Finite Group Databasebeta

← #29590648

Subgroups — #29590648

Order 15616.

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

normal subgroups only

This group has 572 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#21449184C211yesmaximal, characteristic
2C4×#14519694C211yesmaximal, characteristic
3#21443850C214yesmaximal, complemented
4C61×#1465C211yesmaximal, characteristic
5C23×Dic122C411yescharacteristic
6C2×#14519756—21no—
7C2×#14519694—21no—
8C4×#11758194—21no—
9#16839682C2212yes—
10#16839674C412yes—
11#16839668—21no—
12#16839642—21no—
13#16839634—21no—
14#16839622C411yescharacteristic
15#16839531C2212yes—
16C2×C4×D4×C61C2211yescharacteristic
17C61×#407—21no—
18C61×#324C2212yes—
19C61×#323—21no—
20C22×Dic122—21no—
21C22×Dic122—44no—
22C22×Dic122—41no—
23C22×Dic122—41no—
24C22×Dic122C2×C412yes—
25C23×Dic61—21no—
26C2×#11758194—22no—
27#14519756—44no—
28C2×C4⋊Dic61—21no—
29C2×#11758196—22no—
30C2×C22⋊Dic61—22no—
31C2×C22⋊Dic61—21no—
32#14519694—24no—
33#14519688—41no—
34C4×#92418—41no—
35#14519684—22no—
36#14519684—22no—
37#14519684C2×C412yes—
38C22×D4×C61D411yescharacteristic
39C23×C4×C61C2×C411yescharacteristic
40C23×C4×C61D411yescharacteristic
41C2×M16×C61—41no—
42C4×D4×C61—41no—
43C4×D4×C61—41no—
44C2×C4⋊C4×C61C2311yescharacteristic
45C2×C22⋊C4×C61C2×C411yescharacteristic
46C2×C22⋊C4×C61D411yescharacteristic
47C2×C42×C61D411yescharacteristic
48C22⋊C8×C61—22no—
49C22⋊C8×C61—41no—
50C24×C61C22⋊C411yescharacteristic
51C24×C61C22⋊C411yescharacteristic
52C2×D4×C61—22no—
53C2×D4×C61—22no—
54C2×D4×C61—41no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—42no—
60C22×C4×C61—42no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×Dic61—22no—
67C22×Dic61—22no—
68C22×Dic61—44no—
69C22×Dic61—42no—
70C2×Dic122—24no—
71C2×Dic122—42no—
72C2×Dic122—48no—
73C2×Dic122—44no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76C2×Dic122—42no—
77C2×Dic122—44no—
78C2×Dic122—44no—
79M16×C61—82no—
80C2×C8×C61—42no—
81C4⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C42×C61—21no—
85C42×C61—21no—
86C22⋊Dic61—44no—
87C22⋊Dic61—42no—
88C4⋊Dic61—42no—
89#11758196—44no—
90#11758194—24no—
91#11758194—42no—
92C2×#92418—42no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—41no—
99C23×C61—41no—
100C23×C61—41no—
101C23×C61—41no—
102C23×C61#10412yes—
103C23×C61C2×C22⋊C411yescharacteristic
104D4×C61—44no—
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—42no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—81no—
118C2×C4×C61#9911yescharacteristic
119C2×C4×C61#9911yescharacteristic
120C2×C4×C61#13712yes—
121C2×Dic61—24no—
122C2×Dic61—42no—
123C2×Dic61—48no—
124C2×Dic61—42no—
125C2×Dic61—42no—
126C2×Dic61—42no—
127C2×Dic61—42no—
128Dic122—44no—
129Dic122—44no—
130Dic122—44no—
131Dic122—44no—
132C8×C61—82no—
133#92418—44no—
134#11791—611nomaximal, Sylow
135C22×C61—21no—
136C22×C61—21no—
137C22×C61—22no—
138C22×C61—42no—
139C22×C61—42no—
140C22×C61—42no—
141C22×C61—41no—
142C22×C61—41no—
143C22×C61—41no—
144C22×C61—41no—
145C22×C61—41no—
146C22×C61—81no—
147C22×C61C2×#9911yescharacteristic
148C22×C61#41911yescharacteristic
149C22×C61C2×#10411yescharacteristic
150C4×C61—21no—
151C4×C61—22no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61AΣL(1,𝔽16)12yes—
156Dic61—44no—
157Dic61—82no—
158#2409—611no—
159C4×#100—611no—
160#1465D6111yescharacteristic
161#1354—614no—
