Finite Group Databasebeta

← #30599018

Subgroups — #30599018

Order 15616.

398 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 106 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#21461685C212yesmaximal
2#21461373C212yesmaximal
3#21460689C212yesmaximal
4C2×#16839886C211yesmaximal, characteristic
5#16840765C2214yes—
6C2×#14519838—22no—
7#16840642—22no—
8#16840624—22no—
9#16840623—22no—
10C2×C4×Dic122C2211yescharacteristic
11#16839886—22no—
12#16839886—22no—
13C2×#14519706C411yescharacteristic
14C2×#14519706C2211yescharacteristic
15C2×C4×#92418C411yescharacteristic
16C2×C8×Dic61C411yescharacteristic
17C2×C8×Dic61C2211yescharacteristic
18C2×C4⋊C8×C61C411yescharacteristic
19C2×#11758217—24no—
20#14519844—24no—
21C4⋊#92420—24no—
22#14519838—44no—
23C22×Dic122D411yescharacteristic
24C22×#92418C2×C411yescharacteristic
25C22×#92418C2×C411yescharacteristic
26C4×Dic122—22no—
27C4×Dic122—22no—
28C2×C4⋊Dic61Q811yescharacteristic
29C2×#11758196D411yescharacteristic
30C2×#11758196Q811yescharacteristic
31C2×C4×Dic61C2×C411yescharacteristic
32C2×C4×Dic61C2311yescharacteristic
33#14519706—22no—
34#14519706—22no—
35C4×#92418—21no—
36C4×#92418—21no—
37C8×Dic61—21no—
38C8×Dic61—21no—
39C8×Dic61D412yes—
40C8×Dic61D412yes—
41C22×C8×C61C2×C411yescharacteristic
42C22×C8×C61C2×C411yescharacteristic
43C2×C42×C61C2×C411yescharacteristic
44C4⋊C8×C61—22no—
45C22×C4×C61C4⋊C411yescharacteristic
46C22×C4×C61C4⋊C411yescharacteristic
47C22×C4×C61C22×C411yescharacteristic
48C22×Dic61C4⋊C411yescharacteristic
49C22×Dic61C4⋊C411yescharacteristic
50C22×Dic61C2×D411yescharacteristic
51C22×Dic61C2×Q811yescharacteristic
52C2×Dic122—22no—
53C2×Dic122—22no—
54C2×Dic122SD1614yes—
55#11758217—44no—
56#11758217—44no—
57C2×#92420—44no—
58C2×C8×C61—21no—
59C2×C8×C61—41no—
60C2×C8×C61—41no—
61C2×C8×C61C22⋊C412yes—
62C42×C61—21no—
63C42×C61—21no—
64C4⋊Dic61—22no—
65#11758196—22no—
66#11758196—22no—
67C4×Dic61—21no—
68C4×Dic61—21no—
69C4×Dic61C2×D412yes—
70C4×Dic61#4112yes—
71C2×#92418—22no—
72C2×#92418—21no—
73C2×#92418—41no—
74C2×#92418C22⋊C411yescharacteristic
75C2×#92418C22⋊C411yescharacteristic
76C23×C61C2×C4⋊C411yescharacteristic
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—41no—
83C2×C4×C61#10612yes—
84C2×C4×C61C2×C22⋊C411yescharacteristic
85C2×C4×C61#11711yescharacteristic
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61#10612yes—
92C2×Dic61#12112yes—
93C2×Dic61C22⋊Q812yes—
94C2×Dic61C2×SD1612yes—
95C2×Dic61#13512yes—
96Dic122—28no—
97#92420—84no—
98C8×C61—22no—
99C8×C61—41no—
100#92418—21no—
101#92418—41no—
102#92418#10112yescomplemented
103#8615—611nomaximal, Sylow
104C22×C61—21no—
105C22×C61—21no—
106C22×C61#38011yescharacteristic
107C22×C61C2×#10611yescharacteristic
108C22×C61#42711yescharacteristic
109C4×C61—21no—
110C4×C61—22no—
111C4×C61—41no—
112C4×C61C2×#10111yescharacteristic
113C4×C61#41311yescharacteristic
114Dic61—22no—
115Dic61—22no—
116Dic61—41no—
