Finite Group Databasebeta

← #29593684

Subgroups — #29593684

Order 15616.

286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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#21458393C211yesmaximal, characteristic
2#21448065C211yesmaximal, characteristic, complemented
3#21447870C211yesmaximal, characteristic, complemented
4#21445308C211yesmaximal, characteristic
5#21443870C211yesmaximal, characteristic, complemented
6#21443790C211yesmaximal, characteristic, complemented
7C61×#1330C211yesmaximal, characteristic
8#16840452—21no—
9C2×Dic488—21no—
10#16840164C2211yescharacteristic
11#16840142C2211yescharacteristic
12#16840104—21no—
13#16840098—21no—
14#16840070—21no—
15#16840042—21no—
16#16840020—21no—
17C4×Dic244C2211yescharacteristic
18#16839804—21no—
19#16839567—21no—
20#16839567—21no—
21#16839567—21no—
22#16839513C2211yescharacteristic
23#16839509—21no—
24C61×#436C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#346C2211yescharacteristic
27C2×Dic244—21no—
28C2×Dic244—21no—
29C2×Dic244D411yescharacteristic
30#14519777—21no—
31#14519770—41no—
32#14519769—21no—
33#14519767—41no—
34#14519758—41no—
35#14519756—21no—
36#14519756—21no—
37C4×Dic122—21no—
38#14519736—21no—
39#14519733—41no—
40C2×C4⋊Dic61—21no—
41Dic488—42no—
42#14519711—21no—
43#14519711D411yescharacteristic
44#14519711D411yescharacteristic
45#14519711D411yescharacteristic
46#14519710—41no—
47#14519709—21no—
48#14519709—21no—
49C4⋊#92418—21no—
50#14519702—21no—
51#14519702—21no—
52#14519702—21no—
53#14519698—41no—
54C2×M16×C61—21no—
55C4×D4×C61D411yescharacteristic
56C2×C16×C61—21no—
57C2×C16×C61—21no—
58C4⋊C8×C61D411yescharacteristic
59C22⋊C8×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×D4×C61D811yescharacteristic
62C22×C4×C61—21no—
63C22×Dic61—41no—
64C2×Dic122—21no—
65C2×Dic122—41no—
66M16×C61—41no—
67M16×C61—41no—
68C2×C8×C61—21no—
69C2×C8×C61C2×D411yescharacteristic
70C2×C8×C61C2×D411yescharacteristic
71C4⋊C4×C61D811yescharacteristic
72C22⋊C4×C61—21no—
73C42×C61C2×D411yescharacteristic
74C22⋊Dic61—41no—
75C22⋊Dic61—41no—
76C22⋊Dic61—41no—
77C4⋊Dic61—21no—
78C4⋊Dic61—21no—
79C4⋊Dic61—21no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83#11758196—41no—
84#11758196—41no—
85#11758196—41no—
86#11758196—41no—
87#11758196—41no—
88C4×Dic61—41no—
89C4×Dic61—41no—
90C2×#92418—41no—
91Dic244—21no—
92Dic244—21no—
93Dic244—42no—
94Dic244—41no—
95Dic244—41no—
96C16×C61—41no—
97C16×C61—41no—
98C23×C61—21no—
99D4×C61—41no—
100C2×C4×C61—21no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61#12011yescharacteristic
104C2×C4×C61C2×D811yescharacteristic
105C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—82no—
111C2×Dic61—81no—
112Dic122—41no—
113Dic122—41no—
114Dic122—81no—
115Dic122—81no—
116C8×C61—21no—
117C8×C61—41no—
118C8×C61#13511yescharacteristic
119C8×C61AGL(1,ℤ/8)11yescharacteristic
120#92418—81no—
121#12351—611nomaximal, Sylow
122C22×C61—41no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61#44711yescharacteristic
126C4×C61—21no—
127C4×C61—21no—
128C4×C61—41no—
129C4×C61#44911yescharacteristic
130C4×C61#45411yescharacteristic
131Dic61—81no—
132Dic61—81no—
133Dic61—81no—
134Dic61—81no—
135Dic61—161no—
136#3352—611no—
