Finite Group Databasebeta

← #30605728

Subgroups — #30605728

Order 15616.

280 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 62 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#21462195C211yesmaximal, characteristic, complemented
2#21462161C211yesmaximal, characteristic, complemented
3#21460840C211yesmaximal, characteristic, complemented
4#21460839C211yesmaximal, characteristic, complemented
5#21460830C211yesmaximal, characteristic, complemented
6#21460830C211yesmaximal, characteristic, complemented
7#21456450C211yesmaximal, characteristic
8D61⋊M32—21no—
9#16840685C2211yescharacteristic
10#16840685C2211yescharacteristic
11#16840685C2211yescharacteristic
12#16840685C2211yescharacteristic
13#16840684—21no—
14#16840659—21no—
15#16840655—21no—
16#16840373C411yescharacteristic
17#16840368C411yescharacteristic
18#16840161C2211yescharacteristic
19#16840136C2211yescharacteristic
20#16840127C411yescharacteristic
21#16840011—21no—
22#16839994—21no—
23#16839865—21no—
24#16839847—21no—
25#16839719C2211yescharacteristic
26C61×#491C411yescharacteristic
27#14519852—41no—
28#14519851—21no—
29#14519851—21no—
30#14519851—21no—
31#14519851—21no—
32D61⋊C16—41no—
33C2×#11758201—21no—
34C2×#11758201—21no—
35C2×#11758189D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37#14519774C2×C411yescharacteristic
38#14519772—41no—
39#14519769C2×C411yescharacteristic
40#14519767—41no—
41#14519762—41no—
42#14519753—21no—
43#14519752—21no—
44#14519752—41no—
45Q8×Dic61—21no—
46#14519739—21no—
47#14519734C2×C411yescharacteristic
48#14519710—21no—
49#14519708—21no—
50#14519699—21no—
51#14519699—21no—
52#14519687D411yescharacteristic
53C4×#92418C2311yescharacteristic
54C8×Dic61D411yescharacteristic
55C4⋊Q8×C61C2×C411yescharacteristic
56#125×C61C2×C411yescharacteristic
57#103×C61—21no—
58#103×C61—21no—
59#97×C61C2×C411yescharacteristic
60C2×Q8×C61—21no—
61C2×D244—21no—
62C2×D244—41no—
63C2×D244—41no—
64C2×C4×D61—41no—
65C2×C4×D61C22⋊C411yescharacteristic
66C2×C8×C61C22⋊C411yescharacteristic
67C2×C8×C61C22⋊C411yescharacteristic
68C4⋊C4×C61—21no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C42×C61C22×C411yescharacteristic
72#11758201—41no—
73#11758201—41no—
74#11758201—41no—
75#11758201—41no—
76#11758198—21no—
77#11758198—41no—
78#11758198—41no—
79#11758198—41no—
80C4⋊Dic61—21no—
81C4⋊Dic61—41no—
82#11758196—21no—
83#11758196—41no—
84#11758196—41no—
85C4×Dic61—41no—
86C4×Dic61C22⋊C411yescharacteristic
87C2×#92418C2×D411yescharacteristic
88C2×#92418C2×D411yescharacteristic
89#11758189—21no—
90#11758189—21no—
91C8×D61—21no—
92C8×D61—21no—
93#11758187—41no—
94#11758187—41no—
95#11758187—41no—
96#11758187—41no—
97C22×D61—41no—
98C22×D61#10011yescharacteristic
99Q8×C61—41no—
100Q8×C61—41no—
101C2×C4×C61—21no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61C2×C22⋊C411yescharacteristic
105C2×Dic61—21no—
106C2×Dic61—41no—
107C2×Dic61#10011yescharacteristic
108D244—41no—
109D244—41no—
110D244—161no—
111D244—161no—
112C4×D61—21no—
113C4×D61—21no—
114C4×D61—161no—
115C8×C61—21no—
116C8×C61—21no—
117#92418#13511yescharacteristic
118#92418#13511yescharacteristic
119#92418AGL(1,ℤ/8)11yescharacteristic
120#92418#13711yescharacteristic
121#11991—611nomaximal, Sylow
122C22×C61C2×#10011yescharacteristic
123C2×D61—21no—
124C2×D61—41no—
125C2×D61—81no—
