Finite Group Databasebeta

← #29592972

Subgroups — #29592972

Order 15616.

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

normal subgroups only

This group has 324 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#21447169C211yesmaximal, characteristic
2#21444860C211yesmaximal, characteristic
3#21444826C211yesmaximal, characteristic
4#21443846C211yesmaximal, characteristic
5#21443825C211yesmaximal, characteristic
6#21443763C211yesmaximal, characteristic
7C61×#2769C211yesmaximal, characteristic
8#16840393C2211yescharacteristic
9#16840097—21no—
10#16840092—21no—
11#16839802—21no—
12#16839531C2211yescharacteristic
13#16839522—21no—
14#16839498—21no—
15#16839498—21no—
16#16839488C2211yescharacteristic
17#16839488C2211yescharacteristic
18C61×#400—21no—
19C61×#400C2211yescharacteristic
20C61×#398—21no—
21C61×#398C2211yescharacteristic
22C61×#389—21no—
23C61×#387—21no—
24C61×#387—21no—
25C61×#383—21no—
26C61×#382C2211yescharacteristic
27C2×#11758194—21no—
28#14519776—41no—
29#14519768—41no—
30#14519756—21no—
31#14519756—21no—
32#14519736—21no—
33#14519710—41no—
34#14519710—41no—
35#14519708—41no—
36#14519708—41no—
37#14519700—41no—
38#14519700—41no—
39C22⋊#92418—21no—
40C22⋊#92418—21no—
41C2×C4⋊C4×C61—21no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C4⋊C4×C61D411yescharacteristic
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C4⋊C4×C61C2311yescharacteristic
49C2×C42×C61—21no—
50C2×C42×C61D411yescharacteristic
51#95×C61—21no—
52#95×C61—21no—
53#95×C61—21no—
54#95×C61—21no—
55#95×C61—21no—
56#95×C61—21no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61D411yescharacteristic
61#95×C61D411yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C2×Dic122—21no—
72C2×Dic122—21no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—42no—
75C4⋊C4×C61—42no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—81no—
82C42×C61—21no—
83C42×C61—21no—
84C42×C61—42no—
85C22⋊Dic61—41no—
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61—21no—
89C4⋊Dic61—21no—
90#11758196—41no—
91#11758196—41no—
92C4×Dic61—41no—
93#11758194—22no—
94#11758194—41no—
95C2×#92418—41no—
96C2×#92418—41no—
97C2×#92418—41no—
98C23×C61#12011yescharacteristic
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
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×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61#13511yescharacteristic
124C2×C4×C61#13711yescharacteristic
125C2×Dic61—41no—
126C2×Dic61—41no—
127Dic122—81no—
128Dic122—81no—
129#92418—42no—
130#92418—81no—
131#92418—81no—
132#12241—611nomaximal, Sylow
133C22×C61—21no—
134C22×C61—21no—
135C22×C61#45211yescharacteristic
136C22×C61#45611yescharacteristic
137C22×C61B(4,𝔽2)11yescharacteristic
138C4×C61—21no—
139C4×C61—21no—
140C4×C61—42no—
141C4×C61—41no—
142C4×C61—41no—
143C4×C61—81no—
144C4×C61—81no—
145C4×C61—81no—
146C4×C61—81no—
147C4×C61—81no—
148Dic61—81no—
149Dic61—81no—
150#2769D6111yescharacteristic
151#2061—611no—
152#1617—611no—
153#1611—611no—
154#1353—611no—
155#1346—611no—
156#1324—611no—
157C2×C61—21no—
158C2×C61—21no—
159C2×C61#160311yescharacteristic
160C2×C61#220111yescharacteristic
161C2×C61#220411yescharacteristic
162#544—611no—
163#484—1221no—
164#483—1221no—
165#428—1221no—
166#400—21no—
167#400C2×D6111yescharacteristic
168#398—21no—
169#398C2×D6111yescharacteristic
170#389—21no—
171#387—21no—
172#387—21no—
173#383—21no—
174#382C2×D6111yescharacteristic
175#343—611no—
176#339—1221no—
177#328—1221no—
178#328—1221no—
179#324—611no—
180#324—611no—
181C61#1224111yescharacteristic, complemented, Sylow
182C2×M16—1221no—
183C4⋊Q8—2441no—
184#125—2441no—
185C22⋊Q8—1221no—
186C22⋊Q8—1221no—
187#117—1221no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C22⋊D6111yescharacteristic
193C2×C4⋊C4C22⋊D6111yescharacteristic
194C2×C4⋊C4C22⋊D6111yescharacteristic
195C2×C4⋊C4C22×D6111yescharacteristic
196C2×C42—21no—
197C2×C42C22⋊D6111yescharacteristic
198#107—2441no—
199#107—2441no—
200#106—2441no—
201#106—2441no—
202#103—2441no—
203#103—2441no—
204C22⋊C8—1221no—
205C22⋊C8—1221no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95C22⋊D6111yescharacteristic
216#95C22⋊D6111yescharacteristic
217C2×Q8—1221no—
218C2×Q8—1221no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4C2×C22⋊D6111yescharacteristic
226C22×C4C2×C22⋊D6111yescharacteristic
227C22×C4C2×C22⋊D6111yescharacteristic
228M16—1222no—
229M16—2441no—
230C2×C8—2441no—
231C2×C8—2441no—
232C2×C8—2441no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—81no—
242C4⋊C4—1221no—
243C4⋊C4—1221no—
244C4⋊C4—1221no—
245C4⋊C4—1221no—
246C4⋊C4—2441no—
247C4⋊C4—2441no—
248C22⋊C4—2441no—
249C42—21no—
250C42—21no—
251C42—42no—
252C42—2441no—
253C23#1451974611yescharacteristic
254Q8—4881no—
255Q8—4881no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
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—41no—
279C2×C4—41no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4#1451979711yescharacteristic
283C2×C4#1451980711yescharacteristic
284C8—4881no—
285C8—4881no—
286C8—2442no—
287C22—21no—
288C22—21no—
289C22#1683992411yescharacteristic
290C22#1683994511yescharacteristic
291C22#1683994911yescharacteristic
292C4—21no—
293C4—21no—
294C4—42no—
295C4—41no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—81no—
300C4—81no—
301C4—81no—
302C4—4881no—
303C4—4881no—
304C2—21no—
305C2—21no—
306C2#2144478211yescharacteristic
307C2#2144783211yescharacteristic
308C2#2144784511yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2769C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#2769D61
hypocenterC61#12241
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2769

Complements

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

NH ≅ G/Ntype
181. C61#12241semidirect

Maximal subgroups

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

subgroupindex
#214471692
#214448602
#214448262
#214438462
#214438252
#214437632
C61×#27692
#1224161