Finite Group Databasebeta

← #29593221

Subgroups — #29593221

Order 15616.

344 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 67 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#21456594C211yesmaximal, characteristic
2#21448017C212yesmaximal, complemented
3#21447242C211yesmaximal, characteristic
4#21443832C212yesmaximal, complemented
5C61×#1314C211yesmaximal, characteristic
6C2×#14519756—21no—
7#16840098—22no—
8#16840003—21no—
9#16840003C2212yes—
10#16839920—22no—
11C2×#14519711C2211yescharacteristic
12#16839622—21no—
13#16839590—22no—
14#16839567—22no—
15#16839525—21no—
16#16839525C2211yescharacteristic
17C2×C22⋊C8×C61C2211yescharacteristic
18C61×C22⋊C16C2212yes—
19C22×Dic122—21no—
20C2×Dic244—21no—
21C2×Dic244D412yes—
22#14519756—22no—
23#14519756—22no—
24#14519756—41no—
25#14519756—41no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×#11758196—41no—
30C2×C22⋊Dic61—41no—
31C2×C22⋊Dic61—41no—
32#14519711—21no—
33#14519711—22no—
34#14519711D412yes—
35#14519702—22no—
36#14519702—22no—
37#14519684—41no—
38C23×C4×C61D411yescharacteristic
39C22×C8×C61D411yescharacteristic
40C22×C8×C61C2311yescharacteristic
41C2×C16×C61—22no—
42C22⋊C8×C61—22no—
43C24×C61D811yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61—41no—
47C22×C4×C61—41no—
48C22×C4×C61D811yescharacteristic
49C22×C4×C61C2×D411yescharacteristic
50C22×Dic61—41no—
51C22×Dic61—41no—
52C22×Dic61—41no—
53C22×Dic61—41no—
54C2×Dic122—22no—
55C2×Dic122—41no—
56C2×Dic122—81no—
57C2×Dic122—81no—
58C2×C8×C61—21no—
59C2×C8×C61—41no—
60C2×C8×C61—41no—
61C2×C8×C61C2×D412yes—
62C22⋊Dic61—42no—
63C22⋊Dic61—42no—
64C22⋊Dic61—82no—
65C4⋊Dic61—22no—
66C4⋊Dic61—41no—
67C4⋊Dic61—41no—
68C4⋊Dic61—41no—
69C4⋊Dic61—41no—
70C4⋊Dic61—41no—
71#11758196—42no—
72#11758196—42no—
73Dic244—42no—
74Dic244—81no—
75C16×C61—42no—
76C23×C61—21no—
77C23×C61—21no—
78C23×C61—41no—
79C23×C61—41no—
80C23×C61SD3212yes—
81C23×C61C2×D811yescharacteristic
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61—81no—
89C2×C4×C61#12011yescharacteristic
90C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
91C2×Dic61—42no—
92C2×Dic61—42no—
93C2×Dic61—82no—
94C2×Dic61—82no—
95C2×Dic61—81no—
96C2×Dic61—81no—
97C2×Dic61—81no—
98C2×Dic61—81no—
99C2×Dic61—81no—
100C2×Dic61—81no—
101Dic122—42no—
102Dic122—42no—
103Dic122—82no—
104C8×C61—22no—
105C8×C61—41no—
106#12279—611nomaximal, Sylow
107C22×C61—21no—
108C22×C61—21no—
109C22×C61—22no—
110C22×C61—42no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61—81no—
114C22×C61#44711yescharacteristic
115C22×C61C2×SD3211yescharacteristic
116C22×C61#51011yescharacteristic
117C4×C61—21no—
118C4×C61—41no—
119C4×C61#45511yescharacteristic
120C4×C61#45811yescharacteristic
121Dic61—82no—
122Dic61—82no—
123Dic61—161no—
124Dic61—161no—
125#3189—611no—
126#2235—612no—
127#2075—611no—
128#1348—612no—
129#1314D6111yescharacteristic
