Finite Group Databasebeta

← #47985139

Subgroups — #47985139

Order 35456.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#31800804C211yesmaximal, characteristic
2#31800442C211yesmaximal, characteristic, complemented
3C2×#22579825C211yesmaximal, characteristic, complemented
4#31800278C211yesmaximal, characteristic, complemented
5#31799814C211yesmaximal, characteristic, complemented
6#31799785C211yesmaximal, characteristic, complemented
7#359×C277C211yesmaximal, characteristic, complemented
8#22579926—21no—
9#22579913—21no—
10#22579907—22no—
11#22579905—21no—
12#22579903—21no—
13C2×Dic1108C2211yescharacteristic, complemented
14C2×D2216C2211yescharacteristic
15D8×D277—21no—
16#22579886C2211yescharacteristic
17#22579826—21no—
18#22579825—22no—
19#22579824—21no—
20#22579820C2211yescharacteristic, complemented
21#22579798—21no—
22#135×C277C2211yescharacteristic
23C2×C16×C277C2211yescharacteristic, complemented
24#108×C277C2211yescharacteristic, complemented
25#17984564—22no—
26#17984563—41no—
27#17984563D411yescharacteristic
28C2×Dic554—21no—
29C2×D1108—21no—
30C2×D1108—41no—
31D4×D277—22no—
32D4×D277—42no—
33Dic1108—21no—
34Dic1108—21no—
35Dic1108—41no—
36#17984552—41no—
37#17984550—22no—
38D2216—21no—
39D2216D412yes—
40#17984548—22no—
41#17984547D411yescharacteristic
42#17984546—21no—
43C8×D277—21no—
44#17984538—21no—
45#41×C277—21no—
46Q16×C277D411yescharacteristic
47SD16×C277—21no—
48D8×C277D411yescharacteristic
49M16×C277—21no—
50C2×C8×C277C2311yescharacteristic
51C16×C277—21no—
52C22×D277—42no—
53C22×D277—41no—
54Dic554—41no—
55Dic554—41no—
56Dic554D811yescharacteristic
57D1108—22no—
58D1108—42no—
59D1108—41no—
60D1108D811yescharacteristic
61C22⋊D277—21no—
62C22⋊D277—42no—
63C2×Dic277—41no—
64C4×D277—21no—
65C4×D277—42no—
66#14555660—21no—
67Q8×C277—21no—
68D4×C277—21no—
69D4×C277—41no—
70C2×C4×C277—41no—
71C2×C4×C277C2×D411yescharacteristic
72C8×C277—41no—
73C8×C277C2×D411yescharacteristic
74C8×C277C2×D411yescharacteristic
75C22×C277—41no—
76C22×C277AGL(1,ℤ/8)11yescharacteristic
77C2×D277—21no—
78C2×D277—42no—
79C2×D277—162no—
80C2×D277—161no—
81C4×C277—41no—
82C4×C277#12011yescharacteristic
83C4×C277C2×D811yescharacteristic
84Dic277—21no—
85Dic277—81no—
86C2×C277—21no—
87C2×C277—81no—
88C2×C277#44711yescharacteristic
89D277—41no—
90D277—82no—
91C277#219411yescharacteristic, complemented, Sylow
92#2194—2771nomaximal, Sylow
93#576—2771no—
94#510—2771no—
95C2×SD32—2771no—
96#473—2771no—
97#361—2771no—
98#359D27711yescharacteristic, complemented
99#350—2771no—
100H(5,𝔽2)—5541no—
101#137—5541no—
102AGL(1,ℤ/8)—5541no—
103AGL(1,ℤ/8)—5542no—
104#135—5541no—
105#135C2×D27711yescharacteristic
106C2×Q16—2771no—
107C2×D8—2771no—
108C2×D8—5541no—
109#131—2771no—
110Q32—5541no—
111SD32—5542no—
112SD32—5541no—
113M32—2771no—
114C2×C16C2×D27711yescharacteristic, complemented
115#108C2×D27711yescharacteristic, complemented
116#101—5541no—
117#41—21no—
118#41—2771no—
119#41—5542no—
120#41—11081no—
121C2×Q8—5541no—
122C2×D4—5542no—
123C2×D4—5541no—
124C2×D4—11081no—
125C2×D4—11082no—
126Q16—5541no—
127Q16—5541no—
128Q16—11081no—
129Q16D110811yescharacteristic
130SD16—21no—
131SD16—5542no—
132SD16—11081no—
133D8—2772no—
134D8—5542no—
135D8—5541no—
136D8D110811yescharacteristic
137M16—21no—
138M16—2771no—
139M16—5541no—
140C2×C8—5541no—
141C2×C8C22×D27711yescharacteristic
142C16—21no—
143C16—5541no—
144C23—11082no—
145C23—11081no—
146Q8—21no—
147Q8—2771no—
148Q8—11081no—
149Q8—11081no—
150D4—21no—
151D4—41no—
152D4—2771no—
153D4—5541no—
154D4—5542no—
155D4—11082no—
156D4—11082no—
157D4—11081no—
158C2×C4—41no—
159C2×C4—5541no—
160C2×C4—11082no—
161C2×C4—11081no—
162C2×C4D4×D27711yescharacteristic
163C8—41no—
164C8—5541no—
165C8D4×D27711yescharacteristic
166C8C2×D110811yescharacteristic
167C22—41no—
168C22—5541no—
169C22—44321no—
170C22—44322no—
171C22—11082no—
172C22#2257990711yescharacteristic
173C4—41no—
174C4—5541no—
175C4—22161no—
176C4#2257985011yescharacteristic
177C4D8×D27711yescharacteristic
178C2—21no—
179C2—81no—
180C2—11081no—
181C2—22162no—
182C2#3180013711yescharacteristic
subgroupG/H
centerC2#31800137
commutator, cosocleC2×C8×C277C23
FrattiniC2×C8C22×D277
Fitting#359×C277C2
socleC2×C277#447
prime radical#31800804C2
hypercenter#359D277
hypocenterC277#2194
LCSG ▷ C2×C8×C277 ▷ C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #359

Complements

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

NH ≅ G/Ntype
2. #31800442C2semidirect
3. C2×#22579825C2semidirect
4. #31800278C2semidirect
5. #31799814C2semidirect
6. #31799785C2semidirect
7. #359×C277C2semidirect
13. C2×Dic1108C22semidirect
20. #22579820C22semidirect
23. C2×C16×C277C22semidirect
24. #108×C277C22semidirect
91. C277#2194semidirect
98. #359D277semidirect
114. C2×C16C2×D277semidirect
115. #108C2×D277semidirect

Maximal subgroups

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

subgroupindex
#318008042
#318004422
C2×#225798252
#318002782
#317998142
#317997852
#359×C2772
#2194277