Finite Group Databasebeta

← #30604782

Subgroups — #30604782

Order 15616.

508 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 90 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#21462048C211yesmaximal, characteristic, complemented
2#21461505C211yesmaximal, characteristic, complemented
3#21460806C214yesmaximal, complemented
4C2×#16839999C211yesmaximal, characteristic
5C2×#14519856—21no—
6C2×#14519851—21no—
7#16840657—21no—
8#16840657C2212yescomplemented
9#16840636—21no—
10#16840636C2212yescomplemented
11C22×D488C411yescharacteristic, complemented
12C22×C8×D61C2211yescharacteristic
13C2×#14519752—21no—
14#16839999—21no—
15#16839999—21no—
16#16839999C412yescomplemented
17#16839999C2212yes—
18C2×#14519697—21no—
19C2×#107×C61C411yescharacteristic, complemented
20#14519856—24no—
21#14519856—42no—
22C2×C4⋊#6923—22no—
23C2×C22⋊#6923—41no—
24C2×C4×#6923—41no—
25#14519851—42no—
26C2×#11758187—22no—
27C22×D244—21no—
28C22×D244—41no—
29C22×C4×D61D411yescharacteristic
30C2×D488—21no—
31C2×D488—42no—
32C2×D488C2×C412yes—
33C22×#92418D411yescharacteristic
34C2×C8×D61—42no—
35C2×C8×D61C2×C411yescharacteristic
36C2×C8×D61D411yescharacteristic
37C2×C8×D61D411yescharacteristic
38C2×C8×D61C2311yescharacteristic
39#14519752—22no—
40#14519752—22no—
41#14519752—41no—
42#14519752—41no—
43C2×#11758198—41no—
44#14519697—22no—
45#14519697—22no—
46C22×C8×C61C2×C411yescharacteristic
47C2×C4⋊C4×C61—21no—
48#107×C61—21no—
49#107×C61C2×C412yes—
50C23×D61—41no—
51C23×D61D811yescharacteristic
52C22×#6923—42no—
53C22×C4×C61—41no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×Dic61SD1611yescharacteristic
56C2×D244—22no—
57C2×D244—42no—
58C2×D244—42no—
59C2×D244—42no—
60C2×D244—42no—
61C2×D244—41no—
62C2×D244—84no—
63C2×C4×D61—22no—
64C2×C4×D61—22no—
65C2×C4×D61C22⋊C411yescharacteristic
66C2×C4×D61D811yescharacteristic
67C2×C4×D61SD1611yescharacteristic
68C2×C4×D61C2×D411yescharacteristic
69C22⋊#6923—44no—
70C4⋊#6923—24no—
71C4⋊#6923—42no—
72C4×#6923—44no—
73C2×C8×C61—22no—
74C2×C8×C61C22⋊C411yescharacteristic
75C2×C8×C61C22×C411yescharacteristic
76C4⋊C4×C61—22no—
77C4⋊C4×C61—41no—
78#11758198—42no—
79#11758198—42no—
80C2×#92418—22no—
81C2×#92418C22⋊C411yescharacteristic
82C2×#92418C2×D411yescharacteristic
83D488—42no—
84D488—42no—
85C8×D61—41no—
86C8×D61—41no—
87C8×D61—41no—
88C8×D61—41no—
89#11758187—42no—
90C23×C61#10211yescharacteristic
91C22×D61—22no—
92C22×D61—22no—
93C22×D61—41no—
94C22×D61—42no—
95C22×D61—82no—
96C22×D61—82no—
97C22×D61—82no—
98C22×D61#10211yescharacteristic
99C22×D61C2×D811yescharacteristic
100C2×#6923—44no—
101C2×#6923—82no—
102C2×#6923—82no—
103C2×C4×C61—42no—
104C2×C4×C61—82no—
105C2×C4×C61#9912yes—
106C2×C4×C61#10211yescharacteristic
107C2×C4×C61#10412yes—
108C2×C4×C61C2×C22⋊C411yescharacteristic
109C2×Dic61—22no—
110C2×Dic61#10211yescharacteristic
111C2×Dic61C2×SD1611yescharacteristic
112D244—42no—
113D244—42no—
114D244—84no—
115D244—84no—
116D244—82no—
117C4×D61—22no—
118C4×D61—22no—
119C4×D61—21no—
120C4×D61—21no—
121C4×D61—21no—
122C4×D61—21no—
123C8×C61—21no—
124C8×C61—21no—
125#92418—21no—
126#92418—21no—
127#11705—611nomaximal, Sylow
128C22×C61—21no—
129C22×C61—21no—
130C22×C61#32712yes—
131C22×C61C2×#10211yescharacteristic
132C2×D61—21no—
133C2×D61—21no—
134C2×D61—21no—
135C2×D61—21no—
136C2×D61—21no—
137C2×D61—44no—
138C2×D61—82no—
139C2×D61—82no—
140C2×D61—82no—
141C2×D61—164no—
142C2×D61#50912yes—
143#6923—84no—
144C4×C61—82no—
145C4×C61#32712yes—
146C4×C61C2×#9911yescharacteristic
147C4×C61C2×#10411yescharacteristic
148Dic61—21no—
149Dic61—21no—
150C2×#466—611no—
151#2112—611no—
