Finite Group Databasebeta

← #30599308

Subgroups — #30599308

Order 15616.

622 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 120 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
1C2×#16840605C212yesmaximal
2#21460662C214yesmaximal, complemented
3#21448172C211yesmaximal, characteristic
4C2×C22⋊#92420C2214yes—
5#16840605—22no—
6#16840605—22no—
7C22×C22⋊Dic61C411yescharacteristic
8C22×C22⋊Dic61C2211yescharacteristic
9C22⋊C4×Dic61—22no—
10C22⋊C4×Dic61C412yes—
11C22⋊C4×Dic61C2212yes—
12C4×C22⋊Dic61—22no—
13C22×C22⋊C4×C61C411yescharacteristic
14C22×#92420—24no—
15C22⋊#92420—24no—
16C22⋊#92420—24no—
17C23×Dic61—21no—
18C23×Dic61C2×C411yescharacteristic
19C23×Dic61C2311yescharacteristic
20C2×C22⋊Dic61—21no—
21C2×C22⋊Dic61—22no—
22C2×C22⋊Dic61—24no—
23C2×C22⋊Dic61C814yescomplemented
24C2×C22⋊Dic61C2×C412yes—
25C2×C22⋊Dic61D412yes—
26C2×C22⋊Dic61D412yes—
27C2×C4×Dic61—22no—
28C2×C4×Dic61—22no—
29#14519684—22no—
30#14519684—22no—
31C25×C61C2×C411yescharacteristic
32C23×C4×C61—21no—
33C2×C22⋊C4×C61—21no—
34C2×C22⋊C4×C61—24no—
35C2×C22⋊C4×C61C2×C412yes—
36C24×C61—22no—
37C24×C61—22no—
38C24×C61—81no—
39C24×C61—81no—
40C24×C61C22⋊C411yescharacteristic
41C24×C61C22⋊C411yescharacteristic
42C24×C61C2×C812yes—
43C24×C61M1612yes—
44C24×C61C22×C411yescharacteristic
45C22×C4×C61—22no—
46C22×C4×C61—24no—
47C22×C4×C61—81no—
48C22×C4×C61—81no—
49C22×Dic61—22no—
50C22×Dic61—24no—
51C22×Dic61—22no—
52C22×Dic61—81no—
53C22×Dic61—81no—
54C22×Dic61—81no—
55C22×Dic61—81no—
56C22×Dic61C22⋊C412yes—
57C22×Dic61C2×D412yes—
58C22×Dic61#4114yes—
59C2×#92420—44no—
60C2×#92420—84no—
61C22⋊C4×C61—24no—
62C22⋊C4×C61—22no—
63C22⋊C4×C61M1614yes—
64C22⋊Dic61—24no—
65C22⋊Dic61—22no—
66C22⋊Dic61—24no—
67C22⋊Dic61—24no—
68C22⋊Dic61C2×C814yes—
69C4×Dic61—82no—
70C4×Dic61—82no—
71C23×C61—21no—
72C23×C61—21no—
73C23×C61—21no—
74C23×C61—21no—
75C23×C61—24no—
76C23×C61—24no—
77C23×C61—41no—
78C23×C61—41no—
79C23×C61—41no—
80C23×C61—41no—
81C23×C61—41no—
82C23×C61—41no—
83C23×C61—82no—
84C23×C61—82no—
85C23×C61—84no—
86C23×C61—82no—
87C23×C61—82no—
88C23×C61C22⋊C812yes—
89C23×C61C22⋊C812yes—
90C23×C61C2×C22⋊C411yescharacteristic
91C23×C61#11712yes—
92C23×C61C22×C811yescharacteristic
93C23×C61C2×M1611yescharacteristic
94C23×C61C2×M1612yes—
95C2×C4×C61—24no—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61—84no—
99C2×Dic61—22no—
100C2×Dic61—24no—
101C2×Dic61—42no—
102C2×Dic61—44no—
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61—42no—
106C2×Dic61—82no—
107C2×Dic61—84no—
108C2×Dic61#12314yes—
109#92420—84no—
110#8734—611nomaximal, Sylow
111C22×C61—21no—
112C22×C61—22no—
113C22×C61—21no—
114C22×C61—22no—
115C22×C61—22no—
116C22×C61—22no—
117C22×C61—41no—
118C22×C61—42no—
119C22×C61—41no—
120C22×C61—42no—
121C22×C61—42no—
122C22×C61—42no—
123C22×C61—42no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61—41no—
128C22×C61—84no—
129C22×C61—84no—
130C22×C61#38111yescharacteristic
131C22×C61C2×C22⋊C811yescharacteristic
132C22×C61#40711yescharacteristic
133C22×C61#43112yes—
134C22×C61#43212yes—
135C4×C61—44no—
136Dic61—24no—
137Dic61—44no—
138Dic61—42no—
139#2273—611no—
140C2×#323—612no—
141#1282—614no—
142C2×C61—21no—
143C2×C61—21no—
