Finite Group Databasebeta

← #46811421

Subgroups — #46811421

Order 34432.

314 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 79 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#31771181C211yesmaximal, characteristic
2#31771082C211yesmaximal, characteristic, complemented
3#31770623C211yesmaximal, characteristic
4#31770621C211yesmaximal, characteristic
5C2×#22575371C211yesmaximal, characteristic, complemented
6#31770361C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C269C211yesmaximal, characteristic, complemented
8C2×#16864402C2211yescharacteristic
9C22×Dic538C2211yescharacteristic
10C2×#16864386C2211yescharacteristic
11#22575453C412yescomplemented
12#22575441C412yescomplemented
13#22575437—22no—
14#22575433—22no—
15C4×Dic538—22no—
16#22575418—22no—
17#22575412C2211yescharacteristic
18#22575409—22no—
19#22575381—22no—
20#22575379—22no—
21#22575371—22no—
22C2×M16×C269C2211yescharacteristic
23#117×C269C2211yescharacteristic
24#117×C269C2211yescharacteristic
25#16864402—21no—
26#16864402—21no—
27#16864402—21no—
28#16864402—21no—
29C2×Dic538—21no—
30C2×Dic538—21no—
31C2×Dic538—21no—
32C2×Dic538—21no—
33C2×Dic538C2×C411yescharacteristic
34C2×Dic538C2×C412yes—
35C2×Dic538D412yes—
36C2×D1076C2×C411yescharacteristic
37C2×C22⋊D269—21no—
38C22×Dic269D412yes—
39C2×C4×D269—21no—
40#16864386—21no—
41#16864386—21no—
42C2×#14524130—21no—
43C4⋊Dic269—24no—
44C4⋊Dic269—21no—
45#16864381—24no—
46C22⋊Dic269—21no—
47#16864379—24no—
48C4×Dic269—24no—
49C4×Dic269D412yes—
50C22×C4×C269C2311yescharacteristic
51M16×C269—21no—
52M16×C269—21no—
53C2×C8×C269—21no—
54C4⋊C4×C269—21no—
55C4⋊C4×C269—21no—
56C22⋊C4×C269—21no—
57C22⋊C4×C269—21no—
58C42×C269C2×C412yes—
59C42×C269D412yes—
60C22×D269—21no—
61Dic538—22no—
62Dic538—22no—
63Dic538—22no—
64Dic538—22no—
65Dic538—21no—
66Dic538—21no—
67D1076—21no—
68D1076—21no—
69C22⋊D269—41no—
70C22⋊D269—41no—
71C2×Dic269—22no—
72C2×Dic269—22no—
73C2×Dic269—21no—
74C2×Dic269—22no—
75C2×Dic269C22⋊C414yes—
76C4×D269—41no—
77C4×D269—41no—
78#14524130—41no—
79C23×C269C2×D411yescharacteristic
80C2×C4×C269—22no—
81C2×C4×C269—22no—
82C2×C4×C269C22×C411yescharacteristic
83C2×C4×C269C2×D411yescharacteristic
84C2×C4×C269C2×D411yescharacteristic
85C2×C4×C269C2×D411yescharacteristic
86C2×C4×C269#4111yescharacteristic
87C2×C4×C269#4111yescharacteristic
88C8×C269—41no—
89C22×C269—41no—
90C22×C269C2×C22⋊C411yescharacteristic
91C22×C269#12011yescharacteristic
92C22×C269#12311yescharacteristic
93C2×D269—42no—
94C2×D269—41no—
95C4×C269—42no—
96C4×C269—42no—
97C4×C269C4×D411yescharacteristic
98C4×C269C4×D411yescharacteristic
99C4×C269#12111yescharacteristic
100C4×C269#12111yescharacteristic
101Dic269—24no—
102Dic269—42no—
103Dic269—41no—
104C2×C269—21no—
105C2×C269—21no—
106C2×C269—21no—
107C2×C269#38611yescharacteristic
108D269—81no—
109C269#191211yescharacteristic, complemented, Sylow
