Finite Group Databasebeta

← #30599241

Subgroups — #30599241

Order 15616.

540 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 126 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#21461674C211yesmaximal, characteristic
2C4×#14519834C211yesmaximal, characteristic
3#21460655C214yesmaximal, complemented
4#21448224C211yesmaximal, characteristic
5C2×C4⋊#92420C2212yes—
6C2×#14519834—21no—
7C2×#14519834—21no—
8C2×C4×#92420C2212yes—
9#16840628—21no—
10#16840628—21no—
11C2×#14519735—21no—
12C2×C42×D61C2211yescharacteristic
13#16839632C411yescharacteristic
14#16839627—21no—
15#16839619—21no—
16#16839619C412yes—
17C4⋊C4×Dic61—21no—
18C4⋊C4×Dic61C2212yes—
19C61×#384C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22C4⋊#92420—24no—
23#14519834—24no—
24#14519834—42no—
25C4×#92420—24no—
26C22×C4×D61C2×C411yescharacteristic
27C22×C4×D61D411yescharacteristic
28C22×C4×D61D411yescharacteristic
29#14519735—44no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61C2×C412yes—
33C2×#11758198—22no—
34C2×C4×Dic61—22no—
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61C2311yescharacteristic
38C42×D61—24no—
39#14519684—22no—
40#14519684—22no—
41C2×C4⋊C4×C61—21no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61C2×C412yes—
44C2×C42×C61C2×C411yescharacteristic
45C23×D61C22⋊C411yescharacteristic
46C22×C4×C61—22no—
47C22×C4×C61C22⋊C411yescharacteristic
48C22×C4×C61C22⋊C411yescharacteristic
49C22×C4×C61C22×C411yescharacteristic
50C22×Dic61—22no—
51C22×Dic61C22⋊C411yescharacteristic
52C22×Dic61C2×D411yescharacteristic
53C22×Dic61C2×D411yescharacteristic
54C2×C4×D61—22no—
55C2×C4×D61—22no—
56C2×C4×D61—22no—
57C2×C4×D61—22no—
58C2×C4×D61—22no—
59C2×C4×D61—22no—
60C2×C4×D61—22no—
61C2×C4×D61—41no—
62C2×C4×D61SD1612yes—
63C2×C4×D61Q1612yes—
64C2×#92420—24no—
65C2×#92420—42no—
66C2×#92420—42no—
67C2×#92420—42no—
68C2×#92420—42no—
69C2×#92420—42no—
70C4⋊C4×C61—24no—
71C4⋊C4×C61—42no—
72C4⋊C4×C61—42no—
73C42×C61—22no—
74#11758198—44no—
75C4⋊Dic61—24no—
76C4⋊Dic61—42no—
77C4⋊Dic61—42no—
78C4×Dic61—22no—
79C4×Dic61—22no—
80C4×Dic61—44no—
81C4×Dic61#4114yes—
82C23×C61C2×C22⋊C411yescharacteristic
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—21no—
86C22×D61—21no—
87C22×D61—21no—
88C22×D61—21no—
89C22×D61#10312yes—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61#10312yes—
98C2×C4×C61#10412yes—
99C2×C4×C61#11712yes—
100C2×C4×C61#13112yes—
101C2×C4×C61#13112yes—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109C2×Dic61—42no—
110C2×Dic61#12312yes—
111C2×Dic61#12312yes—
112C2×Dic61C2×SD1611yescharacteristic
113C2×Dic61C2×Q1611yescharacteristic
114C2×Dic61AGL(1,ℤ/8)12yes—
115C4×D61—24no—
116C4×D61—24no—
117C4×D61—44no—
118C4×D61—44no—
119#92420—44no—
120#92420—82no—
121#8710—611nomaximal, Sylow
122C22×C61#38111yescharacteristic
123C22×C61#40811yescharacteristic
124C22×C61#40811yescharacteristic
125C22×C61C2×#10311yescharacteristic
126C22×C61#41811yescharacteristic
127C22×C61C2×#10411yescharacteristic
128C22×C61#42111yescharacteristic
129C2×D61—22no—
130C2×D61—22no—
131C2×D61—22no—
132C2×D61—41no—
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—41no—
136C4×C61—22no—
137C4×C61—22no—
138C4×C61—82no—
139C4×C61#43314yes—
140Dic61—22no—
141Dic61—41no—
142Dic61—82no—
143Dic61#48112yes—
144Dic61#48412yes—
145#2285—611no—
146#1797—611no—
147C4×C22⋊C8—611no—
148#1279—614no—
