Finite Group Databasebeta

← #46810034

Subgroups — #46810034

Order 34432.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#31771259C211yesmaximal, characteristic
2#31770955C211yesmaximal, characteristic, complemented
3#31770892C211yesmaximal, characteristic, complemented
4#31770352C211yesmaximal, characteristic, complemented
5D4⋊#14524130C211yesmaximal, characteristic, complemented
6#31770332C211yesmaximal, characteristic, complemented
7#476×C269C211yesmaximal, characteristic, complemented
8C2×#16864401—21no—
9#22575453C2211yescharacteristic
10#22575437—22no—
11#22575433—21no—
12#22575427—21no—
13C4×D1076C2211yescharacteristic
14C2×C4⋊Dic269—21no—
15#22575384—21no—
16C4⋊#14524130C2211yescharacteristic
17#22575377—22no—
18#22575373—21no—
19C4×#14524130C2211yescharacteristic
20C4⋊Q8×C269C2211yescharacteristic
21C4×D4×C269C2211yescharacteristic
22#106×C269—21no—
23C4⋊C8×C269C2211yescharacteristic
24#102×C269—21no—
25#16864401—42no—
26#16864401—42no—
27C2×Dic538—21no—
28C2×D1076D411yescharacteristic
29C2×C22⋊D269—22no—
30C22×Dic269—22no—
31C2×C4×D269—21no—
32C2×#14524130—21no—
33C2×#14524130—21no—
34C4⋊Dic269—22no—
35C4⋊Dic269—21no—
36C4⋊Dic269D412yes—
37C4⋊Dic269D411yescharacteristic
38#16864379—22no—
39#16864379—21no—
40C2×Q8×C269—21no—
41C2×D4×C269D411yescharacteristic
42C22×C4×C269—21no—
43C2×C8×C269—21no—
44C4⋊C4×C269—21no—
45C4⋊C4×C269—21no—
46C4⋊C4×C269D411yescharacteristic
47C22⋊C4×C269—21no—
48C42×C269C2311yescharacteristic
49C22×D269—21no—
50Dic538—41no—
51Dic538—41no—
52D1076—21no—
53D1076—21no—
54C22⋊D269—44no—
55C2×Dic269—21no—
56C2×Dic269—22no—
57C2×Dic269—44no—
58C4×D269—41no—
59C4×D269—41no—
60#14524130—41no—
61#14524130—41no—
62C23×C269—21no—
63Q8×C269—42no—
64D4×C269—21no—
65D4×C269SD1612yes—
66C2×C4×C269—21no—
67C2×C4×C269—41no—
68C2×C4×C269—41no—
69C2×C4×C269—41no—
70C2×C4×C269C2×D411yescharacteristic
71C2×C4×C269C2×D411yescharacteristic
72C2×C4×C269C2×D411yescharacteristic
73C8×C269—41no—
74C22×C269—22no—
75C22×C269—41no—
76C22×C269—41no—
77C22×C269#12011yescharacteristic
78C2×D269—41no—
79C2×D269—41no—
80C2×D269—41no—
81C4×C269—21no—
82C4×C269—41no—
83C4×C269—81no—
84C4×C269C2×SD1611yescharacteristic
85C4×C269#13511yescharacteristic
86C4×C269AGL(1,ℤ/8)11yescharacteristic
87C4×C269#13711yescharacteristic
88Dic269—41no—
89Dic269—42no—
90C2×C269—42no—
91C2×C269#45011yescharacteristic
92C2×C269#45211yescharacteristic
93C2×C269#45411yescharacteristic
94D269—81no—
95C269#163511yescharacteristic, complemented, Sylow
96#1635—2691nomaximal, Sylow
97#547—2691no—
98#487—2691no—
99#476—2691no—
100#476D26911yescharacteristic, complemented
101#332—2691no—
102D4⋊C8—2691no—
103D4⋊C8—2691no—
104C2×#41—5381no—
105C4⋊Q8—2691no—
106C4⋊Q8C2×D26911yescharacteristic
107#123—5382no—
108C22⋊Q8—5381no—
109#121—5381no—
110C4×D4—2691no—
111C4×D4C2×D26911yescharacteristic
112C2×C4⋊C4—5381no—
113#106—21no—
114#106—5381no—
115C4⋊C8—2691no—
116C4⋊C8C2×D26911yescharacteristic
117#103—5382no—
118#102—21no—
119#102—5381no—
120C4×C8—2691no—
121#41—10762no—
122#41—10762no—
123C2×Q8—21no—
124C2×Q8—5381no—
125C2×D4—2691no—
126C2×D4—5382no—
127C2×D4C22⋊D26911yescharacteristic
128C22×C4—21no—
129C22×C4—5382no—
130C22×C4—5381no—
131C2×C8—21no—
132C2×C8—5381no—
133C2×C8—5381no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—2692no—
137C4⋊C4—2691no—
138C4⋊C4—5382no—
139C4⋊C4—5381no—
140C4⋊C4C22⋊D26911yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—5382no—
143C22⋊C4—5381no—
144C42C22×D26911yescharacteristic
145C23—21no—
146C23—5381no—
147Q8—42no—
148Q8—10761no—
149Q8—10761no—
150D4—21no—
151D4—5381no—
152D4—5381no—
153D4—10764no—
154D4#1686438912yes—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—5381no—
160C2×C4—5382no—
161C2×C4—10764no—
162C2×C4—10761no—
163C2×C4—10761no—
164C2×C4D4×D26911yescharacteristic
165C2×C4D4×D26911yescharacteristic
166C2×C4C2×C22⋊D26911yescharacteristic
167C8—41no—
168C8—10761no—
169C8—10761no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—10761no—
174C22—10761no—
175C22—10761no—
176C22#2257542111yescharacteristic
177C4—21no—
178C4—41no—
179C4—81no—
180C4—10761no—
181C4—10762no—
182C4C2×#1686438911yescharacteristic
183C4#2257547411yescharacteristic
184C4#2257547811yescharacteristic
185C4#2257548211yescharacteristic
186C2—42no—
187C2—21521no—
188C2#3177075511yescharacteristic
189C2#3177076411yescharacteristic
190C2#3177077611yescharacteristic
subgroupG/H
centerC22#22575421
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
Fitting#476×C269C2
socleC22×C269#120
prime radical#31771259C2
hypercenter#476D269
hypocenterC269#1635
LCSG ▷ C42×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #31770955C2semidirect
3. #31770892C2semidirect
4. #31770352C2semidirect
5. D4⋊#14524130C2semidirect
6. #31770332C2semidirect
7. #476×C269C2semidirect
95. C269#1635semidirect
100. #476D269semidirect

Maximal subgroups

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

subgroupindex
#317712592
#317709552
#317708922
#317703522
D4⋊#145241302
#317703322
#476×C2692
#1635269