Finite Group Databasebeta

← #46812035

Subgroups — #46812035

Order 34432.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#22575444C211yesmaximal, characteristic
2C2×#22575378C211yesmaximal, characteristic
3C2×#22575376C211yesmaximal, characteristic
4#31770510C211yesmaximal, characteristic
5#31770367C211yesmaximal, characteristic
6#31770359C211yesmaximal, characteristic
7#340×C269C211yesmaximal, characteristic
8C22×Dic538C2211yescharacteristic
9C22×#14524130C2211yescharacteristic
10#22575444—22no—
11#22575444—22no—
12C2×C4⋊Dic269—21no—
13C2×C4⋊Dic269C2211yescharacteristic
14C2×#16864381—21no—
15C2×C4×Dic269C2211yescharacteristic
16#22575378—22no—
17#22575376—22no—
18#22575360—21no—
19#22575360—21no—
20C22×C8×C269C2211yescharacteristic
21C2×C4⋊C4×C269C2211yescharacteristic
22C2×C4⋊C4×C269C2211yescharacteristic
23C2×Dic538—21no—
24C2×Dic538—21no—
25C2×Dic538—21no—
26C2×Dic538—21no—
27C2×Dic538—21no—
28C2×Dic538Q812yes—
29C22×Dic269—21no—
30C22×Dic269—21no—
31C22×Dic269D411yescharacteristic
32C22×Dic269D411yescharacteristic
33C2×#14524130—21no—
34C2×#14524130—21no—
35C2×#14524130—21no—
36C4⋊Dic269—24no—
37C4⋊Dic269—21no—
38C4⋊Dic269D412yes—
39#16864381—24no—
40C4×Dic269—21no—
41C4×Dic269—21no—
42C22×C4×C269—21no—
43C22×C4×C269—21no—
44C22×C4×C269C2311yescharacteristic
45C2×C8×C269—21no—
46C2×C8×C269—21no—
47C2×C8×C269—21no—
48C4⋊C4×C269—21no—
49C4⋊C4×C269—21no—
50C4⋊C4×C269—21no—
51C4⋊C4×C269D412yes—
52Dic538—22no—
53Dic538—22no—
54Dic538—41no—
55Dic538—41no—
56C2×Dic269—21no—
57C2×Dic269—21no—
58C2×Dic269—22no—
59C2×Dic269—22no—
60C2×Dic269—21no—
61C2×Dic269—21no—
62C2×Dic269—21no—
63C2×Dic269—21no—
64C2×Dic269—41no—
65C2×Dic269—41no—
66C2×Dic269—41no—
67C2×Dic269—41no—
68#14524130—41no—
69C23×C269C2×D411yescharacteristic
70C2×C4×C269—22no—
71C2×C4×C269—41no—
72C2×C4×C269—41no—
73C2×C4×C269—41no—
74C2×C4×C269—41no—
75C2×C4×C269—41no—
76C2×C4×C269C2×D411yescharacteristic
77C2×C4×C269C2×D411yescharacteristic
78C2×C4×C269C2×Q811yescharacteristic
79C2×C4×C269#4111yescharacteristic
80C2×C4×C269#4111yescharacteristic
81C2×C4×C269#4111yescharacteristic
82C8×C269—41no—
83C22×C269#12011yescharacteristic
84C22×C269C22⋊Q811yescharacteristic
85C22×C269#12411yescharacteristic
86C22×C269#13511yescharacteristic
87C22×C269#13511yescharacteristic
88C22×C269#13711yescharacteristic
89C22×C269#13711yescharacteristic
90C4×C269—42no—
91C4×C269—81no—
92C4×C269C22⋊Q811yescharacteristic
93C4×C269C22⋊Q811yescharacteristic
94C4×C269#12411yescharacteristic
95C4×C269#12411yescharacteristic
96Dic269—42no—
97Dic269—41no—
98Dic269—41no—
99Dic269—42no—
100C2×C269#39311yescharacteristic
101C2×C269#45211yescharacteristic
102C2×C269#45211yescharacteristic
103C2×C269#47911yescharacteristic
104C2×C269#47911yescharacteristic
105C2×C269#48811yescharacteristic
