Finite Group Databasebeta

← #29654918

Subgroups — #29654918

Order 15616.

870 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 870 conjugacy classes of subgroups — too many to draw. Only its 191 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#21459629C211yesmaximal, characteristic
2#21456970C212yesmaximal
3#21444860C218yesmaximal
4#21444317C212yesmaximal
5#21444143C211yesmaximal, characteristic
6C61×#2568C211yesmaximal, characteristic
7Q8×Dic122—22no—
8#16840491—22no—
9#16840488—24no—
10#16840393—21no—
11#16840393C2214yes—
12#16840319—22no—
13#16840319C2212yes—
14#16840240—21no—
15#16840165—22no—
16#16840114—22no—
17#16840097C2218yes—
18#16840054—24no—
19#16839815C2212yes—
20#16839498C2218yes—
21#16839488C2214yes—
22C2×C4⋊Q8×C61C2211yescharacteristic
23C2×C4×Q8×C61C2211yescharacteristic
24C61×#400C2214yes—
25C61×#391—21no—
26C61×#391—22no—
27C61×#382—21no—
28C4×C4⋊C4×C61C2211yescharacteristic
29#14519777—22no—
30#14519777—22no—
31#14519777D412yes—
32#14519777D412yes—
33#14519776—24no—
34#14519776—28no—
35#14519769—24no—
36#14519769—22no—
37#14519768—24no—
38#14519768—28no—
39#14519756—22no—
40#14519756—24no—
41#14519756C2314yes—
42Q8×Dic61—24no—
43Q8×Dic61—24no—
44C4×Dic122—24no—
45C4×Dic122—24no—
46C4×Dic122—22no—
47C4×Dic122D414yes—
48#14519736—24no—
49#14519736—22no—
50#14519710—28no—
51C4⋊#92418—22no—
52#14519700—28no—
53C22⋊#92418C2314yes—
54C4×#92418—22no—
55C22×Q8×C61—21no—
56C22×Q8×C61D411yescharacteristic
57C4⋊Q8×C61—22no—
58C4⋊Q8×C61—22no—
59C4×Q8×C61—22no—
60C4×Q8×C61—22no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61D411yescharacteristic
64C2×C4⋊C4×C61C2312yes—
65C2×C4⋊C4×C61C2312yes—
66C2×C42×C61—21no—
67C2×C42×C61D412yes—
68C2×C42×C61C2311yescharacteristic
69#95×C61—24no—
70#95×C61—24no—
71#95×C61C2312yes—
72C2×Q8×C61—22no—
73C2×Q8×C61—22no—
74C2×Q8×C61—44no—
75C2×Q8×C61—41no—
76C2×Q8×C61—41no—
77C2×Q8×C61Q1614yes—
78C22×C4×C61—22no—
79C22×C4×C61—22no—
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D412yes—
82C22×C4×C61C2×D412yes—
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2411yescharacteristic
85C2×Dic122—22no—
86C2×Dic122—24no—
87C2×Dic122C2×D414yes—
88C4⋊C4×C61—22no—
89C4⋊C4×C61—24no—
90C4⋊C4×C61—24no—
91C4⋊C4×C61—42no—
92C4⋊C4×C61—42no—
93C42×C61—22no—
94C42×C61—22no—
95C42×C61—42no—
96C42×C61C2×D412yes—
97C42×C61C2×D412yes—
98C22⋊Dic61—24no—
99C4⋊Dic61—24no—
100C4⋊Dic61—24no—
101C4⋊Dic61—24no—
102C4⋊Dic61—22no—
103C4⋊Dic61—22no—
104C4⋊Dic61—22no—
105C4⋊Dic61C2×D414yes—
106#11758196—28no—
107#11758196—24no—
108#11758196—24no—
109C4×Dic61—28no—
110C4×Dic61—24no—
111C2×#92418—24no—
112C23×C61C22×D411yescharacteristic
113Q8×C61—28no—
114Q8×C61—82no—
115Q8×C61—82no—
116C2×C4×C61—22no—
117C2×C4×C61—22no—
118C2×C4×C61—22no—
119C2×C4×C61—22no—
120C2×C4×C61—41no—
121C2×C4×C61—42no—
122C2×C4×C61—42no—
123C2×C4×C61—42no—
124C2×C4×C61—44no—
125C2×C4×C61—42no—
126C2×C4×C61—42no—
127C2×C4×C61#12011yescharacteristic
128C2×C4×C61#12012yes—
129C2×C4×C61#12011yescharacteristic
130C2×C4×C61C2×Q1614yes—
131C2×C4×C61C2×Q1612yes—
132C2×C4×C61#13712yes—
133C2×C4×C61C22×D412yes—
134C2×Dic61—24no—
135C2×Dic61—24no—
136Dic122—44no—
137Dic122—44no—
138Dic122—84no—
139#92418—44no—
140#18411—611nomaximal, Sylow
141C22×C61—21no—
142C22×C61—21no—
143C22×C61C2×#12011yescharacteristic
144C22×C61C22×Q1611yescharacteristic
145C22×C61C2×#13711yescharacteristic
146C4×C61—24no—
147C4×C61—21no—
148C4×C61—22no—
149C4×C61—42no—
150C4×C61—82no—
151C4×C61—82no—
152C4×C61#45114yes—
153C4×C61#45412yes—
154Dic61—44no—
155Dic61—44no—
156#3502—611no—
157#3230—612no—
158#2568D6111yescharacteristic
159#1617—618no—
