Finite Group Databasebeta

← #29598686

Subgroups — #29598686

Order 15616.

500 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 103 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#21450992C211yesmaximal, characteristic
2C4×#14519692C211yesmaximal, characteristic
3#21443943C214yesmaximal
4C61×#1799C211yesmaximal, characteristic
5C2×#14519777C411yescharacteristic, complemented
6C2×#14519692C2212yes—
7#16839674—21no—
8#16839674—21no—
9#16839665C2212yes—
10#16839627C412yescomplemented
11#16839622—21no—
12#16839622—21no—
13C4×C4⋊Dic61C411yescharacteristic, complemented
14C4×C22⋊Dic61—21no—
15#16839529—21no—
16C2×C4×D4×C61C2211yescharacteristic
17C2×#99×C61C2212yes—
18C61×#380—21no—
19C61×#342—21no—
20C22×Dic122—21no—
21#14519777—41no—
22#14519777—41no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61C2×C412yes—
26C2×C22⋊Dic61—22no—
27C2×C22⋊Dic61—22no—
28C2×C22⋊Dic61—22no—
29C2×C4×Dic61—41no—
30C2×C4×Dic61C2×C412yes—
31#14519692—22no—
32#14519692Q814yescomplemented
33#14519684—21no—
34#14519684—22no—
35#14519684—22no—
36#14519684—41no—
37C22×D4×C61C2311yescharacteristic
38C23×C4×C61D411yescharacteristic
39C23×C4×C61D411yescharacteristic
40C4×D4×C61—41no—
41C4×D4×C61—41no—
42C2×C4⋊C4×C61—41no—
43C2×C4⋊C4×C61C2×C411yescharacteristic
44C2×C22⋊C4×C61—22no—
45C2×C22⋊C4×C61D411yescharacteristic
46C2×C22⋊C4×C61D411yescharacteristic
47C2×C42×C61C2×C411yescharacteristic
48#99×C61—24no—
49#95×C61—41no—
50C24×C61C2×D411yescharacteristic
51C24×C61C2×D411yescharacteristic
52C2×D4×C61—41no—
53C2×D4×C61—41no—
54C2×D4×C61C2×Q812yes—
55C2×D4×C61#4112yes—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—42no—
61C22×C4×C61—42no—
62C22×C4×C61—42no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×Dic61—22no—
69C22×Dic61—22no—
70C22×Dic61—42no—
71C2×Dic122—42no—
72C2×Dic122—82no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—82no—
75C22⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C22⋊C4×C61—42no—
78C22⋊C4×C61—42no—
79C42×C61—21no—
80C42×C61—21no—
81C22⋊Dic61—24no—
82C22⋊Dic61—42no—
83C22⋊Dic61—82no—
84C22⋊Dic61—82no—
85C4⋊Dic61—42no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88C4⋊Dic61—42no—
89C4×Dic61—42no—
90C4×Dic61—82no—
91C23×C61—21no—
92C23×C61—21no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—41no—
96C23×C61—41no—
97C23×C61—41no—
98C23×C61—41no—
99C23×C61C2×C22⋊C411yescharacteristic
100C23×C61C22⋊Q812yes—
101C23×C61#12411yescharacteristic
102C23×C61C4⋊Q811yescharacteristic
103D4×C61—42no—
104D4×C61—42no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—22no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—42no—
112C2×C4×C61—42no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—81no—
117C2×C4×C61—81no—
118C2×C4×C61—82no—
119C2×C4×C61—82no—
120C2×C4×C61—82no—
121C2×C4×C61#9911yescharacteristic
122C2×C4×C61#9911yescharacteristic
123C2×C4×C61C4×Q812yes—
124C2×Dic61—42no—
125C2×Dic61—44no—
126C2×Dic61—42no—
127C2×Dic61—42no—
128C2×Dic61—42no—
129C2×Dic61—42no—
130C2×Dic61—42no—
131C2×Dic61—82no—
132C2×Dic61—82no—
133Dic122—84no—
134#13299—611nomaximal, Sylow
135C22×C61—21no—
136C22×C61—21no—
137C22×C61—22no—
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—42no—
141C22×C61—41no—
142C22×C61—41no—
143C22×C61—41no—
144C22×C61—41no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61—81no—
148C22×C61—81no—
149C22×C61#39111yescharacteristic
150C22×C61C2×#9911yescharacteristic
151C22×C61#41011yescharacteristic
152C4×C61—21no—
153C4×C61—22no—
154C4×C61—41no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61—162no—
158C4×C61#35412yes—
159Dic61—82no—
160Dic61—84no—
161Dic61—82no—