117Dic61#46514yes—
118C2×C8×Q8—611no—
119#1801—612no—
120#1566—612no—
121#1292—612no—
122C2×C61—21no—
123C2×C61—21no—
124C2×C61#180111yescharacteristic
125C2×C61#180711yescharacteristic
126C2×C61#181311yescharacteristic
127C2×C4×Q8—611no—
128C8×Q8—1222no—
129C8×Q8—1222no—
130#423—614no—
131C2×C4⋊C8—611no—
132C2×C4⋊C8—611no—
133C2×C4⋊C8#692311yescharacteristic
134C2×#101—1222no—
135C2×C4×C8—611no—
136C2×C4×C8—611no—
137C2×C4×C8—611no—
138#343—1222no—
139#334—1222no—
140#334—1222no—
141C61#861511yescharacteristic, complemented, Sylow
142C22×Q8—611no—
143C2×M16—1224no—
144C22×C8—611no—
145C22×C8—611no—
146C22×C8C2×#692311yescharacteristic
147C22×C8C2×#692311yescharacteristic
148C4×Q8—1222no—
149C4×Q8—1222no—
150C2×C4⋊C4—611no—
151C2×C4⋊C4—611no—
152C2×C4⋊C4—611no—
153C2×C42—611no—
154C2×C42—611no—
155C2×C42C2×#692311yescharacteristic
156C4⋊C8—22no—
157C4⋊C8—1222no—
158C4⋊C8—1224no—
159C4⋊C8—1224no—
160C4⋊C8—1222no—
161#101—2444no—
162C4×C8—612no—
163C4×C8—612no—
164C4×C8—1221no—
165C4×C8—1221no—
166C4×C8—1221no—
167C4×C8—1221no—
168C2×Q8—614no—
169C2×Q8—1222no—
170C2×Q8—1222no—
171C22×C4—611no—
172C22×C4—611no—
173C22×C4—611no—
174C22×C4—611no—
175C22×C4C4⋊#692311yescharacteristic
176C22×C4C4⋊#692311yescharacteristic
177C22×C4C22×#692311yescharacteristic
178M16—2444no—
179M16—2444no—
180C2×C8—21no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—611no—
184C2×C8—611no—
185C2×C8—1222no—
186C2×C8—1221no—
187C2×C8—2444no—
188C2×C8—2441no—
189C2×C8C22⋊#692312yes—
190C4⋊C4—1222no—
191C4⋊C4—1222no—
192C4⋊C4—1222no—
193C42—21no—
194C42—21no—
195C42—612no—
196C42—612no—
197C42—1221no—
198C42—1221no—
199C23C2×C4⋊#692311yescharacteristic
200Q8—1228no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—612no—
208C2×C4—612no—
209C2×C4—612no—
210C2×C4—612no—
211C2×C4—612no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—2441no—
216C2×C4—2441no—
217C2×C4#1451984512yes—
218C2×C4C2×C22⋊#692311yescharacteristic
219C2×C4#1451985611yescharacteristic
220C8—22no—
221C8—41no—
222C8—612no—
223C8—1221no—
224C8—4884no—
225C8—2441no—
226C22—21no—
227C22—21no—
228C22#1684070411yescharacteristic
229C22C2×#1451984511yescharacteristic
230C22#1684077211yescharacteristic
231C4—21no—
232C4—22no—
233C4—41no—
234C4—614no—
235C4—1222no—
236C4—1222no—
237C4—2441no—
238C4D61⋊#10111yescharacteristic
239C4#1684074911yescharacteristic
240C2—21no—
241C2—21no—
242C2#2146168611yescharacteristic
243C2#2146169511yescharacteristic
244C2#2146170411yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊C8×C61C4
socleC22×C61#380
prime radicalC23×C61C2×C4⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4⋊C8#6923
hypocenterC61#8615
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
102. #92418#101semidirect
141. C61#8615semidirect

Maximal subgroups

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

subgroupindex
#214616852
#214613732
#214606892
C2×#168398862
#861561