Finite Group Databasebeta

← #30598151

Subgroups — #30598151

Order 15616.

874 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 874 conjugacy classes of subgroups — too many to draw. Only its 124 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#21461710C212yesmaximal, complemented
2C2×#16840607C212yesmaximal, complemented
3C2×#16840605C212yesmaximal
4C22×#14519770C211yesmaximal, characteristic
5C2×C22⋊#92420C2214yes—
6#16840628—24no—
7#16840607—24no—
8#16840605—24no—
9C2×#14519770—24no—
10C2×#14519770—24no—
11C2×#14519770—24no—
12C22×C4⋊Dic61C2211yescharacteristic
13C22×#11758196C411yescharacteristic
14C22×#11758196C411yescharacteristic
15C22×C22⋊Dic61C411yescharacteristic
16C22×C22⋊Dic61C2211yescharacteristic
17C22×C4×Dic61C2211yescharacteristic
18C22×C22⋊C4×C61C411yescharacteristic
19C22×#92420—24no—
20C22⋊#92420—24no—
21C22⋊#92420—24no—
22C23×Dic61C2×C411yescharacteristic
23C23×Dic61C2×C411yescharacteristic
24C23×Dic61C2×C411yescharacteristic
25C23×Dic61C2311yescharacteristic
26#14519770—232no—
27C2×C4⋊Dic61—22no—
28C2×C4⋊Dic61—22no—
29C2×C4⋊Dic61D414yes—
30C2×#11758196—22no—
31C2×#11758196—22no—
32C2×#11758196—22no—
33C2×#11758196—22no—
34C2×#11758196—22no—
35C2×#11758196—22no—
36C2×C22⋊Dic61—22no—
37C2×C22⋊Dic61—22no—
38C2×C22⋊Dic61—22no—
39C2×C22⋊Dic61—22no—
40C2×C22⋊Dic61—22no—
41C2×C22⋊Dic61D414yes—
42C2×C4×Dic61—22no—
43C2×C4×Dic61—22no—
44C2×C4×Dic61D414yes—
45C25×C61C2×C411yescharacteristic
46C23×C4×C61C2×C411yescharacteristic
47C23×C4×C61C2×C411yescharacteristic
48C2×C22⋊C4×C61—22no—
49C2×C22⋊C4×C61—22no—
50C2×C22⋊C4×C61—22no—
51C24×C61—21no—
52C24×C61—21no—
53C24×C61—24no—
54C24×C61—42no—
55C24×C61—42no—
56C24×C61C22⋊C412yes—
57C24×C61C22×C411yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—24no—
63C22×C4×C61—42no—
64C22×C4×C61C22⋊C412yes—
65C22×C4×C61C22⋊C412yes—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—24no—
73C22×Dic61—42no—
74C22×Dic61—42no—
75C22×Dic61—42no—
76C22×Dic61C22⋊C412yes—
77C22×Dic61C22⋊C412yes—
78C22×Dic61C22⋊C412yes—
79C22×Dic61C2×D412yes—
80C22×Dic61C2×D412yes—
81C22×Dic61C2×D412yes—
82C2×#92420—48no—
83C2×#92420—44no—
84C22⋊C4×C61—28no—
85C22⋊Dic61—28no—
86C22⋊Dic61—28no—
87C4⋊Dic61—28no—
88#11758196—28no—
89#11758196—28no—
90C4×Dic61—28no—
91C23×C61—22no—
92C23×C61—22no—
93C23×C61—22no—
94C23×C61—24no—
95C23×C61—42no—
96C23×C61—42no—
97C23×C61—42no—
98C23×C61—42no—
99C23×C61—42no—
100C23×C61—42no—
101C23×C61—42no—
102C23×C61—42no—
103C23×C61—88no—
104C23×C61C2×C22⋊C411yescharacteristic
105C23×C61C2×C22⋊C411yescharacteristic
106C23×C61C2×C22⋊C411yescharacteristic
107C23×C61#13114yes—
108C2×C4×C61—22no—
109C2×C4×C61—22no—
110C2×C4×C61—24no—
111C2×C4×C61—24no—
112C2×C4×C61—42no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61—42no—
116C2×Dic61—24no—
117C2×Dic61—22no—
118C2×Dic61—22no—
119C2×Dic61—22no—
120C2×Dic61—24no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61—42no—
124C2×Dic61—42no—
125C2×Dic61—42no—
126C2×Dic61—42no—
127C2×Dic61—42no—
128C2×Dic61—42no—
129C2×Dic61—42no—
130C2×Dic61—42no—
131C2×Dic61#12014yes—
132#92420—84no—
133#8309—611nomaximal, Sylow
134C22×C61—28no—
135C22×C61—21no—
136C22×C61—21no—
137C22×C61—21no—
138C22×C61—21no—
139C22×C61—42no—
140C22×C61—42no—
141C22×C61—42no—
142C22×C61—84no—
143C22×C61—84no—
144C22×C61—84no—
145C22×C61#37911yescharacteristic
146C22×C61#40812yes—
147C22×C61#40812yes—
148C22×C61#40812yes—
149C22×C61#41012yes—
150C22×C61#41312yes—
151C4×C61—42no—
152C4×C61—42no—
