Finite Group Databasebeta

← #46822218

Subgroups — #46822218

Order 34432.

354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 115 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#31771160C211yesmaximal, characteristic, complemented
2#31771137C211yesmaximal, characteristic
3#31770910C212yesmaximal, complemented
4#31770891C211yesmaximal, characteristic, complemented
5#31770885C211yesmaximal, characteristic, complemented
6#31770845C212yesmaximal, complemented
7#31770831C212yesmaximal
8#31770825C212yesmaximal, complemented
9#31770812C211yesmaximal, characteristic, complemented
10C4⋊C8×D269C211yesmaximal, characteristic, complemented
11#461×C269C211yesmaximal, characteristic, complemented
12C2×#16864392C2212yes—
13C2×C8×D269C2212yes—
14#22575453C2211yescharacteristic
15#22575446—21no—
16#22575444—21no—
17#22575444C2211yescharacteristic
18#22575440C2211yescharacteristic
19#22575435—21no—
20#22575433—21no—
21#22575433C2211yescharacteristic
22#22575429C2212yes—
23#22575424C2211yescharacteristic
24Q8×Dic269C2212yes—
25C4×Dic538C2211yescharacteristic
26#22575418—21no—
27C4×C22⋊D269—21no—
28#22575412—21no—
29#22575411—21no—
30C42×D269C2211yescharacteristic
31#22575386C2212yes—
32#22575385C2212yes—
33C4⋊#14524130C2211yescharacteristic
34#22575382C2212yes—
35#22575378C2212yes—
36#22575377C2212yes—
37#22575374C2212yes—
38C2×SD16×C269C2212yes—
39C4⋊Q8×C269C2211yescharacteristic
40C4×D4×C269C2211yescharacteristic
41C4⋊C8×C269C2211yescharacteristic
42#103×C269C2212yes—
43C2×Dic538—21no—
44C2×Dic538C2311yescharacteristic
45C2×C22⋊D269—21no—
46C2×C4×D269D411yescharacteristic
47C2×C4×D269D411yescharacteristic
48C2×C4×D269C2311yescharacteristic
49#16864392—42no—
50C2×#14524130C2312yes—
51C8×D269—42no—
52C4⋊Dic269—21no—
53C4⋊Dic269—21no—
54C4⋊Dic269—22no—
55C4⋊Dic269—21no—
56C4⋊Dic269C2312yes—
57C4⋊Dic269C2311yescharacteristic
58#16864381—21no—
59#16864381—22no—
60#16864381—21no—
61C22⋊Dic269—21no—
62C22⋊Dic269—21no—
63C22⋊Dic269—21no—
64#16864379—22no—
65#16864379—21no—
66C4×Dic269—22no—
67C4×Dic269—21no—
68C4×Dic269D411yescharacteristic
69C4×Dic269D411yescharacteristic
70C4×Dic269C2311yescharacteristic
71C2×Q8×C269C2312yes—
72C2×D4×C269C2311yescharacteristic
73C22×C4×C269—21no—
74SD16×C269—42no—
75C2×C8×C269C2312yes—
76C4⋊C4×C269—21no—
77C4⋊C4×C269—21no—
78C4⋊C4×C269C2311yescharacteristic
79C22⋊C4×C269—21no—
80C42×C269C2311yescharacteristic
81C22×D269C2×D411yescharacteristic
82Dic538—21no—
83Dic538—21no—
84Dic538—42no—
85C22⋊D269—42no—
86C2×Dic269—21no—
87C2×Dic269—22no—
88C2×Dic269—21no—
89C2×Dic269C2×D411yescharacteristic
90C2×Dic269C2×D411yescharacteristic
91C2×Dic269C2×D411yescharacteristic
92C4×D269—22no—
93C4×D269—22no—
94C4×D269—21no—
95C4×D269—21no—
96#14524130—22no—
97C23×C269—21no—
98Q8×C269—22no—
99Q8×C269—22no—
100D4×C269—21no—
101D4×C269—21no—
102C2×C4×C269—21no—
103C2×C4×C269—22no—
104C2×C4×C269—42no—
105C2×C4×C269C2×D411yescharacteristic
106C2×C4×C269C2×D411yescharacteristic
107C2×C4×C269C2411yescharacteristic
108C8×C269—22no—
109C22×C269—41no—
110C22×C269—41no—
111C22×C269—41no—
112C22×C269C22×D411yescharacteristic
113C2×D269—21no—
114C2×D269—21no—
115C2×D269#13712yes—
116C4×C269—21no—
117C4×C269—42no—
118C4×C269—41no—
119C4×C269#13512yes—
120C4×C269H(5,𝔽2)11yescharacteristic
121C4×C2692−1+411yescharacteristic
122Dic269—21no—
123Dic269—21no—
124Dic269—21no—
125Dic269—41no—
126Dic269—42no—
127Dic269—41no—
