Finite Group Databasebeta

← #46823538

Subgroups — #46823538

Order 34432.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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#31771329C211yesmaximal, characteristic, complemented
2#31771312C211yesmaximal, characteristic, complemented
3#31770961C212yesmaximal, complemented
4#31770955C211yesmaximal, characteristic, complemented
5#31770910C212yesmaximal, complemented
6#31770896C211yesmaximal, characteristic, complemented
7#31770822C212yesmaximal
8#31770729C211yesmaximal, characteristic, complemented
9SD16×Dic269C212yesmaximal, complemented
10C4×#16864387C211yesmaximal, characteristic
11#461×C269C211yesmaximal, characteristic, complemented
12C2×#16864387C2211yescharacteristic
13#22575453C2211yescharacteristic
14#22575448—22no—
15#22575444C2212yes—
16#22575442C2212yes—
17#22575433—21no—
18#22575432—21no—
19#22575430—22no—
20Q8×Dic269C2212yes—
21C4×Dic538C2211yescharacteristic
22C4×D1076C2211yescharacteristic
23D4×Dic269C2212yes—
24#22575411—21no—
25C2×C4⋊Dic269—21no—
26#22575386C2211yescharacteristic
27#22575385C2212yes—
28#22575382C2212yes—
29#22575377C2212yes—
30#22575377C2212yes—
31#22575375C2212yes—
32#22575374C2211yescharacteristic
33#22575373C2211yescharacteristic
34C4×#14524130C2211yescharacteristic
35C8×Dic269C2212yes—
36C2×SD16×C269C2212yes—
37C4⋊Q8×C269C2211yescharacteristic
38C4×D4×C269C2211yescharacteristic
39C4⋊C8×C269C2211yescharacteristic
40#103×C269C2212yes—
41C2×Dic538—21no—
42C2×Dic538D411yescharacteristic
43C2×D1076C2311yescharacteristic
44C22×Dic269—22no—
45C2×C4×D269—21no—
46#16864387—22no—
47C2×#14524130C2311yescharacteristic
48C2×#14524130C2311yescharacteristic
49C4⋊Dic269—22no—
50C4⋊Dic269—22no—
51C4⋊Dic269—21no—
52C4⋊Dic269D411yescharacteristic
53C4⋊Dic269C2311yescharacteristic
54C4⋊Dic269C2312yes—
55#16864381—22no—
56#16864381D412yes—
57C22⋊Dic269—22no—
58#16864379—22no—
59#16864379—22no—
60#16864379—21no—
61C4×Dic269—22no—
62C4×Dic269C2312yes—
63C2×Q8×C269C2312yes—
64C2×D4×C269C2311yescharacteristic
65C22×C4×C269—21no—
66SD16×C269—24no—
67C2×C8×C269C2312yes—
68C4⋊C4×C269—21no—
69C4⋊C4×C269—21no—
70C4⋊C4×C269C2311yescharacteristic
71C22⋊C4×C269—21no—
72C42×C269C2311yescharacteristic
73C22×D269—21no—
74Dic538—22no—
75Dic538—81no—
76D1076—21no—
77D1076—21no—
78C2×Dic269—21no—
79C2×Dic269—22no—
80C2×Dic269—82no—
81C2×Dic269C2×D412yes—
82C2×Dic269C2×D412yes—
83C4×D269—42no—
84#14524130—21no—
85#14524130—21no—
86C23×C269—21no—
87Q8×C269—22no—
88Q8×C269—22no—
89D4×C269—21no—
90D4×C269#4112yes—
91C2×C4×C269—21no—
92C2×C4×C269—22no—
93C2×C4×C269—42no—
94C2×C4×C269C2×D411yescharacteristic
95C2×C4×C269C2×D411yescharacteristic
96C2×C4×C269C2411yescharacteristic
97C8×C269—22no—
98C22×C269—22no—
99C22×C269—41no—
100C22×C269—41no—
101C22×C269C22×D411yescharacteristic
102C2×D269—41no—
103C2×D269—41no—
104C2×D269—41no—
105C4×C269—21no—
106C4×C269—42no—
107C4×C269—41no—
108C4×C269#13512yes—
109C4×C269C2×#4111yescharacteristic
110C4×C2692−1+411yescharacteristic
111Dic269—22no—
112Dic269—22no—
113Dic269—41no—
114Dic269—42no—
115C2×C269—42no—
116C2×C269#54811yescharacteristic
