Finite Group Databasebeta

← #30606022

Subgroups — #30606022

Order 15616.

226 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 64 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#21461459C211yesmaximal, characteristic, complemented
2#21461400C211yesmaximal, characteristic
3#21460850C211yesmaximal, characteristic, complemented
4#21460775C211yesmaximal, characteristic, complemented
5#21460774C211yesmaximal, characteristic
6#92420⋊C16C211yesmaximal, characteristic, complemented
7#21447668C211yesmaximal, characteristic
8#16840813—21no—
9#16840790—21no—
10#16840648C2211yescharacteristic
11#16840625C2211yescharacteristic
12#16840625C2211yescharacteristic
13Q8⋊#92420—21no—
14#16840610—21no—
15C8×#92420C2211yescharacteristic
16C2×#14519720C411yescharacteristic
17Q16×Dic61C2211yescharacteristic
18#16839844C2211yescharacteristic
19#16839589C411yescharacteristic
20#16839564C411yescharacteristic
21C16×Dic61C2211yescharacteristic
22C61×#358C411yescharacteristic
23C2×D61⋊C8—41no—
24C2×#11758187—21no—
25#14519844—41no—
26C4⋊#92420—21no—
27C4⋊#92420—21no—
28#14519834—41no—
29#14519832—41no—
30C4×#92420D411yescharacteristic
31C4×#92420D411yescharacteristic
32C2×D488C2×C411yescharacteristic
33Q8×Dic61—21no—
34#14519739—21no—
35#14519720—22no—
36C2×#11758185C2×C411yescharacteristic
37#14519711C2×C411yescharacteristic
38#14519701—21no—
39#14519697—21no—
40C8×Dic61C2311yescharacteristic
41C2×Q16×C61C2×C411yescharacteristic
42C2×C16×C61C2×C411yescharacteristic
43#107×C61C2×C411yescharacteristic
44C2×Q8×C61—21no—
45C2×D244—21no—
46C2×C4×D61—41no—
47C2×#92420—21no—
48C2×#92420—41no—
49C2×#92420—41no—
50C2×#92420D811yescharacteristic
51C2×#92420D811yescharacteristic
52D61⋊C8—82no—
53Q16×C61—21no—
54Q16×C61—21no—
55C2×C8×C61C22×C411yescharacteristic
56C4⋊C4×C61—21no—
57#11758198—41no—
58C4⋊Dic61—21no—
59C4⋊Dic61—41no—
60C4×Dic61—41no—
61C4×Dic61C2×D411yescharacteristic
62C2×#92418#4111yescharacteristic
63D488—21no—
64D488M1612yes—
65#11758187—41no—
66C16×C61—21no—
67#11758185—21no—
68C22×D61—41no—
69Q8×C61—41no—
70Q8×C61—41no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61C4×D411yescharacteristic
74C2×Dic61—41no—
75C2×Dic61C2×D811yescharacteristic
76C2×Dic61#13511yescharacteristic
77D244—22no—
78D244—41no—
79C4×D61—81no—
80C4×D61—81no—
81#92420—22no—
82#92420—21no—
83#92420—21no—
84#92420—81no—
85#92420—81no—
86C8×C61C2×M1611yescharacteristic
87C8×C61#13111yescharacteristic
88#92418—21no—
89#12074—611nomaximal, Sylow
90C22×C61C4×D811yescharacteristic
91C2×D61—42no—
92C2×D61—81no—
93C2×D61—81no—
94C4×C61—81no—
95C4×C61—81no—
96C4×C61#43511yescharacteristic
97C4×C61#44411yescharacteristic
98Dic61—21no—
99Dic61—81no—
100Dic61#50911yescharacteristic
101Dic61#51011yescharacteristic
102C4×SD32—611no—
103#1591—611no—
104C8×D8—611no—
105#1371—611no—
106#1332—611no—
107#1331—611no—
108#1312—611no—
109C2×C61#158111yescharacteristic
110C2×C61#217511yescharacteristic
111C2×C61#217811yescharacteristic
112D61—82no—
113C2×SD32—611no—
114#446—1221no—
115C4×Q16—611no—
116C4×D8—611no—
117C8×D4—1221no—
118#367—611no—
119#358#692311yescharacteristic
120#357—611no—
121C4×C16—611no—
122C4×C16—611no—
123#335—611no—
124#335—611no—
125Q8⋊C8—1221no—
126D4⋊C8—1221no—
127C82—611no—
128C61#1207411yescharacteristic, complemented, Sylow
129C2×Q16C2×#692311yescharacteristic
130C2×D8—611no—
131C22×C8—2441no—
132C4×Q8—1221no—
133C4×D4—1221no—
134SD32—1222no—
135C2×C16—611no—
136C2×C16—1221no—
137C2×C16C2×#692311yescharacteristic
138#107—611no—
139#107C2×#692311yescharacteristic
140C4⋊C8—1221no—
141C4⋊C8—1221no—
142C4⋊C8—2441no—
143#103—1221no—
144#102—1221no—
145C22⋊C8—2441no—
146#97—2441no—
147C4×C8—611no—
148C4×C8—611no—
149C4×C8—611no—
150C2×Q8—21no—
151C2×D4—1221no—
152C22×C4—2441no—
153Q16—21no—
154Q16—21no—
155D8—612no—
156D8—1221no—
157C2×C8—611no—
158C2×C8—611no—
159C2×C8—611no—
160C2×C8—1221no—
161C2×C8—4882no—
162C2×C8—2441no—
163C2×C8—2441no—
164C2×C8C22×#692311yescharacteristic
165C4⋊C4—21no—
166C4⋊C4—1221no—
167C4⋊C4—2441no—
168C22⋊C4—2441no—
169C42—611no—
170C42—2441no—
171C16—21no—
172C16—1221no—
173C16—2441no—
174C23—2441no—
175Q8—41no—
176Q8—41no—
177D4—1222no—
178D4—2441no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—611no—
182C2×C4—611no—
183C2×C4—4881no—
184C2×C4—4881no—
185C2×C4—2441no—
186C2×C4D4×#692311yescharacteristic
187C8—1221no—
188C8—1221no—
189C8—1222no—
190C8—1221no—
191C8—4881no—
192C8—4881no—
193C8D61⋊M1611yescharacteristic
194C8#1451986411yescharacteristic
195C22—4881no—
196C22—4881no—
197C22—2442no—
198C22D8×#692311yescharacteristic
199C4—81no—
200C4—81no—
201C4—611no—
202C4—611no—
203C4—1221no—
204C4—4881no—
205C4#1684079411yescharacteristic
206C4#1684080711yescharacteristic
207C2—4882no—
208C2#2146142111yescharacteristic
209C2#2146221511yescharacteristic
210C2#2146222011yescharacteristic
subgroupG/H
centerC22D8×#6923
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#358C4
socleC22×C61C4×D8
prime radicalC2×D488C2×C4
cosocleC8×Dic61C23
hypercenter#358#6923
hypocenterC61#12074
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
1. #21461459C2semidirect
3. #21460850C2semidirect
4. #21460775C2semidirect
6. #92420⋊C16C2semidirect
128. C61#12074semidirect

Maximal subgroups

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

subgroupindex
#214614592
#214614002
#214608502
#214607752
#214607742
#92420⋊C162
#214476682
#1207461