Finite Group Databasebeta

← #29584981

Subgroups — #29584981

Order 15616.

356 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 89 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#21446616C211yesmaximal, characteristic
2#21445959C211yesmaximal, characteristic, complemented
3#21444589C211yesmaximal, characteristic, complemented
4#21444245C211yesmaximal, characteristic
5#21444243C211yesmaximal, characteristic
6#21443649C211yesmaximal, characteristic, complemented
7C61×#1571C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9#16839815C2211yescharacteristic
10#16839786C2211yescharacteristic
11C2×#14519689—22no—
12C2×#14519688C2211yescharacteristic
13#16839526—22no—
14#16839512—22no—
15#16839491—22no—
16#16839489—22no—
17C61×#431C2211yescharacteristic
18C61×#423C2211yescharacteristic
19C2×C4⋊C8×C61C2211yescharacteristic
20C61×#335—22no—
21C22×D244Q811yescharacteristic
22C22×C4×D61—21no—
23C2×#11758194—21no—
24C22×#92418D412yes—
25C4×D244—21no—
26C4×D244—21no—
27C4×D244—21no—
28C4×D244—21no—
29C2×C4⋊Dic61Q811yescharacteristic
30C2×#11758198—21no—
31C4⋊#92418—21no—
32C4⋊#92418—21no—
33C4⋊#92418—21no—
34C22⋊#92418—21no—
35#14519689—44no—
36#14519688—21no—
37#14519688—21no—
38C4×#92418D412yes—
39C2×M16×C61—21no—
40C22×C8×C61—21no—
41C2×C42×C61C2311yescharacteristic
42C4⋊C8×C61—21no—
43C4⋊C8×C61—21no—
44C4⋊C8×C61—21no—
45C4⋊C8×C61—21no—
46C4⋊C8×C61—21no—
47C22⋊C8×C61—21no—
48C4×C8×C61D412yes—
49C23×D61—21no—
50C22×C4×C61C2×D411yescharacteristic
51C22×C4×C61C2×Q811yescharacteristic
52C22×C4×C61#4111yescharacteristic
53C22×Dic61—21no—
54C2×D244—21no—
55C2×D244—21no—
56C2×D244—42no—
57C2×C4×D61—41no—
58C2×C4×D61—41no—
59C2×C4×D61—42no—
60C2×C4×D61—42no—
61M16×C61—42no—
62C2×C8×C61—22no—
63C2×C8×C61—41no—
64C2×C8×C61—41no—
65C2×C8×C61—42no—
66C42×C61C2×D411yescharacteristic
67C42×C61C2×D411yescharacteristic
68C42×C61#4111yescharacteristic
69C42×C61#4111yescharacteristic
70#11758198—41no—
71#11758198—41no—
72C4⋊Dic61—21no—
73C4⋊Dic61—21no—
74#11758194—42no—
75C2×#92418—22no—
76C2×#92418—22no—
77C2×#92418—22no—
78C2×#92418—22no—
79C2×#92418—41no—
80C23×C61C22⋊Q811yescharacteristic
81C22×D61—22no—
82C22×D61—41no—
83C22×D61—42no—
84C22×D61—41no—
85C22×D61—42no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61C22⋊Q811yescharacteristic
89C2×C4×C61C22⋊Q811yescharacteristic
90C2×C4×C61#12311yescharacteristic
91C2×C4×C61#12311yescharacteristic
92C2×C4×C61#12311yescharacteristic
93C2×C4×C61#12711yescharacteristic
94C2×C4×C61#13512yes—
95C2×C4×C61AGL(1,ℤ/8)12yes—
96C2×Dic61—41no—
97C2×Dic61—42no—
98D244—22no—
99D244—22no—
100D244—41no—
101D244—41no—
102C4×D61—82no—
103C4×D61—81no—
104C4×D61—81no—
105C8×C61—42no—
106C8×C61—81no—
107C8×C61—81no—
108#92418—42no—
109#92418—42no—
110#92418—81no—
111#10659—611nomaximal, Sylow
112C22×C61—21no—
113C22×C61—21no—
114C22×C61#39911yescharacteristic
115C22×C61#47812yes—
116C2×D61—44no—
117C2×D61—42no—
118C2×D61—82no—
119C2×D61—81no—
120C2×D61—81no—
121C4×C61—21no—
122C4×C61—21no—
123C4×C61—21no—
124C4×C61—21no—
125C4×C61#48212yes—
126C4×C61#49511yescharacteristic
127C4×C61#49611yescharacteristic
128Dic61—81no—
129#1955—611no—
130#1838—611no—
131#1571D6111yescharacteristic, complemented
132#1570—611no—
133#1486—611no—
134#1486—611no—
