Finite Group Databasebeta

← #29573604

Subgroups — #29573604

Order 15616.

378 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 115 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#21445815C211yesmaximal, characteristic
2#21444143C211yesmaximal, characteristic
3#21443722C212yesmaximal
4#21443677C212yesmaximal
5C61×#2356C211yesmaximal, characteristic
6#16839815C2212yes—
7#16839786C2212yes—
8C2×#14519696—21no—
9#16839531—21no—
10#16839488—22no—
11C2×C4×Q8×C61C2211yescharacteristic
12C61×#391—21no—
13C61×#387—22no—
14C61×#383C412yes—
15C61×#382C2211yescharacteristic
16C4×C4⋊C4×C61—21no—
17C4×C4⋊C4×C61C2211yescharacteristic
18C61×#376C412yes—
19C2×#11758194—22no—
20C4⋊#92418—22no—
21C4⋊#92418—22no—
22C4⋊#92418—22no—
23#14519696—42no—
24C22⋊#92418—22no—
25C4×#92418—22no—
26C22×Q8×C61D411yescharacteristic
27C4×Q8×C61—22no—
28C4×Q8×C61—22no—
29C2×C4⋊C4×C61—21no—
30C2×C4⋊C4×C61—21no—
31C2×C4⋊C4×C61D412yes—
32C2×C4⋊C4×C61D411yescharacteristic
33C2×C42×C61—22no—
34C2×C42×C61—21no—
35C2×C42×C61C2×C412yes—
36C2×C42×C61C2311yescharacteristic
37#95×C61—22no—
38#95×C61—22no—
39#95×C61—22no—
40#95×C61—21no—
41#95×C61C2×C411yescharacteristic
42#95×C61C2×C412yes—
43#95×C61C2×C411yescharacteristic
44C2×Q8×C61—22no—
45C2×Q8×C61—22no—
46C2×Q8×C61—21no—
47C2×Q8×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61—22no—
50C22×C4×C61—21no—
51C22×C4×C61C22⋊C412yes—
52C22×C4×C61C22⋊C412yes—
53C22×C4×C61C22×C411yescharacteristic
54C22×C4×C61C2×D411yescharacteristic
55C22×C4×C61C2×D411yescharacteristic
56C4⋊C4×C61—22no—
57C4⋊C4×C61—24no—
58C4⋊C4×C61—42no—
59C4⋊C4×C61—41no—
60C4⋊C4×C61—41no—
61C42×C61—22no—
62C42×C61—22no—
63C42×C61—44no—
64C42×C61—42no—
65C42×C61#4112yes—
66C42×C61#4112yes—
67#11758194—42no—
68#11758194—42no—
69C2×#92418—42no—
70C2×#92418—42no—
71C23×C61C2×C22⋊C411yescharacteristic
72Q8×C61—42no—
73Q8×C61—42no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61—42no—
84C2×C4×C61—42no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61—42no—
88C2×C4×C61—41no—
89C2×C4×C61—42no—
90C2×C4×C61#11711yescharacteristic
91C2×C4×C61#11711yescharacteristic
92C2×C4×C61#12312yes—
93C2×C4×C61#12312yes—
94C2×C4×C61#13512yes—
95C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
96C2×C4×C61#13711yescharacteristic
97#92418—82no—
98#92418—82no—
99#8769—611nomaximal, Sylow
100C22×C61—21no—
101C22×C61—21no—
102C22×C61#38111yescharacteristic
103C22×C61#41611yescharacteristic
104C22×C61#41711yescharacteristic
105C4×C61—22no—
106C4×C61—21no—
107C4×C61—21no—
108C4×C61—42no—
109C4×C61—42no—
110C4×C61—42no—
111C4×C61—81no—
112C4×C61—82no—
113C4×C61#48212yes—
114C4×C61#48512yes—
115#2356D6111yescharacteristic
116#1801—611no—
117#1461—611no—
118#1303—612no—
119#1286—612no—
120C2×C61—21no—
121C2×C61—21no—
122C2×C61#182511yescharacteristic
123C2×C61#182711yescharacteristic
124C2×C61#183011yescharacteristic
125C2×C4×Q8C2×D6111yescharacteristic
126#431—612no—
127#423—612no—
128C2×#101—1221no—
129#391—21no—
130#387—22no—
131#383Dic6112yes—
132#382C2×D6111yescharacteristic
133C4×C4⋊C4—21no—
134C4×C4⋊C4C2×D6111yescharacteristic
135#376Dic6112yes—
136#343—1221no—
137#324—1222no—
138C61#876911yescharacteristic, complemented, Sylow
139C22×Q8C22⋊D6111yescharacteristic
140C2×M16—1222no—
141C4×Q8—22no—
142C4×Q8—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4C22⋊D6112yes—
146C2×C4⋊C4C22⋊D6111yescharacteristic
147C2×C42—22no—
148C2×C42—21no—
149C2×C42C2×Dic6112yes—
150C2×C42C22×D6111yescharacteristic
151C4⋊C8—1222no—
152C4⋊C8—1222no—
153C4⋊C8—1222no—
154#101—2442no—
155C22⋊C8—1222no—
156C4×C8—1222no—
157#95—22no—
158#95—22no—
159#95—22no—
160#95—21no—
161#95C2×Dic6111yescharacteristic
162#95C2×Dic6112yes—
163#95C2×Dic6111yescharacteristic
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—21no—
167C2×Q8—21no—
168C22×C4—21no—
169C22×C4—22no—
170C22×C4—21no—
171C22×C4C22⋊Dic6112yes—
172C22×C4C22⋊Dic6112yes—
173C22×C4C22×Dic6111yescharacteristic
174C22×C4C2×C22⋊D6111yescharacteristic
175C22×C4C2×C22⋊D6111yescharacteristic
176M16—2442no—
177M16—2442no—
178C2×C8—2442no—
179C2×C8—2442no—
180C4⋊C4—22no—
181C4⋊C4—24no—
182C4⋊C4—42no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C42—22no—
186C42—22no—
187C42—44no—
188C42—42no—
189C42#1175822212yes—
190C42#1175822212yes—
191C23C2×C22⋊Dic6111yescharacteristic
192Q8—42no—
193Q8—42no—
194C2×C4—22no—
195C2×C4—22no—
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—42no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4#1451973611yescharacteristic
211C2×C4#1451973611yescharacteristic
212C2×C4#1451976012yes—
213C2×C4#1451976012yes—
214C2×C4#1451979712yes—
215C2×C4#1451980211yescharacteristic
216C2×C4#1451980711yescharacteristic
217C8—4882no—
218C8—4882no—
219C22—21no—
220C22—21no—
221C22#1683962511yescharacteristic
222C22#1683975811yescharacteristic
223C22#1683976311yescharacteristic
224C4—22no—
225C4—21no—
226C4—21no—
227C4—42no—
228C4—42no—
229C4—42no—
230C4—81no—
231C4—82no—
232C4#1684008612yes—
233C4#1684010312yes—
234C2—21no—
235C2—21no—
236C2#2144591411yescharacteristic
237C2#2144592311yescharacteristic
238C2#2144593311yescharacteristic
subgroupG/H
centerC22#16839625
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2356C2
socleC22×C61#381
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2356D61
hypocenterC61#8769
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2356

Complements

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

NH ≅ G/Ntype
138. C61#8769semidirect

Maximal subgroups

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

subgroupindex
#214458152
#214441432
#214437222
#214436772
C61×#23562
#876961