Finite Group Databasebeta

← #29584904

Subgroups — #29584904

Order 15616.

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

normal subgroups only

This group has 236 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#21444593C211yesmaximal, characteristic
2#21444550C211yesmaximal, characteristic
3#21444517C211yesmaximal, characteristic
4#21444291C211yesmaximal, characteristic
5#21443729C211yesmaximal, characteristic
6#21443682C211yesmaximal, characteristic
7C61×#1290C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16839819C2211yescharacteristic
10#16839815C2211yescharacteristic
11#16839786C2211yescharacteristic
12#16839514—22no—
13#16839510—21no—
14#16839509—21no—
15#16839507—21no—
16#16839507—21no—
17#16839492—22no—
18C61×#432C2211yescharacteristic
19C61×#432C2211yescharacteristic
20C2×C4⋊C8×C61C2211yescharacteristic
21C2×#11758194—21no—
22#14519777D411yescharacteristic
23#14519777D411yescharacteristic
24#14519769—21no—
25#14519756—21no—
26#14519756—21no—
27C4×Dic122—21no—
28C4×Dic122—21no—
29#14519736—21no—
30C4⋊#92418—21no—
31C4⋊#92418—21no—
32C4⋊#92418—21no—
33C4⋊#92418—21no—
34C22⋊#92418—21no—
35C22⋊#92418—21no—
36#14519688—21no—
37C4×#92418D412yes—
38C22×C8×C61—21no—
39C2×C42×C61C2311yescharacteristic
40C4⋊C8×C61—21no—
41C4⋊C8×C61—21no—
42C4⋊C8×C61—21no—
43C4⋊C8×C61—21no—
44C22⋊C8×C61—21no—
45C22⋊C8×C61—21no—
46#97×C61—21no—
47#97×C61—21no—
48C22×C4×C61#4111yescharacteristic
49C22×C4×C61#4111yescharacteristic
50C22×C4×C61#4111yescharacteristic
51C2×Dic122—21no—
52C2×Dic122—21no—
53C2×C8×C61—41no—
54C2×C8×C61—41no—
55C2×C8×C61—41no—
56C2×C8×C61—81no—
57C42×C61C2×D411yescharacteristic
58C42×C61C2×D411yescharacteristic
59C42×C61#4111yescharacteristic
60C42×C61#4111yescharacteristic
61C22⋊Dic61—41no—
62C4⋊Dic61—21no—
63C4⋊Dic61—21no—
64C4⋊Dic61—21no—
65C4⋊Dic61—21no—
66#11758196—41no—
67#11758196—41no—
68C4×Dic61—41no—
69#11758194—81no—
70C2×#92418—22no—
71C2×#92418—41no—
72C2×#92418—41no—
73C23×C61#12611yescharacteristic
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61#12111yescharacteristic
79C2×C4×C61#12311yescharacteristic
80C2×C4×C61#12311yescharacteristic
81C2×C4×C61#12311yescharacteristic
82C2×C4×C61#12411yescharacteristic
83C2×C4×C61#12611yescharacteristic
84C2×Dic61—41no—
85C2×Dic61—41no—
86Dic122—41no—
87Dic122—41no—
88Dic122—81no—
89C8×C61—81no—
90C8×C61—81no—
91C8×C61—81no—
92#92418—42no—
93#92418—81no—
94#92418—81no—
95#10646—611nomaximal, Sylow
96C22×C61—21no—
97C22×C61—21no—
98C22×C61—21no—
99C22×C61#39711yescharacteristic
100C4×C61—21no—
101C4×C61—21no—
102C4×C61—21no—
103C4×C61—21no—
104C4×C61—21no—
105C4×C61#47211yescharacteristic
106C4×C61#47311yescharacteristic
107Dic61—81no—
108Dic61—81no—
109#1571—611no—
110#1559—611no—
111#1552—611no—
112#1497—611no—
113#1307—611no—
114#1290D6111yescharacteristic
115#1287—611no—
116C2×C61—41no—
117C2×C61#207811yescharacteristic
118C2×C61#208011yescharacteristic
119C2×C61#208211yescharacteristic
120#533—611no—
121#432—611no—
122#432C2×D6111yescharacteristic
123#432C2×D6111yescharacteristic
124#431—611no—
125#423—611no—
126C2×C4⋊C8C2×D6111yescharacteristic
127#335—1222no—
128#333—1221no—
129#332—1221no—
130#332—1221no—
131#332—1221no—
132Q8⋊C8—1222no—
133C61#1064611yescharacteristic, complemented, Sylow
134C2×M16—1221no—
135C22×C8—21no—
136C4⋊Q8—611no—
137C4⋊Q8—611no—
138#125—1221no—
139C22⋊Q8—1221no—
140C22⋊Q8—1221no—
141C4×Q8—1221no—
142C4×Q8—1221no—
143#117—1221no—
144C2×C42C22×D6111yescharacteristic
145C4⋊C8—21no—
146C4⋊C8—21no—
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—1221no—
150C4⋊C8—1221no—
151C4⋊C8—1221no—
152C4⋊C8—1221no—
153C22⋊C8—21no—
154C22⋊C8—21no—
155C22⋊C8—1221no—
156C22⋊C8—1221no—
157#97—21no—
158#97—21no—
159#97—1221no—
160C4×C8—612no—
161C2×Q8—1221no—
162C2×Q8—1221no—
163C22×C4#1175822211yescharacteristic
164C22×C4#1175822411yescharacteristic
165C22×C4#1175822611yescharacteristic
166M16—4881no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—81no—
171C2×C8—1222no—
172C2×C8—2441no—
173C2×C8—2441no—
174C4⋊C4—1221no—
175C4⋊C4—1221no—
176C4⋊C4—1221no—
177C4⋊C4—1221no—
178C4⋊C4—2441no—
179C4⋊C4—2441no—
180C22⋊C4—2441no—
181C42—2441no—
182C42#1175822211yescharacteristic
183C42#1175822211yescharacteristic
184C42D4×D6111yescharacteristic
185C42D4×D6111yescharacteristic
186C23#1451977211yescharacteristic
187Q8—4881no—
188Q8—2441no—
189Q8—2441no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—2441no—
195C2×C4—2441no—
196C2×C4#1451975011yescharacteristic
197C2×C4#1451975911yescharacteristic
198C2×C4#1451976211yescharacteristic
199C2×C4#1451976211yescharacteristic
200C2×C4#1451976311yescharacteristic
201C2×C4#1451977111yescharacteristic
202C8—81no—
203C8—81no—
204C8—81no—
205C8—4881no—
206C8—4881no—
207C8—2442no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#1683969111yescharacteristic
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—21no—
217C4—4881no—
218C4—4881no—
219C4#1684003111yescharacteristic
220C4#1684003611yescharacteristic
221C2—41no—
222C2#2144726311yescharacteristic
223C2#2144727511yescharacteristic
224C2#2144728811yescharacteristic
subgroupG/H
centerC22#16839691
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1290C2
socleC22×C61#397
prime radicalC23×C61#126
hypercenter#1290D61
hypocenterC61#10646
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
133. C61#10646semidirect

Maximal subgroups

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

subgroupindex
#214445932
#214445502
#214445172
#214442912
#214437292
#214436822
C61×#12902
#1064661