Finite Group Databasebeta

← #30604353

Subgroups — #30604353

Order 15616.

426 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461078C211yesmaximal, characteristic
2#21461054C211yesmaximal, characteristic
3#21460764C214yesmaximal, complemented
4#21450130C211yesmaximal, characteristic
5#16840783—21no—
6D61⋊(C22⋊C8)—21no—
7#16840608—21no—
8#16840606—21no—
9#16840605C2212yes—
10#16840605C2212yes—
11C2×C4×C22⋊D61C2211yescharacteristic
12#16839700—21no—
13#16839697—21no—
14#16839658—21no—
15#16839641C412yes—
16#16839635C2212yes—
17#16839622C411yescharacteristic
18#16839619—21no—
19C22×C4⋊C4×C61C411yescharacteristic
20C2×D61⋊C8—41no—
21C4⋊#92420—41no—
22#14519834—41no—
23C22⋊#92420—22no—
24C22⋊#92420—22no—
25#14519832—41no—
26C22×C22⋊D61C2×C411yescharacteristic
27C22×C4×D61D411yescharacteristic
28C4×C22⋊D61—41no—
29C4×C22⋊D61—41no—
30C2×C4⋊Dic61—21no—
31C2×#11758196—22no—
32C2×#11758196D411yescharacteristic
33C2×C22⋊Dic61C2×C412yes—
34C2×C22⋊Dic61C2311yescharacteristic
35C2×#11758198—22no—
36C2×#11758198D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38#14519684—21no—
39#14519684—22no—
40#14519684—22no—
41C23×C4×C61C2×C412yes—
42C23×C4×C61C2×C411yescharacteristic
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—41no—
46C2×C4⋊C4×C61—41no—
47C24×C61C22×C411yescharacteristic
48C23×D61C22⋊C411yescharacteristic
49C22×C4×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61—22no—
52C22×C4×C61—42no—
53C22×C4×C61—42no—
54C22×C4×C61—82no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C2×C22⋊D61—22no—
58C2×C22⋊D61—22no—
59C2×C22⋊D61—41no—
60C22×Dic61—22no—
61C22×Dic61C22⋊C411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C2×C4×D61—21no—
65C2×C4×D61—21no—
66C2×C4×D61—42no—
67C2×#92420—42no—
68C2×#92420—42no—
69D61⋊C8—82no—
70C4⋊C4×C61—42no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61—41no—
73C22⋊Dic61—24no—
74C22⋊Dic61—41no—
75#11758198—41no—
76#11758198—82no—
77C4⋊Dic61—42no—
78#11758196—41no—
79#11758196—82no—
80C4×Dic61—21no—
81C4×Dic61—21no—
82C23×C61—21no—
83C23×C61—21no—
84C23×C61—41no—
85C23×C61—41no—
86C23×C61C2×C22⋊C411yescharacteristic
87C23×C61#13112yes—
88C22×D61—21no—
89C22×D61—21no—
90C22×D61—41no—
91C22×D61—41no—
92C22×D61#10112yes—
93C2×C4×C61—22no—
94C2×C4×C61—21no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61—41no—
98C2×C4×C61—42no—
99C2×C4×C61—42no—
100C2×C4×C61—42no—
101C2×C4×C61—84no—
102C2×C4×C61#9911yescharacteristic
103C2×C4×C61#9911yescharacteristic
104C22⋊D61—44no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—42no—
113C2×Dic61—42no—
114C2×Dic61—42no—
115C4×D61—42no—
116C4×D61—81no—
117#92420—82no—
118#92420—82no—
119#11576—611nomaximal, Sylow
120C22×C61—21no—
121C22×C61—21no—
122C22×C61—22no—
123C22×C61—42no—
124C22×C61—42no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61#40811yescharacteristic
128C22×C61C2×#9911yescharacteristic
129C22×C61C2×#10111yescharacteristic
130C2×D61—22no—
131C2×D61—41no—
132C2×D61—41no—
133C2×D61—42no—
134C2×D61—81no—
135C4×C61—21no—
136C4×C61—41no—
137C4×C61—82no—
138C4×C61#35212yes—
139Dic61—41no—
140Dic61—41no—
141Dic61—41no—
142Dic61—82no—
143#2487—611no—
144#1466—611no—
