Finite Group Databasebeta

← #29590637

Subgroups — #29590637

Order 15616.

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

normal subgroups only

This group has 462 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#21450995C211yesmaximal, characteristic
2#21444160C211yesmaximal, characteristic
3#21443842C212yesmaximal, complemented
4#21443839C212yesmaximal, complemented
5C4×#99×C61C211yesmaximal, characteristic
6C2×#14519756C411yescharacteristic, complemented
7#16839819—21no—
8#16839701C411yescharacteristic, complemented
9#16839698C2211yescharacteristic
10#16839682C411yescharacteristic, complemented
11#16839674C2211yescharacteristic
12#16839646—21no—
13#16839642—21no—
14#16839635—21no—
15#16839620—21no—
16C2×#14519684C411yescharacteristic, complemented
17#16839486—21no—
18#16839486C2212yes—
19C2×C4×D4×C61C2211yescharacteristic
20C2×#99×C61—21no—
21C4×C22⋊C4×C61—21no—
22C61×#342C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C23×Dic61—21no—
25#14519756—41no—
26#14519756—41no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×C22⋊Dic61—21no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—21no—
34C4⋊#92418—41no—
35C22⋊#92418—22no—
36#14519688—41no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684C2×C411yescharacteristic
43#14519684C2×C411yescharacteristic
44C22×D4×C61D411yescharacteristic
45C23×C4×C61C2×C411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C4×D4×C61—41no—
48C4×D4×C61—41no—
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C22⋊C4×C61—22no—
51C2×C22⋊C4×C61D411yescharacteristic
52C2×C22⋊C4×C61C2311yescharacteristic
53C2×C42×C61—41no—
54C2×C42×C61D411yescharacteristic
55#99×C61—24no—
56#95×C61—41no—
57C24×C61C22⋊C411yescharacteristic
58C24×C61C2×D411yescharacteristic
59C2×D4×C61—22no—
60C2×D4×C61—22no—
61C2×D4×C61—41no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—42no—
67C22×C4×C61—81no—
68C22×C4×C61—81no—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—42no—
79C22×Dic61—42no—
80C22×Dic61—81no—
81C2×Dic122—41no—
82C2×Dic122—81no—
83C4⋊C4×C61—41no—
84C22⋊C4×C61—24no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—42no—
88C42×C61—21no—
89C42×C61—21no—
90C42×C61—82no—
91C22⋊Dic61—42no—
92C22⋊Dic61—42no—
93C22⋊Dic61—81no—
94C4⋊Dic61—41no—
95#11758196—42no—
96#11758196—41no—
97#11758196—41no—
98#11758196—81no—
99C2×#92418—42no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61#10412yes—
109C23×C61C2×C22⋊C411yescharacteristic
110C23×C61#13712yes—
111D4×C61—44no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—42no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—44no—
124C2×C4×C61—81no—
125C2×C4×C61—81no—
126C2×C4×C61—81no—
127C2×C4×C61—82no—
128C2×C4×C61—82no—
129C2×C4×C61#9911yescharacteristic
130C2×C4×C61#9911yescharacteristic
131C2×Dic61—22no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—84no—
144Dic122—82no—
145#92418—82no—
146#11789—611nomaximal, Sylow
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—22no—
150C22×C61—22no—
151C22×C61—42no—
152C22×C61—42no—
153C22×C61—42no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—81no—
159C22×C61C2×#9911yescharacteristic
160C22×C61#41911yescharacteristic
161C22×C61C2×#10411yescharacteristic
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—84no—
169Dic61—42no—
170Dic61—81no—
171Dic61—81no—
172Dic61—81no—
173#2564—611no—
174C4×#99D6111yescharacteristic
175#1466—611no—
176#1352—612no—
177#1351—612no—
178C2×C61—21no—
179C2×C61—21no—
180C2×C61—42no—
181C2×C61—42no—
182C2×C61#150811yescharacteristic
183C2×C61#212111yescharacteristic
184C2×C61#212611yescharacteristic
185C2×C22⋊Q8—611no—
186C2×C4×D4C2×D6111yescharacteristic
187#432—1221no—
188C2×#99—21no—
189#400—611no—
190#399—611no—
191#395—611no—
192#393—611no—
193#387—1221no—
194#386—1221no—
195#385—1221no—
196#380—1221no—
197C4×C22⋊C4—21no—
198C2×#95—611no—
199#342C2×D6112yes—
200#323—612no—
201#323—1221no—
202C61#1178911yescharacteristic, complemented, Sylow
203C22×Q8—611no—
204C22×D4C22⋊D6111yescharacteristic
205C23×C4—1221no—
206C23×C4C4×D6111yescharacteristic
207C23×C4C22⋊D6111yescharacteristic
208C22⋊Q8—2441no—
209C22⋊Q8—2441no—
210C4×D4—41no—
211C4×D4—41no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4C4×D6111yescharacteristic
217C2×C22⋊C4—22no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4D24411yescharacteristic
222C2×C22⋊C4C22×D6111yescharacteristic
223C2×C42—41no—
224C2×C42D24411yescharacteristic
225C4⋊C8—2441no—
226#99—24no—
227C22⋊C8—1222no—
228#97—2441no—
229#95—41no—
230#95—611no—
231#95—611no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237C24#1175819811yescharacteristic
238C24C2×C22⋊D6111yescharacteristic
239C2×Q8—4881no—
240C2×Q8—2441no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—41no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—42no—
249C22×C4—81no—
250C22×C4—81no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—4881no—
256C22×C4—2442no—
257C22×C4—2442no—
258C22×C4#1175819811yescharacteristic
259C22×C4#1175819811yescharacteristic
260C22×C4#1175819811yescharacteristic
261C22×C4C2×C4×D6111yescharacteristic
262C22×C4C2×D24411yescharacteristic
263C2×C8—2442no—
264C4⋊C4—41no—
265C4⋊C4—4881no—
266C4⋊C4—2441no—
267C4⋊C4—2442no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C22⋊C4—24no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—42no—
274C22⋊C4—4881no—
275C22⋊C4—2442no—
276C22⋊C4—2442no—
277C42—21no—
278C42—21no—
279C42—82no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23#1451970512yes—
289C23C2×#1175819811yescharacteristic
290C23#1451980712yes—
291Q8—4882no—
292D4—44no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—44no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—1222no—
311C2×C4—4884no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4#1451969111yescharacteristic
324C2×C4#1451969111yescharacteristic
325C8—4882no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22C2×#1451969111yescharacteristic
339C22#1683977011yescharacteristic
340C22C2×#1451970511yescharacteristic
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—84no—
348C4—4881no—
349C4—4881no—
350C4—4881no—
351C4—2442no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—42no—
356C2#2144433811yescharacteristic
357C2#2144746311yescharacteristic
358C2#2144748211yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC4×#99×C61C2
socleC22×C61C2×#99
prime radicalC22×D4×C61D4
cosocleC2×C22⋊C4×C61C23
hypercenterC4×#99D61
hypocenterC61#11789
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #21443842C2semidirect
4. #21443839C2semidirect
6. C2×#14519756C4semidirect
8. #16839701C4semidirect
10. #16839682C4semidirect
16. C2×#14519684C4semidirect
202. C61#11789semidirect

Maximal subgroups

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

subgroupindex
#214509952
#214441602
#214438422
#214438392
C4×#99×C612
#1178961