Finite Group Databasebeta

← #29593571

Subgroups — #29593571

Order 15616.

312 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 65 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#21458809C211yesmaximal, characteristic
2#21448071C211yesmaximal, characteristic, complemented
3#21447865C211yesmaximal, characteristic
4#21445190C211yesmaximal, characteristic, complemented
5#21443797C211yesmaximal, characteristic, complemented
6#21443779C211yesmaximal, characteristic
7C61×#1362C211yesmaximal, characteristic, complemented
8#16840486—21no—
9C2×#14519723—22no—
10C2×#14519722—21no—
11#16840147—21no—
12#16840142C2211yescharacteristic
13#16840048—21no—
14#16839986—22no—
15#16839964—21no—
16C8×Dic122C2211yescharacteristic
17Q16×Dic61—21no—
18C4×D488C2211yescharacteristic
19#16839567—21no—
20C4×#11758185C2211yescharacteristic
21#16839507—21no—
22C61×#494C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×Dic244—21no—
26C2×Dic244—21no—
27C2×#11758201—22no—
28C2×D488D411yescharacteristic
29#14519777—21no—
30#14519772—42no—
31#14519766—22no—
32#14519757—41no—
33Q8×Dic61—22no—
34C4×Dic122D411yescharacteristic
35C4×D244—21no—
36#14519735—41no—
37#14519723—44no—
38#14519722—42no—
39C2×#11758185—21no—
40#14519711D411yescharacteristic
41#14519709—41no—
42C4⋊#92418D411yescharacteristic
43#14519706—21no—
44#14519702—41no—
45#14519701—22no—
46#14519699—21no—
47C8×Dic61—21no—
48C2×Q16×C61—21no—
49C2×Q16×C61D412yes—
50C4⋊Q8×C61—21no—
51C2×C16×C61—21no—
52C4⋊C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—22no—
55C2×D244—21no—
56C2×C4×D61—41no—
57C2×Dic122—41no—
58C2×Dic122D811yescharacteristic
59Q16×C61—42no—
60Q16×C61—41no—
61Q16×C61—41no—
62C2×C8×C61—41no—
63C2×C8×C61C2×D411yescharacteristic
64C2×C8×C61C2×D411yescharacteristic
65C4⋊C4×C61—41no—
66C4⋊C4×C61—41no—
67C42×C61C2×D411yescharacteristic
68#11758201—82no—
69#11758198—42no—
70#11758198—42no—
71#11758198—41no—
72C4⋊Dic61—21no—
73C4⋊Dic61—42no—
74C4⋊Dic61—41no—
75C4⋊Dic61—41no—
76C4⋊Dic61D811yescharacteristic
77#11758196—21no—
78C4×Dic61—21no—
79C4×Dic61—42no—
80C2×#92418—21no—
81Dic244—42no—
82Dic244—41no—
83Dic244—41no—
84D488—21no—
85D488—21no—
86C16×C61—41no—
87#11758185—22no—
88C22×D61—41no—
89Q8×C61—42no—
90Q8×C61—42no—
91C2×C4×C61—42no—
92C2×C4×C61#12011yescharacteristic
93C2×C4×C61C2×D811yescharacteristic
94C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—41no—
98C2×Dic61—81no—
99D244—41no—
100D244—41no—
101C4×D61—81no—
102C4×D61—81no—
103Dic122—21no—
104Dic122—21no—
105Dic122—81no—
106Dic122—81no—
107C8×C61—21no—
108C8×C61—81no—
109C8×C61#13511yescharacteristic
110C8×C61AGL(1,ℤ/8)11yescharacteristic
111#92418—41no—
112#12335—611nomaximal, Sylow
113C22×C61#44711yescharacteristic
114C2×D61—81no—
115C2×D61—81no—
116C2×D61—81no—
117C4×C61—21no—
118C4×C61—82no—
119C4×C61#44911yescharacteristic
120C4×C61#45311yescharacteristic
121C4×C61#50811yescharacteristic
122C4×C61#51011yescharacteristic
123Dic61—41no—
124Dic61—41no—
125Dic61—81no—
126Dic61—161no—
127#3393—611no—
128#2247—611no—
129#2208—611no—
130#1670—611no—
