Finite Group Databasebeta

← #29595186

Subgroups — #29595186

Order 15616.

628 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 113 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#21448543C211yesmaximal, characteristic
2C2×#16839554C212yesmaximal
3#99×Dic61C212yesmaximal, complemented
4#21443944C211yesmaximal, characteristic, complemented
5C61×#1393C211yesmaximal, characteristic, complemented
6C2×#14519773C2211yescharacteristic
7C2×D4×Dic61C2211yescharacteristic
8C2×#14519739C411yescharacteristic, complemented
9C2×#14519692C2212yes—
10#16839664C411yescharacteristic, complemented
11#16839639—22no—
12#16839638—22no—
13#16839627C411yescharacteristic, complemented
14C22⋊C4×Dic61—22no—
15#16839608C411yescharacteristic, complemented
16#16839554C418yescomplemented
17#16839528—22no—
18C2×#99×C61C2212yes—
19C61×#390C2211yescharacteristic
20C22×D244C2×C411yescharacteristic
21C22×C22⋊D61—22no—
22C23×Dic61D412yes—
23C22×C4×D61—21no—
24#14519773—21no—
25#14519773—21no—
26#14519773C2×C414yes—
27D4×Dic61—42no—
28#14519739—42no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C22⋊Dic61—22no—
31C2×C22⋊Dic61D412yes—
32C2×#11758198—21no—
33C2×#11758198—22no—
34C2×C4×Dic61—42no—
35C2×C4×Dic61C2×C411yescharacteristic
36C2×C4×Dic61C2×C411yescharacteristic
37#14519692—22no—
38#14519692C2×C414yescomplemented
39#14519684—21no—
40#14519684—21no—
41#14519684—22no—
42#14519684—42no—
43C22×D4×C61C2311yescharacteristic
44C2×C4⋊C4×C61C2×C411yescharacteristic
45C2×C22⋊C4×C61—22no—
46C2×C22⋊C4×C61—22no—
47C2×C42×C61C2×C411yescharacteristic
48#99×C61—22no—
49#99×C61C2×C414yescomplemented
50C24×C61C2×D412yes—
51C23×D61—21no—
52C2×D4×C61—41no—
53C2×D4×C61—41no—
54C2×D4×C61C22×C412yes—
55C2×D4×C61#4111yescharacteristic
56C2×D4×C61#4111yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—42no—
60C22×C4×C61C22×C411yescharacteristic
61C2×C22⋊D61—24no—
62C2×C22⋊D61—24no—
63C2×C22⋊D61—82no—
64C2×C22⋊D61—82no—
65C22×Dic61—21no—
66C22×Dic61—22no—
67C22×Dic61—22no—
68C22×Dic61—42no—
69C22×Dic61—82no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C412yes—
72C22×Dic61C22⋊C411yescharacteristic
73C2×D244—21no—
74C2×D244—41no—
75C2×D244—41no—
76C2×D244C4212yescomplemented
77C2×C4×D61—42no—
78C2×C4×D61—82no—
79C4⋊C4×C61—41no—
80C22⋊C4×C61—24no—
81C22⋊C4×C61—42no—
82C22⋊C4×C61—82no—
83C42×C61—41no—
84C22⋊Dic61—24no—
85C22⋊Dic61—42no—
86C22⋊Dic61—42no—
87#11758198—42no—
88#11758198—82no—
89C4⋊Dic61—41no—
90C4×Dic61—21no—
91C4×Dic61—22no—
92C4×Dic61—84no—
93C4×Dic61C4212yescomplemented
94C23×C61—22no—
95C23×C61—22no—
96C23×C61—42no—
97C23×C61—42no—
98C23×C61C2×C22⋊C411yescharacteristic
99C23×C61C4×D412yes—
100C23×C61C4×D412yes—
101C22×D61—22no—
102C22×D61—42no—
103C22×D61—42no—
104C22×D61—41no—
105C22×D61—41no—
106D4×C61—42no—
107D4×C61—41no—
108D4×C61—41no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—41no—
112C2×C4×C61—44no—
113C2×C4×C61—41no—
114C2×C4×C61—42no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—82no—
118C2×C4×C61—82no—
119C2×C4×C61C2×C4211yescharacteristic
120C2×C4×C61#11711yescharacteristic
121C22⋊D61—84no—
122C22⋊D61—84no—
123C2×Dic61—22no—
124C2×Dic61—21no—
125C2×Dic61—22no—
126C2×Dic61—41no—
127C2×Dic61—44no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—42no—
131C2×Dic61—41no—
132C2×Dic61—44no—
133C2×Dic61—82no—
134C2×Dic61—82no—
135C2×Dic61—82no—
136C2×Dic61#9912yes—
137D244—42no—
138D244—42no—
139C4×D61—84no—
140#12628—611nomaximal, Sylow
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—22no—
144C22×C61—22no—
145C22×C61—42no—
146C22×C61—42no—
147C22×C61—42no—
148C22×C61—42no—
149C22×C61—82no—
150C22×C61C4×C22⋊C411yescharacteristic
151C22×C61C2×#9911yescharacteristic
152C22×C61#41011yescharacteristic
153C2×D61—44no—
154C2×D61—42no—
155C2×D61—82no—
156C2×D61—81no—
157C2×D61—81no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—81no—
161C4×C61—84no—
162C4×C61—81no—
163Dic61—22no—
164Dic61—42no—
165Dic61—42no—
166Dic61—41no—
167Dic61—84no—
168#2328—611no—
169C2×#353—612no—
170C4×#99—612no—
171#1393—611no—
172#1393D6111yescharacteristic, complemented
