Finite Group Databasebeta

← #46822340

Subgroups — #46822340

Order 34432.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#31771222C212yesmaximal, complemented
2#31770899C212yesmaximal, complemented
3#31770883C212yesmaximal, complemented
4#31770849C212yesmaximal, complemented
5#31770846C211yesmaximal, characteristic, complemented
6#31770826C212yesmaximal, complemented
7#31770818C212yesmaximal, complemented
8#31770631C211yesmaximal, characteristic, complemented
9#466×C269C211yesmaximal, characteristic
10C2×Dic1076C2211yescharacteristic
11C2×#16864390C2212yes—
12C2×#16864386C2211yescharacteristic
13#22575452C2212yes—
14#22575446—22no—
15#22575440—22no—
16#22575440C2212yes—
17#22575434—22no—
18#22575432C2212yes—
19#22575430—22no—
20#22575418C2212yes—
21D4×Dic269C2212yes—
22#22575412C2211yescharacteristic
23#22575387C2211yescharacteristic
24#22575386C2212yes—
25#22575382C2212yes—
26#22575382C2212yes—
27#22575378C2212yes—
28#22575376C2212yes—
29#22575374C2212yes—
30C2×D8×C269C2211yescharacteristic
31C22×C8×C269C2211yescharacteristic
32#121×C269C2212yes—
33#107×C269C2211yescharacteristic
34#102×C269C2212yes—
35C2×Dic538—22no—
36C2×Dic538C2312yes—
37C22×Dic269—22no—
38Dic1076—41no—
39#16864390—42no—
40#16864386—41no—
41C2×#14524130C2312yes—
42C4⋊Dic269D411yescharacteristic
43C4⋊Dic269D411yescharacteristic
44C4⋊Dic269C2312yes—
45#16864381—22no—
46#16864381—22no—
47#16864381—22no—
48C22⋊Dic269—22no—
49C22⋊Dic269—22no—
50C22⋊Dic269—22no—
51C22⋊Dic269—22no—
52C22⋊Dic269D412yes—
53C4×Dic269—22no—
54C4×Dic269C2312yes—
55C2×D4×C269—22no—
56C2×D4×C269C2312yes—
57C22×C4×C269C2311yescharacteristic
58D8×C269—41no—
59C2×C8×C269—41no—
60C2×C8×C269C2311yescharacteristic
61C2×C8×C269C2311yescharacteristic
62C4⋊C4×C269C2312yes—
63C22⋊C4×C269—22no—
64Dic538—22no—
65Dic538—22no—
66Dic538—82no—
67C2×Dic269—22no—
68C2×Dic269—22no—
69C2×Dic269—82no—
70C2×Dic269C2×D412yes—
71C2×Dic269C2×D412yes—
72#14524130—22no—
73C23×C269—22no—
74C23×C269C2×D411yescharacteristic
75D4×C269—22no—
76D4×C269—22no—
77D4×C269—82no—
78C2×C4×C269—21no—
79C2×C4×C269—21no—
80C2×C4×C269—22no—
81C2×C4×C269C2×D411yescharacteristic
82C2×C4×C269C2411yescharacteristic
83C8×C269—21no—
84C8×C269—21no—
85C22×C269—21no—
86C22×C269—21no—
87C22×C269—21no—
88C22×C269—42no—
89C22×C269—42no—
90C22×C269—42no—
91C22×C269C22×D411yescharacteristic
92C4×C269—21no—
93C4×C269—42no—
94C4×C269H(5,𝔽2)11yescharacteristic
95C4×C2692−1+411yescharacteristic
96Dic269—22no—
97Dic269—22no—
98Dic269—42no—
99Dic269—42no—
100C2×C269—41no—
101C2×C269—82no—
102C2×C269#53711yescharacteristic
103C2×C269#57611yescharacteristic
104C2×C269#57811yescharacteristic
105C269#326211yescharacteristic, complemented, Sylow
106#3262—2691nomaximal, Sylow
107#542—2692no—
108#477—2692no—
109#474—2692no—
110#468—2692no—
111#467—2691no—
112#466D26911yescharacteristic
113#464—2692no—
114#463—2692no—
115#424—2691no—
116C2×Q16—2691no—
117C2×SD16—2692no—
118C2×D8C2×D26911yescharacteristic
119C2×M16—2691no—
120C22×C8C2×D26911yescharacteristic
121C4⋊Q8—2692no—
122#126—5382no—
123#124—2692no—
124#124—5382no—
125#123—5382no—
126C22⋊Q8—2692no—
127C22⋊Q8—5382no—
128#121C2×D26912yes—
129C4×Q8—2692no—
130C4×D4—2692no—
131#117—2691no—
132#107—2691no—
133#107—2692no—
134#107C2×D26911yescharacteristic
135C4⋊C8—2692no—
136C4⋊C8—2692no—
137#103—2692no—
138#103—2692no—
139#102—2692no—
140#102C2×D26912yes—
141C2×Q8—2692no—
142C2×Q8—5382no—
143C2×D4—22no—
144C2×D4C22×D26912yes—
145C22×C4—5382no—
146C22×C4C22×D26911yescharacteristic
147Q16—10761no—
148SD16—10762no—
149D8—41no—
150M16—10761no—
151C2×C8—41no—
152C2×C8—2692no—
153C2×C8C22×D26911yescharacteristic
154C2×C8C22×D26911yescharacteristic
155C4⋊C4—2691no—
156C4⋊C4—2691no—
157C4⋊C4—2692no—
158C4⋊C4—5382no—
159C4⋊C4—5382no—
160C4⋊C4—5382no—
161C4⋊C4C22×D26912yes—
162C22⋊C4—22no—
163C22⋊C4—2692no—
164C22⋊C4—5382no—
165C22⋊C4—5382no—
166C22⋊C4—5382no—
167C22⋊C4—5382no—
168C42—2692no—
169C42—5382no—
170C23—22no—
171C23D4×D26911yescharacteristic
172Q8—5382no—
173Q8—5382no—
174Q8—21522no—
175D4—22no—
176D4—22no—
177D4—82no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—2692no—
182C2×C4—2692no—
183C2×C4—5382no—
184C2×C4—5382no—
185C2×C4—21522no—
186C2×C4D4×D26911yescharacteristic
187C2×C4C23×D26911yescharacteristic
188C8—21no—
189C8—21no—
190C8—5382no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22C2×D4×D26911yescharacteristic
198C4—21no—
199C4—42no—
200C4—5382no—
201C4—5382no—
202C4—10762no—
203C4—10762no—
204C4#2257549811yescharacteristic
205C4#2257550011yescharacteristic
206C2—41no—
207C2—82no—
208C2#3177118211yescharacteristic
209C2#3177140611yescharacteristic
210C2#3177141911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting, prime radical#466×C269C2
socleC22×C269C22×D4
hypercenter#466D269
hypocenterC269#3262
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #31771222C2semidirect
2. #31770899C2semidirect
3. #31770883C2semidirect
4. #31770849C2semidirect
5. #31770846C2semidirect
6. #31770826C2semidirect
7. #31770818C2semidirect
8. #31770631C2semidirect
105. C269#3262semidirect

Maximal subgroups

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

subgroupindex
#317712222
#317708992
#317708832
#317708492
#317708462
#317708262
#317708182
#317706312
#466×C2692
#3262269