Finite Group Databasebeta

← #47982431

Subgroups — #47982431

Order 35456.

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

normal subgroups only

This group has 234 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#31800667C211yesmaximal, characteristic
2#31800398C211yesmaximal, characteristic, complemented
3#31800288C211yesmaximal, characteristic, complemented
4#31800208C211yesmaximal, characteristic
5#31799732C211yesmaximal, characteristic, complemented
6#31799729C211yesmaximal, characteristic
7#332×C277C211yesmaximal, characteristic, complemented
8C2×Q8×D277—21no—
9C2×#17984552—21no—
10#22579880C2211yescharacteristic
11#22579879—21no—
12#22579858—22no—
13#22579856—21no—
14C4×Dic554C2211yescharacteristic
15C4×D1108C2211yescharacteristic
16#22579842—21no—
17#22579812—21no—
18#22579811—22no—
19#22579805—21no—
20#22579805—21no—
21C4×#14555660C2211yescharacteristic
22C4⋊Q8×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4⋊C8×C277C2211yescharacteristic
25C2×Dic554—22no—
26C2×Dic554—21no—
27C2×Dic554D411yescharacteristic
28Q8×D277—42no—
29Q8×D277—42no—
30C2×D1108D411yescharacteristic
31C2×C4×D277—22no—
32C2×C4×D277—21no—
33#17984552—42no—
34C2×#14555660—21no—
35C4⋊Dic277—21no—
36C4⋊Dic277—21no—
37C4⋊Dic277D411yescharacteristic
38C4⋊Dic277D411yescharacteristic
39#17984542—22no—
40#17984542—21no—
41#17984540—22no—
42#17984540—21no—
43C4×Dic277—21no—
44C2×Q8×C277—21no—
45C2×C8×C277—21no—
46C2×C8×C277—21no—
47C4⋊C4×C277—21no—
48C4⋊C4×C277D412yes—
49C42×C277C2311yescharacteristic
50C22×D277—21no—
51Dic554—21no—
52Dic554—44no—
53Dic554—41no—
54Dic554—41no—
55Dic554SD1612yescomplemented
56D1108—21no—
57D1108SD1612yes—
58C2×Dic277—21no—
59C2×Dic277—21no—
60C2×Dic277—21no—
61C2×Dic277—41no—
62C4×D277—44no—
63C4×D277—41no—
64C4×D277—41no—
65#14555660—22no—
66Q8×C277—41no—
67Q8×C277—41no—
68C2×C4×C277—22no—
69C2×C4×C277C2×D411yescharacteristic
70C2×C4×C277C2×D411yescharacteristic
71C2×C4×C277C2×D411yescharacteristic
72C8×C277—41no—
73C8×C277—41no—
74C22×C277#12011yescharacteristic
75C2×D277—22no—
76C2×D277—41no—
77C2×D277—41no—
78C4×C277—21no—
79C4×C277—42no—
80C4×C277C2×SD1611yescharacteristic
81C4×C277C2×SD1611yescharacteristic
82C4×C277AGL(1,ℤ/8)11yescharacteristic
83C4×C277#13711yescharacteristic
84Dic277—22no—
85Dic277—41no—
86Dic277—41no—
87Dic277—81no—
88C2×C277#44811yescharacteristic
89C2×C277#45011yescharacteristic
90C2×C277#45611yescharacteristic
91D277—42no—
92C277#165111yescharacteristic, complemented, Sylow
93#1651—2771nomaximal, Sylow
94D4×Q8—2771no—
95#498—2771no—
96#475—2771no—
97#461—2771no—
98#332D27711yescharacteristic, complemented
99Q8⋊C8—2771no—
100D4⋊C8—2771no—
101C22×Q8—5541no—
102C2×SD16—5541no—
103C4⋊Q8—2771no—
104C4⋊Q8—5541no—
105C4⋊Q8C2×D27711yescharacteristic
106C22⋊Q8—5541no—
107C22⋊Q8—5542no—
108C4×Q8—2771no—
109C4×D4—2771no—
110C4×D4—5541no—
111#106—5541no—
112#106—5542no—
113C4⋊C8C2×D27711yescharacteristic
114C4⋊C8C2×D27711yescharacteristic
115#103—5541no—
116#103—5541no—
117C4×C8—2771no—
118C2×Q8—21no—
119C2×Q8—2771no—
120C2×Q8—5542no—
121C2×Q8—5541no—
122C2×Q8—11082no—
123C2×Q8—11082no—
124C2×D4—2771no—
125C22×C4—5542no—
126C22×C4—5541no—
127SD16—11082no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—5541no—
131C4⋊C4—21no—
132C4⋊C4—2771no—
133C4⋊C4—2771no—
134C4⋊C4—5542no—
135C4⋊C4—5541no—
136C4⋊C4—5541no—
137C4⋊C4—5541no—
138C4⋊C4D110812yes—
139C22⋊C4—5542no—
140C22⋊C4—5541no—
141C42—5541no—
142C42C22×D27711yescharacteristic
143C23—5541no—
144Q8—41no—
145Q8—41no—
146Q8—2772no—
147Q8—5541no—
148Q8—11084no—
149Q8—11081no—
150Q8—11081no—
151D4—2772no—
152D4—5541no—
153C2×C4—22no—
154C2×C4—5541no—
155C2×C4—5541no—
156C2×C4—5541no—
157C2×C4—11084no—
158C2×C4—11081no—
159C2×C4—11081no—
160C2×C4—11081no—
161C2×C4D4×D27711yescharacteristic
162C2×C4D4×D27711yescharacteristic
163C2×C4C2×D110811yescharacteristic
164C8—41no—
165C8—41no—
166C8—5542no—
167C22—5542no—
168C22—11081no—
169C22—11081no—
170C22#2257985011yescharacteristic
171C4—21no—
172C4—42no—
173C4—5542no—
174C4—11081no—
175C4—11081no—
176C4—22161no—
177C4SD16×D27711yescharacteristic
178C4SD16×D27711yescharacteristic
179C4#2257990411yescharacteristic
180C4#2257991211yescharacteristic
181C2—11082no—
182C2#3180014211yescharacteristic
183C2#3180015411yescharacteristic
184C2#3180018711yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#332×C277C2
socleC22×C277#120
prime radicalC2×D1108D4
hypercenter#332D277
hypocenterC277#1651
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #31800398C2semidirect
3. #31800288C2semidirect
5. #31799732C2semidirect
7. #332×C277C2semidirect
55. Dic554SD16semidirect
92. C277#1651semidirect
98. #332D277semidirect

Maximal subgroups

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

subgroupindex
#318006672
#318003982
#318002882
#318002082
#317997322
#317997292
#332×C2772
#1651277