Finite Group Databasebeta

← #47982329

Subgroups — #47982329

Order 35456.

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

normal subgroups only

This group has 228 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#31800294C211yesmaximal, characteristic, complemented
3#31800289C211yesmaximal, characteristic
4#31799748C211yesmaximal, characteristic, complemented
5#31799734C211yesmaximal, characteristic, complemented
6#31799731C211yesmaximal, characteristic
7#487×C277C211yesmaximal, characteristic, complemented
8C2×Q8×D277—21no—
9#22579879—21no—
10#22579858—22no—
11#22579856—21no—
12C4×Dic554C2211yescharacteristic
13C4×D1108C2211yescharacteristic
14#22579842—21no—
15#22579813—21no—
16#22579811—21no—
17C4⋊#14555660C2211yescharacteristic
18C4⋊#14555660C2211yescharacteristic
19#22579803—21no—
20#22579800—21no—
21C4⋊Q8×C277C2211yescharacteristic
22C4⋊Q8×C277C2211yescharacteristic
23#103×C277—22no—
24C4×C8×C277C2211yescharacteristic
25C2×Dic554—22no—
26C2×Dic554D411yescharacteristic
27Q8×D277—42no—
28Q8×D277—42no—
29C2×D1108D411yescharacteristic
30C2×C4×D277—22no—
31C2×C4×D277—21no—
32C2×#14555660—21no—
33C2×#14555660—21no—
34C4⋊Dic277D411yescharacteristic
35C4⋊Dic277D411yescharacteristic
36#17984542—22no—
37#17984542—21no—
38#17984540—22no—
39#17984540—21no—
40C4×Dic277—21no—
41C2×Q8×C277—21no—
42C2×Q8×C277—21no—
43C2×C8×C277—21no—
44C4⋊C4×C277—21no—
45C4⋊C4×C277—21no—
46C4⋊C4×C277—21no—
47C4⋊C4×C277D412yes—
48C42×C277C2311yescharacteristic
49C22×D277—21no—
50Dic554—21no—
51Dic554—44no—
52Dic554SD1612yes—
53D1108—21no—
54D1108Q1612yes—
55C2×Dic277—21no—
56C2×Dic277—21no—
57C2×Dic277—21no—
58C4×D277—44no—
59C4×D277—41no—
60C4×D277—41no—
61#14555660—41no—
62#14555660—41no—
63Q8×C277—42no—
64Q8×C277—41no—
65Q8×C277—41no—
66C2×C4×C277—22no—
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—21no—
77C4×C277—42no—
78C4×C277—81no—
79C4×C277C2×SD1611yescharacteristic
80C4×C277C2×Q1611yescharacteristic
81C4×C277AGL(1,ℤ/8)11yescharacteristic
82C4×C277#13711yescharacteristic
83Dic277—22no—
84Dic277—41no—
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#487D27711yescharacteristic, complemented
94#477—2771no—
95#476—2771no—
96#332—2771no—
97Q8⋊C8—2771no—
98D4⋊C8—2771no—
99C22×Q8—5541no—
100C4⋊Q8—5541no—
101C4⋊Q8C2×D27711yescharacteristic
102C4⋊Q8C2×D27711yescharacteristic
103C22⋊Q8—5541no—
104C22⋊Q8—5542no—
105C4×Q8—2771no—
106C4×D4—2771no—
107C4×D4—5541no—
108#107—5541no—
109#106—5541no—
110C4⋊C8—2771no—
111C4⋊C8—2771no—
112#103—22no—
113#103—5541no—
114#102—5541no—
115C4×C8C2×D27711yescharacteristic
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—2771no—
119C2×Q8—5542no—
120C2×Q8—11082no—
121C2×Q8—11082no—
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—2771no—
132C4⋊C4—2771no—
133C4⋊C4—5542no—
134C4⋊C4—5541no—
135C4⋊C4C22⋊D27712yes—
136C22⋊C4—5542no—
137C22⋊C4—5541no—
138C42—5541no—
139C42C22×D27711yescharacteristic
140C23—5541no—
141Q8—42no—
142Q8—41no—
143Q8—41no—
144Q8—2772no—
145Q8—5541no—
146Q8—11084no—
147D4—2772no—
148D4—5541no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—5541no—
152C2×C4—5541no—
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—21no—
168C4—42no—
169C4—81no—
170C4—5542no—
171C4—11081no—
172C4—11081no—
173C4SD16×D27711yescharacteristic
174C4Q16×D27711yescharacteristic
175C4#2257990711yescharacteristic
176C4#2257991211yescharacteristic
177C2—11082no—
178C2#3180015111yescharacteristic
179C2#3180015611yescharacteristic
180C2#3180017411yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#487×C277C2
socleC22×C277#120
prime radicalC2×D1108D4
hypercenter#487D277
hypocenterC277#1637
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #31800294C2semidirect
4. #31799748C2semidirect
5. #31799734C2semidirect
7. #487×C277C2semidirect
90. C277#1637semidirect
93. #487D277semidirect

Maximal subgroups

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

subgroupindex
#318006672
#318002942
#318002892
#317997482
#317997342
#317997312
#487×C2772
#1637277