110#1912—2691nomaximal, Sylow
111#536—2691no—
112#519—2691no—
113#421—2691no—
114#421—2691no—
115C2×#101—2691no—
116H(3,ℤ/4)—2691no—
117H(3,ℤ/4)D26911yescharacteristic, complemented
118C2×#41—2691no—
119C22×Q8—2691no—
120C2×M16—2691no—
121C2×M16C2×D26911yescharacteristic
122C4⋊Q8—2692no—
123#124—2692no—
124#123—5382no—
125C22⋊Q8—5382no—
126C4×Q8—5382no—
127C4×Q8—5382no—
128#117—2691no—
129#117—5382no—
130#117C2×D26911yescharacteristic
131#117C2×D26911yescharacteristic
132#104—5382no—
133#104—5382no—
134#101—5382no—
135#41—5381no—
136#41—5381no—
137#41—5381no—
138#41—5381no—
139C2×Q8—2692no—
140C2×Q8—2692no—
141C2×Q8—2691no—
142C2×Q8—5381no—
143C2×Q8—5381no—
144C2×Q8—5381no—
145C2×Q8—5381no—
146C2×D4—2691no—
147C2×D4—5381no—
148C22×C4—2692no—
149C22×C4—5381no—
150C22×C4C22×D26911yescharacteristic
151M16—21no—
152M16—21no—
153M16—5381no—
154M16—5381no—
155C2×C8—21no—
156C2×C8—5381no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—5384no—
160C4⋊C4—5384no—
161C4⋊C4—5381no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—5384no—
165C22⋊C4—5381no—
166C42—2692no—
167C42—5384no—
168C42C4×D26912yes—
169C42D107612yes—
170C23—5381no—
171C23D4×D26911yescharacteristic
172Q8—5382no—
173Q8—5382no—
174Q8—5382no—
175Q8—5382no—
176Q8—5381no—
177Q8—5381no—
178D4—5381no—
179D4—5381no—
180D4—10761no—
181D4—10761no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—2694no—
185C2×C4—5382no—
186C2×C4—5382no—
187C2×C4—5381no—
188C2×C4—5382no—
189C2×C4—10761no—
190C2×C4—10761no—
191C2×C4C2×C4×D26911yescharacteristic
192C2×C4D4×D26911yescharacteristic
193C2×C4D4×D26911yescharacteristic
194C2×C4C2×D107611yescharacteristic
195C2×C4#1686440211yescharacteristic
196C2×C4#1686440311yescharacteristic
197C8—41no—
198C8—10761no—
199C22—41no—
200C22—10762no—
201C22—10761no—
202C22C22⋊C4×D26911yescharacteristic
203C22#2257542311yescharacteristic
204C22#2257543811yescharacteristic
205C4—42no—
206C4—42no—
207C4—5384no—
208C4—10762no—
209C4—10761no—
210C4#2257541511yescharacteristic
211C4C4×D107611yescharacteristic
212C4#2257542611yescharacteristic
213C4#2257542811yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—21521no—
218C2#3177048311yescharacteristic
subgroupG/H
centerC2#31770483
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
FittingH(3,ℤ/4)×C269C2
socleC2×C269#386
prime radicalC2×#16864402C22
cosocleC22×C4×C269C23
hypercenterH(3,ℤ/4)D269
hypocenterC269#1912
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. #31771082C2semidirect
5. C2×#22575371C2semidirect
6. #31770361C2semidirect
7. H(3,ℤ/4)×C269C2semidirect
11. #22575453C4semidirect
12. #22575441C4semidirect
109. C269#1912semidirect
117. H(3,ℤ/4)D269semidirect

Maximal subgroups

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

subgroupindex
#317711812
#317710822
#317706232
#317706212
C2×#225753712
#317703612
H(3,ℤ/4)×C2692
#1912269