153Dic61—24no—
154Dic61—42no—
155Dic61—42no—
156Dic61—42no—
157C22×#126—611no—
158#1817—612no—
159C2×#324—612no—
160C2×#323—612no—
161C2×C61—22no—
162C2×C61—22no—
163C2×C61—82no—
164C2×C61#147314yes—
165C2×C61#178011yescharacteristic
166C2×C61#178211yescharacteristic
167C2×C61#178511yescharacteristic
168C2×#126—1224no—
169C2×#126—1224no—
170C2×#126—1224no—
171C22×C4⋊C4—611no—
172C22×C4⋊C4—611no—
173C22×C4⋊C4—611no—
174C22×C22⋊C4—611no—
175C22×C22⋊C4—611no—
176C22×C22⋊C4#692311yescharacteristic
177C22×C42—611no—
178C2×C22⋊C8—614no—
179#336—1224no—
180#324—1224no—
181#323—1224no—
182C61#830911yescharacteristic, complemented, Sylow
183C25C2×#692311yescharacteristic
184C23×C4—611no—
185C23×C4—611no—
186C23×C4—611no—
187C23×C4—611no—
188C23×C4C2×#692311yescharacteristic
189C23×C4C2×#692311yescharacteristic
190C22×C8—1224no—
191#126—12232no—
192C2×C4⋊C4—614no—
193C2×C4⋊C4—1222no—
194C2×C4⋊C4—1222no—
195C2×C4⋊C4—1222no—
196C2×C4⋊C4—1222no—
197C2×C4⋊C4—1222no—
198C2×C4⋊C4—1222no—
199C2×C4⋊C4—1222no—
200C2×C4⋊C4—1222no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—614no—
205C2×C22⋊C4—1222no—
206C2×C22⋊C4—1222no—
207C2×C22⋊C4—1222no—
208C2×C22⋊C4—1222no—
209C2×C22⋊C4—1222no—
210C2×C42—614no—
211C2×C42—1222no—
212C2×C42—1222no—
213C22⋊C8—1224no—
214C22⋊C8—1224no—
215C24—21no—
216C24—21no—
217C24—24no—
218C24—42no—
219C24—42no—
220C24C22⋊#692312yes—
221C24C22×#692311yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—24no—
227C22×C4—42no—
228C22×C4—612no—
229C22×C4—612no—
230C22×C4—612no—
231C22×C4—612no—
232C22×C4—612no—
233C22×C4—612no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4—1221no—
240C22×C4—1224no—
241C22×C4—2442no—
242C22×C4—2442no—
243C22×C4—2442no—
244C22×C4C22⋊#692312yes—
245C22×C4C22⋊#692312yes—
246C2×C8—2444no—
247C2×C8—2448no—
248C4⋊C4—1228no—
249C4⋊C4—1228no—
250C4⋊C4—1228no—
251C22⋊C4—28no—
252C22⋊C4—1228no—
253C22⋊C4—1228no—
254C42—1228no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—24no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—42no—
266C23—42no—
267C23—88no—
268C23C2×C22⋊#692311yescharacteristic
269C23C2×C22⋊#692311yescharacteristic
270C23C2×C22⋊#692311yescharacteristic
271C23#1451986414yes—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—614no—
281C2×C4—1224no—
282C2×C4—1224no—
283C2×C4—1222no—
284C2×C4—1222no—
285C2×C4—1222no—
286C2×C4—2442no—
287C2×C4—2442no—
288C2×C4—2442no—
289C2×C4—2442no—
290C2×C4—2442no—
291C2×C4—2442no—
292C2×C4—2442no—
293C2×C4—2442no—
294C2×C4—2442no—
295C2×C4—2442no—
296C8—4884no—
297C22—28no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—84no—
306C22—84no—
307C22—84no—
308C22#1684070311yescharacteristic
309C22#1684073512yes—
310C22#1684073512yes—
311C22#1684073612yes—
312C22#1684074112yes—
313C22#1684074912yes—
314C4—42no—
315C4—42no—
316C4—1224no—
317C4—2442no—
318C4—2442no—
319C4—2442no—
320C2—22no—
321C2—22no—
322C2—82no—
323C2#2146110014yes—
324C2#2146164311yescharacteristic
325C2#2146164811yescharacteristic
326C2#2146165611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C22⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC25×C61C2×C4
cosocleC23×Dic61C23
hypercenterC22×C22⋊C4#6923
hypocenterC61#8309
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #21461710C2semidirect
2. C2×#16840607C2semidirect
182. C61#8309semidirect

Maximal subgroups

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

subgroupindex
#214617102
C2×#168406072
C2×#168406052
C22×#145197702
#830961