Finite Group Databasebeta

← #30603138

Subgroups — #30603138

Order 15616.

2006 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 2006 conjugacy classes of subgroups — too many to draw. Only its 184 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
1C22×#14519837C214yesmaximal, complemented
2#21461482C212yesmaximal, complemented
3C22×#14519773C211yesmaximal, characteristic
4C22×#11758217C2214yes—
5C2×#14519837—216no—
6C2×#14519837—28no—
7#16840628—24no—
8C23×D244C411yescharacteristic
9C23×C22⋊D61C412yes—
10C23×C22⋊D61C2212yes—
11C2×#14519773—24no—
12C2×#14519773—28no—
13C22×C4×Dic61C2211yescharacteristic
14C23×D4×C61C411yescharacteristic
15C2×#11758217—24no—
16C2×#11758217—28no—
17C2×#11758217—28no—
18C2×#11758217D418yescomplemented
19C22×#92420—24no—
20#14519837—232no—
21C24×D61C2×C412yes—
22C22×D244—24no—
23C22×D244—22no—
24C22×D244—44no—
25C22×C22⋊D61—24no—
26C22×C22⋊D61—24no—
27C22×C22⋊D61—24no—
28C22×C22⋊D61—28no—
29C22×C22⋊D61—24no—
30C22×C22⋊D61—24no—
31C22×C22⋊D61—28no—
32C22×C22⋊D61—48no—
33C22×C22⋊D61D418yes—
34C23×Dic61C2×C411yescharacteristic
35C23×Dic61C2311yescharacteristic
36#14519773—232no—
37C2×C4×Dic61—24no—
38C2×C4×Dic61D414yes—
39C25×C61C2×C412yes—
40C22×D4×C61—24no—
41C22×D4×C61—22no—
42C22×D4×C61—44no—
43C23×C4×C61C2×C411yescharacteristic
44C24×C61—22no—
45C24×C61—22no—
46C24×C61—28no—
47C24×C61—44no—
48C24×C61—44no—
49C24×C61C22⋊C414yes—
50C24×C61C22×C411yescharacteristic
51C23×D61—22no—
52C23×D61—22no—
53C23×D61—28no—
54C23×D61—44no—
55C23×D61—44no—
56C23×D61C22⋊C414yes—
57C2×D4×C61—28no—
58C2×D4×C61—416no—
59C2×D4×C61—44no—
60C2×D4×C61—44no—
61C22×C4×C61—22no—
62C22×C4×C61—24no—
63C22×C4×C61C22⋊C412yes—
64C2×C22⋊D61—216no—
65C2×C22⋊D61—28no—
66C2×C22⋊D61—216no—
67C2×C22⋊D61—216no—
68C2×C22⋊D61—28no—
69C2×C22⋊D61—416no—
70C2×C22⋊D61—416no—
71C2×C22⋊D61—48no—
72C2×C22⋊D61—48no—
73C2×C22⋊D61—44no—
74C2×C22⋊D61—48no—
75C2×C22⋊D61—48no—
76C2×C22⋊D61—44no—
77C2×C22⋊D61—44no—
78C2×C22⋊D61—44no—
79C22×Dic61—22no—
80C22×Dic61—24no—
81C22×Dic61C22⋊C412yes—
82C22×Dic61C2×D414yes—
83C22×Dic61C2×D414yes—
84C22×Dic61C2×D412yes—
85C22×Dic61#4114yes—
86C2×D244—28no—
87C2×D244—416no—
88C2×D244—44no—
89C2×D244—44no—
90#11758217—216no—
91#11758217—48no—
92C2×#92420—28no—
93C2×#92420—44no—
94C2×#92420—44no—
95C4×Dic61—28no—
96C23×C61—22no—
97C23×C61—22no—
98C23×C61—24no—
99C23×C61—28no—
100C23×C61—44no—
101C23×C61—44no—
102C23×C61—44no—
103C23×C61—44no—
104C23×C61—44no—
105C23×C61—44no—
106C23×C61—44no—
107C23×C61—44no—
108C23×C61—816no—
109C23×C61C2×C22⋊C412yes—
110C23×C61C2×C22⋊C411yescharacteristic
111C23×C61C4×D414yes—
112C22×D61—24no—
113C22×D61—28no—
114C22×D61—44no—
115C22×D61—44no—
116C22×D61—44no—
117C22×D61—44no—
118C22×D61—44no—
119C22×D61—44no—
120C22×D61—44no—
121C22×D61—44no—
122C22×D61—816no—
123D4×C61—416no—
124C2×C4×C61—28no—
125C2×C4×C61—22no—
126C2×C4×C61—22no—
127C2×C4×C61#10014yescomplemented
128C22⋊D61—432no—
129C22⋊D61—416no—
130C22⋊D61—416no—
131C2×Dic61—28no—
132C2×Dic61—22no—
133C2×Dic61—22no—
134C2×Dic61#10014yescomplemented
135C2×Dic61#12014yes—
136C2×Dic61#12014yes—
137C2×Dic61#12118yes—
138C2×Dic61#12114yes—
139C2×Dic61#12314yes—
140C2×Dic61#12412yes—
141C2×Dic61#12712yes—
142D244—416no—
143#92420—48no—
144#10981—611nomaximal, Sylow
145C22×C61—28no—
146C22×C61—22no—
147C22×C61—22no—
148C22×C61—44no—
149C22×C61—44no—
150C22×C61—44no—
151C22×C61—88no—
152C22×C61—88no—
153C22×C61—88no—
154C22×C61#37911yescharacteristic
155C22×C61#38614yes—
156C22×C61#39012yes—
157C22×C61C2×#10012yes—
158C22×C61C2×#10012yes—
159C2×D61—44no—
160C2×D61—44no—
161C2×D61—44no—
162C2×D61—88no—
163C2×D61—88no—
164C2×D61—88no—
165C4×C61—24no—
166Dic61—24no—
167Dic61#39214yes—
168Dic61#39414yes—
169C22×#127—611no—
170C22×#100—614no—
171#1728—612no—
