Finite Group Databasebeta

← #30595153

Subgroups — #30595153

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#21461820C211yesmaximal, characteristic
2#21461323C211yesmaximal, characteristic
3#21447501C211yesmaximal, characteristic
4#16840840C411yescharacteristic
5#16840780—21no—
6#16840761—21no—
7#16840742C411yescharacteristic
8#16840633—21no—
9#16840622—21no—
10#16840620C412yescomplemented
11#16840311C2211yescharacteristic
12#16839745—21no—
13#16839560—21no—
14#16839559C411yescharacteristic, complemented
15C61×#355C411yescharacteristic, complemented
16#14519864—42no—
17D61⋊M16—21no—
18C2×#11758217—41no—
19#14519856—21no—
20#14519844—22no—
21#14519842—42no—
22#14519835—41no—
23#14519834—41no—
24C4×#92420—41no—
25C2×#11758226D411yescharacteristic
26C2×#11758224C2×C411yescharacteristic
27M16×D61—41no—
28#14519775D411yescharacteristic
29#14519773C2×C411yescharacteristic
30#14519765Q811yescharacteristic
31#14519750—41no—
32#14519737—41no—
33C42×D61D411yescharacteristic
34#14519696—21no—
35#14519693—41no—
36#124×C61C2×C411yescharacteristic
37#101×C61—21no—
38C2×Q8×C61C22⋊C411yescharacteristic
39C2×D4×C61C4211yescharacteristic
40C2×C22⋊D61—21no—
41C2×C22⋊D61—41no—
42C22×Dic61—21no—
43#11758226—41no—
44#11758226—41no—
45#11758224—41no—
46#11758224—41no—
47C2×D244—21no—
48C2×D244C4⋊C411yescharacteristic
49C2×C4×D61—21no—
50C2×C4×D61—21no—
51C2×C4×D61C22⋊C411yescharacteristic
52C2×Dic122C4⋊C411yescharacteristic
53C22⋊#6923—41no—
54#11758217—42no—
55#11758217—41no—
56C2×#92420—42no—
57C2×#92420—42no—
58C4⋊#6923—41no—
59C4×#6923—41no—
60#11758213—22no—
61D61⋊C8—41no—
62M16×C61—41no—
63C22⋊C4×C61—41no—
64C42×C61C4⋊C411yescharacteristic
65#11758198—41no—
66#11758196—41no—
67C4×Dic61—21no—
68C4×Dic61C22⋊C411yescharacteristic
69#11758194—41no—
70#11758189—81no—
71C8×D61—81no—
72C23×C61—21no—
73C22×D61—21no—
74C22×D61#9911yescharacteristic
75C2×#6923—81no—
76Q8×C61—41no—
77D4×C61—41no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61#9511yescharacteristic
81C22⋊D61—42no—
82C22⋊D61—82no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—41no—
86C2×Dic61—41no—
87C2×Dic61#9911yescharacteristic
88D244—41no—
89D244—81no—
90C4×D61—21no—
91C4×D61—21no—
92C4×D61—42no—
93C4×D61—41no—
94C4×D61—41no—
95Dic122—41no—
96#92420—42no—
97#92420—82no—
98C8×C61—81no—
99#92418—81no—
100#7488—611nomaximal, Sylow
101C22×C61—41no—
102C22×C61—81no—
103C22×C61#34211yescharacteristic
104C2×D61—21no—
105C2×D61—41no—
106C2×D61—41no—
107C2×D61—81no—
108#6923—161no—
109C4×C61—21no—
110C4×C61—41no—
111C4×C61—41no—
112Dic61—22no—
113Dic61—41no—
114Dic61AΣL(1,𝔽16)11yescharacteristic
115Dic61#35211yescharacteristic
116#2132—611no—
117#1884—611no—
118#1543—611no—
119C2×C61—21no—
120C2×C61—81no—
121C2×C61#139011yescharacteristic
122D61—41no—
123D61—81no—
124#568—611no—
125#532—611no—
126#431—1221no—
127#421—1221no—
128#413—1221no—
129#410—611no—
130#356—1221no—
131#355—611no—
132#355#692311yescharacteristic, complemented
133#339—1221no—
134#333—1221no—
135#331—612no—
136C61#748811yescharacteristic, complemented, Sylow
137C2×#41—611no—
138C2×#41—611no—
139#131—2442no—
140C2×M16—1221no—
141C2×M16—2441no—
142C2×M16—2441no—
143C4⋊Q8—611no—
144#127—611no—
145#124—611no—
146#124C2×#692311yescharacteristic
147#121—2441no—
148C4×D4—2441no—
149#117—1221no—
150C2×C42—611no—
151C4⋊C8—1222no—
152#104—2442no—
153#101—21no—
154#101—1221no—
155#100—2441no—
156#99—2441no—
157C22⋊C8—2441no—
158C4×C8—2441no—
159#41—2441no—
160#41—2441no—
161#41—2441no—
162#41—2441no—
163C2×Q8—611no—
164C2×Q8C22⋊#692311yescharacteristic
165C2×D4—611no—
166C2×D4—1221no—
167C2×D4—1221no—
168C2×D4—2441no—
169C2×D4C4×#692311yescharacteristic
170C22×C4—611no—
171C22×C4—1221no—
172C22×C4—1221no—
173C22×C4—1221no—
174M16—41no—
175M16—1222no—
176M16—4881no—
177M16—2441no—
178M16—2441no—
179M16—2442no—
180C2×C8—4881no—
181C2×C8—2442no—
182C2×C8—2441no—
183C2×C8—2442no—
184C4⋊C4—2441no—
185C4⋊C4—2441no—
186C22⋊C4—41no—
187C22⋊C4—2441no—
188C22⋊C4—2441no—
189C42—611no—
190C42—1221no—
191C42—2441no—
192C42C4⋊#692311yescharacteristic
193C23—21no—
194C23—611no—
195C23—1221no—
196Q8—41no—
197Q8—2441no—
198D4—41no—
199D4—4881no—
200D4—4882no—
201D4—2441no—
202D4—2442no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—611no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—4881no—
211C2×C4—2441no—
212C2×C4—2441no—
213C2×C4—2442no—
214C2×C4—2441no—
215C2×C4—2441no—
216C2×C4(C2×#6923)⋊C411yescharacteristic
217C8—81no—
218C8—4881no—
219C8—4882no—
220C8—2442no—
221C22—41no—
222C22—81no—
223C22—1221no—
224C22—4881no—
225C22—2441no—
226C22—2441no—
227C22#1684063911yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—611no—
232C4—611no—
233C4—1222no—
234C4—9761no—
235C4—2441no—
236C2—21no—
237C2—81no—
238C2—4881no—
239C2—2441no—
240C2#2146090211yescharacteristic
subgroupG/H
centerC2#21460902
commutatorC2×D4×C61C42
Frattini#124C2×#6923
FittingC61×#355C4
socleC2×C61#1390
prime radical, cosocle#16840311C22
hypercenter#355#6923
hypocenterC61#7488
LCSG ▷ C2×D4×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #355

Complements

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

NH ≅ G/Ntype
10. #16840620C4semidirect
14. #16839559C4semidirect
15. C61×#355C4semidirect
132. #355#6923semidirect
136. C61#7488semidirect

Maximal subgroups

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

subgroupindex
#214618202
#214613232
#214475012
#748861