Finite Group Databasebeta

← #46811411

Subgroups — #46811411

Order 34432.

344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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#31771371C211yesmaximal, characteristic, complemented
2#31771174C211yesmaximal, characteristic
3#31770611C211yesmaximal, characteristic, complemented
4#31770609C211yesmaximal, characteristic, complemented
5#31770578C211yesmaximal, characteristic, complemented
6#31770361C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C269C211yesmaximal, characteristic, complemented
8C2×#16864402C2211yescharacteristic
9C22×D1076C2211yescharacteristic
10#22575461—22no—
11#22575459—22no—
12C2×#16864386C2211yescharacteristic
13M16×D269—22no—
14#22575450C412yescomplemented
15#22575441C412yescomplemented
16#22575428—22no—
17#22575423—22no—
18#22575412C2211yescharacteristic
19#22575375—22no—
20#22575373—22no—
21#22575367—22no—
22C2×M16×C269C2211yescharacteristic
23#117×C269C2211yescharacteristic
24#117×C269C2211yescharacteristic
25C23×D269—21no—
26#16864402—21no—
27#16864402—21no—
28#16864402—21no—
29#16864402—21no—
30C2×Dic538C2×C411yescharacteristic
31C2×D1076—24no—
32C2×D1076—21no—
33C2×D1076—21no—
34C2×D1076—21no—
35C2×D1076—21no—
36C2×D1076—21no—
37C2×D1076C2×C412yes—
38C2×D1076C2×C411yescharacteristic
39C2×C22⋊D269D412yes—
40C2×C4×D269D412yes—
41#16864386—21no—
42#16864386—21no—
43#16864385—24no—
44C2×#14524130D412yescomplemented
45C8×D269—24no—
46C4⋊Dic269—21no—
47C22⋊Dic269—21no—
48#16864379—24no—
49C4×Dic269—21no—
50C22×C4×C269C2311yescharacteristic
51M16×C269—21no—
52M16×C269—21no—
53C2×C8×C269D412yescomplemented
54C4⋊C4×C269—21no—
55C4⋊C4×C269—21no—
56C22⋊C4×C269—21no—
57C22⋊C4×C269—21no—
58C42×C269—21no—
59C42×C269C2×C412yes—
60C22×D269—22no—
61C22×D269—41no—
62C22×D269—41no—
63C22×D269—82no—
64C22×D269C22⋊C412yes—
65Dic538—21no—
66Dic538—21no—
67D1076—21no—
68D1076—21no—
69D1076—22no—
70D1076—22no—
71D1076—41no—
72D1076—41no—
73D1076—84no—
74C22⋊D269—22no—
75C22⋊D269—22no—
76C2×Dic269—41no—
77C2×Dic269C22⋊C412yes—
78C4×D269—22no—
79C4×D269—22no—
80#14524130—22no—
81C23×C269C2×D411yescharacteristic
82C2×C4×C269—22no—
83C2×C4×C269—41no—
84C2×C4×C269C22×C411yescharacteristic
85C2×C4×C269C2×D411yescharacteristic
86C2×C4×C269C2×D411yescharacteristic
87C2×C4×C269C2×D411yescharacteristic
88C2×C4×C269#4111yescharacteristic
89C2×C4×C269#4111yescharacteristic
90C8×C269—22no—
91C22×C269—41no—
92C22×C269C2×C22⋊C411yescharacteristic
93C22×C269#12111yescharacteristic
94C22×C269#12111yescharacteristic
95C2×D269—22no—
96C2×D269—42no—
97C2×D269—44no—
98C2×D269—42no—
99C2×D269—82no—
100C2×D269—82no—
101C4×C269—42no—
102C4×C269—81no—
103C4×C269C4×D411yescharacteristic
104C4×C269C4×D411yescharacteristic
105C4×C269#12011yescharacteristic
106C4×C269#12311yescharacteristic
107Dic269—22no—
108Dic269—81no—
109C2×C269—21no—
110C2×C269—21no—
111C2×C269—21no—
112C2×C269#38611yescharacteristic
113D269—42no—
114D269—82no—
115C269#191011yescharacteristic, complemented, Sylow
116#1910—2691nomaximal, Sylow
