Finite Group Databasebeta

← #30605358

Subgroups — #30605358

Order 15616.

306 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 72 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#21462182C211yesmaximal, characteristic, complemented
2#21461743C211yesmaximal, characteristic, complemented
3#21460811C212yesmaximal, complemented
4#21460809C212yesmaximal
5#21456386C211yesmaximal, characteristic
6#16840766—21no—
7#16840683—21no—
8#16840657C2212yes—
9#16840650—21no—
10#16840638—21no—
11#16840638C2212yes—
12#16840291—21no—
13#16840164C411yescharacteristic
14#16840116—21no—
15#16840000C2211yescharacteristic
16#16839995C2211yescharacteristic
17#16839988—21no—
18Q16×Dic61C411yescharacteristic
19SD16×Dic61—21no—
20D8×Dic61C411yescharacteristic
21C4×C8×D61C2211yescharacteristic
22C61×#495C411yescharacteristic
23C2×#11758213—22no—
24C2×#11758187—22no—
25C4⋊#92420—41no—
26C4⋊#92420—41no—
27C2×C8×D61D411yescharacteristic
28C2×C8×D61C2311yescharacteristic
29#14519770—41no—
30#14519769—21no—
31#14519759—41no—
32#14519753—21no—
33#14519748—21no—
34Q8×Dic61—21no—
35D4×Dic61—21no—
36#14519737—41no—
37#14519733—41no—
38C42×D61D411yescharacteristic
39#14519711C2×C411yescharacteristic
40#14519711C2×C411yescharacteristic
41#14519709—21no—
42#14519701—21no—
43#14519701—21no—
44#14519698—21no—
45#14519698—21no—
46C4×#92418D411yescharacteristic
47C8×Dic61C2×C411yescharacteristic
48C8×Dic61D411yescharacteristic
49C2×Q16×C61C2×C411yescharacteristic
50C2×SD16×C61—21no—
51C2×D8×C61C2×C411yescharacteristic
52#124×C61—21no—
53C4×C8×C61C2×C411yescharacteristic
54C2×Q8×C61—21no—
55C2×D4×C61—21no—
56C2×C22⋊D61—41no—
57C22×Dic61—41no—
58C2×C4×D61SD1611yescharacteristic
59C2×C4×D61SD1611yescharacteristic
60C2×C4×D61C2×D411yescharacteristic
61C2×#92420—42no—
62#11758213—42no—
63#11758213—42no—
64Q16×C61—41no—
65SD16×C61—42no—
66D8×C61—41no—
67C2×C8×C61C22⋊C411yescharacteristic
68C2×C8×C61C22×C411yescharacteristic
69C22⋊C4×C61—41no—
70C22⋊C4×C61—41no—
71C42×C61C22⋊C411yescharacteristic
72C22⋊Dic61—41no—
73C22⋊Dic61—41no—
74#11758198—41no—
75C4⋊Dic61—21no—
76C4⋊Dic61—21no—
77C4⋊Dic61—41no—
78#11758196—41no—
79#11758196—41no—
80#11758196—41no—
81C4×Dic61—41no—
82C4×Dic61C22⋊C411yescharacteristic
83C4×Dic61D811yescharacteristic
84C4×Dic61D811yescharacteristic
85C2×#92418C22⋊C411yescharacteristic
86C2×#92418C2×D411yescharacteristic
87C8×D61—41no—
88C8×D61—41no—
89#11758187—42no—
90C23×C61—41no—
91C22×D61C2×SD1611yescharacteristic
92Q8×C61—41no—
93Q8×C61—41no—
94D4×C61—41no—
95D4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61#10211yescharacteristic
98C2×C4×C61#10211yescharacteristic
99C2×C4×C61C2×C22⋊C411yescharacteristic
100C22⋊D61—82no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61—82no—
104C2×Dic61#10211yescharacteristic
105C2×Dic61#10211yescharacteristic
106C2×Dic61C2×D811yescharacteristic
107C4×D61—21no—
108C4×D61—21no—
109C4×D61—41no—
110C4×D61—41no—
111#92420—82no—
112C8×C61—21no—
113C8×C61—21no—
114#92418—21no—
115#92418—21no—
116#11866—611nomaximal, Sylow
117C22×C61—81no—
118C22×C61—81no—
119C22×C61—81no—
120C22×C61C2×#10211yescharacteristic
121C2×D61—21no—
122C2×D61—21no—
123C2×D61—21no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—81no—
