Finite Group Databasebeta

← #29575102

Subgroups — #29575102

Order 15616.

528 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21449087C211yesmaximal, characteristic
2#21444247C212yesmaximal, complemented
3#21444133C211yesmaximal, characteristic
4#21443720C212yesmaximal, complemented
5C61×#2905C211yesmaximal, characteristic
6C2×C4×Dic122C2211yescharacteristic
7#16839815C2212yes—
8#16839701C411yescharacteristic
9#16839698C411yescharacteristic
10#16839695—21no—
11#16839685—21no—
12#16839682C411yescharacteristic
13#16839674C411yescharacteristic
14C4×#11758196—21no—
15C4×C4⋊Dic61C2211yescharacteristic
16C4×C22⋊Dic61—21no—
17#16839492—24no—
18#16839488—21no—
19#16839486—21no—
20C22×M16×C61—21no—
21C2×#117×C61C2211yescharacteristic
22C61×#424—24no—
23C61×#423—21no—
24C61×#423C2212yes—
25C22×Dic122C2×C411yescharacteristic
26C4×Dic122—22no—
27C4×Dic122—22no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61—21no—
37C4⋊#92418—22no—
38C22⋊#92418—22no—
39C4×#92418—22no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684C2×C411yescharacteristic
45#14519684C2×C411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C2×M16×C61—22no—
48C2×M16×C61—22no—
49C2×M16×C61—42no—
50C2×M16×C61—42no—
51C22×C8×C61—22no—
52#117×C61—22no—
53#117×C61—22no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C22⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61D411yescharacteristic
58C2×C42×C61D411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—24no—
61C4⋊C8×C61—22no—
62C4⋊C8×C61D414yes—
63C24×C61C22⋊C411yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61SD1612yes—
72C22×C4×C61Q1612yes—
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C2×Dic122—22no—
81C2×Dic122—42no—
82M16×C61—44no—
83M16×C61—42no—
84M16×C61—42no—
85C2×C8×C61—24no—
86C2×C8×C61—44no—
87C4⋊C4×C61—22no—
88C4⋊C4×C61—22no—
89C22⋊C4×C61—22no—
90C22⋊C4×C61—22no—
91C42×C61—21no—
92C42×C61—21no—
93C42×C61C2×D412yes—
94C42×C61#4112yes—
95C22⋊Dic61—42no—
96C22⋊Dic61—42no—
97C4⋊Dic61—22no—
98C4⋊Dic61—42no—
99#11758196—42no—
100#11758196—42no—
101#11758196—42no—
102C4×Dic61—41no—
103C4×Dic61—41no—
104C4×Dic61—41no—
105C4×Dic61—41no—
106C2×#92418—42no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61#10312yes—
112C23×C61C2×C22⋊C411yescharacteristic
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—22no—
116C2×C4×C61—22no—
117C2×C4×C61—22no—
118C2×C4×C61—22no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61#10312yes—
126C2×C4×C61C4×D412yes—
127C2×C4×C61#12011yescharacteristic
128C2×C4×C61#12112yes—
129C2×C4×C61#12311yescharacteristic
130C2×C4×C61C2×SD1611yescharacteristic
131C2×C4×C61C2×Q1611yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C61#13711yescharacteristic
134C2×Dic61—22no—
135C2×Dic61—22no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146Dic122—24no—
147Dic122—42no—
148C8×C61—44no—
149#92418—82no—
150#9033—611nomaximal, Sylow
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—22no—
154C22×C61—42no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—81no—
158C22×C61#38611yescharacteristic
159C22×C61C2×#10311yescharacteristic
160C22×C61#41711yescharacteristic
161C4×C61—22no—
162C4×C61—22no—
163C4×C61—22no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61#45011yescharacteristic
167C4×C61#45111yescharacteristic
168C4×C61#48311yescharacteristic
169C4×C61#48411yescharacteristic
170Dic61—42no—
171Dic61—42no—
172Dic61—81no—
173Dic61—81no—
174#2905D6111yescharacteristic
175#2396—611no—
176#1487—612no—
177#1458—611no—
178#1303—612no—
179C2×C61—21no—
180C2×C61—21no—
181C2×C61—42no—
182C2×C61#187211yescharacteristic
183C2×C61#188411yescharacteristic
184C2×C61#189111yescharacteristic
185C22×M16—21no—
