Finite Group Databasebeta

← #29579008

Subgroups — #29579008

Order 15616.

630 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454171C211yesmaximal, characteristic
2#21445581C211yesmaximal, characteristic
3C2×#16839498C214yesmaximal
4C61×#1434C211yesmaximal, characteristic
5C2×#14519777C411yescharacteristic, complemented
6C2×#14519756C2212yes—
7C2×C22⋊#92418C2212yes—
8C2×#14519688—21no—
9#16839668C412yescomplemented
10#16839660—21no—
11#16839660—21no—
12#16839632C411yescharacteristic, complemented
13#16839622—21no—
14#16839622—21no—
15#16839517—21no—
16#16839498—28no—
17C22×C42×C61C2211yescharacteristic
18C2×#95×C61—21no—
19C2×#95×C61—21no—
20C2×#95×C61C2212yes—
21C22×Dic122C2×C412yes—
22C22×#92418—22no—
23#14519777—42no—
24#14519756—24no—
25#14519756—24no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61C2×C412yes—
31C2×#11758196—22no—
32C2×C22⋊Dic61—22no—
33C22⋊#92418—22no—
34C22⋊#92418D414yes—
35#14519688—42no—
36#14519684—22no—
37#14519684—22no—
38C23×C4×C61—22no—
39C23×C4×C61D411yescharacteristic
40C23×C4×C61D411yescharacteristic
41C23×C4×C61C2311yescharacteristic
42C2×C42×C61—42no—
43C2×C42×C61C2×C411yescharacteristic
44C2×C42×C61C2×C411yescharacteristic
45C2×C42×C61D411yescharacteristic
46C2×C42×C61D411yescharacteristic
47#95×C61—24no—
48#95×C61—24no—
49#95×C61—42no—
50C24×C61C2×D411yescharacteristic
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61—22no—
55C22×C4×C61—24no—
56C22×C4×C61—41no—
57C22×C4×C61—41no—
58C22×C4×C61—41no—
59C22×C4×C61—41no—
60C22×C4×C61—42no—
61C22×C4×C61—42no—
62C22×C4×C61—42no—
63C22×C4×C61—42no—
64C22×C4×C61—42no—
65C22×C4×C61—42no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D412yes—
73C22×C4×C61#4112yes—
74C22×Dic61—22no—
75C22×Dic61—22no—
76C2×Dic122—24no—
77C2×Dic122—42no—
78C2×Dic122—42no—
79C42×C61—22no—
80C42×C61—22no—
81C42×C61—41no—
82C42×C61—41no—
83C22⋊Dic61—42no—
84C22⋊Dic61—42no—
85C4⋊Dic61—24no—
86C4⋊Dic61—42no—
87C4⋊Dic61—42no—
88C4⋊Dic61—42no—
89C4⋊Dic61—42no—
90#11758196—44no—
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×C61#12411yescharacteristic
100C23×C61#12711yescharacteristic
101C23×C61#13712yes—
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—21no—
117C2×C4×C61—42no—
118C2×C4×C61—42no—
119C2×C4×C61—44no—
120C2×C4×C61—44no—
121C2×C4×C61—44no—
122C2×C4×C61—44no—
123C2×C4×C61—44no—
124C2×C4×C61—82no—
125C2×C4×C61—82no—
126C2×C4×C61—82no—
127C2×C4×C61—82no—
128C2×C4×C61#9912yes—
129C2×C4×C61#10412yes—
130C2×C4×C61C4×D412yes—
131C2×C4×C61#12112yes—
132C2×Dic61—42no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137C2×Dic61—42no—
138Dic122—84no—
139#92418—44no—
140#9683—611nomaximal, Sylow
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—21no—
144C22×C61—21no—
145C22×C61—22no—
146C22×C61—22no—
147C22×C61—22no—
148C22×C61—22no—
149C22×C61#39011yescharacteristic
150C22×C61C2×#9911yescharacteristic
151C22×C61#41011yescharacteristic
152C22×C61#41911yescharacteristic
153C22×C61#41911yescharacteristic
154C22×C61C2×#10411yescharacteristic
155C22×C61#42111yescharacteristic
156C22×C61#49112yes—
157C22×C61#49712yes—
158C4×C61—22no—
159C4×C61—22no—
160C4×C61—22no—
161C4×C61—22no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—84no—
165Dic61—82no—
166Dic61—82no—
167#2857—611no—
168#1749—611no—
169C2×#328—614no—
170#1434D6111yescharacteristic
171C2×C61—22no—
172C2×C61—22no—
173C2×C61#150611yescharacteristic
174C2×C61#150811yescharacteristic
175C2×C61#151111yescharacteristic
176C2×C61#151511yescharacteristic
