Finite Group Databasebeta

← #29593685

Subgroups — #29593685

Order 15616.

286 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 61 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#21458395C211yesmaximal, characteristic
2#21448065C211yesmaximal, characteristic, complemented
3#21447869C211yesmaximal, characteristic, complemented
4#21445309C211yesmaximal, characteristic
5#21443872C211yesmaximal, characteristic, complemented
6#21443778C211yesmaximal, characteristic
7C61×#1334C211yesmaximal, characteristic, complemented
8#16840453—21no—
9C2×#14519723—21no—
10#16840164C2211yescharacteristic
11#16840142C2211yescharacteristic
12#16840102—21no—
13#16840096—21no—
14#16840069—21no—
15#16840043—21no—
16#16840017—21no—
17#16839841C2211yescharacteristic
18#16839803—21no—
19C4⋊#11758185C2211yescharacteristic
20#16839567—21no—
21#16839567—21no—
22#16839565—21no—
23#16839507—21no—
24C4×Q16×C61C2211yescharacteristic
25C61×#346C2211yescharacteristic
26C61×#334C2211yescharacteristic
27C2×Dic244—21no—
28C2×Dic244—21no—
29C2×#11758189—21no—
30#14519777—21no—
31#14519771—41no—
32#14519769—21no—
33#14519767—41no—
34#14519762—41no—
35#14519753—21no—
36#14519753—21no—
37C4×D244D411yescharacteristic
38#14519735—21no—
39#14519734—41no—
40C4⋊C4×D61—21no—
41#14519723—42no—
42C2×#11758185—21no—
43#14519711—41no—
44#14519711D411yescharacteristic
45#14519711D411yescharacteristic
46#14519710—21no—
47#14519709—21no—
48#14519708—21no—
49C4⋊#92418D411yescharacteristic
50#14519701—21no—
51#14519701—21no—
52#14519699—41no—
53#14519689—21no—
54C2×Q16×C61D411yescharacteristic
55C4×Q8×C61—21no—
56C2×C16×C61—21no—
57#107×C61D411yescharacteristic
58C4⋊C8×C61—21no—
59#103×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×Q8×C61—21no—
62C2×D244D811yescharacteristic
63C2×C4×D61—21no—
64C2×C4×D61—41no—
65C2×Dic122—41no—
66Q16×C61—21no—
67Q16×C61—21no—
68C2×C8×C61—41no—
69C2×C8×C61C2×D411yescharacteristic
70C2×C8×C61C2×D411yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊C4×C61—41no—
73C42×C61—41no—
74C42×C61C2×D411yescharacteristic
75#11758198—21no—
76#11758198—41no—
77#11758198—41no—
78#11758198—41no—
79C4⋊Dic61—21no—
80C4⋊Dic61—21no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83C4⋊Dic61D811yescharacteristic
84#11758196—41no—
85#11758196—41no—
86#11758196—41no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—41no—
90C2×#92418—21no—
91Dic244—42no—
92Dic244—41no—
93Dic244—41no—
94#11758189—41no—
95#11758189—41no—
96C16×C61—41no—
97#11758185—41no—
98C22×D61—21no—
99Q8×C61—41no—
100Q8×C61—41no—
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—21no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—81no—
110D244—41no—
111C4×D61—41no—
112C4×D61—41no—
113C4×D61—82no—
114Dic122—81no—
115Dic122—81no—
116C8×C61—21no—
117C8×C61—81no—
118C8×C61#13511yescharacteristic
119C8×C61AGL(1,ℤ/8)11yescharacteristic
120#92418—41no—
121#12351—611nomaximal, Sylow
122C22×C61#44711yescharacteristic
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—41no—
126C4×C61—21no—
127C4×C61—21no—
128C4×C61—81no—
129C4×C61—81no—
130C4×C61#44911yescharacteristic
131C4×C61#45411yescharacteristic
132Dic61—41no—
133Dic61—81no—
134Dic61—81no—
135Dic61—161no—