162C2×C61—21no—
163C2×C61—21no—
164C2×C61—42no—
165C2×C61—81no—
166C2×C61#150811yescharacteristic
167C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
168C2×C61#213511yescharacteristic
169C23×Q8—611no—
170C2×C22⋊Q8—1221no—
171C2×C4×D4C2×D6111yescharacteristic
172C2×#100—1221no—
173#407—21no—
174C4×M16—1221no—
175#395—612no—
176#393—612no—
177#391—1221no—
178#386—1221no—
179#385—1221no—
180#380—611no—
181#343—612no—
182#324C2×D6112yes—
183#323—21no—
184C61#1179111yescharacteristic, complemented, Sylow
185C22×Q8—612no—
186C22×Q8—1221no—
187C22×Q8—2441no—
188C22×Q8—2441no—
189C22×Q8—2444no—
190C22×D4D24411yescharacteristic
191C23×C4—1221no—
192C23×C4C4×D6111yescharacteristic
193C23×C4C22⋊D6111yescharacteristic
194C2×M16—41no—
195C2×M16—1222no—
196C22⋊Q8—2444no—
197C4×D4—41no—
198C4×D4—41no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4—1222no—
201C2×C4⋊C4C22×D6111yescharacteristic
202C2×C22⋊C4—1222no—
203C2×C22⋊C4—1221no—
204C2×C22⋊C4C4×D6111yescharacteristic
205C2×C22⋊C4C22⋊D6111yescharacteristic
206C2×C42D24411yescharacteristic
207#100—1224no—
208C22⋊C8—22no—
209C22⋊C8—41no—
210#97—2441no—
211C4×C8—2441no—
212#95—612no—
213#95—1222no—
214#95—1222no—
215C24#1175819811yescharacteristic
216C24#1175819811yescharacteristic
217C2×Q8—1224no—
218C2×Q8—2442no—
219C2×Q8—2442no—
220C2×Q8—2444no—
221C2×Q8—2444no—
222C2×Q8—2448no—
223C2×Q8—2444no—
224C2×Q8—2441no—
225C2×Q8—2441no—
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—41no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—1222no—
236C22×C4—1222no—
237C22×C4—2444no—
238C22×C4—2442no—
239C22×C4#1175819811yescharacteristic
240C22×C4#1175819811yescharacteristic
241C22×C4C2×C4×D6111yescharacteristic
242C22×C4C2×D24411yescharacteristic
243C22×C4C2×C22⋊D6111yescharacteristic
244M16—82no—
245M16—1224no—
246M16—2442no—
247C2×C8—42no—
248C2×C8—2442no—
249C4⋊C4—41no—
250C4⋊C4—2442no—
251C4⋊C4—2444no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—2444no—
255C22⋊C4—2442no—
256C42—21no—
257C42—21no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23#1451970312yes—
268C23C2×#1175819811yescharacteristic
269Q8—2444no—
270Q8—2444no—
271Q8—2444no—
272Q8—2444no—
273D4—44no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—81no—
287C2×C4—1224no—
288C2×C4—2442no—
289C2×C4—2442no—
290C2×C4—2442no—
291C2×C4—2442no—
292C2×C4—2448no—
293C2×C4—2442no—
294C2×C4#1451969111yescharacteristic
295C2×C4#1451969111yescharacteristic
296C2×C4#1451981012yes—
297C8—82no—
298C8—2444no—
299C22—21no—
300C22—21no—
301C22—22no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—81no—
311C22C2×#1451969111yescharacteristic
312C22#1683977211yescharacteristic
313C22C2×#1451970311yescharacteristic
314C4—21no—
315C4—22no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—4882no—
320C4—2444no—
321C4#1683954812yes—
322C2—21no—
323C2—21no—
324C2—42no—
325C2—81no—
326C2#2144434011yescharacteristic
327C2C2×#1683954811yescharacteristic
328C2#2144751311yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1465C2
socleC22×C61C2×#99
prime radicalC22×D4×C61D4
cosocleC2×C4⋊C4×C61C23
hypercenter#1465D61
hypocenterC61#11791
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #21443850C2semidirect
184. C61#11791semidirect

Maximal subgroups

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

subgroupindex
#214491842
C4×#145196942
#214438502
C61×#14652
#1179161