Finite Group Databasebeta

← #47982255

Subgroups — #47982255

Order 35456.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#31800657C211yesmaximal, characteristic, complemented
2#31800348C211yesmaximal, characteristic, complemented
3#31800194C211yesmaximal, characteristic, complemented
4#31799747C211yesmaximal, characteristic, complemented
5D4⋊#14555660C211yesmaximal, characteristic, complemented
6#31799729C211yesmaximal, characteristic, complemented
7#459×C277C211yesmaximal, characteristic, complemented
8C2×#17984563—21no—
9C2×#17984548—21no—
10#22579880C2211yescharacteristic
11#22579862—22no—
12#22579859—21no—
13#22579851—21no—
14C4×D1108C2211yescharacteristic
15C4⋊C4×D277—21no—
16C4⋊#14555660C2211yescharacteristic
17#22579801—22no—
18#22579801—21no—
19C4×#14555660C2211yescharacteristic
20C2×D8×C277—21no—
21#127×C277C2211yescharacteristic
22C4×D4×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24#102×C277—21no—
25#17984563—42no—
26#17984563—42no—
27C2×Dic554—21no—
28C2×D1108D411yescharacteristic
29C2×C22⋊D277—22no—
30C2×C4×D277—22no—
31C2×C4×D277—21no—
32#17984548—42no—
33C2×#14555660—21no—
34C2×#14555660—21no—
35C4⋊Dic277—21no—
36C4⋊Dic277D411yescharacteristic
37C4⋊Dic277D412yes—
38#17984542—22no—
39C22⋊Dic277—22no—
40#17984540—21no—
41C2×D4×C277—21no—
42C2×D4×C277—21no—
43C2×D4×C277—21no—
44C2×D4×C277D411yescharacteristic
45C22×C4×C277—21no—
46D8×C277—42no—
47C2×C8×C277—21no—
48C4⋊C4×C277D411yescharacteristic
49C22⋊C4×C277—21no—
50C42×C277C2311yescharacteristic
51C22×D277—21no—
52Dic554—41no—
53Dic554—41no—
54D1108—21no—
55D1108D812yescomplemented
56C22⋊D277—44no—
57C2×Dic277—21no—
58C2×Dic277—22no—
59C4×D277—44no—
60C4×D277—41no—
61C4×D277—41no—
62#14555660—41no—
63#14555660—41no—
64C23×C277—21no—
65C23×C277—41no—
66D4×C277—21no—
67D4×C277—21no—
68D4×C277—42no—
69D4×C277—41no—
70D4×C277—41no—
71D4×C277—41no—
72D4×C277—41no—
73C2×C4×C277—21no—
74C2×C4×C277—41no—
75C2×C4×C277—41no—
76C2×C4×C277C2×D411yescharacteristic
77C2×C4×C277C2×D411yescharacteristic
78C2×C4×C277C2×D411yescharacteristic
79C8×C277—41no—
80C22×C277—41no—
81C22×C277—41no—
82C22×C277—41no—
83C22×C277—81no—
84C22×C277—81no—
85C22×C277—81no—
86C22×C277#12011yescharacteristic
87C2×D277—22no—
88C2×D277—41no—
89C2×D277—41no—
90C4×C277—21no—
91C4×C277—41no—
92C4×C277C2×D811yescharacteristic
93C4×C277#13511yescharacteristic
94C4×C277AGL(1,ℤ/8)11yescharacteristic
95C4×C277AGL(1,ℤ/8)11yescharacteristic
96Dic277—42no—
97Dic277—41no—
98C2×C277—81no—
99C2×C277—161no—
100C2×C277#44711yescharacteristic
101C2×C277#44911yescharacteristic
102C2×C277#45411yescharacteristic
103D277—42no—
104C277#162511yescharacteristic, complemented, Sylow
105#1625—2771nomaximal, Sylow
106#547—2771no—
107#486—2771no—
108#459—2771no—
109#459D27711yescharacteristic, complemented
110#332—2771no—
111D4⋊C8—2771no—
112D4⋊C8—2771no—
113C2×#41—5541no—
114C2×D8—21no—
115C2×D8—5541no—
116C4⋊Q8—2771no—
117#127C2×D27711yescharacteristic
118#123—5542no—
119C22⋊Q8—5541no—
120#121—5541no—
121C4×D4—2771no—
122C4×D4C2×D27711yescharacteristic
123C2×C4⋊C4—5541no—
124C4⋊C8—2771no—
125C4⋊C8C2×D27711yescharacteristic
126#102—21no—
127#102—5541no—
128#102—5542no—
129C4×C8—2771no—
130#41—11082no—
131#41—11082no—
132C2×Q8—5541no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—2771no—
137C2×D4—5542no—
138C2×D4C22⋊D27711yescharacteristic
139C22×C4—21no—
140C22×C4—5542no—
141C22×C4—5541no—
142D8—42no—
143D8—11082no—
144C2×C8—21no—
145C2×C8—5541no—
146C2×C8—5541no—
147C4⋊C4—2771no—
148C4⋊C4—2772no—
149C4⋊C4—5542no—
150C4⋊C4—5541no—
151C4⋊C4C22⋊D27711yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—5542no—
154C22⋊C4—5541no—
155C42C22×D27711yescharacteristic
156C23—21no—
157C23—41no—
158C23—5541no—
159Q8—11081no—
160Q8—11081no—
161D4—21no—
162D4—21no—
163D4—42no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168D4—2772no—
169D4—5541no—
170D4—11084no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—5541no—
175C2×C4—5542no—
176C2×C4—11084no—
177C2×C4—11081no—
178C2×C4—11081no—
179C2×C4D4×D27711yescharacteristic
180C2×C4D4×D27711yescharacteristic
181C2×C4C2×C22⋊D27711yescharacteristic
182C8—41no—
183C8—11081no—
184C8—11081no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—5542no—
192C22—11081no—
193C22—11081no—
194C22#2257984811yescharacteristic
195C4—21no—
196C4—41no—
197C4—11082no—
198C4—11081no—
199C4D8×D27711yescharacteristic
200C4#2257990011yescharacteristic
201C4#2257990411yescharacteristic
202C4#2257990611yescharacteristic
203C2—81no—
204C2—161no—
205C2—11082no—
206C2#3180013411yescharacteristic
207C2#3180014511yescharacteristic
208C2#3180017311yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#459×C277C2
socleC22×C277#120
hypercenter#459D277
hypocenterC277#1625
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #31800657C2semidirect
2. #31800348C2semidirect
3. #31800194C2semidirect
4. #31799747C2semidirect
5. D4⋊#14555660C2semidirect
6. #31799729C2semidirect
7. #459×C277C2semidirect
55. D1108D8semidirect
104. C277#1625semidirect
109. #459D277semidirect

Maximal subgroups

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

subgroupindex
#318006572
#318003482
#318001942
#317997472
D4⋊#145556602
#317997292
#459×C2772
#1625277