Finite Group Databasebeta

← #46835348

Subgroups — #46835348

Order 34688.

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#31774455C211yesmaximal, characteristic
2#31774210C211yesmaximal, characteristic, complemented
3#31773823C211yesmaximal, characteristic, complemented
4#31773632C211yesmaximal, characteristic, complemented
5#31773631C211yesmaximal, characteristic, complemented
6#31773620C211yesmaximal, characteristic, complemented
7#480×C271C211yesmaximal, characteristic, complemented
8C2×D4×D271—21no—
9#22576145—21no—
10#22576142—21no—
11#22576134C2211yescharacteristic
12#22576132—21no—
13#22576130—21no—
14#22576128—21no—
15C2×(C2×D271)⋊C4—21no—
16C2×(C2×D271)⋊C4C2211yescharacteristic
17#22576093—21no—
18#22576080—21no—
19C22⋊(C271⋊C8)C2211yescharacteristic, complemented
20C271⋊#95—21no—
21C271⋊#95C2211yescharacteristic, complemented
22#121×C271C2211yescharacteristic
23C2×C4⋊C4×C271C2211yescharacteristic, complemented
24#107×C271—21no—
25#102×C271—21no—
26C22⋊C8×C271C2211yescharacteristic, complemented
27C23×D271—21no—
28C23×D271D411yescharacteristic
29C2×D1084—21no—
30C2×D1084D411yescharacteristic
31C2×C22⋊D271—21no—
32C2×C22⋊D271—21no—
33C2×C22⋊D271—21no—
34D4×D271—42no—
35D4×D271—42no—
36C22×Dic271—21no—
37C22×Dic271D411yescharacteristic
38C2×C4×D271—21no—
39C2×C271⋊C8—21no—
40C4⋊Dic271D411yescharacteristic
41Dic271⋊C4—21no—
42C22⋊Dic271—21no—
43(C2×D271)⋊C4—21no—
44(C2×D271)⋊C4—21no—
45(C2×D271)⋊C4—21no—
46(C2×D271)⋊C4—21no—
47(C2×D271)⋊C4—42no—
48C2×D4×C271—21no—
49C2×D4×C271D411yescharacteristic
50C22×C4×C271—21no—
51C22×C4×C271C2311yescharacteristic
52C2×C8×C271—21no—
53C4⋊C4×C271—21no—
54C4⋊C4×C271—21no—
55C4⋊C4×C271D411yescharacteristic
56C22⋊C4×C271—21no—
57C22×D271—21no—
58C22×D271—21no—
59C22×D271—21no—
60C22×D271—42no—
61C22×D271—41no—
62C22×D271—41no—
63C22×D271—81no—
64C22×D271—81no—
65C22×D271D812yes—
66D1084—41no—
67D1084—42no—
68C22⋊D271—42no—
69C22⋊D271—41no—
70C22⋊D271—41no—
71C22⋊D271—81no—
72C2×Dic271—21no—
73C2×Dic271—21no—
74C2×Dic271—41no—
75C2×Dic271—41no—
76C2×Dic271—41no—
77C2×Dic271—41no—
78C4×D271—42no—
79C271⋊C8—41no—
80C23×C271—21no—
81C23×C271C2×D411yescharacteristic
82D4×C271—41no—
83D4×C271—41no—
84D4×C271—41no—
85C2×C4×C271—21no—
86C2×C4×C271—41no—
87C2×C4×C271—41no—
88C2×C4×C271—41no—
89C2×C4×C271—41no—
90C2×C4×C271C2×D411yescharacteristic
91C2×C4×C271C2×D411yescharacteristic
92C8×C271—41no—
93C22×C271—21no—
94C22×C271—21no—
95C22×C271—41no—
96C22×C271—41no—
97C22×C271—41no—
98C22×C271#12011yescharacteristic
99C22×C271C2×D811yescharacteristic
100C22×C271AGL(1,ℤ/8)11yescharacteristic
101C2×D271—22no—
102C2×D271—41no—
103C2×D271—41no—
104C2×D271—42no—
105C2×D271—41no—
106C2×D271—41no—
107C2×D271—41no—
108C2×D271—81no—
109C2×D271—84no—
110C4×C271—21no—
111C4×C271—21no—
112C4×C271—41no—
113C4×C271—81no—
114Dic271—41no—
115Dic271—41no—
116Dic271—81no—
117C2×C271—21no—
118C2×C271—21no—
119C2×C271—81no—
120C2×C271#44711yescharacteristic
121C2×C271#45511yescharacteristic
122C2×C271#45811yescharacteristic
123D271—42no—
124D271—81no—
125C271#160711yescharacteristic, complemented, Sylow
