Finite Group Databasebeta

← #29580664

Subgroups — #29580664

Order 15616.

602 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 79 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#21455759C212yesmaximal, complemented
2#21453843C211yesmaximal, characteristic
3#21444347C212yesmaximal, complemented
4#21443727C211yesmaximal, characteristic, complemented
5C61×#1820C211yesmaximal, characteristic, complemented
6C2×#14519751C2212yes—
7#16840086—24no—
8#16840080—22no—
9#16840075—22no—
10#16839805—22no—
11#16839766—22no—
12#16839726C2212yes—
13#16839689—22no—
14#16839672—22no—
15#16839671—22no—
16#16839495—24no—
17C2×#117×C61C2211yescharacteristic
18C61×#381C2211yescharacteristic
19C61×#381C2211yescharacteristic
20C61×#342—22no—
21C22×D244—22no—
22C22×D244D412yes—
23C22×C22⋊D61—22no—
24C2×#11758194—22no—
25#14519751—22no—
26#14519751—22no—
27#14519751—22no—
28#14519751—22no—
29C2×C4⋊Dic61D412yes—
30C2×#11758198—22no—
31C2×#11758198—24no—
32#14519710—24no—
33#14519708—24no—
34#14519697—24no—
35#14519697—24no—
36C22⋊#92418—22no—
37C22⋊#92418D414yescomplemented
38#14519684—22no—
39C23×C4×C61C2311yescharacteristic
40#117×C61—22no—
41#117×C61—22no—
42C2×C4⋊C4×C61D412yescomplemented
43C2×C22⋊C4×C61—21no—
44C2×C22⋊C4×C61—21no—
45C2×C22⋊C4×C61D412yes—
46C2×C42×C61—21no—
47#95×C61—22no—
48#95×C61—22no—
49C24×C61C2×D411yescharacteristic
50C23×D61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61—42no—
54C22×C4×C61—41no—
55C22×C4×C61C2×D412yes—
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61C2×D412yes—
58C22×C4×C61#4111yescharacteristic
59C2×C22⋊D61—42no—
60C2×C22⋊D61—42no—
61C2×C22⋊D61—84no—
62C22×Dic61—22no—
63C2×D244—22no—
64C2×D244—22no—
65C2×D244—44no—
66C2×D244—84no—
67C2×D244—82no—
68C4⋊C4×C61—22no—
69C4⋊C4×C61—22no—
70C22⋊C4×C61—41no—
71C22⋊C4×C61—41no—
72C22⋊C4×C61—42no—
73C22⋊C4×C61—42no—
74C42×C61—42no—
75#11758198—42no—
76#11758198—42no—
77#11758198—84no—
78C4⋊Dic61—22no—
79C4⋊Dic61—22no—
80#11758194—44no—
81C2×#92418—24no—
82C23×C61—22no—
83C23×C61—42no—
84C23×C61#12011yescharacteristic
85C23×C61#12111yescharacteristic
86C23×C61#12711yescharacteristic
87C22×D61—42no—
88C22×D61—42no—
89C22×D61—44no—
90C22×D61—42no—
91C22×D61—44no—
92C2×C4×C61—24no—
93C2×C4×C61—41no—
94C2×C4×C61—42no—
95C2×C4×C61—41no—
96C2×C4×C61—44no—
97C2×C4×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61—82no—
100C2×C4×C61—81no—
101C2×C4×C61—82no—
102C2×C4×C61#12012yes—
103C2×C4×C61#12112yes—
104C22⋊D61—84no—
105C22⋊D61—84no—
106C2×Dic61—44no—
107C2×Dic61—42no—
108D244—44no—
109D244—82no—
110D244—88no—
111#92418—44no—
112#9983—611nomaximal, Sylow
113C22×C61—22no—
114C22×C61—22no—
115C22×C61—22no—
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—82no—
119C22×C61#39211yescharacteristic
120C22×C61#45812yes—
121C2×D61—84no—
122C2×D61—84no—
123C2×D61—82no—
124C2×D61—82no—
125C2×D61—82no—
126C4×C61—22no—
127C4×C61—22no—
128C4×C61—82no—
129C4×C61—82no—
130C4×C61—161no—
131Dic61—82no—
132#3094—612no—
133#2815—611no—
134#1820D6111yescharacteristic, complemented
135#1510—612no—
136#1306—611no—
137C2×C61—22no—
138C2×C61—41no—
