Finite Group Databasebeta

← #47983695

Subgroups — #47983695

Order 35456.

344 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 93 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#31800769C211yesmaximal, characteristic, complemented
2#31800007C212yesmaximal, complemented
3#31799976C211yesmaximal, characteristic, complemented
4#31799758C212yesmaximal, complemented
5#535×C277C211yesmaximal, characteristic
6#22579887—24no—
7C2×#17984547—22no—
8C2×#17984547C2212yes—
9#22579839C2212yes—
10#22579801—24no—
11#22579795—22no—
12C2×#41×C277C2211yescharacteristic
13C22×D4×C277C2211yescharacteristic
14#127×C277C412yescomplemented
15#124×C277C412yescomplemented
16#121×C277—22no—
17#120×C277—22no—
18#117×C277C2211yescharacteristic
19#17984547—24no—
20#17984547—22no—
21#17984547—22no—
22C2×#14555660—24no—
23C2×#14555660D414yescomplemented
24C4⋊Dic277—22no—
25C22⋊Dic277—22no—
26C4×Dic277—22no—
27C24×C277—21no—
28#41×C277—22no—
29#41×C277—22no—
30C2×Q8×C277C2×C411yescharacteristic
31C2×D4×C277—24no—
32C2×D4×C277—22no—
33C2×D4×C277—21no—
34C2×D4×C277—22no—
35C2×D4×C277C2×C412yes—
36C2×D4×C277C2×C411yescharacteristic
37C2×D4×C277D412yes—
38C22×C4×C277D412yes—
39C22×C4×C277C2311yescharacteristic
40C4⋊C4×C277—21no—
41C22⋊C4×C277—21no—
42C22⋊C4×C277—24no—
43C42×C277C2×C412yes—
44C2×Dic277—42no—
45#14555660—24no—
46C23×C277—22no—
47C23×C277—42no—
48C23×C277—82no—
49C23×C277C22⋊C412yes—
50C23×C277C2×D411yescharacteristic
51Q8×C277—22no—
52D4×C277—24no—
53D4×C277—22no—
54D4×C277—24no—
55D4×C277—41no—
56D4×C277—41no—
57D4×C277—84no—
58C2×C4×C277—22no—
59C2×C4×C277—22no—
60C2×C4×C277—22no—
61C2×C4×C277C22⋊C412yes—
62C2×C4×C277C22×C411yescharacteristic
63C2×C4×C277C2×D412yes—
64C2×C4×C277C2×D411yescharacteristic
65C2×C4×C277#4112yes—
66C22×C277—22no—
67C22×C277—41no—
68C22×C277—42no—
69C22×C277—44no—
70C22×C277—42no—
71C22×C277—84no—
72C22×C277C2×C22⋊C411yescharacteristic
73C22×C277#12112yes—
74C4×C277—22no—
75C4×C277—42no—
76C4×C277C4×D412yes—
77C4×C277#12011yescharacteristic
78C4×C277#12311yescharacteristic
79Dic277—82no—
80C2×C277—22no—
81C2×C277—21no—
82C2×C277—42no—
83C2×C277—82no—
84C2×C277#38611yescharacteristic
85C277#191011yescharacteristic, complemented, Sylow
86#1910—2771nomaximal, Sylow
87#568—2771no—
88#535D27711yescharacteristic
89#418—2772no—
90#410—2771no—
91H(3,ℤ/4)—2772no—
92C2×#41C2×D27711yescharacteristic
93C22×D4C2×D27711yescharacteristic
94#131—5544no—
95C2×M16—2772no—
96C2×M16—5542no—
97#127Dic27712yescomplemented
98#124Dic27712yescomplemented
99#121—22no—
100#120—22no—
101#117—2772no—
102#117C2×D27711yescharacteristic
103#102—5544no—
104#99—5542no—
105C24—21no—
106#41—22no—
107#41—22no—
108C2×Q8C2×Dic27711yescharacteristic
109C2×D4—24no—
110C2×D4—22no—
111C2×D4—21no—
112C2×D4—22no—
113C2×D4C2×Dic27712yes—
114C2×D4C2×Dic27711yescharacteristic
115C2×D4C22⋊D27712yes—
116C22×C4C22⋊D27712yes—
117C22×C4C22×D27711yescharacteristic
118M16—5544no—
119M16—5542no—
120M16—5542no—
121C2×C8—2774no—
122C2×C8—5544no—
123C4⋊C4—21no—
124C4⋊C4—5542no—
125C22⋊C4—21no—
126C22⋊C4—24no—
127C22⋊C4—5542no—
128C42—5542no—
129C42C2×Dic27712yes—
130C23—22no—
131C23—42no—
132C23—82no—
133C23C22⋊Dic27712yes—
134C23C2×C22⋊D27711yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—24no—
139D4—41no—
140D4—41no—
141D4—84no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—11082no—
146C2×C4C22⋊Dic27712yes—
147C2×C4C22×Dic27711yescharacteristic
148C2×C4D4×D27712yes—
149C2×C4C2×C22⋊D27711yescharacteristic
150C2×C4#1798456212yes—
151C8—5544no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—44no—
156C22—42no—
157C22—84no—
158C22C2×C22⋊Dic27711yescharacteristic
159C22#2257985212yes—
160C4—22no—
161C4—42no—
162C4—22162no—
163C4D4×Dic27712yes—
164C4#2257984811yescharacteristic
165C4#2257986111yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—82no—
170C2#3179988211yescharacteristic
subgroupG/H
centerC2#31799882
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
Fitting, prime radical#535×C277C2
socleC2×C277#386
cosocleC22×C4×C277C23
hypercenter#535D277
hypocenterC277#1910
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #31800769C2semidirect
2. #31800007C2semidirect
3. #31799976C2semidirect
4. #31799758C2semidirect
14. #127×C277C4semidirect
15. #124×C277C4semidirect
23. C2×#14555660D4semidirect
85. C277#1910semidirect
97. #127Dic277semidirect
98. #124Dic277semidirect

Maximal subgroups

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

subgroupindex
#318007692
#318000072
#317999762
#317997582
#535×C2772
#1910277