Finite Group Databasebeta

← #30606847

Subgroups — #30606847

Order 15616.

1154 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 100 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×#16840670C214yesmaximal, complemented
2#21461655C212yesmaximal, complemented
3C2×#16840329C211yesmaximal, characteristic
4C2×#14519838C2214yescomplemented
5C2×#14519837—22no—
6#16840734—22no—
7#16840670—28no—
8C22×#11758222C2211yescharacteristic
9#16840329—28no—
10C2×#14519773C412yes—
11C2×#14519764C2212yes—
12C2×#14519748—22no—
13C2×#14519746—22no—
14C2×#14519736C411yescharacteristic
15C23×D4×C61C411yescharacteristic
16C2×#11758217—24no—
17#14519838—28no—
18#14519837—44no—
19#14519834—44no—
20C2×#11758222—24no—
21C2×#11758222—42no—
22C2×#11758222—42no—
23C22×Dic122C2311yescharacteristic
24C22×D244C2×C411yescharacteristic
25C22×C22⋊D61—24no—
26C22×C22⋊D61D412yes—
27C22×C4×D61D412yes—
28#14519773—24no—
29#14519773—24no—
30#14519764—24no—
31#14519764D418yes—
32#14519748—216no—
33#14519746—216no—
34#14519736—24no—
35C2×C4⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—24no—
38C2×C4×Dic61C2×C412yes—
39C25×C61—21no—
40C22×D4×C61—24no—
41C22×D4×C61—21no—
42C22×D4×C61—42no—
43C22×D4×C61—42no—
44C22×D4×C61C2×C412yes—
45C23×C4×C61C2×C411yescharacteristic
46C24×C61—24no—
47C24×C61—22no—
48C24×C61—42no—
49C24×C61—42no—
50C24×C61—84no—
51C24×C61C22⋊C411yescharacteristic
52C23×D61C22⋊C412yes—
53C2×D4×C61—24no—
54C2×D4×C61—22no—
55C2×D4×C61—416no—
56C2×D4×C61—42no—
57C2×D4×C61—42no—
58C2×D4×C61—42no—
59C2×D4×C61—42no—
60C2×D4×C61C22⋊C414yes—
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61—22no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C2×C22⋊D61—24no—
67C2×C22⋊D61—216no—
68C2×C22⋊D61—24no—
69C2×C22⋊D61—42no—
70C2×C22⋊D61—88no—
71C22×Dic61—22no—
72C22×Dic61C2×D412yes—
73#11758222—416no—
74C2×D244—22no—
75C2×D244—41no—
76C2×D244—41no—
77C2×C4×D61—24no—
78C2×C4×D61—24no—
79C2×C4×D61—42no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82C2×Dic122C2×D414yes—
83#11758217—44no—
84#11758217—44no—
85C2×#92420—44no—
86C22⋊Dic61—24no—
87C22⋊Dic61—216no—
88C4⋊Dic61—24no—
89C4×Dic61—22no—
90C4×Dic61C22⋊C414yes—
91C23×C61—21no—
92C23×C61—21no—
93C23×C61—24no—
94C23×C61—42no—
95C23×C61—48no—
96C23×C61—48no—
97C23×C61—42no—
98C23×C61—42no—
99C23×C61—88no—
100C23×C61—88no—
101C23×C61—88no—
102C23×C61#9912yes—
103C23×C61C2×C22⋊C411yescharacteristic
104C22×D61—22no—
105C22×D61—22no—
106C22×D61—22no—
107C22×D61—44no—
108D4×C61—44no—
109D4×C61—44no—
110D4×C61—48no—
111C2×C4×C61—28no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61#9912yes—
117C2×C4×C61C2×C22⋊C412yes—
118C22⋊D61—48no—
119C22⋊D61—816no—
120C2×Dic61—22no—
121C2×Dic61—22no—
122C2×Dic61—24no—
123C2×Dic61—44no—
124C2×Dic61#12014yes—
125D244—44no—
126C4×D61—48no—
127Dic122—44no—
128#92420—84no—
129#12703—611nomaximal, Sylow
130C22×C61—22no—
131C22×C61—22no—
132C22×C61—42no—
133C22×C61—42no—
134C22×C61—48no—
135C22×C61—42no—
136C22×C61—44no—
137C22×C61—84no—
138C22×C61—816no—
139C22×C61—84no—
140C22×C61#37911yescharacteristic
141C22×C61C2×#9911yescharacteristic
142C22×C61C2×#9911yescharacteristic
143C2×D61—44no—
144C2×D61—44no—
145C2×D61—42no—
146C2×D61—82no—
147C4×C61—22no—
148C4×C61—22no—
149Dic61—24no—
150Dic61—44no—
151C2×#535—611no—
152C2×#355—614no—
153#1785—612no—