137#2245—611no—
138#2209—611no—
139#1689—611no—
140#1363—611no—
141#1334—611no—
142#1330D6111yescharacteristic
143C2×C61—81no—
144C2×C61#162511yescharacteristic
145C2×C61#219111yescharacteristic
146C2×C61#219511yescharacteristic
147#552—1221no—
148C2×Q32—1221no—
149#499—611no—
150#494—611no—
151#485—1221no—
152#484—1221no—
153#479—1221no—
154#474—1221no—
155#470—1221no—
156C4×Q16—611no—
157#436C2×D6111yescharacteristic
158#428—1221no—
159C4⋊C16C2×D6111yescharacteristic
160#358—1221no—
161#358—1221no—
162#358—1221no—
163#346C2×D6111yescharacteristic
164#334—611no—
165#332—1221no—
166C61#1235111yescharacteristic, complemented, Sylow
167C2×Q16—611no—
168C2×Q16—1221no—
169C2×Q16—1221no—
170C2×M16—21no—
171C4⋊Q8—1221no—
172#126—2441no—
173#125—1221no—
174#125—2441no—
175#123—2441no—
176C22⋊Q8—1221no—
177C22⋊Q8—1221no—
178C4×Q8—1221no—
179C4×D4D24411yescharacteristic
180#117—1221no—
181#117—2441no—
182C2×C4⋊C4—1221no—
183Q32—2442no—
184C2×C16—21no—
185C2×C16—21no—
186#107—611no—
187#107—611no—
188#107—611no—
189#107—1221no—
190#107—2441no—
191#106—1221no—
192#106—1221no—
193C4⋊C8—1221no—
194C4⋊C8D24411yescharacteristic
195#103—1221no—
196#103—1221no—
197#103—1221no—
198#102—2441no—
199C22⋊C8—21no—
200C4×C8C22×D6111yescharacteristic
201C2×Q8—1221no—
202C2×Q8—2441no—
203C2×D4D48811yescharacteristic
204C22×C4—21no—
205C22×C4—2441no—
206Q16—1221no—
207Q16—1221no—
208Q16—2442no—
209Q16—2441no—
210Q16—2441no—
211M16—41no—
212M16—41no—
213C2×C8—21no—
214C2×C8—2441no—
215C2×C8D4×D6111yescharacteristic
216C2×C8D4×D6111yescharacteristic
217C4⋊C4—1221no—
218C4⋊C4—1221no—
219C4⋊C4—1221no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C4⋊C4D48811yescharacteristic
229C22⋊C4—21no—
230C22⋊C4—2441no—
231C22⋊C4—2441no—
232C22⋊C4—2441no—
233C42—2441no—
234C42—2441no—
235C42C2×D24411yescharacteristic
236C16—41no—
237C16—41no—
238C23—21no—
239Q8—4881no—
240Q8—4881no—
241Q8—2441no—
242Q8—2441no—
243D4—41no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—4881no—
248C2×C4—4882no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4#1451974711yescharacteristic
254C2×C4C2×D48811yescharacteristic
255C2×C4#1451980511yescharacteristic
256C8—21no—
257C8—41no—
258C8—4881no—
259C8#1451979811yescharacteristic
260C8#1451980111yescharacteristic
261C22—41no—
262C22—41no—
263C22—41no—
264C22#1683989811yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—9761no—
269C4—4881no—
270C4—4881no—
271C4—4881no—
272C4—4881no—
273C4#1683990811yescharacteristic
274C4#1683993611yescharacteristic
275C2—81no—
276C2#2144491011yescharacteristic
277C2#2144777211yescharacteristic
278C2#2144779911yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1330C2
socleC22×C61#447
prime radicalC2×D4×C61D8
hypercenter#1330D61
hypocenterC61#12351
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #436 ◁ #1330

Complements

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

NH ≅ G/Ntype
2. #21448065C2semidirect
3. #21447870C2semidirect
5. #21443870C2semidirect
6. #21443790C2semidirect
166. C61#12351semidirect

Maximal subgroups

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

subgroupindex
#214583932
#214480652
#214478702
#214453082
#214438702
#214437902
C61×#13302
#1235161