Finite Group Databasebeta

← #29573630

Subgroups — #29573630

Order 15616.

384 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 95 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#21448784C211yesmaximal, characteristic
2#21444163C211yesmaximal, characteristic
3#21443713C212yesmaximal
4#21443684C212yesmaximal
5C4×#101×C61C211yesmaximal, characteristic
6#16839819C2212yes—
7#16839669—21no—
8#16839648—21no—
9#16839648—21no—
10#16839630C411yescharacteristic
11#16839630C2211yescharacteristic
12#16839628C411yescharacteristic
13C4⋊C4×Dic61—21no—
14C4×C4⋊Dic61C411yescharacteristic
15#16839608C411yescharacteristic
16#16839608C2211yescharacteristic
17#16839488—21no—
18#16839488—21no—
19C2×C4×Q8×C61C2211yescharacteristic
20C2×#101×C61—21no—
21C4×M16×C61C2212yes—
22C61×#343—21no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—21no—
25C2×C4×Dic61—21no—
26C2×C4×Dic61—21no—
27C2×C4×Dic61—21no—
28C4⋊#92418—22no—
29C22⋊#92418—22no—
30#14519688—22no—
31#14519684—21no—
32#14519684—21no—
33#14519684—21no—
34#14519684—21no—
35#14519684—21no—
36#14519684—21no—
37#14519684—21no—
38#14519684C2×C411yescharacteristic
39#14519684C2×C411yescharacteristic
40#14519684C2×C411yescharacteristic
41#14519684C2×C411yescharacteristic
42C22×Q8×C61D411yescharacteristic
43C2×M16×C61—22no—
44C4×Q8×C61—22no—
45C4×Q8×C61—22no—
46C2×C4⋊C4×C61D411yescharacteristic
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C42×C61C2×C411yescharacteristic
50C2×C42×C61C2×C411yescharacteristic
51C2×C42×C61C2311yescharacteristic
52#101×C61—24no—
53#97×C61—22no—
54C4×C8×C61—22no—
55C2×Q8×C61—22no—
56C2×Q8×C61—22no—
57C2×Q8×C61—41no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69M16×C61—24no—
70M16×C61—42no—
71C2×C8×C61—42no—
72C4⋊C4×C61—22no—
73C4⋊C4×C61—22no—
74C4⋊C4×C61—22no—
75C42×C61—21no—
76C42×C61—21no—
77C42×C61—21no—
78C42×C61—21no—
79C42×C61#4112yes—
80C42×C61#4112yes—
81C4⋊Dic61—42no—
82C4⋊Dic61—42no—
83C4×Dic61—42no—
84C4×Dic61—42no—
85C4×Dic61—42no—
86C2×#92418—42no—
87C23×C61C2×C22⋊C411yescharacteristic
88Q8×C61—44no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61#10412yes—
103C2×C4×C61#11711yescharacteristic
104C2×C4×C61#11711yescharacteristic
105C2×C4×C61#12312yes—
106C2×C4×C61#12312yes—
107C2×Dic61—22no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C8×C61—44no—
120#92418—82no—
121#8774—611nomaximal, Sylow
122C22×C61—21no—
123C22×C61—21no—
124C22×C61#38111yescharacteristic
125C22×C61C2×#10411yescharacteristic
126C22×C61#42111yescharacteristic
127C4×C61—22no—
128C4×C61—22no—
129C4×C61—22no—
130C4×C61—21no—
131C4×C61—21no—
132C4×C61—41no—
133C4×C61—41no—
134C4×C61—41no—
135Dic61—42no—
136Dic61—81no—
137Dic61—81no—
138Dic61—81no—
139#2356—611no—
140C4×#101D6111yescharacteristic
141#1467—611no—
142#1300—612no—
143#1288—612no—
144C2×C61—21no—
145C2×C61—21no—
146C2×C61#182611yescharacteristic
147C2×C61#182711yescharacteristic
148C2×C61#183011yescharacteristic
149C2×C4×Q8C2×D6111yescharacteristic
150#432—612no—
151C2×#101—21no—
152C4×M16C2×D6112yes—
153#391—1221no—
154#387—1221no—
155#387—1221no—
156#383—611no—
157#383—611no—
158#382—611no—
159C4×C4⋊C4—611no—
160C4×C4⋊C4—1221no—
161#376—611no—
162#376—611no—
163#343—21no—
164#324—1221no—
165#324—1221no—
166C61#877411yescharacteristic, complemented, Sylow
167C22×Q8C22⋊D6111yescharacteristic
168C2×M16—22no—
169C4×Q8—22no—
170C4×Q8—22no—
171C2×C4⋊C4—1221no—
172C2×C4⋊C4—1221no—
173C2×C4⋊C4D24411yescharacteristic
174C2×C4⋊C4D24411yescharacteristic
175C2×C4⋊C4C22⋊D6111yescharacteristic
176C2×C42—1221no—
177C2×C42—1221no—
178C2×C42—1221no—
179C2×C42C4×D6111yescharacteristic
180C2×C42C4×D6111yescharacteristic
181C2×C42C22×D6111yescharacteristic
182C4⋊C8—1222no—
183#101—24no—
184C22⋊C8—1222no—
185#97—22no—
186#97—1222no—
187C4×C8—22no—
188#95—611no—
189#95—611no—
190#95—611no—
191#95—611no—
192#95—1221no—
193#95—1221no—
194#95—1221no—
195#95—1221no—
196#95—1221no—
197#95—1221no—
198#95—1221no—
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—41no—
202C22×C4—1221no—
203C22×C4—1221no—
204C22×C4—1221no—
205C22×C4—1221no—
206C22×C4#1175819811yescharacteristic
207C22×C4#1175819811yescharacteristic
208C22×C4#1175819811yescharacteristic
209C22×C4#1175819811yescharacteristic
210C22×C4C2×C4×D6111yescharacteristic
211C22×C4C2×D24411yescharacteristic
212C22×C4C2×C22⋊D6111yescharacteristic
213M16—24no—
214M16—42no—
215C2×C8—42no—
216C2×C8—2442no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—2442no—
221C4⋊C4—2442no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—2442no—
227C42—2442no—
228C42—2442no—
229C42#1175822412yes—
230C42#1175822412yes—
231C23C2×#1175819811yescharacteristic
232Q8—44no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—1222no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4—2441no—
254C2×C4—2441no—
255C2×C4—2441no—
256C2×C4—2441no—
257C2×C4—2441no—
258C2×C4#1451970512yes—
259C2×C4#1451973311yescharacteristic
260C2×C4#1451973311yescharacteristic
261C2×C4#1451975812yes—
262C2×C4#1451976112yes—
263C8—44no—
264C8—4882no—
265C22—21no—
266C22—21no—
267C22#1683962311yescharacteristic
268C22C2×#1451970511yescharacteristic
269C22#1683978011yescharacteristic
270C4—22no—
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—41no—
276C4—41no—
277C4—41no—
278C4—4881no—
279C4—4881no—
280C4—4881no—
281C4—2442no—
282C2—21no—
283C2—21no—
284C2#2144591911yescharacteristic
285C2#2144592411yescharacteristic
286C2#2144593111yescharacteristic
subgroupG/H
centerC22#16839623
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC4×#101×C61C2
socleC22×C61#381
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenterC4×#101D61
hypocenterC61#8774
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
166. C61#8774semidirect

Maximal subgroups

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

subgroupindex
#214487842
#214441632
#214437132
#214436842
C4×#101×C612
#877461