Finite Group Databasebeta

← #47982209

Subgroups — #47982209

Order 35456.

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

normal subgroups only

This group has 202 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#31800335C212yesmaximal
2#31799941C211yesmaximal, characteristic
3#31799739C212yesmaximal
4#31799728C211yesmaximal, characteristic
5#544×C277C211yesmaximal, characteristic
6C2×C4⋊Dic277C2211yescharacteristic
7#22579813—22no—
8#22579804—22no—
9C22⋊#14555660C2212yes—
10#22579787—21no—
11#22579787—21no—
12#22579787C2211yescharacteristic
13C4⋊Q8×C277—22no—
14#125×C277—22no—
15C22⋊Q8×C277—21no—
16C22⋊Q8×C277C2212yes—
17#117×C277—21no—
18C2×C4⋊C4×C277C2211yescharacteristic
19C22×Dic277—21no—
20C22×Dic277—21no—
21C2×#14555660—22no—
22C4⋊Dic277—22no—
23C2×Q8×C277—21no—
24C2×Q8×C277D412yes—
25C22×C4×C277D411yescharacteristic
26C22×C4×C277D411yescharacteristic
27C22×C4×C277C2311yescharacteristic
28C4⋊C4×C277—21no—
29C4⋊C4×C277—21no—
30C4⋊C4×C277—21no—
31C4⋊C4×C277—22no—
32C4⋊C4×C277—22no—
33C4⋊C4×C277—22no—
34C4⋊C4×C277D412yes—
35C22⋊C4×C277—22no—
36C42×C277—22no—
37C2×Dic277—41no—
38C2×Dic277—41no—
39C2×Dic277—42no—
40C2×Dic277—41no—
41C2×Dic277—41no—
42#14555660—42no—
43C23×C277C2×D411yescharacteristic
44Q8×C277—42no—
45Q8×C277—81no—
46C2×C4×C277—21no—
47C2×C4×C277—21no—
48C2×C4×C277—22no—
49C2×C4×C277—22no—
50C2×C4×C277—21no—
51C2×C4×C277—41no—
52C2×C4×C277—41no—
53C2×C4×C277Q1612yes—
54C2×C4×C277C2×D412yes—
55C22×C277—21no—
56C22×C277—21no—
57C22×C277#12011yescharacteristic
58C22×C277C2×Q1611yescharacteristic
59C22×C277#13711yescharacteristic
60C4×C277—22no—
61C4×C277—22no—
62C4×C277—42no—
63C4×C277—41no—
64C4×C277—42no—
65Dic277—81no—
66Dic277—81no—
67C2×C277—21no—
68C2×C277—21no—
69C2×C277#45111yescharacteristic
70C2×C277#45411yescharacteristic
71C2×C277#45811yescharacteristic
72C277#161711yescharacteristic, complemented, Sylow
73#1617—2771nomaximal, Sylow
74#544D27711yescharacteristic
75#484—2772no—
76#400—2771no—
77#328—2772no—
78#324—2771no—
79C4⋊Q8—22no—
80#125—22no—
81C22⋊Q8—21no—
82C22⋊Q8C2×D27712yes—
83#117—21no—
84C2×C4⋊C4—2771no—
85C2×C4⋊C4C2×D27711yescharacteristic
86#107—5542no—
87#103—5542no—
88C22⋊C8—2772no—
89#95—2771no—
90#95—5541no—
91#95—5541no—
92C2×Q8—21no—
93C2×Q8C22⋊D27712yes—
94C22×C4—5541no—
95C22×C4—5541no—
96C22×C4C22⋊D27711yescharacteristic
97C22×C4C22⋊D27711yescharacteristic
98C22×C4C22×D27711yescharacteristic
99C2×C8—5542no—
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—22no—
104C4⋊C4—22no—
105C4⋊C4—22no—
106C4⋊C4—5542no—
107C4⋊C4C22⋊D27712yes—
108C22⋊C4—22no—
109C42—22no—
110C23C2×C22⋊D27711yescharacteristic
111Q8—42no—
112Q8—81no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—21no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—11081no—
121C2×C4—11081no—
122C2×C4—11082no—
123C2×C4—11081no—
124C2×C4—11081no—
125C2×C4#1798455312yes—
126C2×C4C2×C22⋊D27712yes—
127C8—11082no—
128C22—21no—
129C22—21no—
130C22#2257984911yescharacteristic
131C22C2×#1798455311yescharacteristic
132C22#2257991111yescharacteristic
133C4—22no—
134C4—22no—
135C4—42no—
136C4—41no—
137C4—42no—
138C4—22161no—
139C4—22161no—
140C2—21no—
141C2—21no—
142C2#3180015811yescharacteristic
143C2#3180017511yescharacteristic
144C2#3180019211yescharacteristic
subgroupG/H
centerC22#22579849
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#544×C277C2
socleC22×C277#120
prime radicalC23×C277C2×D4
hypercenter#544D277
hypocenterC277#1617
LCSG ▷ C22×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
72. C277#1617semidirect

Maximal subgroups

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

subgroupindex
#318003352
#317999412
#317997392
#317997282
#544×C2772
#1617277