Finite Group Databasebeta

← #29568413

Subgroups — #29568413

Order 15616.

384 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454201C211yesmaximal, characteristic
2#21445565C211yesmaximal, characteristic
3#21443644C212yesmaximal
4#21443641C212yesmaximal
5C61×#1831C211yesmaximal, characteristic
6C2×C4×#92418—21no—
7#16839668C411yescharacteristic
8#16839668C411yescharacteristic
9#16839668C2211yescharacteristic
10#16839660C411yescharacteristic
11#16839660C411yescharacteristic
12#16839660C2211yescharacteristic
13#16839646—21no—
14#16839646—21no—
15#16839646—21no—
16#16839630—21no—
17#16839517—21no—
18#16839517C2212yes—
19C2×C4⋊C8×C61—21no—
20C43×C61C2211yescharacteristic
21C61×#336—21no—
22C61×#336C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C22×#92418—22no—
25C2×C4⋊Dic61C2×C411yescharacteristic
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—21no—
30C2×#11758196—21no—
31C4×#92418—24no—
32#14519684—21no—
33#14519684—21no—
34#14519684—21no—
35#14519684—21no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41C22×C8×C61—22no—
42C2×C42×C61C2×C411yescharacteristic
43C2×C42×C61C2×C411yescharacteristic
44C2×C42×C61D411yescharacteristic
45C2×C42×C61D411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C2×C42×C61D411yescharacteristic
48C2×C42×C61C2311yescharacteristic
49C4⋊C8×C61—42no—
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—21no—
58C22×Dic61—21no—
59C22×Dic61—21no—
60C22×Dic61—21no—
61C2×Dic122—22no—
62C2×Dic122—41no—
63C2×Dic122—41no—
64C2×C8×C61—42no—
65C2×C8×C61—42no—
66C2×C8×C61—42no—
67C42×C61—22no—
68C42×C61—22no—
69C42×C61—22no—
70C42×C61—41no—
71C42×C61—41no—
72C42×C61—41no—
73C42×C61SD1612yes—
74C42×C61Q1612yes—
75C4⋊Dic61—22no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78#11758196—42no—
79#11758196—42no—
80#11758196—42no—
81C2×#92418—24no—
82C2×#92418—42no—
83C2×#92418—42no—
84C23×C61C2×C22⋊C411yescharacteristic
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61#10312yes—
101C2×C4×C61#10312yes—
102C2×C4×C61#10412yes—
103C2×C4×C61#13112yes—
104C2×C4×C61C2×SD1611yescharacteristic
105C2×C4×C61C2×Q1611yescharacteristic
106C2×C4×C61#13512yes—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119Dic122—82no—
120C8×C61—82no—
121#92418—44no—
122#7669—611nomaximal, Sylow
123C22×C61#40811yescharacteristic
124C22×C61#41011yescharacteristic
125C22×C61#41311yescharacteristic
126C22×C61C2×#10311yescharacteristic
127C22×C61#41611yescharacteristic
128C22×C61C2×#10411yescharacteristic
129C22×C61#42111yescharacteristic
130C4×C61—22no—
131C4×C61—22no—
132C4×C61—22no—
133C4×C61—22no—
134C4×C61—21no—
135C4×C61—21no—
136C4×C61—22no—
137C4×C61—41no—
138Dic61—81no—
139Dic61—81no—
140Dic61—81no—
141Dic61—81no—
142#2863—611no—
143#1831D6111yescharacteristic
144#1744—611no—
145#1272—612no—
146#1271—612no—
147C2×C61#147311yescharacteristic
148C2×C61#148211yescharacteristic
149C2×C61#149311yescharacteristic
150C2×C61#150011yescharacteristic
151C2×C61#151811yescharacteristic
152C2×C61#153211yescharacteristic
153C2×C61#154211yescharacteristic
154C2×C4⋊C8—21no—
155C2×C4×C8—1221no—
156#391—611no—
157#391—611no—
158#391—611no—
159#389—611no—
160#389—611no—
161#389—611no—
162#387—1221no—
163#387—1221no—
164#387—1221no—
165#383—1221no—
166C43C2×D6111yescharacteristic
167#336—21no—
168#336—612no—
169#336—1221no—
170#336C2×D6112yes—
171C61#766911yescharacteristic, complemented, Sylow
172C22×Q8—611no—
173C22×C8—22no—
174C22×C8—1222no—
175C2×C4⋊C4—611no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—611no—
178C2×C4⋊C4—1221no—
179C2×C4⋊C4—1221no—
180C2×C4⋊C4—1221no—
181C2×C42C4×D6111yescharacteristic
182C2×C42C4×D6111yescharacteristic
183C2×C42D24411yescharacteristic
184C2×C42D24411yescharacteristic
185C2×C42C22⋊D6111yescharacteristic
186C2×C42C22⋊D6111yescharacteristic
187C2×C42C22×D6111yescharacteristic
188C4⋊C8—42no—
189C4×C8—1224no—
190#95—1221no—
191#95—1221no—
192#95—1221no—
193#95—1221no—
194#95—1221no—
195#95—1221no—
196#95—1221no—
197#95—1221no—
198#95—1221no—
199C2×Q8—1222no—
200C2×Q8—2441no—
201C2×Q8—2441no—
202C22×C4—1221no—
203C22×C4—1221no—
204C22×C4—1221no—
205C22×C4—1221no—
206C22×C4#1175819811yescharacteristic
207C22×C4#1175819811yescharacteristic
208C22×C4#1175819811yescharacteristic
209C22×C4#1175819811yescharacteristic
210C22×C4C2×C4×D6111yescharacteristic
211C22×C4C2×D24411yescharacteristic
212C22×C4C2×C22⋊D6111yescharacteristic
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—1224no—
217C2×C8—2442no—
218C2×C8—2442no—
219C4⋊C4—1222no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2442no—
223C4⋊C4—2442no—
224C4⋊C4—2442no—
225C42—22no—
226C42—22no—
227C42—22no—
228C42—41no—
229C42—41no—
230C42—41no—
231C42#1175820012yes—
232C42#1175820212yes—
233C23C2×#1175819811yescharacteristic
234Q8—4882no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4—2441no—
254C2×C4—2441no—
255C2×C4—2441no—
256C2×C4—2441no—
257C2×C4—2441no—
258C2×C4—2441no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4#1451970012yes—
263C2×C4#1451970012yes—
264C2×C4#1451970312yes—
265C2×C4#1451978512yes—
266C2×C4C2×#1175820011yescharacteristic
267C2×C4C2×#1175820211yescharacteristic
268C2×C4#1451979912yes—
269C8—82no—
270C8—2444no—
271C22#1683973011yescharacteristic
272C22#1683973511yescharacteristic
273C22#1683974411yescharacteristic
274C22C2×#1451970011yescharacteristic
275C22#1683975911yescharacteristic
276C22C2×#1451970311yescharacteristic
277C22#1683978011yescharacteristic
278C4—21no—
279C4—21no—
280C4—22no—
281C4—22no—
282C4—22no—
283C4—22no—
284C4—22no—
285C4—41no—
286C4—4881no—
287C4—4881no—
288C4—4881no—
289C4—4881no—
290C2#2144418911yescharacteristic
291C2#2144422811yescharacteristic
292C2#2144427311yescharacteristic
293C2#2144430611yescharacteristic
294C2#2144438211yescharacteristic
295C2#2144444011yescharacteristic
296C2#2144447711yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1831C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1831D61
hypocenterC61#7669
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
171. C61#7669semidirect

Maximal subgroups

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

subgroupindex
#214542012
#214455652
#214436442
#214436412
C61×#18312
#766961