139C2×C61—41no—
140C2×C61#200812yes—
141C2×C61#202211yescharacteristic
142D61—162no—
143C2×#121—612no—
144C2×#117C2×D6111yescharacteristic
145#482—1224no—
146#481—1222no—
147#480—1222no—
148#428—1222no—
149#418—1222no—
150#407—612no—
151#397—1222no—
152#392—1222no—
153#392—1222no—
154#381C2×D6111yescharacteristic
155#381C2×D6111yescharacteristic
156#342—22no—
157#327—1224no—
158C61#998311yescharacteristic, complemented, Sylow
159C22×D4—612no—
160C22×D4—1222no—
161C22×D4—1222no—
162C23×C4C22×D6111yescharacteristic
163C2×M16—1222no—
164#121—1222no—
165#121—1222no—
166#121—1222no—
167#121—1222no—
168#117—22no—
169#117—22no—
170C2×C4⋊C4—612no—
171C2×C4⋊C4D24412yescomplemented
172C2×C22⋊C4—21no—
173C2×C22⋊C4—21no—
174C2×C22⋊C4—1224no—
175C2×C22⋊C4—1222no—
176C2×C22⋊C4C22⋊D6112yes—
177C2×C42—21no—
178#107—1224no—
179#106—1224no—
180#102—1224no—
181#102—1224no—
182C22⋊C8—614no—
183C22⋊C8—1222no—
184#95—22no—
185#95—22no—
186#95—1222no—
187C24—1222no—
188C24C2×C22⋊D6111yescharacteristic
189C2×D4—1222no—
190C2×D4—1222no—
191C2×D4—4884no—
192C2×D4—4882no—
193C2×D4—4884no—
194C2×D4—2444no—
195C2×D4—2442no—
196C2×D4—2442no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—42no—
200C22×C4—41no—
201C22×C4—1222no—
202C22×C4C2×D24411yescharacteristic
203C22×C4#1175822211yescharacteristic
204C22×C4D4×D6112yes—
205C22×C4D4×D6112yes—
206M16—2444no—
207C2×C8—1224no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—1222no—
211C4⋊C4—1222no—
212C22⋊C4—41no—
213C22⋊C4—41no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—4884no—
217C22⋊C4—2442no—
218C22⋊C4—2442no—
219C42—42no—
220C23—22no—
221C23—42no—
222C23—2442no—
223C23—2442no—
224C23—2444no—
225C23—2444no—
226C23—2442no—
227C23#1451974511yescharacteristic
228C23#1451975111yescharacteristic
229C23#1451977311yescharacteristic
230D4—4882no—
231D4—4888no—
232D4—4884no—
233D4—4884no—
234D4—2444no—
235C2×C4—24no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—44no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—82no—
243C2×C4—81no—
244C2×C4—82no—
245C2×C4—2444no—
246C2×C4—2442no—
247C2×C4#1451974712yes—
248C2×C4#1451975012yes—
249C8—2444no—
250C22—22no—
251C22—21no—
252C22—21no—
253C22—22no—
254C22—22no—
255C22—82no—
256C22—4884no—
257C22—4884no—
258C22—4882no—
259C22—4882no—
260C22—4882no—
261C22#1683967111yescharacteristic
262C22#1683995112yes—
263C4—22no—
264C4—22no—
265C4—82no—
266C4—82no—
267C4—161no—
268C4—4882no—
269C2—22no—
270C2—41no—
271C2—41no—
272C2—9762no—
273C2#2144687112yes—
274C2#2144695011yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1820C2
socleC22×C61#392
prime radical#21453843C2
hypercenter#1820D61
hypocenterC61#9983
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
1. #21455759C2semidirect
3. #21444347C2semidirect
4. #21443727C2semidirect
5. C61×#1820C2semidirect
37. C22⋊#92418D4semidirect
42. C2×C4⋊C4×C61D4semidirect
134. #1820D61semidirect
158. C61#9983semidirect
171. C2×C4⋊C4D244semidirect

Maximal subgroups

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

subgroupindex
#214557592
#214538432
#214443472
#214437272
C61×#18202
#998361