Finite Group Databasebeta

← #46819256

Subgroups — #46819256

Order 34432.

524 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 153 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×#22575444C211yesmaximal, characteristic, complemented
2C2×#22575440C211yesmaximal, characteristic
3#31770511C211yesmaximal, characteristic, complemented
4#31770510C211yesmaximal, characteristic, complemented
5#31770508C211yesmaximal, characteristic
6#31770498C214yesmaximal, complemented
7#31770493C214yesmaximal, complemented
8C42×Dic269C211yesmaximal, characteristic, complemented
9#390×C269C211yesmaximal, characteristic
10C22×Dic538C2211yescharacteristic
11#22575444—24no—
12#22575440—24no—
13C2×C4⋊Dic269C2212yes—
14C2×C4⋊Dic269C2211yescharacteristic
15C2×#16864381C2212yes—
16C2×C22⋊Dic269C2212yes—
17C2×C22⋊Dic269C2214yes—
18C2×C22⋊Dic269C2212yes—
19C2×C4×Dic269C2212yes—
20C2×C4×Dic269C2212yes—
21C2×C4×Dic269C2211yescharacteristic
22C2×C4×Dic269C2211yescharacteristic
23#22575360C2214yes—
24#22575360C2214yes—
25C22×D4×C269C2211yescharacteristic
26C2×C4⋊C4×C269C2211yescharacteristic
27C2×C22⋊C4×C269C2214yes—
28C2×C42×C269C2211yescharacteristic
29C2×Dic538—22no—
30C2×Dic538—22no—
31C2×Dic538—22no—
32C22×Dic269C2312yes—
33C22×Dic269C2312yes—
34C22×Dic269C2311yescharacteristic
35C22×Dic269C2311yescharacteristic
36C22×Dic269C2312yes—
37C4⋊Dic269—24no—
38C4⋊Dic269—22no—
39#16864381—24no—
40C22⋊Dic269—24no—
41C22⋊Dic269—24no—
42C22⋊Dic269—28no—
43C4×Dic269—24no—
44C4×Dic269—24no—
45C4×Dic269—22no—
46C4×Dic269D414yes—
47C24×C269C2312yes—
48C2×D4×C269—22no—
49C2×D4×C269—22no—
50C2×D4×C269—22no—
51C22×C4×C269C2312yes—
52C22×C4×C269C2312yes—
53C22×C4×C269C2311yescharacteristic
54C4⋊C4×C269—22no—
55C22⋊C4×C269—28no—
56C42×C269—22no—
57Dic538—44no—
58C2×Dic269—22no—
59C2×Dic269—22no—
60C2×Dic269—22no—
61C2×Dic269—22no—
62C2×Dic269—22no—
63C2×Dic269—22no—
64C2×Dic269—24no—
65C2×Dic269—22no—
66C2×Dic269—22no—
67C2×Dic269C2×D412yes—
68C2×Dic269C2×D412yes—
69C2×Dic269#4114yes—
70C23×C269—22no—
71C23×C269—24no—
72C23×C269—22no—
73C23×C269—22no—
74C23×C269—24no—
75C23×C269C2411yescharacteristic
76D4×C269—44no—
77C2×C4×C269—22no—
78C2×C4×C269—22no—
79C2×C4×C269—22no—
80C2×C4×C269—24no—
81C2×C4×C269C2×D412yes—
82C2×C4×C269#4114yes—
83C2×C4×C269#4112yes—
84C2×C4×C269#4112yes—
85C22×C269—42no—
86C22×C269—44no—
87C22×C269—44no—
88C22×C269—42no—
89C22×C269—42no—
90C22×C269C22×D411yescharacteristic
91C22×C269C2×#4112yes—
92C22×C269C2×#4111yescharacteristic
93C22×C269C2×#4112yes—
94C22×C269C2×#4111yescharacteristic
95C4×C269—24no—
96C4×C269—42no—
97C4×C269#12414yes—
98Dic269—24no—
99Dic269—22no—
100Dic269—22no—
101Dic269—42no—
102Dic269—42no—
103C2×C269—82no—
104C2×C269C2×#12411yescharacteristic
105C2×C269#52912yes—
106C2×C269#52912yes—
107C2×C269#53211yescharacteristic