128C2×C269—81no—
129C2×C269#53711yescharacteristic
130C2×C269C2×#13511yescharacteristic
131C2×C269C2×#13711yescharacteristic
132D269—22no—
133C269#324811yescharacteristic, complemented, Sylow
134#3248—2691nomaximal, Sylow
135#533—2691no—
136#529—2691no—
137#479—2692no—
138#475—2691no—
139#474—2691no—
140#467—2692no—
141#465—2692no—
142#464—2692no—
143#462—2691no—
144#461D26911yescharacteristic, complemented
145C2×C4⋊C8—2691no—
146C2×Q16—2692no—
147C2×SD16C2×D26912yes—
148C22×C8—2692no—
149C4⋊Q8—2691no—
150C4⋊Q8C2×D26911yescharacteristic
151#126—5381no—
152#125—2691no—
153#125—5381no—
154#124—2691no—
155#123—5381no—
156C22⋊Q8—2692no—
157C22⋊Q8—2691no—
158C22⋊Q8—5381no—
159#121—2691no—
160C4×Q8—2692no—
161C4×Q8—2691no—
162C4×Q8—5381no—
163C4×D4—5381no—
164C4×D4C2×D26911yescharacteristic
165#117—5381no—
166#117—5381no—
167C2×C42—2691no—
168#107—2692no—
169#106—2692no—
170C4⋊C8—2692no—
171C4⋊C8—2691no—
172C4⋊C8C2×D26911yescharacteristic
173#103—2692no—
174#103—2692no—
175#103C2×D26912yes—
176#102—2692no—
177C2×Q8—2691no—
178C2×Q8—5381no—
179C2×Q8C22×D26912yes—
180C2×D4—5381no—
181C2×D4C22×D26911yescharacteristic
182C22×C4—21no—
183C22×C4—2691no—
184C22×C4—2691no—
185C22×C4—2691no—
186Q16—10762no—
187SD16—42no—
188C2×C8—2692no—
189C2×C8—10762no—
190C2×C8C22×D26912yes—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—2692no—
194C4⋊C4—2691no—
195C4⋊C4—5381no—
196C4⋊C4—5381no—
197C4⋊C4—5381no—
198C4⋊C4—5382no—
199C4⋊C4—5382no—
200C4⋊C4—5381no—
201C4⋊C4—5381no—
202C4⋊C4C22×D26911yescharacteristic
203C22⋊C4—21no—
204C22⋊C4—5382no—
205C22⋊C4—5381no—
206C22⋊C4—5381no—
207C22⋊C4—5381no—
208C22⋊C4—5381no—
209C42—2691no—
210C42—2691no—
211C42—2691no—
212C42—5382no—
213C42—5381no—
214C42C22×D26911yescharacteristic
215C23—21no—
216C23—2691no—
217Q8—22no—
218Q8—22no—
219Q8—5381no—
220Q8—5381no—
221Q8—10762no—
222D4—21no—
223D4—21no—
224D4—10762no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—2691no—
229C2×C4—2691no—
230C2×C4—2691no—
231C2×C4—5382no—
232C2×C4—5382no—
233C2×C4—5381no—
234C2×C4—5381no—
235C2×C4—5381no—
236C2×C4—5381no—
237C2×C4—5382no—
238C2×C4D4×D26911yescharacteristic
239C2×C4D4×D26911yescharacteristic
240C2×C4C23×D26911yescharacteristic
241C8—22no—
242C8—5382no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—2692no—
247C22—5381no—
248C22—5381no—
249C22C2×D4×D26911yescharacteristic
250C4—21no—
251C4—42no—
252C4—41no—
253C4—5381no—
254C4—5381no—
255C4—5381no—
256C4—10761no—
257C4—10761no—
258C4—10762no—
259C4#2257547412yes—
260C4#2257549811yescharacteristic
261C4#2257550011yescharacteristic
262C2—81no—
263C2—5382no—
264C2#3177118411yescharacteristic
265C2C2×#2257547411yescharacteristic
266C2#137×D26911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#461×C269C2
socleC22×C269C22×D4
prime radical#22575424C22
hypercenter#461D269
hypocenterC269#3248
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. #31771160C2semidirect
3. #31770910C2semidirect
4. #31770891C2semidirect
5. #31770885C2semidirect
6. #31770845C2semidirect
8. #31770825C2semidirect
9. #31770812C2semidirect
10. C4⋊C8×D269C2semidirect
11. #461×C269C2semidirect
133. C269#3248semidirect
144. #461D269semidirect

Maximal subgroups

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

subgroupindex
#317711602
#317711372
#317709102
#317708912
#317708852
#317708452
#317708312
#317708252
#317708122
C4⋊C8×D2692
#461×C2692
#3248269