Finite Group Databasebeta

← #46809409

Subgroups — #46809409

Order 34432.

242 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 63 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#31771141C211yesmaximal, characteristic
2#31770659C211yesmaximal, characteristic, complemented
3#31770456C211yesmaximal, characteristic, complemented
4#31770342C211yesmaximal, characteristic, complemented
5#31770340C211yesmaximal, characteristic
6#31770338C211yesmaximal, characteristic
7#328×C269C211yesmaximal, characteristic, complemented
8#22575448—21no—
9#22575444C411yescharacteristic, complemented
10#22575442C411yescharacteristic, complemented
11#22575437—21no—
12#22575427C2211yescharacteristic
13Q8×Dic269C411yescharacteristic, complemented
14#22575415C411yescharacteristic, complemented
15#22575413—21no—
16#22575411—21no—
17C2×#16864381—21no—
18C2×C4×Dic269—21no—
19C2×C4×Dic269C2211yescharacteristic
20#22575382—21no—
21C22⋊#14524130C2211yescharacteristic
22#22575363—21no—
23#22575360C2211yescharacteristic
24C22⋊Q8×C269C2211yescharacteristic
25C22⋊C8×C269C2211yescharacteristic
26#95×C269C2211yescharacteristic
27C2×D1076C2×C411yescharacteristic
28C2×C22⋊D269—21no—
29C22×Dic269—21no—
30C22×Dic269D411yescharacteristic
31C22×Dic269D411yescharacteristic
32C2×C4×D269—21no—
33C2×#14524130—21no—
34C4⋊Dic269—21no—
35C4⋊Dic269—21no—
36C4⋊Dic269C2×C411yescharacteristic
37#16864381—24no—
38#16864381—21no—
39#16864379—21no—
40#16864379—21no—
41#16864379—21no—
42#16864379—21no—
43C4×Dic269—21no—
44C4×Dic269—42no—
45C4×Dic269C2×C411yescharacteristic
46C4×Dic269C2×C411yescharacteristic
47C4×Dic269D411yescharacteristic
48C4×Dic269D411yescharacteristic
49C2×Q8×C269C2×C411yescharacteristic
50C22×C4×C269—21no—
51C22×C4×C269C2311yescharacteristic
52C2×C8×C269—21no—
53C4⋊C4×C269—21no—
54C4⋊C4×C269C2×C411yescharacteristic
55C22⋊C4×C269—21no—
56C22×D269—21no—
57D1076—41no—
58C22⋊D269—41no—
59C22⋊D269—41no—
60C2×Dic269—21no—
61C2×Dic269—21no—
62C2×Dic269—22no—
63C2×Dic269—22no—
64C2×Dic269—21no—
65C2×Dic269—41no—
66C2×Dic269—41no—
67C2×Dic269C22⋊C411yescharacteristic
68C2×Dic269C22⋊C411yescharacteristic
69C2×Dic269C22⋊C411yescharacteristic
70C2×Dic269C22⋊C411yescharacteristic
71C4×D269—42no—
72#14524130—41no—
73C23×C269C2×D411yescharacteristic
74Q8×C269—41no—
75C2×C4×C269—22no—
76C2×C4×C269—21no—
77C2×C4×C269—21no—
78C2×C4×C269—41no—
79C2×C4×C269—41no—
80C2×C4×C269—41no—
81C2×C4×C269C22×C411yescharacteristic
82C2×C4×C269C2×D411yescharacteristic
83C8×C269—41no—
84C22×C269—21no—
85C22×C269—21no—
86C22×C269C2×C22⋊C411yescharacteristic
87C22×C269AGL(1,ℤ/8)11yescharacteristic
88C22×C269#13711yescharacteristic
89C2×D269—41no—
90C2×D269—41no—
91C2×D269—41no—
92C4×C269—21no—
93C4×C269—21no—
94C4×C269—42no—
95C4×C269—41no—
96C4×C269—41no—
97Dic269—21no—
98Dic269—21no—
99Dic269—21no—
100Dic269—42no—
101Dic269—41no—
102Dic269#10412yes—
103C2×C269—21no—
104C2×C269—21no—
