Finite Group Databasebeta

← #29573479

Subgroups — #29573479

Order 15616.

418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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#21448422C211yesmaximal, characteristic
2C2×#16839488C211yesmaximal, characteristic
3#21443666C212yesmaximal
4#21443665C212yesmaximal
5C2×C61×#324C211yesmaximal, characteristic
6C2×C22⋊#92418C2212yes—
7#16839648—21no—
8#16839648—21no—
9#16839648—21no—
10#16839648—21no—
11#16839625C411yescharacteristic
12#16839625C411yescharacteristic
13#16839622C411yescharacteristic
14#16839622C411yescharacteristic
15C4×C22⋊Dic61C2211yescharacteristic
16C4×C22⋊Dic61C2211yescharacteristic
17#16839488—21no—
18#16839488—21no—
19C22×C4⋊C4×C61C2211yescharacteristic
20C2×C22⋊C8×C61C2212yes—
21C61×#324—21no—
22C61×#324—21no—
23C22×#92418—22no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—21no—
26C2×C22⋊Dic61C2×C411yescharacteristic
27C2×C22⋊Dic61C2×C411yescharacteristic
28C2×C22⋊Dic61C2×C411yescharacteristic
29C2×C22⋊Dic61C2×C411yescharacteristic
30C2×C4×Dic61—21no—
31C2×C4×Dic61—21no—
32C22⋊#92418—22no—
33C22⋊#92418—22no—
34#14519684—21no—
35#14519684—21no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42C23×C4×C61C2×C411yescharacteristic
43C23×C4×C61C2×C411yescharacteristic
44C23×C4×C61C2311yescharacteristic
45C22×C8×C61—22no—
46C2×C4⋊C4×C61—22no—
47C2×C4⋊C4×C61—22no—
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C4⋊C4×C61D411yescharacteristic
51C2×C4⋊C4×C61D411yescharacteristic
52C22⋊C8×C61—22no—
53C22⋊C8×C61—22no—
54C24×C61C22×C411yescharacteristic
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—81no—
62C22×C4×C61—81no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61#4112yes—
70C22×C4×C61#4112yes—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C2×C8×C61—42no—
76C2×C8×C61—82no—
77C4⋊C4×C61—22no—
78C4⋊C4×C61—22no—
79C4⋊C4×C61—22no—
80C4⋊C4×C61—22no—
81C22⋊Dic61—22no—
82C22⋊Dic61—22no—
83C22⋊Dic61—22no—
84C22⋊Dic61—22no—
85C4⋊Dic61—81no—
86C4⋊Dic61—81no—
87C4×Dic61—81no—
88C4×Dic61—81no—
89C2×#92418—42no—
90C2×#92418—82no—
91C23×C61—41no—
92C23×C61—41no—
93C23×C61C2×C22⋊C411yescharacteristic
94C23×C61#11711yescharacteristic
95C23×C61#11711yescharacteristic
96C23×C61#13112yes—
97C23×C61#13112yes—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—42no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—42no—
110C2×C4×C61—42no—
111C2×C4×C61—42no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—81no—
115C2×C4×C61—81no—
116C2×C4×C61#12312yes—
117C2×C4×C61#12312yes—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C8×C61—82no—
131#92418—82no—
132#8737—611nomaximal, Sylow
133C22×C61—21no—
134C22×C61—21no—
135C22×C61—21no—
136C22×C61—21no—
137C22×C61—21no—
138C22×C61—21no—
139C22×C61—42no—
140C22×C61—42no—
141C22×C61#38111yescharacteristic
142C22×C61#40811yescharacteristic
143C22×C61#40811yescharacteristic
144C22×C61#43312yes—
145C22×C61#43312yes—
146C4×C61—22no—
147C4×C61—22no—
148C4×C61—41no—
149C4×C61—41no—
150C4×C61—41no—
151C4×C61—41no—
152Dic61—81no—
153Dic61—81no—
154Dic61—81no—
155Dic61—81no—
156#2313—611no—
157C2×#324—611no—