177C2×C61#196011yescharacteristic
178C2×C61#196411yescharacteristic
179C2×C61#198011yescharacteristic
180C2×C4⋊Q8—611no—
181C2×C22⋊Q8—612no—
182C22×C42C2×D6111yescharacteristic
183C2×C22⋊C8—612no—
184C2×#97—1221no—
185#391—612no—
186#389—1221no—
187#389—1221no—
188#384—611no—
189#380—1221no—
190#380—1221no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95C2×D6112yes—
194#336—1221no—
195#328—1228no—
196C61#968311yescharacteristic, complemented, Sylow
197C22×Q8—612no—
198C23×C4—22no—
199C23×C4C22⋊D6111yescharacteristic
200C23×C4C22⋊D6111yescharacteristic
201C23×C4C22×D6111yescharacteristic
202C22×C8—1222no—
203C4⋊Q8—2442no—
204C22⋊Q8—1224no—
205C22⋊Q8—1224no—
206C2×C4⋊C4—612no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1222no—
212C2×C22⋊C4—1222no—
213C2×C42—42no—
214C2×C42C4×D6111yescharacteristic
215C2×C42C4×D6111yescharacteristic
216C2×C42D24411yescharacteristic
217C2×C42D24411yescharacteristic
218C22⋊C8—614no—
219C22⋊C8—1222no—
220#97—2442no—
221#95—24no—
222#95—24no—
223#95—42no—
224#95—1222no—
225#95—1222no—
226C24C2×C22⋊D6111yescharacteristic
227C2×Q8—1224no—
228C2×Q8—2442no—
229C2×Q8—2442no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—24no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—1222no—
246C22×C4—1222no—
247C22×C4#1175819811yescharacteristic
248C22×C4#1175819811yescharacteristic
249C22×C4#1175819811yescharacteristic
250C22×C4#1175819811yescharacteristic
251C22×C4C2×C4×D6111yescharacteristic
252C22×C4C2×D24411yescharacteristic
253C22×C4D4×D6112yes—
254C22×C4#1175822612yes—
255C2×C8—1224no—
256C2×C8—2442no—
257C2×C8—2442no—
258C4⋊C4—1224no—
259C4⋊C4—2442no—
260C4⋊C4—2442no—
261C4⋊C4—2442no—
262C4⋊C4—2442no—
263C4⋊C4—2444no—
264C22⋊C4—2442no—
265C22⋊C4—2442no—
266C42—22no—
267C42—22no—
268C42—41no—
269C42—41no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23C2×#1175819811yescharacteristic
275C23#1451976611yescharacteristic
276C23#1451977311yescharacteristic
277C23#1451980712yes—
278C23#1451980712yes—
279Q8—4884no—
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—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—82no—
304C2×C4—82no—
305C2×C4—2442no—
306C2×C4—2442no—
307C2×C4—2442no—
308C2×C4—2442no—
309C2×C4—2442no—
310C2×C4—2442no—
311C2×C4#1451969112yes—
312C2×C4#1451970512yes—
313C2×C4#1451973912yes—
314C2×C4#1451975212yes—
315C8—2444no—
316C22—22no—
317C22—21no—
318C22—21no—
319C22—22no—
320C22—22no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22#1683966311yescharacteristic
325C22C2×#1451969111yescharacteristic
326C22#1683973511yescharacteristic
327C22#1683977011yescharacteristic
328C22#1683977011yescharacteristic
329C22C2×#1451970511yescharacteristic
330C22#1683978011yescharacteristic
331C22#1684013212yes—
332C22#1684015712yes—
333C4—22no—
334C4—22no—
335C4—22no—
336C4—22no—
337C4—41no—
338C4—41no—
339C4—84no—
340C4—4882no—
341C4—4882no—
342C2—22no—
343C2—22no—
344C2#2144433011yescharacteristic
345C2#2144433811yescharacteristic
346C2#2144435111yescharacteristic
347C2#2144436911yescharacteristic
348C2#2144663811yescharacteristic
349C2#2144665411yescharacteristic
350C2#2144673711yescharacteristic
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#9683
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
9. #16839668C4semidirect
12. #16839632C4semidirect
196. C61#9683semidirect

Maximal subgroups

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

subgroupindex
#214541712
#214455812
C2×#168394982
C61×#14342
#968361