Finite Group Databasebeta

← #30595188

Subgroups — #30595188

Order 15616.

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

normal subgroups only

This group has 274 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#21461822C211yesmaximal, characteristic
3#21444551C211yesmaximal, characteristic
4#16840840C411yescharacteristic
5#16840760—21no—
6#16840749—21no—
7#16840742C411yescharacteristic
8#16840673—21no—
9#16840670C412yescomplemented
10#16840633—21no—
11#16840310C2211yescharacteristic
12#16839784—21no—
13#16839510—21no—
14#16839506C411yescharacteristic, complemented
15C61×#331C411yescharacteristic, complemented
16#14519864—42no—
17D61⋊M16—21no—
18C2×#11758217—41no—
19C2×#11758217—41no—
20#14519856—21no—
21#14519841—42no—
22#14519838—22no—
23#14519837—41no—
24#14519835—41no—
25C2×#11758224C2×C411yescharacteristic
26C2×#11758224D411yescharacteristic
27C2×#11758189—41no—
28#14519777D411yescharacteristic
29#14519764C2×C411yescharacteristic
30#14519764Q811yescharacteristic
31#14519748—41no—
32D4×Dic61—41no—
33C42×D61D411yescharacteristic
34C4⋊#92418—21no—
35#14519706—41no—
36#127×C61C2×C411yescharacteristic
37C4⋊C8×C61—21no—
38C2×D4×C61—41no—
39C2×D4×C61C4211yescharacteristic
40C2×D4×C61C4⋊C411yescharacteristic
41C2×C22⋊D61—21no—
42C2×C22⋊D61—21no—
43C22×Dic61—21no—
44C22×Dic61—21no—
45#11758224—41no—
46#11758224—41no—
47#11758224—41no—
48#11758224—41no—
49C2×C4×D61—21no—
50C2×C4×D61C22⋊C411yescharacteristic
51C2×Dic122C22⋊C411yescharacteristic
52C2×Dic122C4⋊C411yescharacteristic
53C22⋊#6923—41no—
54#11758217—41no—
55#11758217—42no—
56#11758217—42no—
57#11758217—81no—
58C2×#92420—42no—
59C2×#92420—81no—
60C4⋊#6923—41no—
61C4×#6923—41no—
62#11758213—22no—
63D61⋊C8—41no—
64C2×C8×C61—41no—
65C42×C61C22⋊C411yescharacteristic
66C22⋊Dic61—41no—
67C22⋊Dic61—41no—
68C4⋊Dic61—41no—
69C4×Dic61—21no—
70C4×Dic61C4⋊C411yescharacteristic
71C2×#92418—41no—
72#11758189—82no—
73C23×C61—21no—
74C23×C61—21no—
75C22×D61#9911yescharacteristic
76C2×#6923—81no—
77D4×C61—41no—
78D4×C61—41no—
79D4×C61—81no—
80D4×C61—81no—
81C2×C4×C61—21no—
82C2×C4×C61#9511yescharacteristic
83C22⋊D61—42no—
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#9911yescharacteristic
93C4×D61—21no—
94C4×D61—21no—
95C4×D61—41no—
96C4×D61—41no—
97Dic122—41no—
98Dic122—41no—
99#92420—42no—
100#92420—82no—
101C8×C61—81no—
102#92418—81no—
103#7496—611nomaximal, Sylow
104C22×C61—41no—
105C22×C61—41no—
106C22×C61—81no—
107C22×C61—81no—
108C22×C61#34211yescharacteristic
109C2×D61—21no—
110C2×D61—41no—
111#6923—161no—
112C4×C61—21no—
113C4×C61—21no—
114C4×C61—21no—
115Dic61—41no—
116Dic61—41no—
117Dic61—41no—
118Dic61AΣL(1,𝔽16)11yescharacteristic
119Dic61#35211yescharacteristic
120#2132—611no—
121#1884—611no—
122#1560—611no—
123C2×C61—21no—
124C2×C61—81no—
125C2×C61—81no—
126C2×C61#139011yescharacteristic
127D61—41no—
128#568—611no—
129#532—611no—
130#423—1221no—
131#421—1221no—
132#413—1221no—
133#410—611no—
134#356—1221no—
135#355—612no—
136#339—1221no—
137#333—1221no—
138#331—611no—
139#331#692311yescharacteristic, complemented
140C61#749611yescharacteristic, complemented, Sylow
141C2×#41—611no—
142C2×#41—611no—
143#131—2442no—
144C2×M16—1221no—
145C2×M16—2441no—
146C2×M16—2441no—
147C2×M16—2441no—
148C4⋊Q8—611no—
149#127C2×#692311yescharacteristic
150#124—611no—
151#124—611no—
152#121—2441no—
153C4×D4—2441no—
154#117—1221no—
155C2×C42—611no—
156C4⋊C8—21no—
157C4⋊C8—1221no—
158C4⋊C8—2441no—
159#104—2442no—
160#101—1222no—
161#100—2441no—
162#99—2441no—
163#41—2441no—
164#41—2441no—
165#41—2441no—
166#41—2441no—
167C2×Q8—611no—
168C2×Q8—611no—
169C2×D4—41no—
170C2×D4—1221no—
171C2×D4—1221no—
172C2×D4C4×#692311yescharacteristic
173C2×D4C4⋊#692311yescharacteristic
174C22×C4—611no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4—1221no—
178M16—1222no—
179M16—4882no—
180M16—4881no—
181M16—2442no—
182M16—2441no—
183M16—2442no—
184C2×C8—41no—
185C2×C8—4881no—
186C2×C8—2441no—
187C2×C8—2441no—
188C2×C8—2442no—
189C4⋊C4—2441no—
190C4⋊C4—2441no—
191C22⋊C4—2441no—
192C22⋊C4—2441no—
193C22⋊C4—2441no—
194C42—611no—
195C42—1221no—
196C42—2441no—
197C42C22⋊#692311yescharacteristic
198C23—21no—
199C23—21no—
200C23—611no—
201Q8—2441no—
202Q8—2441no—
203D4—41no—
204D4—41no—
205D4—81no—
206D4—81no—
207D4—4881no—
208D4—2442no—
209C2×C4—21no—
210C2×C4—611no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—4881no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4—2441no—
220C2×C4—2441no—
221C2×C4—2441no—
222C2×C4—2441no—
223C2×C4(C2×#6923)⋊C411yescharacteristic
224C8—81no—
225C8—4881no—
226C8—4882no—
227C8—2442no—
228C22—41no—
229C22—41no—
230C22—81no—
231C22—81no—
232C22—1221no—
233C22—2441no—
234C22#1684063911yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—611no—
239C4—611no—
240C4—9761no—
241C4—2441no—
242C4—2441no—
243C4—2441no—
244C2—21no—
245C2—81no—
246C2—81no—
247C2—2441no—
248C2#2146090511yescharacteristic
subgroupG/H
centerC2#21460905
commutatorC2×D4×C61C42
Frattini#127C2×#6923
FittingC61×#331C4
socleC2×C61#1390
prime radical, cosocle#16840310C22
hypercenter#331#6923
hypocenterC61#7496
LCSG ▷ C2×D4×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #331

Complements

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

NH ≅ G/Ntype
9. #16840670C4semidirect
14. #16839506C4semidirect
15. C61×#331C4semidirect
139. #331#6923semidirect
140. C61#7496semidirect

Maximal subgroups

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

subgroupindex
#214621112
#214618222
#214445512
#749661