Finite Group Databasebeta

← #46835471

Subgroups — #46835471

Order 34688.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#31774621C211yesmaximal, characteristic, complemented
2#31774094C211yesmaximal, characteristic, complemented
3#31774089C211yesmaximal, characteristic
4#31773643C211yesmaximal, characteristic, complemented
5#31773629C211yesmaximal, characteristic, complemented
6#31773626C211yesmaximal, characteristic, complemented
7#486×C271C211yesmaximal, characteristic, complemented
8C2×#16864642—21no—
9C2×#16864639—21no—
10#22576155—22no—
11#22576149—21no—
12#22576140—21no—
13Q8×Dic271—21no—
14C4×Dic542C2211yescharacteristic
15C4×D1084C2211yescharacteristic
16#22576118—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
25C2×Dic542D411yescharacteristic
26C2×D1084D411yescharacteristic
27C2×C4×D271—21no—
28#16864642—42no—
29#16864639—42no—
30C2×C271⋊C8—21no—
31C2×C271⋊C8—21no—
32C4⋊Dic271—22no—
33C4⋊Dic271D411yescharacteristic
34C4⋊Dic271D411yescharacteristic
35Dic271⋊C4—21no—
36(C2×D271)⋊C4—22no—
37(C2×D271)⋊C4—22no—
38(C2×D271)⋊C4—21no—
39C4×Dic271—22no—
40C4×Dic271—21no—
41C2×Q8×C271—21no—
42C2×D4×C271—21no—
43C2×D4×C271—21no—
44C2×D4×C271—21no—
45C2×C8×C271—21no—
46C4⋊C4×C271—21no—
47C4⋊C4×C271D412yes—
48C42×C271C2311yescharacteristic
49C22×D271—21no—
50Dic542—21no—
51Dic542—21no—
52D1084—21no—
53D1084—21no—
54C2×Dic271—21no—
55C2×Dic271—21no—
56C2×Dic271—21no—
57C4×D271—41no—
58C4×D271—41no—
59C271⋊C8—41no—
60C271⋊C8—41no—
61C23×C271—41no—
62Q8×C271—41no—
63Q8×C271—41no—
64D4×C271—42no—
65D4×C271—41no—
66D4×C271—41no—
67D4×C271—41no—
68D4×C271—41no—
69C2×C4×C271—22no—
70C2×C4×C271C2×D411yescharacteristic
71C2×C4×C271C2×D411yescharacteristic
72C2×C4×C271C2×D411yescharacteristic
73C8×C271—41no—
74C22×C271—81no—
75C22×C271—81no—
76C22×C271—81no—
77C22×C271#12011yescharacteristic
78C2×D271—41no—
79C2×D271—41no—
80C2×D271—41no—
81C4×C271—21no—
82C4×C271—42no—
83C4×C271#13511yescharacteristic
84C4×C271#13511yescharacteristic
85C4×C271AGL(1,ℤ/8)11yescharacteristic
86C4×C271AGL(1,ℤ/8)11yescharacteristic
87Dic271—41no—
88Dic271—41no—
89Dic271—41no—
90C2×C271—161no—
91C2×C271#44911yescharacteristic
92C2×C271#44911yescharacteristic
93C2×C271#45411yescharacteristic
94D271—81no—
95C271#162811yescharacteristic, complemented, Sylow
96#1628—2711nomaximal, Sylow
97#556—2711no—
98#486D27111yescharacteristic, complemented
99#460—2711no—
100#459—2711no—
101#332—2711no—
102Q8⋊C8—2711no—
103D4⋊C8—2711no—
104C2×SD16—5421no—
105C2×D8—5421no—
106C4⋊Q8C2×D27111yescharacteristic
107#127C2×D27111yescharacteristic
108#126—5422no—
109#124—5421no—
110C22⋊Q8—5421no—
111C4×Q8—2711no—
112C4×Q8—5421no—
113C4×D4—2711no—
114#117—5421no—
115C4⋊C8—2711no—
116C4⋊C8—2711no—
117#102—22no—
118#102—5421no—
119#102—5421no—
120C4×C8C2×D27111yescharacteristic
121C2×Q8—21no—
122C2×Q8—2711no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—2711no—
127C22×C4—5421no—
128SD16—10842no—
129D8—10842no—
130C2×C8—21no—
131C2×C8—5421no—
132C2×C8—5421no—
133C4⋊C4—21no—
134C4⋊C4—2711no—
135C4⋊C4—2711no—
136C4⋊C4—5422no—
137C4⋊C4—5421no—
138C4⋊C4C22⋊D27112yes—
139C22⋊C4—5422no—
140C22⋊C4—5422no—
141C22⋊C4—5421no—
142C42—5422no—
143C42—5421no—
144C42C22×D27111yescharacteristic
145C23—41no—
146C23—5421no—
147Q8—41no—
148Q8—41no—
149Q8—5421no—
150Q8—5421no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—5421no—
157D4—5421no—
158C2×C4—22no—
159C2×C4—5421no—
160C2×C4—5421no—
161C2×C4—5421no—
162C2×C4—10841no—
163C2×C4—10841no—
164C2×C4D4×D27111yescharacteristic
165C2×C4D4×D27111yescharacteristic
166C2×C4C2×C22⋊D27111yescharacteristic
167C8—41no—
168C8—10841no—
169C8—10841no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—10841no—
174C22—10841no—
175C22—10841no—
176C22#2257612811yescharacteristic
177C4—21no—
178C4—42no—
179C4—10841no—
180C4—10841no—
181C4—10841no—
182C4#2257617911yescharacteristic
183C4#2257618111yescharacteristic
184C4#2257618411yescharacteristic
185C4#2257618711yescharacteristic
186C2—161no—
187C2—21681no—
188C2#3177403911yescharacteristic
189C2#3177404111yescharacteristic
190C2#3177406911yescharacteristic
subgroupG/H
centerC22#22576128
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
Fitting#486×C271C2
socleC22×C271#120
prime radical#31774089C2
hypercenter#486D271
hypocenterC271#1628
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. #31774621C2semidirect
2. #31774094C2semidirect
4. #31773643C2semidirect
5. #31773629C2semidirect
6. #31773626C2semidirect
7. #486×C271C2semidirect
95. C271#1628semidirect
98. #486D271semidirect

Maximal subgroups

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

subgroupindex
#317746212
#317740942
#317740892
#317736432
#317736292
#317736262
#486×C2712
#1628271