130C2×C61—21no—
131C2×C61—21no—
132C2×C61—42no—
133C2×C61#160711yescharacteristic
134C2×C61#218511yescharacteristic
135C2×C61#219111yescharacteristic
136C2×C22⋊Q8—1221no—
137#484—1222no—
138#467—612no—
139#467—1221no—
140#451—1222no—
141C2×#107—611no—
142C2×C22⋊C8C2×D6111yescharacteristic
143#380—1221no—
144#367—1222no—
145#358—1222no—
146C22⋊C16C2×D6112yes—
147#340—611no—
148#340—1221no—
149C61#1227911yescharacteristic, complemented, Sylow
150C22×Q8—1221no—
151C23×C4D24411yescharacteristic
152C2×Q16—612no—
153C2×Q16—1221no—
154C22×C8D24411yescharacteristic
155C22×C8C22×D6111yescharacteristic
156C22⋊Q8—1222no—
157C22⋊Q8—1222no—
158C22⋊Q8—2441no—
159C22⋊Q8—2441no—
160C2×C4⋊C4—1221no—
161C2×C4⋊C4—1221no—
162C2×C4⋊C4—1221no—
163C2×C4⋊C4—2441no—
164C2×C22⋊C4—2441no—
165C2×C22⋊C4—2441no—
166C2×C16—22no—
167#107—612no—
168#107—1221no—
169#107—1222no—
170#103—1222no—
171#103—1222no—
172C22⋊C8—22no—
173#95—2441no—
174C24D48811yescharacteristic
175C2×Q8—1222no—
176C2×Q8—4881no—
177C2×Q8—4881no—
178C2×Q8—2441no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—2441no—
184C22×C4—2441no—
185C22×C4—2441no—
186C22×C4—2441no—
187C22×C4D48811yescharacteristic
188C22×C4C2×D24411yescharacteristic
189Q16—4881no—
190Q16—2442no—
191C2×C8—21no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8D4×D6112yes—
195C4⋊C4—1222no—
196C4⋊C4—2441no—
197C4⋊C4—2441no—
198C4⋊C4—2441no—
199C4⋊C4—2442no—
200C4⋊C4—2441no—
201C4⋊C4—2441no—
202C4⋊C4—2442no—
203C22⋊C4—4882no—
204C22⋊C4—2442no—
205C22⋊C4—2442no—
206C16—42no—
207C23—21no—
208C23—21no—
209C23—41no—
210C23—41no—
211C23#1451972212yes—
212C23C2×D48811yescharacteristic
213Q8—4882no—
214Q8—2442no—
215Q8—2442no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—81no—
223C2×C4—4881no—
224C2×C4—4881no—
225C2×C4—4881no—
226C2×C4—4881no—
227C2×C4—4881no—
228C2×C4—4881no—
229C2×C4—4882no—
230C2×C4—4882no—
231C2×C4—2442no—
232C2×C4—2442no—
233C2×C4#1451974711yescharacteristic
234C2×C4#1451980511yescharacteristic
235C8—22no—
236C8—41no—
237C22—21no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—81no—
244C22#1683989811yescharacteristic
245C22C2×#1451972211yescharacteristic
246C22#1684020511yescharacteristic
247C4—21no—
248C4—41no—
249C4—9761no—
250C4—9761no—
251C4—4882no—
252C4—4882no—
253C4#1683994211yescharacteristic
254C4#1683995311yescharacteristic
255C2—21no—
256C2—21no—
257C2—42no—
258C2#2144480711yescharacteristic
259C2#2144773811yescharacteristic
260C2#2144777211yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1314C2
socleC22×C61#447
prime radicalC24×C61D8
hypercenter#1314D61
hypocenterC61#12279
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. #21448017C2semidirect
4. #21443832C2semidirect
149. C61#12279semidirect

Maximal subgroups

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

subgroupindex
#214565942
#214480172
#214472422
#214438322
C61×#13142
#1227961