Finite Group Databasebeta

← #29589600

Subgroups — #29589600

Order 15616.

414 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 83 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#21450293C211yesmaximal, characteristic
2C2×#16839488C211yesmaximal, characteristic
3#21443764C212yesmaximal, complemented
4#21443752C212yesmaximal, complemented
5C61×#1463C211yesmaximal, characteristic
6C2×#14519756C411yescharacteristic
7C2×C22⋊#92418—21no—
8#16839693—21no—
9#16839693—21no—
10#16839667C411yescharacteristic
11#16839667C2211yescharacteristic
12#16839635—21no—
13#16839635—21no—
14#16839631C411yescharacteristic
15#16839631C2211yescharacteristic
16C4×C22⋊Dic61C411yescharacteristic
17#16839488—21no—
18#16839488C2212yes—
19C22×C4⋊C4×C61C2211yescharacteristic
20C61×#407—21no—
21C61×#324—21no—
22C61×#324C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C22×#92418—41no—
25#14519756—41no—
26#14519756—41no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C4×Dic61C2×C411yescharacteristic
36C2×C4×Dic61C2×C411yescharacteristic
37C22⋊#92418—22no—
38C22⋊#92418—41no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44C23×C4×C61C2×C411yescharacteristic
45C23×C4×C61D411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C2×M16×C61—41no—
48C2×C4⋊C4×C61—41no—
49C2×C4⋊C4×C61—41no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C4⋊C4×C61C2311yescharacteristic
54C22⋊C8×C61—22no—
55C22⋊C8×C61—41no—
56C24×C61C22⋊C411yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—22no—
64C22×C4×C61—41no—
65C22×C4×C61—81no—
66C22×C4×C61—81no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C2×Dic122—22no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80M16×C61—82no—
81C2×C8×C61—42no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C22⋊Dic61—24no—
87C22⋊Dic61—41no—
88C22⋊Dic61—41no—
89C4⋊Dic61—41no—
90#11758196—42no—
91#11758196—81no—
92#11758196—81no—
93#11758196—81no—
94#11758196—81no—
95C4×Dic61—22no—
96C4×Dic61—41no—
97C2×#92418—42no—
98C2×#92418—82no—
99C23×C61—22no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—41no—
103C23×C61#9911yescharacteristic
104C23×C61#9911yescharacteristic
105C23×C61C2×C22⋊C411yescharacteristic
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—42no—
116C2×C4×C61—42no—
117C2×C4×C61—42no—
118C2×C4×C61—42no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—81no—
124C2×C4×C61—81no—
125C2×C4×C61#13112yes—
126C2×Dic61—22no—
127C2×Dic61—22no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138Dic122—82no—
139C8×C61—82no—
140#92418—82no—
141#11555—611nomaximal, Sylow
142C22×C61—21no—
143C22×C61—21no—
144C22×C61—21no—
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—42no—
150C22×C61—42no—
151C22×C61#35612yes—
152C22×C61#40811yescharacteristic
153C22×C61C2×#9911yescharacteristic
154C22×C61#41311yescharacteristic
155C4×C61—22no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61—41no—
161Dic61—42no—
162Dic61—42no—
163Dic61—81no—
164Dic61—81no—
165#2502—611no—
166#1463D6111yescharacteristic
167C2×#324—611no—
168#1325—612no—
169#1319—612no—
170C2×C61—21no—
171C2×C61—21no—
172C2×C61—22no—
173C2×C61—41no—
174C2×C61#146811yescharacteristic
175C2×C61#212711yescharacteristic
176C2×C61C2×#35611yescharacteristic
177C2×C22⋊Q8—611no—
178C22×C4⋊C4C2×D6111yescharacteristic
179#407—21no—
180C2×C22⋊C8—1221no—
181#398—1221no—
182#398—1221no—
183#391—611no—
184#391—611no—
185#385—1221no—
186#385—1221no—
187#384—611no—
188#384—611no—
189C4×C22⋊C4—611no—
190#324—21no—
191#324—612no—
192#324—1221no—
193#324C2×D6112yes—
194C61#1155511yescharacteristic, complemented, Sylow
195C22×Q8—611no—
196C23×C4C4×D6111yescharacteristic
197C23×C4D24411yescharacteristic
198C23×C4C22⋊D6111yescharacteristic
199C2×M16—41no—
200C22×C8—2441no—
201C22⋊Q8—2441no—
202C22⋊Q8—2441no—
203C2×C4⋊C4—41no—
204C2×C4⋊C4—41no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4C4×D6111yescharacteristic
212C2×C4⋊C4D24411yescharacteristic
213C2×C4⋊C4C22⋊D6111yescharacteristic
214C2×C4⋊C4C22×D6111yescharacteristic
215C2×C22⋊C4—1221no—
216C2×C22⋊C4—1221no—
217C2×C42—611no—
218C2×C42—611no—
219C22⋊C8—22no—
220C22⋊C8—41no—
221C22⋊C8—1222no—
222C22⋊C8—2441no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228C24#1175819811yescharacteristic
229C2×Q8—1222no—
230C2×Q8—2441no—
231C2×Q8—2441no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—41no—
240C22×C4—81no—
241C22×C4—81no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4#1175819811yescharacteristic
247C22×C4#1175819811yescharacteristic
248C22×C4#1175819811yescharacteristic
249C22×C4C2×C4×D6111yescharacteristic
250C22×C4C2×D24411yescharacteristic
251C22×C4C2×C22⋊D6111yescharacteristic
252M16—82no—
253C2×C8—42no—
254C2×C8—4882no—
255C2×C8—2442no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—4881no—
261C4⋊C4—4881no—
262C4⋊C4—4881no—
263C4⋊C4—4881no—
264C4⋊C4—2441no—
265C4⋊C4—2442no—
266C22⋊C4—1224no—
267C22⋊C4—2441no—
268C22⋊C4—2441no—
269C42—1222no—
270C42—2441no—
271C23—21no—
272C23—21no—
273C23—22no—
274C23—41no—
275C23#1451969111yescharacteristic
276C23#1451969111yescharacteristic
277C23C2×#1175819811yescharacteristic
278Q8—4882no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—1222no—
299C2×C4—1222no—
300C2×C4—2441no—
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#1451978512yes—
311C8—82no—
312C8—4882no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—42no—
321C22—42no—
322C22#1683956012yes—
323C22#1683973011yescharacteristic
324C22C2×#1451969111yescharacteristic
325C22#1683974411yescharacteristic
326C4—22no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—4881no—
333C4—4881no—
334C4—2442no—
335C4—2442no—
336C2—21no—
337C2—21no—
338C2—22no—
339C2—41no—
340C2#2144416811yescharacteristic
341C2#2144748611yescharacteristic
342C2C2×#1683956011yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1463C2
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1463D61
hypocenterC61#11555
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
3. #21443764C2semidirect
4. #21443752C2semidirect
194. C61#11555semidirect

Maximal subgroups

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

subgroupindex
#214502932
C2×#168394882
#214437642
#214437522
C61×#14632
#1155561