Finite Group Databasebeta

← #46835526

Subgroups — #46835526

Order 34688.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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#31774562C211yesmaximal, characteristic
2#31774189C211yesmaximal, characteristic, complemented
3#31774184C211yesmaximal, characteristic
4#31773643C211yesmaximal, characteristic, complemented
5#31773629C211yesmaximal, characteristic, complemented
6#31773626C211yesmaximal, characteristic
7#487×C271C211yesmaximal, characteristic, complemented
8C2×Q8×D271—21no—
9#22576159—21no—
10#22576138—22no—
11#22576136—21no—
12C4×Dic542C2211yescharacteristic
13C4×D1084C2211yescharacteristic
14#22576122—21no—
15#22576093—21no—
16#22576091—21no—
17C4⋊(C271⋊C8)C2211yescharacteristic
18C4⋊(C271⋊C8)C2211yescharacteristic
19#22576083—21no—
20#22576080—21no—
21C4⋊Q8×C271C2211yescharacteristic
22C4⋊Q8×C271C2211yescharacteristic
23#103×C271—22no—
24C4×C8×C271C2211yescharacteristic
25C2×Dic542—22no—
26C2×Dic542D411yescharacteristic
27Q8×D271—42no—
28Q8×D271—42no—
29C2×D1084D411yescharacteristic
30C2×C4×D271—22no—
31C2×C4×D271—21no—
32C2×C271⋊C8—21no—
33C2×C271⋊C8—21no—
34C4⋊Dic271D411yescharacteristic
35C4⋊Dic271D411yescharacteristic
36Dic271⋊C4—22no—
37Dic271⋊C4—21no—
38(C2×D271)⋊C4—22no—
39(C2×D271)⋊C4—21no—
40C4×Dic271—21no—
41C2×Q8×C271—21no—
42C2×Q8×C271—21no—
43C2×C8×C271—21no—
44C4⋊C4×C271—21no—
45C4⋊C4×C271—21no—
46C4⋊C4×C271—21no—
47C4⋊C4×C271D412yes—
48C42×C271C2311yescharacteristic
49C22×D271—21no—
50Dic542—21no—
51Dic542—44no—
52Dic542SD1612yes—
53D1084—21no—
54D1084Q1612yes—
55C2×Dic271—21no—
56C2×Dic271—21no—
57C2×Dic271—21no—
58C4×D271—44no—
59C4×D271—41no—
60C4×D271—41no—
61C271⋊C8—41no—
62C271⋊C8—41no—
63Q8×C271—42no—
64Q8×C271—41no—
65Q8×C271—41no—
66C2×C4×C271—22no—
67C2×C4×C271—41no—
68C2×C4×C271C2×D411yescharacteristic
69C2×C4×C271C2×D411yescharacteristic
70C2×C4×C271C2×D411yescharacteristic
71C8×C271—41no—
72C22×C271#12011yescharacteristic
73C2×D271—22no—
74C2×D271—41no—
75C2×D271—41no—
76C4×C271—21no—
77C4×C271—42no—
78C4×C271—81no—
79C4×C271C2×SD1611yescharacteristic
80C4×C271C2×Q1611yescharacteristic
81C4×C271AGL(1,ℤ/8)11yescharacteristic
82C4×C271#13711yescharacteristic
83Dic271—22no—
84Dic271—41no—
85Dic271—41no—
86C2×C271#45011yescharacteristic
87C2×C271#45111yescharacteristic
88C2×C271#45411yescharacteristic
89D271—42no—
90C271#163711yescharacteristic, complemented, Sylow
91#1637—2711nomaximal, Sylow
92D4×Q8—2711no—
93#487D27111yescharacteristic, complemented
94#477—2711no—
95#476—2711no—
96#332—2711no—
97Q8⋊C8—2711no—
98D4⋊C8—2711no—
99C22×Q8—5421no—
100C4⋊Q8—5421no—
101C4⋊Q8C2×D27111yescharacteristic
102C4⋊Q8C2×D27111yescharacteristic
103C22⋊Q8—5421no—
104C22⋊Q8—5422no—
105C4×Q8—2711no—
106C4×D4—2711no—
107C4×D4—5421no—
108#107—5421no—
109#106—5421no—
110C4⋊C8—2711no—
111C4⋊C8—2711no—
112#103—22no—
113#103—5421no—
114#102—5421no—
115C4×C8C2×D27111yescharacteristic
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—2711no—
119C2×Q8—5422no—
120C2×Q8—10842no—
121C2×Q8—10842no—
122C2×D4—2711no—
123C22×C4—5422no—
124C22×C4—5421no—
125C2×C8—21no—
126C2×C8—5421no—
127C2×C8—5421no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—2711no—
132C4⋊C4—2711no—
133C4⋊C4—5422no—
134C4⋊C4—5421no—
135C4⋊C4C22⋊D27112yes—
136C22⋊C4—5422no—
137C22⋊C4—5421no—
138C42—5421no—
139C42C22×D27111yescharacteristic
140C23—5421no—
141Q8—42no—
142Q8—41no—
143Q8—41no—
144Q8—2712no—
145Q8—5421no—
146Q8—10844no—
147D4—2712no—
148D4—5421no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—5421no—
152C2×C4—5421no—
153C2×C4—5421no—
154C2×C4—10844no—
155C2×C4—10841no—
156C2×C4—10841no—
157C2×C4D4×D27111yescharacteristic
158C2×C4D4×D27111yescharacteristic
159C2×C4C2×C22⋊D27111yescharacteristic
160C8—41no—
161C8—10841no—
162C8—10841no—
163C22—5422no—
164C22—10841no—
165C22—10841no—
166C22#2257612811yescharacteristic
167C4—21no—
168C4—42no—
169C4—81no—
170C4—5422no—
171C4—10841no—
172C4—10841no—
173C4SD16×D27111yescharacteristic
174C4Q16×D27111yescharacteristic
175C4#2257618711yescharacteristic
176C4#2257619211yescharacteristic
177C2—10842no—
178C2#3177404611yescharacteristic
179C2#3177405111yescharacteristic
180C2#3177406911yescharacteristic
subgroupG/H
centerC22#22576128
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
Fitting#487×C271C2
socleC22×C271#120
prime radicalC2×D1084D4
hypercenter#487D271
hypocenterC271#1637
LCSG ▷ C42×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #31774189C2semidirect
4. #31773643C2semidirect
5. #31773629C2semidirect
7. #487×C271C2semidirect
90. C271#1637semidirect
93. #487D271semidirect

Maximal subgroups

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

subgroupindex
#317745622
#317741892
#317741842
#317736432
#317736292
#317736262
#487×C2712
#1637271