149C2×C61#148111yescharacteristic
150C2×C61#148411yescharacteristic
151C2×C61#149311yescharacteristic
152C2×C61#149611yescharacteristic
153C2×C61#181811yescharacteristic
154C2×C61#182411yescharacteristic
155C2×C61#182611yescharacteristic
156D61—42no—
157C2×#117—1221no—
158C22×C42—611no—
159C2×C4⋊C8—612no—
160C2×C22⋊C8—1221no—
161C2×C22⋊C8—1221no—
162C2×C4×C8—612no—
163#384—611no—
164#384#692311yescharacteristic
165#382—1221no—
166#380—612no—
167#380—1221no—
168C4×C4⋊C4—612no—
169C4×C4⋊C4—1221no—
170#336—1221no—
171#336—1221no—
172C61#871011yescharacteristic, complemented, Sylow
173C23×C4—611no—
174C23×C4—611no—
175C23×C4—611no—
176C22×C8—1222no—
177C22×C8—1222no—
178#117—2444no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—612no—
182C2×C4⋊C4—1221no—
183C2×C4⋊C4—1221no—
184C2×C4⋊C4C2×#692312yes—
185C2×C22⋊C4—1222no—
186C2×C42—611no—
187C2×C42—611no—
188C2×C42—611no—
189C2×C42—1224no—
190C2×C42—1222no—
191C2×C42C2×#692311yescharacteristic
192C4⋊C8—1224no—
193C22⋊C8—1224no—
194C22⋊C8—2442no—
195C4×C8—1224no—
196#95—1222no—
197#95—1222no—
198C24—611no—
199C22×C4—22no—
200C22×C4—611no—
201C22×C4—611no—
202C22×C4—612no—
203C22×C4—612no—
204C22×C4—611no—
205C22×C4—1222no—
206C22×C4—1222no—
207C22×C4—1222no—
208C22×C4—1222no—
209C22×C4—1222no—
210C22×C4—1222no—
211C22×C4—1222no—
212C22×C4—1222no—
213C22×C4—2441no—
214C22×C4C22⋊#692311yescharacteristic
215C22×C4C22⋊#692311yescharacteristic
216C22×C4C22×#692311yescharacteristic
217C2×C8—1224no—
218C2×C8—2442no—
219C2×C8—2442no—
220C2×C8—2442no—
221C2×C8—2442no—
222C2×C8—2442no—
223C4⋊C4—24no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—1224no—
227C4⋊C4—2442no—
228C4⋊C4—2442no—
229C22⋊C4—2444no—
230C42—22no—
231C42—614no—
232C42—1222no—
233C42—1222no—
234C42—2444no—
235C23—612no—
236C23—1221no—
237C23—1221no—
238C23—1221no—
239C23—1221no—
240C23—1221no—
241C23—1221no—
242C23C2×C22⋊#692311yescharacteristic
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—612no—
251C2×C4—611no—
252C2×C4—611no—
253C2×C4—612no—
254C2×C4—612no—
255C2×C4—1224no—
256C2×C4—1224no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—2444no—
263C2×C4—2442no—
264C2×C4—2442no—
265C2×C4—2442no—
266C2×C4—2444no—
267C2×C4#1451984012yes—
268C2×C4#1451984112yes—
269C2×C4#1451985612yes—
270C2×C4#1451986412yes—
271C2×C4#1451986512yes—
272C8—4882no—
273C8—2444no—
274C22—1222no—
275C22—1222no—
276C22—1222no—
277C22—2441no—
278C22—2441no—
279C22—2441no—
280C22—2441no—
281C22#1684070511yescharacteristic
282C22#1684073611yescharacteristic
283C22#1684073711yescharacteristic
284C22C2×#1451984011yescharacteristic
285C22#1684075411yescharacteristic
286C22C2×#1451984111yescharacteristic
287C22#1684076111yescharacteristic
288C4—22no—
289C4—22no—
290C4—82no—
291C4—612no—
292C4—612no—
293C4—1222no—
294C4—4882no—
295C4—2441no—
296C4#1684078714yes—
297C2—2442no—
298C2#2146112811yescharacteristic
299C2#2146113911yescharacteristic
300C2#2146116911yescharacteristic
301C2#2146118011yescharacteristic
302C2#2146171311yescharacteristic
303C2#2146172311yescharacteristic
304C2#2146172511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#8710
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
3. #21460655C2semidirect
172. C61#8710semidirect

Maximal subgroups

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

subgroupindex
#214616742
C4×#145198342
#214606552
#214482242
#871061