Finite Group Databasebeta

← #29569325

Subgroups — #29569325

Order 15616.

350 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 83 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#21447383C212yesmaximal
3#21447357C211yesmaximal, characteristic
4#21443643C212yesmaximal
5C61×#1272C211yesmaximal, characteristic
6C2×#14519710—21no—
7C2×#14519701—21no—
8#16839701—21no—
9#16839694—22no—
10#16839669—21no—
11#16839660C2212yes—
12#16839649—22no—
13#16839632C2211yescharacteristic
14#16839525—22no—
15#16839525—22no—
16#16839517C2211yescharacteristic
17C61×#391C2211yescharacteristic
18C61×#336C2212yes—
19C22×#92418—21no—
20C2×C4⋊Dic61—21no—
21C2×C4⋊Dic61—22no—
22C2×C4⋊Dic61—21no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61D412yes—
25C2×C4⋊Dic61D412yes—
26C2×#11758196—22no—
27C2×C4×Dic61—21no—
28#14519710—42no—
29#14519701—42no—
30#14519684—22no—
31#14519684—22no—
32#14519684—21no—
33#14519684—22no—
34C22×Q8×C61D411yescharacteristic
35C22×C8×C61—22no—
36C2×C4⋊C4×C61D411yescharacteristic
37C2×C42×C61C2311yescharacteristic
38#95×C61—22no—
39C2×Q8×C61—21no—
40C2×Q8×C61—41no—
41C2×Q8×C61—41no—
42C2×Q8×C61Q1612yes—
43C22×C4×C61—21no—
44C22×C4×C61—21no—
45C22×C4×C61C2×D411yescharacteristic
46C22×C4×C61C2×D412yes—
47C22×Dic61—22no—
48C22×Dic61—22no—
49C22×Dic61—41no—
50C2×C8×C61—42no—
51C2×C8×C61—42no—
52C2×C8×C61—42no—
53C4⋊C4×C61—41no—
54C42×C61—41no—
55C4⋊Dic61—22no—
56C4⋊Dic61—22no—
57C4⋊Dic61—42no—
58C4⋊Dic61—41no—
59C4⋊Dic61—41no—
60C4⋊Dic61—44no—
61C4⋊Dic61—81no—
62C4⋊Dic61—81no—
63#11758196—42no—
64#11758196—42no—
65C4×Dic61—81no—
66C2×#92418—22no—
67C2×#92418—41no—
68C2×#92418—41no—
69C23×C61#12011yescharacteristic
70Q8×C61—42no—
71Q8×C61—81no—
72C2×C4×C61—21no—
73C2×C4×C61—22no—
74C2×C4×C61—21no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61—42no—
81C2×C4×C61C2×Q1611yescharacteristic
82C2×C4×C61#13512yes—
83C2×C4×C61#13712yes—
84C2×C4×C61#13711yescharacteristic
85C2×Dic61—42no—
86C2×Dic61—42no—
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61—42no—
90C2×Dic61—42no—
91C2×Dic61—81no—
92C2×Dic61—82no—
93C8×C61—82no—
94#92418—42no—
95#7831—611nomaximal, Sylow
96C22×C61#45111yescharacteristic
97C22×C61#45212yes—
98C22×C61#45311yescharacteristic
99C22×C61#45412yes—
100C22×C61#45811yescharacteristic
101C4×C61—21no—
102C4×C61—21no—
103C4×C61—22no—
104C4×C61—22no—
105C4×C61—42no—
106C4×C61—81no—
107Dic61—82no—
108Dic61—82no—
109Dic61—161no—
110#2809—611no—
111#2100—612no—
112#2095—611no—
113#1272D6111yescharacteristic
114#1271—612no—
115C2×C61#161411yescharacteristic
116C2×C61#161512yes—
117C2×C61#163411yescharacteristic
118C2×C61#163612yes—
119C2×C61#165711yescharacteristic
120C2×#107—1221no—
121C2×#103—1221no—
122#400—1221no—
123#398—1222no—
124#391—1221no—
125#391C2×D6111yescharacteristic
126#389—612no—
127#387—1222no—
128#384—611no—
129#340—1222no—
130#340—1222no—
131#336—611no—
132#336C2×D6112yes—
133C61#783111yescharacteristic, complemented, Sylow
134C22×Q8D24411yescharacteristic
135C22×C8—22no—
136C22×C8—1221no—
137C2×C4⋊C4—612no—
138C2×C4⋊C4—612no—
139C2×C4⋊C4—1221no—
140C2×C4⋊C4—1221no—
141C2×C4⋊C4—1222no—
142C2×C4⋊C4—1221no—
143C2×C4⋊C4—1222no—
144C2×C4⋊C4D24411yescharacteristic
145C2×C42—1221no—
146C2×C42C22×D6111yescharacteristic
147#107—2442no—
148#103—2442no—
149#95—22no—
150#95—1221no—
151#95—1222no—
152#95—1222no—
153#95—1222no—
154C2×Q8—21no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8Dic24412yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—1222no—
161C22×C4—1222no—
162C22×C4—2441no—
163C22×C4C2×D24411yescharacteristic
164C22×C4D4×D6112yes—
165C2×C8—42no—
166C2×C8—42no—
167C2×C8—42no—
168C2×C8—1222no—
169C2×C8—2441no—
170C2×C8—2441no—
171C4⋊C4—41no—
172C4⋊C4—1222no—
173C4⋊C4—1222no—
174C4⋊C4—4881no—
175C4⋊C4—4881no—
176C4⋊C4—2441no—
177C4⋊C4—2441no—
178C4⋊C4—2444no—
179C4⋊C4—2442no—
180C4⋊C4—2442no—
181C4⋊C4—2442no—
182C42—41no—
183C42—4881no—
184C23#1451974711yescharacteristic
185Q8—42no—
186Q8—81no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—41no—
196C2×C4—4882no—
197C2×C4—4881no—
198C2×C4—2442no—
199C2×C4—2442no—
200C2×C4—2442no—
201C2×C4—2442no—
202C2×C4—2442no—
203C2×C4—2442no—
204C2×C4C2×Dic24411yescharacteristic
205C2×C4#1451979812yes—
206C2×C4#1451980912yes—
207C2×C4#1451981011yescharacteristic
208C8—82no—
209C8—2442no—
210C22#1683992011yescharacteristic
211C22#1683992712yes—
212C22#1683993211yescharacteristic
213C22#1683993612yes—
214C22#1683995311yescharacteristic
215C4—21no—
216C4—21no—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—81no—
221C4—9761no—
222C4—4882no—
223C4—4882no—
224C2#2144484611yescharacteristic
225C2#2144485312yes—
226C2#2144496511yescharacteristic
227C2#2144498012yes—
228C2#2144511811yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socle, prime radicalC23×C61#120
hypercenter#1272D61
hypocenterC61#7831
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
133. C61#7831semidirect

Maximal subgroups

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

subgroupindex
#214538072
#214473832
#214473572
#214436432
C61×#12722
#783161