Finite Group Databasebeta

← #30605434

Subgroups — #30605434

Order 15616.

464 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462047C211yesmaximal, characteristic, complemented
2#21461695C211yesmaximal, characteristic, complemented
3#21460806C214yesmaximal, complemented
4C2×#16839999C211yesmaximal, characteristic
5C2×#14519852—21no—
6C2×#14519845—21no—
7#16840704—21no—
8#16840657C2212yescomplemented
9C22⋊#11758187—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
20C2×C4⋊#6923—22no—
21C2×C22⋊#6923—41no—
22#14519852—42no—
23C2×#11758187—22no—
24#14519845—42no—
25(C2×#6923)⋊C4—41no—
26C22×D244—21no—
27C22×D244—41no—
28C22×C4×D61D411yescharacteristic
29C2×D488—21no—
30C2×D488—42no—
31C2×D488C2×C412yes—
32C22×#92418D411yescharacteristic
33C2×C8×D61—42no—
34C2×C8×D61C2×C411yescharacteristic
35C2×C8×D61D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37C2×C8×D61C2311yescharacteristic
38#14519752—22no—
39#14519752—22no—
40#14519752—41no—
41#14519752—41no—
42C2×#11758198—41no—
43#14519697—22no—
44#14519697—22no—
45C22×C8×C61C2×C411yescharacteristic
46C2×C4⋊C4×C61—21no—
47#107×C61—21no—
48#107×C61C2×C412yes—
49C23×D61—41no—
50C23×D61D811yescharacteristic
51C22×#6923—42no—
52C22×C4×C61—41no—
53C22×C4×C61C22⋊C411yescharacteristic
54C22×Dic61SD1611yescharacteristic
55C2×D244—22no—
56C2×D244—42no—
57C2×D244—42no—
58C2×D244—42no—
59C2×D244—42no—
60C2×D244—41no—
61C2×D244—84no—
62C2×C4×D61—41no—
63C2×C4×D61—41no—
64C2×C4×D61C22⋊C411yescharacteristic
65C2×C4×D61D811yescharacteristic
66C2×C4×D61SD1611yescharacteristic
67C2×C4×D61C2×D411yescharacteristic
68C22⋊#6923—82no—
69C4⋊#6923—42no—
70C4⋊#6923—42no—
71C2×C8×C61—22no—
72C2×C8×C61C22⋊C411yescharacteristic
73C2×C8×C61C22×C411yescharacteristic
74C4⋊C4×C61—22no—
75C4⋊C4×C61—41no—
76#11758198—42no—
77#11758198—42no—
78C2×#92418—41no—
79C2×#92418C22⋊C411yescharacteristic
80C2×#92418C2×D411yescharacteristic
81D488—42no—
82D488—42no—
83C8×D61—22no—
84C8×D61—22no—
85C8×D61—41no—
86C8×D61—41no—
87#11758187—42no—
88C23×C61#10211yescharacteristic
89C22×D61—22no—
90C22×D61—22no—
91C22×D61—41no—
92C22×D61—42no—
93C22×D61—82no—
94C22×D61—82no—
95C22×D61—82no—
96C22×D61#10211yescharacteristic
97C22×D61C2×D811yescharacteristic
98C2×#6923—82no—
99C2×#6923—82no—
100C2×#6923—82no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—42no—
104C2×C4×C61—82no—
105C2×C4×C61#10211yescharacteristic
106C2×C4×C61C2×C22⋊C411yescharacteristic
107C2×Dic61—41no—
108C2×Dic61#10211yescharacteristic
109C2×Dic61C2×SD1611yescharacteristic
110D244—42no—
111D244—42no—
112D244—82no—
113D244—84no—
114D244—84no—
115C4×D61—21no—
116C4×D61—21no—
117C4×D61—21no—
118C4×D61—21no—
119C4×D61—41no—
120C4×D61—41no—
121C8×C61—21no—
122C8×C61#9912yes—
123#92418—21no—
124#92418—21no—
125#11888—611nomaximal, Sylow
126C22×C61—21no—
127C22×C61—21no—
128C22×C61#36012yes—
129C22×C61C2×#10211yescharacteristic
130C2×D61—21no—
131C2×D61—21no—
132C2×D61—21no—
133C2×D61—21no—
134C2×D61—21no—
135C2×D61—44no—
136C2×D61—82no—
137C2×D61—82no—
138C2×D61—82no—
139C2×D61—164no—
140C2×D61#50912yes—
141#6923—162no—
142C4×C61—21no—
143C4×C61—82no—
144C4×C61C2×#9911yescharacteristic
145C4×C61#42111yescharacteristic
146Dic61—21no—
147Dic61—21no—
148C2×#466—611no—
149#2112—611no—
150#1807—611no—
151#1347—614no—
152C2×C61—22no—
153C2×C61#151911yescharacteristic
