Finite Group Databasebeta

← #47982335

Subgroups — #47982335

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
1D4×Dic554C211yesmaximal, characteristic
2#31800353C211yesmaximal, characteristic, complemented
3#31800298C211yesmaximal, characteristic, complemented
4#31800292C211yesmaximal, characteristic
5#31799749C211yesmaximal, characteristic, complemented
6#31799734C211yesmaximal, characteristic, complemented
7D4⋊C8×C277C211yesmaximal, characteristic
8C22×Dic554—21no—
9#22579880C2211yescharacteristic
10#22579880C2211yescharacteristic
11#22579879—21no—
12#22579859—21no—
13#22579857—22no—
14C4×Dic554C2211yescharacteristic
15D4×Dic277—21no—
16#22579814—21no—
17#22579811—21no—
18C4⋊#14555660C2211yescharacteristic
19#22579805—21no—
20#22579805—22no—
21#22579801—21no—
22C4×D4×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4×C8×C277C2211yescharacteristic
25C2×Dic554—22no—
26C2×Dic554—21no—
27C2×Dic554—21no—
28C2×Dic554—42no—
29C2×Dic554—42no—
30C2×Dic554D411yescharacteristic
31C22×Dic277—22no—
32C2×#14555660—21no—
33C4⋊Dic277—21no—
34C4⋊Dic277—21no—
35C4⋊Dic277—21no—
36C4⋊Dic277D412yes—
37C4⋊Dic277D411yescharacteristic
38#17984542—22no—
39#17984542—21no—
40C22⋊Dic277—22no—
41C4×Dic277—21no—
42C2×D4×C277D411yescharacteristic
43C22×C4×C277—21no—
44C2×C8×C277—21no—
45C2×C8×C277—21no—
46C4⋊C4×C277D411yescharacteristic
47C22⋊C4×C277—21no—
48C42×C277C2311yescharacteristic
49Dic554—21no—
50Dic554—44no—
51Dic554—41no—
52Dic554—41no—
53Dic554—42no—
54Dic554SD1612yes—
55C2×Dic277—21no—
56C2×Dic277—21no—
57C2×Dic277—22no—
58C2×Dic277—44no—
59C2×Dic277—41no—
60#14555660—41no—
61C23×C277—21no—
62D4×C277—21no—
63D4×C277Q1612yes—
64C2×C4×C277—21no—
65C2×C4×C277—41no—
66C2×C4×C277—41no—
67C2×C4×C277C2×D411yescharacteristic
68C2×C4×C277C2×D411yescharacteristic
69C2×C4×C277C2×D411yescharacteristic
70C8×C277—41no—
71C8×C277—41no—
72C22×C277—22no—
73C22×C277—41no—
74C22×C277—41no—
75C22×C277#12011yescharacteristic
76C4×C277—21no—
77C4×C277—41no—
78C4×C277C2×SD1611yescharacteristic
79C4×C277C2×Q1611yescharacteristic
80C4×C277AGL(1,ℤ/8)11yescharacteristic
81C4×C277#13711yescharacteristic
82Dic277—22no—
83Dic277—42no—
84Dic277—41no—
85Dic277—81no—
86C2×C277—42no—
87C2×C277#45011yescharacteristic
88C2×C277#45111yescharacteristic
89C2×C277#45411yescharacteristic
90C277#163711yescharacteristic, complemented, Sylow
91#1637—2771nomaximal, Sylow
92D4×Q8—2771no—
93#487—2771no—
94#477—2771no—
95#476—2771no—
96#332—2771no—
97Q8⋊C8—2771no—
98D4⋊C8D27711yescharacteristic
99C22×Q8—5541no—
100C4⋊Q8—2771no—
101C4⋊Q8—2771no—
102C4⋊Q8—5541no—
103C22⋊Q8—5542no—
104C22⋊Q8—5541no—
105C4×Q8—2771no—
106C4×D4—5541no—
107C4×D4C2×D27711yescharacteristic
108#107—5541no—
109#106—5541no—
110C4⋊C8—2771no—
111C4⋊C8C2×D27711yescharacteristic
112#103—5542no—
113#103—5541no—
114#102—5541no—
115C4×C8C2×D27711yescharacteristic
116C2×Q8—2771no—
117C2×Q8—5542no—
118C2×Q8—5541no—
119C2×Q8—5541no—
120C2×Q8—11082no—
121C2×Q8—11082no—
122C2×D4D110811yescharacteristic
123C22×C4—21no—
124C22×C4—5542no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—5541no—
128C4⋊C4—2772no—
129C4⋊C4—2771no—
130C4⋊C4—5542no—
131C4⋊C4—5541no—
132C4⋊C4—5541no—
133C4⋊C4—5541no—
134C4⋊C4—5541no—
135C4⋊C4D110811yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—5542no—
138C42—5541no—
139C42C22×D27711yescharacteristic
140C23—21no—
141Q8—2772no—
142Q8—5541no—
143Q8—11082no—
144Q8—11084no—
145Q8—11081no—
146Q8—11081no—
147D4—21no—
148D4Dic110812yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—5541no—
153C2×C4—5541no—
154C2×C4—5542no—
155C2×C4—11084no—
156C2×C4—11081no—
157C2×C4D4×D27711yescharacteristic
158C2×C4D4×D27711yescharacteristic
159C2×C4C2×D110811yescharacteristic
160C8—41no—
161C8—41no—
162C8—11081no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#2257985011yescharacteristic
167C4—21no—
168C4—41no—
169C4—5542no—
170C4—11082no—
171C4—11081no—
172C4—22161no—
173C4SD16×D27711yescharacteristic
174C4C2×Dic110811yescharacteristic
175C4#2257990411yescharacteristic
176C4#2257991311yescharacteristic
177C2—42no—
178C2#3180015411yescharacteristic
179C2#3180016011yescharacteristic
180C2#3180017611yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
FittingD4⋊C8×C277C2
socleC22×C277#120
prime radicalC2×D4×C277D4
hypercenterD4⋊C8D277
hypocenterC277#1637
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #31800353C2semidirect
3. #31800298C2semidirect
5. #31799749C2semidirect
6. #31799734C2semidirect
90. C277#1637semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5542
#318003532
#318002982
#318002922
#317997492
#317997342
D4⋊C8×C2772
#1637277