126#1607—2711nomaximal, Sylow
127#534—2711no—
128#480—2711no—
129#480D27111yescharacteristic, complemented
130#397—2711no—
131#327—2711no—
132#327—2711no—
133#323—2711no—
134C22×D4—5421no—
135#123—5421no—
136#123—5421no—
137#121—2711no—
138#121—5421no—
139#121C2×D27111yescharacteristic
140#120—5421no—
141#120—5421no—
142C2×C4⋊C4C2×D27111yescharacteristic, complemented
143C2×C22⋊C4—2711no—
144C2×C22⋊C4—5421no—
145#107—21no—
146#107—5421no—
147#102—21no—
148#102—5421no—
149C22⋊C8—2711no—
150C22⋊C8C2×D27111yescharacteristic, complemented
151#95—2711no—
152#95—5421no—
153C24—2711no—
154C24—5421no—
155C2×D4—21no—
156C2×D4—2711no—
157C2×D4—5421no—
158C2×D4—5421no—
159C2×D4—5421no—
160C2×D4—5421no—
161C2×D4—10842no—
162C2×D4—10842no—
163C2×D4C22⋊D27111yescharacteristic
164C22×C4—21no—
165C22×C4—2711no—
166C22×C4—5421no—
167C22×C4—5421no—
168C22×C4C22×D27111yescharacteristic
169C2×C8—21no—
170C2×C8—5421no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—2711no—
174C4⋊C4—5421no—
175C4⋊C4C22⋊D27111yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—5421no—
178C22⋊C4—5421no—
179C22⋊C4—5421no—
180C22⋊C4—5421no—
181C22⋊C4—5421no—
182C22⋊C4—10842no—
183C23—21no—
184C23—2712no—
185C23—5421no—
186C23—5421no—
187C23—5421no—
188C23—10841no—
189C23—10841no—
190C23—10842no—
191C23—21681no—
192C23—21681no—
193C23D4×D27111yescharacteristic
194D4—41no—
195D4—41no—
196D4—41no—
197D4—10841no—
198D4—10842no—
199D4—10842no—
200D4—10841no—
201D4—10841no—
202D4—21681no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—5421no—
209C2×C4—5421no—
210C2×C4—10842no—
211C2×C4—10841no—
212C2×C4—10841no—
213C2×C4—10841no—
214C2×C4—10841no—
215C2×C4D4×D27111yescharacteristic
216C2×C4C2×C22⋊D27111yescharacteristic
217C8—41no—
218C8—10841no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—5422no—
225C22—10842no—
226C22—10841no—
227C22—10841no—
228C22—10841no—
229C22—10841no—
230C22—10841no—
231C22—21681no—
232C22—21684no—
233C22#2257612811yescharacteristic
234C22D8×D27111yescharacteristic
235C22#2257618411yescharacteristic
236C4—21no—
237C4—21no—
238C4—41no—
239C4—81no—
240C4—10841no—
241C4—10841no—
242C4—21681no—
243C2—21no—
244C2—21no—
245C2—81no—
246C2—10842no—
247C2—21681no—
248C2#3177402911yescharacteristic
249C2#3177407311yescharacteristic
250C2#3177408611yescharacteristic
subgroupG/H
centerC22#22576128
commutator, cosocleC22×C4×C271C23
FrattiniC22×C4C22×D271
Fitting#480×C271C2
socleC22×C271#120
prime radical#31774455C2
hypercenter#480D271
hypocenterC271#1607
LCSG ▷ C22×C4×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #31774210C2semidirect
3. #31773823C2semidirect
4. #31773632C2semidirect
5. #31773631C2semidirect
6. #31773620C2semidirect
7. #480×C271C2semidirect
19. C22⋊(C271⋊C8)C22semidirect
21. C271⋊#95C22semidirect
23. C2×C4⋊C4×C271C22semidirect
26. C22⋊C8×C271C22semidirect
125. C271#1607semidirect
129. #480D271semidirect
142. C2×C4⋊C4C2×D271semidirect
150. C22⋊C8C2×D271semidirect

Maximal subgroups

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

subgroupindex
#317744552
#317742102
#317738232
#317736322
#317736312
#317736202
#480×C2712
#1607271