Finite Group Databasebeta

← #46835398

Subgroups — #46835398

Order 34688.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#31774496C211yesmaximal, characteristic
2#31774230C211yesmaximal, characteristic, complemented
3#31774216C211yesmaximal, characteristic
4#31773837C211yesmaximal, characteristic, complemented
5#31773630C211yesmaximal, characteristic
6#31773622C211yesmaximal, characteristic, complemented
7#328×C271C211yesmaximal, characteristic, complemented
8#22576155—21no—
9#22576151—21no—
10#22576145—21no—
11#22576144—21no—
12#22576136—21no—
13#22576134C2211yescharacteristic
14(C22⋊D271)⋊C4—21no—
15C2×C4⋊Dic271C2211yescharacteristic
16C2×Dic271⋊C4C2211yescharacteristic
17#22576093—21no—
18#22576092—21no—
19#22576084—21no—
20#22576082—21no—
21C22⋊(C271⋊C8)C2211yescharacteristic
22C271⋊#95—21no—
23C271⋊#95—21no—
24C22⋊Q8×C271C2211yescharacteristic
25C22⋊C8×C271C2211yescharacteristic
26#95×C271C2211yescharacteristic
27C2×D1084D411yescharacteristic
28C2×C22⋊D271—21no—
29C22×Dic271—21no—
30C22×Dic271D411yescharacteristic
31C22×Dic271D411yescharacteristic
32C2×C4×D271—21no—
33C2×C271⋊C8—21no—
34C4⋊Dic271—21no—
35C4⋊Dic271—21no—
36C4⋊Dic271—21no—
37C4⋊Dic271—21no—
38C4⋊Dic271D411yescharacteristic
39Dic271⋊C4—21no—
40Dic271⋊C4—21no—
41Dic271⋊C4—21no—
42(C2×D271)⋊C4—21no—
43(C2×D271)⋊C4—21no—
44(C2×D271)⋊C4—21no—
45(C2×D271)⋊C4—21no—
46C4×Dic271—21no—
47C2×Q8×C271D411yescharacteristic
48C22×C4×C271—21no—
49C22×C4×C271C2311yescharacteristic
50C2×C8×C271—21no—
51C4⋊C4×C271—21no—
52C4⋊C4×C271D411yescharacteristic
53C22⋊C4×C271—21no—
54C22×D271—21no—
55D1084—41no—
56C22⋊D271—41no—
57C22⋊D271—41no—
58C2×Dic271—21no—
59C2×Dic271—21no—
60C2×Dic271—21no—
61C2×Dic271—21no—
62C2×Dic271—21no—
63C2×Dic271—41no—
64C2×Dic271—42no—
65C2×Dic271—41no—
66C4×D271—81no—
67C271⋊C8—41no—
68C23×C271C2×D411yescharacteristic
69Q8×C271—41no—
70C2×C4×C271—21no—
71C2×C4×C271—21no—
72C2×C4×C271—41no—
73C2×C4×C271—41no—
74C2×C4×C271—41no—
75C2×C4×C271—41no—
76C2×C4×C271C2×D411yescharacteristic
77C2×C4×C271C2×D411yescharacteristic
78C8×C271—41no—
79C22×C271—21no—
80C22×C271—21no—
81C22×C271#12011yescharacteristic
82C22×C271#13511yescharacteristic
83C22×C271#13711yescharacteristic
84C2×D271—41no—
85C2×D271—41no—
86C2×D271—41no—
87C4×C271—21no—
88C4×C271—21no—
89C4×C271—41no—
90C4×C271—41no—
91C4×C271—81no—
92Dic271—41no—
93Dic271—41no—
94Dic271—41no—
95Dic271—81no—
96C2×C271—21no—
97C2×C271—21no—
98C2×C271#45211yescharacteristic
99C2×C271#45411yescharacteristic
100C2×C271#45811yescharacteristic
101D271—81no—
102C271#161511yescharacteristic, complemented, Sylow
103#1615—2711nomaximal, Sylow
104#539—2711no—
105#484—2711no—
106#481—2711no—
107#400—2711no—
108#328D27111yescharacteristic, complemented
109#327—2711no—
110#324—2711no—
111#126—5421no—
112#125—5421no—
113#123—5421no—
114#123—5421no—
115C22⋊Q8—5421no—
116C22⋊Q8C2×D27111yescharacteristic
117#121—2711no—
118C4×D4—5421no—
119C2×C4⋊C4—2711no—
120C2×C4⋊C4—2711no—
121#107—5421no—
122#106—5421no—
123#103—5421no—
124#102—5421no—
125C22⋊C8—2711no—
126C22⋊C8C2×D27111yescharacteristic
127#95—5421no—
128#95—5421no—
129#95C2×D27111yescharacteristic
130C2×Q8D108411yescharacteristic
131C2×D4—2711no—
132C2×D4—5421no—
133C22×C4—21no—
134C22×C4—2711no—
135C22×C4—2711no—
136C22×C4—5421no—
137C22×C4—5421no—
138C22×C4C22×D27111yescharacteristic
139C2×C8—21no—
140C2×C8—5421no—
141C4⋊C4—21no—
142C4⋊C4—2711no—
143C4⋊C4—5421no—
144C4⋊C4—5421no—
145C4⋊C4—5421no—
146C4⋊C4—5421no—
147C4⋊C4—5421no—
148C4⋊C4—5421no—
149C4⋊C4—5421no—
150C4⋊C4D108411yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—5421no—
153C22⋊C4—5421no—
154C22⋊C4—5421no—
155C22⋊C4—5421no—
156C42—5421no—
157C23—5421no—
158C23D4×D27111yescharacteristic
159Q8—41no—
160D4—10841no—
161D4—10841no—
162D4—10841no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—5421no—
170C2×C4—5421no—
171C2×C4—5421no—
172C2×C4—5421no—
173C2×C4—5421no—
174C2×C4—10841no—
175C2×C4—10842no—
176C2×C4—10841no—
177C2×C4—21681no—
178C2×C4D4×D27111yescharacteristic
179C2×C4C2×D108411yescharacteristic
180C8—41no—
181C8—10841no—
182C22—21no—
183C22—21no—
184C22—10841no—
185C22—10841no—
186C22—10841no—
187C22#2257613011yescharacteristic
188C22#2257618111yescharacteristic
189C22#2257619211yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—10841no—
196C4—10841no—
197C4—10841no—
198C4—21681no—
199C2—21no—
200C2—21no—
201C2—21681no—
202C2#3177406211yescharacteristic
203C2#3177407111yescharacteristic
204C2#3177408811yescharacteristic
subgroupG/H
centerC22#22576130
commutator, cosocleC22×C4×C271C23
FrattiniC22×C4C22×D271
Fitting#328×C271C2
socleC22×C271#120
prime radical#22576134C22
hypercenter#328D271
hypocenterC271#1615
LCSG ▷ C22×C4×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #31774230C2semidirect
4. #31773837C2semidirect
6. #31773622C2semidirect
7. #328×C271C2semidirect
102. C271#1615semidirect
108. #328D271semidirect

Maximal subgroups

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

subgroupindex
#317744962
#317742302
#317742162
#317738372
#317736302
#317736222
#328×C2712
#1615271