Finite Group Databasebeta

← #46812044

Subgroups — #46812044

Order 34432.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#31771233C211yesmaximal, characteristic
2#31770614C211yesmaximal, characteristic
3#31770512C211yesmaximal, characteristic
4#31770373C211yesmaximal, characteristic
5#31770366C211yesmaximal, characteristic
6#31770364C211yesmaximal, characteristic
7#419×C269C211yesmaximal, characteristic
8C2×#16864386C2211yescharacteristic
9#22575453—21no—
10#22575452—21no—
11#22575445—21no—
12#22575444—21no—
13#22575430—22no—
14#22575412C2211yescharacteristic
15C2×C4⋊Dic269C2211yescharacteristic
16C2×C4×Dic269C2211yescharacteristic
17#22575377—21no—
18#22575377—21no—
19#22575360—22no—
20C22×Q8×C269C2211yescharacteristic
21C2×M16×C269C2211yescharacteristic
22#117×C269C2211yescharacteristic
23#103×C269—21no—
24#103×C269—21no—
25C2×Dic538—22no—
26C22×Dic269—21no—
27C22×Dic269D412yes—
28#16864386—21no—
29#16864386—21no—
30C2×#14524130—21no—
31C4⋊Dic269—22no—
32C4⋊Dic269—21no—
33C4⋊Dic269—21no—
34C4⋊Dic269D411yescharacteristic
35C4⋊Dic269D411yescharacteristic
36#16864381—22no—
37#16864381—22no—
38C22⋊Dic269—21no—
39C4×Dic269—21no—
40C4×Dic269—21no—
41C4×Dic269—21no—
42C2×Q8×C269—21no—
43C2×Q8×C269—21no—
44C2×Q8×C269—21no—
45C2×Q8×C269—21no—
46C2×Q8×C269—21no—
47C2×Q8×C269Q812yescomplemented
48C22×C4×C269—21no—
49C22×C4×C269C2311yescharacteristic
50M16×C269—21no—
51M16×C269—21no—
52C2×C8×C269—21no—
53C4⋊C4×C269D411yescharacteristic
54C4⋊C4×C269D411yescharacteristic
55C22⋊C4×C269—21no—
56C42×C269—21no—
57Dic538—82no—
58C2×Dic269—22no—
59C2×Dic269—21no—
60C2×Dic269—21no—
61C2×Dic269—22no—
62C2×Dic269—41no—
63C2×Dic269—41no—
64C2×Dic269—42no—
65#14524130—41no—
66C23×C269C2×D411yescharacteristic
67Q8×C269—22no—
68Q8×C269—22no—
69Q8×C269—41no—
70Q8×C269—41no—
71C2×C4×C269—21no—
72C2×C4×C269—21no—
73C2×C4×C269—22no—
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—21no—
84C22×C269—21no—
85C22×C269#12011yescharacteristic
86C22×C269C22⋊Q811yescharacteristic
87C22×C269#12411yescharacteristic
88C4×C269—42no—
89C4×C269—41no—
90C4×C269—41no—
91C4×C269C22⋊Q811yescharacteristic
92C4×C269C22⋊Q811yescharacteristic
93C4×C269#12411yescharacteristic
94C4×C269#12411yescharacteristic
95Dic269—42no—
96Dic269—42no—
97Dic269—41no—
98Dic269—41no—
99C2×C269—21no—
100C2×C269—21no—
101C2×C269#39311yescharacteristic
102C2×C269#45511yescharacteristic
103C2×C269#45611yescharacteristic
104C269#202811yescharacteristic, complemented, Sylow
105#2028—2691nomaximal, Sylow
106#544—2691no—
107#419—2691no—
108#419D26911yescharacteristic
109#391—2691no—
110#343—2691no—
111#339—2691no—
112#339—2691no—
113C22×Q8C2×D26911yescharacteristic
114C2×M16—2691no—
115C2×M16C2×D26911yescharacteristic
116C4⋊Q8—5381no—
117C4⋊Q8—5381no—
118#125—5381no—
119#125—5381no—
120C22⋊Q8—5382no—
121#117—2691no—
122#117C2×D26911yescharacteristic
123C2×C4⋊C4—2691no—
124C2×C42—2691no—
125#103—21no—
126#103—21no—
127#103—5381no—
128#103—5381no—
129#95—5382no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—5382no—
136C2×Q8Dic53812yescomplemented
137C22×C4—21no—
138C22×C4—2692no—
139C22×C4—5381no—
140C22×C4C22×D26911yescharacteristic
141M16—21no—
142M16—21no—
143M16—5381no—
144M16—5381no—
145C2×C8—21no—
146C2×C8—5381no—
147C4⋊C4—2691no—
148C4⋊C4—2691no—
149C4⋊C4—5382no—
150C4⋊C4—5382no—
151C4⋊C4—5382no—
152C4⋊C4—5381no—
153C4⋊C4—5381no—
154C4⋊C4C22⋊D26911yescharacteristic
155C4⋊C4C22⋊D26911yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—5381no—
158C42—21no—
159C42—5381no—
160C42—5381no—
161C42—5381no—
162C23D4×D26911yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—21522no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—5382no—
174C2×C4—5381no—
175C2×C4—5381no—
176C2×C4—5382no—
177C2×C4—10761no—
178C2×C4—10761no—
179C2×C4—10762no—
180C2×C4D4×D26911yescharacteristic
181C2×C4C2×C22⋊D26911yescharacteristic
182C2×C4C2×Dic53811yescharacteristic
183C2×C4#1686440111yescharacteristic
184C2×C4#1686440111yescharacteristic
185C2×C4#1686440211yescharacteristic
186C8—41no—
187C8—10761no—
188C22—21no—
189C22—21no—
190C22#2257542111yescharacteristic
191C22#2257543011yescharacteristic
192C22#2257543911yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—10762no—
197C4—10762no—
198C4—10761no—
199C4—10761no—
200C4#2257543011yescharacteristic
201C4#2257543211yescharacteristic
202C4#2257543911yescharacteristic
203C4#2257544011yescharacteristic
204C2—21no—
205C2—21no—
206C2#3177051711yescharacteristic
207C2#3177078111yescharacteristic
208C2#3177078611yescharacteristic
subgroupG/H
centerC22#22575421
commutator, cosocleC22×C4×C269C23
FrattiniC22×C4C22×D269
Fitting#419×C269C2
socleC22×C269#120
prime radicalC23×C269C2×D4
hypercenter#419D269
hypocenterC269#2028
LCSG ▷ C22×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
47. C2×Q8×C269Q8semidirect
104. C269#2028semidirect
136. C2×Q8Dic538semidirect

Maximal subgroups

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

subgroupindex
#317712332
#317706142
#317705122
#317703732
#317703662
#317703642
#419×C2692
#2028269