Finite Group Databasebeta

← #29580073

Subgroups — #29580073

Order 15616.

600 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839660C211yesmaximal, characteristic
2#21445581C211yesmaximal, characteristic
3#21443661C214yesmaximal
4C61×#1797C211yesmaximal, characteristic
5C22×C4⋊Dic61C411yescharacteristic
6C22×C4⋊Dic61C411yescharacteristic
7C22×#11758196C412yes—
8C2×C22⋊#92418C2212yes—
9C2×#14519688—21no—
10#16839660—21no—
11#16839660—21no—
12#16839660—21no—
13#16839660—21no—
14C2×#14519684C2212yes—
15#16839517—21no—
16C22×C42×C61C2211yescharacteristic
17C2×C4⋊C8×C61—21no—
18C2×C22⋊C8×C61C2212yes—
19C61×#336—21no—
20C23×Dic61C2×C412yes—
21C23×Dic61C2×C412yes—
22C22×#92418—22no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—24no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—42no—
29C2×#11758196—22no—
30C2×#11758196—22no—
31C2×#11758196—44no—
32C22⋊#92418—22no—
33C22⋊#92418Q814yes—
34#14519688—42no—
35#14519684—22no—
36#14519684—22no—
37C23×C4×C61C2×C411yescharacteristic
38C23×C4×C61C2×C411yescharacteristic
39C23×C4×C61C2311yescharacteristic
40C22×C8×C61—22no—
41C2×C42×C61—42no—
42C2×C42×C61D411yescharacteristic
43C2×C42×C61D411yescharacteristic
44C2×C42×C61D411yescharacteristic
45C2×C42×C61D411yescharacteristic
46C4⋊C8×C61—42no—
47C22⋊C8×C61—24no—
48C24×C61C22×C411yescharacteristic
49C22×C4×C61—22no—
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61—41no—
55C22×C4×C61—41no—
56C22×C4×C61—41no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×Q812yes—
64C22×C4×C61#4112yes—
65C22×Dic61—22no—
66C22×Dic61—22no—
67C22×Dic61—22no—
68C22×Dic61—24no—
69C22×Dic61—42no—
70C22×Dic61—42no—
71C22×Dic61—42no—
72C22×Dic61—42no—
73C22×Dic61M1614yes—
74C2×C8×C61—42no—
75C2×C8×C61—42no—
76C2×C8×C61—42no—
77C42×C61—22no—
78C42×C61—22no—
79C42×C61—41no—
80C42×C61—41no—
81C4⋊Dic61—24no—
82C4⋊Dic61—24no—
83C4⋊Dic61—42no—
84C4⋊Dic61—42no—
85#11758196—44no—
86#11758196—44no—
87C2×#92418—24no—
88C2×#92418—42no—
89C2×#92418—42no—
90C23×C61—21no—
91C23×C61—21no—
92C23×C61—21no—
93C23×C61—21no—
94C23×C61C2×C22⋊C411yescharacteristic
95C23×C61C4×Q812yes—
96C23×C61C2×M1612yes—
97C23×C61#13112yes—
98C2×C4×C61—28no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—42no—
113C2×C4×C61—42no—
114C2×C4×C61—44no—
115C2×C4×C61#9912yes—
116C2×C4×C61#10012yes—
117C2×C4×C61#10112yes—
118C2×C4×C61C22⋊Q812yes—
119C2×C4×C61#12411yescharacteristic
120C2×C4×C61C4⋊Q811yescharacteristic
121C2×Dic61—24no—
122C2×Dic61—44no—
123C2×Dic61—42no—
124C2×Dic61—42no—
125C2×Dic61—44no—
126C2×Dic61—42no—
127C2×Dic61—42no—
128C2×Dic61—42no—
129C2×Dic61—84no—
130C8×C61—82no—
131#92418—44no—
132#9883—611nomaximal, Sylow
133C22×C61—22no—
134C22×C61—22no—
135C22×C61—22no—
136C22×C61—22no—
137C22×C61—22no—
138C22×C61—22no—
139C22×C61#39111yescharacteristic
140C22×C61#40711yescharacteristic
141C22×C61#40811yescharacteristic
142C22×C61C2×#9911yescharacteristic
143C22×C61#41011yescharacteristic
144C22×C61C2×#10011yescharacteristic
145C22×C61C2×#10111yescharacteristic
146C22×C61#44614yes—
147C4×C61—22no—
148C4×C61—22no—
149C4×C61—22no—
150C4×C61—22no—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—41no—
154Dic61—44no—
155Dic61—82no—
156C2×#389—611no—
157#1797D6111yescharacteristic
158#1749—611no—
159#1280—614no—
160C2×C61—24no—
161C2×C61#146311yescharacteristic
162C2×C61#146611yescharacteristic
163C2×C61#147011yescharacteristic
164C2×C61#147111yescharacteristic
165C2×C61#198511yescharacteristic
166C2×C61#199611yescharacteristic