126C2×D61—81no—
127C2×D61—81no—
128C4×C61—41no—
129C4×C61—81no—
130C4×C61—81no—
131C4×C61#41611yescharacteristic
132C4×C61#41711yescharacteristic
133Dic61—21no—
134Dic61—41no—
135Dic61—81no—
136#3174—611no—
137#2166—611no—
138#2153—611no—
139#1366—611no—
140#1366—611no—
141#1359—611no—
142#1359—611no—
143C2×C61—21no—
144C2×C61#155111yescharacteristic
145D61—41no—
146D61—161no—
147#541—611no—
148#540—611no—
149C2×M32—1221no—
150#499—611no—
151#492—611no—
152#491#692311yescharacteristic
153#490—611no—
154#468—1221no—
155#465—1221no—
156#440—1221no—
157C4×SD16—1221no—
158#405—611no—
159#364—611no—
160#364—611no—
161#364—611no—
162#364—611no—
163#364—1221no—
164#349—1221no—
165#347—1221no—
166C61#1199111yescharacteristic, complemented, Sylow
167C2×SD16—1221no—
168C2×SD16—1221no—
169C2×M16—611no—
170C22×C8—611no—
171C4⋊Q8C2×#692311yescharacteristic
172#127—611no—
173#126—2441no—
174#125—611no—
175#125—2441no—
176#125C2×#692311yescharacteristic
177#123—2441no—
178C22⋊Q8—1221no—
179#121—1221no—
180#121—2441no—
181C4×Q8—1221no—
182C4×D4—1221no—
183#117—611no—
184M32—1221no—
185M32—1221no—
186M32—1221no—
187M32—1221no—
188M32—2441no—
189C2×C16—2441no—
190#107—1221no—
191#106—1221no—
192#103—21no—
193#103—21no—
194#102—1221no—
195#102—1221no—
196#97—611no—
197#97C2×#692311yescharacteristic
198C4×C8—611no—
199C4×C8—611no—
200C2×Q8—21no—
201C2×D4—1221no—
202C2×D4—2441no—
203C2×D4—2441no—
204C22×C4—611no—
205C22×C4—2441no—
206SD16—2441no—
207SD16—2441no—
208SD16—2441no—
209SD16—2441no—
210M16—1221no—
211M16—1221no—
212C2×C8—611no—
213C2×C8—611no—
214C2×C8—1221no—
215C2×C8—1221no—
216C2×C8C22⋊#692311yescharacteristic
217C2×C8C22⋊#692311yescharacteristic
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—1221no—
222C4⋊C4—1221no—
223C4⋊C4—2441no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C22⋊C4—1221no—
227C22⋊C4—2441no—
228C22⋊C4—2441no—
229C22⋊C4—2441no—
230C42—611no—
231C42—2441no—
232C42C22×#692311yescharacteristic
233C16—2441no—
234C16—2441no—
235C16—2441no—
236C16—2441no—
237C23—611no—
238C23—2441no—
239Q8—41no—
240Q8—41no—
241D4—9761no—
242D4—9761no—
243D4—2441no—
244D4—2441no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—611no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—1221no—
252C2×C4—9761no—
253C2×C4—2441no—
254C2×C4C2×C22⋊#692311yescharacteristic
255C8—21no—
256C8—21no—
257C8—611no—
258C8—611no—
259C8—611no—
260C8—611no—
261C22—1221no—
262C22—4881no—
263C22—4881no—
264C22—4881no—
265C22—2441no—
266C22D61⋊#10011yescharacteristic
267C4—41no—
268C4—81no—
269C4—81no—
270C4—1221no—
271C4—4881no—
272C4—2441no—
273C4#1684075211yescharacteristic
274C4#1684075311yescharacteristic
275C2—21no—
276C2—9761no—
277C2—2441no—
278C2#2146133911yescharacteristic
subgroupG/H
centerC2#21461339
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#491C4
socleC2×C61#1551
prime radical#16840368C4
cosocleC4×#92418C23
hypercenter#491#6923
hypocenterC61#11991
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #21462195C2semidirect
2. #21462161C2semidirect
3. #21460840C2semidirect
4. #21460839C2semidirect
5. #21460830C2semidirect
6. #21460830C2semidirect
166. C61#11991semidirect

Maximal subgroups

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

subgroupindex
#214621952
#214621612
#214608402
#214608392
#214608302
#214564502
#1199161