Finite Group Databasebeta

← #46811416

Subgroups — #46811416

Order 34432.

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

normal subgroups only

This group has 362 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#31771174C211yesmaximal, characteristic
2#31771079C211yesmaximal, characteristic, complemented
3#31770623C211yesmaximal, characteristic, complemented
4#31770621C211yesmaximal, characteristic, complemented
5C2×#22575369C211yesmaximal, characteristic, complemented
6#31770361C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C269C211yesmaximal, characteristic, complemented
8C2×#16864402C2211yescharacteristic
9C22×D1076C2211yescharacteristic
10C2×#16864386C2211yescharacteristic
11#22575450C412yescomplemented
12#22575441C412yescomplemented
13#22575428—22no—
14#22575423—22no—
15C4×D1076—22no—
16#22575415—22no—
17#22575412C2211yescharacteristic
18C22⋊C4×D269—22no—
19#22575381—22no—
20#22575379—22no—
21#22575369—22no—
22C2×M16×C269C2211yescharacteristic
23#117×C269C2211yescharacteristic
24#117×C269C2211yescharacteristic
25C23×D269D412yes—
26#16864402—21no—
27#16864402—21no—
28#16864402—21no—
29#16864402—21no—
30C2×Dic538C2×C411yescharacteristic, complemented
31C2×D1076—24no—
32C2×D1076—21no—
33C2×D1076—21no—
34C2×D1076—21no—
35C2×D1076—21no—
36C2×D1076C2×C412yes—
37C2×D1076C2×C411yescharacteristic, complemented
38C2×D1076D412yes—
39C2×C22⋊D269—21no—
40C2×C4×D269—24no—
41C2×C4×D269—21no—
42#16864386—21no—
43#16864386—21no—
44C2×#14524130—21no—
45C4⋊Dic269—21no—
46C22⋊Dic269—21no—
47#16864379—24no—
48#16864379—24no—
49C4×Dic269D412yescomplemented
50C22×C4×C269C2311yescharacteristic
51M16×C269—21no—
52M16×C269—21no—
53C2×C8×C269—21no—
54C4⋊C4×C269—21no—
55C4⋊C4×C269—21no—
56C22⋊C4×C269—21no—
57C22⋊C4×C269—21no—
58C42×C269C2×C412yescomplemented
59C42×C269D412yescomplemented
60C22×D269—22no—
61C22×D269—22no—
62C22×D269—21no—
63C22×D269—82no—
64C22×D269C22⋊C414yes—
65Dic538—21no—
66Dic538—21no—
67D1076—22no—
68D1076—22no—
69D1076—21no—
70D1076—21no—
71D1076—22no—
72D1076—22no—
73D1076—84no—
74C22⋊D269—41no—
75C22⋊D269—41no—
76C2×Dic269—21no—
77C2×Dic269—22no—
78C4×D269—41no—
79C4×D269—41no—
80C4×D269—84no—
81#14524130—41no—
82C23×C269C2×D411yescharacteristic
83C2×C4×C269—22no—
84C2×C4×C269—22no—
85C2×C4×C269C22×C411yescharacteristic
86C2×C4×C269C2×D411yescharacteristic
87C2×C4×C269C2×D411yescharacteristic
88C2×C4×C269C2×D411yescharacteristic
89C2×C4×C269#4111yescharacteristic
90C2×C4×C269#4111yescharacteristic
91C8×C269—41no—
92C22×C269—41no—
93C22×C269C2×C22⋊C411yescharacteristic
94C22×C269#12011yescharacteristic
95C22×C269#12311yescharacteristic
96C2×D269—24no—
97C2×D269—44no—
98C2×D269—44no—
99C2×D269—42no—
100C2×D269—41no—
101C2×D269—82no—
102C4×C269—42no—
103C4×C269—42no—
104C4×C269C4×D411yescharacteristic
105C4×C269C4×D411yescharacteristic
106C4×C269#12111yescharacteristic
107C4×C269#12111yescharacteristic
108Dic269—42no—
109Dic269—41no—
110C2×C269—21no—
111C2×C269—21no—
112C2×C269—21no—
113C2×C269#38611yescharacteristic
114D269—44no—
115D269—81no—
