Finite Group Databasebeta

← #30605604

Subgroups — #30605604

Order 15616.

316 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 80 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#21462178C211yesmaximal, characteristic, complemented
2D61⋊#334C211yesmaximal, characteristic, complemented
3#21460836C212yesmaximal, complemented
4#21460831C212yesmaximal, complemented
5#21456387C211yesmaximal, characteristic
6D61⋊(C4⋊C8)—21no—
7#16840683C2212yes—
8#16840657—21no—
9C4×#11758187—21no—
10#16840624C2212yes—
11#16840623—21no—
12#16840294—21no—
13#16840163C2211yescharacteristic
14#16840145C2211yescharacteristic
15#16840115—21no—
16#16840004C411yescharacteristic
17#16839995C411yescharacteristic
18#16839990—21no—
19C4×Dic244C411yescharacteristic
20C4×#11758200—21no—
21C4×C8×D61C2211yescharacteristic
22C4×D8×C61C411yescharacteristic
23C2×D61⋊C8—41no—
24C2×#11758187—22no—
25#14519844—41no—
26C4⋊#92420—22no—
27C2×Dic244C2×C411yescharacteristic
28C2×#11758200—21no—
29C2×C8×D61C2×C411yescharacteristic
30C2×C8×D61D411yescharacteristic
31#14519770—41no—
32#14519768—21no—
33#14519764—21no—
34#14519759—41no—
35#14519757—21no—
36#14519748—21no—
37C4×Dic122—21no—
38C4×C22⋊D61—41no—
39#14519736—41no—
40C42×D61D411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519708—21no—
43#14519702—21no—
44#14519700—21no—
45#14519698—21no—
46C4×#92418D411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61C2311yescharacteristic
49C2×D8×C61C2×C411yescharacteristic
50C4×D4×C61—21no—
51#107×C61C2×C411yescharacteristic
52#102×C61—21no—
53C4×C8×C61C2×C411yescharacteristic
54C2×D4×C61—21no—
55C22×C4×C61—41no—
56C2×C22⋊D61—41no—
57C2×C4×D61C22⋊C411yescharacteristic
58C2×C4×D61D811yescharacteristic
59C2×C4×D61SD1611yescharacteristic
60C2×Dic122—21no—
61C2×#92420—42no—
62D61⋊C8—82no—
63D8×C61—41no—
64C2×C8×C61C22⋊C411yescharacteristic
65C2×C8×C61C22×C411yescharacteristic
66C4⋊C4×C61—21no—
67C22⋊C4×C61—41no—
68C42×C61C22⋊C411yescharacteristic
69C22⋊Dic61—41no—
70C22⋊Dic61—41no—
71C22⋊Dic61—41no—
72#11758200—42no—
73#11758198—41no—
74C4⋊Dic61—21no—
75C4⋊Dic61—41no—
76C4⋊Dic61—41no—
77#11758196—41no—
78#11758196—41no—
79C4×Dic61—41no—
80C4×Dic61D811yescharacteristic
81C4×Dic61SD1611yescharacteristic
82C4×Dic61C2×D411yescharacteristic
83C2×#92418C22⋊C411yescharacteristic
84C2×#92418C2×D411yescharacteristic
85Dic244—41no—
86C8×D61—22no—
87C8×D61—41no—
88#11758187—42no—
89C23×C61—41no—
90C22×D61#10211yescharacteristic
91D4×C61—41no—
92D4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—82no—
95C2×C4×C61#10211yescharacteristic
96C2×C4×C61#10211yescharacteristic
97C2×C4×C61C2×C22⋊C411yescharacteristic
98C22⋊D61—82no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101C2×Dic61#10211yescharacteristic
102C2×Dic61C2×D811yescharacteristic
103C2×Dic61C2×SD1611yescharacteristic
104C4×D61—22no—
105C4×D61—22no—
106C4×D61—21no—
107C4×D61—21no—
108Dic122—41no—
109Dic122—41no—
110#92420—82no—
111C8×C61—21no—
112C8×C61—21no—
113#92418—21no—
114#92418#13512yes—
115#11944—611nomaximal, Sylow
116C22×C61—81no—
117C22×C61—81no—
118C22×C61—81no—
119C22×C61C2×#10211yescharacteristic
120C2×D61—21no—
121C2×D61—21no—
122C2×D61#35912yes—
123C4×C61—21no—
124C4×C61—81no—
125C4×C61#36012yes—
126C4×C61#41311yescharacteristic
127C4×C61#41611yescharacteristic
128Dic61—21no—
