Finite Group Databasebeta

← #29580069

Subgroups — #29580069

Order 15616.

664 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839668C211yesmaximal, characteristic
2#21445581C211yesmaximal, characteristic
3#21443661C214yesmaximal
4C61×#1797C211yesmaximal, characteristic
5C23×Dic122C411yescharacteristic
6C22×C4⋊Dic61C411yescharacteristic
7C2×C22⋊#92418C2212yes—
8C2×#14519688—21no—
9#16839668—21no—
10#16839668—21no—
11#16839668—21no—
12#16839668—21no—
13C2×#14519684C412yes—
14C2×#14519684C2212yes—
15#16839517—21no—
16C22×C42×C61C2211yescharacteristic
17C2×C4⋊C8×C61—21no—
18C2×C22⋊C8×C61C2212yes—
19C61×#336—21no—
20C22×Dic122—21no—
21C22×Dic122—21no—
22C22×Dic122—24no—
23C22×Dic122—42no—
24C22×Dic122—42no—
25C23×Dic61C2×C412yes—
26C23×Dic61C2×C412yes—
27C22×#92418—22no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—42no—
31C22⋊#92418—22no—
32C22⋊#92418Q814yescomplemented
33#14519688—42no—
34#14519684—22no—
35#14519684—22no—
36#14519684—22no—
37#14519684—22no—
38C23×C4×C61C2×C411yescharacteristic
39C23×C4×C61C2×C411yescharacteristic
40C23×C4×C61C2311yescharacteristic
41C22×C8×C61—22no—
42C2×C42×C61—42no—
43C2×C42×C61D411yescharacteristic
44C2×C42×C61D411yescharacteristic
45C2×C42×C61D411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C4⋊C8×C61—42no—
48C22⋊C8×C61—24no—
49C24×C61C22×C411yescharacteristic
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61—22no—
55C22×C4×C61—41no—
56C22×C4×C61—41no—
57C22×C4×C61—41no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×Q812yes—
65C22×C4×C61#4112yes—
66C22×Dic61—22no—
67C22×Dic61—22no—
68C22×Dic61—22no—
69C22×Dic61—24no—
70C22×Dic61—42no—
71C22×Dic61—42no—
72C22×Dic61—42no—
73C22×Dic61—42no—
74C22×Dic61M1614yes—
75C2×Dic122—24no—
76C2×Dic122—24no—
77C2×Dic122—416no—
78C2×Dic122—42no—
79C2×Dic122—42no—
80C2×Dic122—42no—
81C2×Dic122—42no—
82C2×C8×C61—42no—
83C2×C8×C61—42no—
84C2×C8×C61—42no—
85C42×C61—22no—
86C42×C61—22no—
87C42×C61—41no—
88C42×C61—41no—
89C4⋊Dic61—42no—
90C4⋊Dic61—42no—
91C2×#92418—24no—
92C2×#92418—42no—
93C2×#92418—42no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61C2×C22⋊C411yescharacteristic
99C23×C61C4×Q812yes—
100C23×C61C2×M1612yes—
101C23×C61#13112yes—
102C2×C4×C61—28no—
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—44no—
119C2×C4×C61#9912yes—
120C2×C4×C61#10012yes—
121C2×C4×C61#10112yes—
122C2×C4×C61C22⋊Q812yes—
123C2×C4×C61#12411yescharacteristic
124C2×C4×C61C4⋊Q811yescharacteristic
125C2×Dic61—24no—
126C2×Dic61—44no—
127C2×Dic61—42no—
128C2×Dic61—42no—
129C2×Dic61—44no—
130C2×Dic61—42no—
131C2×Dic61—42no—
132C2×Dic61—42no—
133C2×Dic61—84no—
134Dic122—48no—
135Dic122—48no—
136C8×C61—82no—
137#92418—44no—
138#9882—611nomaximal, Sylow
139C22×C61—22no—
140C22×C61—22no—
141C22×C61—22no—
142C22×C61—22no—
143C22×C61—22no—
144C22×C61—22no—
145C22×C61#39111yescharacteristic
146C22×C61#40711yescharacteristic
147C22×C61#40811yescharacteristic
148C22×C61C2×#9911yescharacteristic
149C22×C61#41011yescharacteristic
150C22×C61C2×#10011yescharacteristic
151C22×C61C2×#10111yescharacteristic
152C22×C61#44614yes—
153C4×C61—22no—
154C4×C61—22no—
155C4×C61—22no—
156C4×C61—22no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—41no—
160Dic61—44no—
161Dic61—82no—
162C2×#391—611no—
163#1797D6111yescharacteristic
164#1749—611no—
165#1280—614no—
166C2×C61—24no—
167C2×C61#146211yescharacteristic
168C2×C61#146711yescharacteristic
169C2×C61#146911yescharacteristic
170C2×C61#147211yescharacteristic
