Finite Group Databasebeta

← #47982320

Subgroups — #47982320

Order 35456.

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

normal subgroups only

This group has 234 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#31800656C211yesmaximal, characteristic
2#31800353C211yesmaximal, characteristic, complemented
3#31800293C211yesmaximal, characteristic, complemented
4#31800292C211yesmaximal, characteristic, complemented
5#31799747C211yesmaximal, characteristic, complemented
6#31799731C211yesmaximal, characteristic, complemented
7D4⋊C8×C277C211yesmaximal, characteristic, complemented
8C2×#17984562—21no—
9#22579880C2211yescharacteristic
10#22579880C2211yescharacteristic
11#22579864—22no—
12#22579860—21no—
13#22579854—21no—
14C4×D1108C2211yescharacteristic
15C2×C4⋊Dic277—21no—
16#22579812—21no—
17#22579811—21no—
18C4⋊#14555660C2211yescharacteristic
19#22579805—22no—
20#22579802—21no—
21#22579801—21no—
22C4×D4×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4×C8×C277C2211yescharacteristic
25#17984562—42no—
26#17984562—42no—
27C2×Dic554—21no—
28C2×Dic554—21no—
29C2×D1108D411yescharacteristic
30C2×C22⋊D277—22no—
31C22×Dic277—22no—
32C2×C4×D277—21no—
33C2×#14555660—21no—
34C4⋊Dic277—22no—
35C4⋊Dic277—21no—
36C4⋊Dic277—21no—
37C4⋊Dic277—21no—
38C4⋊Dic277D412yes—
39C4⋊Dic277D411yescharacteristic
40#17984540—22no—
41#17984540—21no—
42C2×D4×C277D411yescharacteristic
43C22×C4×C277—21no—
44C2×C8×C277—21no—
45C2×C8×C277—21no—
46C4⋊C4×C277D411yescharacteristic
47C22⋊C4×C277—21no—
48C42×C277C2311yescharacteristic
49C22×D277—21no—
50Dic554—41no—
51Dic554—41no—
52Dic554—42no—
53D1108—21no—
54D1108—21no—
55C22⋊D277—44no—
56C2×Dic277—21no—
57C2×Dic277—22no—
58C2×Dic277—44no—
59C2×Dic277—41no—
60C4×D277—41no—
61C4×D277—41no—
62#14555660—41no—
63C23×C277—21no—
64D4×C277—21no—
65D4×C277SD1612yes—
66C2×C4×C277—21no—
67C2×C4×C277—41no—
68C2×C4×C277—41no—
69C2×C4×C277C2×D411yescharacteristic
70C2×C4×C277C2×D411yescharacteristic
71C2×C4×C277C2×D411yescharacteristic
72C8×C277—41no—
73C8×C277—41no—
74C22×C277—22no—
75C22×C277—41no—
76C22×C277—41no—
77C22×C277#12011yescharacteristic
78C2×D277—41no—
79C2×D277—41no—
80C2×D277—41no—
81C4×C277—21no—
82C4×C277—41no—
83C4×C277C2×SD1611yescharacteristic
84C4×C277#13511yescharacteristic
85C4×C277AGL(1,ℤ/8)11yescharacteristic
86C4×C277#13711yescharacteristic
87Dic277—41no—
88Dic277—42no—
89Dic277—81no—
90C2×C277—42no—
91C2×C277#45011yescharacteristic
92C2×C277#45211yescharacteristic
93C2×C277#45411yescharacteristic
94D277—81no—
95C277#163511yescharacteristic, complemented, Sylow
96#1635—2771nomaximal, Sylow
97#547—2771no—
98#487—2771no—
99#476—2771no—
100#476—2771no—
101#332—2771no—
102D4⋊C8—2771no—
103D4⋊C8D27711yescharacteristic, complemented
104C2×#41—5541no—
105C4⋊Q8—2771no—
106C4⋊Q8—2771no—
107#123—5542no—
108C22⋊Q8—5541no—
109#121—5541no—
110C4×D4—2771no—
111C4×D4C2×D27711yescharacteristic
112C2×C4⋊C4—5541no—
113#106—5541no—
114#106—5541no—
115C4⋊C8—2771no—
116C4⋊C8C2×D27711yescharacteristic
117#103—5542no—
118#102—5541no—
119#102—5541no—
120C4×C8C2×D27711yescharacteristic
121#41—11082no—
122#41—11082no—
123C2×Q8—5541no—
124C2×Q8—5541no—
125C2×D4—2771no—
126C2×D4—5542no—
127C2×D4D110811yescharacteristic
128C22×C4—21no—
129C22×C4—5542no—
130C22×C4—5541no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—5541no—
134C4⋊C4—2772no—
135C4⋊C4—2771no—
136C4⋊C4—5542no—
137C4⋊C4—5541no—
138C4⋊C4—5541no—
139C4⋊C4—5541no—
140C4⋊C4D110811yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—5542no—
143C22⋊C4—5541no—
144C42C22×D27711yescharacteristic
145C23—21no—
146C23—5541no—
147Q8—11082no—
148Q8—11081no—
149Q8—11081no—
150D4—21no—
151D4—5541no—
152D4—5541no—
153D4—11084no—
154D4#1798455212yes—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—5541no—
159C2×C4—5542no—
160C2×C4—11084no—
161C2×C4—11081no—
162C2×C4—11081no—
163C2×C4—11081no—
164C2×C4D4×D27711yescharacteristic
165C2×C4D4×D27711yescharacteristic
166C2×C4C2×D110811yescharacteristic
167C8—41no—
168C8—41no—
169C8—11081no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—11081no—
174C22—11081no—
175C22—11081no—
176C22#2257985011yescharacteristic
177C4—21no—
178C4—41no—
179C4—11081no—
180C4—11082no—
181C4—22161no—
182C4C2×#1798455211yescharacteristic
183C4#2257989911yescharacteristic
184C4#2257990811yescharacteristic
185C4#2257990911yescharacteristic
186C2—42no—
187C2—22161no—
188C2#3180015511yescharacteristic
189C2#3180016511yescharacteristic
190C2#3180017611yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
FittingD4⋊C8×C277C2
socleC22×C277#120
prime radical#31800656C2
hypercenterD4⋊C8D277
hypocenterC277#1635
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #31800353C2semidirect
3. #31800293C2semidirect
4. #31800292C2semidirect
5. #31799747C2semidirect
6. #31799731C2semidirect
7. D4⋊C8×C277C2semidirect
95. C277#1635semidirect
103. D4⋊C8D277semidirect

Maximal subgroups

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

subgroupindex
#318006562
#318003532
#318002932
#318002922
#317997472
#317997312
D4⋊C8×C2772
#1635277