Finite Group Databasebeta

← #29573636

Subgroups — #29573636

Order 15616.

480 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 95 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#21448759C211yesmaximal, characteristic
2C4×#14519692C211yesmaximal, characteristic
3#21443704C212yesmaximal, complemented
4#21443673C212yesmaximal, complemented
5C61×#1465C211yesmaximal, characteristic
6C2×#14519692—21no—
7#16839655—21no—
8#16839648—21no—
9#16839642—21no—
10#16839630C411yescharacteristic, complemented
11#16839625C2211yescharacteristic
12#16839622C411yescharacteristic, complemented
13C22⋊C4×Dic61—21no—
14C4×C22⋊Dic61C2212yes—
15C4×C22⋊Dic61C2211yescharacteristic
16#16839608C411yescharacteristic, complemented
17C2×#14519684C411yescharacteristic, complemented
18#16839529—21no—
19C2×C4×D4×C61C2211yescharacteristic
20C61×#407C2212yes—
21C61×#324—21no—
22C61×#323—21no—
23C23×Dic61—21no—
24C2×C4⋊Dic61—21no—
25C2×C22⋊Dic61—22no—
26C2×C22⋊Dic61—21no—
27C2×C22⋊Dic61—21no—
28C2×C22⋊Dic61—21no—
29C2×C4×Dic61—21no—
30C2×C4×Dic61—21no—
31C2×C4×Dic61—22no—
32#14519692—24no—
33#14519684—21no—
34#14519684—21no—
35#14519684—21no—
36#14519684—21no—
37#14519684—21no—
38#14519684—22no—
39#14519684C2×C411yescharacteristic
40#14519684C2×C411yescharacteristic
41#14519684C2×C411yescharacteristic
42#14519684C2×C411yescharacteristic
43C22×D4×C61D411yescharacteristic
44C23×C4×C61C2×C411yescharacteristic
45C23×C4×C61C2311yescharacteristic
46C2×M16×C61—22no—
47C4×D4×C61—22no—
48C4×D4×C61—22no—
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C22⋊C4×C61D411yescharacteristic
51C2×C22⋊C4×C61D411yescharacteristic
52C2×C42×C61C2×C411yescharacteristic
53C22⋊C8×C61—22no—
54C22⋊C8×C61—22no—
55C24×C61C22⋊C411yescharacteristic
56C24×C61C2×D411yescharacteristic
57C2×D4×C61—22no—
58C2×D4×C61—22no—
59C2×D4×C61—41no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—81no—
63C22×C4×C61—81no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61#4112yes—
70C22×C4×C61#4112yes—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—42no—
76C22×Dic61—42no—
77C22×Dic61—42no—
78C22×Dic61—81no—
79M16×C61—82no—
80C2×C8×C61—42no—
81C4⋊C4×C61—22no—
82C22⋊C4×C61—22no—
83C22⋊C4×C61—22no—
84C42×C61—21no—
85C42×C61—21no—
86C22⋊Dic61—24no—
87C22⋊Dic61—42no—
88C22⋊Dic61—42no—
89C22⋊Dic61—42no—
90C22⋊Dic61—81no—
91C4⋊Dic61—81no—
92C4×Dic61—42no—
93C4×Dic61—81no—
94C4×Dic61—82no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—41no—
100C23×C61—41no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61#10412yes—
104C23×C61C2×C22⋊C411yescharacteristic
105C23×C61#12312yes—
106D4×C61—44no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—41no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—81no—
119C2×C4×C61—81no—
120C2×C4×C61#11711yescharacteristic
121C2×C4×C61#11711yescharacteristic
122C2×C4×C61#12312yes—
123C2×Dic61—22no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—44no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—84no—
137C2×Dic61—82no—
138C2×Dic61—82no—
139C8×C61—82no—
140#8776—611nomaximal, Sylow
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—22no—
144C22×C61—22no—
145C22×C61—22no—
146C22×C61—22no—
147C22×C61—42no—
148C22×C61—42no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—81no—
152C22×C61—81no—
153C22×C61#38111yescharacteristic
154C22×C61C2×#10411yescharacteristic
155C22×C61#42111yescharacteristic
156C4×C61—22no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61—41no—
162Dic61—42no—
163Dic61—81no—
164Dic61—81no—
165Dic61—81no—
166Dic61—84no—
167#2353—611no—
168C4×#99—611no—
169#1465D6111yescharacteristic
170#1297—612no—
