Finite Group Databasebeta

← #29568177

Subgroups — #29568177

Order 15616.

516 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448302C211yesmaximal, characteristic
2#21445581C211yesmaximal, characteristic
3#21443643C212yesmaximal, complemented
4#21443641C212yesmaximal, complemented
5C61×#1797C211yesmaximal, characteristic
6C2×#14519736C411yescharacteristic
7C2×#14519736C411yescharacteristic
8C2×C22⋊#92418—21no—
9C2×#14519688—21no—
10#16839660C411yescharacteristic
11#16839660C411yescharacteristic
12#16839660C2211yescharacteristic
13#16839660C2211yescharacteristic
14#16839635—21no—
15#16839635—21no—
16C4×#11758196—21no—
17C4×#11758196—21no—
18#16839517C2212yes—
19C22×C42×C61C2211yescharacteristic
20C2×C4⋊C8×C61—21no—
21C2×C22⋊C8×C61—21no—
22C61×#336C2212yes—
23C22×#92418—22no—
24#14519736—22no—
25#14519736—22no—
26#14519736—42no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61—21no—
39C22⋊#92418—24no—
40#14519688—42no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45C23×C4×C61C2×C411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C23×C4×C61D411yescharacteristic
48C22×C8×C61—22no—
49C2×C42×C61—42no—
50C2×C42×C61C2×C411yescharacteristic
51C2×C42×C61D411yescharacteristic
52C2×C42×C61D411yescharacteristic
53C2×C42×C61C2311yescharacteristic
54C4⋊C8×C61—42no—
55C22⋊C8×C61—42no—
56C24×C61C22⋊C411yescharacteristic
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—41no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C2×C8×C61—42no—
79C2×C8×C61—42no—
80C2×C8×C61—42no—
81C42×C61—22no—
82C42×C61—22no—
83C42×C61—41no—
84C42×C61—41no—
85C22⋊Dic61—24no—
86C22⋊Dic61—42no—
87C4⋊Dic61—21no—
88C4⋊Dic61—21no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61M1612yes—
92C4⋊Dic61M1612yes—
93#11758196—42no—
94#11758196—42no—
95#11758196—42no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—24no—
99C4×Dic61—42no—
100C2×#92418—24no—
101C2×#92418—42no—
102C2×#92418—42no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61#10112yes—
110C23×C61C2×C22⋊C411yescharacteristic
111C2×C4×C61—24no—
112C2×C4×C61—24no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—44no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61#9912yes—
130C2×C4×C61#10412yes—
131C2×C4×C61C2×M1611yescharacteristic
132C2×C4×C61C2×M1611yescharacteristic
133C2×C4×C61#13512yes—
134C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C61#13711yescharacteristic
136C2×Dic61—22no—
137C2×Dic61—22no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C8×C61—82no—
149#92418—44no—
150#7613—611nomaximal, Sylow
151C22×C61—22no—
152C22×C61—22no—
153C22×C61—22no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61#40711yescharacteristic
159C22×C61C2×#9911yescharacteristic
160C22×C61C2×#10111yescharacteristic
161C22×C61#41611yescharacteristic
162C22×C61#41711yescharacteristic
163C22×C61C2×#10411yescharacteristic
164C22×C61#42111yescharacteristic
165C4×C61—22no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—22no—
169C4×C61—22no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—41no—
173Dic61—42no—
174Dic61—42no—
175Dic61—81no—
176Dic61—81no—
177#2296—611no—
178#1797D6111yescharacteristic
179#1749—611no—
180#1271—612no—
181#1271—612no—
182C2×C61—42no—
183C2×C61#146311yescharacteristic
184C2×C61#148811yescharacteristic
185C2×C61#148911yescharacteristic
186C2×C61#150111yescharacteristic
187C2×C61#151311yescharacteristic
188C2×C61#153111yescharacteristic
189C2×C61#155211yescharacteristic
190C2×#117—611no—
191C2×#117—611no—
192C22×C42C2×D6111yescharacteristic
193C2×C4⋊C8—21no—
194C2×C22⋊C8—21no—
195C2×C22⋊C8—1221no—
196C2×#97—1221no—
197#389—611no—
198#389—611no—
199#389—611no—
200#389—611no—
201#385—1221no—
202#385—1221no—
203C4×C4⋊C4—1221no—
204C4×C4⋊C4—1221no—
205#336—612no—
206#336C2×D6112yes—
207C61#761311yescharacteristic, complemented, Sylow
208C23×C4C4×D6111yescharacteristic
209C23×C4D24411yescharacteristic
210C23×C4C22⋊D6111yescharacteristic
211C22×C8—22no—
212C22×C8—1222no—
213#117—1222no—
214#117—1222no—
215#117—2442no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C22⋊C4—1221no—
225C2×C22⋊C4—1221no—
226C2×C42—42no—
227C2×C42—1221no—
228C2×C42—1221no—
229C2×C42C4×D6111yescharacteristic
230C2×C42D24411yescharacteristic
231C2×C42C22⋊D6111yescharacteristic
232C2×C42C22×D6111yescharacteristic
233C4⋊C8—42no—
234C22⋊C8—42no—
235C22⋊C8—1224no—
236#97—2442no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241C24#1175819811yescharacteristic
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4#1175819811yescharacteristic
258C22×C4#1175819811yescharacteristic
259C22×C4#1175819811yescharacteristic
260C22×C4C2×C4×D6111yescharacteristic
261C22×C4C2×D24411yescharacteristic
262C22×C4C2×C22⋊D6111yescharacteristic
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—1224no—
267C2×C8—2442no—
268C2×C8—2442no—
269C4⋊C4—612no—
270C4⋊C4—612no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2442no—
276C4⋊C4—2441no—
277C4⋊C4—2442no—
278C4⋊C4—2442no—
279C4⋊C4—2441no—
280C22⋊C4—1224no—
281C22⋊C4—2442no—
282C42—22no—
283C42—22no—
284C42—41no—
285C42—41no—
286C42—1224no—
287C42—2442no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23#1451969512yes—
295C23C2×#1175819811yescharacteristic
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—44no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—1222no—
315C2×C4—1222no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4#1451969112yes—
327C2×C4#1451970312yes—
328C2×C4M16×D6111yescharacteristic
329C2×C4M16×D6111yescharacteristic
330C2×C4#1451979912yes—
331C2×C4#1451980311yescharacteristic
332C2×C4#1451980811yescharacteristic
333C8—82no—
334C8—2444no—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22#1683972511yescharacteristic
343C22C2×#1451969111yescharacteristic
344C22C2×#1451969511yescharacteristic
345C22#1683975911yescharacteristic
346C22#1683976111yescharacteristic
347C22C2×#1451970311yescharacteristic
348C22#1683978011yescharacteristic
349C4—21no—
350C4—21no—
351C4—22no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4—22no—
356C4—41no—
357C4—4881no—
358C4—4881no—
359C4—2442no—
360C4—2442no—
361C2—42no—
362C2#2144414811yescharacteristic
363C2#2144425411yescharacteristic
364C2#2144425611yescharacteristic
365C2#2144431111yescharacteristic
366C2#2144436011yescharacteristic
367C2#2144443511yescharacteristic
368C2#2144451711yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1797C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1797D61
hypocenterC61#7613
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
3. #21443643C2semidirect
4. #21443641C2semidirect
207. C61#7613semidirect

Maximal subgroups

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

subgroupindex
#214483022
#214455812
#214436432
#214436412
C61×#17972
#761361