Finite Group Databasebeta

← #29580198

Subgroups — #29580198

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454171C211yesmaximal, characteristic
2#21444046C211yesmaximal, characteristic
3#21443699C214yesmaximal
4C61×#1797C211yesmaximal, characteristic
5C2×#14519777C411yescharacteristic, complemented
6C2×#14519756—21no—
7#16839668—21no—
8#16839660—21no—
9#16839660C412yescomplemented
10#16839632C411yescharacteristic, complemented
11#16839622—21no—
12#16839622C2212yes—
13C2×#14519684—21no—
14C2×#14519684—21no—
15C2×#14519684C2212yes—
16C22×C42×C61C2211yescharacteristic
17C2×C4⋊C8×C61—21no—
18C2×C22⋊C8×C61C2212yes—
19C61×#336—21no—
20C22×Dic122—21no—
21C23×Dic61—22no—
22#14519777—42no—
23#14519756—42no—
24#14519756—42no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61C2×C412yes—
29C2×C4⋊Dic61C2×C412yes—
30C2×#11758196—22no—
31C2×C22⋊Dic61—22no—
32#14519684—22no—
33#14519684—22no—
34#14519684—22no—
35#14519684—42no—
36#14519684—42no—
37#14519684Q814yescomplemented
38C23×C4×C61D411yescharacteristic
39C23×C4×C61D411yescharacteristic
40C23×C4×C61C2311yescharacteristic
41C22×C8×C61—22no—
42C2×C42×C61—42no—
43C2×C42×C61C2×C411yescharacteristic
44C2×C42×C61C2×C411yescharacteristic
45C2×C42×C61D411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C4⋊C8×C61—42no—
48C22⋊C8×C61—24no—
49C24×C61C2×D411yescharacteristic
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—41no—
53C22×C4×C61—41no—
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×C61D812yes—
62C22×C4×C61SD1612yes—
63C22×C4×C61C22×C411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×Q812yes—
66C22×C4×C61#4112yes—
67C22×Dic61—22no—
68C22×Dic61—22no—
69C22×Dic61—24no—
70C22×Dic61—42no—
71C22×Dic61—42no—
72C22×Dic61—42no—
73C22×Dic61—42no—
74C22×Dic61—42no—
75C22×Dic61—42no—
76C2×Dic122—42no—
77C2×Dic122—42no—
78C2×Dic122—42no—
79C2×C8×C61—42no—
80C2×C8×C61—42no—
81C2×C8×C61—42no—
82C42×C61—22no—
83C42×C61—22no—
84C42×C61—41no—
85C42×C61—41no—
86C22⋊Dic61—42no—
87C22⋊Dic61—42no—
88C4⋊Dic61—42no—
89C4⋊Dic61—42no—
90C4⋊Dic61—42no—
91C4⋊Dic61—42no—
92C4⋊Dic61—42no—
93#11758196—44no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61C2×C22⋊C411yescharacteristic
99C23×C61C22⋊Q812yes—
100C23×C61C2×D811yescharacteristic
101C23×C61C2×SD1611yescharacteristic
102C23×C61#13712yes—
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—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—42no—
117C2×C4×C61—42no—
118C2×C4×C61—42no—
119C2×C4×C61—42no—
120C2×C4×C61—44no—
121C2×C4×C61#9912yes—
122C2×C4×C61#10212yes—
123C2×C4×C61#10212yes—
124C2×C4×C61C4×Q812yes—
125C2×C4×C61#12411yescharacteristic
126C2×C4×C61C4⋊Q811yescharacteristic
127C2×Dic61—44no—
128C2×Dic61—44no—
129C2×Dic61—42no—
130C2×Dic61—42no—
131C2×Dic61—42no—
132C2×Dic61—42no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135C2×Dic61—44no—
136C2×Dic61—82no—
137C2×Dic61—82no—
138C2×Dic61—82no—
139C2×Dic61—82no—
140Dic122—84no—
141C8×C61—82no—
142#9912—611nomaximal, Sylow
143C22×C61—22no—
144C22×C61—22no—
145C22×C61—22no—
146C22×C61—22no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61#39111yescharacteristic
152C22×C61C2×#9911yescharacteristic
153C22×C61#41011yescharacteristic
154C22×C61C2×#10211yescharacteristic
155C22×C61#41911yescharacteristic
156C22×C61#42111yescharacteristic
157C22×C61#42111yescharacteristic
158C22×C61#47412yes—
159C22×C61#47512yes—
160C4×C61—21no—
161C4×C61—22no—
162C4×C61—21no—
163C4×C61—22no—
164C4×C61—22no—
165C4×C61—22no—
166C4×C61—41no—
167Dic61—84no—
168Dic61—82no—
169Dic61—82no—
170#2857—611no—
171#1797D6111yescharacteristic
172#1434—611no—
173#1294—614no—
174C2×C61—22no—
175C2×C61—22no—
176C2×C61#151111yescharacteristic
177C2×C61#151511yescharacteristic
178C2×C61#151711yescharacteristic
179C2×C61#151911yescharacteristic
180C2×C61#198811yescharacteristic
