Finite Group Databasebeta

← #47982330

Subgroups — #47982330

Order 35456.

228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×D1108C211yesmaximal, characteristic
2#31800352C211yesmaximal, characteristic, complemented
3#31800289C211yesmaximal, characteristic
4#31799749C211yesmaximal, characteristic, complemented
5Q8⋊#14555660C211yesmaximal, characteristic, complemented
6#31799729C211yesmaximal, characteristic
7#477×C277C211yesmaximal, characteristic, complemented
8C2×Q8×D277—21no—
9#22579880—21no—
10#22579880C2211yescharacteristic
11#22579860—22no—
12#22579860—21no—
13C4×D1108—21no—
14C4×D1108C2211yescharacteristic
15#22579811—21no—
16C4⋊#14555660C2211yescharacteristic
17#22579804—22no—
18#22579800—21no—
19C4×#14555660C2211yescharacteristic
20C4⋊Q8×C277C2211yescharacteristic
21C4×Q8×C277C2211yescharacteristic
22#107×C277—21no—
23C4⋊C8×C277C2211yescharacteristic
24#103×C277—21no—
25C2×Dic554—22no—
26C2×Dic554—21no—
27Q8×D277—42no—
28Q8×D277—42no—
29C2×D1108D411yescharacteristic
30C2×C4×D277—22no—
31C2×C4×D277—21no—
32C2×#14555660—21no—
33C2×#14555660—21no—
34C4⋊Dic277—22no—
35C4⋊Dic277—21no—
36C4⋊Dic277D412yes—
37C4⋊Dic277D411yescharacteristic
38#17984540—22no—
39#17984540—21no—
40C2×Q8×C277—21no—
41C2×Q8×C277D411yescharacteristic
42C2×C8×C277—21no—
43C4⋊C4×C277—21no—
44C4⋊C4×C277—21no—
45C4⋊C4×C277—21no—
46C4⋊C4×C277D411yescharacteristic
47C42×C277—21no—
48C42×C277C2311yescharacteristic
49C22×D277—21no—
50Dic554—44no—
51Dic554—41no—
52Dic554—41no—
53D1108—21no—
54D1108Q1612yes—
55C2×Dic277—22no—
56C2×Dic277—21no—
57C4×D277—44no—
58C4×D277—41no—
59C4×D277—41no—
60#14555660—41no—
61#14555660—41no—
62Q8×C277—21no—
63Q8×C277—42no—
64Q8×C277SD1612yes—
65C2×C4×C277—21no—
66C2×C4×C277—21no—
67C2×C4×C277—41no—
68C2×C4×C277C2×D411yescharacteristic
69C2×C4×C277C2×D411yescharacteristic
70C2×C4×C277C2×D411yescharacteristic
71C8×C277—41no—
72C22×C277#12011yescharacteristic
73C2×D277—22no—
74C2×D277—41no—
75C2×D277—41no—
76C4×C277—22no—
77C4×C277—21no—
78C4×C277—41no—
79C4×C277—81no—
80C4×C277C2×SD1611yescharacteristic
81C4×C277C2×Q1611yescharacteristic
82C4×C277AGL(1,ℤ/8)11yescharacteristic
83C4×C277#13711yescharacteristic
84Dic277—42no—
85Dic277—41no—
86C2×C277#45011yescharacteristic
87C2×C277#45111yescharacteristic
88C2×C277#45411yescharacteristic
89D277—42no—
90C277#163711yescharacteristic, complemented, Sylow
91#1637—2771nomaximal, Sylow
92D4×Q8—2771no—
93#487—2771no—
94#477D27711yescharacteristic, complemented
95#476—2771no—
96#332—2771no—
97Q8⋊C8—2771no—
98D4⋊C8—2771no—
99C22×Q8—5541no—
100C4⋊Q8—2771no—
101C4⋊Q8—5541no—
102C4⋊Q8C2×D27711yescharacteristic
103C22⋊Q8—5542no—
104C22⋊Q8—5541no—
105C4×Q8C2×D27711yescharacteristic
106C4×D4—2771no—
107C4×D4—5541no—
108#107—21no—
109#106—5541no—
110C4⋊C8—2771no—
111C4⋊C8C2×D27711yescharacteristic
112#103—21no—
113#103—5542no—
114#102—5541no—
115C4×C8—2771no—
116C2×Q8—21no—
117C2×Q8—5542no—
118C2×Q8—5541no—
119C2×Q8—11082no—
120C2×Q8—11082no—
121C2×Q8C22⋊D27711yescharacteristic
122C2×D4—2771no—
123C22×C4—5542no—
124C22×C4—5541no—
125C2×C8—21no—
126C2×C8—5541no—
127C2×C8—5541no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—2772no—
132C4⋊C4—2771no—
133C4⋊C4—5542no—
134C4⋊C4—5541no—
135C4⋊C4C22⋊D27711yescharacteristic
136C22⋊C4—5542no—
137C22⋊C4—5541no—
138C42—21no—
139C42C22×D27711yescharacteristic
140C23—5541no—
141Q8—21no—
142Q8—42no—
143Q8—11084no—
144Q8—11081no—
145Q8—11081no—
146Q8#1798455012yes—
147D4—2772no—
148D4—5541no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—5542no—
153C2×C4—5541no—
154C2×C4—11084no—
155C2×C4—11081no—
156C2×C4—11081no—
157C2×C4D4×D27711yescharacteristic
158C2×C4D4×D27711yescharacteristic
159C2×C4C2×C22⋊D27711yescharacteristic
160C8—41no—
161C8—11081no—
162C8—11081no—
163C22—5542no—
164C22—11081no—
165C22—11081no—
166C22#2257984811yescharacteristic
167C4—22no—
168C4—21no—
169C4—41no—
170C4—81no—
171C4—11082no—
172C4—11081no—
173C4C2×#1798455011yescharacteristic
174C4Q16×D27711yescharacteristic
175C4#2257990511yescharacteristic
176C4#2257991211yescharacteristic
177C2—11082no—
178C2#3180015211yescharacteristic
179C2#3180015611yescharacteristic
180C2#3180017311yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#477×C277C2
socleC22×C277#120
prime radicalC2×D1108D4
hypercenter#477D277
hypocenterC277#1637
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #31800352C2semidirect
4. #31799749C2semidirect
5. Q8⋊#14555660C2semidirect
7. #477×C277C2semidirect
90. C277#1637semidirect
94. #477D277semidirect

Maximal subgroups

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

subgroupindex
Q8×D11082
#318003522
#318002892
#317997492
Q8⋊#145556602
#317997292
#477×C2772
#1637277