173C2×C61—21no—
174C2×C61—21no—
175C2×C61—42no—
176C2×C61—42no—
177C2×C61C4×#9911yescharacteristic
178C2×C61#212711yescharacteristic
179C2×C61#212811yescharacteristic
180D61—82no—
181C2×#127—611no—
182C2×C4×D4—611no—
183C2×C4×D4—611no—
184C2×#99—612no—
185C2×#99C2×D6112yes—
186#390—611no—
187#390C2×D6111yescharacteristic
188#386—1222no—
189#386—1222no—
190#382—611no—
191C4×C22⋊C4—1222no—
192#376—611no—
193#353—618no—
194#342—1222no—
195C61#1262811yescharacteristic, complemented, Sylow
196C22×D4—611no—
197C22×D4—1222no—
198C22×D4C22×D6111yescharacteristic
199C23×C4—612no—
200C23×C4—1221no—
201#127—614no—
202#127—1221no—
203#127—1221no—
204C4×D4—2442no—
205C4×D4—2442no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4C4×D6111yescharacteristic
208C2×C22⋊C4—22no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—612no—
211C2×C22⋊C4—1222no—
212C2×C22⋊C4—1222no—
213C2×C22⋊C4—1221no—
214C2×C42—611no—
215C2×C42—611no—
216C2×C42—2442no—
217C2×C42C4×D6111yescharacteristic
218#99—22no—
219#99—614no—
220#99—1222no—
221#99C4×D6114yescomplemented
222#95—1221no—
223#95—1221no—
224#95—1222no—
225#95—2442no—
226C24—1221no—
227C24D4×D6112yes—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4—612no—
231C2×D4—1224no—
232C2×D4—1224no—
233C2×D4—1221no—
234C2×D4—4882no—
235C2×D4—4882no—
236C2×D4—2441no—
237C2×D4—2441no—
238C2×D4C2×C4×D6112yes—
239C2×D4#1175822411yescharacteristic
240C2×D4#1175822611yescharacteristic
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—42no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—612no—
247C22×C4—1222no—
248C22×C4—1222no—
249C22×C4—1221no—
250C22×C4—4882no—
251C22×C4—4882no—
252C22×C4—2442no—
253C22×C4—2442no—
254C22×C4C2×C4×D6111yescharacteristic
255C4⋊C4—41no—
256C4⋊C4—2441no—
257C22⋊C4—24no—
258C22⋊C4—42no—
259C22⋊C4—82no—
260C22⋊C4—1224no—
261C22⋊C4—4882no—
262C22⋊C4—2442no—
263C22⋊C4—2442no—
264C22⋊C4—2442no—
265C42—41no—
266C42—612no—
267C42—1222no—
268C42—1221no—
269C42—4884no—
270C23—22no—
271C23—22no—
272C23—42no—
273C23—42no—
274C23—1222no—
275C23—2442no—
276C23—2442no—
277C23—2441no—
278C23—2441no—
279C23C22⋊C4×D6111yescharacteristic
280C23#1451973712yes—
281C23#1451973912yes—
282D4—42no—
283D4—41no—
284D4—41no—
285D4—4884no—
286D4—4884no—
287D4—2442no—
288D4—2442no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—44no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—82no—
298C2×C4—82no—
299C2×C4—612no—
300C2×C4—1221no—
301C2×C4—1222no—
302C2×C4—1222no—
303C2×C4—4884no—
304C2×C4—4882no—
305C2×C4—4882no—
306C2×C4—4882no—
307C2×C4—2441no—
308C2×C4—2444no—
309C2×C4—2444no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2442no—
313C2×C4—2441no—
314C2×C4C42×D6111yescharacteristic
315C2×C4#1451973511yescharacteristic
316C22—21no—
317C22—21no—
318C22—22no—
319C22—22no—
320C22—42no—
321C22—42no—
322C22—42no—
323C22—42no—
324C22—82no—
325C22—4882no—
326C22—4881no—
327C22—4881no—
328C22—2444no—
329C22—2442no—
330C22#1683960911yescharacteristic
331C22#99×D6111yescharacteristic
332C22#1683973411yescharacteristic
333C4—21no—
334C4—21no—
335C4—81no—
336C4—84no—
337C4—81no—
338C4—1222no—
339C4—4884no—
340C4—2442no—
341C4—2442no—
342C4—2441no—
343C2—21no—
344C2—21no—
345C2—42no—
346C2—42no—
347C2—4882no—
348C2#2144560611yescharacteristic
349C2#2144748711yescharacteristic
350C2#2144748911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC2×C4×C61C2×C42
FrattiniC22×D4C22×D61
FittingC61×#1393C2
socleC22×C61C2×#99
prime radicalC2×#14519773C22
cosocleC22×D4×C61C23
hypercenter#1393D61
hypocenterC61#12628
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
3. #99×Dic61C2semidirect
4. #21443944C2semidirect
5. C61×#1393C2semidirect
8. C2×#14519739C4semidirect
10. #16839664C4semidirect
13. #16839627C4semidirect
15. #16839608C4semidirect
16. #16839554C4semidirect
38. #14519692C2×C4semidirect
49. #99×C61C2×C4semidirect
76. C2×D244C42semidirect
93. C4×Dic61C42semidirect
172. #1393D61semidirect
195. C61#12628semidirect
221. #99C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214485432
C2×#168395542
#99×Dic612
#214439442
C61×#13932
#1262861