Finite Group Databasebeta

← #30602191

Subgroups — #30602191

Order 15616.

566 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C4×#14519834C211yesmaximal, characteristic
2#21460995C211yesmaximal, characteristic
3#21460692C212yesmaximal
4#21460692C212yesmaximal
5#21454128C211yesmaximal, characteristic
6C2×#14519834C2212yes—
7C2×C4×#92420—21no—
8C2×(C2×#6923)⋊C4—21no—
9C2×(C2×#6923)⋊C4—21no—
10C2×(C2×#6923)⋊C4C2212yes—
11#16840628—21no—
12C2×#14519768C411yescharacteristic, complemented
13C2×C42×D61C2211yescharacteristic
14#16839660C411yescharacteristic, complemented
15#16839648—21no—
16#16839644—21no—
17#16839636—21no—
18#16839633—21no—
19#16839627C411yescharacteristic, complemented
20#16839619C2211yescharacteristic
21#16839619C2211yescharacteristic
22C61×#389C411yescharacteristic, complemented
23C23×#6923—22no—
24C22×#92420—22no—
25#14519834—22no—
26#14519834Q814yes—
27C4×#92420—42no—
28(C2×#6923)⋊C4—24no—
29(C2×#6923)⋊C4—24no—
30(C2×#6923)⋊C4—42no—
31C22×C4×D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61C2311yescharacteristic
34#14519768—42no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C42×D61—42no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C42×C61C2×C411yescharacteristic
55#95×C61—21no—
56C23×D61C2×D411yescharacteristic
57C22×#6923—24no—
58C22×#6923—42no—
59C22×#6923—42no—
60C22×#6923—42no—
61C22×#6923—42no—
62C22×#6923—42no—
63C22×#6923—42no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—22no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82C2×C4×D61C2×Q812yes—
83C2×C4×D61#4112yes—
84C2×#92420—24no—
85C2×#92420—42no—
86C2×#92420—42no—
87C4⋊C4×C61—42no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C42×C61—41no—
91#11758198—42no—
92#11758198—42no—
93C4⋊Dic61—42no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96#11758196—42no—
97#11758196—42no—
98C4×Dic61—22no—
99C4×Dic61—22no—
100C4×Dic61—41no—
101C23×C61C2×C22⋊C411yescharacteristic
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61#12411yescharacteristic
107C22×D61C4⋊Q811yescharacteristic
108C22×D61#13512yes—
109C22×D61#13512yes—
110C2×#6923—44no—
111C2×#6923—44no—
112C2×#6923—44no—
113C2×#6923—82no—
114C2×#6923—82no—
115C2×#6923—82no—
116C2×#6923—82no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61#10412yes—
131C2×C4×C61C4×Q812yes—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61#9912yes—
146C2×Dic61C22⋊Q812yes—
147C4×D61—42no—
148C4×D61—42no—
149C4×D61—44no—
150C4×D61—44no—
151#92420—44no—
152#9886—611nomaximal, Sylow
153C22×C61#39111yescharacteristic
154C22×C61C2×#9911yescharacteristic
155C22×C61#41011yescharacteristic
156C22×C61#41611yescharacteristic
157C22×C61#41611yescharacteristic
158C22×C61C2×#10411yescharacteristic
159C22×C61#42111yescharacteristic
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—22no—
165C2×D61—22no—
166C2×D61—22no—
167C2×D61—22no—
168C2×D61#48812yes—
169C2×D61#49912yes—
170#6923—84no—
171C4×C61—22no—
172C4×C61—22no—
173C4×C61—41no—
174C4×C61—81no—
175C4×C61—81no—
176Dic61—22no—
177Dic61—22no—
178Dic61—41no—
179Dic61—81no—
180Dic61—81no—
181#2851—611no—
182C4×C22⋊C8—611no—
183#1434—611no—
184#1294—612no—
185#1294—612no—
186C2×C61#150011yescharacteristic
187C2×C61#150111yescharacteristic
188C2×C61#151611yescharacteristic
189C2×C61#152111yescharacteristic
190C2×C61#198611yescharacteristic
191C2×C61#199111yescharacteristic
192C2×C61#199611yescharacteristic
193D61—22no—
194D61—22no—
195C2×#125—611no—
196C22×C42—611no—
197C2×C22⋊C8—612no—
