Finite Group Databasebeta

← #46809518

Subgroups — #46809518

Order 34432.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#31771154C211yesmaximal, characteristic
2#31770660C212yesmaximal, complemented
3#31770345C211yesmaximal, characteristic, complemented
4#31770344C212yesmaximal, complemented
5#329×C269C211yesmaximal, characteristic, complemented
6C2×#16864403C411yescharacteristic
7C2×#16864401C411yescharacteristic
8#22575451C411yescharacteristic
9#22575449C411yescharacteristic
10#22575441C2211yescharacteristic
11#22575426—22no—
12#22575413—22no—
13C42×D269C2211yescharacteristic
14#22575382—22no—
15#22575365—22no—
16#22575364C2212yes—
17#124×C269C2211yescharacteristic
18#97×C269C2212yes—
19#16864403—42no—
20#16864401—42no—
21C2×Dic538C2×C411yescharacteristic
22C2×D1076—21no—
23C2×D1076C2×C411yescharacteristic
24C2×C22⋊D269—21no—
25C2×C22⋊D269—22no—
26C22×Dic269—21no—
27C2×C4×D269—21no—
28C2×C4×D269C2×C411yescharacteristic
29C2×C4×D269D412yes—
30C2×#14524130—22no—
31#16864381—22no—
32#16864379—22no—
33C4×Dic269C2×C411yescharacteristic
34C4×Dic269D412yes—
35C2×Q8×C269C2×C411yescharacteristic
36C2×D4×C269C2×C411yescharacteristic
37C2×C8×C269—22no—
38C22⋊C4×C269—22no—
39C42×C269C2311yescharacteristic
40C22×D269—21no—
41C22×D269C22⋊C411yescharacteristic
42Dic538—41no—
43D1076—41no—
44D1076—42no—
45C22⋊D269—44no—
46C22⋊D269—42no—
47C2×Dic269—21no—
48C2×Dic269—42no—
49C2×Dic269C22⋊C412yes—
50C2×Dic269C22⋊C411yescharacteristic
51C4×D269—22no—
52C4×D269—42no—
53C4×D269—42no—
54#14524130—42no—
55C23×C269—21no—
56Q8×C269—41no—
57D4×C269—41no—
58C2×C4×C269—21no—
59C2×C4×C269C22×C411yescharacteristic
60C2×C4×C269C2×D412yes—
61C8×C269—42no—
62C22×C269—41no—
63C22×C269—42no—
64C22×C269C2×C22⋊C411yescharacteristic
65C2×D269—21no—
66C2×D269—22no—
67C2×D269—41no—
68C2×D269—42no—
69C4×C269—21no—
70C4×C269—22no—
71C4×C269—41no—
72Dic269—22no—
73Dic269—41no—
74Dic269#10012yes—
75C2×C269—81no—
76C2×C269C2×#10011yescharacteristic
77C2×C269#42112yes—
78D269—41no—
79D269—81no—
80C269#153611yescharacteristic, complemented, Sylow
81#1536—2691nomaximal, Sylow
82#532—2691no—
83#432—2692no—
84#329—2691no—
85#329—2692no—
86#329D26911yescharacteristic, complemented
87C2×#41—2691no—
88C2×#41—2691no—
89C4⋊Q8—2691no—
90#127—2691no—
91#124—2691no—
92#124C2×D26911yescharacteristic
93#121—5382no—
94C4×D4—5382no—
95C2×C42—2691no—
96C4⋊C8—5382no—
97C22⋊C8—5382no—
98#97—2692no—
99#97C2×D26912yes—
100#41—10762no—
101#41—10762no—
102C2×Q8—2691no—
103C2×Q8C4×D26911yescharacteristic
104C2×D4—2691no—
105C2×D4—5381no—
106C2×D4—5382no—
107C2×D4—5381no—
108C2×D4C4×D26911yescharacteristic
109C22×C4—2691no—
110C22×C4—2692no—
111C22×C4—5381no—
112C22×C4—5381no—
113C2×C8—22no—
114C2×C8—5382no—
115C4⋊C4—5382no—
116C22⋊C4—22no—
117C22⋊C4—5382no—
118C42—2691no—
119C42—2692no—
120C42C22×D26911yescharacteristic
121C23—21no—
122C23—2691no—
123C23—5381no—
124Q8—41no—
125Q8—10761no—
126D4—41no—
127D4—10761no—
128D4—10762no—
129D4—10764no—
130D4—10762no—
131C2×C4—21no—
132C2×C4—2691no—
133C2×C4—2692no—
134C2×C4—5382no—
135C2×C4—5381no—
136C2×C4—10762no—
137C2×C4—10762no—
138C2×C4—10762no—
139C2×C4C2×C4×D26911yescharacteristic
140C2×C4D4×D26912yes—
141C8—42no—
142C8—10762no—
143C22—41no—
144C22—42no—
145C22—5381no—
146C22—5382no—
147C22—10761no—
148C22—10762no—
149C22C22⋊C4×D26911yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—2692no—
154C4—5382no—
155C4—10761no—
156C2—81no—
157C2—10761no—
158C2—21521no—
159C2#100×D26911yescharacteristic
160C2#3177062012yes—
subgroupG/H
centerC22C22⋊C4×D269
commutatorC2×C4×C269C22×C4
FrattiniC42C22×D269
Fitting#329×C269C2
socleC22×C269C2×C22⋊C4
prime radical#31771154C2
cosocleC42×C269C23
hypercenter#329D269
hypocenterC269#1536
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31770660C2semidirect
3. #31770345C2semidirect
4. #31770344C2semidirect
5. #329×C269C2semidirect
80. C269#1536semidirect
86. #329D269semidirect

Maximal subgroups

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

subgroupindex
#317711542
#317706602
#317703452
#317703442
#329×C2692
#1536269