Finite Group Databasebeta

← #29593886

Subgroups — #29593886

Order 15616.

306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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#21458832C211yesmaximal, characteristic
2#21448043C211yesmaximal, characteristic
3#21447962C211yesmaximal, characteristic, complemented
4#21445213C211yesmaximal, characteristic, complemented
5#21443866C211yesmaximal, characteristic
6#21443784C211yesmaximal, characteristic, complemented
7C61×Q8⋊C16C211yesmaximal, characteristic, complemented
8#16840497—21no—
9#16840167C2211yescharacteristic
10#16840146—21no—
11#16840139C2211yescharacteristic
12#16839978—22no—
13#16839972—21no—
14#16839963—21no—
15C4×Dic244C2211yescharacteristic
16C4×D488—21no—
17#16839590—21no—
18#16839567—21no—
19#16839564—22no—
20#16839515C2211yescharacteristic
21#16839507—21no—
22C8×Q8×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×Dic244D411yescharacteristic
26C2×#11758202—41no—
27C2×#11758190—22no—
28C2×D488—21no—
29C2×D488D412yes—
30#14519777—21no—
31#14519774—21no—
32#14519766—41no—
33#14519765—22no—
34#14519762—42no—
35C4×Dic122—21no—
36C4×D244—22no—
37#14519739—41no—
38#14519711—21no—
39#14519711—21no—
40#14519711D411yescharacteristic
41C4⋊#92418—21no—
42#14519702—21no—
43#14519700—41no—
44#14519699—22no—
45C4×Q8×C61D411yescharacteristic
46C2×C16×C61—21no—
47C2×C16×C61—21no—
48C4⋊C8×C61—21no—
49C4⋊C8×C61D411yescharacteristic
50C4×C8×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×Q8×C61D811yescharacteristic
53C2×D244—22no—
54C2×D244—41no—
55C2×D244—41no—
56C2×C4×D61—42no—
57C2×Dic122—21no—
58C2×Dic122—41no—
59C2×C8×C61—21no—
60C2×C8×C61C2×D411yescharacteristic
61C2×C8×C61C2×D411yescharacteristic
62C4⋊C4×C61—21no—
63C4⋊C4×C61D811yescharacteristic
64C42×C61—21no—
65C42×C61C2×D411yescharacteristic
66#11758202—82no—
67#11758198—42no—
68#11758198—42no—
69#11758198—42no—
70C4⋊Dic61—21no—
71C4⋊Dic61—41no—
72C4⋊Dic61—41no—
73#11758196—41no—
74C4×Dic61—41no—
75C2×#92418—41no—
76Dic244—21no—
77Dic244—21no—
78D488—42no—
79D488—41no—
80D488—41no—
81#11758190—82no—
82C16×C61—41no—
83C16×C61—41no—
84C22×D61—42no—
85Q8×C61—21no—
86Q8×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61#12011yescharacteristic
90C2×C4×C61C2×D811yescharacteristic
91C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
92C2×Dic61—41no—
93C2×Dic61—41no—
94C2×Dic61—81no—
95D244—42no—
96D244—42no—
97D244—81no—
98D244—81no—
99D244—161no—
100C4×D61—162no—
101Dic122—41no—
102Dic122—41no—
103Dic122—81no—
104Dic122—81no—
105C8×C61—21no—
106C8×C61—41no—
107C8×C61#13511yescharacteristic
108C8×C61#13711yescharacteristic
109#92418—81no—
110#12381—611nomaximal, Sylow
111C22×C61#44711yescharacteristic
112C2×D61—82no—
113C2×D61—82no—
114C2×D61—82no—
115C4×C61—21no—
116C4×C61—41no—
117C4×C61—41no—
118C4×C61#45211yescharacteristic
119C4×C61#45511yescharacteristic
120C4×C61#50811yescharacteristic
121C4×C61#50911yescharacteristic
122Dic61—81no—
123Dic61—81no—
124Dic61—161no—
125#3396—611no—
126#2240—611no—
127#2225—611no—
128#1674—611no—
129#1361—611no—
