Finite Group Databasebeta

← #46810812

Subgroups — #46810812

Order 34432.

584 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#16864403C211yesmaximal, characteristic
2C2×#22575372C211yesmaximal, characteristic, complemented
3C2×#22575369C212yesmaximal, complemented
4#31770568C212yesmaximal, complemented
5C2×#101×C269C211yesmaximal, characteristic, complemented
6C2×#16864403—24no—
7C2×#16864403—24no—
8C2×#16864403—22no—
9C2×#16864403—22no—
10C22×D1076C412yes—
11C22×D1076C2211yescharacteristic
12C22×C4×D269C412yes—
13C22×C4×D269C2211yescharacteristic
14C2×#16864386C2212yes—
15#22575372—22no—
16#22575369—24no—
17#22575365—24no—
18C22×Q8×C269C2211yescharacteristic
19C2×M16×C269C2212yes—
20#101×C269—22no—
21C23×D269C2×C412yes—
22C23×D269C2×C411yescharacteristic
23#16864403—216no—
24#16864403—216no—
25C2×D1076—24no—
26C2×D1076—24no—
27C2×D1076—24no—
28C2×D1076—22no—
29C2×D1076—21no—
30C2×D1076—21no—
31C2×D1076D414yes—
32C22×Dic269C2×C411yescharacteristic
33C2×C4×D269—24no—
34C2×C4×D269—24no—
35C2×C4×D269—24no—
36C2×C4×D269—22no—
37C2×C4×D269—21no—
38C2×C4×D269—21no—
39C2×C4×D269D414yes—
40#16864386—22no—
41#16864386—22no—
42C2×#14524130—22no—
43C2×Q8×C269—22no—
44C2×Q8×C269—22no—
45C2×Q8×C269D412yes—
46C2×Q8×C269D412yes—
47C22×C4×C269C2×C412yes—
48C22×C4×C269C2311yescharacteristic
49M16×C269—22no—
50M16×C269—22no—
51C2×C8×C269—22no—
52C22×D269—21no—
53C22×D269—22no—
54C22×D269—22no—
55C22×D269—21no—
56C22×D269—42no—
57C22×D269—44no—
58C22×D269C22⋊C412yes—
59C22×D269C22⋊C414yes—
60D1076—216no—
61D1076—24no—
62D1076—24no—
63C2×Dic269—21no—
64C2×Dic269—21no—
65C2×Dic269C22⋊C412yes—
66C4×D269—216no—
67C4×D269—24no—
68C4×D269—24no—
69#14524130—42no—
70C23×C269C22×C411yescharacteristic
71Q8×C269—24no—
72Q8×C269—24no—
73C2×C4×C269—22no—
74C2×C4×C269—22no—
75C2×C4×C269C22⋊C414yes—
76C2×C4×C269C2×D412yes—
77C2×C4×C269C2×D412yes—
78C2×C4×C269C2×D411yescharacteristic
79C2×C4×C269C2×D411yescharacteristic
80C8×C269—42no—
81C22×C269—22no—
82C22×C269C2×C22⋊C411yescharacteristic
83C22×C269C2×C22⋊C411yescharacteristic
84C22×C269C2×C22⋊C411yescharacteristic
85C2×D269—22no—
86C2×D269—24no—
87C2×D269—24no—
88C2×D269—42no—
89C2×D269—42no—
90C2×D269—44no—
91C2×D269—44no—
92C2×D269—44no—
93C4×C269—24no—
94C4×C269#12012yes—
95C4×C269#12012yes—
96Dic269—22no—
97C2×C269—21no—
98C2×C269—21no—
99C2×C269#37911yescharacteristic
100C2×C269#41312yes—
101D269—42no—
102D269—44no—
103C269#178511yescharacteristic, complemented, Sylow
104#1785—2691nomaximal, Sylow
105C22×#41—2691no—
106C2×#101—2691no—
107C2×#101D26911yescharacteristic, complemented
108C2×#100—2692no—
109#407—2692no—
110C2×#41—5384no—
111C2×#41—5384no—
112C2×#41—5382no—
113C2×#41—5382no—
114C22×Q8C2×D26911yescharacteristic
115C22×D4—2692no—
116C22×D4—2691no—
117C23×C4—2691no—
118C23×C4—2692no—
119C2×M16—2692no—
120C2×M16C2×D26912yes—
121#101—22no—
122#101—5382no—
123#100—5384no—
124C22⋊C8—5384no—
125C24—2691no—
126C24—2692no—
127#41—53816no—
128#41—53816no—
129C2×Q8—22no—
130C2×Q8—22no—
131C2×Q8C22⋊D26912yes—
132C2×Q8D107612yes—
133C2×D4—2694no—
134C2×D4—5384no—
135C2×D4—5384no—
136C2×D4—5384no—
137C2×D4—5382no—
138C2×D4—5381no—
139C2×D4—5381no—
140C22×C4—2691no—
141C22×C4—2694no—
142C22×C4—5384no—
143C22×C4—5384no—
144C22×C4—5384no—
145C22×C4—5382no—
146C22×C4—5381no—
147C22×C4—5381no—
148C22×C4C4×D26912yes—
149C22×C4C22×D26911yescharacteristic
150M16—22no—
151M16—22no—
152M16—5382no—
153M16—5382no—
154C2×C8—22no—
155C2×C8—5382no—
156C23—2692no—
157C23—2694no—
158C23—5381no—
159C23—5382no—
160C23—5382no—
161C23—5381no—
162C23—10762no—
163C23—10764no—
164C23C2×C4×D26911yescharacteristic
165Q8—24no—
166Q8—24no—
167D4—53816no—
168D4—5384no—
169D4—5384no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—2692no—
173C2×C4—53816no—
174C2×C4—5381no—
175C2×C4—5381no—
176C2×C4—5384no—
177C2×C4—5384no—
178C2×C4#1686437914yes—
179C2×C4D4×D26912yes—
180C2×C4D4×D26912yes—
181C2×C4C2×C22⋊D26911yescharacteristic
182C2×C4C2×D107611yescharacteristic
183C8—42no—
184C8—10762no—
185C22—22no—
186C22—5382no—
187C22—5384no—
188C22—5384no—
189C22—10764no—
190C22—10762no—
191C22—10762no—
192C22—10764no—
193C22—10764no—
194C22C22⋊C4×D26911yescharacteristic
195C22C22⋊C4×D26911yescharacteristic
196C22C2×#1686437911yescharacteristic
197C4—24no—
198C4—5382no—
199C4#2257542112yes—
200C4#2257542312yes—
201C2—21no—
202C2—21no—
203C2—10762no—
204C2—10764no—
205C2#3177046011yescharacteristic
206C2#3177058812yes—
subgroupG/H
centerC22C22⋊C4×D269
commutatorC23×C269C22×C4
FrattiniC22×C4C22×D269
FittingC2×#101×C269C2
socleC22×C269C2×C22⋊C4
prime radicalC22×#16864403C2
cosocleC22×C4×C269C23
hypercenterC2×#101D269
hypocenterC269#1785
LCSG ▷ C23×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#22575372C2semidirect
3. C2×#22575369C2semidirect
4. #31770568C2semidirect
5. C2×#101×C269C2semidirect
103. C269#1785semidirect
107. C2×#101D269semidirect

Maximal subgroups

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

subgroupindex
C22×#168644032
C2×#225753722
C2×#225753692
#317705682
C2×#101×C2692
#1785269