160#1503—612no—
161#1461—611no—
162C2×C61—21no—
163C2×C61—21no—
164C2×C61C2×#45111yescharacteristic
165C2×C61C2×#45411yescharacteristic
166C2×C61#302811yescharacteristic
167Q82—1222no—
168#557—1224no—
169#557—1222no—
170#544—614no—
171#544—1221no—
172#533—612no—
173#533—1222no—
174C2×C4⋊Q8C2×D6111yescharacteristic
175#519—1221no—
176C2×C4×Q8C2×D6111yescharacteristic
177#500—1222no—
178#487—1222no—
179#484—618no—
180#477—1224no—
181#431—612no—
182#400C2×D6114yes—
183#391—21no—
184#391—22no—
185#382—21no—
186C4×C4⋊C4C2×D6111yescharacteristic
187#328—618no—
188#324—614no—
189C61#1841111yescharacteristic, complemented, Sylow
190C22×Q8—21no—
191C22×Q8C22⋊D6111yescharacteristic
192C4⋊Q8—22no—
193C4⋊Q8—22no—
194C4⋊Q8—612no—
195C4⋊Q8—612no—
196C4⋊Q8—1222no—
197C4⋊Q8—1222no—
198C4⋊Q8—1228no—
199C4⋊Q8—1224no—
200#125—1224no—
201#125—1228no—
202#125—1224no—
203#125—1222no—
204C22⋊Q8—614no—
205C22⋊Q8—1222no—
206C22⋊Q8—1224no—
207C4×Q8—22no—
208C4×Q8—22no—
209C4×Q8—614no—
210C4×Q8—1224no—
211C4×Q8—1224no—
212C4×Q8—1224no—
213C4×Q8—1224no—
214C4×Q8—1222no—
215#117—1222no—
216#117—1224no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4C22⋊D6111yescharacteristic
220C2×C4⋊C4C22×D6112yes—
221C2×C4⋊C4C22×D6112yes—
222C2×C42—21no—
223C2×C42C22⋊D6112yes—
224C2×C42C22×D6111yescharacteristic
225#107—1228no—
226C4⋊C8—1222no—
227#103—1228no—
228C22⋊C8—614no—
229C4×C8—1222no—
230#95—24no—
231#95—24no—
232#95C22×D6112yes—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—44no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—614no—
239C2×Q8—1224no—
240C2×Q8—1222no—
241C2×Q8#1175820214yes—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4C2×C22⋊D6111yescharacteristic
245C22×C4C2×C22⋊D6112yes—
246C22×C4C2×C22⋊D6112yes—
247C22×C4C2×C22⋊D6111yescharacteristic
248C22×C4C23×D6111yescharacteristic
249C2×C8—1224no—
250C4⋊C4—24no—
251C4⋊C4—22no—
252C4⋊C4—24no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—614no—
256C4⋊C4—1228no—
257C4⋊C4—1224no—
258C4⋊C4—1224no—
259C4⋊C4—1224no—
260C4⋊C4—1224no—
261C4⋊C4—1224no—
262C4⋊C4—1222no—
263C4⋊C4—1222no—
264C4⋊C4—1222no—
265C22⋊C4—1224no—
266C42—22no—
267C42—22no—
268C42—42no—
269C42—1228no—
270C42—1224no—
271C42D4×D6112yes—
272C42D4×D6112yes—
273C23C22×C22⋊D6111yescharacteristic
274Q8—28no—
275Q8—82no—
276Q8—82no—
277Q8—4884no—
278Q8—2444no—
279Q8—2444no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—44no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—1224no—
292C2×C4—1224no—
293C2×C4#1451974511yescharacteristic
294C2×C4#1451974512yes—
295C2×C4#1451974511yescharacteristic
296C2×C4C2×#1175820214yes—
297C2×C4C2×#1175820212yes—
298C2×C4#1451980712yes—
299C2×C4C2×D4×D6112yes—
300C8—2444no—
301C22—21no—
302C22—21no—
303C22C2×#1451974511yescharacteristic
304C22C22×#1175820211yescharacteristic
305C22C2×#1451980711yescharacteristic
306C4—21no—
307C4—22no—
308C4—24no—
309C4—42no—
310C4—82no—
311C4—82no—
312C4—2444no—
313C4—2444no—
314C4#1683991714yes—
315C4#1683993412yes—
316C2—21no—
317C2—21no—
318C2C2×#1683991711yescharacteristic
319C2C2×#1683993411yescharacteristic
320C2#2145522411yescharacteristic
subgroupG/H
centerC22C2×#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2568C2
socleC22×C61C2×#120
prime radicalC23×C61C22×D4
hypercenter#2568D61
hypocenterC61#18411
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2568

Complements

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

NH ≅ G/Ntype
189. C61#18411semidirect

Maximal subgroups

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

subgroupindex
#214596292
#214569702
#214448602
#214443172
#214441432
C61×#25682
#1841161