145#1459—611no—
146#1326—614no—
147C2×C61—21no—
148C2×C61—21no—
149C2×C61—42no—
150C2×C61#147211yescharacteristic
151C2×C61C2×#35211yescharacteristic
152C2×C61#212211yescharacteristic
153D61—42no—
154C2×C4×D4—611no—
155C22×C4⋊C4#692311yescharacteristic
156#432—1221no—
157C2×C22⋊C8—1221no—
158#400—1221no—
159#399—1221no—
160#389—1221no—
161#386—612no—
162#385—612no—
163#380—611no—
164#380—1221no—
165#324—1221no—
166#323—612no—
167#323—612no—
168#323—1221no—
169C61#1157611yescharacteristic, complemented, Sylow
170C22×D4—611no—
171C23×C4—611no—
172C23×C4C2×#692312yes—
173C23×C4C2×#692311yescharacteristic
174C22×C8—2441no—
175C4×D4—2441no—
176C4×D4—2441no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—611no—
182C2×C4⋊C4—1222no—
183C2×C4⋊C4—1221no—
184C2×C22⋊C4—612no—
185C2×C22⋊C4—611no—
186C2×C22⋊C4—611no—
187C2×C22⋊C4—1222no—
188C2×C42—611no—
189C4⋊C8—2441no—
190C22⋊C8—1222no—
191C22⋊C8—1222no—
192C22⋊C8—2441no—
193#97—2441no—
194#95—1222no—
195#95—1222no—
196#95—1221no—
197C24—611no—
198C24C22×#692311yescharacteristic
199C2×D4—1222no—
200C2×D4—1222no—
201C2×D4—2441no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—22no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—82no—
208C22×C4—611no—
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—1221no—
212C22×C4—1221no—
213C22×C4—1222no—
214C22×C4—2442no—
215C22×C4C22⋊#692311yescharacteristic
216C22×C4C22⋊#692311yescharacteristic
217C2×C8—4882no—
218C2×C8—2442no—
219C2×C8—2442no—
220C4⋊C4—42no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—4882no—
224C4⋊C4—2441no—
225C4⋊C4—2442no—
226C22⋊C4—1224no—
227C22⋊C4—4882no—
228C22⋊C4—2441no—
229C22⋊C4—2441no—
230C42—1221no—
231C42—1221no—
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23—612no—
237C23—1221no—
238C23—1221no—
239C23—2441no—
240C23—2441no—
241C23C2×C22⋊#692311yescharacteristic
242C23#1451986512yes—
243D4—2444no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—84no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—4881no—
259C2×C4—2442no—
260C2×C4—2442no—
261C2×C4—2442no—
262C2×C4—2442no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4#1451983511yescharacteristic
266C2×C4#1451983511yescharacteristic
267C8—4882no—
268C8—4882no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—42no—
273C22—42no—
274C22—41no—
275C22—41no—
276C22—1222no—
277C22—4881no—
278C22—2442no—
279C22—2441no—
280C22—2441no—
281C22#1684073711yescharacteristic
282C22C2×#1451983511yescharacteristic
283C22D61⋊#10111yescharacteristic
284C4—21no—
285C4—41no—
286C4—82no—
287C4—4882no—
288C4—2441no—
289C4—2441no—
290C4—2441no—
291C4#1684066412yes—
292C2—21no—
293C2—21no—
294C2—42no—
295C2—2442no—
296C2#2146109911yescharacteristic
297C2C2×#1684066411yescharacteristic
298C2#2146207811yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C2×#99
prime radicalC22×C22⋊D61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#11576
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460764C2semidirect
169. C61#11576semidirect

Maximal subgroups

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

subgroupindex
#214610782
#214610542
#214607642
#214501302
#1157661