Finite Group Databasebeta

← #46820248

Subgroups — #46820248

Order 34432.

698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×#22575501C211yesmaximal, characteristic, complemented
2#31771403C212yesmaximal, complemented
3#31770787C214yesmaximal, complemented
4#31770777C214yesmaximal, complemented
5#31770623C212yesmaximal, complemented
6C2×#22575372C211yesmaximal, characteristic, complemented
7#536×C269C211yesmaximal, characteristic, complemented
8#22575501—24no—
9#22575501—22no—
10#22575501C2214yes—
11C2×#16864403—22no—
12C2×#16864402—22no—
13C2×#16864402C2212yes—
14C2×Q8×D269—22no—
15#22575484C2214yescomplemented
16#22575483—22no—
17#22575479C2214yescomplemented
18#22575478—22no—
19#22575473—24no—
20C2×#16864386C2212yes—
21#22575381C2218yescomplemented
22#22575372C2214yescomplemented
23C2×#41×C269C2211yescharacteristic
24C22×Q8×C269C2211yescharacteristic
25C4⋊Q8×C269C2212yescomplemented
26#124×C269C2212yescomplemented
27#123×C269—22no—
28C22⋊Q8×C269—22no—
29#117×C269C2211yescharacteristic
30#16864403—28no—
31#16864403—28no—
32#16864402—28no—
33#16864402—28no—
34#16864402—22no—
35#16864402—22no—
36#16864402D414yes—
37#16864402C2314yes—
38C2×Dic538—22no—
39C2×Dic538D412yes—
40Q8×D269—28no—
41Q8×D269—28no—
42C2×D1076—22no—
43C2×D1076D412yes—
44C2×C22⋊D269—22no—
45C2×C4×D269—24no—
46C2×C4×D269—22no—
47#16864392—24no—
48#16864390—24no—
49#16864389—24no—
50#16864387—24no—
51#16864386—22no—
52#16864386C2314yes—
53C2×#14524130—22no—
54#41×C269—22no—
55#41×C269—22no—
56C2×Q8×C269—22no—
57C2×Q8×C269—22no—
58C2×Q8×C269D412yes—
59C2×Q8×C269C2311yescharacteristic
60C2×Q8×C269C2312yes—
61C2×D4×C269—21no—
62C2×D4×C269C2311yescharacteristic
63C22×C4×C269—21no—
64C22×C4×C269D412yes—
65C22×C4×C269C2311yescharacteristic
66C4⋊C4×C269—21no—
67C4⋊C4×C269—24no—
68C22⋊C4×C269—21no—
69C22⋊C4×C269—24no—
70C42×C269C2312yes—
71C22×D269—22no—
72Dic538—28no—
73Dic538—22no—
74Dic538C2×D414yes—
75D1076—28no—
76D1076—22no—
77D1076C2×D414yes—
78C22⋊D269—24no—
79C22⋊D269—24no—
80C2×Dic269—22no—
81C4×D269—216no—
82C4×D269—24no—
83C4×D269—24no—
84#14524130—24no—
85C23×C269—21no—
86C23×C269C2×D411yescharacteristic
87Q8×C269—24no—
88Q8×C269—24no—
89Q8×C269—22no—
90D4×C269—22no—
91D4×C269—41no—
92D4×C269—41no—
93C2×C4×C269—22no—
94C2×C4×C269—22no—
95C2×C4×C269—22no—
96C2×C4×C269—21no—
97C2×C4×C269—42no—
98C2×C4×C269C2×D412yes—
99C2×C4×C269C2×D412yes—
100C2×C4×C269C2×D414yes—
101C2×C4×C269C2×D411yescharacteristic
102C2×C4×C269C2411yescharacteristic
103C22×C269—41no—
104C22×C269—42no—
105C22×C269—41no—
106C22×C269#12011yescharacteristic
107C22×C269#12011yescharacteristic
108C22×C269C22×D411yescharacteristic
109C2×D269—24no—
110C2×D269—44no—
111C4×C269—24no—
112C4×C269—42no—
113C4×C269—41no—
114C4×C269#12012yes—
115C4×C269C22×D412yes—
116Dic269—24no—
117C2×C269—21no—
118C2×C269—21no—
119C2×C269—21no—
120C2×C269—81no—
121C2×C269C2×#12011yescharacteristic
122D269—44no—
123C269#302011yescharacteristic, complemented, Sylow
124#3020—2691nomaximal, Sylow
125C2×2−1+4—2691no—
126#575—2692no—