172C2×C61—24no—
173C2×C61—84no—
174C2×C61#143811yescharacteristic
175C2×C61#178311yescharacteristic
176C2×C61#178311yescharacteristic
177C2×C61#196514yes—
178D61—84no—
179C23×D4—612no—
180C23×D4—612no—
181C23×D4—611no—
182C23×D4#692311yescharacteristic
183C22×M16—614no—
184C2×#127—1224no—
185C2×#127—1228no—
186C22×C42—611no—
187C2×#100—12216no—
188C2×#100—1228no—
189#336—1224no—
190C61#1098111yescharacteristic, complemented, Sylow
191C25—612no—
192C25C2×#692312yes—
193C22×D4—24no—
194C22×D4—22no—
195C22×D4—44no—
196C22×D4—618no—
197C22×D4—1224no—
198C22×D4—1224no—
199C22×D4—1224no—
200C22×D4—1224no—
201C22×D4—1228no—
202C22×D4—1228no—
203C22×D4—1224no—
204C22×D4—1224no—
205C22×D4—1222no—
206C22×D4—2444no—
207C22×D4—2448no—
208C23×C4—611no—
209C23×C4—611no—
210C23×C4C2×#692311yescharacteristic
211C2×M16—618no—
212C2×M16—1224no—
213C2×M16—1228no—
214C2×M16—1228no—
215C22×C8—1224no—
216#127—12232no—
217C2×C42—614no—
218C2×C42—1224no—
219#100—12232no—
220C24—22no—
221C24—22no—
222C24—28no—
223C24—44no—
224C24—44no—
225C24—614no—
226C24—1228no—
227C24—1222no—
228C24—1222no—
229C24—2444no—
230C24—2444no—
231C24C22⋊#692314yes—
232C24C22×#692311yescharacteristic
233C2×D4—28no—
234C2×D4—416no—
235C2×D4—44no—
236C2×D4—44no—
237C2×D4—1228no—
238C2×D4—1228no—
239C2×D4—12216no—
240C2×D4—12216no—
241C2×D4—1228no—
242C2×D4—12216no—
243C2×D4—24416no—
244C2×D4—2444no—
245C2×D4—2444no—
246C2×D4—2448no—
247C2×D4—2444no—
248C2×D4—2448no—
249C2×D4—2444no—
250C2×D4—2444no—
251C2×D4—2448no—
252C2×D4—24416no—
253C2×D4—24416no—
254C2×D4—2448no—
255C2×D4—2444no—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—614no—
259C22×C4—612no—
260C22×C4—614no—
261C22×C4—614no—
262C22×C4—612no—
263C22×C4—1224no—
264C22×C4—1222no—
265C22×C4C22⋊#692312yes—
266M16—12216no—
267M16—2448no—
268C2×C8—1228no—
269C2×C8—2444no—
270C2×C8—2444no—
271C42—1228no—
272C23—22no—
273C23—22no—
274C23—24no—
275C23—28no—
276C23—44no—
277C23—44no—
278C23—44no—
279C23—44no—
280C23—44no—
281C23—44no—
282C23—44no—
283C23—44no—
284C23—816no—
285C23—1228no—
286C23—1224no—
287C23—48816no—
288C23—2444no—
289C23—2444no—
290C23—2444no—
291C23—2444no—
292C23—2444no—
293C23—2444no—
294C23—2444no—
295C23—2444no—
296C23C2×C22⋊#692312yes—
297C23C2×C22⋊#692311yescharacteristic
298C23D4×#692314yes—
299D4—416no—
300D4—24416no—
301D4—24416no—
302D4—24416no—
303D4—24432no—
304C2×C4—28no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—614no—
308C2×C4—618no—
309C2×C4—614no—
310C2×C4—614no—
311C2×C4—612no—
312C2×C4—612no—
313C2×C4—614no—
314C2×C4—614no—
315C2×C4—1228no—
316C2×C4—1222no—
317C2×C4—1222no—
318C2×C4#1451983714yescomplemented
319C8—2448no—
320C22—22no—
321C22—22no—
322C22—28no—
323C22—44no—
324C22—44no—
325C22—44no—
326C22—88no—
327C22—88no—
328C22—88no—
329C22—4888no—
330C22—4888no—
331C22—4888no—
332C22—2444no—
333C22—2444no—
334C22—2444no—
335C22#1684070311yescharacteristic
336C22#1684071014yes—
337C22#1684071412yes—
338C22C2×#1451983712yes—
339C22D61⋊#10012yes—
340C4—24no—
341C4—614no—
342C4—614no—
343C4—1224no—
344C2—24no—
345C2—84no—
346C2—4884no—
347C2#2146100111yescharacteristic
348C2#2146165111yescharacteristic
349C2#2146165211yescharacteristic
350C2#2146196114yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC23×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×#14519773C2
cosocleC23×Dic61C23
hypercenterC23×D4#6923
hypocenterC61#10981
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C22×#14519837C2semidirect
2. #21461482C2semidirect
18. C2×#11758217D4semidirect
127. C2×C4×C61#100semidirect
134. C2×Dic61#100semidirect
190. C61#10981semidirect
318. C2×C4#14519837semidirect

Maximal subgroups

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

subgroupindex
C22×#145198372
#214614822
C22×#145197732
#1098161