Finite Group Databasebeta

← #46810201

Subgroups — #46810201

Order 34432.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#31771349C211yesmaximal, characteristic
2#31771011C211yesmaximal, characteristic, complemented
3#31770997C211yesmaximal, characteristic, complemented
4#31770346C211yesmaximal, characteristic, complemented
5#31770345C211yesmaximal, characteristic, complemented
6#31770344C211yesmaximal, characteristic, complemented
7#489×C269C211yesmaximal, characteristic, complemented
8C2×#16864392—21no—
9C2×#16864389—21no—
10#22575445C2211yescharacteristic
11#22575441C2211yescharacteristic
12#22575437—21no—
13#22575435—21no—
14#22575430—21no—
15#22575429—21no—
16#22575426—21no—
17#22575425—21no—
18#22575386—21no—
19#22575384—21no—
20#22575364C2211yescharacteristic
21#22575364C2211yescharacteristic
22C4⋊Q8×C269C2211yescharacteristic
23#124×C269C2211yescharacteristic
24#103×C269—21no—
25#102×C269—21no—
26#97×C269C2211yescharacteristic
27C2×Dic538D411yescharacteristic
28C2×D1076D411yescharacteristic
29C2×C22⋊D269—21no—
30C2×C22⋊D269—21no—
31C22×Dic269—21no—
32C2×C4×D269—21no—
33#16864392—42no—
34#16864389—42no—
35C2×#14524130—21no—
36C2×#14524130—21no—
37C4⋊Dic269—21no—
38C4⋊Dic269D411yescharacteristic
39C4⋊Dic269D411yescharacteristic
40#16864381—21no—
41#16864381—21no—
42#16864381—21no—
43C22⋊Dic269—21no—
44#16864379—21no—
45#16864379—21no—
46#16864379—21no—
47C2×Q8×C269—21no—
48C2×Q8×C269D411yescharacteristic
49C2×D4×C269D411yescharacteristic
50C2×C8×C269—21no—
51C4⋊C4×C269—21no—
52C4⋊C4×C269—21no—
53C22⋊C4×C269—21no—
54C22⋊C4×C269—21no—
55C42×C269C2311yescharacteristic
56C22×D269—21no—
57Dic538—41no—
58D1076—41no—
59C22⋊D269—81no—
60C22⋊D269—81no—
61C2×Dic269—21no—
62C2×Dic269—21no—
63C2×Dic269—21no—
64C2×Dic269—81no—
65C4×D269—81no—
66#14524130—22no—
67#14524130—22no—
68C23×C269—21no—
69Q8×C269—41no—
70Q8×C269—41no—
71Q8×C269—41no—
72D4×C269—41no—
73C2×C4×C269—21no—
74C2×C4×C269—41no—
75C2×C4×C269C2×D411yescharacteristic
76C2×C4×C269C2×D411yescharacteristic
77C2×C4×C269C2×D411yescharacteristic
78C8×C269—41no—
79C22×C269—41no—
80C22×C269—41no—
81C22×C269—41no—
82C22×C269#12011yescharacteristic
83C2×D269—41no—
84C2×D269—41no—
85C2×D269—41no—
86C4×C269—21no—
87C4×C269—21no—
88C4×C269—21no—
89C4×C269—41no—
90C4×C269—81no—
91Dic269—41no—
92Dic269—41no—
93Dic269—41no—
94C2×C269—81no—
95C2×C269#45311yescharacteristic
96C2×C269#45511yescharacteristic
97C2×C269#45611yescharacteristic
98D269—81no—
99C269#166111yescharacteristic, complemented, Sylow
100#1661—2691nomaximal, Sylow
101#562—2691no—
102#501—2691no—
103#497—2691no—
104#489D26911yescharacteristic, complemented
105#330—2691no—
106#329—2691no—
107#329—2691no—
108C2×Q16—5381no—
109C2×SD16—5381no—
110C4⋊Q8C2×D26911yescharacteristic
111#125—2691no—
112#124—2691no—
113#124C2×D26911yescharacteristic
114#123—5381no—
115#123—5381no—
116C22⋊Q8—5381no—
117C22⋊Q8—5381no—
118#121—5381no—
119#121—5381no—
120#107—5381no—
121#106—5381no—
122#103—21no—
123#102—21no—
124#97—2691no—
125#97—2691no—
126#97C2×D26911yescharacteristic
127C2×Q8—21no—
128C2×Q8—2691no—
129C2×Q8C22⋊D26911yescharacteristic
130C2×D4—2691no—
131C2×D4—5381no—
132C2×D4—5381no—
133C2×D4C22⋊D26911yescharacteristic
134C22×C4—5381no—
135C22×C4—5381no—
136Q16—10762no—
137SD16—10762no—
138C2×C8—21no—
139C2×C8—5381no—
140C2×C8—5381no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2691no—
144C4⋊C4—2691no—
145C4⋊C4—5381no—
146C4⋊C4—5381no—
147C4⋊C4—5381no—
148C4⋊C4—5381no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—5381no—
152C22⋊C4—5381no—
153C22⋊C4—5381no—
154C22⋊C4—5381no—
155C42C22×D26911yescharacteristic
156C23—21no—
157C23—5381no—
158Q8—41no—
159Q8—41no—
160Q8—41no—
161Q8—10761no—
162D4—41no—
163D4—10761no—
164D4—21521no—
165D4—21521no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—5381no—
169C2×C4—5381no—
170C2×C4—5381no—
171C2×C4—21521no—
172C2×C4—21521no—
173C2×C4D4×D26911yescharacteristic
174C2×C4D4×D26911yescharacteristic
175C2×C4C2×C22⋊D26911yescharacteristic
176C8—41no—
177C8—5382no—
178C8—5382no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—10761no—
183C22—10761no—
184C22—10761no—
185C22#2257542111yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—81no—
191C4—10761no—
192C4—10761no—
193C4—10761no—
194C2—81no—
195C2—21521no—
196C2#3177077111yescharacteristic
197C2#3177078211yescharacteristic
198C2#3177078611yescharacteristic
subgroupG/H
centerC22#22575421
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
Fitting#489×C269C2
socleC22×C269#120
prime radical#31771349C2
hypercenter#489D269
hypocenterC269#1661
LCSG ▷ C42×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #31771011C2semidirect
3. #31770997C2semidirect
4. #31770346C2semidirect
5. #31770345C2semidirect
6. #31770344C2semidirect
7. #489×C269C2semidirect
99. C269#1661semidirect
104. #489D269semidirect

Maximal subgroups

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

subgroupindex
#317713492
#317710112
#317709972
#317703462
#317703452
#317703442
#489×C2692
#1661269