Finite Group Databasebeta

← #29589679

Subgroups — #29589679

Order 15616.

358 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 87 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#21451031C211yesmaximal, characteristic
2#21444143C211yesmaximal, characteristic
3#21443762C214yesmaximal
4C61×#1467C211yesmaximal, characteristic
5C2×#14519777C411yescharacteristic
6#16839815—21no—
7#16839701—21no—
8#16839701—21no—
9#16839669C412yes—
10#16839668—21no—
11#16839668—21no—
12#16839627C2212yes—
13C4×C4⋊Dic61C411yescharacteristic
14#16839488—21no—
15#16839488C2212yes—
16C2×C4×Q8×C61C2211yescharacteristic
17C61×#432—21no—
18C61×#324—21no—
19C61×#324C2212yes—
20C22×Dic122—21no—
21#14519777—41no—
22#14519777—41no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61C2×C412yes—
26C2×C4×Dic61C2×C412yes—
27C4⋊#92418—41no—
28C22⋊#92418—22no—
29C4×#92418—41no—
30#14519684—21no—
31#14519684—22no—
32#14519684—22no—
33#14519684—22no—
34#14519684—22no—
35C22×Q8×C61C2×C411yescharacteristic
36C4×Q8×C61—41no—
37C4×Q8×C61—41no—
38C2×C4⋊C4×C61D411yescharacteristic
39C2×C4⋊C4×C61D411yescharacteristic
40C2×C4⋊C4×C61C2311yescharacteristic
41C2×C42×C61C2×C411yescharacteristic
42C2×C42×C61D411yescharacteristic
43C2×C42×C61D411yescharacteristic
44C4⋊C8×C61—41no—
45C22⋊C8×C61—22no—
46#97×C61—41no—
47C2×Q8×C61—22no—
48C2×Q8×C61—22no—
49C2×Q8×C61—41no—
50C22×C4×C61C22⋊C411yescharacteristic
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22×C411yescharacteristic
55C22×C4×C61C2×D411yescharacteristic
56C22×C4×C61C2×D411yescharacteristic
57C22×Dic61—22no—
58C22×Dic61—22no—
59C2×Dic122—44no—
60C2×Dic122—41no—
61C2×Dic122—41no—
62C2×C8×C61—42no—
63C4⋊C4×C61—41no—
64C4⋊C4×C61—41no—
65C4⋊C4×C61—41no—
66C42×C61—21no—
67C42×C61—21no—
68C42×C61—21no—
69C42×C61—21no—
70C42×C61—21no—
71C42×C61—21no—
72C4⋊Dic61—42no—
73C4⋊Dic61—42no—
74C4⋊Dic61—42no—
75C4×Dic61—24no—
76C2×#92418—42no—
77C23×C61C2×C22⋊C411yescharacteristic
78Q8×C61—44no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61#9911yescharacteristic
94C2×C4×C61#9911yescharacteristic
95C2×C4×C61#10112yes—
96C2×C4×C61#13112yes—
97C2×Dic61—42no—
98C2×Dic61—44no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61—42no—
102Dic122—82no—
103Dic122—82no—
104C8×C61—82no—
105#92418—82no—
106#11573—611nomaximal, Sylow
107C22×C61—21no—
108C22×C61—21no—
109C22×C61#40811yescharacteristic
110C22×C61C2×#9911yescharacteristic
111C22×C61C2×#10111yescharacteristic
112C4×C61—21no—
113C4×C61—22no—
114C4×C61—22no—
115C4×C61—41no—
116C4×C61—41no—
117C4×C61—41no—
118C4×C61—41no—
119C4×C61#35512yes—
120Dic61—82no—
121Dic61—82no—
122#2568—611no—
123#1467D6111yescharacteristic
124#1461—611no—
125#1324—614no—
126C2×C61—21no—
127C2×C61—21no—
128C2×C61#147211yescharacteristic
129C2×C61#212911yescharacteristic
130C2×C61C2×#35511yescharacteristic
131C2×C4⋊Q8—611no—
132C2×C4×Q8C2×D6111yescharacteristic
133#432—21no—
134#431—1221no—
135#400—1221no—
136#400—1221no—
137#391—612no—
138#391—1221no—
139#391—1221no—
140#382—612no—
141C4×C4⋊C4—611no—
142#324—21no—
143#324—612no—
144#324—1221no—
145#324C2×D6112yes—
146C61#1157311yescharacteristic, complemented, Sylow
147C22×Q8—1221no—
148C22×Q8C4×D6111yescharacteristic
149C4⋊Q8—2441no—
150C4⋊Q8—2441no—
151C4×Q8—41no—
152C4×Q8—41no—
153C2×C4⋊C4—612no—
154C2×C4⋊C4—1221no—
155C2×C4⋊C4—1221no—
156C2×C4⋊C4D24411yescharacteristic
157C2×C4⋊C4C22⋊D6111yescharacteristic
158C2×C4⋊C4C22×D6111yescharacteristic
159C2×C42—612no—
160C2×C42C4×D6111yescharacteristic
161C2×C42D24411yescharacteristic
162C2×C42C22⋊D6111yescharacteristic
163C4⋊C8—41no—
164C4⋊C8—2441no—
165C22⋊C8—22no—
166C22⋊C8—1222no—
167#97—41no—
168C4×C8—2441no—
169#95—1221no—
170#95—1222no—
171#95—1222no—
172#95—1222no—
173#95—1222no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—41no—
177C2×Q8—2444no—
178C2×Q8—2441no—
179C2×Q8—2441no—
180C22×C4—1222no—
181C22×C4—1222no—
182C22×C4#1175819811yescharacteristic
183C22×C4#1175819811yescharacteristic
184C22×C4#1175819811yescharacteristic
185C22×C4#1175819811yescharacteristic
186C22×C4C2×C4×D6111yescharacteristic
187C22×C4C2×D24411yescharacteristic
188C22×C4C2×C22⋊D6111yescharacteristic
189C2×C8—42no—
190C2×C8—2442no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—2442no—
195C4⋊C4—2442no—
196C4⋊C4—2442no—
197C42—21no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—21no—
202C42—21no—
203C42—1224no—
204C23C2×#1175819811yescharacteristic
205Q8—44no—
206Q8—4882no—
207Q8—4882no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—2442no—
223C2×C4—2442no—
224C2×C4—2444no—
225C2×C4—2442no—
226C2×C4—2442no—
227C2×C4#1451969111yescharacteristic
228C2×C4#1451969111yescharacteristic
229C2×C4#1451969512yes—
230C2×C4#1451978512yes—
231C8—82no—
232C8—4882no—
233C22—21no—
234C22—21no—
235C22#1683973011yescharacteristic
236C22C2×#1451969111yescharacteristic
237C22C2×#1451969511yescharacteristic
238C4—21no—
239C4—22no—
240C4—22no—
241C4—41no—
242C4—41no—
243C4—41no—
244C4—41no—
245C4—4882no—
246C4—4882no—
247C4#1683955812yes—
248C2—21no—
249C2—21no—
250C2#2144418411yescharacteristic
251C2#2144749311yescharacteristic
252C2C2×#1683955811yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1467C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1467D61
hypocenterC61#11573
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
146. C61#11573semidirect

Maximal subgroups

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

subgroupindex
#214510312
#214441432
#214437622
C61×#14672
#1157361