130Q8⋊C16D6111yescharacteristic, complemented
131#1332—611no—
132C2×C61#164111yescharacteristic
133C2×C61#218611yescharacteristic
134C2×C61#219411yescharacteristic
135D61—162no—
136#559—1221no—
137#500—611no—
138#495—1221no—
139#493—611no—
140#463—1222no—
141#462—1221no—
142#460—1221no—
143C8×Q8C2×D6111yescharacteristic
144C4×Q16—611no—
145C4×D8—1221no—
146#367—1221no—
147C4⋊C16C2×D6111yescharacteristic
148#358—1221no—
149#357—1222no—
150C4×C16C2×D6111yescharacteristic
151#335—611no—
152#332—1221no—
153C61#1238111yescharacteristic, complemented, Sylow
154C2×Q16—611no—
155C2×Q16—2441no—
156C2×SD16—1222no—
157C2×D8—612no—
158C2×D8—1221no—
159C4⋊Q8—1221no—
160#127—1221no—
161#124—1222no—
162#124—2441no—
163#123—2442no—
164C4×Q8—1221no—
165C4×Q8D24411yescharacteristic
166C4×D4—1222no—
167C4×D4—2441no—
168C2×C16—21no—
169C2×C16—21no—
170#107—611no—
171#107—1221no—
172#107—1221no—
173C4⋊C8—21no—
174C4⋊C8—1221no—
175C4⋊C8D24411yescharacteristic
176#103—1221no—
177#103—2441no—
178#102—1222no—
179C4×C8—21no—
180C4×C8C22×D6111yescharacteristic
181C2×Q8—1221no—
182C2×Q8—2441no—
183C2×Q8D48811yescharacteristic
184C2×D4—1222no—
185C2×D4—2441no—
186C2×D4—2441no—
187C22×C4—2442no—
188Q16—1221no—
189Q16—1221no—
190Q16—4882no—
191SD16—4882no—
192D8—2442no—
193D8—2441no—
194D8—2441no—
195C2×C8—21no—
196C2×C8—2441no—
197C2×C8D4×D6111yescharacteristic
198C2×C8D4×D6111yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—1221no—
201C4⋊C4—2441no—
202C4⋊C4—2441no—
203C4⋊C4—2441no—
204C4⋊C4D48811yescharacteristic
205C22⋊C4—2442no—
206C22⋊C4—2442no—
207C22⋊C4—2442no—
208C42—21no—
209C42—2441no—
210C42C2×D24411yescharacteristic
211C16—41no—
212C16—41no—
213C23—2442no—
214Q8—21no—
215Q8—21no—
216Q8—4881no—
217Q8—4881no—
218Q8—2441no—
219Q8—2441no—
220D4—9761no—
221D4—4881no—
222D4—4881no—
223D4—2442no—
224D4—2442no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—9762no—
228C2×C4—4881no—
229C2×C4—2441no—
230C2×C4—2441no—
231C2×C4#1451974711yescharacteristic
232C2×C4C2×D48811yescharacteristic
233C2×C4#1451980511yescharacteristic
234C8—21no—
235C8—41no—
236C8—4881no—
237C8#1451979811yescharacteristic
238C8#1451980911yescharacteristic
239C22—4882no—
240C22—4882no—
241C22—4882no—
242C22#1683989811yescharacteristic
243C4—21no—
244C4—41no—
245C4—41no—
246C4—9761no—
247C4—4881no—
248C4—4881no—
249C4#1683992711yescharacteristic
250C4#1683994111yescharacteristic
251C4#1684019411yescharacteristic
252C4#1684020011yescharacteristic
253C2—9762no—
254C2#2144501411yescharacteristic
255C2#2144774411yescharacteristic
256C2#2144779211yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×Q8⋊C16C2
socleC22×C61#447
prime radical#16840139C22
hypercenterQ8⋊C16D61
hypocenterC61#12381
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
3. #21447962C2semidirect
4. #21445213C2semidirect
6. #21443784C2semidirect
7. C61×Q8⋊C16C2semidirect
130. Q8⋊C16D61semidirect
153. C61#12381semidirect

Maximal subgroups

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

subgroupindex
#214588322
#214480432
#214479622
#214452132
#214438662
#214437842
C61×Q8⋊C162
#1238161