Finite Group Databasebeta

← #47983704

Subgroups — #47983704

Order 35456.

314 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 89 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#31800576C211yesmaximal, characteristic
2#31800020C212yesmaximal
3C2×#22579799C211yesmaximal, characteristic, complemented
4#31799758C212yesmaximal, complemented
5#519×C277C211yesmaximal, characteristic, complemented
6C2×#17984563C2211yescharacteristic
7C2×#17984547C2212yes—
8#22579878C412yescomplemented
9#22579869C412yescomplemented
10#22579863—22no—
11#22579856—22no—
12#22579839C2211yescharacteristic
13#22579808—24no—
14#22579799—22no—
15C22×Q8×C277C2211yescharacteristic
16C4×Q8×C277—24no—
17#117×C277—22no—
18#117×C277C2212yes—
19#17984563—22no—
20#17984563—22no—
21C2×Dic554C2×C411yescharacteristic
22C2×D1108C2×C411yescharacteristic
23C2×C22⋊D277—21no—
24C2×C4×D277—21no—
25#17984547—22no—
26#17984547—22no—
27C2×#14555660—22no—
28C4⋊Dic277—21no—
29#17984542—24no—
30C22⋊Dic277—21no—
31#17984540—24no—
32C4×Dic277C2×C412yes—
33C2×Q8×C277—22no—
34C2×Q8×C277—22no—
35C2×Q8×C277C2×C412yes—
36C2×Q8×C277D412yes—
37C22×C4×C277D412yes—
38C22×C4×C277C2311yescharacteristic
39C4⋊C4×C277—24no—
40C4⋊C4×C277—22no—
41C22⋊C4×C277—22no—
42C42×C277—24no—
43C42×C277D414yes—
44C22×D277—21no—
45Dic554—22no—
46D1108—22no—
47C22⋊D277—41no—
48C22⋊D277—41no—
49C2×Dic277—22no—
50C2×Dic277—21no—
51C4×D277—42no—
52#14555660—42no—
53C23×C277C2×D411yescharacteristic
54Q8×C277—24no—
55Q8×C277—24no—
56C2×C4×C277—22no—
57C2×C4×C277—22no—
58C2×C4×C277—24no—
59C2×C4×C277C22⋊C414yes—
60C2×C4×C277C22×C411yescharacteristic
61C2×C4×C277C2×D412yes—
62C2×C4×C277C2×D411yescharacteristic
63C2×C4×C277#4112yes—
64C22×C277—41no—
65C22×C277C2×C22⋊C411yescharacteristic
66C22×C277#12011yescharacteristic
67C22×C277#12311yescharacteristic
68C2×D277—42no—
69C2×D277—41no—
70C4×C277—24no—
71C4×C277—44no—
72C4×C277C4×D412yes—
73C4×C277#12112yes—
74Dic277—42no—
75Dic277—41no—
76C2×C277—21no—
77C2×C277—21no—
78C2×C277—21no—
79C2×C277#38611yescharacteristic
80D277—81no—
81C277#191211yescharacteristic, complemented, Sylow
82#1912—2771nomaximal, Sylow
83#536—2771no—
84#519D27711yescharacteristic, complemented
85#421—2772no—
86C2×#101—2771no—
87H(3,ℤ/4)—2772no—
88C2×#41—2771no—
89C22×Q8C2×D27711yescharacteristic
90C2×M16—2772no—
91C4⋊Q8—2772no—
92#124—2772no—
93#123—5542no—
94C22⋊Q8—5542no—
95C4×Q8—24no—
96#117—22no—
97#117—2771no—
98#117C2×D27712yes—
99#104—5544no—
100#101—5542no—
101#41—5542no—
102#41—5542no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—2771no—
106C2×Q8C4×D27712yes—
107C2×Q8D110812yes—
108C2×D4—2771no—
109C2×D4—5541no—
110C22×C4—5541no—
111C22×C4C22⋊D27712yes—
112C22×C4C22×D27711yescharacteristic
113M16—5542no—
114M16—5542no—
115C2×C8—5542no—
116C4⋊C4—24no—
117C4⋊C4—22no—
118C4⋊C4—5544no—
119C4⋊C4—5541no—
120C22⋊C4—22no—
121C22⋊C4—5541no—
122C22⋊C4—5544no—
123C42—24no—
124C42—2772no—
125C42C22⋊D27714yes—
126C23—5541no—
127C23C2×C22⋊D27711yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—5542no—
131D4—5542no—
132D4—11081no—
133D4—11081no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—24no—
137C2×C4—5542no—
138C2×C4—5541no—
139C2×C4—11082no—
140C2×C4#1798454014yes—
141C2×C4C2×C4×D27711yescharacteristic
142C2×C4C2×C22⋊D27712yes—
143C2×C4C2×D110811yescharacteristic
144C2×C4#1798456312yes—
145C8—11082no—
146C22—41no—
147C22—11082no—
148C22—11081no—
149C22C2×#1798454011yescharacteristic
150C22#2257984911yescharacteristic
151C22#2257986311yescharacteristic
152C4—24no—
153C4—44no—
154C4—11082no—
155C4—11081no—
156C4C4×C22⋊D27712yes—
157C4#2257985412yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—22161no—
162C2#3179988111yescharacteristic
subgroupG/H
centerC2#31799881
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
Fitting#519×C277C2
socleC2×C277#386
prime radicalC2×#17984563C22
cosocleC22×C4×C277C23
hypercenter#519D277
hypocenterC277#1912
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
3. C2×#22579799C2semidirect
4. #31799758C2semidirect
5. #519×C277C2semidirect
8. #22579878C4semidirect
9. #22579869C4semidirect
81. C277#1912semidirect
84. #519D277semidirect

Maximal subgroups

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

subgroupindex
#318005762
#318000202
C2×#225797992
#317997582
#519×C2772
#1912277