167C2×C61#199711yescharacteristic
168C22×C4⋊C4—611no—
169C22×C4⋊C4—612no—
170C22×C4⋊C4—611no—
171C22×C42C2×D6111yescharacteristic
172C2×C4⋊C8—21no—
173C2×C22⋊C8—612no—
174C2×C22⋊C8C2×D6112yes—
175C2×#97—1221no—
176#389—1221no—
177#389—1221no—
178#389—1221no—
179#389—1221no—
180C2×#95—612no—
181#336—21no—
182#336—1221no—
183C61#988311yescharacteristic, complemented, Sylow
184C23×C4—612no—
185C23×C4—612no—
186C23×C4C4×D6111yescharacteristic
187C23×C4C4×D6111yescharacteristic
188C23×C4C22×D6111yescharacteristic
189C22×C8—22no—
190C22×C8—1222no—
191C2×C4⋊C4—1224no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1222no—
195C2×C4⋊C4—1222no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4—2444no—
199C2×C4⋊C4—2442no—
200C2×C42—42no—
201C2×C42D24411yescharacteristic
202C2×C42D24411yescharacteristic
203C2×C42C22⋊D6111yescharacteristic
204C2×C42C22⋊D6111yescharacteristic
205C4⋊C8—42no—
206C22⋊C8—24no—
207C22⋊C8—614no—
208C22⋊C8—1222no—
209#97—2442no—
210#95—1222no—
211#95—1222no—
212C24C2×C4×D6111yescharacteristic
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—614no—
222C22×C4—1222no—
223C22×C4—1222no—
224C22×C4—1224no—
225C22×C4—1222no—
226C22×C4—2442no—
227C22×C4—2442no—
228C22×C4—2442no—
229C22×C4—2442no—
230C22×C4#1175819811yescharacteristic
231C22×C4#1175819811yescharacteristic
232C22×C4#1175819811yescharacteristic
233C22×C4#1175819811yescharacteristic
234C22×C4C2×D24411yescharacteristic
235C22×C4#1175822412yes—
236C22×C4Q8×D6112yes—
237C22×C4C2×C22⋊D6111yescharacteristic
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—1224no—
242C2×C8—2442no—
243C2×C8—2442no—
244C4⋊C4—1224no—
245C4⋊C4—1224no—
246C4⋊C4—2444no—
247C4⋊C4—2442no—
248C4⋊C4—2442no—
249C4⋊C4—2444no—
250C42—22no—
251C42—22no—
252C42—41no—
253C42—41no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23C2×#1175819811yescharacteristic
259C23#1451974212yes—
260C23M16×D6112yes—
261C23#1451978312yes—
262C2×C4—28no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—44no—
279C2×C4—1224no—
280C2×C4—4884no—
281C2×C4—2442no—
282C2×C4—2442no—
283C2×C4—2442no—
284C2×C4—2444no—
285C2×C4—2442no—
286C2×C4—2442no—
287C2×C4—2444no—
288C2×C4#1451969112yes—
289C2×C4#1451969312yes—
290C2×C4#1451969512yes—
291C2×C4#1451975712yes—
292C2×C4#1451976411yescharacteristic
293C2×C4#1451977511yescharacteristic
294C8—82no—
295C8—2444no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22#1683966711yescharacteristic
303C22#1683972511yescharacteristic
304C22#1683972811yescharacteristic
305C22C2×#1451969111yescharacteristic
306C22#1683973511yescharacteristic
307C22C2×#1451969311yescharacteristic
308C22C2×#1451969511yescharacteristic
309C22#1683989114yes—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—21no—
314C4—22no—
315C4—21no—
316C4—41no—
317C4—4882no—
318C4—2444no—
319C2—24no—
320C2#2144414811yescharacteristic
321C2#2144415911yescharacteristic
322C2#2144417411yescharacteristic
323C2#2144417811yescharacteristic
324C2#2144675811yescharacteristic
325C2#2144680311yescharacteristic
326C2#2144680711yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutator, prime radicalC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1797C2
socleC23×C61C2×C22⋊C4
cosocleC23×C4×C61C23
hypercenter#1797D61
hypocenterC61#9883
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
183. C61#9883semidirect

Maximal subgroups

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

subgroupindex
C2×#168396602
#214455812
#214436612
C61×#17972
#988361