Finite Group Databasebeta

← #46834964

Subgroups — #46834964

Order 34688.

212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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#125×D271C211yesmaximal, characteristic
2#31773952C211yesmaximal, characteristic
3#31773849C211yesmaximal, characteristic
4#31773639C211yesmaximal, characteristic, complemented
5#31773638C211yesmaximal, characteristic, complemented
6#31773638C211yesmaximal, characteristic, complemented
7#330×C271C211yesmaximal, characteristic, complemented
8C2×#16864637—21no—
9#22576152C2211yescharacteristic
10#22576151C411yescharacteristic
11#22576151C411yescharacteristic
12#22576150—21no—
13#22576150—21no—
14C4⋊C4×D271—21no—
15C4⋊C4×D271—21no—
16C4⋊C4×D271C411yescharacteristic
17C4⋊C4×D271C411yescharacteristic
18C42×D271C2211yescharacteristic
19Dic271⋊C8—21no—
20(C2×D271)⋊C8—21no—
21#22576071C2211yescharacteristic
22#22576071C2211yescharacteristic
23C8×Dic271—21no—
24#125×C271C2211yescharacteristic
25#97×C271C2211yescharacteristic
26#97×C271C2211yescharacteristic
27C2×C4×D271—21no—
28C2×C4×D271—21no—
29C2×C4×D271C2×C411yescharacteristic
30C2×C4×D271D411yescharacteristic
31C2×C4×D271D411yescharacteristic
32#16864637—24no—
33C2×C271⋊C8—21no—
34C2×C271⋊C8—21no—
35C4⋊Dic271—21no—
36C4⋊Dic271—21no—
37C4⋊Dic271C2×C411yescharacteristic
38C4⋊Dic271C2×C411yescharacteristic
39Dic271⋊C4—21no—
40Dic271⋊C4—21no—
41Dic271⋊C4—21no—
42Dic271⋊C4—21no—
43Dic271⋊C4—21no—
44Dic271⋊C4—21no—
45C4×Dic271C2×C411yescharacteristic
46C4×Dic271D411yescharacteristic
47C4×Dic271D411yescharacteristic
48C2×C8×C271—21no—
49C2×C8×C271—21no—
50C4⋊C4×C271—21no—
51C4⋊C4×C271—21no—
52C4⋊C4×C271C2×C411yescharacteristic
53C4⋊C4×C271C2×C411yescharacteristic
54C42×C271C2311yescharacteristic
55C22×D271C22⋊C411yescharacteristic
56C2×Dic271—21no—
57C2×Dic271—21no—
58C2×Dic271C22⋊C411yescharacteristic
59C2×Dic271C22⋊C411yescharacteristic
60C2×Dic271C22⋊C411yescharacteristic
61C4×D271—22no—
62C4×D271—22no—
63C4×D271—41no—
64C4×D271—42no—
65C4×D271—42no—
66C271⋊C8—22no—
67C271⋊C8—41no—
68C2×C4×C271—21no—
69C2×C4×C271—21no—
70C2×C4×C271C22×C411yescharacteristic
71C2×C4×C271C2×D411yescharacteristic
72C2×C4×C271C2×D411yescharacteristic
73C8×C271—22no—
74C8×C271—41no—
75C22×C271C2×C22⋊C411yescharacteristic
76C2×D271—21no—
77C2×D271—21no—
78C2×D271#10412yes—
79C4×C271—21no—
80C4×C271—21no—
81C4×C271—21no—
82C4×C271—41no—
83C4×C271—41no—
84Dic271—21no—
85Dic271—21no—
86Dic271—41no—
87Dic271—41no—
88Dic271#10112yes—
89C2×C271C2×#10111yescharacteristic
90C2×C271C2×#10411yescharacteristic
91C2×C271#42111yescharacteristic
92D271—22no—
93C271#152811yescharacteristic, complemented, Sylow
94#1528—2711nomaximal, Sylow
95C2×#125—2711no—
96#432—2711no—
97C4×M16—2711no—
98#330—2711no—
99#330—2711no—
100#330—2711no—
101#330D27111yescharacteristic, complemented
102C2×M16—5421no—
103#125—2711no—
104#125—2711no—
105#125—2711no—
106#125—5421no—
107#125—5421no—
108#125C2×D27111yescharacteristic
109C2×C4⋊C4—2711no—
110C2×C4⋊C4—2711no—
111C2×C4⋊C4—5421no—
112C2×C4⋊C4—5421no—
113C2×C42—2711no—
114C4⋊C8—5421no—
115C22⋊C8—5421no—
116#97—2711no—
117#97—2711no—
118#97C2×D27111yescharacteristic
119#97C2×D27111yescharacteristic
120C4×C8—5421no—
121C22×C4—2711no—
122C22×C4—2711no—
123C22×C4—2711no—
124C22×C4—5421no—
125C22×C4—5421no—
126M16—5424no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—5421no—
130C2×C8—5421no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—2711no—
134C4⋊C4—2711no—
135C4⋊C4—5421no—
136C4⋊C4—5421no—
137C4⋊C4—5421no—
138C4⋊C4—5421no—
139C4⋊C4—5421no—
140C4⋊C4—5421no—
141C4⋊C4—5421no—
142C4⋊C4—5421no—
143C4⋊C4C4×D27111yescharacteristic
144C4⋊C4C4×D27111yescharacteristic
145C42—2711no—
146C42—2711no—
147C42—2711no—
148C42C22×D27111yescharacteristic
149C23—2711no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—2711no—
153C2×C4—2711no—
154C2×C4—2711no—
155C2×C4—5422no—
156C2×C4—5422no—
157C2×C4—5421no—
158C2×C4—5421no—
159C2×C4—10841no—
160C2×C4—10842no—
161C2×C4—10842no—
162C2×C4C2×C4×D27111yescharacteristic
163C2×C4D4×D27111yescharacteristic
164C2×C4D4×D27111yescharacteristic
165C8—22no—
166C8—41no—
167C8—5422no—
168C8—10841no—
169C22—2712no—
170C22—5421no—
171C22—5421no—
172C22C22⋊C4×D27111yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—2712no—
179C4—5421no—
180C4—5421no—
181C4—10841no—
182C4—10841no—
183C2—5422no—
184C2#101×D27111yescharacteristic
185C2#104×D27111yescharacteristic
186C2#3177391211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D271
commutatorC2×C4×C271C22×C4
FrattiniC42C22×D271
Fitting#330×C271C2
socleC22×C271C2×C22⋊C4
prime radicalC22×D271C22⋊C4
cosocleC42×C271C23
hypercenter#330D271
hypocenterC271#1528
LCSG ▷ C2×C4×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. #31773639C2semidirect
5. #31773638C2semidirect
6. #31773638C2semidirect
7. #330×C271C2semidirect
93. C271#1528semidirect
101. #330D271semidirect

Maximal subgroups

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

subgroupindex
#125×D2712
#317739522
#317738492
#317736392
#317736382
#330×C2712
#1528271