181C2×C61#199511yescharacteristic
182C2×C61#199611yescharacteristic
183C2×C4⋊Q8—611no—
184C2×C22⋊Q8—1221no—
185C22×C42C2×D6111yescharacteristic
186C2×C4⋊C8—21no—
187C2×C22⋊C8C2×D6112yes—
188#391—1221no—
189#389—612no—
190#389—1221no—
191#384—611no—
192#380—612no—
193#380—1221no—
194C2×#95—612no—
195C2×#95—1221no—
196C2×#95—1221no—
197#336—21no—
198C61#991211yescharacteristic, complemented, Sylow
199C22×Q8—1221no—
200C23×C4—1222no—
201C23×C4D24411yescharacteristic
202C23×C4D24411yescharacteristic
203C23×C4C22×D6111yescharacteristic
204C22×C8—22no—
205C4⋊Q8—2442no—
206C22⋊Q8—2442no—
207C22⋊Q8—2442no—
208C2×C4⋊C4—612no—
209C2×C4⋊C4—612no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1222no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C22⋊C4—1222no—
215C2×C42—42no—
216C2×C42C4×D6111yescharacteristic
217C2×C42C4×D6111yescharacteristic
218C2×C42C22⋊D6111yescharacteristic
219C2×C42C22⋊D6111yescharacteristic
220C4⋊C8—42no—
221C22⋊C8—24no—
222#95—614no—
223#95—1222no—
224#95—1222no—
225#95—1222no—
226#95—2442no—
227#95—2442no—
228C24C2×D24411yescharacteristic
229C2×Q8—2442no—
230C2×Q8—2442no—
231C2×Q8—2442no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—1222no—
240C22×C4—1222no—
241C22×C4—1224no—
242C22×C4—2442no—
243C22×C4—2442no—
244C22×C4—2442no—
245C22×C4—2442no—
246C22×C4—2442no—
247C22×C4—2442no—
248C22×C4#1175819012yes—
249C22×C4D48812yes—
250C22×C4#1175819811yescharacteristic
251C22×C4#1175819811yescharacteristic
252C22×C4#1175819811yescharacteristic
253C22×C4#1175819811yescharacteristic
254C22×C4C2×C4×D6111yescharacteristic
255C22×C4#1175822412yes—
256C22×C4Q8×D6112yes—
257C22×C4C2×C22⋊D6111yescharacteristic
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C4⋊C4—2442no—
262C4⋊C4—2442no—
263C4⋊C4—2442no—
264C4⋊C4—2442no—
265C4⋊C4—2444no—
266C4⋊C4—2442no—
267C22⋊C4—2442no—
268C22⋊C4—2442no—
269C42—22no—
270C42—22no—
271C42—41no—
272C42—41no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23C2×#1175819811yescharacteristic
278C23#1451975712yes—
279C23C2×D48811yescharacteristic
280C23C2×#1175819011yescharacteristic
281C23#1451981012yes—
282Q8—4884no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—44no—
301C2×C4—4882no—
302C2×C4—4882no—
303C2×C4—4882no—
304C2×C4—4882no—
305C2×C4—2444no—
306C2×C4—2444no—
307C2×C4—2442no—
308C2×C4—2442no—
309C2×C4—2442no—
310C2×C4—2442no—
311C2×C4—2442no—
312C2×C4—2442no—
313C2×C4—2444no—
314C2×C4#1451969112yes—
315C2×C4#1451969912yes—
316C2×C4#1451969912yes—
317C2×C4#1451974212yes—
318C2×C4#1451976411yescharacteristic
319C2×C4#1451977511yescharacteristic
320C8—82no—
321C22—22no—
322C22—22no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—22no—
328C22—22no—
329C22#1683966711yescharacteristic
330C22C2×#1451969111yescharacteristic
331C22#1683973511yescharacteristic
332C22C2×#1451969911yescharacteristic
333C22#1683977211yescharacteristic
334C22#1683977811yescharacteristic
335C22#1683977811yescharacteristic
336C22#1684004312yes—
337C22#1684004812yes—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—21no—
342C4—22no—
343C4—21no—
344C4—41no—
345C4—4884no—
346C4—4882no—
347C4—4882no—
348C2—22no—
349C2—22no—
350C2#2144435311yescharacteristic
351C2#2144437111yescharacteristic
352C2#2144438011yescharacteristic
353C2#2144438811yescharacteristic
354C2#2144677011yescharacteristic
355C2#2144679911yescharacteristic
356C2#2144680311yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1797C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#1797D61
hypocenterC61#9912
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
5. C2×#14519777C4semidirect
9. #16839660C4semidirect
10. #16839632C4semidirect
37. #14519684Q8semidirect
198. C61#9912semidirect

Maximal subgroups

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

subgroupindex
#214541712
#214440462
#214436992
C61×#17972
#991261