Finite Group Databasebeta

← #29593725

Subgroups — #29593725

Order 15616.

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

normal subgroups only

This group has 282 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#21458712C211yesmaximal, characteristic
2#21448048C211yesmaximal, characteristic
3#21447870C211yesmaximal, characteristic
4#21445190C211yesmaximal, characteristic
5#21443797C211yesmaximal, characteristic
6#21443782C211yesmaximal, characteristic
7C61×#1364C211yesmaximal, characteristic
8#16840487—21no—
9C2×Dic488—21no—
10#16840163—21no—
11#16840142C2211yescharacteristic
12#16840068—22no—
13#16840048—21no—
14#16840044—21no—
15C8×Dic122C2211yescharacteristic
16C4×Dic244C2211yescharacteristic
17#16839856—21no—
18#16839567—21no—
19#16839565—22no—
20C4×#11758185C2211yescharacteristic
21#16839507—21no—
22C61×#500C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×Dic244—21no—
26C2×Dic244—21no—
27C2×Dic244D411yescharacteristic
28#14519777—21no—
29#14519775—41no—
30#14519768—22no—
31#14519767—42no—
32Q8×Dic61—41no—
33C4×Dic122—21no—
34C4×Dic122D411yescharacteristic
35#14519742—22no—
36Dic488—42no—
37C2×#11758185—21no—
38#14519711D411yescharacteristic
39#14519709—41no—
40#14519708—22no—
41C4⋊#92418D411yescharacteristic
42#14519706—21no—
43#14519702—21no—
44#14519702—41no—
45#14519700—22no—
46C8×Dic61—21no—
47C4⋊Q8×C61—21no—
48C2×C16×C61—21no—
49#107×C61—21no—
50#107×C61D412yes—
51C4⋊C8×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61—41no—
54C2×Dic122—21no—
55C2×Dic122—41no—
56C2×Dic122D811yescharacteristic
57C2×C8×C61—41no—
58C2×C8×C61C2×D411yescharacteristic
59C2×C8×C61C2×D411yescharacteristic
60C4⋊C4×C61—22no—
61C4⋊C4×C61—41no—
62C42×C61C2×D411yescharacteristic
63C4⋊Dic61—21no—
64C4⋊Dic61—42no—
65C4⋊Dic61—41no—
66C4⋊Dic61—41no—
67C4⋊Dic61D811yescharacteristic
68#11758196—21no—
69#11758196—42no—
70#11758196—42no—
71#11758196—41no—
72C4×Dic61—21no—
73C4×Dic61—42no—
74C4×Dic61—41no—
75C2×#92418—21no—
76Dic244—21no—
77Dic244—42no—
78Dic244—41no—
79Dic244—41no—
80Dic244SD1612yes—
81C16×C61—41no—
82#11758185—41no—
83Q8×C61—81no—
84Q8×C61—81no—
85C2×C4×C61—42no—
86C2×C4×C61#12011yescharacteristic
87C2×C4×C61C2×D811yescharacteristic
88C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93C2×Dic61—81no—
94Dic122—22no—
95Dic122—21no—
96Dic122—21no—
97Dic122—41no—
98Dic122—81no—
99Dic122—81no—
100C8×C61—21no—
101C8×C61—81no—
102C8×C61C2×SD1611yescharacteristic
103C8×C61#13711yescharacteristic
104#92418—41no—
105#12357—611nomaximal, Sylow
106C22×C61#44711yescharacteristic
107C4×C61—21no—
108C4×C61—82no—
109C4×C61#44811yescharacteristic
110C4×C61#45411yescharacteristic
111C4×C61#50811yescharacteristic
112C4×C61#51011yescharacteristic
113Dic61—42no—
114Dic61—41no—
115Dic61—41no—
116Dic61—81no—
117Dic61—161no—