117#568—2691no—
118#535—2691no—
119#418—2691no—
120#418—2691no—
121#410—2691no—
122H(3,ℤ/4)—2691no—
123H(3,ℤ/4)D26911yescharacteristic, complemented
124C2×#41—2691no—
125C22×D4—2691no—
126#131—5382no—
127#131—5382no—
128C2×M16—2691no—
129C2×M16—5382no—
130C2×M16C2×D26911yescharacteristic
131#127—2692no—
132#124—2692no—
133#121—5382no—
134#120—5382no—
135#117—2691no—
136#117C2×D26911yescharacteristic
137#117C2×D26911yescharacteristic
138#102—5382no—
139#102—5382no—
140#99—5382no—
141C24—5381no—
142#41—5381no—
143#41—5381no—
144#41—5381no—
145#41—5381no—
146C2×Q8—2691no—
147C2×D4—2692no—
148C2×D4—2691no—
149C2×D4—2692no—
150C2×D4—5384no—
151C2×D4—5381no—
152C2×D4—5381no—
153C2×D4—5381no—
154C2×D4—5381no—
155C2×D4—5381no—
156C22×C4—2692no—
157C22×C4C22×D26911yescharacteristic
158M16—21no—
159M16—21no—
160M16—5384no—
161M16—5381no—
162M16—5381no—
163C2×C8—2692no—
164C2×C8—5384no—
165C2×C8D107612yescomplemented
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—5381no—
169C22⋊C4—21no—
170C22⋊C4—21no—
171C22⋊C4—5384no—
172C22⋊C4—5381no—
173C42—21no—
174C42—5381no—
175C42C4×D26912yes—
176C23—2692no—
177C23—5382no—
178C23—10761no—
179C23—10761no—
180C23—21522no—
181C23D4×D26911yescharacteristic
182Q8—5381no—
183Q8—5381no—
184D4—5382no—
185D4—5382no—
186D4—5381no—
187D4—5382no—
188D4—5381no—
189D4—5382no—
190D4—10761no—
191D4—10761no—
192D4—21524no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—2692no—
196C2×C4—5382no—
197C2×C4—5382no—
198C2×C4—10761no—
199C2×C4C2×C4×D26911yescharacteristic
200C2×C4D4×D26911yescharacteristic
201C2×C4D4×D26911yescharacteristic
202C2×C4C2×D107611yescharacteristic
203C2×C4#1686440211yescharacteristic
204C2×C4#1686440311yescharacteristic
205C8—22no—
206C8—5382no—
207C22—41no—
208C22—5382no—
209C22—10762no—
210C22—10764no—
211C22—10762no—
212C22—21522no—
213C22—21522no—
214C22C22⋊C4×D26911yescharacteristic
215C22#2257542611yescharacteristic
216C22#2257542811yescharacteristic
217C4—42no—
218C4—81no—
219C4—5382no—
220C4—21521no—
221C4#2257541511yescharacteristic
222C4C4×D107611yescharacteristic
223C4#2257542311yescharacteristic
224C4#2257543811yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—10762no—
229C2—21522no—
230C2#3177048311yescharacteristic
subgroupG/H
centerC2#31770483
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
FittingH(3,ℤ/4)×C269C2
socleC2×C269#386
prime radical#31771174C2
cosocleC22×C4×C269C23
hypercenterH(3,ℤ/4)D269
hypocenterC269#1910
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #31771371C2semidirect
3. #31770611C2semidirect
4. #31770609C2semidirect
5. #31770578C2semidirect
6. #31770361C2semidirect
7. H(3,ℤ/4)×C269C2semidirect
14. #22575450C4semidirect
15. #22575441C4semidirect
44. C2×#14524130D4semidirect
53. C2×C8×C269D4semidirect
115. C269#1910semidirect
123. H(3,ℤ/4)D269semidirect
165. C2×C8D1076semidirect

Maximal subgroups

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

subgroupindex
#317713712
#317711742
#317706112
#317706092
#317705782
#317703612
H(3,ℤ/4)×C2692
#1910269