Finite Group Databasebeta

← #30594735

Subgroups — #30594735

Order 15616.

470 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 50 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#21461656C211yesmaximal, characteristic
2#21461649C211yesmaximal, characteristic
3#21445735C211yesmaximal, characteristic
4C2×#14519838C412yescomplemented
5C2×#14519837—21no—
6C2×#14519835—21no—
7C2×#14519835—21no—
8#16840732—21no—
9#16840705C412yescomplemented
10C22×#11758224C2211yescharacteristic
11C2×#14519692C411yescharacteristic, complemented
12C2×#14519691—21no—
13#16839623—21no—
14C2×#99×C61C411yescharacteristic, complemented
15C2×#11758217—22no—
16C2×C22⋊#6923—22no—
17#14519838—42no—
18#14519837—42no—
19#14519835—41no—
20#14519835—41no—
21#14519835—42no—
22C22⋊#92420—41no—
23C22⋊#92420—41no—
24(C2×#6923)⋊C4—42no—
25C2×#11758224—42no—
26C2×#11758224—42no—
27C2×#11758224—41no—
28C2×#11758224—41no—
29C22×Dic122C2×C411yescharacteristic
30C22×C22⋊D61D411yescharacteristic
31C22×C22⋊D61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33C23×Dic61Q811yescharacteristic
34C22×C4×D61C2×C411yescharacteristic
35C2×C22⋊Dic61—21no—
36#14519692—41no—
37#14519691—42no—
38#14519684—42no—
39C22×D4×C61C2×C411yescharacteristic
40C2×C22⋊C4×C61—21no—
41#99×C61—41no—
42C24×C61C22⋊C411yescharacteristic
43C24×C61C4⋊C411yescharacteristic
44C23×D61C22⋊C411yescharacteristic
45C22×#6923—42no—
46C2×D4×C61—21no—
47C2×D4×C61—21no—
48C2×D4×C61—41no—
49C2×D4×C61—41no—
50C22×C4×C61—41no—
51C22×C4×C61C4211yescharacteristic
52C2×C22⋊D61—21no—
53C2×C22⋊D61—21no—
54C2×C22⋊D61—22no—
55C2×C22⋊D61—22no—
56C2×C22⋊D61—22no—
57C2×C22⋊D61—41no—
58C2×C22⋊D61—41no—
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61—22no—
62C22×Dic61—41no—
63C22×Dic61—41no—
64C22×Dic61—41no—
65C22×Dic61—41no—
66C22×Dic61—41no—
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C4⋊C411yescharacteristic
69C22×Dic61C4⋊C411yescharacteristic
70#11758224—48no—
71#11758224—48no—
72C2×C4×D61—22no—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×Dic122—22no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C22⋊#6923—42no—
79C22⋊#6923—42no—
80#11758217—42no—
81#11758217—42no—
82C2×#92420—42no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C22⋊Dic61—41no—
86C22⋊Dic61—41no—
87C23×C61—21no—
88C23×C61—21no—
89C23×C61—21no—
90C23×C61—21no—
91C23×C61—21no—
92C23×C61—81no—
93C23×C61—81no—
94C23×C61#9511yescharacteristic
95C23×C61#9911yescharacteristic
96C23×C61#9911yescharacteristic
97C22×D61—21no—
98C22×D61—21no—
99C22×D61—81no—
100C22×D61#9912yes—
101C2×#6923—82no—
102C2×#6923—84no—
103D4×C61—42no—
104D4×C61—42no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—81no—
109C2×C4×C61—82no—
110C22⋊D61—44no—
111C22⋊D61—42no—
112C22⋊D61—42no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61—44no—
124C2×Dic61—81no—
125C2×Dic61—82no—
126C2×Dic61#9912yes—
127C4×D61—44no—
128Dic122—44no—
129#92420—82no—
130#7313—611nomaximal, Sylow
131C22×C61—21no—
132C22×C61—21no—
133C22×C61—41no—
134C22×C61—41no—
135C22×C61—41no—
136C22×C61—42no—
137C22×C61—41no—
138C22×C61—81no—
139C22×C61—81no—
140C22×C61—81no—
141C22×C61—81no—
142C22×C61#34211yescharacteristic
143C22×C61#34211yescharacteristic
144C22×C61#34211yescharacteristic
145C2×D61—22no—
146C2×D61—42no—
147C2×D61—81no—
148C2×D61—81no—
149#6923—162no—
150C4×C61—41no—
151C4×C61—161no—
152Dic61—22no—
153Dic61—41no—
154Dic61—41no—
155Dic61—161no—
156#1785—611no—
