Finite Group Databasebeta

← #29568249

Subgroups — #29568249

Order 15616.

434 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448294C211yesmaximal, characteristic
2#21445671C211yesmaximal, characteristic
3#21445566C211yesmaximal, characteristic
4#21443645C211yesmaximal, characteristic
5#21443643C211yesmaximal, characteristic
6#21443641C211yesmaximal, characteristic
7C61×#1272C211yesmaximal, characteristic
8C2×Q8×Dic61C411yescharacteristic
9C2×#14519706—21no—
10C2×#14519687—21no—
11C2×#14519687—21no—
12#16839669C411yescharacteristic
13#16839660C2211yescharacteristic
14#16839658C411yescharacteristic
15#16839647—21no—
16#16839645—21no—
17C4⋊C4×Dic61C411yescharacteristic
18#16839613—21no—
19#16839607—21no—
20C42×Dic61C2211yescharacteristic
21#16839517C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839516—21no—
24C61×#391C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×#92418—21no—
28C22×#92418—21no—
29Q8×Dic61—22no—
30Q8×Dic61—22no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44#14519706—24no—
45#14519687—24no—
46#14519687—42no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C22×Q8×C61C2×C411yescharacteristic
53C22×C8×C61—21no—
54C22×C8×C61—21no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C42×C61C2311yescharacteristic
57#95×C61—21no—
58#95×C61—21no—
59C2×Q8×C61—21no—
60C2×Q8×C61—41no—
61C2×Q8×C61—41no—
62C2×Q8×C61M1612yes—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C2×C8×C61—22no—
75C2×C8×C61—22no—
76C2×C8×C61—41no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C4⋊C4×C61—41no—
81C42×C61—41no—
82C4⋊Dic61—24no—
83C4⋊Dic61—21no—
84C4⋊Dic61—41no—
85C4⋊Dic61M1612yes—
86#11758196—41no—
87#11758196—41no—
88#11758196—42no—
89C4×Dic61—24no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—22no—
97C4×Dic61—22no—
98C4×Dic61—41no—
99C4×Dic61—42no—
100C2×#92418—22no—
101C2×#92418—22no—
102C2×#92418—41no—
103C2×#92418—41no—
104C2×#92418—41no—
105C2×#92418—41no—
106C23×C61C2×C22⋊C411yescharacteristic
107Q8×C61—42no—
108Q8×C61—42no—
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—22no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61C2×M1611yescharacteristic
122C2×C4×C61C2×M1611yescharacteristic
123C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C61#13711yescharacteristic
125C2×C4×C61#13711yescharacteristic
126C2×C4×C61#13711yescharacteristic
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—22no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61#10412yes—
144C2×Dic61#10412yes—
145C8×C61—42no—
146C8×C61—42no—
147#92418—42no—
148#92418—42no—
149#7630—611nomaximal, Sylow
150C22×C61#40711yescharacteristic
151C22×C61#41011yescharacteristic
152C22×C61#41311yescharacteristic
153C22×C61#41711yescharacteristic
154C22×C61#41911yescharacteristic
155C22×C61C2×#10411yescharacteristic
156C22×C61C2×#10411yescharacteristic
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—42no—
164C4×C61—81no—
165Dic61—22no—
166Dic61—22no—
167Dic61—41no—
168Dic61—41no—
169Dic61—42no—
170Dic61—81no—
171#2295—611no—
172#1767—611no—
173#1745—611no—
174#1272—611no—
175#1272D6111yescharacteristic
176#1271—611no—
177#1271—611no—
178C2×C61#146411yescharacteristic
179C2×C61#148911yescharacteristic
180C2×C61#149111yescharacteristic
181C2×C61#150611yescharacteristic
182C2×C61#150911yescharacteristic
183C2×C61#152411yescharacteristic
184C2×C61#155911yescharacteristic
185C2×C4×Q8—611no—
186C2×C4⋊C8—1221no—
187C2×#97—1221no—
188C2×#97—1221no—
189#391—611no—
190#391C2×D6111yescharacteristic
191#389—611no—
192#389—611no—
193#387—1221no—
194#387—1221no—
195C4×C4⋊C4—611no—
196C4×C4⋊C4—1221no—
197#376—1221no—
198C43—611no—
199#336—611no—
200#336—611no—
201#336—1221no—
202#336C2×D6111yescharacteristic
203#336C2×D6111yescharacteristic
204C61#763011yescharacteristic, complemented, Sylow
205C22×Q8C4×D6111yescharacteristic
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—1221no—
209C22×C8—1221no—
210C4×Q8—1222no—
211C4×Q8—1222no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4C4×D6111yescharacteristic
218C2×C42—611no—
219C2×C42—611no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42—611no—
224C2×C42—1221no—
225C2×C42—1221no—
226C2×C42C22×D6111yescharacteristic
227C4⋊C8—1224no—
228#97—1224no—
229#97—2442no—
230#95—21no—
231#95—21no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237C2×Q8—21no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8#1175818912yes—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4C2×C4×D6111yescharacteristic
250C22×C4D4×D6111yescharacteristic
251C22×C4D4×D6111yescharacteristic
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—1222no—
259C2×C8—1222no—
260C2×C8—2441no—
261C2×C8—2441no—
262C2×C8—2441no—
263C2×C8—2441no—
264C4⋊C4—41no—
265C4⋊C4—612no—
266C4⋊C4—1224no—
267C4⋊C4—1221no—
268C4⋊C4—2441no—
269C4⋊C4—2442no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C42—41no—
273C42—1222no—
274C42—1222no—
275C42—1224no—
276C42—1221no—
277C42—1221no—
278C42—1221no—
279C42—1221no—
280C42—1221no—
281C42—1221no—
282C42—2441no—
283C42—2442no—
284C23C22⋊C4×D6111yescharacteristic
285Q8—42no—
286Q8—42no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—612no—
300C2×C4—612no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1222no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4M16×D6111yescharacteristic
318C2×C4C2×#1175818911yescharacteristic
319C2×C4#1451980411yescharacteristic
320C2×C4#1451980611yescharacteristic
321C2×C4#1451980911yescharacteristic
322C2×C4#1451980911yescharacteristic
323C8—42no—
324C8—42no—
325C8—2442no—
326C8—2442no—
327C22#1683972411yescharacteristic
328C22#1683973411yescharacteristic
329C22#1683974311yescharacteristic
330C22#1683976211yescharacteristic
331C22#1683976911yescharacteristic
332C22#104×D6111yescharacteristic
333C22#104×D6111yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—81no—
342C4—1222no—
343C4—1222no—
344C4—4881no—
345C4—2441no—
346C4—2442no—
347C4—2441no—
348C2#2144415011yescharacteristic
349C2#2144425711yescharacteristic
350C2#2144426411yescharacteristic
351C2#2144432911yescharacteristic
352C2#2144434311yescharacteristic
353C2#2144440411yescharacteristic
354C2#2144454611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1272D61
hypocenterC61#7630
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
204. C61#7630semidirect

Maximal subgroups

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

subgroupindex
#214482942
#214456712
#214455662
#214436452
#214436432
#214436412
C61×#12722
#763061