Finite Group Databasebeta

← #29576019

Subgroups — #29576019

Order 15616.

458 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 111 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#21454457C211yesmaximal, characteristic
2#21451640C211yesmaximal, characteristic
3#21444499C212yesmaximal, complemented
4#21443678C212yesmaximal, complemented
5C61×#1458C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7#16839823—24no—
8#16839786C2212yes—
9#16839726—21no—
10C4×#11758194—21no—
11#16839701—21no—
12#16839698—21no—
13#16839682C412yes—
14#16839674C412yes—
15#16839660—21no—
16#16839628C2211yescharacteristic
17#16839622—21no—
18#16839510—24no—
19C2×#117×C61C2211yescharacteristic
20C61×#431C2212yes—
21C61×#324—21no—
22C61×#323—21no—
23C22×Dic122C2×C412yes—
24C2×#11758194—22no—
25#14519777—22no—
26#14519777—22no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C2×#11758196—22no—
31C2×C22⋊Dic61—22no—
32C4⋊#92418—22no—
33C4⋊#92418D414yes—
34C22⋊#92418—24no—
35#14519688—22no—
36C4×#92418—22no—
37#14519684—22no—
38#14519684—22no—
39#14519684—21no—
40#14519684C2×C412yes—
41C23×C4×C61D411yescharacteristic
42#117×C61—22no—
43#117×C61—22no—
44C2×C4⋊C4×C61C2×C411yescharacteristic
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C22⋊C4×C61C2×C411yescharacteristic
47C2×C22⋊C4×C61D411yescharacteristic
48C2×C42×C61D411yescharacteristic
49C2×C42×C61C2311yescharacteristic
50C4⋊C8×C61—22no—
51C22⋊C8×C61—22no—
52C4×C8×C61—22no—
53C24×C61C22⋊C411yescharacteristic
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—22no—
57C22×C4×C61—22no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×Dic61—22no—
65C22×Dic61—22no—
66C2×Dic122—24no—
67C2×Dic122—82no—
68C2×C8×C61—42no—
69C4⋊C4×C61—22no—
70C4⋊C4×C61—22no—
71C22⋊C4×C61—22no—
72C22⋊C4×C61—22no—
73C42×C61—21no—
74C42×C61—21no—
75C42×C61C2×D412yes—
76C42×C61#4112yes—
77C22⋊Dic61—82no—
78C4⋊Dic61—41no—
79C4⋊Dic61—42no—
80C4⋊Dic61—41no—
81C4⋊Dic61—42no—
82#11758196—82no—
83#11758194—42no—
84#11758194—42no—
85C2×#92418—24no—
86C23×C61—21no—
87C23×C61—21no—
88C23×C61—21no—
89C23×C61—41no—
90C23×C61—41no—
91C23×C61C2×C22⋊C411yescharacteristic
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—42no—
100C2×C4×C61—42no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61C4×D412yes—
104C2×C4×C61#12011yescharacteristic
105C2×C4×C61#12112yes—
106C2×C4×C61#12311yescharacteristic
107C2×C4×C61#13512yes—
108C2×C4×C61#13712yes—
109C2×Dic61—42no—
110C2×Dic61—42no—
111C2×Dic61—42no—
112C2×Dic61—42no—
113C2×Dic61—42no—
114C2×Dic61—42no—
115Dic122—84no—
116C8×C61—82no—
117#92418—44no—
118#9192—611nomaximal, Sylow
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—42no—
122C22×C61—41no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61—81no—
126C22×C61#38611yescharacteristic
127C22×C61#41611yescharacteristic
128C22×C61#41911yescharacteristic
129C4×C61—22no—
130C4×C61—22no—
131C4×C61—41no—
132C4×C61—41no—
133C4×C61—41no—
134C4×C61#45212yes—
135C4×C61#48512yes—
136Dic61—82no—
137Dic61—82no—
138#2921—611no—
139#2628—611no—
140#1548—612no—
141#1458D6111yescharacteristic
142#1286—612no—
143C2×C61—21no—
144C2×C61—21no—
145C2×C61—81no—