186C2×C4×Q8—611no—
187C2×#117C2×D6111yescharacteristic
188#431—612no—
189#424—24no—
190#423—21no—
191#423C2×D6112yes—
192#400—611no—
193#399—611no—
194#398—1221no—
195#396—1221no—
196#395—611no—
197#393—611no—
198C4×C4⋊C4—611no—
199C4×C4⋊C4—1221no—
200C4×C22⋊C4—1221no—
201Q8⋊C8—1224no—
202#324—1221no—
203#323—1221no—
204C61#903311yescharacteristic, complemented, Sylow
205C22×Q8—611no—
206C23×C4C22⋊D6111yescharacteristic
207C2×M16—22no—
208C2×M16—22no—
209C2×M16—42no—
210C2×M16—42no—
211C22×C8—22no—
212C4×Q8—1222no—
213C4×Q8—1222no—
214#117—22no—
215#117—22no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4C4×D6111yescharacteristic
222C2×C4⋊C4D24411yescharacteristic
223C2×C22⋊C4—1221no—
224C2×C22⋊C4—1221no—
225C2×C22⋊C4C4×D6111yescharacteristic
226C2×C22⋊C4D24411yescharacteristic
227C2×C42—1221no—
228C2×C42—1221no—
229C2×C42C22⋊D6111yescharacteristic
230C2×C42C22×D6111yescharacteristic
231C4⋊C8—24no—
232C4⋊C8—22no—
233C4⋊C8—1222no—
234C4⋊C8C22⋊D6114yes—
235C22⋊C8—1222no—
236C4×C8—1222no—
237#95—611no—
238#95—611no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243C24#1175819811yescharacteristic
244C2×Q8—1222no—
245C2×Q8—2442no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4#1175819811yescharacteristic
255C22×C4#1175819811yescharacteristic
256C22×C4#1175819811yescharacteristic
257C22×C4#1175820012yes—
258C22×C4#1175820212yes—
259C22×C4C2×C4×D6111yescharacteristic
260C22×C4C2×D24411yescharacteristic
261C22×C4C2×C22⋊D6111yescharacteristic
262M16—44no—
263M16—42no—
264M16—42no—
265C2×C8—24no—
266C2×C8—44no—
267C2×C8—2442no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—1222no—
271C4⋊C4—2442no—
272C4⋊C4—2442no—
273C4⋊C4—2442no—
274C4⋊C4—2442no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—2442no—
278C22⋊C4—2442no—
279C42—21no—
280C42—21no—
281C42—2441no—
282C42—2441no—
283C42—2441no—
284C42—2441no—
285C42#1175822212yes—
286C42C2×C22⋊D6112yes—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23#1451970012yes—
292C23C2×#1175819811yescharacteristic
293Q8—1224no—
294Q8—2442no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—1222no—
308C2×C4—1222no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4#1451970012yes—
320C2×C4C4×C22⋊D6112yes—
321C2×C4#1451974611yescharacteristic
322C2×C4#1451975112yes—
323C2×C4#1451976011yescharacteristic
324C2×C4C2×#1175820011yescharacteristic
325C2×C4C2×#1175820211yescharacteristic
326C2×C4#1451980311yescharacteristic
327C2×C4#1451980811yescharacteristic
328C8—44no—
329C8—4882no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—42no—
334C22—41no—
335C22—41no—
336C22—81no—
337C22#1683964111yescharacteristic
338C22C2×#1451970011yescharacteristic
339C22#1683976111yescharacteristic
340C4—22no—
341C4—22no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—4881no—
346C4—4881no—
347C4—2442no—
348C4—2442no—
349C4#1683991311yescharacteristic
350C4#1683991811yescharacteristic
351C4#1684009211yescharacteristic
352C4#1684009711yescharacteristic
353C2—21no—
354C2—21no—
355C2—42no—
356C2#2144612611yescharacteristic
357C2#2144620211yescharacteristic
358C2#2144623711yescharacteristic
subgroupG/H
centerC2×C4#14519746
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2905C2
socleC22×C61#386
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2905D61
hypocenterC61#9033
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2905

Complements

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

NH ≅ G/Ntype
2. #21444247C2semidirect
4. #21443720C2semidirect
204. C61#9033semidirect

Maximal subgroups

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

subgroupindex
#214490872
#214442472
#214441332
#214437202
C61×#29052
#903361