Finite Group Databasebeta

← #46809869

Subgroups — #46809869

Order 34432.

280 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 51 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#31771163C211yesmaximal, characteristic
2#31770918C211yesmaximal, characteristic, complemented
3#31770531C211yesmaximal, characteristic, complemented
4#31770340C211yesmaximal, characteristic, complemented
5#31770339C211yesmaximal, characteristic, complemented
6#31770328C211yesmaximal, characteristic, complemented
7#480×C269C211yesmaximal, characteristic, complemented
8C2×D4×D269—21no—
9#22575438—21no—
10#22575435—21no—
11#22575427C2211yescharacteristic
12#22575425—21no—
13#22575423—21no—
14#22575421—21no—
15C2×#16864379—21no—
16C2×#16864379C2211yescharacteristic
17#22575386—21no—
18#22575373—21no—
19C22⋊#14524130C2211yescharacteristic, complemented
20#22575360—21no—
21#22575360C2211yescharacteristic, complemented
22#121×C269C2211yescharacteristic
23C2×C4⋊C4×C269C2211yescharacteristic, complemented
24#107×C269—21no—
25#102×C269—21no—
26C22⋊C8×C269C2211yescharacteristic, complemented
27C23×D269—21no—
28C23×D269D411yescharacteristic
29C2×D1076—21no—
30C2×D1076D411yescharacteristic
31C2×C22⋊D269—21no—
32C2×C22⋊D269—21no—
33C2×C22⋊D269—21no—
34D4×D269—42no—
35D4×D269—42no—
36C22×Dic269—21no—
37C22×Dic269D411yescharacteristic
38C2×C4×D269—21no—
39C2×#14524130—21no—
40C4⋊Dic269D411yescharacteristic
41#16864381—21no—
42C22⋊Dic269—21no—
43#16864379—21no—
44#16864379—21no—
45#16864379—21no—
46#16864379—21no—
47#16864379—42no—
48C2×D4×C269—21no—
49C2×D4×C269D411yescharacteristic
50C22×C4×C269—21no—
51C22×C4×C269C2311yescharacteristic
52C2×C8×C269—21no—
53C4⋊C4×C269—21no—
54C4⋊C4×C269—21no—
55C4⋊C4×C269D411yescharacteristic
56C22⋊C4×C269—21no—
57C22×D269—21no—
58C22×D269—21no—
59C22×D269—21no—
60C22×D269—42no—
61C22×D269—41no—
62C22×D269—41no—
63C22×D269—81no—
64C22×D269—81no—
65C22×D269D812yes—
66D1076—41no—
67D1076—42no—
68C22⋊D269—42no—
69C22⋊D269—41no—
70C22⋊D269—41no—
71C22⋊D269—81no—
72C2×Dic269—21no—
73C2×Dic269—21no—
74C2×Dic269—41no—
75C2×Dic269—41no—
76C2×Dic269—41no—
77C2×Dic269—41no—
78C4×D269—42no—
79#14524130—41no—
80C23×C269—21no—
81C23×C269C2×D411yescharacteristic
82D4×C269—41no—
83D4×C269—41no—
84D4×C269—41no—
85C2×C4×C269—21no—
86C2×C4×C269—41no—
87C2×C4×C269—41no—
88C2×C4×C269—41no—
89C2×C4×C269—41no—
90C2×C4×C269C2×D411yescharacteristic
91C2×C4×C269C2×D411yescharacteristic
92C8×C269—41no—
93C22×C269—21no—
94C22×C269—21no—
95C22×C269—41no—
96C22×C269—41no—
97C22×C269—41no—
98C22×C269#12011yescharacteristic
99C22×C269C2×D811yescharacteristic
100C22×C269AGL(1,ℤ/8)11yescharacteristic
101C2×D269—22no—
102C2×D269—41no—
103C2×D269—41no—
104C2×D269—42no—
105C2×D269—41no—
106C2×D269—41no—
107C2×D269—41no—
108C2×D269—81no—
109C2×D269—84no—
110C4×C269—21no—
111C4×C269—21no—
112C4×C269—41no—
113C4×C269—81no—
114Dic269—41no—
115Dic269—41no—
116Dic269—81no—
117C2×C269—21no—
118C2×C269—21no—
119C2×C269—81no—
120C2×C269#44711yescharacteristic
121C2×C269#45511yescharacteristic
122C2×C269#45811yescharacteristic
123D269—42no—
124D269—81no—
