Finite Group Databasebeta

← #29569212

Subgroups — #29569212

Order 15616.

398 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 87 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#21453812C211yesmaximal, characteristic
2#21447362C211yesmaximal, characteristic
3#21447229C212yesmaximal
4#21443644C212yesmaximal
5C61×#1272C211yesmaximal, characteristic
6C2×#14519708—21no—
7C2×#14519702—22no—
8C2×#14519701—21no—
9#16839683—22no—
10#16839682—21no—
11#16839669—21no—
12#16839668C2212yes—
13#16839666—22no—
14#16839632C2211yescharacteristic
15#16839525—22no—
16#16839517C2211yescharacteristic
17C61×#391C2211yescharacteristic
18C61×#336C2212yes—
19C22×Dic122—21no—
20C22×Dic122D412yes—
21C22×#92418—21no—
22C2×C4⋊Dic61—21no—
23C2×C4⋊Dic61—22no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61D412yes—
26C2×#11758196—22no—
27C2×C4×Dic61—21no—
28#14519708—42no—
29#14519702—44no—
30#14519701—42no—
31#14519684—21no—
32#14519684—22no—
33#14519684—22no—
34#14519684—22no—
35C22×Q8×C61D411yescharacteristic
36C22×C8×C61—22no—
37C2×C4⋊C4×C61D411yescharacteristic
38C2×C42×C61C2311yescharacteristic
39#95×C61—22no—
40C2×Q8×C61—21no—
41C2×Q8×C61—41no—
42C2×Q8×C61—41no—
43C2×Q8×C61Q1612yes—
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61C2×D412yes—
47C22×C4×C61C2×D411yescharacteristic
48C22×Dic61—22no—
49C22×Dic61—22no—
50C22×Dic61—41no—
51C2×Dic122—22no—
52C2×Dic122—42no—
53C2×Dic122—42no—
54C2×Dic122—81no—
55C2×Dic122—82no—
56C2×Dic122SD1614yes—
57C2×C8×C61—42no—
58C2×C8×C61—42no—
59C2×C8×C61—42no—
60C4⋊C4×C61—41no—
61C42×C61—41no—
62C4⋊Dic61—42no—
63C4⋊Dic61—41no—
64C4⋊Dic61—41no—
65C4⋊Dic61—42no—
66C4⋊Dic61—42no—
67C4⋊Dic61—81no—
68#11758196—82no—
69C4×Dic61—81no—
70C2×#92418—22no—
71C2×#92418—41no—
72C2×#92418—41no—
73C23×C61#12011yescharacteristic
74Q8×C61—42no—
75Q8×C61—81no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61—42no—
85C2×C4×C61C2×SD1612yes—
86C2×C4×C61C2×Q1611yescharacteristic
87C2×C4×C61#13712yes—
88C2×C4×C61#13711yescharacteristic
89C2×Dic61—24no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—42no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C2×Dic61—82no—
96C2×Dic61—81no—
97Dic122—44no—
98Dic122—82no—
99Dic122—84no—
100C8×C61—82no—
101#92418—42no—
102#7812—611nomaximal, Sylow
103C22×C61#44812yes—
104C22×C61#45111yescharacteristic
105C22×C61#45311yescharacteristic
106C22×C61#45512yes—
107C22×C61#45811yescharacteristic
108C4×C61—22no—
109C4×C61—22no—
110C4×C61—21no—
111C4×C61—21no—
112C4×C61—42no—
113C4×C61—81no—
114Dic61—44no—
115Dic61—82no—
116Dic61—161no—
117#2811—611no—
118#2096—611no—
119#2072—612no—
120#1272—612no—
121#1272D6111yescharacteristic
122C2×C61#160812yes—
123C2×C61#161411yescharacteristic
124C2×C61#162311yescharacteristic
125C2×C61#164512yes—
126C2×C61#165911yescharacteristic
127C2×#106—1221no—
128C2×#103—1222no—
129C2×#103—1221no—
130#395—1222no—
131#395—1221no—
132#391—612no—
133#391—1222no—
134#391—1221no—
135#391C2×D6111yescharacteristic
136#384—611no—
137#340—1222no—
138#336—611no—
139#336C2×D6112yes—
140C61#781211yescharacteristic, complemented, Sylow
141C22×Q8—612no—
142C22×Q8—1221no—
143C22×Q8D24411yescharacteristic
144C22×C8—22no—
145C22×C8—1221no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4—1222no—
148C2×C4⋊C4—1221no—
149C2×C4⋊C4—1221no—
150C2×C4⋊C4—1222no—
151C2×C4⋊C4D24411yescharacteristic
152C2×C42—1221no—
153C2×C42C22×D6111yescharacteristic
154#106—2442no—
155#103—2444no—
156#103—2442no—
157#95—22no—
158#95—1222no—
159#95—1221no—
160#95—1222no—
161#95—1222no—
162C2×Q8—21no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—614no—
166C2×Q8—1222no—
167C2×Q8—4882no—
168C2×Q8—4881no—
169C2×Q8—2442no—
170C2×Q8—2442no—
171C2×Q8Dic24412yes—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—1222no—
175C22×C4—1222no—
176C22×C4—2441no—
177C22×C4C2×D24411yescharacteristic
178C22×C4D4×D6112yes—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—1222no—
183C2×C8—2441no—
184C2×C8—2441no—
185C4⋊C4—41no—
186C4⋊C4—4882no—
187C4⋊C4—4881no—
188C4⋊C4—2441no—
189C4⋊C4—2441no—
190C4⋊C4—2442no—
191C4⋊C4—2442no—
192C4⋊C4—2442no—
193C42—41no—
194C42—4881no—
195C23#1451974711yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—4882no—
199Q8—4884no—
200Q8—2444no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—1224no—
211C2×C4—4882no—
212C2×C4—4881no—
213C2×C4—2442no—
214C2×C4—2442no—
215C2×C4—2442no—
216C2×C4—2442no—
217C2×C4—2442no—
218C2×C4SD16×D6112yes—
219C2×C4C2×Dic24411yescharacteristic
220C2×C4#1451980912yes—
221C2×C4#1451981011yescharacteristic
222C8—82no—
223C8—2442no—
224C22#1683990212yes—
225C22#1683992011yescharacteristic
226C22#1683993211yescharacteristic
227C22#1683994112yes—
228C22#1683995311yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—42no—
234C4—81no—
235C4—9761no—
236C4—4882no—
237C4—2444no—
238C2#2144481112yes—
239C2#2144484611yescharacteristic
240C2#2144489811yescharacteristic
241C2#2144504312yes—
242C2#2144512611yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socle, prime radicalC23×C61#120
hypercenter#1272D61
hypocenterC61#7812
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
140. C61#7812semidirect

Maximal subgroups

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

subgroupindex
#214538122
#214473622
#214472292
#214436442
C61×#12722
#781261