154C2×C61—21no—
155C2×C61—21no—
156C2×C61—42no—
157C2×C61—84no—
158C2×C61#178111yescharacteristic
159C2×C61#213412yes—
160D61—82no—
161C22×#41—611no—
162C23×D4#692311yescharacteristic
163#535—1228no—
164C2×#127—612no—
165C2×#124—612no—
166C2×#121—1222no—
167C2×#120—1222no—
168C2×#117—611no—
169C2×#101—614no—
170C2×#100—1222no—
171#407—1222no—
172#355—1228no—
173C61#1270311yescharacteristic, complemented, Sylow
174C25—21no—
175C2×#41—1224no—
176C2×#41—2442no—
177C2×#41—2442no—
178C22×Q8—611no—
179C22×D4—24no—
180C22×D4—21no—
181C22×D4—42no—
182C22×D4—42no—
183C22×D4—612no—
184C22×D4—611no—
185C22×D4—1224no—
186C22×D4C2×#692312yes—
187C23×C4—612no—
188C23×C4C2×#692311yescharacteristic
189C2×M16—1224no—
190#127—1224no—
191#127—1224no—
192#124—618no—
193#124—1224no—
194#121—12216no—
195#120—12216no—
196#117—1224no—
197C2×C4⋊C4—1221no—
198C2×C22⋊C4—1224no—
199C2×C22⋊C4—1221no—
200C2×C42—612no—
201#101—1228no—
202#100—2444no—
203C22⋊C8—2444no—
204C24—24no—
205C24—22no—
206C24—42no—
207C24—42no—
208C24—84no—
209C24—612no—
210C24C22⋊#692311yescharacteristic
211#41—24416no—
212C2×Q8—614no—
213C2×Q8—2441no—
214C2×Q8—2441no—
215C2×D4—24no—
216C2×D4—22no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—416no—
220C2×D4—42no—
221C2×D4—42no—
222C2×D4—1224no—
223C2×D4—12216no—
224C2×D4—1224no—
225C2×D4—1222no—
226C2×D4—4888no—
227C2×D4—2441no—
228C2×D4—2441no—
229C2×D4—2442no—
230C2×D4C22⋊#692314yes—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—612no—
235C22×C4—1224no—
236C22×C4—1222no—
237C22×C4—1224no—
238C22×C4—2442no—
239C22×C4C22⋊#692311yescharacteristic
240C22×C4C22×#692311yescharacteristic
241M16—2444no—
242M16—2444no—
243C2×C8—2444no—
244C4⋊C4—1224no—
245C22⋊C4—12216no—
246C22⋊C4—1224no—
247C42—614no—
248C42—1222no—
249C23—21no—
250C23—21no—
251C23—24no—
252C23—42no—
253C23—48no—
254C23—48no—
255C23—42no—
256C23—42no—
257C23—88no—
258C23—88no—
259C23—88no—
260C23—1222no—
261C23—1222no—
262C23—1222no—
263C23—2444no—
264C23#1451983512yes—
265C23C2×C22⋊#692311yescharacteristic
266Q8—2444no—
267D4—44no—
268D4—48no—
269D4—44no—
270D4—48816no—
271D4—2444no—
272D4—2448no—
273C2×C4—28no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—614no—
279C2×C4—1222no—
280C2×C4—1222no—
281C2×C4—1224no—
282C2×C4—2448no—
283C2×C4—2444no—
284C2×C4#1451983512yes—
285C2×C4C2×C22⋊#692312yes—
286C8—4884no—
287C22—22no—
288C22—22no—
289C22—42no—
290C22—42no—
291C22—48no—
292C22—42no—
293C22—44no—
294C22—84no—
295C22—816no—
296C22—84no—
297C22—4882no—
298C22—2444no—
299C22—2444no—
300C22—2442no—
301C22#1684070311yescharacteristic
302C22C2×#1451983511yescharacteristic
303C22C2×#1451983511yescharacteristic
304C4—22no—
305C4—22no—
306C4—1224no—
307C4—2444no—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—84no—
312C2—4882no—
313C2#2146164511yescharacteristic
314C2#2146211812yes—
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC23×D4×C61C4
socleC22×C61C2×#99
prime radicalC2×#16840329C2
cosocleC22×Dic122C23
hypercenterC23×D4#6923
hypocenterC61#12703
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16840670C2semidirect
2. #21461655C2semidirect
4. C2×#14519838C22semidirect
173. C61#12703semidirect

Maximal subgroups

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

subgroupindex
C2×#168406702
#214616552
C2×#168403292
#1270361