Finite Group Databasebeta

← #47982483

Subgroups — #47982483

Order 35456.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#31800746C211yesmaximal, characteristic
2#31800408C211yesmaximal, characteristic, complemented
3#31800394C211yesmaximal, characteristic, complemented
4#31799743C211yesmaximal, characteristic, complemented
5#31799742C211yesmaximal, characteristic, complemented
6#31799741C211yesmaximal, characteristic, complemented
7#489×C277C211yesmaximal, characteristic, complemented
8C2×#17984553—21no—
9C2×#17984550—21no—
10#22579872C2211yescharacteristic
11#22579868C2211yescharacteristic
12#22579864—21no—
13#22579862—21no—
14#22579857—21no—
15#22579856—21no—
16#22579853—21no—
17#22579852—21no—
18#22579813—21no—
19#22579811—21no—
20#22579791C2211yescharacteristic
21#22579791C2211yescharacteristic
22C4⋊Q8×C277C2211yescharacteristic
23#124×C277C2211yescharacteristic
24#103×C277—21no—
25#102×C277—21no—
26#97×C277C2211yescharacteristic
27C2×Dic554D411yescharacteristic
28C2×D1108D411yescharacteristic
29C2×C22⋊D277—21no—
30C2×C22⋊D277—21no—
31C22×Dic277—21no—
32C2×C4×D277—21no—
33#17984553—42no—
34#17984550—42no—
35C2×#14555660—21no—
36C2×#14555660—21no—
37C4⋊Dic277—21no—
38C4⋊Dic277D411yescharacteristic
39C4⋊Dic277D411yescharacteristic
40#17984542—21no—
41#17984542—21no—
42#17984542—21no—
43C22⋊Dic277—21no—
44#17984540—21no—
45#17984540—21no—
46#17984540—21no—
47C2×Q8×C277—21no—
48C2×Q8×C277D411yescharacteristic
49C2×D4×C277D411yescharacteristic
50C2×C8×C277—21no—
51C4⋊C4×C277—21no—
52C4⋊C4×C277—21no—
53C22⋊C4×C277—21no—
54C22⋊C4×C277—21no—
55C42×C277C2311yescharacteristic
56C22×D277—21no—
57Dic554—41no—
58D1108—41no—
59C22⋊D277—81no—
60C22⋊D277—81no—
61C2×Dic277—21no—
62C2×Dic277—21no—
63C2×Dic277—21no—
64C2×Dic277—81no—
65C4×D277—81no—
66#14555660—22no—
67#14555660—22no—
68C23×C277—21no—
69Q8×C277—41no—
70Q8×C277—41no—
71Q8×C277—41no—
72D4×C277—41no—
73C2×C4×C277—21no—
74C2×C4×C277—41no—
75C2×C4×C277C2×D411yescharacteristic
76C2×C4×C277C2×D411yescharacteristic
77C2×C4×C277C2×D411yescharacteristic
78C8×C277—41no—
79C22×C277—41no—
80C22×C277—41no—
81C22×C277—41no—
82C22×C277#12011yescharacteristic
83C2×D277—41no—
84C2×D277—41no—
85C2×D277—41no—
86C4×C277—21no—
87C4×C277—21no—
88C4×C277—21no—
89C4×C277—41no—
90C4×C277—81no—
91Dic277—41no—
92Dic277—41no—
93Dic277—41no—
94C2×C277—81no—
95C2×C277#45311yescharacteristic
96C2×C277#45511yescharacteristic
97C2×C277#45611yescharacteristic
98D277—81no—
99C277#166111yescharacteristic, complemented, Sylow
100#1661—2771nomaximal, Sylow
101#562—2771no—
102#501—2771no—
103#497—2771no—
104#489D27711yescharacteristic, complemented
105#330—2771no—
106#329—2771no—
107#329—2771no—
108C2×Q16—5541no—
109C2×SD16—5541no—
110C4⋊Q8C2×D27711yescharacteristic
111#125—2771no—
112#124—2771no—
113#124C2×D27711yescharacteristic
114#123—5541no—
115#123—5541no—
116C22⋊Q8—5541no—
117C22⋊Q8—5541no—
118#121—5541no—
119#121—5541no—
120#107—5541no—
121#106—5541no—
122#103—21no—
123#102—21no—
124#97—2771no—
125#97—2771no—
126#97C2×D27711yescharacteristic
127C2×Q8—21no—
128C2×Q8—2771no—
129C2×Q8C22⋊D27711yescharacteristic
130C2×D4—2771no—
131C2×D4—5541no—
132C2×D4—5541no—
133C2×D4C22⋊D27711yescharacteristic
134C22×C4—5541no—
135C22×C4—5541no—
136Q16—11082no—
137SD16—11082no—
138C2×C8—21no—
139C2×C8—5541no—
140C2×C8—5541no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2771no—
144C4⋊C4—2771no—
145C4⋊C4—5541no—
146C4⋊C4—5541no—
147C4⋊C4—5541no—
148C4⋊C4—5541no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—5541no—
152C22⋊C4—5541no—
153C22⋊C4—5541no—
154C22⋊C4—5541no—
155C42C22×D27711yescharacteristic
156C23—21no—
157C23—5541no—
158Q8—41no—
159Q8—41no—
160Q8—41no—
161Q8—11081no—
162D4—41no—
163D4—11081no—
164D4—22161no—
165D4—22161no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—5541no—
169C2×C4—5541no—
170C2×C4—5541no—
171C2×C4—22161no—
172C2×C4—22161no—
173C2×C4D4×D27711yescharacteristic
174C2×C4D4×D27711yescharacteristic
175C2×C4C2×C22⋊D27711yescharacteristic
176C8—41no—
177C8—5542no—
178C8—5542no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—11081no—
183C22—11081no—
184C22—11081no—
185C22#2257984811yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—81no—
191C4—11081no—
192C4—11081no—
193C4—11081no—
194C2—81no—
195C2—22161no—
196C2#3180016811yescharacteristic
197C2#3180017911yescharacteristic
198C2#3180018311yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#489×C277C2
socleC22×C277#120
prime radical#31800746C2
hypercenter#489D277
hypocenterC277#1661
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #31800408C2semidirect
3. #31800394C2semidirect
4. #31799743C2semidirect
5. #31799742C2semidirect
6. #31799741C2semidirect
7. #489×C277C2semidirect
99. C277#1661semidirect
104. #489D277semidirect

Maximal subgroups

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

subgroupindex
#318007462
#318004082
#318003942
#317997432
#317997422
#317997412
#489×C2772
#1661277