Finite Group Databasebeta

← #30604082

Subgroups — #30604082

Order 15616.

714 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 714 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461064C212yesmaximal, complemented
2#21460745C212yesmaximal, complemented
3#21460743C212yesmaximal, complemented
4#21448397C211yesmaximal, characteristic
5#16840732—22no—
6#16840605—22no—
7#16840605C2214yes—
8C22×C22⋊Dic61C411yescharacteristic
9C22×C22⋊Dic61C2211yescharacteristic
10#16839642—22no—
11#16839642—22no—
12#16839625C411yescharacteristic
13#16839625C2211yescharacteristic
14#16839618C411yescharacteristic
15#16839618C2211yescharacteristic
16C23×D4×C61C411yescharacteristic
17C2×#11758217—42no—
18C22⋊#92420—24no—
19C22⋊#92420—42no—
20C23×Dic61—21no—
21C23×Dic61D412yes—
22C2×C22⋊Dic61—21no—
23C2×C22⋊Dic61—22no—
24C2×C22⋊Dic61—22no—
25C2×C22⋊Dic61—41no—
26C2×C22⋊Dic61—41no—
27C2×C22⋊Dic61—42no—
28C2×C22⋊Dic61C2×C411yescharacteristic
29C2×C22⋊Dic61C2×C411yescharacteristic
30C2×C22⋊Dic61C2×C411yescharacteristic
31C2×C22⋊Dic61D412yes—
32C2×C22⋊Dic61C2311yescharacteristic
33#14519684—22no—
34#14519684—22no—
35C25×C61C2×C411yescharacteristic
36C25×C61C2×C411yescharacteristic
37C22×D4×C61—21no—
38C22×D4×C61—21no—
39C22×D4×C61—22no—
40C22×D4×C61—22no—
41C22×D4×C61—41no—
42C22×D4×C61—41no—
43C22×D4×C61—42no—
44C23×C4×C61C2×C411yescharacteristic
45C24×C61—21no—
46C24×C61—21no—
47C24×C61—22no—
48C24×C61—21no—
49C24×C61—21no—
50C24×C61—21no—
51C24×C61—21no—
52C24×C61—41no—
53C24×C61—41no—
54C24×C61—82no—
55C24×C61—82no—
56C24×C61C22⋊C411yescharacteristic
57C24×C61C22⋊C411yescharacteristic
58C24×C61M1612yescomplemented
59C24×C61C22×C411yescharacteristic
60C2×D4×C61—24no—
61C2×D4×C61—24no—
62C2×D4×C61—44no—
63C2×D4×C61—44no—
64C2×D4×C61—42no—
65C2×D4×C61—42no—
66C2×D4×C61—44no—
67C2×D4×C61—44no—
68C2×D4×C61—41no—
69C2×D4×C61—41no—
70C2×D4×C61—42no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—41no—
74C22×C4×C61—41no—
75C22×C4×C61M1612yescomplemented
76C22×Dic61—22no—
77C22×Dic61—22no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—42no—
81C22×Dic61—82no—
82C22×Dic61—82no—
83C22×Dic61C22⋊C412yes—
84C22×Dic61C2×D412yes—
85#11758217—84no—
86C2×#92420—44no—
87C22⋊Dic61—41no—
88C22⋊Dic61—42no—
89C22⋊Dic61—41no—
90C22⋊Dic61—42no—
91C22⋊Dic61—41no—
92C22⋊Dic61—41no—
93C22⋊Dic61—82no—
94C22⋊Dic61—82no—
95C23×C61—22no—
96C23×C61—22no—
97C23×C61—22no—
98C23×C61—22no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—22no—
106C23×C61—42no—
107C23×C61—42no—
108C23×C61—42no—
109C23×C61—42no—
110C23×C61—42no—
111C23×C61—42no—
112C23×C61—42no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—82no—
116C23×C61—82no—
117C23×C61—84no—
118C23×C61—82no—
119C23×C61—82no—
120C23×C61—82no—
121C23×C61—82no—
122C23×C61—84no—
123C23×C61—84no—
124C23×C61#9911yescharacteristic
125C23×C61#9911yescharacteristic
126C23×C61#10012yes—
127C23×C61C2×C22⋊C411yescharacteristic
128C23×C61C2×M1611yescharacteristic
129C23×C61C2×M1611yescharacteristic
130D4×C61—44no—
131D4×C61—44no—
132D4×C61—48no—
133C2×C4×C61—22no—
134C2×C4×C61—42no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×Dic61—22no—
139C2×Dic61—22no—
140C2×Dic61—44no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—42no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—82no—
148C2×Dic61—84no—
149#92420—84no—
150#11502—611nomaximal, Sylow
151C22×C61—22no—
152C22×C61—22no—
153C22×C61—22no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—22no—
159C22×C61—42no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—42no—
163C22×C61—42no—
164C22×C61—42no—
165C22×C61—42no—
166C22×C61—42no—
167C22×C61—42no—
168C22×C61—42no—
169C22×C61—42no—
170C22×C61—42no—
171C22×C61—82no—
172C22×C61—82no—
173C22×C61—82no—
174C22×C61—82no—
175C22×C61—82no—
176C22×C61—84no—
177C22×C61—84no—
178C22×C61—82no—
179C22×C61#40711yescharacteristic
180C22×C61C2×#9911yescharacteristic
181C22×C61C2×#10011yescharacteristic
182C4×C61—42no—
183Dic61—42no—
184Dic61—42no—
185Dic61—81no—
186Dic61—81no—
