Finite Group Databasebeta

← #46822238

Subgroups — #46822238

Order 34432.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#31771141C212yesmaximal, complemented
2#31770914C212yesmaximal, complemented
3#31770908C212yesmaximal, complemented
4#31770841C211yesmaximal, characteristic
5#31770836C212yesmaximal, complemented
6#31770829C212yesmaximal, complemented
7#31770823C212yesmaximal, complemented
8C2×#22575382C211yesmaximal, characteristic, complemented
9#467×C269C211yesmaximal, characteristic, complemented
10C2×#16864389C2212yes—
11C2×D2152C2211yescharacteristic
12C22×#14524130C2211yescharacteristic
13#22575448—22no—
14#22575444C2212yes—
15#22575442C2212yes—
16#22575437—22no—
17#22575427C2212yes—
18Q8×Dic269C2212yes—
19#22575415C2212yes—
20#22575413—22no—
21#22575411—22no—
22C2×C4×Dic269C2211yescharacteristic
23#22575387C2211yescharacteristic
24#22575384C2212yes—
25#22575382C2212yes—
26#22575382C2212yes—
27#22575377C2212yes—
28#22575375C2212yes—
29#22575373C2212yes—
30C2×Q16×C269C2211yescharacteristic
31C22×C8×C269C2211yescharacteristic
32C22⋊Q8×C269C2212yes—
33#107×C269C2211yescharacteristic
34#103×C269C2212yes—
35C2×D1076C2312yes—
36C2×C22⋊D269—22no—
37C22×Dic269D411yescharacteristic
38C22×Dic269D411yescharacteristic
39C2×C4×D269—22no—
40#16864389—42no—
41D2152—41no—
42C2×#14524130—41no—
43C2×#14524130C2312yes—
44C4⋊Dic269—22no—
45C4⋊Dic269—22no—
46C4⋊Dic269C2312yes—
47#16864381—22no—
48#16864379—22no—
49#16864379—22no—
50#16864379—22no—
51#16864379—22no—
52C4×Dic269—22no—
53C4×Dic269D412yes—
54C4×Dic269C2312yes—
55C2×Q8×C269C2312yes—
56C22×C4×C269C2311yescharacteristic
57Q16×C269—41no—
58C2×C8×C269—41no—
59C2×C8×C269C2311yescharacteristic
60C2×C8×C269C2311yescharacteristic
61C4⋊C4×C269—22no—
62C4⋊C4×C269C2312yes—
63C22⋊C4×C269—22no—
64C22×D269—22no—
65D1076—22no—
66D1076—22no—
67C22⋊D269—44no—
68C2×Dic269—22no—
69C2×Dic269—22no—
70C2×Dic269—41no—
71C2×Dic269C2×D412yes—
72C2×Dic269C2×D412yes—
73C4×D269—44no—
74#14524130—22no—
75C23×C269C2×D411yescharacteristic
76Q8×C269—22no—
77Q8×C269—22no—
78C2×C4×C269—21no—
79C2×C4×C269—21no—
80C2×C4×C269—22no—
81C2×C4×C269—22no—
82C2×C4×C269C2×D411yescharacteristic
83C2×C4×C269C2411yescharacteristic
84C8×C269—21no—
85C8×C269—21no—
86C22×C269—21no—
87C22×C269—21no—
88C22×C269#13512yes—
89C22×C269C22×D411yescharacteristic
90C2×D269—42no—
91C2×D269—42no—
92C2×D269—42no—
93C4×C269—21no—
94C4×C269—42no—
95C4×C269—42no—
96C4×C269H(5,𝔽2)11yescharacteristic
97C4×C2692−1+411yescharacteristic
98Dic269—22no—
99Dic269—22no—
100Dic269—42no—
101C2×C269—22no—
102C2×C269#53711yescharacteristic
103C2×C269C2×#13511yescharacteristic
104C2×C269#57511yescharacteristic
105D269—82no—
106C269#325011yescharacteristic, complemented, Sylow
107#3250—2691nomaximal, Sylow
108#529—2692no—
109#479—2692no—
110#478—2692no—
111#467D26911yescharacteristic, complemented
112#466—2691no—
113#465—2692no—
114#464—2692no—
115#463—2692no—
116C2×C4⋊C8—2691no—
117C2×Q16C2×D26911yescharacteristic
118C2×SD16—2692no—
119C2×D8—2691no—
120C22×C8—2691no—
121C22×C8C2×D26911yescharacteristic
122#126—5382no—
123#125—2692no—
124#124—2692no—
125#123—5382no—
126C22⋊Q8C2×D26912yes—
127#121—2692no—
128C4×Q8—2692no—
129C4×D4—2692no—
130C4×D4—5382no—
131#117—5382no—
132C2×C42—2691no—
133#107—2691no—
134#107C2×D26911yescharacteristic
135#106—2692no—
136C4⋊C8—2692no—
137C4⋊C8—2692no—
138#103—2692no—
139#103C2×D26912yes—
140#102—2692no—
141#102—2692no—
142C2×Q8C22×D26912yes—
143C2×D4—2692no—
144C2×D4—5382no—
145C22×C4—2691no—
146C22×C4—2691no—
147C22×C4—5382no—
148C22×C4C22×D26911yescharacteristic
149Q16—41no—
150SD16—10762no—
151D8—10761no—
152C2×C8—41no—
153C2×C8—2692no—
154C2×C8—10761no—
155C2×C8C22×D26911yescharacteristic
156C2×C8C22×D26911yescharacteristic
157C4⋊C4—22no—
158C4⋊C4—2692no—
159C4⋊C4—5382no—
160C4⋊C4—5382no—
161C4⋊C4—5382no—
162C4⋊C4C22×D26912yes—
163C22⋊C4—22no—
164C22⋊C4—5382no—
165C22⋊C4—5382no—
166C22⋊C4—5382no—
167C22⋊C4—5382no—
168C42—2692no—
169C42—2692no—
170C42—5382no—
171C23—5382no—
172C23D4×D26911yescharacteristic
173Q8—22no—
174Q8—22no—
175D4—5382no—
176D4—5382no—
177D4—10764no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—2692no—
183C2×C4—2692no—
184C2×C4—5382no—
185C2×C4—5382no—
186C2×C4—10764no—
187C2×C4—10761no—
188C2×C4D4×D26911yescharacteristic
189C2×C4C23×D26911yescharacteristic
190C8—21no—
191C8—21no—
192C8—5382no—
193C22—21no—
194C22—21no—
195C22—10762no—
196C22—10762no—
197C22—10762no—
198C22#2257547612yes—
199C22C2×D4×D26911yescharacteristic
200C4—21no—
201C4—42no—
202C4—42no—
203C4—5382no—
204C4—5382no—
205C4—10762no—
206C4#2257549811yescharacteristic
207C4#2257550011yescharacteristic
208C2—22no—
209C2—21522no—
210C2#3177118211yescharacteristic
211C2C2×#2257547611yescharacteristic
212C2#3177140211yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#467×C269C2
socleC22×C269C22×D4
prime radical#31770841C2
hypercenter#467D269
hypocenterC269#3250
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #31771141C2semidirect
2. #31770914C2semidirect
3. #31770908C2semidirect
5. #31770836C2semidirect
6. #31770829C2semidirect
7. #31770823C2semidirect
8. C2×#22575382C2semidirect
9. #467×C269C2semidirect
106. C269#3250semidirect
111. #467D269semidirect

Maximal subgroups

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

subgroupindex
#317711412
#317709142
#317709082
#317708412
#317708362
#317708292
#317708232
C2×#225753822
#467×C2692
#3250269