Finite Group Databasebeta

← #29592859

Subgroups — #29592859

Order 15616.

336 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 57 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#21453802C211yesmaximal, characteristic
2#21446977C211yesmaximal, characteristic
3#21444861C211yesmaximal, characteristic
4#21443847C211yesmaximal, characteristic
5#21443846C211yesmaximal, characteristic
6#21443752C211yesmaximal, characteristic
7C61×#1617C211yesmaximal, characteristic
8#16840095—21no—
9#16839770—21no—
10#16839701C2211yescharacteristic
11#16839696—21no—
12#16839695—21no—
13#16839667C2211yescharacteristic
14#16839666—21no—
15#16839659—21no—
16#16839647—21no—
17#16839644—21no—
18#16839531C2211yescharacteristic
19#16839521—21no—
20#16839499—21no—
21#16839488C2211yescharacteristic
22C61×#544C2211yescharacteristic
23C61×#484—21no—
24C61×#400C2211yescharacteristic
25C61×#328—21no—
26C61×#324C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C2×#11758194—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61D411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61D411yescharacteristic
37#14519710—41no—
38#14519701—41no—
39#14519700—41no—
40#14519700—41no—
41C22⋊#92418—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684D411yescharacteristic
49C4⋊Q8×C61—41no—
50#125×C61—41no—
51C22⋊Q8×C61—21no—
52C22⋊Q8×C61—21no—
53#117×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C4⋊C4×C61C2311yescharacteristic
56#107×C61—41no—
57#103×C61—41no—
58C22⋊C8×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61D411yescharacteristic
62C2×Q8×C61—21no—
63C2×Q8×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C2×Dic122—21no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76C2×Dic122Q1612yes—
77C2×C8×C61—41no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C42×C61—41no—
88C4⋊Dic61—42no—
89C4⋊Dic61—41no—
90#11758196—42no—
91#11758196—42no—
92#11758196—81no—
93#11758196—81no—
94C4×Dic61—41no—
95C4×Dic61—81no—
96#11758194—41no—
97#11758194—41no—
98C2×#92418—41no—
99C2×#92418—41no—
100C23×C61#12011yescharacteristic
101Q8×C61—81no—
102Q8×C61—81no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61C2×Q1611yescharacteristic
118C2×C4×C61#13711yescharacteristic
119C2×Dic61—22no—
120C2×Dic61—22no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131Dic122—42no—
132Dic122—81no—
133C8×C61—81no—
134#92418—81no—
135#92418—81no—
136#12225—611nomaximal, Sylow
137C22×C61—21no—
138C22×C61—21no—
139C22×C61#45111yescharacteristic
140C22×C61#45511yescharacteristic
141C22×C61B(4,𝔽2)11yescharacteristic
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—41no—
145C4×C61—41no—
146C4×C61—81no—
147C4×C61—81no—
148C4×C61—81no—
149C4×C61—81no—
150Dic61—42no—
151Dic61—42no—
152Dic61—81no—
153Dic61—81no—
154#2809—611no—
155#2028—611no—
156#1617—611no—
157#1617D6111yescharacteristic
158#1353—611no—
159#1353—611no—
160#1319—611no—
161C2×C61—21no—
162C2×C61—21no—
163C2×C61#160211yescharacteristic
164C2×C61#220111yescharacteristic
165C2×C61#220411yescharacteristic
166#544C2×D6111yescharacteristic
167#484—21no—
168#484—1221no—
169#419—1221no—
170#400—611no—
171#400C2×D6111yescharacteristic
172#398—1221no—
173#398—1221no—
174#391—611no—
175#391—1221no—
176#389—1221no—
177#387—1221no—
178#387—1221no—
179#343—611no—
180#339—1221no—
181#328—21no—
182#328—1221no—
183#324—611no—
184#324C2×D6111yescharacteristic
185C61#1222511yescharacteristic, complemented, Sylow
186C22×Q8—611no—
187C2×M16—1221no—
188C4⋊Q8—41no—
189#125—41no—
190C22⋊Q8—21no—
191C22⋊Q8—21no—
192#117—21no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4—1221no—
199C2×C4⋊C4C22⋊D6111yescharacteristic
200C2×C4⋊C4C22×D6111yescharacteristic
201C2×C42—611no—
202C2×C42—1221no—
203#107—41no—
204#107—2441no—
205#103—41no—
206#103—2441no—
207#103—2441no—
208#103—2441no—
209C22⋊C8—21no—
210C22⋊C8—1221no—
211#95—21no—
212#95—21no—
213#95—611no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217#95—1221no—
218#95—1221no—
219#95—1221no—
220#95C22⋊D6111yescharacteristic
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—612no—
224C2×Q8—1221no—
225C2×Q8—2441no—
226C2×Q8—2441no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—1221no—
230C22×C4—1221no—
231C22×C4—1221no—
232C22×C4—1221no—
233C22×C4D4×D6111yescharacteristic
234C22×C4D4×D6111yescharacteristic
235C22×C4C2×C22⋊D6111yescharacteristic
236M16—2441no—
237M16—2441no—
238C2×C8—41no—
239C2×C8—2441no—
240C2×C8—2441no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—4881no—
250C4⋊C4—4881no—
251C4⋊C4—2441no—
252C4⋊C4—2442no—
253C4⋊C4—2442no—
254C4⋊C4—2442no—
255C22⋊C4—41no—
256C42—41no—
257C42—4881no—
258C42—2441no—
259C23#1451974511yescharacteristic
260Q8—81no—
261Q8—81no—
262Q8—4881no—
263Q8—2442no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—1222no—
279C2×C4—1222no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4Q16×D6111yescharacteristic
291C2×C4#1451980911yescharacteristic
292C8—81no—
293C8—4881no—
294C8—4881no—
295C22—21no—
296C22—21no—
297C22#1683991611yescharacteristic
298C22#1683993811yescharacteristic
299C22#1683994811yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—81no—
305C4—81no—
306C4—81no—
307C4—81no—
308C4—4881no—
309C4—4881no—
310C4—2442no—
311C4—2442no—
312C2—21no—
313C2—21no—
314C2#2144477411yescharacteristic
315C2#2144783011yescharacteristic
316C2#2144784311yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1617C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#1617D61
hypocenterC61#12225
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1617

Complements

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

NH ≅ G/Ntype
185. C61#12225semidirect

Maximal subgroups

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

subgroupindex
#214538022
#214469772
#214448612
#214438472
#214438462
#214437522
C61×#16172
#1222561