187#2308—611no—
188#1462—612no—
189#1317—612no—
190#1316—612no—
191C2×C61—21no—
192C2×C61—21no—
193C2×C61—41no—
194C2×C61—41no—
195C2×C61—42no—
196C2×C61—41no—
197C2×C61—41no—
198C2×C61—82no—
199C2×C61#146211yescharacteristic
200C2×C61#212112yes—
201C23×D4#692311yescharacteristic
202C22×C22⋊C4—611no—
203C22×C22⋊C4—611no—
204#407—1222no—
205#386—1222no—
206#386—1222no—
207#381—611no—
208#381—611no—
209#379—611no—
210#379—611no—
211#323—614no—
212#323—1222no—
213C61#1150211yescharacteristic, complemented, Sylow
214C25C2×#692311yescharacteristic
215C25C2×#692311yescharacteristic
216C22×D4—22no—
217C22×D4—21no—
218C22×D4—21no—
219C22×D4—22no—
220C22×D4—41no—
221C22×D4—41no—
222C22×D4—42no—
223C23×C4—612no—
224C23×C4—1221no—
225C23×C4C2×#692311yescharacteristic
226C2×M16—2442no—
227C2×C22⋊C4—612no—
228C2×C22⋊C4—611no—
229C2×C22⋊C4—611no—
230C2×C22⋊C4—611no—
231C2×C22⋊C4—611no—
232C2×C22⋊C4—1222no—
233C2×C22⋊C4—1222no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—2441no—
236C2×C22⋊C4—2441no—
237C2×C22⋊C4—2442no—
238C22⋊C8—1224no—
239C22⋊C8—2442no—
240#95—1222no—
241#95—1222no—
242C24—21no—
243C24—21no—
244C24—22no—
245C24—21no—
246C24—21no—
247C24—21no—
248C24—21no—
249C24—41no—
250C24—41no—
251C24—82no—
252C24—82no—
253C24#1175821712yescomplemented
254C24C22⋊#692311yescharacteristic
255C24C22⋊#692311yescharacteristic
256C24C22×#692311yescharacteristic
257C2×D4—24no—
258C2×D4—24no—
259C2×D4—44no—
260C2×D4—44no—
261C2×D4—42no—
262C2×D4—42no—
263C2×D4—44no—
264C2×D4—44no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—42no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—612no—
273C22×C4—612no—
274C22×C4—1222no—
275C22×C4—1222no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—4882no—
279C22×C4—4882no—
280C22×C4—2442no—
281C22×C4#1175821712yescomplemented
282M16—4884no—
283C2×C8—2444no—
284C22⋊C4—4882no—
285C22⋊C4—4882no—
286C22⋊C4—2441no—
287C22⋊C4—2442no—
288C22⋊C4—2441no—
289C22⋊C4—2442no—
290C22⋊C4—2441no—
291C22⋊C4—2441no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—22no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23—42no—
307C23—42no—
308C23—42no—
309C23—42no—
310C23—41no—
311C23—41no—
312C23—82no—
313C23—82no—
314C23—82no—
315C23—84no—
316C23—82no—
317C23—82no—
318C23—82no—
319C23—84no—
320C23—84no—
321C23#1451983511yescharacteristic
322C23#1451983511yescharacteristic
323C23#1451983712yes—
324C23C2×C22⋊#692311yescharacteristic
325C23C2×#1175821711yescharacteristic
326C23C2×#1175821711yescharacteristic
327D4—44no—
328D4—44no—
329D4—48no—
330C2×C4—22no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—1222no—
336C2×C4—1222no—
337C2×C4—4884no—
338C2×C4—4882no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2444no—
344C2×C4—2442no—
345C2×C4—2442no—
346C8—4884no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—22no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—82no—
368C22—82no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22—84no—
373C22—84no—
374C22—82no—
375C22#1684073211yescharacteristic
376C22C2×#1451983511yescharacteristic
377C22C2×#1451983711yescharacteristic
378C4—42no—
379C4—4881no—
380C4—4881no—
381C4—2442no—
382C4—2442no—
383C2—21no—
384C2—21no—
385C2—41no—
386C2—41no—
387C2—41no—
388C2—41no—
389C2—42no—
390C2—82no—
391C2#2146106411yescharacteristic
392C2#2146207412yes—
subgroupG/H
centerC22C2×#14519835
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
Fitting, prime radicalC23×D4×C61C4
socleC22×C61C2×#99
cosocleC2×C22⋊Dic61C23
hypercenterC23×D4#6923
hypocenterC61#11502
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C25 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. #21461064C2semidirect
2. #21460745C2semidirect
3. #21460743C2semidirect
58. C24×C61M16semidirect
75. C22×C4×C61M16semidirect
213. C61#11502semidirect
253. C24#11758217semidirect
281. C22×C4#11758217semidirect

Maximal subgroups

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

subgroupindex
#214610642
#214607452
#214607432
#214483972
#1150261