135#1275—611no—
136C2×C61—22no—
137C2×C61#209111yescharacteristic
138C2×C61#209211yescharacteristic
139C2×C61#209811yescharacteristic
140D61—82no—
141C2×C4×D4—611no—
142#431—611no—
143#431C2×D6111yescharacteristic
144#423—611no—
145#423C2×D6111yescharacteristic
146C2×C4⋊C8C2×D6111yescharacteristic
147C2×C22⋊C8—1222no—
148C2×#97—611no—
149#341—1222no—
150#335—22no—
151#334—1222no—
152D4⋊C8—1222no—
153D4⋊C8—1222no—
154C61#1065911yescharacteristic, complemented, Sylow
155C22×D4—611no—
156C23×C4—1221no—
157C2×M16—21no—
158C2×M16—1221no—
159C22×C8—21no—
160C22×C8—612no—
161C4×D4—1221no—
162C4×D4—1221no—
163C4×D4—1221no—
164C4×D4—1221no—
165C2×C4⋊C4—611no—
166C2×C22⋊C4—1221no—
167C2×C42C22×D6111yescharacteristic
168C4⋊C8—21no—
169C4⋊C8—21no—
170C4⋊C8—21no—
171C4⋊C8—21no—
172C4⋊C8—21no—
173C4⋊C8—1221no—
174C4⋊C8—1221no—
175C4⋊C8—1221no—
176C22⋊C8—21no—
177C22⋊C8—1221no—
178C22⋊C8—2444no—
179#97—1221no—
180#97—1221no—
181C4×C8—612no—
182C4×C8C22⋊D6112yes—
183C24—1221no—
184C2×D4—1221no—
185C2×D4—1221no—
186C2×D4—2442no—
187C22×C4—1221no—
188C22×C4—2441no—
189C22×C4—2441no—
190C22×C4—2442no—
191C22×C4—2442no—
192C22×C4#1175822211yescharacteristic
193C22×C4D4×D6111yescharacteristic
194C22×C4Q8×D6111yescharacteristic
195M16—42no—
196M16—2442no—
197C2×C8—22no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—42no—
201C2×C8—1222no—
202C2×C8—1222no—
203C2×C8—1222no—
204C2×C8—1222no—
205C2×C8—2441no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C22⋊C4—2441no—
209C22⋊C4—2441no—
210C42#1175822211yescharacteristic
211C42D4×D6111yescharacteristic
212C42#1175822611yescharacteristic
213C42C2×C22⋊D6111yescharacteristic
214C23—1222no—
215C23—2441no—
216C23—2442no—
217C23—2441no—
218C23—2442no—
219C23#1451975511yescharacteristic
220D4—1222no—
221D4—1222no—
222D4—2441no—
223D4—2441no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—4882no—
227C2×C4—4881no—
228C2×C4—4881no—
229C2×C4—2441no—
230C2×C4—2442no—
231C2×C4#1451975311yescharacteristic
232C2×C4#1451975511yescharacteristic
233C2×C4#1451976011yescharacteristic
234C2×C4#1451976211yescharacteristic
235C2×C4#1451976211yescharacteristic
236C2×C4#1451977311yescharacteristic
237C2×C4#1451980012yes—
238C2×C4#1451980112yes—
239C8—42no—
240C8—81no—
241C8—81no—
242C8—4881no—
243C8—2442no—
244C8—2442no—
245C22—21no—
246C22—21no—
247C22—4882no—
248C22—4881no—
249C22—4881no—
250C22—2444no—
251C22—2442no—
252C22#1683969711yescharacteristic
253C22#1684006512yes—
254C4—21no—
255C4—21no—
256C4—21no—
257C4—21no—
258C4—4881no—
259C4#1684008912yes—
260C4#1684014711yescharacteristic
261C4#1684015011yescharacteristic
262C2—22no—
263C2—4882no—
264C2#2144733411yescharacteristic
265C2#2144733711yescharacteristic
266C2#2144737511yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1571C2
socleC22×C61#399
prime radicalC22×D244Q8
hypercenter#1571D61
hypocenterC61#10659
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
2. #21445959C2semidirect
3. #21444589C2semidirect
6. #21443649C2semidirect
7. C61×#1571C2semidirect
131. #1571D61semidirect
154. C61#10659semidirect

Maximal subgroups

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

subgroupindex
#214466162
#214459592
#214445892
#214442452
#214442432
#214436492
C61×#15712
#1065961