C277#44811yescharacteristic
92C2×C277#44911yescharacteristic
93C2×C277#45311yescharacteristic
94D277—42no—
95D277—161no—
96C277#162211yescharacteristic, complemented, Sylow
97#1622—2771nomaximal, Sylow
98#554—2771no—
99#492—2771no—
100#460—2771no—
101#459—2771no—
102#333—2771no—
103Q8⋊C8D27711yescharacteristic, complemented
104D4⋊C8—2771no—
105C2×SD16—5542no—
106C2×SD16—5541no—
107C2×D8—5541no—
108C4⋊Q8—2771no—
109#127—2771no—
110#125—5541no—
111C22⋊Q8—5542no—
112C22⋊Q8—5541no—
113C4×Q8C2×D27711yescharacteristic
114C4×D4—2771no—
115C4×D4—5541no—
116C2×C4⋊C4—5541no—
117C4⋊C8—2771no—
118C4⋊C8C2×D27711yescharacteristic
119#102—5541no—
120#102—5541no—
121C4×C8C2×D27711yescharacteristic
122C2×Q8—2772no—
123C2×Q8D110811yescharacteristic
124C2×D4—2771no—
125C2×D4—5541no—
126C2×D4—5541no—
127C2×D4—5541no—
128C22×C4—5542no—
129C22×C4—5541no—
130SD16—11084no—
131SD16—11082no—
132D8—11082no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—5541no—
136C4⋊C4—21no—
137C4⋊C4—2771no—
138C4⋊C4—5542no—
139C4⋊C4—5542no—
140C4⋊C4—5541no—
141C4⋊C4—5541no—
142C4⋊C4D110811yescharacteristic
143C22⋊C4—5542no—
144C22⋊C4—5541no—
145C42—21no—
146C42C22×D27711yescharacteristic
147C23—5541no—
148C23—11081no—
149Q8—21no—
150Q8—21no—
151Q8—11082no—
152D4—2772no—
153D4—5541no—
154D4—11082no—
155D4—11081no—
156D4—11081no—
157D4—11081no—
158D4—11081no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—5541no—
162C2×C4—5542no—
163C2×C4—11081no—
164C2×C4—11081no—
165C2×C4—22162no—
166C2×C4D4×D27711yescharacteristic
167C2×C4D4×D27711yescharacteristic
168C2×C4C2×D110811yescharacteristic
169C8—22no—
170C8—41no—
171C8—11081no—
172C22—5542no—
173C22—11081no—
174C22—11081no—
175C22—22161no—
176C22—22161no—
177C22—22161no—
178C22#2257985011yescharacteristic
179C4—21no—
180C4—41no—
181C4—41no—
182C4—11081no—
183C4—11082no—
184C4SD16×D27711yescharacteristic
185C4#2257990211yescharacteristic
186C4#2257990811yescharacteristic
187C4#2257991211yescharacteristic
188C2—44321no—
189C2—11082no—
190C2#3180014211yescharacteristic
191C2#3180014911yescharacteristic
192C2#3180017111yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
FittingQ8⋊C8×C277C2
socleC22×C277#120
prime radical#31800198C2
hypercenterQ8⋊C8D277
hypocenterC277#1622
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #31800712C2semidirect
2. #31800375C2semidirect
3. #31800202C2semidirect
5. #31799750C2semidirect
6. #31799731C2semidirect
7. Q8⋊C8×C277C2semidirect
59. D1108SD16semidirect
96. C277#1622semidirect
103. Q8⋊C8D277semidirect

Maximal subgroups

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

subgroupindex
#318007122
#318003752
#318002022
#318001982
#317997502
#317997312
Q8⋊C8×C2772
#1622277