162#2563—611no—
163#1799D6111yescharacteristic
164C4×#99—611no—
165#1393—614no—
166C2×C61—21no—
167C2×C61—21no—
168C2×C61—42no—
169C2×C61—41no—
170C2×C61—41no—
171C2×C61#199611yescharacteristic
172C2×C61C2×#35411yescharacteristic
173C2×C61#212811yescharacteristic
174C2×C4⋊Q8—611no—
175C2×C4×D4C2×D6111yescharacteristic
176C2×#99—612no—
177C2×#99C2×D6112yes—
178#393—1221no—
179#393—1221no—
180#390—612no—
181#382—612no—
182#380—21no—
183#380—1221no—
184#380—1221no—
185C4×C4⋊C4—611no—
186C4×C22⋊C4—1221no—
187#342—21no—
188#342—1221no—
189C61#1329911yescharacteristic, complemented, Sylow
190C22×Q8—1221no—
191C22×D4C22×D6111yescharacteristic
192C23×C4D24411yescharacteristic
193C23×C4C22⋊D6111yescharacteristic
194C4⋊Q8—2441no—
195C4⋊Q8—2441no—
196C4×D4—41no—
197C4×D4—41no—
198C2×C4⋊C4—41no—
199C2×C4⋊C4—612no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4C4×D6111yescharacteristic
203C2×C22⋊C4—22no—
204C2×C22⋊C4—1222no—
205C2×C22⋊C4—1222no—
206C2×C22⋊C4—1222no—
207C2×C22⋊C4D24411yescharacteristic
208C2×C22⋊C4C22⋊D6111yescharacteristic
209C2×C42—612no—
210C2×C42—2441no—
211C2×C42C4×D6111yescharacteristic
212#99—24no—
213#99—614no—
214#99—1222no—
215#95—41no—
216#95—1221no—
217#95—1222no—
218#95—1222no—
219#95—2441no—
220C24C2×D24411yescharacteristic
221C24C2×C22⋊D6111yescharacteristic
222C2×Q8—4882no—
223C2×Q8—2442no—
224C2×D4—41no—
225C2×D4—41no—
226C2×D4#1175822412yes—
227C2×D4Q8×D6112yes—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—1222no—
236C22×C4—1222no—
237C22×C4—2442no—
238C22×C4#1175819811yescharacteristic
239C22×C4#1175819811yescharacteristic
240C22×C4#1175819811yescharacteristic
241C22×C4#1175819811yescharacteristic
242C22×C4C2×C4×D6111yescharacteristic
243C4⋊C4—41no—
244C4⋊C4—82no—
245C4⋊C4—2442no—
246C4⋊C4—2442no—
247C4⋊C4—2441no—
248C4⋊C4—2441no—
249C22⋊C4—41no—
250C22⋊C4—41no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—1224no—
254C22⋊C4—4882no—
255C22⋊C4—4882no—
256C22⋊C4—2442no—
257C42—21no—
258C42—21no—
259C42—4882no—
260C42—2442no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23C2×#1175819811yescharacteristic
270C23#1451975712yes—
271C23#1451976411yescharacteristic
272C23#1451977511yescharacteristic
273Q8—4884no—
274D4—42no—
275D4—42no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—82no—
290C2×C4—82no—
291C2×C4—82no—
292C2×C4—4882no—
293C2×C4—4882no—
294C2×C4—2444no—
295C2×C4—2442no—
296C2×C4—2442no—
297C2×C4—2442no—
298C2×C4—2442no—
299C2×C4—2442no—
300C2×C4—2442no—
301C2×C4#1451969111yescharacteristic
302C2×C4#1451969111yescharacteristic
303C2×C4#1451974212yes—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—21no—
309C22—42no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22—81no—
318C22#1683966711yescharacteristic
319C22C2×#1451969111yescharacteristic
320C22#1683973511yescharacteristic
321C4—21no—
322C4—22no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—162no—
327C4—4882no—
328C4—4884no—
329C4—4882no—
330C4#1683955612yes—
331C2—21no—
332C2—21no—
333C2—41no—
334C2—42no—
335C2—41no—
336C2#2144680311yescharacteristic
337C2C2×#1683955611yescharacteristic
338C2#2144749011yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC22×D4C22×D61
FittingC61×#1799C2
socleC22×C61C2×#99
prime radical, cosocleC22×D4×C61C23
hypercenter#1799D61
hypocenterC61#13299
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
5. C2×#14519777C4semidirect
10. #16839627C4semidirect
13. C4×C4⋊Dic61C4semidirect
32. #14519692Q8semidirect
189. C61#13299semidirect

Maximal subgroups

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

subgroupindex
#214509922
C4×#145196922
#214439432
C61×#17992
#1329961