154C2×C61#214011yescharacteristic
155C2×C61C2×#36011yescharacteristic
156D61—22no—
157D61—41no—
158D61—162no—
159C22×D8—611no—
160C23×C8—611no—
161C2×#121—1221no—
162C2×M32—1221no—
163#466—612no—
164#466—612no—
165#466—1221no—
166#466—1221no—
167C2×#107#692311yescharacteristic, complemented
168C2×#106—1221no—
169C2×#102—1221no—
170#380—1221no—
171C22⋊C16—612no—
172C22⋊C16—1221no—
173#340—612no—
174C61#1188811yescharacteristic, complemented, Sylow
175C22×D4—1221no—
176C22×D4—2441no—
177C23×C4—611no—
178C2×D8—612no—
179C2×D8—1221no—
180C2×D8—2442no—
181C22×C8—611no—
182C22×C8—611no—
183C22×C8—611no—
184C22×C8—611no—
185C22×C8—611no—
186C22×C8—2442no—
187C22×C8C2×#692311yescharacteristic
188#121—1222no—
189#121—1222no—
190#121—2441no—
191#121—2441no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—1222no—
194C2×C22⋊C4—2441no—
195C2×C22⋊C4—2441no—
196M32—2442no—
197C2×C16—1222no—
198#107—21no—
199#107C2×#692312yes—
200#106—2442no—
201#102—1222no—
202#102—1222no—
203#95—2441no—
204C24—611no—
205C24—2441no—
206C2×D4—1222no—
207C2×D4—4884no—
208C2×D4—2442no—
209C2×D4—2442no—
210C2×D4—2442no—
211C2×D4—2442no—
212C2×D4—2441no—
213C22×C4—41no—
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—2441no—
220C22×C4—2441no—
221C22×C4—2442no—
222C22×C4C22⋊#692311yescharacteristic
223D8—2442no—
224D8—2442no—
225C2×C8—22no—
226C2×C8—611no—
227C2×C8—611no—
228C2×C8—1222no—
229C2×C8—1222no—
230C2×C8—2441no—
231C2×C8—2441no—
232C2×C8—2441no—
233C2×C8C22⋊#692311yescharacteristic
234C2×C8C22×#692311yescharacteristic
235C4⋊C4—22no—
236C4⋊C4—41no—
237C4⋊C4—2442no—
238C4⋊C4—2442no—
239C22⋊C4—4882no—
240C22⋊C4—2442no—
241C22⋊C4—2442no—
242C16—2442no—
243C23—611no—
244C23—611no—
245C23—1222no—
246C23—1222no—
247C23—4882no—
248C23—4882no—
249C23—4882no—
250C23—2441no—
251C23—2442no—
252C23#1451983911yescharacteristic
253D4—4882no—
254D4—4884no—
255D4—4884no—
256D4—2442no—
257D4—2442no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—82no—
262C2×C4—611no—
263C2×C4—611no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—4882no—
269C2×C4—4882no—
270C2×C4—4882no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4#1451983911yescharacteristic
275C2×C4C2×C22⋊#692311yescharacteristic
276C8—21no—
277C8—1221no—
278C8—1221no—
279C8#1451983612yes—
280C22—21no—
281C22—21no—
282C22—612no—
283C22—1221no—
284C22—1221no—
285C22—1221no—
286C22—1221no—
287C22—1221no—
288C22—9764no—
289C22—4882no—
290C22—4882no—
291C22—4882no—
292C22—2444no—
293C22#1684067912yes—
294C22C2×#1451983911yescharacteristic
295C4—21no—
296C4—82no—
297C4—1221no—
298C4—1221no—
299C4—9762no—
300C4C2×#1451983611yescharacteristic
301C4#1684076111yescharacteristic
302C2—22no—
303C2—1222no—
304C2—9762no—
305C2—2441no—
306C2#2146125611yescharacteristic
307C2#2146212811yescharacteristic
308C2C2×#1684067911yescharacteristic
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#11888
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. #21462047C2semidirect
2. #21461695C2semidirect
3. #21460806C2semidirect
8. #16840657C22semidirect
10. #16840636C22semidirect
11. C22×D488C4semidirect
16. #16839999C4semidirect
19. C2×#107×C61C4semidirect
167. C2×#107#6923semidirect
174. C61#11888semidirect

Maximal subgroups

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

subgroupindex
#214620472
#214616952
#214608062
C2×#168399992
#1188861