118#3383—611no—
119#2241—611no—
120#2209—611no—
121#1670—611no—
122#1364D6111yescharacteristic
123Q8⋊C16—611no—
124#1332—611no—
125C2×C61#162711yescharacteristic
126C2×C61#218911yescharacteristic
127C2×C61#219511yescharacteristic
128#557—1221no—
129C2×Q32—1221no—
130#500C2×D6111yescharacteristic
131#499—1221no—
132#494—611no—
133#479—1222no—
134#475—1221no—
135#475—1221no—
136C8×Q8—611no—
137C4×Q16—611no—
138C4×Q16—1221no—
139C4⋊C16C2×D6111yescharacteristic
140#358—1221no—
141#358—1222no—
142C4×C16—611no—
143#335C2×D6111yescharacteristic
144#332—1221no—
145C61#1235711yescharacteristic, complemented, Sylow
146C2×Q16—611no—
147C2×Q16—1221no—
148C2×Q16—1221no—
149C4⋊Q8—21no—
150C4⋊Q8—1221no—
151C4⋊Q8—2441no—
152#125—1222no—
153#125—2442no—
154C4×Q8—611no—
155C4×Q8—1222no—
156C4×Q8—1221no—
157C4×Q8—2441no—
158Q32—2442no—
159C2×C16—21no—
160C2×C16—1221no—
161#107—21no—
162#107—611no—
163#107D24412yes—
164#106—1222no—
165#106—2441no—
166C4⋊C8—21no—
167C4⋊C8—611no—
168C4⋊C8—1221no—
169#103—1222no—
170#103—1221no—
171#103—2441no—
172C4×C8—1221no—
173C4×C8C22×D6111yescharacteristic
174C2×Q8—41no—
175C2×Q8—611no—
176C2×Q8—1221no—
177C2×Q8—2441no—
178Q16—612no—
179Q16—1221no—
180Q16—2442no—
181Q16—2441no—
182Q16—2441no—
183C2×C8—41no—
184C2×C8—1221no—
185C2×C8C2×D24411yescharacteristic
186C2×C8D4×D6111yescharacteristic
187C4⋊C4—22no—
188C4⋊C4—41no—
189C4⋊C4—611no—
190C4⋊C4—1221no—
191C4⋊C4—1221no—
192C4⋊C4—2442no—
193C4⋊C4—2442no—
194C4⋊C4—2442no—
195C4⋊C4—2441no—
196C4⋊C4—2441no—
197C4⋊C4—2441no—
198C42—1221no—
199C42—2442no—
200C42—2441no—
201C42D4×D6111yescharacteristic
202C16—41no—
203C16—2441no—
204Q8—81no—
205Q8—81no—
206Q8—1221no—
207Q8—1222no—
208Q8—1221no—
209Q8—4881no—
210Q8—4881no—
211Q8—2441no—
212C2×C4—42no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—4881no—
216C2×C4—2441no—
217C2×C4—2441no—
218C2×C4#1451974711yescharacteristic
219C2×C4D8×D6111yescharacteristic
220C2×C4#1451980411yescharacteristic
221C8—21no—
222C8—81no—
223C8—2441no—
224C8SD16×D6111yescharacteristic
225C8#1451980911yescharacteristic
226C22#1683989711yescharacteristic
227C4—21no—
228C4—82no—
229C4—9761no—
230C4—4881no—
231C4—2442no—
232C4—2441no—
233C4—2441no—
234C4#1683990211yescharacteristic
235C4#1683993711yescharacteristic
236C4#1684019111yescharacteristic
237C4#1684020111yescharacteristic
238C2#2144492311yescharacteristic
239C2#2144776011yescharacteristic
240C2#2144780011yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1364C2
socle, prime radicalC22×C61#447
hypercenter#1364D61
hypocenterC61#12357
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
145. C61#12357semidirect

Maximal subgroups

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

subgroupindex
#214587122
#214480482
#214478702
#214451902
#214437972
#214437822
C61×#13642
#1235761