125C269#160711yescharacteristic, complemented, Sylow
126#1607—2691nomaximal, Sylow
127#534—2691no—
128#480—2691no—
129#480D26911yescharacteristic, complemented
130#397—2691no—
131#327—2691no—
132#327—2691no—
133#323—2691no—
134C22×D4—5381no—
135#123—5381no—
136#123—5381no—
137#121—2691no—
138#121—5381no—
139#121C2×D26911yescharacteristic
140#120—5381no—
141#120—5381no—
142C2×C4⋊C4C2×D26911yescharacteristic, complemented
143C2×C22⋊C4—2691no—
144C2×C22⋊C4—5381no—
145#107—21no—
146#107—5381no—
147#102—21no—
148#102—5381no—
149C22⋊C8—2691no—
150C22⋊C8C2×D26911yescharacteristic, complemented
151#95—2691no—
152#95—5381no—
153C24—2691no—
154C24—5381no—
155C2×D4—21no—
156C2×D4—2691no—
157C2×D4—5381no—
158C2×D4—5381no—
159C2×D4—5381no—
160C2×D4—5381no—
161C2×D4—10762no—
162C2×D4—10762no—
163C2×D4C22⋊D26911yescharacteristic
164C22×C4—21no—
165C22×C4—2691no—
166C22×C4—5381no—
167C22×C4—5381no—
168C22×C4C22×D26911yescharacteristic
169C2×C8—21no—
170C2×C8—5381no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—2691no—
174C4⋊C4—5381no—
175C4⋊C4C22⋊D26911yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—5381no—
178C22⋊C4—5381no—
179C22⋊C4—5381no—
180C22⋊C4—5381no—
181C22⋊C4—5381no—
182C22⋊C4—10762no—
183C23—21no—
184C23—2692no—
185C23—5381no—
186C23—5381no—
187C23—5381no—
188C23—10761no—
189C23—10761no—
190C23—10762no—
191C23—21521no—
192C23—21521no—
193C23D4×D26911yescharacteristic
194D4—41no—
195D4—41no—
196D4—41no—
197D4—10761no—
198D4—10762no—
199D4—10762no—
200D4—10761no—
201D4—10761no—
202D4—21521no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—5381no—
209C2×C4—5381no—
210C2×C4—10762no—
211C2×C4—10761no—
212C2×C4—10761no—
213C2×C4—10761no—
214C2×C4—10761no—
215C2×C4D4×D26911yescharacteristic
216C2×C4C2×C22⋊D26911yescharacteristic
217C8—41no—
218C8—10761no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—5382no—
225C22—10762no—
226C22—10761no—
227C22—10761no—
228C22—10761no—
229C22—10761no—
230C22—10761no—
231C22—21521no—
232C22—21524no—
233C22#2257542111yescharacteristic
234C22D8×D26911yescharacteristic
235C22#2257547711yescharacteristic
236C4—21no—
237C4—21no—
238C4—41no—
239C4—81no—
240C4—10761no—
241C4—10761no—
242C4—21521no—
243C2—21no—
244C2—21no—
245C2—81no—
246C2—10762no—
247C2—21521no—
248C2#3177073711yescharacteristic
249C2#3177078111yescharacteristic
250C2#3177079411yescharacteristic
subgroupG/H
centerC22#22575421
commutator, cosocleC22×C4×C269C23
FrattiniC22×C4C22×D269
Fitting#480×C269C2
socleC22×C269#120
prime radical#31771163C2
hypercenter#480D269
hypocenterC269#1607
LCSG ▷ C22×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #31770918C2semidirect
3. #31770531C2semidirect
4. #31770340C2semidirect
5. #31770339C2semidirect
6. #31770328C2semidirect
7. #480×C269C2semidirect
19. C22⋊#14524130C22semidirect
21. #22575360C22semidirect
23. C2×C4⋊C4×C269C22semidirect
26. C22⋊C8×C269C22semidirect
125. C269#1607semidirect
129. #480D269semidirect
142. C2×C4⋊C4C2×D269semidirect
150. C22⋊C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317711632
#317709182
#317705312
#317703402
#317703392
#317703282
#480×C2692
#1607269