Finite Group Databasebeta

← #30605249

Subgroups — #30605249

Order 15616.

286 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 58 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#21462191C211yesmaximal, characteristic, complemented
2#21461749C211yesmaximal, characteristic, complemented
3#21460795C211yesmaximal, characteristic, complemented
4#21460793C211yesmaximal, characteristic
5#21460791C211yesmaximal, characteristic, complemented
6#21460789C211yesmaximal, characteristic
7#21456545C211yesmaximal, characteristic
8#16840685—21no—
9#16840659C2211yescharacteristic
10#16840659C2211yescharacteristic
11#16840655—21no—
12#16840644—21no—
13#16840633—21no—
14#16840631C2211yescharacteristic
15#16840630C2211yescharacteristic
16#16840291—21no—
17#16840164C411yescharacteristic, complemented
18#16840116—21no—
19#16840017C2211yescharacteristic
20#16840012C2211yescharacteristic
21#16840005—21no—
22#16839874C411yescharacteristic, complemented
23#16839869C411yescharacteristic, complemented
24#16839863—21no—
25C4×#11758189C2211yescharacteristic
26C61×#495C411yescharacteristic, complemented
27D61⋊M16—21no—
28#14519856—21no—
29#14519851—21no—
30#14519851—21no—
31C2×#11758189D411yescharacteristic
32C2×#11758189C2311yescharacteristic
33#14519770—41no—
34#14519769—21no—
35#14519759—41no—
36#14519753—21no—
37#14519748—21no—
38Q8×Dic61—21no—
39D4×Dic61—21no—
40#14519737—41no—
41#14519733—41no—
42C42×D61D411yescharacteristic
43#14519711—21no—
44#14519709C2×C411yescharacteristic
45#14519709C2×C411yescharacteristic
46#14519701—21no—
47#14519701—21no—
48#14519698—21no—
49#14519698—21no—
50#14519687C2×C411yescharacteristic
51#14519687D411yescharacteristic
52C4×#92418D411yescharacteristic
53C2×Q16×C61C2×C411yescharacteristic
54C2×SD16×C61—21no—
55C2×D8×C61C2×C411yescharacteristic
56#124×C61—21no—
57C4×C8×C61C2×C411yescharacteristic
58C2×Q8×C61—21no—
59C2×D4×C61—21no—
60C2×C22⋊D61—41no—
61C22×Dic61—41no—
62C2×C4×D61—21no—
63C2×C4×D61C2×D411yescharacteristic
64C22⋊#6923—41no—
65#11758217—41no—
66C4⋊#6923—41no—
67C4×#6923—41no—
68#11758213—41no—
69D61⋊C8—41no—
70Q16×C61—41no—
71SD16×C61—42no—
72D8×C61—41no—
73C2×C8×C61C22⋊C411yescharacteristic
74C2×C8×C61C22×C411yescharacteristic
75C22⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C42×C61C22⋊C411yescharacteristic
78C22⋊Dic61—41no—
79C22⋊Dic61—41no—
80#11758198—41no—
81C4⋊Dic61—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61—41no—
84#11758196—41no—
85#11758196—41no—
86#11758196—41no—
87C4×Dic61—21no—
88C4×Dic61—41no—
89C4×Dic61C22⋊C411yescharacteristic
90C2×#92418C22⋊C411yescharacteristic
91C2×#92418C2×D411yescharacteristic
92#11758189—41no—
93#11758189—41no—
94#11758187—41no—
95#11758187—41no—
96C23×C61—41no—
97C22×D61AGL(1,ℤ/8)11yescharacteristic
98C2×#6923—81no—
99Q8×C61—41no—
100Q8×C61—41no—
101D4×C61—41no—
102D4×C61—41no—
103C2×C4×C61—21no—
104C2×C4×C61—41no—
105C2×C4×C61C2×C22⋊C411yescharacteristic
106C22⋊D61—82no—
107C2×Dic61—21no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—82no—
111C2×Dic61AGL(1,ℤ/8)11yescharacteristic
112C4×D61—21no—
113C4×D61—21no—
114C4×D61—81no—
115#92420—81no—
116C8×C61—21no—
117C8×C61—21no—
118#92418—21no—
119#92418—21no—
120#11836—611nomaximal, Sylow
121C22×C61—81no—
122C22×C61—81no—
123C22×C61—81no—
124C22×C61#41811yescharacteristic
125C2×D61—21no—
126C2×D61—41no—
