Finite Group Databasebeta

← #29590201

Subgroups — #29590201

Order 15616.

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

normal subgroups only

This group has 468 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#21451585C211yesmaximal, characteristic
2#21444133C211yesmaximal, characteristic
3#21443818C214yesmaximal
4C61×#1740C211yesmaximal, characteristic
5C2×#14519777C411yescharacteristic, complemented
6C2×#14519756—21no—
7#16839815—21no—
8#16839692—21no—
9#16839692C412yescomplemented
10#16839687—21no—
11#16839687C2212yes—
12#16839668—21no—
13#16839628C411yescharacteristic, complemented
14#16839488—21no—
15#16839486C2212yes—
16C2×#117×C61—21no—
17C2×#117×C61C2211yescharacteristic
18C61×#342—21no—
19C61×#342C2212yes—
20C22×Dic122—21no—
21#14519777—41no—
22#14519777—41no—
23#14519756—42no—
24#14519756—42no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61C2×C412yes—
28C2×#11758196—22no—
29C2×C22⋊Dic61—22no—
30C4⋊#92418—41no—
31C22⋊#92418—22no—
32C4×#92418—41no—
33#14519684—21no—
34#14519684—22no—
35#14519684—22no—
36#14519684C2×C412yes—
37C23×C4×C61D411yescharacteristic
38#117×C61—24no—
39#117×C61—41no—
40#117×C61—41no—
41#117×C61—42no—
42C2×C4⋊C4×C61—41no—
43C2×C4⋊C4×C61C2×C411yescharacteristic
44C2×C4⋊C4×C61D411yescharacteristic
45C2×C22⋊C4×C61—22no—
46C2×C22⋊C4×C61D411yescharacteristic
47C2×C22⋊C4×C61C2311yescharacteristic
48C2×C42×C61—41no—
49C2×C42×C61C2×C411yescharacteristic
50C2×C42×C61D411yescharacteristic
51C24×C61C2×D411yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—22no—
55C22×C4×C61—42no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61D812yes—
61C22×C4×C61SD1612yes—
62C22×C4×C61C22×C411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×Dic61—22no—
65C22×Dic61—22no—
66C2×Dic122—41no—
67C2×Dic122—41no—
68C2×Dic122—42no—
69C2×Dic122—42no—
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61—44no—
73C22⋊C4×C61—24no—
74C22⋊C4×C61—41no—
75C22⋊C4×C61—41no—
76C22⋊C4×C61—42no—
77C42×C61—21no—
78C42×C61—21no—
79C42×C61—21no—
80C42×C61—21no—
81C42×C61—44no—
82C22⋊Dic61—42no—
83C22⋊Dic61—42no—
84C4⋊Dic61—42no—
85C4⋊Dic61—42no—
86C4⋊Dic61—42no—
87#11758196—44no—
88C2×#92418—42no—
89C23×C61—21no—
90C23×C61—21no—
91C23×C61—41no—
92C23×C61—41no—
93C23×C61C2×C22⋊C411yescharacteristic
94C23×C61C2×D811yescharacteristic
95C23×C61C2×SD1611yescharacteristic
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—44no—
111C2×C4×C61—82no—
112C2×C4×C61—82no—
113C2×C4×C61#9911yescharacteristic
114C2×C4×C61#9911yescharacteristic
115C2×C4×C61#10212yes—
116C2×C4×C61#10212yes—
117C2×C4×C61#10412yes—
118C2×Dic61—42no—
119C2×Dic61—42no—
120C2×Dic61—42no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61—42no—
124Dic122—82no—
125Dic122—82no—
126#92418—82no—
127#11694—611nomaximal, Sylow
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—21no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61—41no—
135C22×C61—41no—
136C22×C61—81no—
137C22×C61C2×#9911yescharacteristic
138C22×C61C2×#10211yescharacteristic
139C22×C61C2×#10411yescharacteristic
140C4×C61—22no—
141C4×C61—41no—
142C4×C61—41no—
143C4×C61—41no—
144C4×C61—41no—
145C4×C61—84no—
146C4×C61#32712yes—
147C4×C61#32712yes—
148Dic61—82no—
149Dic61—82no—
150#2621—611no—
151#1740D6111yescharacteristic
152#1458—611no—
153#1344—614no—
154C2×C61—21no—
155C2×C61—21no—
156C2×C61—41no—
157C2×C61—41no—
158C2×C61C2×#32711yescharacteristic
159C2×C61#212311yescharacteristic
