Finite Group Databasebeta

← #29589419

Subgroups — #29589419

Order 15616.

434 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 87 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#21448443C211yesmaximal, characteristic
2#21444149C211yesmaximal, characteristic
3#21443764C212yesmaximal, complemented
4#21443762C212yesmaximal, complemented
5C61×#1463C211yesmaximal, characteristic
6C2×#14519736C411yescharacteristic
7C2×#14519736C411yescharacteristic
8#16839726—21no—
9#16839658—21no—
10#16839658—21no—
11#16839635—21no—
12#16839635—21no—
13#16839631C411yescharacteristic
14#16839631C2211yescharacteristic
15#16839627C411yescharacteristic
16#16839627C2211yescharacteristic
17#16839488—21no—
18#16839488C2212yes—
19C22×C4⋊C4×C61C2211yescharacteristic
20C61×#407—21no—
21C61×#324—21no—
22C61×#324C2212yes—
23C2×#11758194—41no—
24#14519736—22no—
25#14519736—22no—
26#14519736—41no—
27#14519736—41no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61C2×C411yescharacteristic
40C22⋊#92418—22no—
41C22⋊#92418—41no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46C23×C4×C61C2×C411yescharacteristic
47C23×C4×C61D411yescharacteristic
48C23×C4×C61D411yescharacteristic
49C2×M16×C61—41no—
50C2×C4⋊C4×C61—41no—
51C2×C4⋊C4×C61—41no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61D411yescharacteristic
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C4⋊C4×C61C2311yescharacteristic
56C22⋊C8×C61—22no—
57C22⋊C8×C61—41no—
58C24×C61C22⋊C411yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—22no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—81no—
69C22×C4×C61—81no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
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—24no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92#11758196—81no—
93#11758196—81no—
94#11758196—81no—
95#11758196—81no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—42no—
99C4×Dic61M1612yescomplemented
100C4×Dic61M1612yescomplemented
101#11758194—82no—
102C2×#92418—42no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61#9911yescharacteristic
108C23×C61#9911yescharacteristic
109C23×C61C2×C22⋊C411yescharacteristic
110C2×C4×C61—22no—
111C2×C4×C61—22no—
112C2×C4×C61—22no—
113C2×C4×C61—22no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—42no—
123C2×C4×C61—42no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61#10112yes—
131C2×C4×C61C2×M1611yescharacteristic
132C2×C4×C61C2×M1611yescharacteristic
133C2×Dic61—22no—
134C2×Dic61—22no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—42no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C8×C61—82no—
145#92418—82no—
146#11514—611nomaximal, Sylow
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—42no—
156C22×C61—42no—
157C22×C61#40711yescharacteristic
158C22×C61C2×#9911yescharacteristic
159C22×C61C2×#10111yescharacteristic
160C4×C61—22no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61—41no—
167Dic61—42no—
168Dic61—42no—
169Dic61—81no—
170Dic61—81no—
171#2317—611no—
172#1463—611no—
173#1463D6111yescharacteristic
174#1325—612no—
175#1324—612no—
176C2×C61—21no—
177C2×C61—21no—
178C2×C61—41no—
179C2×C61—41no—
180C2×C61#146311yescharacteristic
181C2×C61#212711yescharacteristic
182C2×C61#213311yescharacteristic
183C2×#117—611no—
184C2×#117—611no—
185C22×C4⋊C4C2×D6111yescharacteristic
186#407—21no—
187#407—1221no—
188#389—1221no—
189#389—1221no—
190#385—1221no—
191#385—1221no—
192#384—611no—
193#384—611no—
194#382—611no—
195#382—611no—
196#324—21no—
197#324—612no—
198#324—1221no—
199#324C2×D6112yes—
200C61#1151411yescharacteristic, complemented, Sylow
201C23×C4C4×D6111yescharacteristic
202C23×C4D24411yescharacteristic
203C23×C4C22⋊D6111yescharacteristic
204C2×M16—41no—
205C2×M16—2441no—
206#117—1222no—
207#117—1222no—
208#117—2441no—
209#117—2441no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4C4×D6111yescharacteristic
220C2×C4⋊C4D24411yescharacteristic
221C2×C4⋊C4C22⋊D6111yescharacteristic
222C2×C4⋊C4C22×D6111yescharacteristic
223C2×C22⋊C4—1221no—
224C2×C22⋊C4—1221no—
225C2×C42—611no—
226C2×C42—611no—
227C2×C42—1221no—
228C22⋊C8—22no—
229C22⋊C8—41no—
230C22⋊C8—1222no—
231C22⋊C8—2441no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236C24#1175819811yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—81no—
247C22×C4—81no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4#1175819811yescharacteristic
253C22×C4#1175819811yescharacteristic
254C22×C4#1175819811yescharacteristic
255C22×C4C2×C4×D6111yescharacteristic
256C22×C4C2×D24411yescharacteristic
257C22×C4C2×C22⋊D6111yescharacteristic
258M16—82no—
259M16—4882no—
260C2×C8—42no—
261C2×C8—2442no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—1224no—
267C4⋊C4—4881no—
268C4⋊C4—4881no—
269C4⋊C4—4881no—
270C4⋊C4—4881no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C22⋊C4—1224no—
274C22⋊C4—2441no—
275C22⋊C4—2441no—
276C42—612no—
277C42—612no—
278C42—1221no—
279C42—1221no—
280C42—2442no—
281C23—21no—
282C23—21no—
283C23—41no—
284C23—41no—
285C23#1451969111yescharacteristic
286C23#1451969111yescharacteristic
287C23C2×#1175819811yescharacteristic
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—1222no—
309C2×C4—1222no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2442no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4#1451969512yes—
320C2×C4M16×D6111yescharacteristic
321C2×C4M16×D6111yescharacteristic
322C8—82no—
323C8—4882no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—42no—
333C22—42no—
334C22#1683972511yescharacteristic
335C22C2×#1451969111yescharacteristic
336C22C2×#1451969511yescharacteristic
337C4—22no—
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—4881no—
345C4—4881no—
346C4—2442no—
347C4—2442no—
348C2—21no—
349C2—21no—
350C2—41no—
351C2—41no—
352C2#2144414811yescharacteristic
353C2#2144748611yescharacteristic
354C2#2144750611yescharacteristic
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#11514
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. #21443762C2semidirect
99. C4×Dic61M16semidirect
100. C4×Dic61M16semidirect
200. C61#11514semidirect

Maximal subgroups

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

subgroupindex
#214484432
#214441492
#214437642
#214437622
C61×#14632
#1151461