Finite Group Databasebeta

← #29590927

Subgroups — #29590927

Order 15616.

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

normal subgroups only

This group has 396 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#21450106C211yesmaximal, characteristic
2#21445899C211yesmaximal, characteristic
3#21443847C212yesmaximal, complemented
4#21443826C212yesmaximal, complemented
5C2×C61×#324C211yesmaximal, characteristic
6C2×#14519736C411yescharacteristic
7#16839726—21no—
8#16839701C411yescharacteristic
9#16839701C2211yescharacteristic
10#16839692C411yescharacteristic
11#16839692C2211yescharacteristic
12#16839643—21no—
13#16839643—21no—
14#16839635—21no—
15#16839625—21no—
16#16839625C411yescharacteristic
17#16839531—21no—
18#16839531C2212yes—
19C22×C4⋊C4×C61C2211yescharacteristic
20C2×C22⋊C8×C61—21no—
21C61×#324—21no—
22C61×#324C2212yes—
23C2×#11758194—22no—
24#14519736—41no—
25#14519736—41no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—21no—
30C2×C22⋊Dic61—21no—
31C2×C22⋊Dic61—21no—
32C2×C4×Dic61—21no—
33C22⋊#92418—41no—
34C22⋊#92418—41no—
35#14519684—21no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684C2×C411yescharacteristic
43#14519684C2×C411yescharacteristic
44C23×C4×C61C2×C411yescharacteristic
45C23×C4×C61D411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C22×C8×C61—41no—
48C2×C4⋊C4×C61—41no—
49C2×C4⋊C4×C61—41no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C4⋊C4×C61C2311yescharacteristic
54C22⋊C8×C61—22no—
55C22⋊C8×C61—41no—
56C24×C61C22⋊C411yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—22no—
64C22×C4×C61—41no—
65C22×C4×C61—42no—
66C22×C4×C61—42no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C2×C8×C61—42no—
78C2×C8×C61—82no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C22⋊Dic61—42no—
84C22⋊Dic61—41no—
85C22⋊Dic61—41no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88#11758196—42no—
89#11758196—42no—
90C4×Dic61—42no—
91#11758194—42no—
92#11758194—42no—
93C2×#92418—42no—
94C23×C61—22no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—41no—
98C23×C61#9911yescharacteristic
99C23×C61#9911yescharacteristic
100C23×C61C2×C22⋊C411yescharacteristic
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—42no—
111C2×C4×C61—42no—
112C2×C4×C61—42no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—81no—
120C2×C4×C61#13512yes—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—42no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C8×C61—82no—
133#92418—82no—
134#11850—611nomaximal, Sylow
135C22×C61—21no—
136C22×C61—21no—
137C22×C61—21no—
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—42no—
143C22×C61—42no—
144C22×C61#35212yes—
145C22×C61C2×#9911yescharacteristic
146C22×C61#41611yescharacteristic
147C22×C61#42111yescharacteristic
148C4×C61—22no—
149C4×C61—41no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C61—41no—
153C4×C61—41no—
154Dic61—81no—
155Dic61—81no—
156Dic61—81no—
157Dic61—81no—
158#2484—611no—
159#1821—611no—
160C2×#324D6111yescharacteristic
161#1353—612no—
162#1346—612no—
163C2×C61—21no—
164C2×C61—21no—
165C2×C61—22no—
166C2×C61—41no—
167C2×C61#151611yescharacteristic
168C2×C61C2×#35211yescharacteristic
169C2×C61#213311yescharacteristic
170C2×#117—611no—
171C22×C4⋊C4C2×D6111yescharacteristic
172#407—1221no—
173C2×C22⋊C8—21no—
174#400—611no—
175#400—611no—
176#398—611no—
177#398—611no—
178#387—1221no—
179#387—1221no—
180#385—1221no—
181#381—611no—
182#381—1221no—
183#343—612no—
184#343—1221no—
185#324—21no—
186#324C2×D6112yes—
187C61#1185011yescharacteristic, complemented, Sylow
188C23×C4C4×D6111yescharacteristic
189C23×C4D24411yescharacteristic
190C23×C4C22⋊D6111yescharacteristic
191C2×M16—1222no—
192C22×C8—41no—
193#117—2441no—
194#117—2441no—
195C2×C4⋊C4—41no—
196C2×C4⋊C4—41no—
197C2×C4⋊C4—611no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4C4×D6111yescharacteristic
202C2×C4⋊C4D24411yescharacteristic
203C2×C4⋊C4C22⋊D6111yescharacteristic
204C2×C4⋊C4C22×D6111yescharacteristic
205C2×C22⋊C4—1221no—
206C2×C22⋊C4—1221no—
207C2×C42—1221no—
208C22⋊C8—22no—
209C22⋊C8—41no—
210C22⋊C8—2441no—
211C22⋊C8—2441no—
212#95—611no—
213#95—611no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217#95—1221no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221C24#1175819811yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—41no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—1221no—
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4#1175819811yescharacteristic
237C22×C4#1175819811yescharacteristic
238C22×C4#1175819811yescharacteristic
239C22×C4C2×C4×D6111yescharacteristic
240C22×C4C2×D24411yescharacteristic
241C22×C4C2×C22⋊D6111yescharacteristic
242M16—2442no—
243M16—2442no—
244C2×C8—42no—
245C2×C8—82no—
246C2×C8—2442no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—2441no—
252C4⋊C4—2441no—
253C4⋊C4—2442no—
254C4⋊C4—2442no—
255C22⋊C4—2442no—
256C22⋊C4—2441no—
257C22⋊C4—2441no—
258C42—2442no—
259C23—21no—
260C23—21no—
261C23—22no—
262C23—41no—
263C23#1451969111yescharacteristic
264C23#1451969111yescharacteristic
265C23C2×#1175819811yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—81no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2442no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4#1451979912yes—
297C8—82no—
298C8—4882no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—42no—
307C22—42no—
308C22#1683955112yes—
309C22C2×#1451969111yescharacteristic
310C22#1683975911yescharacteristic
311C22#1683977811yescharacteristic
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—4881no—
319C4—4881no—
320C4—4881no—
321C4—4881no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—41no—
326C2#2144437611yescharacteristic
327C2C2×#1683955111yescharacteristic
328C2#2144750611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC2×C61×#324C2
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenterC2×#324D61
hypocenterC61#11850
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. #21443847C2semidirect
4. #21443826C2semidirect
187. C61#11850semidirect

Maximal subgroups

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

subgroupindex
#214501062
#214458992
#214438472
#214438262
C2×C61×#3242
#1185061