Finite Group Databasebeta

← #46835450

Subgroups — #46835450

Order 34688.

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#31774550C211yesmaximal, characteristic, complemented
2#31774089C211yesmaximal, characteristic, complemented
3#31774089C211yesmaximal, characteristic, complemented
4#31773643C211yesmaximal, characteristic, complemented
5#31773626C211yesmaximal, characteristic, complemented
6#31773626C211yesmaximal, characteristic, complemented
7#486×C271C211yesmaximal, characteristic, complemented
8C2×#16864655—21no—
9C2×#16864639—21no—
10C2×#16864639—21no—
11#22576145—22no—
12#22576136—21no—
13#22576135—21no—
14C4×D1084C2211yescharacteristic
15C4×D1084C2211yescharacteristic
16C4⋊C4×D271—21no—
17C4⋊(C271⋊C8)C2211yescharacteristic
18C4⋊(C271⋊C8)C2211yescharacteristic
19#22576081—21no—
20#22576081—21no—
21C4⋊Q8×C271C2211yescharacteristic
22#127×C271C2211yescharacteristic
23#102×C271—22no—
24C4×C8×C271C2211yescharacteristic
25#16864655—42no—
26#16864655—42no—
27C2×D1084—22no—
28C2×D1084D411yescharacteristic
29C2×D1084D411yescharacteristic
30C2×C4×D271—22no—
31C2×C4×D271—21no—
32C2×C4×D271—21no—
33#16864639—42no—
34#16864639—42no—
35C2×C271⋊C8—21no—
36C2×C271⋊C8—21no—
37C4⋊Dic271D411yescharacteristic
38C4⋊Dic271D411yescharacteristic
39Dic271⋊C4—22no—
40(C2×D271)⋊C4—22no—
41(C2×D271)⋊C4—21no—
42(C2×D271)⋊C4—21no—
43C2×Q8×C271—21no—
44C2×D4×C271—21no—
45C2×D4×C271—21no—
46C2×D4×C271—21no—
47C2×C8×C271—21no—
48C4⋊C4×C271—21no—
49C4⋊C4×C271D412yes—
50C42×C271C2311yescharacteristic
51C22×D271—21no—
52C22×D271—21no—
53D1084—21no—
54D1084—21no—
55D1084—21no—
56D1084—44no—
57D1084D812yescomplemented
58C2×Dic271—21no—
59C2×Dic271—21no—
60C4×D271—44no—
61C4×D271—41no—
62C4×D271—41no—
63C4×D271—41no—
64C4×D271—41no—
65C271⋊C8—41no—
66C271⋊C8—41no—
67C23×C271—41no—
68Q8×C271—41no—
69Q8×C271—41no—
70D4×C271—42no—
71D4×C271—41no—
72D4×C271—41no—
73D4×C271—41no—
74D4×C271—41no—
75C2×C4×C271—22no—
76C2×C4×C271C2×D411yescharacteristic
77C2×C4×C271C2×D411yescharacteristic
78C2×C4×C271C2×D411yescharacteristic
79C8×C271—41no—
80C22×C271—81no—
81C22×C271—81no—
82C22×C271—81no—
83C22×C271#12011yescharacteristic
84C2×D271—22no—
85C2×D271—41no—
86C2×D271—41no—
87C2×D271—41no—
88C2×D271—41no—
89C2×D271—41no—
90C4×C271—21no—
91C4×C271—42no—
92C4×C271C2×D811yescharacteristic
93C4×C271#13511yescharacteristic
94C4×C271AGL(1,ℤ/8)11yescharacteristic
95C4×C271AGL(1,ℤ/8)11yescharacteristic
96Dic271—41no—
97Dic271—41no—
98C2×C271—161no—
99C2×C271#44711yescharacteristic
100C2×C271#44911yescharacteristic
101C2×C271#45411yescharacteristic
102D271—42no—
103D271—81no—
104C271#162511yescharacteristic, complemented, Sylow
105#1625—2711nomaximal, Sylow
106#547—2711no—
107#486D27111yescharacteristic, complemented
108#459—2711no—
109#459—2711no—
110#332—2711no—
111D4⋊C8—2711no—
112D4⋊C8—2711no—
113C2×#41—5421no—
114C2×D8—5421no—
115C2×D8—5421no—
116C4⋊Q8C2×D27111yescharacteristic
117#127C2×D27111yescharacteristic
118#123—5422no—
119C22⋊Q8—5421no—
120#121—5421no—
121C4×D4—2711no—
122C4×D4—2711no—
123C2×C4⋊C4—5421no—
124C4⋊C8—2711no—
125C4⋊C8—2711no—
126#102—22no—
127#102—5421no—
128#102—5421no—
129C4×C8C2×D27111yescharacteristic
130#41—10842no—
131#41—10842no—
132C2×Q8—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—2711no—
137C2×D4—2711no—
138C2×D4—5422no—
139C22×C4—5422no—
140C22×C4—5421no—
141C22×C4—5421no—
142D8—10842no—
143D8—10842no—
144C2×C8—21no—
145C2×C8—5421no—
146C2×C8—5421no—
147C4⋊C4—21no—
148C4⋊C4—2711no—
149C4⋊C4—2711no—
150C4⋊C4—5422no—
151C4⋊C4C22⋊D27112yes—
152C22⋊C4—5422no—
153C22⋊C4—5421no—
154C22⋊C4—5421no—
155C42C22×D27111yescharacteristic
156C23—41no—
157C23—5421no—
158C23—5421no—
159Q8—41no—
160Q8—41no—
161D4—42no—
162D4—41no—
163D4—41no—
164D4—41no—
165D4—41no—
166D4—2712no—
167D4—5421no—
168D4—5421no—
169D4—5421no—
170D4—10844no—
171C2×C4—22no—
172C2×C4—5421no—
173C2×C4—5421no—
174C2×C4—10844no—
175C2×C4—10841no—
176C2×C4—10841no—
177C2×C4—10841no—
178C2×C4—10841no—
179C2×C4D4×D27111yescharacteristic
180C2×C4D4×D27111yescharacteristic
181C2×C4C2×C22⋊D27111yescharacteristic
182C8—41no—
183C8—10841no—
184C8—10841no—
185C22—81no—
186C22—81no—
187C22—81no—
188C22—5422no—
189C22—10841no—
190C22—10841no—
191C22—10841no—
192C22—10841no—
193C22—10841no—
194C22#2257612811yescharacteristic
195C4—21no—
196C4—42no—
197C4—10841no—
198C4—10841no—
199C4D8×D27111yescharacteristic
200C4#2257618111yescharacteristic
201C4#2257618411yescharacteristic
202C4#2257618711yescharacteristic
203C2—161no—
204C2—10842no—
205C2—21681no—
206C2#3177402911yescharacteristic
207C2#3177404111yescharacteristic
208C2#3177406911yescharacteristic
subgroupG/H
centerC22#22576128
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
Fitting#486×C271C2
socleC22×C271#120
hypercenter#486D271
hypocenterC271#1625
LCSG ▷ C42×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #31774550C2semidirect
2. #31774089C2semidirect
3. #31774089C2semidirect
4. #31773643C2semidirect
5. #31773626C2semidirect
6. #31773626C2semidirect
7. #486×C271C2semidirect
57. D1084D8semidirect
104. C271#1625semidirect
107. #486D271semidirect

Maximal subgroups

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

subgroupindex
#317745502
#317740892
#317736432
#317736262
#486×C2712
#1625271