Finite Group Databasebeta

← #47984308

Subgroups — #47984308

Order 35456.

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

normal subgroups only

This group has 290 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
1C2×#22579880C211yesmaximal, characteristic
2C2×#22579804C212yesmaximal
3#31799764C212yesmaximal
4#31799757C211yesmaximal, characteristic
5#391×C277C211yesmaximal, characteristic
6C22×Dic554—21no—
7C22×#14555660C2212yes—
8#22579880—24no—
9C2×C4⋊Dic277—21no—
10C2×C4⋊Dic277C2212yes—
11#22579804—24no—
12C22×Q8×C277C2211yescharacteristic
13C2×C4⋊C4×C277C2211yescharacteristic
14C2×C42×C277C2211yescharacteristic
15#95×C277—21no—
16#95×C277—21no—
17C2×Dic554—24no—
18C2×Dic554—42no—
19C2×Dic554—42no—
20C22×Dic277—22no—
21C2×#14555660—22no—
22C2×#14555660—22no—
23C2×#14555660—22no—
24C4⋊Dic277—24no—
25C4⋊Dic277—22no—
26C4⋊Dic277D414yes—
27C2×Q8×C277—21no—
28C2×Q8×C277—22no—
29C2×Q8×C277—22no—
30C2×Q8×C277Q812yescomplemented
31C22×C4×C277—21no—
32C22×C4×C277—21no—
33C22×C4×C277D411yescharacteristic
34C22×C4×C277D411yescharacteristic
35C22×C4×C277C2311yescharacteristic
36C4⋊C4×C277—22no—
37C42×C277—22no—
38Dic554—48no—
39C2×Dic277—24no—
40C2×Dic277—42no—
41C2×Dic277—42no—
42#14555660—42no—
43C23×C277C2×D411yescharacteristic
44Q8×C277—24no—
45Q8×C277—42no—
46C2×C4×C277—21no—
47C2×C4×C277—21no—
48C2×C4×C277—21no—
49C2×C4×C277—21no—
50C2×C4×C277—22no—
51C2×C4×C277—41no—
52C2×C4×C277—41no—
53C2×C4×C277—41no—
54C2×C4×C277—41no—
55C2×C4×C277—41no—
56C2×C4×C277SD1612yes—
57C2×C4×C277Q1612yes—
58C2×C4×C277C2×D412yes—
59C2×C4×C277C2×Q811yescharacteristic
60C2×C4×C277#4112yes—
61C2×C4×C277#4111yescharacteristic
62C22×C277#12011yescharacteristic
63C22×C277C22⋊Q811yescharacteristic
64C22×C277#12411yescharacteristic
65C22×C277C2×SD1611yescharacteristic
66C22×C277C2×Q1611yescharacteristic
67C22×C277AGL(1,ℤ/8)11yescharacteristic
68C22×C277#13711yescharacteristic
69C4×C277—22no—
70C4×C277—22no—
71C4×C277—42no—
72C4×C277—81no—
73C4×C277C22⋊Q812yes—
74C4×C277#12412yes—
75Dic277—44no—
76C2×C277#39311yescharacteristic
77C2×C277#45011yescharacteristic
78C2×C277#45111yescharacteristic
79C2×C277#47511yescharacteristic
80C2×C277#47711yescharacteristic
81C2×C277#48711yescharacteristic
82C2×C277#48911yescharacteristic
83C277#202411yescharacteristic, complemented, Sylow
84#2024—2771nomaximal, Sylow
85C2×C4⋊Q8—2771no—
86C2×#103—2772no—
87#391D27711yescharacteristic
88#340—2772no—
89#336—2771no—
90C22×Q8—5541no—
91C22×Q8C2×D27711yescharacteristic
92C22×C8—2772no—
93C4⋊Q8—5544no—
94C2×C4⋊C4—2772no—
95C2×C4⋊C4—5541no—
96C2×C4⋊C4C2×D27711yescharacteristic
97C2×C42C2×D27711yescharacteristic
98#103—5544no—
99#95—21no—
100#95—21no—
101C2×Q8—21no—
102C2×Q8—22no—
103C2×Q8—22no—
104C2×Q8—5544no—
105C2×Q8—11082no—
106C2×Q8—11082no—
107C2×Q8Dic55412yescomplemented
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—5542no—
111C22×C4C22⋊D27711yescharacteristic
112C22×C4C22⋊D27711yescharacteristic
113C22×C4C22×D27711yescharacteristic
114C2×C8—5542no—
115C2×C8—5542no—
116C2×C8—5542no—
117C4⋊C4—22no—
118C4⋊C4—2774no—
119C4⋊C4—5544no—
120C4⋊C4—5542no—
121C42—22no—
122C23C2×C22⋊D27711yescharacteristic
123Q8—24no—
124Q8—42no—
125Q8—11088no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—5544no—
137C2×C4—11082no—
138C2×C4—11082no—
139C2×C4#1798455012yes—
140C2×C4#1798455312yes—
141C2×C4D4×D27712yes—
142C2×C4C2×Dic55411yescharacteristic
143C2×C4#1798456212yes—
144C2×C4#1798456311yescharacteristic
145C8—11082no—
146C22#2257984811yescharacteristic
147C22#2257985911yescharacteristic
148C22#2257986711yescharacteristic
149C22C2×#1798455011yescharacteristic
150C22C2×#1798455311yescharacteristic
151C22#2257990511yescharacteristic
152C22#2257991011yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—81no—
157C4—11084no—
158C4#2257985712yes—
159C4#2257986612yes—
160C2#3179991411yescharacteristic
161C2#3180015211yescharacteristic
162C2#3180015711yescharacteristic
163C2#3180028711yescharacteristic
164C2#3180029711yescharacteristic
165C2#3180035211yescharacteristic
166C2#3180036111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D277
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#391×C277C2
socle, prime radicalC23×C277C2×D4
hypercenter#391D277
hypocenterC277#2024
LCSG ▷ C22×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C277Q8semidirect
83. C277#2024semidirect
107. C2×Q8Dic554semidirect

Maximal subgroups

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

subgroupindex
C2×#225798802
C2×#225798042
#317997642
#317997572
#391×C2772
#2024277