Finite Group Databasebeta

← #47982160

Subgroups — #47982160

Order 35456.

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

normal subgroups only

This group has 228 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#31800628C211yesmaximal, characteristic
2#31800333C212yesmaximal, complemented
3#31799927C211yesmaximal, characteristic
4#31799740C212yesmaximal, complemented
5#323×C277C211yesmaximal, characteristic
6#22579859—21no—
7#22579859C2212yes—
8#22579857—22no—
9#22579857—22no—
10C2×C4⋊Dic277C2211yescharacteristic
11C2×C22⋊Dic277—21no—
12C2×C22⋊Dic277—21no—
13#22579812—22no—
14#22579805—22no—
15#22579787—21no—
16#22579787C2211yescharacteristic
17C2×C22⋊C4×C277C2211yescharacteristic
18C22⋊C8×C277C2212yes—
19C2×Dic554—21no—
20C2×Dic554D412yes—
21C22×Dic277—21no—
22C22×Dic277—21no—
23C22×Dic277—21no—
24C22×Dic277—21no—
25C4⋊Dic277—21no—
26C4⋊Dic277—22no—
27C4⋊Dic277D412yes—
28#17984542—22no—
29#17984542—22no—
30C22⋊Dic277—22no—
31C22⋊Dic277—22no—
32C22⋊Dic277—42no—
33C24×C277D411yescharacteristic
34C22×C4×C277D411yescharacteristic
35C22×C4×C277C2311yescharacteristic
36C2×C8×C277—22no—
37C22⋊C4×C277—22no—
38Dic554—42no—
39Dic554—81no—
40C2×Dic277—22no—
41C2×Dic277—22no—
42C2×Dic277—41no—
43C2×Dic277—41no—
44C2×Dic277—41no—
45C2×Dic277—41no—
46C2×Dic277—41no—
47C2×Dic277—41no—
48C2×Dic277—81no—
49C2×Dic277—81no—
50C23×C277—21no—
51C23×C277—21no—
52C23×C277—41no—
53C23×C277—41no—
54C23×C277SD1612yes—
55C23×C277C2×D411yescharacteristic
56C2×C4×C277—21no—
57C2×C4×C277—41no—
58C2×C4×C277—41no—
59C2×C4×C277C2×D412yes—
60C8×C277—42no—
61C22×C277—21no—
62C22×C277—21no—
63C22×C277—22no—
64C22×C277—42no—
65C22×C277—41no—
66C22×C277—41no—
67C22×C277—81no—
68C22×C277#12011yescharacteristic
69C22×C277C2×SD1611yescharacteristic
70C22×C277#13711yescharacteristic
71C4×C277—22no—
72C4×C277—41no—
73Dic277—42no—
74Dic277—42no—
75Dic277—81no—
76Dic277—81no—
77C2×C277—21no—
78C2×C277—21no—
79C2×C277—42no—
80C2×C277#44811yescharacteristic
81C2×C277#45511yescharacteristic
82C2×C277#45811yescharacteristic
83C277#160811yescharacteristic, complemented, Sylow
84#1608—2771nomaximal, Sylow
85#543—2771no—
86#483—2772no—
87#397—2771no—
88#328—2772no—
89#323D27711yescharacteristic
90C22⋊Q8—2772no—
91C22⋊Q8—5542no—
92C22⋊Q8—5542no—
93C22⋊Q8—5541no—
94C2×C4⋊C4—2771no—
95C2×C22⋊C4—5541no—
96C2×C22⋊C4—5541no—
97C2×C22⋊C4C2×D27711yescharacteristic
98#106—5542no—
99#103—5542no—
100C22⋊C8C2×D27712yes—
101#95—2771no—
102#95—5541no—
103C24D110811yescharacteristic
104C2×Q8—2772no—
105C2×Q8—5541no—
106C22×C4—5541no—
107C22×C4—5541no—
108C22×C4—5541no—
109C22×C4—5541no—
110C22×C4D110811yescharacteristic
111C22×C4C22×D27711yescharacteristic
112C2×C8—22no—
113C4⋊C4—2772no—
114C4⋊C4—5542no—
115C4⋊C4—5541no—
116C4⋊C4—5542no—
117C4⋊C4—5542no—
118C22⋊C4—22no—
119C22⋊C4—5542no—
120C22⋊C4—5542no—
121C22⋊C4—11082no—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23#1798455212yes—
127C23C2×D110811yescharacteristic
128Q8—11082no—
129Q8—22161no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—5542no—
134C2×C4—5542no—
135C2×C4—11081no—
136C2×C4—11081no—
137C2×C4—11081no—
138C2×C4—11081no—
139C2×C4—11081no—
140C2×C4—11081no—
141C2×C4—22161no—
142C2×C4—22161no—
143C2×C4D4×D27712yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—22no—
148C22—42no—
149C22—41no—
150C22—41no—
151C22—81no—
152C22#2257985011yescharacteristic
153C22C2×#1798455211yescharacteristic
154C22#2257991311yescharacteristic
155C4—22no—
156C4—41no—
157C4—11082no—
158C4—11082no—
159C4—22161no—
160C4—22161no—
161C2—21no—
162C2—21no—
163C2—42no—
164C2#3180014311yescharacteristic
165C2#3180018211yescharacteristic
166C2#3180019311yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#323×C277C2
socleC22×C277#120
prime radicalC24×C277D4
hypercenter#323D277
hypocenterC277#1608
LCSG ▷ C22×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #31800333C2semidirect
4. #31799740C2semidirect
83. C277#1608semidirect

Maximal subgroups

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

subgroupindex
#318006282
#318003332
#317999272
#317997402
#323×C2772
#1608277