Finite Group Databasebeta

← #46809461

Subgroups — #46809461

Order 34432.

218 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 61 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#31770655C211yesmaximal, characteristic, complemented
3#31770472C211yesmaximal, 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×C4×Dic269C2211yescharacteristic
18#22575382—21no—
19C22⋊#14524130C2211yescharacteristic
20C8×Dic269—21no—
21#22575360—21no—
22#22575360—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—21no—
38#16864379—21no—
39#16864379—21no—
40#16864379—21no—
41#16864379—21no—
42C4×Dic269—21no—
43C4×Dic269C2×C411yescharacteristic
44C4×Dic269C2×C411yescharacteristic
45C4×Dic269D411yescharacteristic
46C4×Dic269D411yescharacteristic
47C2×Q8×C269C2×C411yescharacteristic
48C22×C4×C269—21no—
49C22×C4×C269C2311yescharacteristic
50C2×C8×C269—21no—
51C4⋊C4×C269—21no—
52C4⋊C4×C269C2×C411yescharacteristic
53C22⋊C4×C269—21no—
54C22×D269—21no—
55D1076—41no—
56C22⋊D269—41no—
57C22⋊D269—41no—
58C2×Dic269—21no—
59C2×Dic269—21no—
60C2×Dic269—21no—
61C2×Dic269—41no—
62C2×Dic269—41no—
63C2×Dic269—41no—
64C2×Dic269—41no—
65C2×Dic269C22⋊C411yescharacteristic
66C2×Dic269C22⋊C411yescharacteristic
67C2×Dic269C22⋊C411yescharacteristic
68C2×Dic269C22⋊C411yescharacteristic
69C4×D269—42no—
70#14524130—41no—
71C23×C269C2×D411yescharacteristic
72Q8×C269—41no—
73C2×C4×C269—21no—
74C2×C4×C269—21no—
75C2×C4×C269—41no—
76C2×C4×C269—41no—
77C2×C4×C269—41no—
78C2×C4×C269—41no—
79C2×C4×C269C22×C411yescharacteristic
80C2×C4×C269C2×D411yescharacteristic
81C8×C269—41no—
82C22×C269—21no—
83C22×C269—21no—
84C22×C269C2×C22⋊C411yescharacteristic
85C22×C269#13511yescharacteristic
86C22×C269#13511yescharacteristic
87C2×D269—41no—
88C2×D269—41no—
89C2×D269—41no—
90C4×C269—21no—
91C4×C269—21no—
92C4×C269—41no—
93C4×C269—41no—
94C4×C269—81no—
95Dic269—21no—
96Dic269—21no—
97Dic269—21no—
98Dic269—21no—
99Dic269—41no—
100Dic269—81no—
101C2×C269—21no—
102C2×C269—21no—
103C2×C269#41011yescharacteristic
104C2×C269#41611yescharacteristic
105C2×C269#42111yescharacteristic
106D269—81no—
107C269#152111yescharacteristic, complemented, Sylow
108#1521—2691nomaximal, Sylow
109#529—2691no—
110#431—2691no—
111#383—2691no—
112#328—2691no—
113#328D26911yescharacteristic, complemented
114#327—2691no—
115#327—2691no—
116#126—5381no—
117#125—2691no—
118#124—2691no—
119#123—5381no—
120C22⋊Q8C2×D26911yescharacteristic
121#121—2691no—
122C4×Q8—2691no—
123C4×D4—2691no—
124C4×D4—5381no—
125#117—5381no—
126C2×C42—2691no—
127C4⋊C8—5381no—
128C22⋊C8—2691no—
129C22⋊C8C2×D26911yescharacteristic
130C4×C8—5381no—
131#95—2691no—
132#95—5381no—
133#95—5381no—
134#95C2×D26911yescharacteristic
135C2×Q8C4×D26911yescharacteristic
136C2×D4—2691no—
137C2×D4—5381no—
138C22×C4—21no—
139C22×C4—2691no—
140C22×C4—2691no—
141C22×C4—5381no—
142C22×C4—5381no—
143C22×C4C22×D26911yescharacteristic
144C2×C8—21no—
145C2×C8—5381no—
146C4⋊C4—21no—
147C4⋊C4—2691no—
148C4⋊C4—5381no—
149C4⋊C4—5381no—
150C4⋊C4—5381no—
151C4⋊C4C4×D26911yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—5381no—
154C22⋊C4—5381no—
155C22⋊C4—5381no—
156C22⋊C4—5381no—
157C42—2691no—
158C42—2691no—
159C42—2691no—
160C42—2691no—
161C42—5381no—
162C23—5381no—
163C23D4×D26911yescharacteristic
164Q8—41no—
165D4—10761no—
166D4—10761no—
167D4—10761no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—2691no—
175C2×C4—2691no—
176C2×C4—2691no—
177C2×C4—2691no—
178C2×C4—5381no—
179C2×C4—5381no—
180C2×C4—5381no—
181C2×C4—10762no—
182C2×C4—10761no—
183C2×C4—10761no—
184C2×C4—10761no—
185C2×C4—10761no—
186C2×C4C2×C4×D26911yescharacteristic
187C2×C4D4×D26911yescharacteristic
188C8—41no—
189C8—10761no—
190C22—21no—
191C22—21no—
192C22—10761no—
193C22—10761no—
194C22—10761no—
195C22C22⋊C4×D26911yescharacteristic
196C22#2257547411yescharacteristic
197C22#2257547611yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—5381no—
204C4—5381no—
205C4—5381no—
206C4—5381no—
207C4—10761no—
208C4—21521no—
209C2—21no—
210C2—21no—
211C2—21521no—
212C2#3177057711yescharacteristic
213C2#3177060011yescharacteristic
214C2#3177062011yescharacteristic
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#1521
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. #31770655C2semidirect
3. #31770472C2semidirect
4. #31770342C2semidirect
7. #328×C269C2semidirect
9. #22575444C4semidirect
10. #22575442C4semidirect
13. Q8×Dic269C4semidirect
14. #22575415C4semidirect
107. C269#1521semidirect
113. #328D269semidirect

Maximal subgroups

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

subgroupindex
#317711412
#317706552
#317704722
#317703422
#317703402
#317703382
#328×C2692
#1521269