Finite Group Databasebeta

← #30607273

Subgroups — #30607273

Order 15616.

334 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 68 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#21461728C212yesmaximal
2#21460920C212yesmaximal
3#21460911C211yesmaximal, characteristic
4#21460908C211yesmaximal, characteristic
5#21454471C211yesmaximal, characteristic
6#16840748C2212yes—
7#16840741C2212yes—
8#16840633—22no—
9#16840629—22no—
10C4×#11758222C2211yescharacteristic
11#16839821—22no—
12#16839817—22no—
13#16839790C411yescharacteristic, complemented
14#16839790C411yescharacteristic, complemented
15#16839730C2211yescharacteristic
16#16839730C2211yescharacteristic
17C2×#14519688C411yescharacteristic, complemented
18C4×M16×C61C411yescharacteristic, complemented
19D61⋊M16—22no—
20#14519856—22no—
21#14519838—22no—
22#14519837—22no—
23#14519836—22no—
24#14519835—22no—
25C2×#11758222C2311yescharacteristic
26C22×#92418C2×C411yescharacteristic
27C22×#92418C2×C411yescharacteristic
28C4×Dic122—21no—
29C4×D244—21no—
30C4×C22⋊D61—22no—
31#14519736C2×C411yescharacteristic
32#14519734D412yes—
33C42×D61D412yes—
34#14519706—22no—
35#14519706—22no—
36#14519689—22no—
37#14519689—22no—
38#14519688—21no—
39#14519688—21no—
40C2×M16×C61C2×C411yescharacteristic
41C2×M16×C61C2×C411yescharacteristic
42C2×C42×C61C2×C411yescharacteristic
43#97×C61—21no—
44C4×C8×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61C22×C411yescharacteristic
47C2×C22⋊D61#4112yes—
48#11758222—41no—
49#11758222—41no—
50C2×D244#4111yescharacteristic
51C2×C4×D61—22no—
52C2×C4×D61C2×D412yes—
53C2×Dic122#4111yescharacteristic
54C22⋊#6923—42no—
55#11758217—42no—
56C4⋊#6923—42no—
57C4×#6923—42no—
58#11758213—42no—
59D61⋊C8—42no—
60M16×C61—41no—
61M16×C61—41no—
62C2×C8×C61—21no—
63C2×C8×C61—21no—
64C42×C61—21no—
65C42×C61C22⋊C411yescharacteristic
66C42×C61C22⋊C411yescharacteristic
67C22⋊Dic61—21no—
68#11758198—22no—
69C4⋊Dic61—21no—
70#11758196—22no—
71C4×Dic61—22no—
72C4×Dic61C22⋊C412yes—
73C2×#92418—21no—
74C2×#92418—21no—
75C2×#92418—41no—
76C2×#92418—41no—
77C23×C61#11711yescharacteristic
78C22×D61#12312yes—
79C2×#6923—82no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—81no—
85C2×C4×C61C2×C22⋊C411yescharacteristic
86C2×C4×C61#11711yescharacteristic
87C22⋊D61—42no—
88C2×Dic61—22no—
89C2×Dic61#12312yes—
90D244—41no—
91C4×D61—22no—
92C4×D61—22no—
93C4×D61—82no—
94Dic122—41no—
95#92420—82no—
96C8×C61—41no—
97C8×C61—41no—
98#92418—41no—
99#92418—41no—
100#12865—611nomaximal, Sylow
101C22×C61—21no—
102C22×C61—41no—
103C22×C61#38111yescharacteristic
104C2×D61—22no—
105C2×D61—42no—
106#6923—162no—
107C4×C61—21no—
108C4×C61—41no—
109C4×C61—41no—
110C4×C61#41011yescharacteristic
111C4×C61#41011yescharacteristic
112Dic61—22no—
113Dic61—42no—
114#2923—611no—
115#1827—612no—
116#1395—612no—
117#1392—611no—
118#1391—611no—
119C2×C61—21no—
120C2×C61—41no—
121C2×C61#182011yescharacteristic
122D61—42no—
123C4×#41—611no—
124#433—1222no—
125#432—1222no—
126#424—611no—
127#424—611no—
128#413—612no—
129#410—612no—
130#408—611no—
131#408—611no—
132C4×M16#692311yescharacteristic, complemented
133C2×#97—611no—
134#339—1222no—
135H(3,ℤ/4)—1222no—
136C61#1286511yescharacteristic, complemented, Sylow
137C2×#41—611no—
138C2×M16—1222no—
139C2×M16C2×#692311yescharacteristic
140C2×M16C2×#692311yescharacteristic
141C22×C8—611no—
142C22×C8—611no—
143C4×Q8—1221no—
144C4×D4—1221no—
145C4×D4—1222no—
146#117—611no—
147#117—612no—
148#117—1222no—
149C2×C42—612no—
150C2×C42C2×#692311yescharacteristic
151C4⋊C8—1222no—
152C4⋊C8—1222no—
153#101—1222no—
154#100—1222no—
155#99—1222no—
156#99—1222no—
157C22⋊C8—1222no—
158C22⋊C8—1222no—
159#97—21no—
160#97—1221no—
161#97—1221no—
162C4×C8—21no—
163#41—2441no—
164#41—2441no—
165C2×Q8—611no—
166C2×D4—612no—
167C2×D4—611no—
168C22×C4—21no—
169C22×C4—612no—
170C22×C4—1222no—
171C22×C4C22×#692311yescharacteristic
172M16—41no—
173M16—41no—
174M16—2442no—
175M16—2442no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—1221no—
179C2×C8—1221no—
180C2×C8—2442no—
181C2×C8—2441no—
182C2×C8—2441no—
183C4⋊C4—1222no—
184C4⋊C4—1221no—
185C4⋊C4—2442no—
186C22⋊C4—1222no—
187C22⋊C4—1221no—
188C22⋊C4—2442no—
189C42—21no—
190C42—612no—
191C42—1222no—
192C42—2442no—
193C42C22⋊#692311yescharacteristic
194C42C22⋊#692311yescharacteristic
195C23—612no—
196C23#1451985611yescharacteristic
197Q8—2441no—
198D4—2441no—
199D4—2442no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—81no—
205C2×C4—612no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4—1222no—
209C2×C4—4882no—
210C2×C4—4882no—
211C2×C4C2×C22⋊#692311yescharacteristic
212C2×C4#1451985611yescharacteristic
213C8—41no—
214C8—41no—
215C8—4882no—
216C8—2441no—
217C8—2441no—
218C22—21no—
219C22—41no—
220C22—1222no—
221C22—2442no—
222C22#1684070511yescharacteristic
223C4—21no—
224C4—41no—
225C4—41no—
226C4—1222no—
227C4—9762no—
228C4—2442no—
229C4#1684074111yescharacteristic
230C4#1684074111yescharacteristic
231C2—21no—
232C2—41no—
233C2—2442no—
234C2#2146171611yescharacteristic
subgroupG/H
centerC4#16840741
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×M16×C61C4
socleC2×C61#1820
prime radical, cosocleC2×#11758222C23
hypercenterC4×M16#6923
hypocenterC61#12865
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
13. #16839790C4semidirect
14. #16839790C4semidirect
17. C2×#14519688C4semidirect
18. C4×M16×C61C4semidirect
132. C4×M16#6923semidirect
136. C61#12865semidirect

Maximal subgroups

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

subgroupindex
#214617282
#214609202
#214609112
#214609082
#214544712
#1286561