146C2×C61#187311yescharacteristic
147C2×C61#190911yescharacteristic
148C2×C61#191411yescharacteristic
149C2×C4⋊Q8—611no—
150C2×#117C2×D6111yescharacteristic
151#433—1224no—
152#431C2×D6112yes—
153#423—612no—
154#407—1221no—
155C4×M16—1221no—
156#400—1221no—
157#399—1221no—
158#395—612no—
159#393—612no—
160#389—1221no—
161#382—611no—
162#380—1221no—
163#333—1224no—
164#324—21no—
165#323—21no—
166C61#919211yescharacteristic, complemented, Sylow
167C22×Q8—612no—
168C23×C4D24411yescharacteristic
169C2×M16—1222no—
170C4⋊Q8—1222no—
171C4⋊Q8—1222no—
172#117—22no—
173#117—22no—
174C2×C4⋊C4—1222no—
175C2×C4⋊C4—1221no—
176C2×C4⋊C4—1221no—
177C2×C4⋊C4—1221no—
178C2×C4⋊C4C4×D6111yescharacteristic
179C2×C4⋊C4C22⋊D6111yescharacteristic
180C2×C22⋊C4—1222no—
181C2×C22⋊C4C4×D6111yescharacteristic
182C2×C22⋊C4C22⋊D6111yescharacteristic
183C2×C42D24411yescharacteristic
184C2×C42C22×D6111yescharacteristic
185C4⋊C8—22no—
186C4⋊C8—614no—
187C4⋊C8—1222no—
188C22⋊C8—22no—
189C22⋊C8—1224no—
190#97—1222no—
191C4×C8—22no—
192C4×C8—1222no—
193#95—612no—
194#95—1222no—
195#95—1222no—
196#95—1221no—
197C24#1175819811yescharacteristic
198C2×Q8—1224no—
199C2×Q8—4882no—
200C22×C4—22no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—1222no—
205C22×C4—1222no—
206C22×C4#1175819811yescharacteristic
207C22×C4#1175819811yescharacteristic
208C22×C4#1175819811yescharacteristic
209C22×C4C2×C4×D6111yescharacteristic
210C22×C4C2×D24411yescharacteristic
211C22×C4C2×C22⋊D6111yescharacteristic
212M16—2442no—
213M16—2442no—
214C2×C8—42no—
215C2×C8—1224no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—4882no—
219C4⋊C4—2441no—
220C4⋊C4—2442no—
221C4⋊C4—2441no—
222C4⋊C4—2442no—
223C22⋊C4—22no—
224C22⋊C4—22no—
225C22⋊C4—4882no—
226C42—21no—
227C42—21no—
228C42D4×D6112yes—
229C42#1175822412yes—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—41no—
234C23—41no—
235C23C2×#1175819811yescharacteristic
236Q8—4884no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—2442no—
249C2×C4—2442no—
250C2×C4—2442no—
251C2×C4—2442no—
252C2×C4—2442no—
253C2×C4—2442no—
254C2×C4#1451973712yes—
255C2×C4#1451974711yescharacteristic
256C2×C4#1451974912yes—
257C2×C4#1451976111yescharacteristic
258C2×C4#1451979912yes—
259C2×C4#1451981012yes—
260C8—82no—
261C8—2444no—
262C22—21no—
263C22—21no—
264C22—42no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22#1683963911yescharacteristic
270C22#1683975911yescharacteristic
271C22#1683977211yescharacteristic
272C4—22no—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—4882no—
278C4—4882no—
279C4#1683992612yes—
280C4#1684010412yes—
281C2—21no—
282C2—21no—
283C2—81no—
284C2#2144612911yescharacteristic
285C2#2144633911yescharacteristic
286C2#2144636411yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1458C2
socleC22×C61#386
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1458D61
hypocenterC61#9192
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #21444499C2semidirect
4. #21443678C2semidirect
166. C61#9192semidirect

Maximal subgroups

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

subgroupindex
#214544572
#214516402
#214444992
#214436782
C61×#14582
#919261