108C2×C269#53211yescharacteristic
109C269#286111yescharacteristic, complemented, Sylow
110#2861—2691nomaximal, Sylow
111C2×#125—2691no—
112C2×#124—2691no—
113#391—2691no—
114#391—2691no—
115#390—2691no—
116#390D26911yescharacteristic
117#388—2694no—
118#388—2694no—
119C43—2691no—
120C22×Q8—2691no—
121C22×D4C2×D26911yescharacteristic
122#125—5384no—
123#124—5384no—
124C2×C4⋊C4—2692no—
125C2×C4⋊C4—2692no—
126C2×C4⋊C4—2691no—
127C2×C4⋊C4C2×D26911yescharacteristic
128C2×C22⋊C4—2692no—
129C2×C22⋊C4—2692no—
130C2×C22⋊C4—2694no—
131C2×C22⋊C4C2×D26914yes—
132C2×C42—2691no—
133C2×C42—2692no—
134C2×C42—2692no—
135C2×C42—2691no—
136C2×C42C2×D26911yescharacteristic
137#95—2694no—
138#95—2694no—
139C24C22×D26912yes—
140C2×Q8—5382no—
141C2×Q8—5382no—
142C2×Q8—5382no—
143C2×D4—22no—
144C2×D4—22no—
145C2×D4—22no—
146C22×C4—2692no—
147C22×C4—2691no—
148C22×C4—2691no—
149C22×C4—2692no—
150C22×C4—2692no—
151C22×C4C22×D26912yes—
152C22×C4C22×D26912yes—
153C22×C4C22×D26911yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—5384no—
156C4⋊C4—5384no—
157C4⋊C4—5382no—
158C22⋊C4—28no—
159C22⋊C4—5384no—
160C22⋊C4—5384no—
161C22⋊C4—5388no—
162C42—22no—
163C42—2694no—
164C42—5384no—
165C42—5384no—
166C42—5382no—
167C23—22no—
168C23—24no—
169C23—24no—
170C23—22no—
171C23—22no—
172C23C23×D26911yescharacteristic
173Q8—10764no—
174D4—44no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—24no—
179C2×C4—2692no—
180C2×C4—2692no—
181C2×C4—2694no—
182C2×C4—5382no—
183C2×C4—5382no—
184C2×C4—5382no—
185C2×C4—5382no—
186C2×C4—5382no—
187C2×C4—5382no—
188C2×C4—5384no—
189C2×C4—5382no—
190C2×C4—5382no—
191C2×C4D4×D26912yes—
192C2×C4#1686440114yes—
193C2×C4#1686440112yes—
194C2×C4#1686440212yes—
195C22—44no—
196C22—44no—
197C22—42no—
198C22—42no—
199C22—42no—
200C22C2×D4×D26911yescharacteristic
201C22#41×D26912yes—
202C22C2×#1686440111yescharacteristic
203C22C2×#1686440112yes—
204C22C2×#1686440211yescharacteristic
205C4—24no—
206C4—42no—
207C4—5384no—
208C4—5382no—
209C4—5382no—
210C4—10762no—
211C4—10762no—
212C4#2257543914yes—
213C2—82no—
214C2C2×#2257543911yescharacteristic
215C2#3177113612yes—
216C2#3177113712yes—
217C2#3177115311yescharacteristic
218C2#3177115411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutator, socle, cosocleC23×C269C24
Fitting#390×C269C2
prime radicalC22×D4×C269C22
hypercenter#390D269
hypocenterC269#2861
LCSG ▷ C23×C269 ▷ C269
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#22575444C2semidirect
3. #31770511C2semidirect
4. #31770510C2semidirect
6. #31770498C2semidirect
7. #31770493C2semidirect
8. C42×Dic269C2semidirect
109. C269#2861semidirect

Maximal subgroups

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

subgroupindex
C2×#225754442
C2×#225754402
#317705112
#317705102
#317705082
#317704982
#317704932
C42×Dic2692
#390×C2692
#2861269