Finite Group Databasebeta

← #47982340

Subgroups — #47982340

Order 35456.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#31800726C211yesmaximal, characteristic
2#31800354C211yesmaximal, characteristic, complemented
3#31800298C211yesmaximal, characteristic, complemented
4#31800293C211yesmaximal, characteristic
5#31799732C211yesmaximal, characteristic, complemented
6#31799729C211yesmaximal, characteristic
7#332×C277C211yesmaximal, characteristic, complemented
8#22579880C2211yescharacteristic
9#22579875—22no—
10#22579869—21no—
11#22579860—21no—
12Q8×Dic277—21no—
13C4×Dic554C2211yescharacteristic
14C4×D1108C2211yescharacteristic
15#22579838—21no—
16#22579814—21no—
17#22579812—21no—
18#22579805—21no—
19#22579803—22no—
20#22579802—21no—
21C4×#14555660C2211yescharacteristic
22C4⋊Q8×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4⋊C8×C277C2211yescharacteristic
25C2×Dic554—21no—
26C2×Dic554D411yescharacteristic
27C2×D1108D411yescharacteristic
28C2×C4×D277—21no—
29C2×#14555660—21no—
30C4⋊Dic277—22no—
31C4⋊Dic277—21no—
32C4⋊Dic277—21no—
33C4⋊Dic277D411yescharacteristic
34C4⋊Dic277D411yescharacteristic
35#17984542—21no—
36#17984540—22no—
37#17984540—22no—
38#17984540—21no—
39C4×Dic277—22no—
40C4×Dic277—21no—
41C2×Q8×C277—21no—
42C2×C8×C277—21no—
43C2×C8×C277—21no—
44C4⋊C4×C277—21no—
45C4⋊C4×C277D412yes—
46C42×C277C2311yescharacteristic
47C22×D277—21no—
48Dic554—21no—
49Dic554—21no—
50Dic554—42no—
51D1108—21no—
52D1108—21no—
53C2×Dic277—21no—
54C2×Dic277—21no—
55C2×Dic277—21no—
56C2×Dic277—41no—
57C4×D277—41no—
58C4×D277—41no—
59#14555660—41no—
60Q8×C277—41no—
61Q8×C277—41no—
62C2×C4×C277—22no—
63C2×C4×C277C2×D411yescharacteristic
64C2×C4×C277C2×D411yescharacteristic
65C2×C4×C277C2×D411yescharacteristic
66C8×C277—41no—
67C8×C277—41no—
68C22×C277#12011yescharacteristic
69C2×D277—41no—
70C2×D277—41no—
71C2×D277—41no—
72C4×C277—21no—
73C4×C277—42no—
74C4×C277#13511yescharacteristic
75C4×C277#13511yescharacteristic
76C4×C277#13711yescharacteristic
77C4×C277#13711yescharacteristic
78Dic277—41no—
79Dic277—41no—
80Dic277—41no—
81Dic277—81no—
82C2×C277#45211yescharacteristic
83C2×C277#45211yescharacteristic
84C2×C277#45411yescharacteristic
85D277—81no—
86C277#163811yescharacteristic, complemented, Sylow
87#1638—2771nomaximal, Sylow
88#556—2771no—
89#487—2771no—
90#477—2771no—
91#476—2771no—
92#332D27711yescharacteristic, complemented
93Q8⋊C8—2771no—
94D4⋊C8—2771no—
95C4⋊Q8—2771no—
96C4⋊Q8C2×D27711yescharacteristic
97#126—5542no—
98#124—5541no—
99C22⋊Q8—5541no—
100C4×Q8—2771no—
101C4×Q8—5541no—
102C4×D4—2771no—
103#117—5541no—
104#107—5541no—
105#106—5541no—
106C4⋊C8C2×D27711yescharacteristic
107C4⋊C8C2×D27711yescharacteristic
108#103—5541no—
109#103—5542no—
110#102—5541no—
111C4×C8—2771no—
112C2×Q8—21no—
113C2×Q8—2771no—
114C2×Q8—5541no—
115C2×D4—2771no—
116C22×C4—5541no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—5541no—
120C4⋊C4—21no—
121C4⋊C4—2771no—
122C4⋊C4—2771no—
123C4⋊C4—5542no—
124C4⋊C4—5541no—
125C4⋊C4—5541no—
126C4⋊C4—5541no—
127C4⋊C4D110812yes—
128C22⋊C4—5542no—
129C22⋊C4—5542no—
130C22⋊C4—5541no—
131C42—5542no—
132C42—5541no—
133C42C22×D27711yescharacteristic
134C23—5541no—
135Q8—41no—
136Q8—41no—
137Q8—5541no—
138Q8—5541no—
139Q8—11082no—
140D4—5541no—
141D4—5541no—
142C2×C4—22no—
143C2×C4—5541no—
144C2×C4—5541no—
145C2×C4—5541no—
146C2×C4—11081no—
147C2×C4—11081no—
148C2×C4—11081no—
149C2×C4D4×D27711yescharacteristic
150C2×C4D4×D27711yescharacteristic
151C2×C4C2×D110811yescharacteristic
152C8—41no—
153C8—41no—
154C8—11081no—
155C22—11081no—
156C22—11081no—
157C22—11081no—
158C22#2257985011yescharacteristic
159C4—21no—
160C4—42no—
161C4—11081no—
162C4—11081no—
163C4—11081no—
164C4—22161no—
165C4#2257989911yescharacteristic
166C4#2257990111yescharacteristic
167C4#2257990911yescharacteristic
168C4#2257991211yescharacteristic
169C2—22161no—
170C2#3180016511yescharacteristic
171C2#3180016711yescharacteristic
172C2#3180017711yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#332×C277C2
socleC22×C277#120
prime radicalC2×D1108D4
hypercenter#332D277
hypocenterC277#1638
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #31800354C2semidirect
3. #31800298C2semidirect
5. #31799732C2semidirect
7. #332×C277C2semidirect
86. C277#1638semidirect
92. #332D277semidirect

Maximal subgroups

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

subgroupindex
#318007262
#318003542
#318002982
#318002932
#317997322
#317997292
#332×C2772
#1638277