131#1362D6111yescharacteristic, complemented
132Q8⋊C16—611no—
133#1331—611no—
134C2×C61#162111yescharacteristic
135C2×C61#218911yescharacteristic
136C2×C61#219511yescharacteristic
137D61—161no—
138#556—1221no—
139C2×Q32—1222no—
140C2×SD32—1221no—
141#495—1221no—
142#494—611no—
143#494C2×D6111yescharacteristic
144#475—1221no—
145#464—1222no—
146#461—1221no—
147C8×Q8—611no—
148C4×Q16—1221no—
149C4×D8—611no—
150C4⋊C16C2×D6111yescharacteristic
151#358—1221no—
152C4×C16—611no—
153#335C2×D6111yescharacteristic
154#332—1221no—
155C61#1233511yescharacteristic, complemented, Sylow
156C2×Q16—21no—
157C2×Q16—1221no—
158C2×Q16—1221no—
159C2×Q16D24412yes—
160C2×SD16—1222no—
161C2×D8—611no—
162C4⋊Q8—21no—
163C4⋊Q8—1221no—
164#126—2442no—
165#124—1222no—
166C22⋊Q8—2441no—
167C4×Q8—611no—
168C4×Q8—1222no—
169C4×D4—1221no—
170#117—2441no—
171Q32—2444no—
172SD32—2442no—
173C2×C16—21no—
174C2×C16—1221no—
175#107—611no—
176#106—2441no—
177C4⋊C8—21no—
178C4⋊C8—611no—
179C4⋊C8—1221no—
180#103—1222no—
181#103—2441no—
182#102—1221no—
183C4×C8—1221no—
184C4×C8C22×D6111yescharacteristic
185C2×Q8—22no—
186C2×Q8—611no—
187C2×Q8—2441no—
188C2×D4—1221no—
189C22×C4—2441no—
190Q16—42no—
191Q16—41no—
192Q16—41no—
193Q16—2442no—
194Q16—2441no—
195Q16—2441no—
196SD16—4882no—
197D8—1221no—
198D8—1221no—
199C2×C8—41no—
200C2×C8—1221no—
201C2×C8C2×D24411yescharacteristic
202C2×C8D4×D6111yescharacteristic
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—611no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4—2442no—
209C4⋊C4—2441no—
210C4⋊C4—2441no—
211C22⋊C4—2442no—
212C22⋊C4—2442no—
213C22⋊C4—2441no—
214C42—1221no—
215C42—2442no—
216C42D4×D6111yescharacteristic
217C16—41no—
218C16—1222no—
219C23—2441no—
220Q8—42no—
221Q8—42no—
222Q8—1221no—
223Q8—1221no—
224Q8—4881no—
225Q8—4881no—
226D4—2441no—
227D4—2441no—
228C2×C4—42no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—4881no—
232C2×C4—4881no—
233C2×C4—4881no—
234C2×C4—2441no—
235C2×C4#1451974711yescharacteristic
236C2×C4D8×D6111yescharacteristic
237C2×C4#1451980411yescharacteristic
238C8—21no—
239C8—81no—
240C8—2441no—
241C8#1451979811yescharacteristic
242C8#1451980111yescharacteristic
243C22—4881no—
244C22—4881no—
245C22—4881no—
246C22#1683989711yescharacteristic
247C4—21no—
248C4—82no—
249C4—9761no—
250C4—4881no—
251C4—2441no—
252C4—2441no—
253C4#1683990811yescharacteristic
254C4#1683993211yescharacteristic
255C4#1684019311yescharacteristic
256C4#1684020411yescharacteristic
257C2—9761no—
258C2#2144488511yescharacteristic
259C2#2144776211yescharacteristic
260C2#2144780011yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1362C2
socleC22×C61#447
prime radicalC2×D488D4
hypercenter#1362D61
hypocenterC61#12335
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
2. #21448071C2semidirect
4. #21445190C2semidirect
5. #21443797C2semidirect
7. C61×#1362C2semidirect
131. #1362D61semidirect
155. C61#12335semidirect

Maximal subgroups

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

subgroupindex
#214588092
#214480712
#214478652
#214451902
#214437972
#214437792
C61×#13622
#1233561