Finite Group Databasebeta

← #47982341

Subgroups — #47982341

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#31800722C211yesmaximal, characteristic
2#31800353C211yesmaximal, characteristic, complemented
3#31800298C211yesmaximal, characteristic, complemented
4#31800292C211yesmaximal, characteristic
5#31799747C211yesmaximal, characteristic, complemented
6#31799734C211yesmaximal, characteristic, complemented
7D4⋊C8×C277C211yesmaximal, characteristic
8#22579880C2211yescharacteristic
9#22579880C2211yescharacteristic
10#22579873—22no—
11#22579867—21no—
12#22579859—21no—
13C4×Dic554C2211yescharacteristic
14#22579845—21no—
15#22579839—21no—
16#22579814—21no—
17#22579811—21no—
18C4⋊#14555660C2211yescharacteristic
19#22579805—21no—
20#22579805—22no—
21#22579801—21no—
22C4×D4×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4×C8×C277C2211yescharacteristic
25C2×Dic554—21no—
26C2×Dic554—21no—
27C2×Dic554D411yescharacteristic
28C2×#14555660—21no—
29C4⋊Dic277—21no—
30C4⋊Dic277—21no—
31C4⋊Dic277—21no—
32C4⋊Dic277D412yes—
33C4⋊Dic277D411yescharacteristic
34#17984542—22no—
35#17984542—21no—
36C22⋊Dic277—22no—
37C22⋊Dic277—22no—
38C4×Dic277—22no—
39C4×Dic277—21no—
40C2×D4×C277D411yescharacteristic
41C22×C4×C277—21no—
42C2×C8×C277—21no—
43C2×C8×C277—21no—
44C4⋊C4×C277D411yescharacteristic
45C22⋊C4×C277—21no—
46C42×C277C2311yescharacteristic
47Dic554—21no—
48Dic554—21no—
49Dic554—41no—
50Dic554—41no—
51Dic554—42no—
52C2×Dic277—21no—
53C2×Dic277—21no—
54C2×Dic277—22no—
55C2×Dic277—41no—
56#14555660—41no—
57C23×C277—21no—
58D4×C277—21no—
59D4×C277—21no—
60C2×C4×C277—21no—
61C2×C4×C277—41no—
62C2×C4×C277—41no—
63C2×C4×C277C2×D411yescharacteristic
64C2×C4×C277C2×D411yescharacteristic
65C2×C4×C277C2×D411yescharacteristic
66C8×C277—41no—
67C8×C277—41no—
68C22×C277—41no—
69C22×C277—41no—
70C22×C277—41no—
71C22×C277#12011yescharacteristic
72C4×C277—21no—
73C4×C277—41no—
74C4×C277#13511yescharacteristic
75C4×C277#13511yescharacteristic
76C4×C277#13711yescharacteristic
77C4×C277#13711yescharacteristic
78Dic277—41no—
79Dic277—42no—
80Dic277—41no—
81Dic277—81no—
82C2×C277—81no—
83C2×C277#45211yescharacteristic
84C2×C277#45211yescharacteristic
85C2×C277#45411yescharacteristic
86C277#163811yescharacteristic, complemented, Sylow
87#1638—2771nomaximal, Sylow
88#556—2771no—
89#487—2771no—
90#477—2771no—
91#476—2771no—
92#332—2771no—
93Q8⋊C8—2771no—
94D4⋊C8D27711yescharacteristic
95C4⋊Q8—2771no—
96C4⋊Q8—2771no—
97#126—5542no—
98#124—5541no—
99C22⋊Q8—5541no—
100C4×Q8—2771no—
101C4×Q8—5541no—
102C4×D4C2×D27711yescharacteristic
103#117—5541no—
104#107—5541no—
105#106—5541no—
106C4⋊C8—2771no—
107C4⋊C8C2×D27711yescharacteristic
108#103—5542no—
109#103—5541no—
110#102—5541no—
111C4×C8C2×D27711yescharacteristic
112C2×Q8—2771no—
113C2×Q8—5541no—
114C2×Q8—5541no—
115C2×D4D110811yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—5541no—
120C4⋊C4—2772no—
121C4⋊C4—2771no—
122C4⋊C4—5542no—
123C4⋊C4—5541no—
124C4⋊C4—5541no—
125C4⋊C4—5541no—
126C4⋊C4—5541no—
127C4⋊C4D110811yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—5542no—
130C22⋊C4—5542no—
131C42—5542no—
132C42—5541no—
133C42C22×D27711yescharacteristic
134C23—21no—
135Q8—5541no—
136Q8—5541no—
137Q8—11082no—
138Q8—11081no—
139Q8—11081no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—5541no—
146C2×C4—5542no—
147C2×C4—5541no—
148C2×C4—11081no—
149C2×C4D4×D27711yescharacteristic
150C2×C4D4×D27711yescharacteristic
151C2×C4C2×D110811yescharacteristic
152C8—41no—
153C8—41no—
154C8—11081no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#2257985011yescharacteristic
159C4—21no—
160C4—41no—
161C4—11081no—
162C4—11082no—
163C4—11081no—
164C4—22161no—
165C4#2257989911yescharacteristic
166C4#2257990211yescharacteristic
167C4#2257990911yescharacteristic
168C4#2257991311yescharacteristic
169C2—81no—
170C2#3180016511yescharacteristic
171C2#3180016611yescharacteristic
172C2#3180017611yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
FittingD4⋊C8×C277C2
socleC22×C277#120
prime radicalC2×D4×C277D4
hypercenterD4⋊C8D277
hypocenterC277#1638
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. #31800298C2semidirect
5. #31799747C2semidirect
6. #31799734C2semidirect
86. C277#1638semidirect

Maximal subgroups

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

subgroupindex
#318007222
#318003532
#318002982
#318002922
#317997472
#317997342
D4⋊C8×C2772
#1638277