Finite Group Databasebeta

← #30595209

Subgroups — #30595209

Order 15616.

270 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 42 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#21462111C211yesmaximal, characteristic
2#21461957C211yesmaximal, characteristic
3#21447481C211yesmaximal, characteristic
4#16840767C411yescharacteristic, complemented
5C2×#14519841—21no—
6C2×#14519841—21no—
7#16840749—21no—
8#16840698C411yescharacteristic, complemented
9#16840673C412yescomplemented
10#16840670—21no—
11#16840310C2211yescharacteristic
12#16839734—21no—
13#16839556—21no—
14#16839555C411yescharacteristic, complemented
15C61×#353C411yescharacteristic, complemented
16C2×#11758213—21no—
17C2×#11758217—41no—
18C2×C4×#6923—21no—
19#14519844—41no—
20#14519841—42no—
21#14519841—42no—
22#14519838—22no—
23#14519837—41no—
24(C2×#6923)⋊C4—41no—
25C2×#11758224D411yescharacteristic
26C2×#11758224D411yescharacteristic
27#14519777C2×C411yescharacteristic
28#14519764D411yescharacteristic
29#14519764Q811yescharacteristic
30#14519748—41no—
31D4×Dic61—41no—
32#14519733—41no—
33C42×D61C2×C411yescharacteristic
34#14519692—21no—
35#14519691—41no—
36#127×C61C2×C411yescharacteristic
37#99×C61—21no—
38C22×#6923—41no—
39C2×D4×C61—41no—
40C2×D4×C61C22⋊C411yescharacteristic
41C2×D4×C61C4⋊C411yescharacteristic
42C2×C22⋊D61—21no—
43C2×C22⋊D61—21no—
44C22×Dic61—21no—
45C22×Dic61—21no—
46#11758224—41no—
47#11758224—41no—
48#11758224—41no—
49#11758224—41no—
50C2×C4×D61—21no—
51C2×C4×D61C22⋊C411yescharacteristic
52C2×Dic122C22⋊C411yescharacteristic
53C2×Dic122C4⋊C411yescharacteristic
54#11758217—42no—
55#11758217—81no—
56C2×#92420—41no—
57C2×#92420—81no—
58C4×#6923—22no—
59C4×#6923—41no—
60#11758213—41no—
61#11758213—41no—
62C22⋊C4×C61—41no—
63C42×C61C4211yescharacteristic
64C22⋊Dic61—41no—
65C22⋊Dic61—41no—
66C22⋊Dic61—41no—
67C4⋊Dic61—41no—
68#11758196—81no—
69C4×Dic61—21no—
70C4×Dic61—81no—
71C4×Dic61C4⋊C411yescharacteristic
72C23×C61—21no—
73C23×C61—21no—
74C22×D61#9911yescharacteristic
75C2×#6923—42no—
76C2×#6923—82no—
77D4×C61—41no—
78D4×C61—41no—
79D4×C61—82no—
80C2×C4×C61—21no—
81C2×C4×C61—81no—
82C2×C4×C61#9511yescharacteristic
83C22⋊D61—81no—
84C22⋊D61—81no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—41no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61—41no—
92C2×Dic61—81no—
93C2×Dic61#9911yescharacteristic
94C4×D61—21no—
95C4×D61—21no—
96C4×D61—81no—
97Dic122—41no—
98Dic122—41no—
99#92420—82no—
100#92420—81no—
101#7503—611nomaximal, Sylow
102C22×C61—41no—
103C22×C61—41no—
104C22×C61—81no—
105C22×C61—81no—
106C22×C61#34211yescharacteristic
107C2×D61—21no—
108C2×D61—41no—
109#6923—82no—
110C4×C61—21no—
111C4×C61—41no—
112C4×C61—161no—
113Dic61—41no—
114Dic61—41no—
115Dic61—41no—
116Dic61—161no—
117Dic61#35311yescharacteristic
118Dic61#35411yescharacteristic
119#2132—611no—
120#2126—611no—
121#1963—611no—
122C2×C61—21no—
123C2×C61—81no—
124C2×C61—81no—
125C2×C61#139311yescharacteristic
126D61—41no—
127#532—611no—
128#423—611no—
129C2×#104—1221no—
130C2×#104—1221no—
131#413—1221no—
132#410—1221no—
133#376—611no—
134#356—612no—
135#355—1221no—
136#354—1221no—
137#353—611no—
138#353#692311yescharacteristic, complemented
139C61#750311yescharacteristic, complemented, Sylow
140C2×#41—611no—
141C2×#41—611no—
142C2×M16—1221no—
143C2×M16—2441no—
144C4⋊Q8—611no—
145#127C2×#692311yescharacteristic
146#124—611no—
147#124—611no—
148#121—2441no—
149C4×D4—2441no—
150#117—2441no—
151C2×C42—611no—
152C2×C42—1221no—
153C4⋊C8—2441no—
154#104—2442no—
155#104—2442no—
156#101—1222no—
157#100—2441no—
158#99—21no—
159#99—1221no—
160#99—2441no—
161#95—2441no—
162#41—2441no—
163#41—2441no—
164#41—2441no—
165#41—2441no—
166C2×Q8—611no—
167C2×Q8—611no—
168C2×D4—41no—
169C2×D4—1221no—
170C2×D4—1221no—
171C2×D4C4⋊#692311yescharacteristic
172C2×D4C22⋊#692311yescharacteristic
173C22×C4—611no—
174C22×C4—1221no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4—2441no—
178M16—4881no—
179M16—2442no—
180M16—2441no—
181M16—2441no—
182C2×C8—4881no—
183C2×C8—2441no—
184C4⋊C4—4881no—
185C4⋊C4—2441no—
186C22⋊C4—41no—
187C22⋊C4—2441no—
188C22⋊C4—2441no—
189C22⋊C4—2441no—
190C42—611no—
191C42—1221no—
192C42—1222no—
193C42—4881no—
194C42—2441no—
195C42C4×#692311yescharacteristic
196C23—21no—
197C23—21no—
198C23—611no—
199Q8—2441no—
200Q8—2441no—
201D4—41no—
202D4—41no—
203D4—82no—
204D4—4881no—
205D4—4881no—
206C2×C4—21no—
207C2×C4—81no—
208C2×C4—611no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—4881no—
215C2×C4—4881no—
216C2×C4—4882no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4—2441no—
220C2×C4—2441no—
221C2×C4—2442no—
222C2×C4(C2×#6923)⋊C411yescharacteristic
223C8—4881no—
224C8—4882no—
225C22—41no—
226C22—41no—
227C22—81no—
228C22—81no—
229C22—1221no—
230C22—2441no—
231C22#1684063911yescharacteristic
232C4—21no—
233C4—41no—
234C4—161no—
235C4—611no—
236C4—611no—
237C4—9761no—
238C4—4882no—
239C4—2441no—
240C4—2441no—
241C4—2441no—
242C2—21no—
243C2—81no—
244C2—81no—
245C2—2441no—
246C2#2146091211yescharacteristic
subgroupG/H
centerC2#21460912
commutatorC42×C61C42
Frattini#127C2×#6923
FittingC61×#353C4
socleC2×C61#1393
prime radical, cosocle#16840310C22
hypercenter#353#6923
hypocenterC61#7503
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #353

Complements

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

NH ≅ G/Ntype
4. #16840767C4semidirect
8. #16840698C4semidirect
9. #16840673C4semidirect
14. #16839555C4semidirect
15. C61×#353C4semidirect
138. #353#6923semidirect
139. C61#7503semidirect

Maximal subgroups

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

subgroupindex
#214621112
#214619572
#214474812
#750361