Finite Group Databasebeta

← #29580099

Subgroups — #29580099

Order 15616.

598 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454171C211yesmaximal, characteristic
2#21445581C211yesmaximal, characteristic
3#21443698C214yesmaximal
4C61×#1434C211yesmaximal, characteristic
5C2×#14519777C411yescharacteristic, complemented
6C2×#14519756—21no—
7C2×C22⋊#92418C2212yes—
8C2×#14519688—21no—
9#16839668—21no—
10#16839660—21no—
11#16839660C412yescomplemented
12#16839632C411yescharacteristic, complemented
13#16839622—21no—
14#16839622C2212yes—
15#16839517—21no—
16C22×C42×C61C2211yescharacteristic
17C2×#95×C61—21no—
18C2×#95×C61—21no—
19C2×#95×C61C2212yes—
20C22×Dic122—21no—
21C22×#92418—22no—
22#14519777—42no—
23#14519756—44no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61C2×C412yes—
28C2×C4⋊Dic61C2×C412yes—
29C2×#11758196—22no—
30C2×C22⋊Dic61—22no—
31C22⋊#92418—22no—
32C22⋊#92418Q814yescomplemented
33#14519688—42no—
34#14519684—22no—
35#14519684—22no—
36C23×C4×C61—22no—
37C23×C4×C61D411yescharacteristic
38C23×C4×C61D411yescharacteristic
39C23×C4×C61C2311yescharacteristic
40C2×C42×C61—42no—
41C2×C42×C61C2×C411yescharacteristic
42C2×C42×C61C2×C411yescharacteristic
43C2×C42×C61D411yescharacteristic
44C2×C42×C61D411yescharacteristic
45#95×C61—24no—
46#95×C61—24no—
47#95×C61—42no—
48C24×C61C2×D411yescharacteristic
49C22×C4×C61—22no—
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61—24no—
54C22×C4×C61—41no—
55C22×C4×C61—41no—
56C22×C4×C61—41no—
57C22×C4×C61—41no—
58C22×C4×C61—42no—
59C22×C4×C61—42no—
60C22×C4×C61—42no—
61C22×C4×C61—42no—
62C22×C4×C61—42no—
63C22×C4×C61—42no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×Q812yes—
71C22×C4×C61#4112yes—
72C22×Dic61—22no—
73C22×Dic61—22no—
74C2×Dic122—42no—
75C2×Dic122—42no—
76C2×Dic122—42no—
77C42×C61—22no—
78C42×C61—22no—
79C42×C61—41no—
80C42×C61—41no—
81C22⋊Dic61—44no—
82C4⋊Dic61—42no—
83C4⋊Dic61—42no—
84C4⋊Dic61—42no—
85C4⋊Dic61—42no—
86C4⋊Dic61—42no—
87#11758196—44no—
88C2×#92418—24no—
89C2×#92418—42no—
90C2×#92418—42no—
91C23×C61—21no—
92C23×C61—21no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61C2×C22⋊C411yescharacteristic
96C23×C61#12411yescharacteristic
97C23×C61C4⋊Q811yescharacteristic
98C23×C61AGL(1,ℤ/8)12yes—
99C23×C61#13712yes—
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—21no—
113C2×C4×C61—21no—
114C2×C4×C61—42no—
115C2×C4×C61—42no—
116C2×C4×C61—44no—
117C2×C4×C61—44no—
118C2×C4×C61—44no—
119C2×C4×C61—44no—
120C2×C4×C61—44no—
121C2×C4×C61—82no—
122C2×C4×C61—82no—
123C2×C4×C61—82no—
124C2×C4×C61—82no—
125C2×C4×C61#9912yes—
126C2×C4×C61#10412yes—
127C2×C4×C61C4×Q812yes—
128C2×C4×C61C22⋊Q812yes—
129C2×Dic61—42no—
130C2×Dic61—42no—
131C2×Dic61—42no—
132C2×Dic61—42no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135Dic122—84no—
136#92418—44no—
137#9889—611nomaximal, Sylow
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—22no—
143C22×C61—22no—
144C22×C61—22no—
145C22×C61—22no—
146C22×C61#39111yescharacteristic
147C22×C61C2×#9911yescharacteristic
148C22×C61#41011yescharacteristic
149C22×C61#41811yescharacteristic
150C22×C61#41911yescharacteristic
151C22×C61C2×#10411yescharacteristic
152C22×C61#42111yescharacteristic
153C22×C61#48912yes—
154C22×C61#50112yes—
155C4×C61—22no—
156C4×C61—22no—
157C4×C61—22no—
158C4×C61—22no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61—84no—
162Dic61—82no—
163Dic61—82no—
164#2857—611no—
165#1749—611no—
166#1434D6111yescharacteristic
167#1294—614no—
168C2×C61—22no—
169C2×C61—22no—
170C2×C61#150511yescharacteristic
171C2×C61#150811yescharacteristic