127#536D26911yescharacteristic, complemented
128#456—2694no—
129#454—2694no—
130#421—2692no—
131C2×#101—2691no—
1322−1+4—2694no—
1332−1+4—5384no—
1342−1+4—5382no—
135C2×#41—2692no—
136C2×#41—5382no—
137C2×#41—5382no—
138C2×#41C2×D26911yescharacteristic
139C22×Q8—5382no—
140C22×Q8C2×D26911yescharacteristic
141#137—2694no—
142#137—5382no—
143AGL(1,ℤ/8)—2694no—
144AGL(1,ℤ/8)—5382no—
145#135—5384no—
146C2×M16—2692no—
147C4⋊Q8C2×D26912yescomplemented
148#124C2×D26912yescomplemented
149#123—22no—
150C22⋊Q8—22no—
151#117C2×D26911yescharacteristic
152#104—2698no—
153#101—2694no—
154#41—22no—
155#41—22no—
156#41—2694no—
157#41—2694no—
158#41—5388no—
159#41—5388no—
160#41—5388no—
161#41—5382no—
162#41—5382no—
163#41—5388no—
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—2692no—
167C2×Q8—5382no—
168C2×Q8—5388no—
169C2×Q8—5388no—
170C2×Q8C22⋊D26912yes—
171C2×Q8C22×D26911yescharacteristic
172C2×Q8C22×D26912yes—
173C2×D4—21no—
174C2×D4—2692no—
175C2×D4—5382no—
176C2×D4—5382no—
177C2×D4C22×D26911yescharacteristic
178C22×C4—21no—
179C22×C4—5384no—
180C22×C4—5382no—
181C22×C4C22⋊D26912yes—
182C22×C4C22×D26911yescharacteristic
183Q16—5384no—
184SD16—5384no—
185SD16—5384no—
186D8—5384no—
187M16—2694no—
188M16—5382no—
189C2×C8—5382no—
190C4⋊C4—21no—
191C4⋊C4—24no—
192C22⋊C4—21no—
193C22⋊C4—24no—
194C42C22×D26912yes—
195C23—21no—
196C23—5382no—
197C23C2×C22⋊D26911yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—22no—
201Q8—2694no—
202Q8—5388no—
203Q8—5382no—
204D4—22no—
205D4—41no—
206D4—41no—
207D4—2694no—
208D4—5388no—
209D4—5384no—
210D4—5384no—
211D4—5382no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—53816no—
218C2×C4—5382no—
219C2×C4—5384no—
220C2×C4—5384no—
221C2×C4D4×D26912yes—
222C2×C4D4×D26912yes—
223C2×C4C2×C22⋊D26914yes—
224C2×C4C2×C22⋊D26911yescharacteristic
225C2×C4C23×D26911yescharacteristic
226C8—5384no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—5384no—
231C22—10764no—
232C22#2257542111yescharacteristic
233C22#2257542111yescharacteristic
234C22C22×C22⋊D26911yescharacteristic
235C4—24no—
236C4—42no—
237C4—41no—
238C4—5384no—
239C4#2257542112yes—
240C4C2×D4×D26912yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—81no—
245C2—10764no—
246C2C2×#2257542111yescharacteristic
subgroupG/H
centerC2C2×#22575421
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#536×C269C2
socleC2×C269C2×#120
hypercenter#536D269
hypocenterC269#3020
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#22575501C2semidirect
2. #31771403C2semidirect
3. #31770787C2semidirect
4. #31770777C2semidirect
5. #31770623C2semidirect
6. C2×#22575372C2semidirect
7. #536×C269C2semidirect
15. #22575484C22semidirect
17. #22575479C22semidirect
21. #22575381C22semidirect
22. #22575372C22semidirect
25. C4⋊Q8×C269C22semidirect
26. #124×C269C22semidirect
123. C269#3020semidirect
127. #536D269semidirect
147. C4⋊Q8C2×D269semidirect
148. #124C2×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225755012
#317714032
#317707872
#317707772
#317706232
C2×#225753722
#536×C2692
#3020269