127#6923—161no—
128C4×C61—41no—
129C4×C61—81no—
130C4×C61#41011yescharacteristic
131C4×C61#42111yescharacteristic
132Dic61—21no—
133Dic61—41no—
134Dic61—81no—
135Dic61—81no—
136#3183—611no—
137#2165—611no—
138#1841—611no—
139#1342—611no—
140#1341—611no—
141#1340—611no—
142#1339—611no—
143C2×C61—21no—
144C2×C61—161no—
145C2×C61#151411yescharacteristic
146D61—41no—
147#529—1221no—
148#499—611no—
149#495#692311yescharacteristic, complemented
150#488—1221no—
151#470—611no—
152#469—611no—
153#468—1221no—
154#442—611no—
155#441—611no—
156#440—1221no—
157C4×M16—611no—
158#364—1221no—
159#349—611no—
160#349—611no—
161#347—1221no—
162#344—1221no—
163#339—1221no—
164#338—611no—
165H(3,ℤ/4)—611no—
166C61#1183611yescharacteristic, complemented, Sylow
167C2×Q16C2×#692311yescharacteristic
168C2×SD16—21no—
169C2×D8C2×#692311yescharacteristic
170C2×M16—611no—
171C2×M16—611no—
172C2×M16—1221no—
173#126—2441no—
174#125—1221no—
175#124—21no—
176#123—2441no—
177C22⋊Q8—1221no—
178#121—1221no—
179C4×Q8—1221no—
180C4×D4—1221no—
181C4×D4—2441no—
182#117—1221no—
183#117—2441no—
184C2×C42—611no—
185M32—1221no—
186M32—1221no—
187#107—1221no—
188#106—611no—
189#106—611no—
190#103—1221no—
191#103—1221no—
192#102—1221no—
193#102—1221no—
194#97—611no—
195#97—611no—
196C4×C8—611no—
197C4×C8C2×#692311yescharacteristic
198C2×Q8—21no—
199C2×D4—21no—
200C2×D4—2441no—
201C22×C4—611no—
202C22×C4—1221no—
203C22×C4—2441no—
204Q16—41no—
205SD16—42no—
206D8—41no—
207M16—2441no—
208M16—2441no—
209M16—2441no—
210M16—2441no—
211C2×C8—611no—
212C2×C8—611no—
213C2×C8—2441no—
214C2×C8C22⋊#692311yescharacteristic
215C2×C8C22×#692311yescharacteristic
216C4⋊C4—1221no—
217C4⋊C4—1221no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C22⋊C4—2441no—
226C22⋊C4—2441no—
227C22⋊C4—2441no—
228C22⋊C4—2441no—
229C42—611no—
230C42—1221no—
231C42—2441no—
232C42—2441no—
233C42C22⋊#692311yescharacteristic
234C16—2441no—
235C16—2441no—
236C23—41no—
237C23—611no—
238Q8—41no—
239Q8—41no—
240D4—41no—
241D4—41no—
242D4—4882no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—611no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—4881no—
250C2×C4—4881no—
251C2×C4—4882no—
252C2×C4—2441no—
253C2×C4—2441no—
254C2×C4C2×C22⋊#692311yescharacteristic
255C8—21no—
256C8—21no—
257C8—1221no—
258C8—1221no—
259C8—4881no—
260C22—81no—
261C22—81no—
262C22—81no—
263C22—1221no—
264C22—2441no—
265C22#1684075411yescharacteristic
266C4—41no—
267C4—81no—
268C4—1221no—
269C4—9761no—
270C4—4881no—
271C4—4881no—
272C4—2441no—
273C4#1684074211yescharacteristic
274C4#1684076011yescharacteristic
275C2—21no—
276C2—161no—
277C2—2441no—
278C2#2146123911yescharacteristic
subgroupG/H
centerC2#21461239
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#495C4
socleC2×C61#1514
prime radical#16840012C22
cosocleC2×#11758189C23
hypercenter#495#6923
hypocenterC61#11836
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #21462191C2semidirect
2. #21461749C2semidirect
3. #21460795C2semidirect
5. #21460791C2semidirect
17. #16840164C4semidirect
22. #16839874C4semidirect
23. #16839869C4semidirect
26. C61×#495C4semidirect
149. #495#6923semidirect
166. C61#11836semidirect

Maximal subgroups

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

subgroupindex
#214621912
#214617492
#214607952
#214607932
#214607912
#214607892
#214565452
#1183661