105C2×C269#41011yescharacteristic
106C2×C269#41711yescharacteristic
107C2×C269C2×#10411yescharacteristic
108D269—81no—
109C269#150911yescharacteristic, complemented, Sylow
110#1509—2691nomaximal, Sylow
111#529—2691no—
112#432—2691no—
113C4×C4⋊C4—2691no—
114#328—2691no—
115#328D26911yescharacteristic, complemented
116#327—2691no—
117#327—2691no—
118#126—5381no—
119#125—2691no—
120#124—2691no—
121#123—5381no—
122C22⋊Q8C2×D26911yescharacteristic
123#121—2691no—
124C4×Q8—2691no—
125C4×D4—2691no—
126C4×D4—5381no—
127#117—5381no—
128C2×C4⋊C4—5381no—
129C2×C42—2691no—
130C2×C42—5381no—
131C4⋊C8—5381no—
132C22⋊C8—2691no—
133C22⋊C8C2×D26911yescharacteristic
134#97—5381no—
135#95—2691no—
136#95C2×D26911yescharacteristic
137C2×Q8C4×D26911yescharacteristic
138C2×D4—2691no—
139C2×D4—5381no—
140C22×C4—21no—
141C22×C4—2691no—
142C22×C4—2691no—
143C22×C4—5381no—
144C22×C4—5381no—
145C22×C4C22×D26911yescharacteristic
146C2×C8—21no—
147C2×C8—5381no—
148C4⋊C4—21no—
149C4⋊C4—2691no—
150C4⋊C4—5381no—
151C4⋊C4—5381no—
152C4⋊C4—5381no—
153C4⋊C4—5384no—
154C4⋊C4C4×D26911yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—5381no—
157C22⋊C4—5381no—
158C22⋊C4—5381no—
159C22⋊C4—5381no—
160C42—2691no—
161C42—2691no—
162C42—2691no—
163C42—2691no—
164C42—5381no—
165C42—10762no—
166C23—5381no—
167C23D4×D26911yescharacteristic
168Q8—41no—
169D4—10761no—
170D4—10761no—
171D4—10761no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—2691no—
179C2×C4—2691no—
180C2×C4—2691no—
181C2×C4—2691no—
182C2×C4—5382no—
183C2×C4—5381no—
184C2×C4—5381no—
185C2×C4—5382no—
186C2×C4—5381no—
187C2×C4—10762no—
188C2×C4—10761no—
189C2×C4—10761no—
190C2×C4C2×C4×D26911yescharacteristic
191C2×C4D4×D26911yescharacteristic
192C8—41no—
193C8—10761no—
194C22—21no—
195C22—21no—
196C22—10761no—
197C22—10761no—
198C22—10761no—
199C22C22⋊C4×D26911yescharacteristic
200C22#2257548011yescharacteristic
201C22#2257548511yescharacteristic
202C4—21no—
203C4—21no—
204C4—42no—
205C4—41no—
206C4—41no—
207C4—2692no—
208C4—5381no—
209C4—5381no—
210C4—5381no—
211C4—10762no—
212C4—10761no—
213C2—21no—
214C2—21no—
215C2—21521no—
216C2#3177057711yescharacteristic
217C2#3177060511yescharacteristic
218C2#104×D26911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D269
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
Fitting#328×C269C2
socleC22×C269C2×C22⋊C4
prime radical#22575427C22
cosocleC22×C4×C269C23
hypercenter#328D269
hypocenterC269#1509
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #31770659C2semidirect
3. #31770456C2semidirect
4. #31770342C2semidirect
7. #328×C269C2semidirect
9. #22575444C4semidirect
10. #22575442C4semidirect
13. Q8×Dic269C4semidirect
14. #22575415C4semidirect
109. C269#1509semidirect
115. #328D269semidirect

Maximal subgroups

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

subgroupindex
#317711412
#317706592
#317704562
#317703422
#317703402
#317703382
#328×C2692
#1509269