171C2×C61#198511yescharacteristic
172C2×C61#199611yescharacteristic
173C2×C61#199711yescharacteristic
174C23×Q8—611no—
175C22×C4⋊C4—611no—
176C22×C42C2×D6111yescharacteristic
177C2×C4⋊C8—21no—
178C2×C22⋊C8—612no—
179C2×C22⋊C8C2×D6112yes—
180C2×#97—1221no—
181#391—1221no—
182#391—1221no—
183#391—1221no—
184#391—1221no—
185C2×#95—612no—
186C2×#95—612no—
187#336—21no—
188#336—1221no—
189C61#988211yescharacteristic, complemented, Sylow
190C22×Q8—1224no—
191C22×Q8—1221no—
192C22×Q8—1221no—
193C22×Q8—2442no—
194C22×Q8—2442no—
195C23×C4—612no—
196C23×C4—612no—
197C23×C4C4×D6111yescharacteristic
198C23×C4C4×D6111yescharacteristic
199C23×C4C22×D6111yescharacteristic
200C22×C8—22no—
201C22×C8—1222no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—2442no—
205C2×C42—42no—
206C2×C42D24411yescharacteristic
207C2×C42D24411yescharacteristic
208C2×C42C22⋊D6111yescharacteristic
209C2×C42C22⋊D6111yescharacteristic
210C4⋊C8—42no—
211C22⋊C8—24no—
212C22⋊C8—614no—
213C22⋊C8—1222no—
214#97—2442no—
215#95—1222no—
216#95—1222no—
217#95—1222no—
218#95—1222no—
219C24C2×C4×D6111yescharacteristic
220C2×Q8—1224no—
221C2×Q8—1224no—
222C2×Q8—24416no—
223C2×Q8—2442no—
224C2×Q8—2442no—
225C2×Q8—2442no—
226C2×Q8—2442no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—614no—
236C22×C4—1222no—
237C22×C4—1222no—
238C22×C4—1224no—
239C22×C4—1222no—
240C22×C4—2442no—
241C22×C4—2442no—
242C22×C4—2442no—
243C22×C4—2442no—
244C22×C4#1175819811yescharacteristic
245C22×C4#1175819811yescharacteristic
246C22×C4#1175819811yescharacteristic
247C22×C4#1175819811yescharacteristic
248C22×C4C2×D24411yescharacteristic
249C22×C4#1175822412yes—
250C22×C4Q8×D6112yes—
251C22×C4C2×C22⋊D6111yescharacteristic
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—1224no—
256C2×C8—2442no—
257C2×C8—2442no—
258C4⋊C4—2442no—
259C4⋊C4—2442no—
260C42—22no—
261C42—22no—
262C42—41no—
263C42—41no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C2×#1175819811yescharacteristic
269C23#1451974212yes—
270C23M16×D6112yes—
271C23#1451978312yes—
272Q8—2448no—
273Q8—2448no—
274C2×C4—28no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—1224no—
292C2×C4—4884no—
293C2×C4—2442no—
294C2×C4—2442no—
295C2×C4—2442no—
296C2×C4—2444no—
297C2×C4—2442no—
298C2×C4—2442no—
299C2×C4—2444no—
300C2×C4#1451969112yes—
301C2×C4#1451969312yes—
302C2×C4#1451969512yes—
303C2×C4#1451975712yes—
304C2×C4#1451976411yescharacteristic
305C2×C4#1451977511yescharacteristic
306C8—82no—
307C8—2444no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22#1683966711yescharacteristic
315C22#1683972511yescharacteristic
316C22#1683972811yescharacteristic
317C22C2×#1451969111yescharacteristic
318C22#1683973511yescharacteristic
319C22C2×#1451969311yescharacteristic
320C22C2×#1451969511yescharacteristic
321C22#1683989114yes—
322C4—22no—
323C4—22no—
324C4—22no—
325C4—21no—
326C4—22no—
327C4—21no—
328C4—41no—
329C4—4882no—
330C4—2444no—
331C2—24no—
332C2#2144414511yescharacteristic
333C2#2144416211yescharacteristic
334C2#2144417011yescharacteristic
335C2#2144418211yescharacteristic
336C2#2144675811yescharacteristic
337C2#2144680311yescharacteristic
338C2#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#9882
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
32. C22⋊#92418Q8semidirect
189. C61#9882semidirect

Maximal subgroups

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

subgroupindex
C2×#168396682
#214455812
#214436612
C61×#17972
#988261