157#1782—611no—
158#1782—611no—
159C2×C61—21no—
160C2×C61—21no—
161C2×C61—21no—
162C2×C61—41no—
163C2×C61—41no—
164C2×C61—81no—
165C2×C61#130411yescharacteristic
166D61—42no—
167C22×#41—611no—
168C2×#101—612no—
169C2×#100—1221no—
170C2×#99—611no—
171C2×#99—1221no—
172C2×#99—1221no—
173C2×#99—1221no—
174C2×#99#692311yescharacteristic, complemented
175#407—1221no—
176#381—612no—
177#381—1221no—
178C61#731311yescharacteristic, complemented, Sylow
179C2×#41—2441no—
180C2×#41—2441no—
181C2×#41—2442no—
182C2×#41—2442no—
183C22×Q8—611no—
184C22×D4—611no—
185C22×D4—611no—
186C22×D4C2×#692311yescharacteristic
187C23×C4—611no—
188C23×C4—611no—
189C23×C4—611no—
190C2×M16—1222no—
191C2×C22⋊C4—21no—
192C2×C22⋊C4—1222no—
193C2×C22⋊C4—1221no—
194#101—2442no—
195#100—2442no—
196#99—41no—
197#99—2442no—
198#99—2442no—
199#99—2441no—
200#99—2441no—
201#99—2441no—
202C22⋊C8—2441no—
203C22⋊C8—2441no—
204#95—2442no—
205#95—2442no—
206C24—611no—
207C24C4⋊#692311yescharacteristic
208C24C22⋊#692311yescharacteristic
209#41—2448no—
210#41—2448no—
211C2×Q8—1222no—
212C2×Q8—2441no—
213C2×Q8—2441no—
214C2×D4—21no—
215C2×D4—21no—
216C2×D4—41no—
217C2×D4—41no—
218C2×D4—1222no—
219C2×D4—1222no—
220C2×D4—1222no—
221C2×D4—1221no—
222C2×D4—1221no—
223C2×D4—2441no—
224C2×D4—2441no—
225C22×C4—41no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—1222no—
230C22×C4—1222no—
231C22×C4—1221no—
232C22×C4—1221no—
233C22×C4—2441no—
234C22×C4—2441no—
235C22×C4—2441no—
236C22×C4—2441no—
237C22×C4—2441no—
238C22×C4—2441no—
239C22×C4—2441no—
240C22×C4—2442no—
241C22×C4C4×#692311yescharacteristic
242M16—2442no—
243M16—2442no—
244C2×C8—2442no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—2441no—
248C22⋊C4—2442no—
249C22⋊C4—2442no—
250C22⋊C4—2441no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—81no—
257C23—81no—
258C23—612no—
259C23—1221no—
260C23—1221no—
261C23—4881no—
262C23(C2×#6923)⋊C411yescharacteristic
263C23#1451983511yescharacteristic
264C23#1451983611yescharacteristic
265Q8—2444no—
266D4—42no—
267D4—42no—
268D4—2444no—
269D4—2442no—
270D4—2442no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—81no—
275C2×C4—82no—
276C2×C4—612no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—4881no—
286C2×C4—4882no—
287C2×C4—4882no—
288C2×C4—4884no—
289C2×C4—2444no—
290C2×C4—2442no—
291C2×C4—2442no—
292C2×C4—2444no—
293C8—4882no—
294C22—21no—
295C22—21no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—42no—
300C22—41no—
301C22—81no—
302C22—81no—
303C22—81no—
304C22—81no—
305C22—1222no—
306C22—4881no—
307C22—4881no—
308C22—2442no—
309C22#1684063911yescharacteristic
310C22#1684063911yescharacteristic
311C22#1684064011yescharacteristic
312C4—41no—
313C4—161no—
314C4—1222no—
315C4—9761no—
316C4—9762no—
317C4—2441no—
318C4—2441no—
319C2—21no—
320C2—21no—
321C2—21no—
322C2—41no—
323C2—41no—
324C2—81no—
325C2—2442no—
326C2#2146071811yescharacteristic
subgroupG/H
centerC2#21460718
commutatorC22×C4×C61C42
FrattiniC22×D4C2×#6923
FittingC2×#99×C61C4
socleC2×C61#1304
prime radical, cosocleC22×#11758224C22
hypercenterC2×#99#6923
hypocenterC61#7313
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
4. C2×#14519838C4semidirect
9. #16840705C4semidirect
11. C2×#14519692C4semidirect
14. C2×#99×C61C4semidirect
174. C2×#99#6923semidirect
178. C61#7313semidirect

Maximal subgroups

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

subgroupindex
#214616562
#214616492
#214457352
#731361