158C2×#324D6111yescharacteristic
159#1282—612no—
160#1282—612no—
161C2×C61—21no—
162C2×C61—21no—
163C2×C61—22no—
164C2×C61—22no—
165C2×C61#181811yescharacteristic
166C2×C61#182811yescharacteristic
167C2×C61#183011yescharacteristic
168C22×C4⋊C4C2×D6111yescharacteristic
169C2×C22⋊C8—612no—
170C2×C22⋊C8C2×D6112yes—
171#387—1221no—
172#387—1221no—
173#387—1221no—
174#387—1221no—
175#381—611no—
176#381—611no—
177#380—611no—
178#380—611no—
179C4×C22⋊C4—611no—
180C4×C22⋊C4—611no—
181#324—21no—
182#324—21no—
183#324—1221no—
184#324—1221no—
185C61#873711yescharacteristic, complemented, Sylow
186C23×C4C4×D6111yescharacteristic
187C23×C4C4×D6111yescharacteristic
188C23×C4C22×D6111yescharacteristic
189C22×C8—22no—
190C22×C8—1222no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4D24411yescharacteristic
196C2×C4⋊C4D24411yescharacteristic
197C2×C4⋊C4C22⋊D6111yescharacteristic
198C2×C4⋊C4C22⋊D6111yescharacteristic
199C2×C22⋊C4—611no—
200C2×C22⋊C4—611no—
201C2×C22⋊C4—611no—
202C2×C22⋊C4—611no—
203C2×C42—1221no—
204C2×C42—1221no—
205C22⋊C8—22no—
206C22⋊C8—22no—
207C22⋊C8—1222no—
208C22⋊C8—1222no—
209#95—1221no—
210#95—1221no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217C24C2×C4×D6111yescharacteristic
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—81no—
225C22×C4—81no—
226C22×C4—1221no—
227C22×C4—1221no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4#1175819811yescharacteristic
231C22×C4#1175819811yescharacteristic
232C22×C4#1175819811yescharacteristic
233C22×C4#1175819811yescharacteristic
234C22×C4C2×D24411yescharacteristic
235C22×C4#1175822412yes—
236C22×C4#1175822412yes—
237C22×C4C2×C22⋊D6111yescharacteristic
238C2×C8—42no—
239C2×C8—82no—
240C2×C8—4882no—
241C2×C8—2442no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—4881no—
247C4⋊C4—4881no—
248C22⋊C4—1222no—
249C22⋊C4—1222no—
250C22⋊C4—1222no—
251C22⋊C4—1222no—
252C42—4881no—
253C42—4881no—
254C23—41no—
255C23—41no—
256C23C2×#1175819811yescharacteristic
257C23#1451973311yescharacteristic
258C23#1451973311yescharacteristic
259C23#1451978312yes—
260C23#1451978512yes—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4#1451975812yes—
292C2×C4#1451976112yes—
293C8—82no—
294C8—4882no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—42no—
302C22—42no—
303C22#1683962311yescharacteristic
304C22#1683972811yescharacteristic
305C22#1683973011yescharacteristic
306C22#1683982012yes—
307C22#1683982012yes—
308C4—22no—
309C4—22no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—4881no—
315C4—4881no—
316C4—4881no—
317C4—4881no—
318C2—21no—
319C2—21no—
320C2—22no—
321C2—22no—
322C2#2144588811yescharacteristic
323C2#2144592511yescharacteristic
324C2#2144593111yescharacteristic
subgroupG/H
centerC22#16839623
commutator, prime radicalC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#324C2
socleC22×C61#381
cosocleC23×C4×C61C23
hypercenterC2×#324D61
hypocenterC61#8737
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
185. C61#8737semidirect

Maximal subgroups

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

subgroupindex
#214484222
C2×#168394882
#214436662
#214436652
C2×C61×#3242
#873761