136#3352—611no—
137#2245—611no—
138#2209—611no—
139#1689—611no—
140#1363—611no—
141#1334D6111yescharacteristic, complemented
142#1330—611no—
143C2×C61#162511yescharacteristic
144C2×C61#219111yescharacteristic
145C2×C61#219511yescharacteristic
146D61—81no—
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×Q16C2×D6111yescharacteristic
157#436—611no—
158#428—1221no—
159C4⋊C16—611no—
160#358—1221no—
161#358—1221no—
162#358—1221no—
163#346C2×D6111yescharacteristic
164#334C2×D6111yescharacteristic
165#332—1221no—
166C61#1235111yescharacteristic, complemented, Sylow
167C2×Q16—1221no—
168C2×Q16—1221no—
169C2×Q16D24411yescharacteristic
170C2×M16—1221no—
171C4⋊Q8—1221no—
172#126—2441no—
173#125—1221no—
174#125—2441no—
175#123—2441no—
176C22⋊Q8—1221no—
177C22⋊Q8—1221no—
178C4×Q8—21no—
179C4×D4—611no—
180#117—1221no—
181#117—2441no—
182C2×C4⋊C4—1221no—
183Q32—2442no—
184C2×C16—21no—
185C2×C16—1221no—
186#107—611no—
187#107—611no—
188#107—1221no—
189#107—2441no—
190#107D24411yescharacteristic
191#106—1221no—
192#106—1221no—
193C4⋊C8—21no—
194C4⋊C8—611no—
195#103—21no—
196#103—1221no—
197#103—1221no—
198#102—2441no—
199C22⋊C8—1221no—
200C4×C8C22×D6111yescharacteristic
201C2×Q8—21no—
202C2×Q8—2441no—
203C2×D4—611no—
204C22×C4—1221no—
205C22×C4—2441no—
206Q16—21no—
207Q16—21no—
208Q16—2442no—
209Q16—2441no—
210Q16—2441no—
211M16—2441no—
212M16—2441no—
213C2×C8—41no—
214C2×C8—1221no—
215C2×C8C2×D24411yescharacteristic
216C2×C8D4×D6111yescharacteristic
217C4⋊C4—21no—
218C4⋊C4—41no—
219C4⋊C4—611no—
220C4⋊C4—1221no—
221C4⋊C4—1221no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C4⋊C4—2441no—
229C22⋊C4—1221no—
230C22⋊C4—2441no—
231C22⋊C4—2441no—
232C22⋊C4—2441no—
233C42—41no—
234C42—2441no—
235C42D4×D6111yescharacteristic
236C16—41no—
237C16—2441no—
238C23—1221no—
239Q8—41no—
240Q8—41no—
241Q8—4881no—
242Q8—4881no—
243D4—2441no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—1221no—
247C2×C4—4882no—
248C2×C4—4881no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4#1451974711yescharacteristic
254C2×C4D8×D6111yescharacteristic
255C2×C4#1451980411yescharacteristic
256C8—21no—
257C8—81no—
258C8—2441no—
259C8#1451979911yescharacteristic
260C8#1451980511yescharacteristic
261C22—2441no—
262C22—2441no—
263C22—2441no—
264C22#1683989711yescharacteristic
265C4—21no—
266C4—21no—
267C4—81no—
268C4—81no—
269C4—9761no—
270C4—4881no—
271C4—4881no—
272C4—2441no—
273C4#1683990911yescharacteristic
274C4#1683993611yescharacteristic
275C2—4881no—
276C2#2144491111yescharacteristic
277C2#2144777111yescharacteristic
278C2#2144780011yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1334C2
socleC22×C61#447
prime radicalC2×D244D8
hypercenter#1334D61
hypocenterC61#12351
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1334

Complements

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

NH ≅ G/Ntype
2. #21448065C2semidirect
3. #21447869C2semidirect
5. #21443872C2semidirect
7. C61×#1334C2semidirect
141. #1334D61semidirect
166. C61#12351semidirect

Maximal subgroups

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

subgroupindex
#214583952
#214480652
#214478692
#214453092
#214438722
#214437782
C61×#13342
#1235161