106C2×C269#49111yescharacteristic
107C269#202611yescharacteristic, complemented, Sylow
108#2026—2691nomaximal, Sylow
109C2×#125—2691no—
110C2×#103—2691no—
111C2×#103—2691no—
112#391—2691no—
113#340—2691no—
114#340D26911yescharacteristic
115#336—2691no—
116C22×Q8—2691no—
117C22×C8—2691no—
118C22×C8C2×D26911yescharacteristic
119#125—5382no—
120#125—5382no—
121C2×C4⋊C4—2691no—
122C2×C4⋊C4—5381no—
123C2×C4⋊C4—5381no—
124C2×C4⋊C4C2×D26911yescharacteristic
125C2×C4⋊C4C2×D26911yescharacteristic
126C2×C42—2691no—
127#103—5382no—
128#103—5382no—
129#95—5381no—
130#95—5381no—
131C2×Q8—2692no—
132C2×Q8—5381no—
133C2×Q8—5381no—
134C2×Q8—5381no—
135C2×Q8—5381no—
136C2×Q8—5381no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—2691no—
140C22×C4—2691no—
141C22×C4—5381no—
142C22×C4—5381no—
143C22×C4C22×D26911yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—5381no—
148C2×C8—5381no—
149C2×C8—5381no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—2692no—
154C4⋊C4—5384no—
155C4⋊C4—5384no—
156C4⋊C4—5381no—
157C4⋊C4D107612yes—
158C42—5381no—
159C42—5381no—
160C23D4×D26911yescharacteristic
161Q8—5382no—
162Q8—5382no—
163Q8—10761no—
164Q8—10761no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—5381no—
172C2×C4—5381no—
173C2×C4—5382no—
174C2×C4—5382no—
175C2×C4—5381no—
176C2×C4—5381no—
177C2×C4—5381no—
178C2×C4—5381no—
179C2×C4—10761no—
180C2×C4—10761no—
181C2×C4—10761no—
182C2×C4—10761no—
183C2×C4D4×D26911yescharacteristic
184C2×C4C2×D107611yescharacteristic
185C2×C4Q8×D26911yescharacteristic
186C2×C4#1686440111yescharacteristic
187C2×C4#1686440211yescharacteristic
188C2×C4#1686440211yescharacteristic
189C8—41no—
190C8—10761no—
191C22#2257542311yescharacteristic
192C22#2257543111yescharacteristic
193C22#2257543911yescharacteristic
194C22#2257547211yescharacteristic
195C22#2257547411yescharacteristic
196C22#2257548211yescharacteristic
197C22#2257548511yescharacteristic
198C4—42no—
199C4—81no—
200C4—10761no—
201C4—10761no—
202C4—10762no—
203C4—10762no—
204C4#2257543111yescharacteristic
205C4#2257543311yescharacteristic
206C4#2257543911yescharacteristic
207C4#2257544111yescharacteristic
208C2#3177051811yescharacteristic
209C2#3177076811yescharacteristic
210C2#3177077011yescharacteristic
211C2#3177091111yescharacteristic
212C2#3177091511yescharacteristic
213C2#3177095811yescharacteristic
214C2#3177097211yescharacteristic
subgroupG/H
centerC23D4×D269
commutator, cosocleC22×C4×C269C23
FrattiniC22×C4C22×D269
Fitting#340×C269C2
socle, prime radicalC23×C269C2×D4
hypercenter#340D269
hypocenterC269#2026
LCSG ▷ C22×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
107. C269#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#225754442
C2×#225753782
C2×#225753762
#317705102
#317703672
#317703592
#340×C2692
#2026269