144C2×C61—22no—
145C2×C61—22no—
146C2×C61—42no—
147C2×C61—42no—
148C2×C61#181711yescharacteristic
149C2×C61#182811yescharacteristic
150C2×C61#182911yescharacteristic
151C22×C22⋊C4—611no—
152C22×C22⋊C4—611no—
153C22×C22⋊C4#692311yescharacteristic
154C2×C22⋊C8—614no—
155C4×C22⋊C4—612no—
156C4×C22⋊C4—612no—
157C4×C22⋊C4—1222no—
158C4×C22⋊C4—1222no—
159#323—1222no—
160#323—1222no—
161C61#873411yescharacteristic, complemented, Sylow
162C25C2×#692311yescharacteristic
163C23×C4—21no—
164C23×C4—611no—
165C23×C4—611no—
166C23×C4—1221no—
167C22×C8—1224no—
168C2×C22⋊C4—21no—
169C2×C22⋊C4—24no—
170C2×C22⋊C4—614no—
171C2×C22⋊C4—612no—
172C2×C22⋊C4—612no—
173C2×C22⋊C4—612no—
174C2×C22⋊C4—1224no—
175C2×C22⋊C4—1222no—
176C2×C22⋊C4—1221no—
177C2×C22⋊C4C2×#692312yes—
178C2×C42—1222no—
179C2×C42—1222no—
180C22⋊C8—1224no—
181C22⋊C8—1224no—
182#95—1222no—
183#95—1222no—
184C24—22no—
185C24—22no—
186C24—81no—
187C24—81no—
188C24D61⋊C812yes—
189C24#1175821312yes—
190C24C22⋊#692311yescharacteristic
191C24C22⋊#692311yescharacteristic
192C24C22×#692311yescharacteristic
193C22×C4—22no—
194C22×C4—24no—
195C22×C4—81no—
196C22×C4—81no—
197C22×C4—612no—
198C22×C4—614no—
199C22×C4—612no—
200C22×C4—1224no—
201C22×C4—1222no—
202C22×C4—1222no—
203C22×C4—4881no—
204C22×C4—4881no—
205C22×C4—4881no—
206C22×C4—4881no—
207C2×C8—4884no—
208C2×C8—2444no—
209C22⋊C4—24no—
210C22⋊C4—22no—
211C22⋊C4—614no—
212C22⋊C4—1224no—
213C22⋊C4—1224no—
214C22⋊C4—1224no—
215C22⋊C4—1222no—
216C22⋊C4#1175821714yes—
217C42—4882no—
218C42—4882no—
219C23—21no—
220C23—21no—
221C23—21no—
222C23—21no—
223C23—24no—
224C23—24no—
225C23—41no—
226C23—41no—
227C23—41no—
228C23—41no—
229C23—41no—
230C23—41no—
231C23—82no—
232C23—82no—
233C23—82no—
234C23—82no—
235C23—84no—
236C23#1451983412yes—
237C23#1451983412yes—
238C23C2×C22⋊#692311yescharacteristic
239C23#1451985612yes—
240C23C2×D61⋊C811yescharacteristic
241C23C2×#1175821712yes—
242C23C2×#1175821311yescharacteristic
243C2×C4—24no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—84no—
247C2×C4—614no—
248C2×C4—1222no—
249C2×C4—1224no—
250C2×C4—4882no—
251C2×C4—4884no—
252C2×C4—2442no—
253C2×C4—2444no—
254C2×C4—2442no—
255C2×C4—2442no—
256C2×C4—2442no—
257C8—4884no—
258C22—21no—
259C22—22no—
260C22—21no—
261C22—22no—
262C22—22no—
263C22—22no—
264C22—41no—
265C22—42no—
266C22—41no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—41no—
275C22—84no—
276C22—84no—
277C22#1684070511yescharacteristic
278C22C2×#1451983411yescharacteristic
279C22#1684073211yescharacteristic
280C22#1684077912yes—
281C22#1684078312yes—
282C4—44no—
283C4—1224no—
284C4—2444no—
285C4—2442no—
286C2—21no—
287C2—21no—
288C2—22no—
289C2—22no—
290C2—42no—
291C2—42no—
292C2#2146171011yescharacteristic
293C2#2146173011yescharacteristic
294C2#2146173211yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61#381
prime radicalC25×C61C2×C4
cosocleC23×Dic61C23
hypercenterC22×C22⋊C4#6923
hypocenterC61#8734
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #21460662C2semidirect
23. C2×C22⋊Dic61C8semidirect
161. C61#8734semidirect

Maximal subgroups

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

subgroupindex
C2×#168406052
#214606622
#214481722
#873461