Finite Group Databasebeta

← #29573594

Subgroups — #29573594

Order 15616.

422 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 131 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×#2351C211yesmaximal, characteristic
6#16839815C2212yes—
7#16839786C2212yes—
8C2×#14519696—21no—
9#16839531—21no—
10#16839488—22no—
11C2×C4×Q8×C61—21no—
12C2×C4×Q8×C61C2211yescharacteristic
13C61×#389—21no—
14C61×#389—22no—
15C61×#382C412yes—
16C61×#382C2211yescharacteristic
17C4×C4⋊C4×C61C412yes—
18C4×C4⋊C4×C61C2211yescharacteristic
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—
29C4×Q8×C61—44no—
30C2×C4⋊C4×C61—22no—
31C2×C4⋊C4×C61—22no—
32C2×C4⋊C4×C61—21no—
33C2×C4⋊C4×C61—21no—
34C2×C4⋊C4×C61D412yes—
35C2×C4⋊C4×C61D411yescharacteristic
36C2×C42×C61—22no—
37C2×C42×C61—21no—
38C2×C42×C61C2×C412yes—
39C2×C42×C61C2311yescharacteristic
40#95×C61—22no—
41#95×C61—21no—
42#95×C61C2×C411yescharacteristic
43#95×C61C2×C412yes—
44#95×C61C2×C411yescharacteristic
45C2×Q8×C61—22no—
46C2×Q8×C61—22no—
47C2×Q8×C61SD1612yes—
48C2×Q8×C61Q1612yes—
49C22×C4×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61—22no—
52C22×C4×C61C22⋊C412yes—
53C22×C4×C61C22⋊C412yes—
54C22×C4×C61C22×C411yescharacteristic
55C22×C4×C61C2×D411yescharacteristic
56C22×C4×C61C2×D411yescharacteristic
57C4⋊C4×C61—24no—
58C4⋊C4×C61—22no—
59C4⋊C4×C61—42no—
60C4⋊C4×C61—44no—
61C4⋊C4×C61—44no—
62C4⋊C4×C61—42no—
63C42×C61—22no—
64C42×C61—22no—
65C42×C61—44no—
66C42×C61—42no—
67C42×C61#4112yes—
68C42×C61#4112yes—
69#11758194—42no—
70#11758194—42no—
71C2×#92418—42no—
72C2×#92418—42no—
73C23×C61C2×C22⋊C411yescharacteristic
74Q8×C61—24no—
75Q8×C61—24no—
76C2×C4×C61—22no—
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×C61—41no—
86C2×C4×C61—42no—
87C2×C4×C61—41no—
88C2×C4×C61—42no—
89C2×C4×C61—42no—
90C2×C4×C61—41no—
91C2×C4×C61#10314yes—
92C2×C4×C61#11711yescharacteristic
93C2×C4×C61#11711yescharacteristic
94C2×C4×C61#12312yes—
95C2×C4×C61#12312yes—
96C2×C4×C61C2×SD1611yescharacteristic
97C2×C4×C61C2×Q1611yescharacteristic
98C2×C4×C61AGL(1,ℤ/8)12yes—
99#92418—82no—
100#92418—82no—
101#8767—611nomaximal, Sylow
102C22×C61—21no—
103C22×C61—21no—
104C22×C61#38111yescharacteristic
105C22×C61C2×#10311yescharacteristic
106C22×C61#41811yescharacteristic
107C4×C61—24no—
108C4×C61—22no—
109C4×C61—21no—
110C4×C61—21no—
111C4×C61—42no—
112C4×C61—42no—
113C4×C61—82no—
114C4×C61—81no—
115C4×C61#48112yes—
116C4×C61#48412yes—
117#2351D6111yescharacteristic
118#1801—611no—
119#1461—611no—
120#1303—612no—
121#1286—612no—
122C2×C61—21no—
123C2×C61—21no—
124C2×C61#182411yescharacteristic
125C2×C61#182711yescharacteristic
126C2×C61#183011yescharacteristic
127C2×C4×Q8—21no—
128C2×C4×Q8C2×D6111yescharacteristic
129#431—612no—
130#423—612no—
131C2×#101—1221no—
132#389—21no—
133#389—22no—
134#382Dic6112yes—
135#382C2×D6111yescharacteristic
136C4×C4⋊C4Dic6112yes—
137C4×C4⋊C4C2×D6111yescharacteristic
138#343—1221no—
139#324—1222no—
140C61#876711yescharacteristic, complemented, Sylow
141C22×Q8C22⋊D6111yescharacteristic
142C2×M16—1222no—
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8—44no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4C22⋊D6112yes—
151C2×C4⋊C4C22⋊D6111yescharacteristic
152C2×C42—22no—
153C2×C42—21no—
154C2×C42C2×Dic6112yes—
155C2×C42C22×D6111yescharacteristic
156C4⋊C8—1222no—
157C4⋊C8—1222no—
158C4⋊C8—1222no—
159#101—2442no—
160C22⋊C8—1222no—
161C4×C8—1222no—
162#95—22no—
163#95—21no—
164#95C2×Dic6111yescharacteristic
165#95C2×Dic6112yes—
166#95C2×Dic6111yescharacteristic
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8#1175820112yes—
170C2×Q8#1175820212yes—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—22no—
174C22×C4C22⋊Dic6112yes—
175C22×C4C22⋊Dic6112yes—
176C22×C4C22×Dic6111yescharacteristic
177C22×C4C2×C22⋊D6111yescharacteristic
178C22×C4C2×C22⋊D6111yescharacteristic
179M16—2442no—
180M16—2442no—
181C2×C8—2442no—
182C2×C8—2442no—
183C4⋊C4—24no—
184C4⋊C4—22no—
185C4⋊C4—44no—
186C4⋊C4—42no—
187C4⋊C4—44no—
188C4⋊C4—42no—
189C42—22no—
190C42—22no—
191C42—44no—
192C42—42no—
193C42#1175822212yes—
194C42#1175822212yes—
195C23C2×C22⋊Dic6111yescharacteristic
196Q8—24no—
197Q8—24no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—42no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4#1451970114yes—
214C2×C4#1451973611yescharacteristic
215C2×C4#1451973611yescharacteristic
216C2×C4#1451976012yes—
217C2×C4#1451976012yes—
218C2×C4C2×#1175820111yescharacteristic
219C2×C4C2×#1175820211yescharacteristic
220C2×C4#1451980312yes—
221C8—4882no—
222C8—4882no—
223C22—21no—
224C22—21no—
225C22#1683962511yescharacteristic
226C22C2×#1451970111yescharacteristic
227C22#1683976711yescharacteristic
228C4—24no—
229C4—22no—
230C4—21no—
231C4—21no—
232C4—42no—
233C4—42no—
234C4—82no—
235C4—81no—
236C4#1684008012yes—
237C4#1684009712yes—
238C2—21no—
239C2—21no—
240C2#2144590911yescharacteristic
241C2#2144592311yescharacteristic
242C2#2144593311yescharacteristic
subgroupG/H
centerC22#16839625
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2351C2
socleC22×C61#381
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2351D61
hypocenterC61#8767
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2351

Complements

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

NH ≅ G/Ntype
140. C61#8767semidirect

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×#23512
#876761