Finite Group Databasebeta

← #46837495

Subgroups — #46837495

Order 34688.

430 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 73 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#31774459C211yesmaximal, characteristic
2C2×#22576143C212yesmaximal, complemented
3C2×#22576074C212yesmaximal, complemented
4#31773664C211yesmaximal, characteristic, complemented
5#381×C271C211yesmaximal, characteristic, complemented
6C22×C22⋊D271C2212yes—
7#22576144—22no—
8#22576143—24no—
9#22576143—24no—
10#22576134—22no—
11#22576130—22no—
12C2×Dic271⋊C4—22no—
13C2×C22⋊Dic271C2212yes—
14C2×(C2×D271)⋊C4—22no—
15#22576074—24no—
16C23×C4×C271C2211yescharacteristic
17C2×C22⋊C4×C271C2211yescharacteristic
18C2×C22⋊C4×C271C2211yescharacteristic
19#95×C271—22no—
20C23×D271D412yes—
21C2×D1084—22no—
22C2×C22⋊D271—22no—
23C2×C22⋊D271—22no—
24C2×C22⋊D271—22no—
25C2×C22⋊D271—22no—
26C2×C22⋊D271—22no—
27C2×C22⋊D271—22no—
28C22×Dic271—22no—
29C22×Dic271D412yes—
30C4⋊Dic271—22no—
31Dic271⋊C4—28no—
32C22⋊Dic271—22no—
33C22⋊Dic271D414yescomplemented
34(C2×D271)⋊C4—24no—
35(C2×D271)⋊C4—28no—
36C24×C271C2311yescharacteristic
37C22×C4×C271—22no—
38C22×C4×C271—21no—
39C22×C4×C271—22no—
40C22×C4×C271—21no—
41C22×C4×C271—21no—
42C22×C4×C271D412yes—
43C22×C4×C271D412yescomplemented
44C22⋊C4×C271—22no—
45C22⋊C4×C271—22no—
46C22×D271—22no—
47C22×D271—22no—
48C22×D271—22no—
49C22×D271—44no—
50D1084—82no—
51C22⋊D271—42no—
52C22⋊D271—42no—
53C22⋊D271—42no—
54C22⋊D271—42no—
55C2×Dic271—24no—
56C2×Dic271—22no—
57C2×Dic271—22no—
58C2×Dic271—22no—
59C2×Dic271—44no—
60C23×C271—42no—
61C23×C271C2×D412yes—
62C23×C271C2×D412yes—
63C23×C271C2×D411yescharacteristic
64C23×C271C2×D411yescharacteristic
65C23×C271#4111yescharacteristic
66C2×C4×C271—22no—
67C2×C4×C271—24no—
68C2×C4×C271—22no—
69C2×C4×C271—41no—
70C2×C4×C271—42no—
71C2×C4×C271—41no—
72C2×C4×C271—42no—
73C2×C4×C271—42no—
74C2×C4×C271—41no—
75C22×C271—22no—
76C22×C271—24no—
77C22×C271—42no—
78C22×C271—41no—
79C22×C271—41no—
80C22×C271#12011yescharacteristic
81C22×C271#12012yes—
82C22×C271#12112yes—
83C22×C271#12111yescharacteristic
84C22×C271#12711yescharacteristic
85C2×D271—44no—
86C2×D271—42no—
87C2×D271—44no—
88C2×D271—82no—
89C4×C271—42no—
90C4×C271—42no—
91C4×C271—81no—
92Dic271—44no—
93Dic271—42no—
94C2×C271—22no—
95C2×C271—21no—
96C2×C271—22no—
97C2×C271—21no—
98C2×C271#39211yescharacteristic
99C2×C271#45812yes—
100D271—82no—
101C271#202211yescharacteristic, complemented, Sylow
102#2022—2711nomaximal, Sylow
103#534—2711no—
104C2×#123—2712no—
105C2×#99—2712no—
106#381D27111yescharacteristic, complemented
107#342—2711no—
108C22×D4—2712no—
109C23×C4C2×D27111yescharacteristic
110#123—5422no—
111#123—5424no—
112#123—5424no—
113#121—5422no—
114#120—5422no—
115C2×C4⋊C4—5422no—
116C2×C22⋊C4—2712no—
117C2×C22⋊C4—5422no—
118C2×C22⋊C4C2×D27111yescharacteristic
119C2×C22⋊C4C2×D27111yescharacteristic
120#99—5424no—
121#95—22no—
122C24—2712no—
123C24C22×D27111yescharacteristic
124C2×D4—5422no—
125C2×D4—5422no—
126C2×D4—5422no—
127C2×D4—5422no—
128C2×D4—5422no—
129C2×D4—5422no—
130C2×D4—5422no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—2712no—
137C22×C4—5422no—
138C22×C4C22⋊D27112yes—
139C22×C4D108412yescomplemented
140C4⋊C4—5428no—
141C4⋊C4—5422no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—2714no—
145C22⋊C4—5428no—
146C22⋊C4—5424no—
147C22⋊C4—5422no—
148C23—42no—
149C23—5422no—
150C23—5422no—
151C23—5422no—
152C23—10844no—
153C23D4×D27112yes—
154C23D4×D27112yes—
155C23C2×C22⋊D27111yescharacteristic
156C23C2×D108411yescharacteristic
157C23#1686465411yescharacteristic
158D4—10842no—
159D4—10842no—
160D4—10842no—
161D4—10842no—
162D4—21682no—
163C2×C4—22no—
164C2×C4—24no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—42no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—5422no—
173C2×C4—5424no—
174C2×C4—5422no—
175C2×C4—5422no—
176C2×C4—10844no—
177C22—22no—
178C22—24no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—10844no—
183C22—10842no—
184C22—10844no—
185C22—21682no—
186C22#2257612811yescharacteristic
187C22#2257613012yes—
188C22#2257613312yes—
189C22#2257613411yescharacteristic
190C22#2257615611yescharacteristic
191C4—42no—
192C4—42no—
193C4—81no—
194C4—10844no—
195C4—10842no—
196C2—21no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—21682no—
201C2#3177380611yescharacteristic
202C2#3177408612yes—
subgroupG/H
centerC22#22576128
commutator, cosocleC24×C271C23
FrattiniC24C22×D271
Fitting#381×C271C2
socleC22×C271#120
prime radical#31774459C2
hypercenter#381D271
hypocenterC271#2022
LCSG ▷ C24×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#22576143C2semidirect
3. C2×#22576074C2semidirect
4. #31773664C2semidirect
5. #381×C271C2semidirect
33. C22⋊Dic271D4semidirect
43. C22×C4×C271D4semidirect
101. C271#2022semidirect
106. #381D271semidirect
139. C22×C4D1084semidirect

Maximal subgroups

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

subgroupindex
#317744592
C2×#225761432
C2×#225760742
#317736642
#381×C2712
#2022271