Finite Group Databasebeta

← #29592841

Subgroups — #29592841

Order 15616.

346 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 59 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#21453703C211yesmaximal, characteristic
2#21444861C211yesmaximal, characteristic
3#21444793C211yesmaximal, characteristic
4#21443848C211yesmaximal, characteristic
5#21443845C211yesmaximal, characteristic
6#21443753C211yesmaximal, characteristic
7C61×#2028C211yesmaximal, characteristic
8#16840095—21no—
9#16839917—21no—
10#16839704—21no—
11#16839701C2211yescharacteristic
12#16839696—21no—
13#16839682C2211yescharacteristic
14#16839669—21no—
15#16839666—21no—
16#16839649—21no—
17#16839646—21no—
18#16839499—21no—
19#16839499—21no—
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22C61×#544C2211yescharacteristic
23C61×#419—21no—
24C61×#391C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#339—21no—
27C22×Dic122D411yescharacteristic
28C2×#11758202—41no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61D411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×C4×Dic61—21no—
35#14519710—41no—
36#14519701—41no—
37#14519700—41no—
38C22⋊#92418—21no—
39C22⋊#92418—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684D411yescharacteristic
48#14519684D411yescharacteristic
49C22×Q8×C61D411yescharacteristic
50C2×M16×C61—21no—
51C4⋊Q8×C61—41no—
52#125×C61—41no—
53C22⋊Q8×C61—21no—
54C22⋊Q8×C61—21no—
55#117×C61—21no—
56C2×C4⋊C4×C61C2311yescharacteristic
57C2×C42×C61D411yescharacteristic
58#103×C61—41no—
59#103×C61—41no—
60#95×C61—21no—
61#95×C61—21no—
62C2×Q8×C61—21no—
63C2×Q8×C61—21no—
64C2×Q8×C61—21no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C2×Q8×C61Q1612yescomplemented
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C2×Dic122—41no—
78C2×Dic122—42no—
79M16×C61—41no—
80M16×C61—41no—
81C2×C8×C61—41no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61—21no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C42×C61—41no—
91C42×C61—41no—
92#11758202—82no—
93C4⋊Dic61—41no—
94C4⋊Dic61—81no—
95#11758196—42no—
96#11758196—42no—
97#11758196—81no—
98C4×Dic61—81no—
99C2×#92418—41no—
100C2×#92418—41no—
101C23×C61#12011yescharacteristic
102Q8×C61—42no—
103Q8×C61—81no—
104Q8×C61—81no—
105Q8×C61—81no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—22no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
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×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61C2×Q1611yescharacteristic
121C2×C4×C61#13711yescharacteristic
122C2×Dic61—22no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—42no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133Dic122—42no—
134Dic122—81no—
135C8×C61—81no—
136#92418—81no—
137#92418—81no—
138#12222—611nomaximal, Sylow
139C22×C61—21no—
140C22×C61—21no—
141C22×C61#45111yescharacteristic
142C22×C61#45511yescharacteristic
143C22×C61B(4,𝔽2)11yescharacteristic
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—42no—
147C4×C61—41no—
148C4×C61—41no—
149C4×C61—81no—
150C4×C61—81no—
151C4×C61—81no—
152Dic61—42no—
153Dic61—81no—
154Dic61—81no—
155Dic61—81no—
156#2799—611no—
157#2028D6111yescharacteristic
158#1617—611no—
159#1605—611no—
160#1354—611no—
161#1353—611no—
162#1319—611no—
163C2×C61—21no—
164C2×C61—21no—
165C2×C61#160211yescharacteristic
166C2×C61#219711yescharacteristic
167C2×C61#220311yescharacteristic
168#544C2×D6111yescharacteristic
169#484—1221no—
170#451—1221no—
171#419—21no—
172#400—611no—
173#400—1221no—
174#398—1221no—
175#395—611no—
176#391—1221no—
177#391—1221no—
178#391C2×D6111yescharacteristic
179#387—1221no—
180#387—1221no—
181#343C2×D6111yescharacteristic
182#339—21no—
183#328—1221no—
184#328—1221no—
185#324—611no—
186#324—611no—
187C61#1222211yescharacteristic, complemented, Sylow
188C22×Q8—611no—
189C22×Q8C22⋊D6111yescharacteristic
190C2×Q16—2441no—
191C2×M16—21no—
192C4⋊Q8—41no—
193#125—41no—
194C22⋊Q8—21no—
195C22⋊Q8—21no—
196#117—21no—
197C2×C4⋊C4—611no—
198C2×C4⋊C4—1221no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4C22×D6111yescharacteristic
203C2×C42—1221no—
204C2×C42C22⋊D6111yescharacteristic
205#107—2441no—
206#103—41no—
207#103—41no—
208#103—2441no—
209#103—2441no—
210C22⋊C8—1221no—
211C22⋊C8—1221no—
212#95—21no—
213#95—21no—
214#95—611no—
215#95—611no—
216#95—1221no—
217#95—1221no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—21no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—2441no—
229C2×Q8—2442no—
230C2×Q8#1175820212yescomplemented
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4D4×D6111yescharacteristic
238C22×C4D4×D6111yescharacteristic
239C22×C4C2×C22⋊D6111yescharacteristic
240Q16—4882no—
241M16—41no—
242M16—41no—
243C2×C8—41no—
244C2×C8—2441no—
245C2×C8—2441no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—4881no—
254C4⋊C4—4881no—
255C4⋊C4—2441no—
256C4⋊C4—2442no—
257C4⋊C4—2442no—
258C22⋊C4—41no—
259C42—41no—
260C42—41no—
261C42—4881no—
262C23#1451974511yescharacteristic
263Q8—42no—
264Q8—81no—
265Q8—81no—
266Q8—81no—
267Q8—4881no—
268Q8—2442no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—1222no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2442no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4C2×#1175820211yescharacteristic
295C2×C4#1451980711yescharacteristic
296C8—81no—
297C8—4881no—
298C8—4881no—
299C22—21no—
300C22—21no—
301C22#1683991711yescharacteristic
302C22#1683993911yescharacteristic
303C22#1683994811yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—42no—
309C4—81no—
310C4—81no—
311C4—81no—
312C4—4881no—
313C4—4881no—
314C4—4881no—
315C4—2442no—
316C2—21no—
317C2—21no—
318C2#2144477511yescharacteristic
319C2#2144780811yescharacteristic
320C2#2144783811yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2028C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#2028D61
hypocenterC61#12222
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2028

Complements

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

NH ≅ G/Ntype
67. C2×Q8×C61Q16semidirect
187. C61#12222semidirect
230. C2×Q8#11758202semidirect

Maximal subgroups

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

subgroupindex
#214537032
#214448612
#214447932
#214438482
#214438452
#214437532
C61×#20282
#1222261