Finite Group Databasebeta

← #30598209

Subgroups — #30598209

Order 15616.

684 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 108 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#21461121C214yesmaximal, complemented
2#21461052C212yesmaximal
3C2×#16840373C211yesmaximal, characteristic
4#16840778C2214yes—
5Q8⋊#92420—28no—
6#16840608—22no—
7#16840606—22no—
8#16840373—28no—
9C2×#14519772—22no—
10C2×#14519769C411yescharacteristic
11C2×#14519767—22no—
12C2×#14519753C412yes—
13C2×Q8×Dic61C2212yes—
14C2×#14519734C2211yescharacteristic
15C2×C4⋊Q8×C61C411yescharacteristic
16C4⋊#92420—24no—
17C22⋊#92420—24no—
18C4×#92420—24no—
19C22×C4×D61C2×C411yescharacteristic
20#14519772—216no—
21#14519769—24no—
22#14519767—216no—
23#14519753—24no—
24#14519753—24no—
25Q8×Dic61—24no—
26Q8×Dic61D418yes—
27#14519734—24no—
28C2×C4⋊Dic61—22no—
29C2×C4⋊Dic61C2×C412yes—
30C2×#11758196—22no—
31C2×#11758196—22no—
32C2×#11758196D412yes—
33C2×#11758198—22no—
34C2×#11758198D412yes—
35C2×C4×Dic61—22no—
36C2×C4×Dic61C2311yescharacteristic
37C22×Q8×C61C2×C412yes—
38C4⋊Q8×C61—24no—
39C2×C4⋊C4×C61—22no—
40C2×C42×C61C2×C411yescharacteristic
41C23×D61C22⋊C411yescharacteristic
42C2×Q8×C61—22no—
43C2×Q8×C61—28no—
44C2×Q8×C61C22⋊C414yes—
45C22×C4×C61—22no—
46C22×C4×C61C22⋊C412yes—
47C22×C4×C61C22×C411yescharacteristic
48C22×Dic61—22no—
49C22×Dic61C22⋊C411yescharacteristic
50C22×Dic61C2×D412yes—
51C2×C4×D61—22no—
52C2×C4×D61—24no—
53C2×#92420—44no—
54C4⋊C4×C61—28no—
55C42×C61—22no—
56#11758198—28no—
57#11758198—24no—
58C4⋊Dic61—22no—
59C4⋊Dic61—28no—
60C4⋊Dic61C22⋊C414yes—
61#11758196—28no—
62#11758196—28no—
63#11758196—24no—
64C4×Dic61—28no—
65C4×Dic61C2×D414yes—
66C23×C61C2×C22⋊C411yescharacteristic
67C22×D61—21no—
68C22×D61—22no—
69C22×D61—42no—
70Q8×C61—28no—
71Q8×C61—44no—
72C2×C4×C61—24no—
73C2×C4×C61—22no—
74C2×C4×C61—44no—
75C2×C4×C61—42no—
76C2×C4×C61C2×C22⋊C412yes—
77C2×C4×C61#13114yes—
78C2×Dic61—24no—
79C2×Dic61—21no—
80C2×Dic61—22no—
81C2×Dic61—42no—
82C2×Dic61—44no—
83C2×Dic61#12014yes—
84C4×D61—44no—
85#92420—84no—
86#8327—611nomaximal, Sylow
87C22×C61—22no—
88C22×C61#37911yescharacteristic
89C22×C61#40812yes—
90C2×D61—42no—
91C2×D61—41no—
92C2×D61—82no—
93C4×C61—42no—
94C4×C61—44no—
95C4×C61#40814yes—
96Dic61—24no—
97Dic61—44no—
98Dic61—41no—
99C2×#541—611no—
100#1479—614no—
101#1458—612no—
102C2×C61—22no—
103C2×C61#178011yescharacteristic
104C2×C61#179612yes—
105D61—81no—
106#541—1228no—
107C2×C4⋊Q8#692311yescharacteristic
108C2×#126—1222no—
109C2×#125—611no—
110C2×#125—1222no—
111C2×C22⋊Q8—612no—
112C2×C4×Q8—612no—
113C2×#117—611no—
114#431—614no—
115Q8⋊C8—1228no—
116#324—1222no—
117#323—1222no—
118C61#832711yescharacteristic, complemented, Sylow
119C22×Q8C2×#692312yes—
120C23×C4—611no—
121C4⋊Q8—24no—
122#126—12216no—
123#125—1224no—
124#125—12216no—
125C22⋊Q8—1224no—
126C22⋊Q8—1224no—
127C4×Q8—618no—
128C4×Q8—1224no—
129#117—1224no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—612no—
132C2×C4⋊C4—612no—
133C2×C4⋊C4—1222no—
134C2×C4⋊C4—1222no—
135C2×C4⋊C4—1222no—
136C2×C22⋊C4—612no—
137C2×C22⋊C4—1222no—
138C2×C42—611no—
139C2×C42—1222no—
140C2×C42C2×#692311yescharacteristic
141C4⋊C8—1224no—
142C22⋊C8—1224no—
143C4×C8—1224no—
144C24—611no—
145C2×Q8—22no—
146C2×Q8—28no—
147C2×Q8C22⋊#692314yes—
148C22×C4—22no—
149C22×C4—612no—
150C22×C4—611no—
151C22×C4—1222no—
152C22×C4—1222no—
153C22×C4—1224no—
154C22×C4C22⋊#692312yes—
155C22×C4C22×#692311yescharacteristic
156C2×C8—2444no—
157C4⋊C4—28no—
158C4⋊C4—614no—
159C4⋊C4—1224no—
160C4⋊C4—1228no—
161C4⋊C4—1228no—
162C4⋊C4—1228no—
163C4⋊C4—1222no—
164C22⋊C4—1224no—
165C22⋊C4—1228no—
166C42—22no—
167C42—614no—
168C42—1228no—
169C23—1222no—
170C23—1221no—
171C23—2442no—
172C23C2×C22⋊#692311yescharacteristic
173Q8—28no—
174Q8—44no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—44no—
178C2×C4—42no—
179C2×C4—614no—
180C2×C4—1222no—
181C2×C4—1224no—
182C2×C4—1221no—
183C2×C4—2442no—
184C2×C4—2444no—
185C2×C4—2444no—
186C2×C4C2×C22⋊#692312yes—
187C2×C4#1451986414yes—
188C8—4884no—
189C22—22no—
190C22—4882no—
191C22—2441no—
192C22—2442no—
193C22#1684070311yescharacteristic
194C22#1684073612yes—
195C4—44no—
196C4—42no—
197C4—1224no—
198C4—2441no—
199C4—2444no—
200C4#1684073514yes—
201C2—22no—
202C2—4881no—
203C2#2146164311yescharacteristic
204C2#2146167112yes—
subgroupG/H
centerC22#16840703
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61#379
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#8327
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #21461121C2semidirect
118. C61#8327semidirect

Maximal subgroups

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

subgroupindex
#214611212
#214610522
C2×#168403732
#832761