127C4×C61#41011yescharacteristic
128C4×C61#42111yescharacteristic
129Dic61—21no—
130Dic61—21no—
131Dic61—21no—
132Dic61—81no—
133Dic61—81no—
134#3168—611no—
135#2163—611no—
136#1837—611no—
137#1350—612no—
138#1349—612no—
139C2×C61—161no—
140C2×C61#151711yescharacteristic
141C2×C61#214311yescharacteristic
142C2×C61#214811yescharacteristic
143D61—41no—
144#529—1221no—
145#499—611no—
146#495#692311yescharacteristic
147#488—1221no—
148#467—611no—
149#466—611no—
150#465—1221no—
151C4×Q16—611no—
152C4×SD16—1221no—
153C4×D8—611no—
154#423—1221no—
155C2×C4×C8—611no—
156C4⋊C16—1221no—
157C22⋊C16—612no—
158#346—1221no—
159#341—612no—
160#341—1221no—
161C61#1186611yescharacteristic, complemented, Sylow
162C2×Q16C2×#692311yescharacteristic
163C2×SD16—21no—
164C2×D8C2×#692311yescharacteristic
165C2×M16—1222no—
166C22×C8—611no—
167C22×C8—611no—
168#126—2441no—
169#125—1221no—
170#124—21no—
171#123—2441no—
172C22⋊Q8—1221no—
173#121—1221no—
174C4×Q8—1221no—
175C4×D4—1221no—
176C4×D4—2441no—
177#117—2441no—
178C2×C42—611no—
179C2×C16—1222no—
180#107—611no—
181#107—611no—
182#106—1221no—
183C4⋊C8—2441no—
184C4⋊C8—2441no—
185#103—1221no—
186#103—1221no—
187#102—1221no—
188#102—1221no—
189C4×C8—611no—
190C4×C8—611no—
191C4×C8—611no—
192C4×C8C2×#692311yescharacteristic
193C2×Q8—21no—
194C2×D4—21no—
195C2×D4—2441no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—2441no—
200Q16—41no—
201SD16—42no—
202D8—41no—
203M16—2442no—
204M16—2442no—
205C2×C8—611no—
206C2×C8—611no—
207C2×C8—2441no—
208C2×C8—2441no—
209C2×C8—2442no—
210C2×C8C22⋊#692311yescharacteristic
211C2×C8C22×#692311yescharacteristic
212C4⋊C4—1221no—
213C4⋊C4—1221no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C22⋊C4—41no—
219C22⋊C4—41no—
220C22⋊C4—2441no—
221C22⋊C4—2441no—
222C22⋊C4—2441no—
223C42—611no—
224C42—611no—
225C42—611no—
226C42—2441no—
227C42C22⋊#692311yescharacteristic
228C16—2442no—
229C23—41no—
230C23—611no—
231Q8—41no—
232Q8—41no—
233D4—41no—
234D4—41no—
235D4—4882no—
236C2×C4—41no—
237C2×C4—611no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—4882no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4#1451983911yescharacteristic
248C2×C4#1451983911yescharacteristic
249C2×C4C2×C22⋊#692311yescharacteristic
250C8—21no—
251C8—21no—
252C8—1221no—
253C8—1221no—
254C8—4882no—
255C22—81no—
256C22—81no—
257C22—81no—
258C22—1221no—
259C22—1221no—
260C22—1221no—
261C22C2×#1451983911yescharacteristic
262C4—21no—
263C4—21no—
264C4—81no—
265C4—1221no—
266C4—1221no—
267C4—1221no—
268C4—4881no—
269C4—4881no—
270C4#1684074211yescharacteristic
271C4#1684076011yescharacteristic
272C2—161no—
273C2—2441no—
274C2#2146124811yescharacteristic
275C2#2146213311yescharacteristic
276C2#2146214711yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#495C4
socleC22×C61C2×#102
prime radical#16839995C22
cosocleC2×C8×D61C23
hypercenter#495#6923
hypocenterC61#11866
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #21462182C2semidirect
2. #21461743C2semidirect
3. #21460811C2semidirect
161. C61#11866semidirect

Maximal subgroups

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

subgroupindex
#214621822
#214617432
#214608112
#214608092
#214563862
#1186661