171#1284—612no—
172C2×C61—21no—
173C2×C61—21no—
174C2×C61—42no—
175C2×C61—42no—
176C2×C61#182611yescharacteristic
177C2×C61#182711yescharacteristic
178C2×C61#182811yescharacteristic
179C2×C4×D4C2×D6111yescharacteristic
180C2×#99—1221no—
181#407C2×D6112yes—
182#388—1221no—
183#387—1221no—
184#386—1221no—
185#383—611no—
186#381—611no—
187#380—611no—
188C4×C22⋊C4—611no—
189C4×C22⋊C4—612no—
190C4×C22⋊C4—1221no—
191#376—611no—
192C2×#95—611no—
193#342—1221no—
194#324—21no—
195#323—21no—
196C61#877611yescharacteristic, complemented, Sylow
197C22×D4D24411yescharacteristic
198C23×C4—1221no—
199C23×C4C4×D6111yescharacteristic
200C23×C4C22×D6111yescharacteristic
201C2×M16—22no—
202C4×D4—22no—
203C4×D4—22no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4C22⋊D6111yescharacteristic
206C2×C22⋊C4—1222no—
207C2×C22⋊C4—1221no—
208C2×C22⋊C4—1221no—
209C2×C22⋊C4—1221no—
210C2×C22⋊C4D24411yescharacteristic
211C2×C22⋊C4C22⋊D6111yescharacteristic
212C2×C42—1221no—
213C2×C42—1222no—
214C2×C42—1221no—
215C2×C42C4×D6111yescharacteristic
216#99—1224no—
217C22⋊C8—22no—
218C22⋊C8—22no—
219#95—611no—
220#95—611no—
221#95—611no—
222#95—611no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95—1222no—
229C24#1175819811yescharacteristic
230C24C2×D24411yescharacteristic
231C2×D4—22no—
232C2×D4—22no—
233C2×D4—41no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—81no—
237C22×C4—81no—
238C22×C4—1221no—
239C22×C4—1221no—
240C22×C4—1221no—
241C22×C4—1221no—
242C22×C4—4881no—
243C22×C4—2442no—
244C22×C4—2442no—
245C22×C4—2442no—
246C22×C4#1175819811yescharacteristic
247C22×C4#1175819811yescharacteristic
248C22×C4#1175819811yescharacteristic
249C22×C4C2×C4×D6111yescharacteristic
250C22×C4#1175822412yes—
251C22×C4#1175822412yes—
252C22×C4C2×C22⋊D6111yescharacteristic
253M16—82no—
254C2×C8—42no—
255C4⋊C4—22no—
256C4⋊C4—4881no—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—1224no—
260C22⋊C4—4881no—
261C22⋊C4—2442no—
262C22⋊C4—2442no—
263C22⋊C4—2442no—
264C42—21no—
265C42—21no—
266C42—4882no—
267C42—4881no—
268C42—2442no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23#1451970312yes—
278C23C2×#1175819811yescharacteristic
279C23#1451976112yes—
280D4—44no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—1222no—
295C2×C4—4882no—
296C2×C4—4882no—
297C2×C4—4884no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2444no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4#1451973311yescharacteristic
311C2×C4#1451973311yescharacteristic
312C2×C4#1451975812yes—
313C8—82no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—42no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22#1683962311yescharacteristic
327C22C2×#1451970311yescharacteristic
328C22#1683977811yescharacteristic
329C4—22no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—4881no—
336C4—4881no—
337C4—4881no—
338C4—4884no—
339C4—2442no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—42no—
344C2#2144591611yescharacteristic
345C2#2144592411yescharacteristic
346C2#2144592511yescharacteristic
subgroupG/H
centerC22#16839623
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1465C2
socleC22×C61#381
prime radicalC22×D4×C61D4
cosocleC23×C4×C61C23
hypercenter#1465D61
hypocenterC61#8776
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #21443704C2semidirect
4. #21443673C2semidirect
10. #16839630C4semidirect
12. #16839622C4semidirect
16. #16839608C4semidirect
17. C2×#14519684C4semidirect
196. C61#8776semidirect

Maximal subgroups

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

subgroupindex
#214487592
C4×#145196922
#214437042
#214436732
C61×#14652
#877661