Finite Group Databasebeta

← #29593721

Subgroups — #29593721

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#21447866C211yesmaximal, characteristic
3#21445186C211yesmaximal, characteristic
4#21443874C211yesmaximal, characteristic
5#21443799C211yesmaximal, characteristic
6#21443784C211yesmaximal, characteristic
7C61×#2241C211yesmaximal, characteristic
8#16840487—21no—
9C2×#14519723—21no—
10#16840163—21no—
11#16840068—22no—
12#16840044—21no—
13#16840044—21no—
14C8×Dic122C2211yescharacteristic
15C4×Dic244C2211yescharacteristic
16#16839856—21no—
17C4⋊#11758185C2211yescharacteristic
18#16839566—21no—
19#16839515C2211yescharacteristic
20#16839508—21no—
21C61×#500C2211yescharacteristic
22C61×#494C2211yescharacteristic
23C61×#358—22no—
24C4×C16×C61C2211yescharacteristic
25C2×Dic244D411yescharacteristic
26#14519775—41no—
27#14519768—22no—
28#14519767—42no—
29Q8×Dic61—41no—
30C4×Dic122—21no—
31C4×Dic122D411yescharacteristic
32#14519742—22no—
33#14519723—42no—
34C2×#11758185—21no—
35#14519711D411yescharacteristic
36#14519708—22no—
37#14519708—41no—
38C4⋊#92418—21no—
39C4⋊#92418D411yescharacteristic
40#14519706—21no—
41#14519702—21no—
42#14519700—22no—
43#14519700—41no—
44C8×Dic61—21no—
45C2×Q16×C61—21no—
46C2×Q16×C61—21no—
47C4⋊Q8×C61—21no—
48C4⋊Q8×C61—21no—
49C2×C16×C61—21no—
50#107×C61—21no—
51#107×C61D412yes—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61—41no—
54C2×Q8×C61—41no—
55C2×Dic122—21no—
56C2×Dic122D811yescharacteristic
57Q16×C61—42no—
58Q16×C61—41no—
59Q16×C61—41no—
60C2×C8×C61C2×D411yescharacteristic
61C2×C8×C61C2×D411yescharacteristic
62C4⋊C4×C61—22no—
63C4⋊C4×C61—41no—
64C4⋊C4×C61—41no—
65C4⋊C4×C61—41no—
66C42×C61C2×D411yescharacteristic
67C4⋊Dic61—21no—
68C4⋊Dic61—42no—
69C4⋊Dic61D811yescharacteristic
70#11758196—21no—
71#11758196—42no—
72#11758196—42no—
73#11758196—41no—
74C4×Dic61—21no—
75C4×Dic61—42no—
76C4×Dic61—41no—
77C2×#92418—21no—
78C2×#92418—41no—
79Dic244—21no—
80Dic244SD1612yes—
81C16×C61—41no—
82#11758185—41no—
83Q8×C61—81no—
84Q8×C61—81no—
85Q8×C61—81no—
86Q8×C61—81no—
87C2×C4×C61—42no—
88C2×C4×C61—81no—
89C2×C4×C61#12011yescharacteristic
90C2×C4×C61C2×D811yescharacteristic
91C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—41no—
95C2×Dic61—41no—
96Dic122—22no—
97Dic122—21no—
98Dic122—21no—
99Dic122—41no—
100C8×C61—21no—
101C8×C61C2×SD1611yescharacteristic
102C8×C61#13711yescharacteristic
103#92418—41no—
104#92418—81no—
105#12357—611nomaximal, Sylow
106C22×C61#44711yescharacteristic
107C4×C61—21no—
108C4×C61—82no—
109C4×C61—161no—
110C4×C61#44811yescharacteristic
111C4×C61#45411yescharacteristic
112C4×C61#50811yescharacteristic
113C4×C61#51011yescharacteristic
114Dic61—42no—
115Dic61—41no—
116Dic61—41no—
117Dic61—81no—
118#3383—611no—
119#2241D6111yescharacteristic
120#2209—611no—
121#1670—611no—
122#1364—611no—
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#494C2×D6111yescharacteristic
133#479—1222no—
134#475—1221no—
135#475—1221no—
136C8×Q8—611no—
137C4×Q16—611no—
138C4×Q16—1221no—
139C4⋊C16—611no—
140#358—22no—
141#358—1221no—
142C4×C16C2×D6111yescharacteristic
143#335—611no—
144#332—1221no—
145C61#1235711yescharacteristic, complemented, Sylow
146C2×Q16—21no—
147C2×Q16—21no—
148C2×Q16—611no—
149C4⋊Q8—21no—
150C4⋊Q8—21no—
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#107C22⋊D6112yes—
164#106—1222no—
165#106—2441no—
166C4⋊C8—611no—
167C4⋊C8—1221no—
168C4⋊C8—1221no—
169#103—1222no—
170#103—1221no—
171#103—2441no—
172C4×C8—1221no—
173C4×C8C22×D6111yescharacteristic
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—611no—
177C2×Q8—1221no—
178Q16—42no—
179Q16—41no—
180Q16—41no—
181Q16—612no—
182Q16—1221no—
183C2×C8—1221no—
184C2×C8—2441no—
185C2×C8D4×D6111yescharacteristic
186C2×C8C2×C22⋊D6111yescharacteristic
187C4⋊C4—22no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—611no—
192C4⋊C4—1221no—
193C4⋊C4—1221no—
194C4⋊C4—2442no—
195C4⋊C4—2442no—
196C4⋊C4—2442no—
197C4⋊C4—2441no—
198C42—1221no—
199C42—2442no—
200C42—2441no—
201C42D4×D6111yescharacteristic
202C16—41no—
203C16—2441no—
204Q8—81no—
205Q8—81no—
206Q8—81no—
207Q8—81no—
208Q8—1221no—
209Q8—1221no—
210Q8—1222no—
211Q8—2441no—
212C2×C4—42no—
213C2×C4—81no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—2441no—
217C2×C4—2441no—
218C2×C4#1451974511yescharacteristic
219C2×C4D8×D6111yescharacteristic
220C2×C4#1451980111yescharacteristic
221C8—21no—
222C8—4881no—
223C8—2441no—
224C8SD16×D6111yescharacteristic
225C8#1451980611yescharacteristic
226C22#1683989411yescharacteristic
227C4—21no—
228C4—82no—
229C4—161no—
230C4—4881no—
231C4—2442no—
232C4—2441no—
233C4—2441no—
234C4#1683989911yescharacteristic
235C4#1683993411yescharacteristic
236C4#1684019311yescharacteristic
237C4#1684020111yescharacteristic
238C2#2144491911yescharacteristic
239C2#2144775611yescharacteristic
240C2#2144779611yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2241C2
socle, prime radicalC22×C61#447
hypercenter#2241D61
hypocenterC61#12357
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

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
#214478662
#214451862
#214438742
#214437992
#214437842
C61×#22412
#1235761