Finite Group Databasebeta

← #47982429

Subgroups — #47982429

Order 35456.

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

normal subgroups only

This group has 234 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#31800398C211yesmaximal, characteristic, complemented
3#31800204C211yesmaximal, characteristic
4#31799749C211yesmaximal, characteristic, complemented
5Q8⋊#14555660C211yesmaximal, characteristic, complemented
6#31799729C211yesmaximal, characteristic
7#475×C277C211yesmaximal, characteristic, complemented
8C2×Q8×D277—21no—
9C2×#17984550—21no—
10#22579880—21no—
11#22579880C2211yescharacteristic
12#22579860—22no—
13#22579860—21no—
14C4×D1108—21no—
15C4×D1108C2211yescharacteristic
16#22579811—22no—
17C4⋊#14555660C2211yescharacteristic
18#22579804—21no—
19C4×#14555660C2211yescharacteristic
20C4⋊Q8×C277C2211yescharacteristic
21C4×Q8×C277C2211yescharacteristic
22#106×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—
32#17984550—42no—
33C2×#14555660—21no—
34C2×#14555660—21no—
35C4⋊Dic277—22no—
36C4⋊Dic277—21no—
37C4⋊Dic277D411yescharacteristic
38C4⋊Dic277D412yes—
39#17984540—22no—
40#17984540—21no—
41C2×Q8×C277—21no—
42C2×Q8×C277D411yescharacteristic
43C2×C8×C277—21no—
44C4⋊C4×C277—21no—
45C4⋊C4×C277—21no—
46C4⋊C4×C277—21no—
47C4⋊C4×C277D411yescharacteristic
48C42×C277—21no—
49C42×C277C2311yescharacteristic
50C22×D277—21no—
51Dic554—44no—
52Dic554—41no—
53Dic554—41no—
54D1108—21no—
55D1108SD1612yes—
56C2×Dic277—22no—
57C2×Dic277—21no—
58C4×D277—44no—
59C4×D277—41no—
60C4×D277—41no—
61#14555660—22no—
62#14555660—41no—
63Q8×C277—21no—
64Q8×C277—41no—
65Q8×C277—41no—
66Q8×C277SD1612yescomplemented
67C2×C4×C277—21no—
68C2×C4×C277—21no—
69C2×C4×C277—41no—
70C2×C4×C277C2×D411yescharacteristic
71C2×C4×C277C2×D411yescharacteristic
72C2×C4×C277C2×D411yescharacteristic
73C8×C277—41no—
74C22×C277#12011yescharacteristic
75C2×D277—22no—
76C2×D277—41no—
77C2×D277—41no—
78C4×C277—22no—
79C4×C277—21no—
80C4×C277—41no—
81C4×C277—81no—
82C4×C277C2×SD1611yescharacteristic
83C4×C277C2×SD1611yescharacteristic
84C4×C277AGL(1,ℤ/8)11yescharacteristic
85C4×C277#13711yescharacteristic
86Dic277—42no—
87Dic277—41no—
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#475D27711yescharacteristic, complemented
97#461—2771no—
98#332—2771no—
99Q8⋊C8—2771no—
100D4⋊C8—2771no—
101C22×Q8—5541no—
102C2×SD16—5541no—
103C4⋊Q8—2771no—
104C4⋊Q8—5541no—
105C4⋊Q8C2×D27711yescharacteristic
106C22⋊Q8—5542no—
107C22⋊Q8—5541no—
108C4×Q8C2×D27711yescharacteristic
109C4×D4—2771no—
110C4×D4—5541no—
111#106—21no—
112#106—5542no—
113C4⋊C8—2771no—
114C4⋊C8C2×D27711yescharacteristic
115#103—21no—
116#103—5541no—
117C4×C8—2771no—
118C2×Q8—21no—
119C2×Q8—5542no—
120C2×Q8—5541no—
121C2×Q8—11082no—
122C2×Q8—11082no—
123C2×Q8C22⋊D27711yescharacteristic
124C2×D4—2771no—
125C22×C4—5542no—
126C22×C4—5541no—
127SD16—11082no—
128C2×C8—21no—
129C2×C8—5541no—
130C2×C8—5541no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—2771no—
135C4⋊C4—2772no—
136C4⋊C4—5542no—
137C4⋊C4—5541no—
138C4⋊C4C22⋊D27711yescharacteristic
139C22⋊C4—5542no—
140C22⋊C4—5541no—
141C42—21no—
142C42C22×D27711yescharacteristic
143C23—5541no—
144Q8—21no—
145Q8—41no—
146Q8—41no—
147Q8—11084no—
148Q8—11081no—
149Q8—11081no—
150Q8#1798455012yescomplemented
151D4—2772no—
152D4—5541no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—5542no—
157C2×C4—5541no—
158C2×C4—11084no—
159C2×C4—11081no—
160C2×C4—11081no—
161C2×C4D4×D27711yescharacteristic
162C2×C4D4×D27711yescharacteristic
163C2×C4C2×C22⋊D27711yescharacteristic
164C8—41no—
165C8—5542no—
166C8—11081no—
167C22—5542no—
168C22—11081no—
169C22—11081no—
170C22#2257984811yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—81no—
175C4—11082no—
176C4—11081no—
177C4SD16×D27711yescharacteristic
178C4C2×#1798455011yescharacteristic
179C4#2257990511yescharacteristic
180C4#2257990911yescharacteristic
181C2—11082no—
182C2#3180013911yescharacteristic
183C2#3180015211yescharacteristic
184C2#3180018311yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#475×C277C2
socleC22×C277#120
prime radicalC2×D1108D4
hypercenter#475D277
hypocenterC277#1651
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #31800398C2semidirect
4. #31799749C2semidirect
5. Q8⋊#14555660C2semidirect
7. #475×C277C2semidirect
66. Q8×C277SD16semidirect
92. C277#1651semidirect
96. #475D277semidirect
150. Q8#17984550semidirect

Maximal subgroups

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

subgroupindex
Q8×D11082
#318003982
#318002042
#317997492
Q8⋊#145556602
#317997292
#475×C2772
#1651277