172C2×C61#151011yescharacteristic
173C2×C61#151511yescharacteristic
174C2×C61#198611yescharacteristic
175C2×C61#199311yescharacteristic
176C2×C61#199611yescharacteristic
177C2×C4⋊Q8—611no—
178C2×C22⋊Q8—1221no—
179C22×C42C2×D6111yescharacteristic
180C2×C22⋊C8—612no—
181C2×#97—1221no—
182#391—1221no—
183#389—612no—
184#389—1221no—
185#384—611no—
186#380—612no—
187#380—1221no—
188C2×#95—21no—
189C2×#95—21no—
190C2×#95C2×D6112yes—
191#336—1221no—
192C61#988911yescharacteristic, complemented, Sylow
193C22×Q8—1221no—
194C23×C4—22no—
195C23×C4C22⋊D6111yescharacteristic
196C23×C4C22⋊D6111yescharacteristic
197C23×C4C22×D6111yescharacteristic
198C22×C8—1222no—
199C4⋊Q8—2442no—
200C22⋊Q8—2444no—
201C2×C4⋊C4—612no—
202C2×C4⋊C4—612no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—1222no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4—1221no—
207C2×C22⋊C4—1222no—
208C2×C42—42no—
209C2×C42C4×D6111yescharacteristic
210C2×C42C4×D6111yescharacteristic
211C2×C42D24411yescharacteristic
212C2×C42D24411yescharacteristic
213C22⋊C8—614no—
214C22⋊C8—1222no—
215#97—2442no—
216#95—24no—
217#95—24no—
218#95—42no—
219#95—1222no—
220#95—1222no—
221C24C2×C22⋊D6111yescharacteristic
222C2×Q8—2442no—
223C2×Q8—2442no—
224C2×Q8—2442no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—1222no—
241C22×C4—1222no—
242C22×C4#1175819811yescharacteristic
243C22×C4#1175819811yescharacteristic
244C22×C4#1175819811yescharacteristic
245C22×C4#1175819811yescharacteristic
246C22×C4C2×C4×D6111yescharacteristic
247C22×C4C2×D24411yescharacteristic
248C22×C4#1175822412yes—
249C22×C4Q8×D6112yes—
250C2×C8—1224no—
251C2×C8—2442no—
252C2×C8—2442no—
253C4⋊C4—2442no—
254C4⋊C4—2442no—
255C4⋊C4—2444no—
256C4⋊C4—2442no—
257C4⋊C4—2442no—
258C4⋊C4—2442no—
259C22⋊C4—2444no—
260C42—22no—
261C42—22no—
262C42—41no—
263C42—41no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C2×#1175819811yescharacteristic
269C23#1451976411yescharacteristic
270C23#1451977511yescharacteristic
271C23#1451980212yes—
272C23#1451980712yes—
273Q8—4884no—
274C2×C4—21no—
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—44no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4—82no—
298C2×C4—82no—
299C2×C4—2442no—
300C2×C4—2442no—
301C2×C4—2442no—
302C2×C4—2442no—
303C2×C4—2442no—
304C2×C4—2442no—
305C2×C4#1451969112yes—
306C2×C4#1451970512yes—
307C2×C4#1451974212yes—
308C2×C4#1451975712yes—
309C8—2444no—
310C22—22no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22#1683966711yescharacteristic
319C22C2×#1451969111yescharacteristic
320C22#1683973511yescharacteristic
321C22#1683976611yescharacteristic
322C22#1683977011yescharacteristic
323C22C2×#1451970511yescharacteristic
324C22#1683978011yescharacteristic
325C22#1684012112yes—
326C22#1684017212yes—
327C4—22no—
328C4—22no—
329C4—22no—
330C4—22no—
331C4—41no—
332C4—41no—
333C4—84no—
334C4—4882no—
335C4—4882no—
336C2—22no—
337C2—22no—
338C2#2144432611yescharacteristic
339C2#2144433811yescharacteristic
340C2#2144434711yescharacteristic
341C2#2144436911yescharacteristic
342C2#2144676211yescharacteristic
343C2#2144679111yescharacteristic
344C2#2144680311yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1434C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#1434D61
hypocenterC61#9889
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
5. C2×#14519777C4semidirect
11. #16839660C4semidirect
12. #16839632C4semidirect
32. C22⋊#92418Q8semidirect
192. C61#9889semidirect

Maximal subgroups

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

subgroupindex
#214541712
#214455812
#214436982
C61×#14342
#988961