152#1735—611no—
153#1347—614no—
154C2×C61—22no—
155C2×C61C2×#32711yescharacteristic
156C2×C61#214011yescharacteristic
157C2×C61#214511yescharacteristic
158D61—22no—
159D61—41no—
160D61—162no—
161C22×D8—611no—
162C23×C8—611no—
163C2×#121—1221no—
164C2×#117—1221no—
165C2×M32—1221no—
166#466—612no—
167#466—612no—
168#466—1221no—
169#466—1221no—
170C2×#107#692311yescharacteristic, complemented
171C2×#102—1221no—
172C22⋊C16—612no—
173C22⋊C16—1221no—
174#340—612no—
175#340—1221no—
176C61#1170511yescharacteristic, complemented, Sylow
177C22×D4—1221no—
178C22×D4—2441no—
179C23×C4—611no—
180C2×D8—612no—
181C2×D8—1221no—
182C2×D8—2442no—
183C22×C8—611no—
184C22×C8—611no—
185C22×C8—611no—
186C22×C8—611no—
187C22×C8—611no—
188C22×C8—2442no—
189C22×C8C2×#692311yescharacteristic
190#121—1222no—
191#121—1222no—
192#121—2441no—
193#121—2441no—
194#117—1224no—
195#117—2442no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—1222no—
198C2×C22⋊C4—2441no—
199C2×C22⋊C4—2441no—
200C2×C42—2441no—
201M32—2442no—
202C2×C16—1222no—
203#107—21no—
204#107C2×#692312yes—
205#102—1222no—
206#102—1222no—
207C24—611no—
208C24—2441no—
209C2×D4—1222no—
210C2×D4—4884no—
211C2×D4—2442no—
212C2×D4—2442no—
213C2×D4—2442no—
214C2×D4—2441no—
215C2×D4—2442no—
216C22×C4—41no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—1222no—
223C22×C4—1222no—
224C22×C4—2442no—
225C22×C4C22⋊#692311yescharacteristic
226D8—2442no—
227D8—2442no—
228C2×C8—22no—
229C2×C8—611no—
230C2×C8—611no—
231C2×C8—1222no—
232C2×C8—2441no—
233C2×C8—2441no—
234C2×C8—2441no—
235C2×C8—2441no—
236C2×C8C22⋊#692311yescharacteristic
237C2×C8C22×#692311yescharacteristic
238C4⋊C4—22no—
239C4⋊C4—41no—
240C4⋊C4—1224no—
241C4⋊C4—2442no—
242C22⋊C4—2442no—
243C22⋊C4—2442no—
244C22⋊C4—2444no—
245C42—2444no—
246C16—2442no—
247C23—611no—
248C23—611no—
249C23—1222no—
250C23—1222no—
251C23—4882no—
252C23—4882no—
253C23—4882no—
254C23—2441no—
255C23—2442no—
256C23#1451983911yescharacteristic
257D4—4884no—
258D4—4884no—
259D4—4882no—
260D4—2442no—
261D4—2442no—
262C2×C4—42no—
263C2×C4—82no—
264C2×C4—611no—
265C2×C4—611no—
266C2×C4—1222no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1222no—
272C2×C4—1222no—
273C2×C4—4882no—
274C2×C4—4882no—
275C2×C4—2444no—
276C2×C4#1451983612yes—
277C2×C4#1451983911yescharacteristic
278C2×C4#1451984212yes—
279C2×C4C2×C22⋊#692311yescharacteristic
280C8—21no—
281C8—21no—
282C8—1221no—
283C8—1221no—
284C22—21no—
285C22—21no—
286C22—612no—
287C22—1221no—
288C22—1221no—
289C22—1221no—
290C22—1221no—
291C22—1221no—
292C22—9764no—
293C22—4882no—
294C22—4882no—
295C22—4882no—
296C22—2444no—
297C22#1684061412yes—
298C22C2×#1451983911yescharacteristic
299C4—82no—
300C4—1221no—
301C4—1221no—
302C4—4884no—
303C4#1684061412yes—
304C4C2×#1451983611yescharacteristic
305C4C2×#1451984211yescharacteristic
306C2—22no—
307C2—1222no—
308C2—9762no—
309C2—2441no—
310C2C2×#1684061411yescharacteristic
311C2#2146212811yescharacteristic
312C2#2146214111yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC2×#107×C61C4
socleC22×C61C2×#102
prime radicalC2×#16839999C2
cosocleC2×C8×D61C23
hypercenterC2×#107#6923
hypocenterC61#11705
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. #21462048C2semidirect
2. #21461505C2semidirect
3. #21460806C2semidirect
8. #16840657C22semidirect
10. #16840636C22semidirect
11. C22×D488C4semidirect
16. #16839999C4semidirect
19. C2×#107×C61C4semidirect
170. C2×#107#6923semidirect
176. C61#11705semidirect

Maximal subgroups

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

subgroupindex
#214620482
#214615052
#214608062
C2×#168399992
#1170561