117C2×C269C2×#13511yescharacteristic
118C2×C269#57711yescharacteristic
119D269—81no—
120C269#336011yescharacteristic, complemented, Sylow
121#3360—2691nomaximal, Sylow
122#556—2691no—
123#554—2691no—
124#488—2692no—
125#487—2691no—
126#479—2692no—
127#476—2691no—
128#463—2692no—
129#461D26911yescharacteristic, complemented
130C8×Q8—2691no—
131C4×SD16—2692no—
132C4×D8—2691no—
133C2×SD16C2×D26912yes—
134C2×D8—2691no—
135C4⋊Q8—2691no—
136C4⋊Q8C2×D26911yescharacteristic
137#126—5382no—
138#125—2692no—
139#124—2692no—
140C22⋊Q8—5382no—
141C22⋊Q8—5381no—
142C22⋊Q8—5381no—
143C4×Q8—2691no—
144C4×Q8—2692no—
145C4×D4—2692no—
146C4×D4—2691no—
147C4×D4C2×D26911yescharacteristic
148#117—5381no—
149C2×C4⋊C4—5381no—
150#107—2691no—
151#106—2692no—
152C4⋊C8—2692no—
153C4⋊C8C2×D26911yescharacteristic
154#103—2692no—
155#103—2692no—
156#103C2×D26912yes—
157#102—2691no—
158#102—2692no—
159#102—2691no—
160C4×C8—2692no—
161C4×C8—2691no—
162C2×Q8—2691no—
163C2×Q8—5381no—
164C2×Q8C22×D26912yes—
165C2×D4—2691no—
166C2×D4C22×D26911yescharacteristic
167C22×C4—21no—
168C22×C4—5382no—
169C22×C4—5381no—
170SD16—24no—
171D8—5382no—
172C2×C8—2691no—
173C2×C8—2691no—
174C2×C8C22×D26912yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—2691no—
178C4⋊C4—2692no—
179C4⋊C4—2692no—
180C4⋊C4—2691no—
181C4⋊C4—5382no—
182C4⋊C4—5382no—
183C4⋊C4—5382no—
184C4⋊C4—5381no—
185C4⋊C4C22×D26911yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—5382no—
188C22⋊C4—5382no—
189C22⋊C4—5382no—
190C22⋊C4—5381no—
191C42—2692no—
192C42—5382no—
193C42C22×D26911yescharacteristic
194C23—21no—
195C23—5381no—
196Q8—22no—
197Q8—22no—
198Q8—5382no—
199Q8—21521no—
200D4—21no—
201D4—5381no—
202D4—5381no—
203D4#1686440112yes—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—2692no—
208C2×C4—2692no—
209C2×C4—5381no—
210C2×C4—5382no—
211C2×C4—10762no—
212C2×C4—21522no—
213C2×C4D4×D26911yescharacteristic
214C2×C4D4×D26911yescharacteristic
215C2×C4C23×D26911yescharacteristic
216C8—22no—
217C8—5381no—
218C8—5381no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—10761no—
223C22—10761no—
224C22—10761no—
225C22C2×D4×D26911yescharacteristic
226C4—21no—
227C4—42no—
228C4—41no—
229C4—5382no—
230C4—5382no—
231C4—10762no—
232C4—10761no—
233C4#2257547412yes—
234C4C2×#1686440111yescharacteristic
235C4#2257550011yescharacteristic
236C2—42no—
237C2—21521no—
238C2#3177126111yescharacteristic
239C2C2×#2257547411yescharacteristic
240C2#3177141411yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#461×C269C2
socleC22×C269C22×D4
prime radicalC2×#16864387C22
hypercenter#461D269
hypocenterC269#3360
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #31771329C2semidirect
2. #31771312C2semidirect
3. #31770961C2semidirect
4. #31770955C2semidirect
5. #31770910C2semidirect
6. #31770896C2semidirect
8. #31770729C2semidirect
9. SD16×Dic269C2semidirect
11. #461×C269C2semidirect
120. C269#3360semidirect
129. #461D269semidirect

Maximal subgroups

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

subgroupindex
#317713292
#317713122
#317709612
#317709552
#317709102
#317708962
#317708222
#317707292
SD16×Dic2692
C4×#168643872
#461×C2692
#3360269