Finite Group Databasebeta

← #46809404

Subgroups — #46809404

Order 34432.

294 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 77 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×#22575432C211yesmaximal, characteristic
2#31770569C211yesmaximal, characteristic
3#31770341C214yesmaximal, complemented
4C4×C22⋊C4×C269C211yesmaximal, characteristic
5C22×Dic538C411yescharacteristic, complemented
6C2×#16864386—21no—
7#22575432—21no—
8#22575432—21no—
9#22575432C412yescomplemented
10#22575432C2212yes—
11C2×C4⋊Dic269C411yescharacteristic, complemented
12C2×#16864381—21no—
13C2×C22⋊Dic269—21no—
14C22⋊#14524130—21no—
15C22⋊#14524130C2212yes—
16C23×C4×C269C2211yescharacteristic
17C2×C22⋊C4×C269—21no—
18C2×C42×C269—21no—
19#95×C269C2212yes—
20C2×Dic538—21no—
21C2×Dic538—42no—
22C2×Dic538C2×C412yes—
23C22×Dic269—21no—
24C22×Dic269—21no—
25#16864386—42no—
26C2×#14524130—22no—
27C4⋊Dic269—21no—
28C4⋊Dic269C2×C412yes—
29#16864381—22no—
30#16864381—22no—
31C22⋊Dic269—22no—
32C22⋊Dic269—22no—
33C24×C269D411yescharacteristic
34C22×C4×C269—22no—
35C22×C4×C269—42no—
36C22×C4×C269C2×C411yescharacteristic
37C22×C4×C269C2×C411yescharacteristic
38C22×C4×C269D411yescharacteristic
39C22×C4×C269D411yescharacteristic
40C22×C4×C269D411yescharacteristic
41C22×C4×C269C2311yescharacteristic
42C22⋊C4×C269—24no—
43C42×C269—42no—
44Dic538—42no—
45Dic538—42no—
46C2×Dic269—22no—
47C2×Dic269—22no—
48C2×Dic269—42no—
49C2×Dic269—42no—
50#14524130—42no—
51C23×C269—22no—
52C23×C269—22no—
53C23×C269—41no—
54C23×C269C22⋊C411yescharacteristic
55C23×C269C22⋊C411yescharacteristic
56C23×C269C2×D411yescharacteristic
57C2×C4×C269—22no—
58C2×C4×C269—22no—
59C2×C4×C269—22no—
60C2×C4×C269—24no—
61C2×C4×C269—41no—
62C2×C4×C269—41no—
63C2×C4×C269—41no—
64C2×C4×C269—42no—
65C2×C4×C269—42no—
66C2×C4×C269C22⋊C411yescharacteristic
67C2×C4×C269C22⋊C411yescharacteristic
68C2×C4×C269C22×C411yescharacteristic
69C2×C4×C269C2×D411yescharacteristic
70C22×C269—21no—
71C22×C269—21no—
72C22×C269—21no—
73C22×C269—21no—
74C22×C269—21no—
75C22×C269—21no—
76C22×C269—21no—
77C22×C269—44no—
78C22×C269#10412yes—
79C22×C269C2×C22⋊C411yescharacteristic
80C22×C269#13712yes—
81C4×C269—21no—
82C4×C269—21no—
83C4×C269—21no—
84C4×C269—44no—
85C4×C269#9912yes—
86Dic269—42no—
87Dic269—42no—
88C2×C269—22no—
89C2×C269—22no—
90C2×C269—41no—
91C2×C269C2×#9911yescharacteristic
92C2×C269#41911yescharacteristic
93C2×C269C2×#10411yescharacteristic
94C269#150811yescharacteristic, complemented, Sylow
95#1508—2691nomaximal, Sylow
96C2×C22⋊Q8—2691no—
97#407—2691no—
98C4×C22⋊C4D26911yescharacteristic
99#328—2694no—
100C22×Q8—2691no—
101C23×C4C2×D26911yescharacteristic
102C2×M16—5381no—
103C22⋊Q8—2692no—
104C22⋊Q8—2692no—
105C22⋊Q8—5381no—
106C22⋊Q8—5381no—
107C2×C4⋊C4—2691no—
108C2×C4⋊C4—5381no—
109C2×C22⋊C4—21no—
110C2×C22⋊C4—5381no—
111C2×C42—21no—
112C22⋊C8—2692no—
113C22⋊C8—5381no—
114#95C2×D26912yes—
115C24C22⋊D26911yescharacteristic
116C2×Q8—2692no—
117C2×Q8—5381no—
118C2×Q8—10762no—
119C22×C4—22no—
120C22×C4—42no—
121C22×C4—5381no—
122C22×C4—5381no—
123C22×C4C4×D26911yescharacteristic
124C22×C4C4×D26911yescharacteristic
125C22×C4C22⋊D26911yescharacteristic
126C22×C4D107611yescharacteristic
127C22×C4D107611yescharacteristic
128C22×C4C22×D26911yescharacteristic
129M16—10762no—
130C2×C8—5382no—
131C4⋊C4—2692no—
132C4⋊C4—5381no—
133C4⋊C4—5382no—
134C4⋊C4—5382no—
135C22⋊C4—24no—
136C22⋊C4—5382no—
137C22⋊C4—5382no—
138C42—42no—
139C23—22no—
140C23—22no—
141C23—41no—
142C23#1686437911yescharacteristic
143C23#1686437911yescharacteristic
144C23C2×C22⋊D26911yescharacteristic
145Q8—10762no—
146Q8—10762no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—24no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—5382no—
157C2×C4—5382no—
158C2×C4—10762no—
159C2×C4—10762no—
160C2×C4#1686437911yescharacteristic
161C2×C4#1686437911yescharacteristic
162C2×C4C2×C4×D26911yescharacteristic
163C2×C4C2×D107611yescharacteristic
164C8—10762no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—44no—
173C22#2257538112yes—
174C22C2×#1686437911yescharacteristic
175C22#2257548312yes—
176C4—21no—
177C4—21no—
178C4—21no—
179C4—44no—
180C4—10762no—
181C4—10762no—
182C4#2257536712yes—
183C2—22no—
184C2—22no—
185C2—41no—
186C2C2×#2257536711yescharacteristic
187C2#3177061311yescharacteristic
188C2C2×#2257538111yescharacteristic
subgroupG/H
centerC22C2×#16864379
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
FittingC4×C22⋊C4×C269C2
socleC22×C269C2×C22⋊C4
prime radicalC24×C269D4
cosocleC22×C4×C269C23
hypercenterC4×C22⋊C4D269
hypocenterC269#1508
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #31770341C2semidirect
5. C22×Dic538C4semidirect
9. #22575432C4semidirect
11. C2×C4⋊Dic269C4semidirect
94. C269#1508semidirect

Maximal subgroups

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

subgroupindex
C2×#225754322
#317705692
#317703412
C4×C22⋊C4×C2692
#1508269