Finite Group Databasebeta

← #46819259

Subgroups — #46819259

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×#22575442C211yesmaximal, characteristic
3#31770512C211yesmaximal, characteristic, complemented
4#31770507C211yesmaximal, characteristic
5#31770506C211yesmaximal, characteristic
6#31770497C214yesmaximal, complemented
7#31770494C214yesmaximal, complemented
8C42×Dic269C211yesmaximal, characteristic, complemented
9#391×C269C211yesmaximal, characteristic, complemented
10C22×D1076C2211yescharacteristic
11#22575444—24no—
12#22575442—24no—
13C2×C4⋊Dic269C2212yes—
14C2×C4⋊Dic269C2211yescharacteristic
15C2×#16864381C2212yes—
16C2×#16864379C2212yes—
17C2×#16864379C2214yes—
18C2×#16864379C2214yes—
19C2×#16864379C2212yes—
20C2×C4×Dic269C2212yes—
21C2×C4×Dic269C2212yes—
22C2×C4×Dic269C2211yescharacteristic
23C2×C4×Dic269C2211yescharacteristic
24#22575360C2214yes—
25C22×Q8×C269C2211yescharacteristic
26C2×C4⋊C4×C269C2211yescharacteristic
27C2×C42×C269C2211yescharacteristic
28#95×C269C2214yes—
29C23×D269C2312yes—
30C2×D1076—22no—
31C2×D1076—22no—
32C2×D1076—22no—
33C22×Dic269C2312yes—
34C22×Dic269C2311yescharacteristic
35C22×Dic269C2311yescharacteristic
36C22×Dic269C2312yes—
37C4⋊Dic269—24no—
38C4⋊Dic269—22no—
39#16864381—24no—
40#16864379—24no—
41#16864379—24no—
42#16864379—28no—
43#16864379—28no—
44C4×Dic269—24no—
45C4×Dic269—22no—
46C4×Dic269—24no—
47C4×Dic269D414yes—
48C2×Q8×C269—22no—
49C2×Q8×C269—22no—
50C2×Q8×C269—22no—
51C22×C4×C269C2312yes—
52C22×C4×C269C2312yes—
53C22×C4×C269C2312yes—
54C22×C4×C269C2311yescharacteristic
55C4⋊C4×C269—22no—
56C42×C269—22no—
57C22×D269—22no—
58C22×D269—24no—
59C22×D269—24no—
60C22×D269—22no—
61C22×D269—22no—
62D1076—44no—
63C2×Dic269—22no—
64C2×Dic269—22no—
65C2×Dic269—22no—
66C2×Dic269—22no—
67C2×Dic269—22no—
68C2×Dic269—24no—
69C2×Dic269C2×D412yes—
70C2×Dic269C2×D412yes—
71C2×Dic269#4114yes—
72C23×C269C2411yescharacteristic
73Q8×C269—44no—
74C2×C4×C269—22no—
75C2×C4×C269—22no—
76C2×C4×C269—22no—
77C2×C4×C269—22no—
78C2×C4×C269—22no—
79C2×C4×C269—22no—
80C2×C4×C269—24no—
81C2×C4×C269C2×D412yes—
82C2×C4×C269#4112yes—
83C2×C4×C269#4112yes—
84C2×C4×C269#4114yes—
85C22×C269C22×D411yescharacteristic
86C22×C269C2×#4112yes—
87C22×C269C2×#4111yescharacteristic
88C22×C269C2×#4111yescharacteristic
89C22×C269C2×#4112yes—
90C2×D269—42no—
91C2×D269—44no—
92C2×D269—44no—
93C2×D269—42no—
94C2×D269—42no—
95C4×C269—24no—
96C4×C269—42no—
97C4×C269—42no—
98C4×C269#12414yes—
99Dic269—24no—
100Dic269—22no—
101Dic269—22no—
102Dic269—42no—
103C2×C269C2×#12411yescharacteristic
104C2×C269#52912yes—
105C2×C269#52912yes—
106C2×C269#53211yescharacteristic
107C2×C269#53211yescharacteristic
108D269—82no—
109C269#286111yescharacteristic, complemented, Sylow
110#2861—2691nomaximal, Sylow
111C2×#125—2691no—
112C2×#124—2691no—
113#391—2691no—
114#391D26911yescharacteristic, complemented
115#390—2691no—
116#390—2691no—
117#388—2694no—
118#388—2694no—
119C43—2691no—
120C22×Q8C2×D26911yescharacteristic
121C22×D4—2691no—
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⋊C4—2694no—
132C2×C42—2691no—
133C2×C42—2692no—
134C2×C42—2692no—
135C2×C42—2691no—
136C2×C42C2×D26911yescharacteristic
137#95—2694no—
138#95C2×D26914yes—
139C24—2692no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—22no—
143C2×D4—5382no—
144C2×D4—5382no—
145C2×D4—5382no—
146C22×C4—2692no—
147C22×C4—2691no—
148C22×C4—2691no—
149C22×C4—2692no—
150C22×C4C22×D26912yes—
151C22×C4C22×D26912yes—
152C22×C4C22×D26912yes—
153C22×C4C22×D26911yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—5384no—
156C4⋊C4—5384no—
157C4⋊C4—5382no—
158C22⋊C4—5388no—
159C22⋊C4—5384no—
160C22⋊C4—5384no—
161C22⋊C4—5388no—
162C42—22no—
163C42—2694no—
164C42—5384no—
165C42—5382no—
166C42—5384no—
167C23—5382no—
168C23—5384no—
169C23—5382no—
170C23—5382no—
171C23—5384no—
172C23C23×D26911yescharacteristic
173Q8—44no—
174D4—10764no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—2692no—
183C2×C4—2692no—
184C2×C4—2694no—
185C2×C4—5382no—
186C2×C4—5382no—
187C2×C4—5382no—
188C2×C4—5382no—
189C2×C4—5382no—
190C2×C4—5384no—
191C2×C4D4×D26912yes—
192C2×C4#1686440112yes—
193C2×C4#1686440212yes—
194C2×C4#1686440314yes—
195C22—10764no—
196C22—10764no—
197C22—10762no—
198C22—10762no—
199C22—10762no—
200C22C2×D4×D26911yescharacteristic
201C22#41×D26912yes—
202C22C2×#1686440111yescharacteristic
203C22C2×#1686440211yescharacteristic
204C22C2×#1686440312yes—
205C4—24no—
206C4—42no—
207C4—42no—
208C4—5384no—
209C4—5382no—
210C4—5382no—
211C4—10762no—
212C4#2257543914yes—
213C2—21522no—
214C2C2×#2257543911yescharacteristic
215C2#3177114112yes—
216C2#3177114212yes—
217C2#3177115411yescharacteristic
218C2#3177115611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutator, socle, cosocleC23×C269C24
Fitting#391×C269C2
prime radicalC22×D1076C22
hypercenter#391D269
hypocenterC269#2861
LCSG ▷ C23×C269 ▷ C269
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#22575444C2semidirect
3. #31770512C2semidirect
6. #31770497C2semidirect
7. #31770494C2semidirect
8. C42×Dic269C2semidirect
9. #391×C269C2semidirect
109. C269#2861semidirect
114. #391D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754442
C2×#225754422
#317705122
#317705072
#317705062
#317704972
#317704942
C42×Dic2692
#391×C2692
#2861269