160C2×C61#212911yescharacteristic
161C2×C4⋊Q8—611no—
162C2×C22⋊Q8—1221no—
163C2×#117—21no—
164C2×#117C2×D6111yescharacteristic
165#431—1221no—
166#398—612no—
167#398—1221no—
168#397—612no—
169#397—1221no—
170#391—1221no—
171#382—611no—
172#342—21no—
173#342C2×D6112yes—
174#324—1221no—
175#323—612no—
176C61#1169411yescharacteristic, complemented, Sylow
177C22×Q8—1221no—
178C23×C4C22⋊D6111yescharacteristic
179C4⋊Q8—2441no—
180C4⋊Q8—2441no—
181C22⋊Q8—2442no—
182C22⋊Q8—2442no—
183#117—24no—
184#117—41no—
185#117—41no—
186#117—42no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4—612no—
189C2×C4⋊C4—1222no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4C4×D6111yescharacteristic
193C2×C4⋊C4D24411yescharacteristic
194C2×C22⋊C4—22no—
195C2×C22⋊C4—1222no—
196C2×C22⋊C4C22⋊D6111yescharacteristic
197C2×C22⋊C4C22×D6111yescharacteristic
198C2×C42—41no—
199C2×C42C4×D6111yescharacteristic
200C2×C42D24411yescharacteristic
201C4⋊C8—2441no—
202C22⋊C8—1222no—
203C4×C8—2441no—
204#95—612no—
205#95—1221no—
206#95—1222no—
207#95—1222no—
208C24C2×C22⋊D6111yescharacteristic
209C2×Q8—2441no—
210C2×Q8—2441no—
211C2×Q8—2442no—
212C2×Q8—2442no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—42no—
217C22×C4—1222no—
218C22×C4—1222no—
219C22×C4#1175819811yescharacteristic
220C22×C4#1175819811yescharacteristic
221C22×C4#1175819811yescharacteristic
222C22×C4#1175819811yescharacteristic
223C22×C4#1175819912yes—
224C22×C4#1175820112yes—
225C22×C4C2×C4×D6111yescharacteristic
226C22×C4C2×D24411yescharacteristic
227C2×C8—2442no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—44no—
231C4⋊C4—2442no—
232C4⋊C4—2442no—
233C4⋊C4—2444no—
234C4⋊C4—2442no—
235C22⋊C4—24no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—42no—
239C22⋊C4—2442no—
240C22⋊C4—2442no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—44no—
246C23—21no—
247C23—21no—
248C23—41no—
249C23—41no—
250C23C2×#1175819811yescharacteristic
251C23C2×#1175819911yescharacteristic
252C23C2×#1175820111yescharacteristic
253Q8—4882no—
254Q8—4882no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—44no—
270C2×C4—82no—
271C2×C4—82no—
272C2×C4—2442no—
273C2×C4—2442no—
274C2×C4—2442no—
275C2×C4—2442no—
276C2×C4—2442no—
277C2×C4—2442no—
278C2×C4#1451969111yescharacteristic
279C2×C4#1451969111yescharacteristic
280C2×C4#1451969712yes—
281C2×C4#1451969712yes—
282C2×C4#1451970512yes—
283C8—4882no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22C2×#1451969111yescharacteristic
294C22C2×#1451969711yescharacteristic
295C22C2×#1451970511yescharacteristic
296C4—22no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—41no—
301C4—84no—
302C4—4882no—
303C4—4882no—
304C4#1683949512yes—
305C4#1683949512yes—
306C2—21no—
307C2—21no—
308C2—41no—
309C2—41no—
310C2C2×#1683949511yescharacteristic
311C2#2144747211yescharacteristic
312C2#2144749311yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1740C2
socleC22×C61C2×#99
prime radicalC24×C61C2×D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1740D61
hypocenterC61#11694
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1740

Complements

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

NH ≅ G/Ntype
5. C2×#14519777C4semidirect
9. #16839692C4semidirect
13. #16839628C4semidirect
176. C61#11694semidirect

Maximal subgroups

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

subgroupindex
#214515852
#214441332
#214438182
C61×#17402
#1169461