129Dic61—21no—
130Dic61—21no—
131Dic61—81no—
132Dic61—81no—
133#3168—611no—
134#2162—611no—
135C2×#334—611no—
136#1363—612no—
137#1360—612no—
138C2×C61—161no—
139C2×C61#154011yescharacteristic
140C2×C61C2×#35911yescharacteristic
141C2×C61C2×#36011yescharacteristic
142D61—22no—
143#529—1221no—
144#499—611no—
145#495—611no—
146#488—1221no—
147#467—611no—
148#466—611no—
149#465—1221no—
150C4×Q16—611no—
151C4×SD16—1221no—
152C4×D8#692311yescharacteristic
153C2×C4⋊C8—1221no—
154C2×C4×C8—611no—
155C4⋊C16—612no—
156C22⋊C16—1221no—
157C4×C16—1221no—
158#334—612no—
159#334—1221no—
160C61#1194411yescharacteristic, complemented, Sylow
161C2×Q16—611no—
162C2×SD16—1221no—
163C2×D8C2×#692311yescharacteristic
164C22×C8—611no—
165C22×C8—611no—
166C22×C8—2441no—
167#126—2441no—
168#125—1221no—
169#124—1221no—
170#123—2441no—
171C22⋊Q8—1221no—
172#121—1221no—
173C4×Q8—1221no—
174C4×D4—21no—
175C4×D4—2441no—
176#117—2441no—
177C2×C42—611no—
178C2×C16—1222no—
179#107—611no—
180#107C2×#692311yescharacteristic
181#106—1221no—
182C4⋊C8—1222no—
183C4⋊C8—2441no—
184#103—1221no—
185#103—1221no—
186#102—21no—
187#102—1221no—
188C4×C8—611no—
189C4×C8—611no—
190C4×C8—611no—
191C4×C8C2×#692311yescharacteristic
192C2×Q8—1221no—
193C2×D4—21no—
194C2×D4—2441no—
195C22×C4—41no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—611no—
199Q16—2441no—
200SD16—2442no—
201D8—41no—
202C2×C8—611no—
203C2×C8—611no—
204C2×C8—1222no—
205C2×C8—4882no—
206C2×C8—2441no—
207C2×C8—2442no—
208C2×C8C22⋊#692311yescharacteristic
209C2×C8C22×#692311yescharacteristic
210C4⋊C4—21no—
211C4⋊C4—1221no—
212C4⋊C4—2441no—
213C4⋊C4—2441no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C22⋊C4—41no—
217C22⋊C4—2441no—
218C22⋊C4—2441no—
219C22⋊C4—2441no—
220C22⋊C4—2441no—
221C42—611no—
222C42—611no—
223C42—611no—
224C42—2441no—
225C42C22⋊#692311yescharacteristic
226C16—2442no—
227C23—41no—
228C23—611no—
229Q8—2441no—
230Q8—2441no—
231D4—41no—
232D4—41no—
233D4—4882no—
234C2×C4—41no—
235C2×C4—82no—
236C2×C4—611no—
237C2×C4—611no—
238C2×C4—611no—
239C2×C4—1222no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—1222no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4#1451983911yescharacteristic
246C2×C4#1451983911yescharacteristic
247C2×C4C2×C22⋊#692311yescharacteristic
248C8—21no—
249C8—21no—
250C8—612no—
251C8—1221no—
252C8—4882no—
253C22—81no—
254C22—81no—
255C22—81no—
256C22—612no—
257C22—1221no—
258C22—1221no—
259C22C2×#1451983911yescharacteristic
260C4—21no—
261C4—81no—
262C4—1221no—
263C4—1221no—
264C4—1221no—
265C4—4881no—
266C4—4881no—
267C4#1684067812yes—
268C4#1684074811yescharacteristic
269C4#1684075211yescharacteristic
270C2—161no—
271C2—1222no—
272C2#2146131611yescharacteristic
273C2D61⋊#35911yescharacteristic
274C2C2×#1684067811yescharacteristic
subgroupG/H
centerC2×C4#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC4×D8×C61C4
socleC22×C61C2×#102
prime radical#16839995C4
cosocleC8×Dic61C23
hypercenterC4×D8#6923
hypocenterC61#11944
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #21462178C2semidirect
2. D61⋊#334C2semidirect
3. #21460836C2semidirect
4. #21460831C2semidirect
160. C61#11944semidirect

Maximal subgroups

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

subgroupindex
#214621782
D61⋊#3342
#214608362
#214608312
#214563872
#1194461