198C2×C4×C8—1221no—
199#389—611no—
200#389#692311yescharacteristic, complemented
201#387—1221no—
202#387—1221no—
203#385—1221no—
204#385—1221no—
205#382—611no—
206#380—611no—
207#380—611no—
208C2×#95—612no—
209C2×#95—1221no—
210C2×#95—1221no—
211#336—1221no—
212C61#988611yescharacteristic, complemented, Sylow
213C23×C4—611no—
214C23×C4—611no—
215C23×C4—611no—
216C23×C4—1222no—
217C22×C8—1222no—
218#125—2442no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4C2×#692311yescharacteristic
226C2×C4⋊C4C2×#692311yescharacteristic
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229C2×C42—611no—
230C2×C42—611no—
231C2×C42—611no—
232C2×C42—2442no—
233C2×C42C2×#692311yescharacteristic
234C22⋊C8—614no—
235C22⋊C8—1222no—
236C4×C8—2442no—
237#95—21no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242#95—1224no—
243#95—1224no—
244#95—1221no—
245#95—2442no—
246C24—611no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—612no—
252C22×C4—612no—
253C22×C4—611no—
254C22×C4—1222no—
255C22×C4—1222no—
256C22×C4—1222no—
257C22×C4—1222no—
258C22×C4—1224no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—2441no—
262C22×C4—2441no—
263C22×C4—2441no—
264C22×C4—2441no—
265C22×C4—2442no—
266C22×C4—2442no—
267C22×C4—2442no—
268C22×C4—2442no—
269C22×C4—2442no—
270C22×C4—2442no—
271C22×C4C22⋊#692311yescharacteristic
272C22×C4C22⋊#692311yescharacteristic
273C22×C4C22×#692311yescharacteristic
274C2×C8—1224no—
275C2×C8—2442no—
276C2×C8—2442no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2442no—
283C4⋊C4—2442no—
284C4⋊C4—2442no—
285C22⋊C4—2442no—
286C22⋊C4—2442no—
287C42—41no—
288C42—1222no—
289C42—1222no—
290C42—2441no—
291C23—611no—
292C23—611no—
293C23—612no—
294C23—612no—
295C23—1221no—
296C23—1221no—
297C23—1221no—
298C23—1221no—
299C23C2×C22⋊#692311yescharacteristic
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—612no—
314C2×C4—612no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—4882no—
323C2×C4—4882no—
324C2×C4—4882no—
325C2×C4—4882no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2444no—
329C2×C4—2444no—
330C2×C4—2444no—
331C2×C4—2444no—
332C2×C4—2444no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4#1451984212yes—
340C2×C4Q8×#692312yes—
341C8—2444no—
342C22—612no—
343C22—612no—
344C22—1222no—
345C22—1222no—
346C22—1222no—
347C22—1221no—
348C22—1221no—
349C22—1221no—
350C22—1221no—
351C22—1222no—
352C22(C2×#6923)⋊Q811yescharacteristic
353C22D61⋊#9911yescharacteristic
354C22#1684074111yescharacteristic
355C22#1684075211yescharacteristic
356C22#1684075211yescharacteristic
357C22C2×#1451984211yescharacteristic
358C22#1684076011yescharacteristic
359C4—22no—
360C4—22no—
361C4—41no—
362C4—81no—
363C4—81no—
364C4—1222no—
365C4—1222no—
366C4—4884no—
367C4—4881no—
368C4—4881no—
369C4—2441no—
370C2—1222no—
371C2—1222no—
372C2#2146119211yescharacteristic
373C2#2146119711yescharacteristic
374C2#2146124411yescharacteristic
375C2#2146126111yescharacteristic
376C2#2146199411yescharacteristic
377C2#2146200111yescharacteristic
378C2#2146201011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenter#389#6923
hypocenterC61#9886
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
12. C2×#14519768C4semidirect
14. #16839660C4semidirect
19. #16839627C4semidirect
22. C61×#389C4semidirect
200. #389#6923semidirect
212. C61#9886semidirect

Maximal subgroups

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

subgroupindex
C4×#145198342
#214609952
#214606922
#214541282
#988661