Finite Group Databasebeta

← #29592863

Subgroups — #29592863

Order 15616.

336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 59 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#21453807C211yesmaximal, characteristic
2#21446980C211yesmaximal, characteristic
3#21444863C212yesmaximal
4#21443847C212yesmaximal
5C61×#1319C211yesmaximal, characteristic
6#16840393C2211yescharacteristic
7#16840098—22no—
8#16839771—21no—
9#16839701C2212yes—
10#16839694—22no—
11#16839669—21no—
12#16839660—21no—
13#16839649—22no—
14#16839531C2211yescharacteristic
15#16839522—21no—
16#16839500—22no—
17C61×#391C2211yescharacteristic
18C61×#324C2212yes—
19C2×#11758194—21no—
20#14519776—41no—
21#14519768—41no—
22#14519756—22no—
23#14519736—21no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61D412yes—
28C2×#11758196—22no—
29C2×C4×Dic61—21no—
30#14519711—42no—
31#14519702—42no—
32#14519701—41no—
33#14519701—41no—
34#14519684—22no—
35#14519684—22no—
36#14519684—22no—
37#14519684D412yes—
38C22×Q8×C61D411yescharacteristic
39C2×C4⋊C4×C61C2311yescharacteristic
40C2×C42×C61D411yescharacteristic
41C22⋊C8×C61—22no—
42#95×C61—22no—
43C2×Q8×C61—21no—
44C2×Q8×C61—41no—
45C2×Q8×C61—41no—
46C2×Q8×C61Q1612yes—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61C2×D411yescharacteristic
50C22×C4×C61C2×D412yes—
51C22×Dic61—22no—
52C22×Dic61—22no—
53C2×Dic122—22no—
54C2×C8×C61—42no—
55C4⋊C4×C61—41no—
56C42×C61—41no—
57C22⋊Dic61—41no—
58C4⋊Dic61—21no—
59C4⋊Dic61—21no—
60C4⋊Dic61—22no—
61C4⋊Dic61—42no—
62C4⋊Dic61—42no—
63C4⋊Dic61—81no—
64C4⋊Dic61—81no—
65#11758196—44no—
66#11758196—42no—
67C4×Dic61—41no—
68C4×Dic61—81no—
69#11758194—41no—
70#11758194—41no—
71C2×#92418—41no—
72C23×C61#12011yescharacteristic
73Q8×C61—42no—
74Q8×C61—81no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61—42no—
85C2×C4×C61C2×Q1611yescharacteristic
86C2×C4×C61#13711yescharacteristic
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61—42no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—41no—
93C2×Dic61—41no—
94C2×Dic61—42no—
95Dic122—82no—
96C8×C61—82no—
97#92418—81no—
98#12225—611nomaximal, Sylow
99C22×C61—21no—
100C22×C61—21no—
101C22×C61#45111yescharacteristic
102C22×C61#45511yescharacteristic
103C22×C61B(4,𝔽2)11yescharacteristic
104C4×C61—21no—
105C4×C61—21no—
106C4×C61—42no—
107C4×C61—42no—
108C4×C61—42no—
109Dic61—82no—
110Dic61—81no—
111Dic61—81no—
112Dic61—82no—
113#2809—611no—
114#2028—611no—
115#1617—612no—
116#1353—612no—
117#1319D6111yescharacteristic
118C2×C61—21no—
119C2×C61—21no—
120C2×C61#160211yescharacteristic
121C2×C61#220111yescharacteristic
122C2×C61#220411yescharacteristic
123#544—611no—
124#484—1222no—
125#419—1221no—
126#400—612no—
127#398—1222no—
128#391—1221no—
129#391C2×D6111yescharacteristic
130#389—1221no—
131#387—1222no—
132#343—611no—
133#339—1221no—
134#328—1222no—
135#324C2×D6112yes—
136C61#1222511yescharacteristic, complemented, Sylow
137C22×Q8D24411yescharacteristic
138C2×M16—1221no—
139C4⋊Q8—2441no—
140#125—2441no—
141C22⋊Q8—1222no—
142#117—1221no—
143C2×C4⋊C4—612no—
144C2×C4⋊C4—1221no—
145C2×C4⋊C4—1221no—
146C2×C4⋊C4—1222no—
147C2×C4⋊C4—1221no—
148C2×C4⋊C4C22×D6111yescharacteristic
149C2×C42—1221no—
150C2×C42D24411yescharacteristic
151#107—2442no—
152#103—2441no—
153#103—2441no—
154#103—2442no—
155C22⋊C8—22no—
156#95—22no—
157#95—612no—
158#95—1222no—
159#95—1222no—
160#95—1222no—
161C2×Q8—21no—
162C2×Q8—41no—
163C2×Q8—41no—
164C2×Q8—1222no—
165C2×Q8Dic24412yes—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—1222no—
169C22×C4—1222no—
170C22×C4C2×D24411yescharacteristic
171C22×C4D4×D6112yes—
172M16—2441no—
173M16—2441no—
174C2×C8—42no—
175C2×C8—2441no—
176C4⋊C4—41no—
177C4⋊C4—1221no—
178C4⋊C4—1221no—
179C4⋊C4—1222no—
180C4⋊C4—4881no—
181C4⋊C4—4881no—
182C4⋊C4—2442no—
183C4⋊C4—2444no—
184C4⋊C4—2442no—
185C4⋊C4—2442no—
186C22⋊C4—2441no—
187C42—41no—
188C42—4881no—
189C42—2441no—
190C23#1451974711yescharacteristic
191Q8—42no—
192Q8—81no—
193Q8—4882no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4—2442no—
205C2×C4—2442no—
206C2×C4—2442no—
207C2×C4—2442no—
208C2×C4—2442no—
209C2×C4—2441no—
210C2×C4—2441no—
211C2×C4—2442no—
212C2×C4C2×Dic24411yescharacteristic
213C2×C4#1451981011yescharacteristic
214C8—82no—
215C8—4881no—
216C22—21no—
217C22—21no—
218C22#1683992011yescharacteristic
219C22#1683994211yescharacteristic
220C22#1683995011yescharacteristic
221C4—21no—
222C4—21no—
223C4—42no—
224C4—42no—
225C4—42no—
226C4—4882no—
227C4—4881no—
228C4—4881no—
229C4—4882no—
230C2—21no—
231C2—21no—
232C2#2144477811yescharacteristic
233C2#2144783411yescharacteristic
234C2#2144784711yescharacteristic
subgroupG/H
centerC22#16839950
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1319C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#1319D61
hypocenterC61#12225
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
136. C61#12225semidirect

Maximal subgroups

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

subgroupindex
#214538072
#214469802
#214448632
#214438472
C61×#13192
#1222561