116C269#191111yescharacteristic, complemented, Sylow
117#1911—2691nomaximal, Sylow
118#535—2691no—
119#518—2691no—
120#421—2691no—
121#421—2691no—
122C2×#100—2691no—
123H(3,ℤ/4)—2691no—
124H(3,ℤ/4)D26911yescharacteristic, complemented
125C2×#41—2691no—
126C22×D4—2691no—
127C2×M16—2691no—
128C2×M16C2×D26911yescharacteristic
129#127—2692no—
130#124—2692no—
131#121—5382no—
132#120—5382no—
133C4×D4—5382no—
134C4×D4—5382no—
135#117—2691no—
136#117C2×D26911yescharacteristic
137#117C2×D26911yescharacteristic
138C2×C22⋊C4—5382no—
139#104—5382no—
140#104—5382no—
141#100—5382no—
142C24—2692no—
143#41—5381no—
144#41—5381no—
145#41—5381no—
146#41—5381no—
147C2×Q8—2691no—
148C2×D4—2692no—
149C2×D4—2691no—
150C2×D4—2692no—
151C2×D4—5384no—
152C2×D4—5381no—
153C2×D4—5381no—
154C2×D4—5381no—
155C2×D4—5381no—
156C2×D4—5381no—
157C22×C4—5384no—
158C22×C4—5381no—
159C22×C4C22×D26911yescharacteristic
160M16—21no—
161M16—21no—
162M16—5381no—
163M16—5381no—
164C2×C8—21no—
165C2×C8—5381no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—5381no—
169C22⋊C4—21no—
170C22⋊C4—21no—
171C22⋊C4—5384no—
172C22⋊C4—5384no—
173C22⋊C4—5381no—
174C42—2692no—
175C42C4×D26912yescomplemented
176C42D107612yescomplemented
177C23—2694no—
178C23—5382no—
179C23—5382no—
180C23—5381no—
181C23—21522no—
182C23D4×D26911yescharacteristic
183Q8—5381no—
184Q8—5381no—
185D4—5382no—
186D4—5381no—
187D4—5382no—
188D4—5381no—
189D4—5382no—
190D4—5382no—
191D4—10761no—
192D4—10761no—
193D4—21524no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—5381no—
197C2×C4—5382no—
198C2×C4—10761no—
199C2×C4—10761no—
200C2×C4—21524no—
201C2×C4C2×C4×D26911yescharacteristic
202C2×C4D4×D26911yescharacteristic
203C2×C4D4×D26911yescharacteristic
204C2×C4C2×D107611yescharacteristic
205C2×C4#1686440211yescharacteristic
206C2×C4#1686440311yescharacteristic
207C8—41no—
208C8—10761no—
209C22—41no—
210C22—5384no—
211C22—10764no—
212C22—10764no—
213C22—10762no—
214C22—10761no—
215C22—21522no—
216C22C22⋊C4×D26911yescharacteristic
217C22#2257542311yescharacteristic
218C22#2257543811yescharacteristic
219C4—42no—
220C4—42no—
221C4—10762no—
222C4—10761no—
223C4#2257541511yescharacteristic
224C4C4×D107611yescharacteristic
225C4#2257542611yescharacteristic
226C4#2257542811yescharacteristic
227C2—21no—
228C2—21no—
229C2—21no—
230C2—10764no—
231C2—21521no—
232C2#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#1911
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
2. #31771079C2semidirect
3. #31770623C2semidirect
4. #31770621C2semidirect
5. C2×#22575369C2semidirect
6. #31770361C2semidirect
7. H(3,ℤ/4)×C269C2semidirect
11. #22575450C4semidirect
12. #22575441C4semidirect
30. C2×Dic538C2×C4semidirect
37. C2×D1076C2×C4semidirect
49. C4×Dic269D4semidirect
58. C42×C269C2×C4semidirect
59. C42×C269D4semidirect
116. C269#1911semidirect
124. H(3,ℤ/4)D269semidirect
175. C42C4×D269semidirect
176. C42D1076semidirect

Maximal subgroups

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

subgroupindex
#317711742
#317710792
#317706232
#317706212
C2×#225753692
#317703612
H(3,ℤ/4)×C2692
#1911269