Finite Group Databasebeta

← #46823492

Subgroups — #46823492

Order 34432.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#31771305C212yesmaximal, complemented
2#31771007C211yesmaximal, characteristic, complemented
3#31770927C212yesmaximal, complemented
4#31770917C212yesmaximal, complemented
5#31770905C212yesmaximal, complemented
6#31770855C212yesmaximal, complemented
7#31770684C211yesmaximal, characteristic, complemented
8#31770646C212yesmaximal, complemented
9C4×D8×C269C211yesmaximal, characteristic, complemented
10C2×#16864385C2212yes—
11#22575446—22no—
12#22575445C2212yes—
13#22575436—22no—
14#22575426—22no—
15#22575424C2212yes—
16#22575424C2212yes—
17C4×D1076C2211yescharacteristic
18C4×C22⋊D269—22no—
19#22575411C2212yes—
20C4⋊C4×D269C2212yes—
21#22575387C2211yescharacteristic
22#22575387C2211yescharacteristic
23#22575386C2212yes—
24#22575385C2212yes—
25#22575384C2212yes—
26C4⋊#14524130C2211yescharacteristic
27#22575374C2212yes—
28#22575374C2212yes—
29#22575365C2212yes—
30C2×D8×C269C2211yescharacteristic
31C4×D4×C269C2212yes—
32#107×C269C2211yescharacteristic
33#102×C269C2212yes—
34C4×C8×C269C2211yescharacteristic
35C2×D1076D411yescharacteristic
36C2×C22⋊D269—22no—
37C2×C22⋊D269—22no—
38C2×C4×D269—22no—
39C2×C4×D269C2312yes—
40#16864385—24no—
41C2×#14524130C2312yes—
42C4⋊Dic269D411yescharacteristic
43C4⋊Dic269C2312yes—
44C4⋊Dic269C2312yes—
45#16864381—22no—
46#16864381—22no—
47#16864381—22no—
48C22⋊Dic269—22no—
49C22⋊Dic269—22no—
50#16864379—22no—
51#16864379D412yes—
52C4×Dic269—22no—
53C2×D4×C269C2312yes—
54C22×C4×C269—22no—
55D8×C269—22no—
56C2×C8×C269C2311yescharacteristic
57C2×C8×C269C2311yescharacteristic
58C4⋊C4×C269C2312yes—
59C22⋊C4×C269—22no—
60C42×C269C2311yescharacteristic
61C22×D269C2×D412yes—
62D1076—41no—
63C22⋊D269—44no—
64C22⋊D269—82no—
65C2×Dic269—22no—
66C2×Dic269—22no—
67C2×Dic269C2×D412yes—
68C4×D269—22no—
69C4×D269—22no—
70C4×D269—82no—
71#14524130—22no—
72C23×C269—22no—
73D4×C269—22no—
74D4×C269—22no—
75C2×C4×C269—22no—
76C2×C4×C269—82no—
77C2×C4×C269C2×D411yescharacteristic
78C2×C4×C269C2×D411yescharacteristic
79C2×C4×C269C2411yescharacteristic
80C8×C269—21no—
81C8×C269#4112yes—
82C22×C269—42no—
83C22×C269—42no—
84C22×C269—42no—
85C22×C269C22×D411yescharacteristic
86C2×D269—22no—
87C2×D269—22no—
88C2×D269—22no—
89C4×C269—21no—
90C4×C269—21no—
91C4×C269—42no—
92C4×C269C2×#4111yescharacteristic
93C4×C2692−1+411yescharacteristic
94Dic269—22no—
95Dic269—42no—
96Dic269—42no—
97C2×C269—82no—
98C2×C269#54711yescharacteristic
99C2×C269#57511yescharacteristic
100C2×C269#57611yescharacteristic
101D269—42no—
102C269#335511yescharacteristic, complemented, Sylow
103#3355—2691nomaximal, Sylow
104#553—2692no—
105#499—2691no—
106#482—2692no—
107#480—2692no—
108#478—2692no—
109#469—2692no—
110C4×D8D26911yescharacteristic, complemented
111#436—2691no—
112#428—2692no—
113C2×D8C2×D26911yescharacteristic
114C2×M16—2692no—
115#126—5382no—
116#125—2692no—
117#123—5382no—
118#121—2692no—
119#121—2692no—
120#121—5382no—
121C4×D4—2691no—
122C4×D4—5382no—
123C4×D4C2×D26912yes—
124#117—2692no—
125C2×C4⋊C4—2692no—
126#107—2691no—
127#107—2691no—
128#107—2692no—
129#107C2×D26911yescharacteristic
130#106—2692no—
131#106—2692no—
132C4⋊C8—2691no—
133#102—2692no—
134#102—2692no—
135#102C2×D26912yes—
136C22⋊C8—2692no—
137C4×C8C2×D26911yescharacteristic
138C2×D4—2691no—
139C2×D4—5382no—
140C2×D4—5382no—
141C2×D4C22×D26912yes—
142C22×C4—22no—
143C22×C4—2692no—
144C22×C4—5382no—
145D8—22no—
146M16—5384no—
147C2×C8—2692no—
148C2×C8C22×D26911yescharacteristic
149C2×C8C22×D26911yescharacteristic
150C4⋊C4—2691no—
151C4⋊C4—2692no—
152C4⋊C4—2692no—
153C4⋊C4—5382no—
154C4⋊C4—5382no—
155C4⋊C4—5382no—
156C4⋊C4C22×D26912yes—
157C22⋊C4—22no—
158C22⋊C4—2692no—
159C22⋊C4—5382no—
160C22⋊C4—5382no—
161C22⋊C4—5382no—
162C42—5382no—
163C42C22×D26911yescharacteristic
164C23—22no—
165C23—2692no—
166D4—22no—
167D4—22no—
168D4—10761no—
169D4—10764no—
170D4—21522no—
171C2×C4—22no—
172C2×C4—82no—
173C2×C4—2692no—
174C2×C4—5382no—
175C2×C4—5382no—
176C2×C4—5382no—
177C2×C4—5382no—
178C2×C4—21522no—
179C2×C4D4×D26911yescharacteristic
180C2×C4D4×D26911yescharacteristic
181C2×C4C23×D26911yescharacteristic
182C8—21no—
183C8—5382no—
184C8#1686440212yes—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—5382no—
189C22—5382no—
190C22—5382no—
191C22C2×D4×D26911yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—5382no—
196C4—10762no—
197C4—10762no—
198C4C2×#1686440211yescharacteristic
199C4#2257550011yescharacteristic
200C2—82no—
201C2—10762no—
202C2#3177126011yescharacteristic
203C2#3177140211yescharacteristic
204C2#3177140611yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC4×D8×C269C2
socleC22×C269C22×D4
hypercenterC4×D8D269
hypocenterC269#3355
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #31771305C2semidirect
2. #31771007C2semidirect
3. #31770927C2semidirect
4. #31770917C2semidirect
5. #31770905C2semidirect
6. #31770855C2semidirect
7. #31770684C2semidirect
8. #31770646C2semidirect
9. C4×D8×C269C2semidirect
102. C269#3355semidirect
110. C4×D8D269semidirect

Maximal subgroups

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

subgroupindex
#317713052
#317710072
#317709272
#317709172
#317709052
#317708552
#317706842
#317706462
C4×D8×C2692
#3355269