Finite Group Databasebeta

← #29836457

Subgroups — #29836457

Order 15616.

488 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 127 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#21456459C212yesmaximal, complemented
2#21447965C212yesmaximal, complemented
3#21447959C212yesmaximal, complemented
4#21447922C211yesmaximal, characteristic
5#21447917C212yesmaximal, complemented
6#21447883C212yesmaximal, complemented
7#21447877C212yesmaximal, complemented
8#21447579C211yesmaximal, characteristic, complemented
9C61×#2219C211yesmaximal, characteristic, complemented
10#16840385—22no—
11C2×#14519720C2212yes—
12C2×D976C2211yescharacteristic
13C22×#11758185C2211yescharacteristic
14#16840166C2212yes—
15#16840147C2212yes—
16#16840123—22no—
17#16840010—22no—
18#16839998C2212yes—
19#16839865—22no—
20Q16×Dic61C2212yes—
21#16839844C2212yes—
22#16839717C2211yescharacteristic
23#16839590C2211yescharacteristic
24#16839589C2212yes—
25#16839580C2212yes—
26#16839580C2212yes—
27#16839566C2212yes—
28#16839564C2212yes—
29#16839562C2212yes—
30C2×Q32×C61C2211yescharacteristic
31C2×M32×C61C2211yescharacteristic
32C61×#467C2212yes—
33C61×#367C2211yescharacteristic
34C61×#358C2212yes—
35C2×#11758201—22no—
36C2×D488C2312yes—
37C2×#11758194D411yescharacteristic
38#14519776—22no—
39#14519772—42no—
40#14519766—22no—
41#14519763—42no—
42#14519759—42no—
43#14519757—42no—
44#14519751—22no—
45Q8×Dic61—22no—
46#14519739—22no—
47#14519736D411yescharacteristic
48#14519720—42no—
49D976—41no—
50C2×#11758185—41no—
51C2×#11758185C2312yes—
52#14519711C2312yes—
53#14519710—22no—
54#14519701—22no—
55#14519699—22no—
56#14519697—22no—
57#14519687D412yes—
58C8×Dic61C2312yes—
59C2×Q16×C61C2312yes—
60C22×C8×C61C2311yescharacteristic
61C22⋊Q8×C61—22no—
62Q32×C61—41no—
63M32×C61—41no—
64C2×C16×C61C2311yescharacteristic
65C2×C16×C61C2311yescharacteristic
66#107×C61C2312yes—
67#103×C61—22no—
68C2×Q8×C61—22no—
69C22×C4×C61C2×D411yescharacteristic
70C2×C22⋊D61—42no—
71C2×D244—22no—
72C2×C4×D61—42no—
73C2×Dic122—42no—
74Q16×C61—22no—
75Q16×C61—22no—
76C2×C8×C61—21no—
77C2×C8×C61—21no—
78C2×C8×C61C2×D411yescharacteristic
79C2×C8×C61C2411yescharacteristic
80C4⋊C4×C61—22no—
81C4⋊C4×C61—42no—
82C22⋊C4×C61—42no—
83C22⋊Dic61D811yescharacteristic
84C22⋊Dic61D811yescharacteristic
85#11758201—44no—
86#11758198—42no—
87#11758198—42no—
88#11758198—42no—
89#11758198—42no—
90C4⋊Dic61—22no—
91C4⋊Dic61—42no—
92C4⋊Dic61D812yes—
93#11758196—42no—
94C4×Dic61—42no—
95C4×Dic61C2×D412yes—
96#11758194—41no—
97C2×#92418C2×D412yes—
98D488—22no—
99D488—22no—
100C16×C61—21no—
101C16×C61—21no—
102#11758185—22no—
103C23×C61C2×D811yescharacteristic
104C22×D61—42no—
105Q8×C61—42no—
106Q8×C61—42no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—42no—
110C2×C4×C61—42no—
111C2×C4×C61C2×D811yescharacteristic
112C2×C4×C61C22×D411yescharacteristic
113C22⋊D61—162no—
114C2×Dic61—42no—
115C2×Dic61C2×D812yes—
116C2×Dic61C2×D812yes—
117D244—42no—
118D244—42no—
119C4×D61—162no—
120Dic122—162no—
121C8×C61—21no—
122C8×C61H(5,𝔽2)11yescharacteristic
123C8×C612−1+411yescharacteristic
124#92418—22no—
125#33829—611nomaximal, Sylow
126C22×C61—22no—
127C22×C61—21no—
128C22×C61C22×D811yescharacteristic
129C2×D61—82no—
130C2×D61—82no—
131C2×D61—82no—
132C4×C61—21no—
133C4×C61—82no—
134C4×C61—82no—
135C4×C61#53711yescharacteristic
136C4×C61#57511yescharacteristic
137Dic61—22no—
138Dic61—22no—
139Dic61—82no—
140#3175—612no—
141#2226—612no—
142#2225—612no—
143#2219D6111yescharacteristic, complemented
144#2218—611no—
145#2217—612no—
146#2211—612no—
147#2210—612no—
148#2151—611no—
149C2×C61—41no—
150C2×C61#324511yescharacteristic
151C2×C61#341612yes—
152D61—162no—
153#542—1222no—
154C2×Q32C2×D6111yescharacteristic
155C2×SD32—612no—
156C2×D16—611no—
157C2×M32C2×D6111yescharacteristic
158C22×C16—611no—
159#500—612no—
160#495—612no—
161#489—1222no—
162#468—1222no—
163#467C2×D6112yes—
164#466—612no—
165#440—1222no—
166C4×Q16—612no—
167C4×D8—612no—
168#405—611no—
169#367—611no—
170#367—612no—
171#367C2×D6111yescharacteristic
172C4⋊C16—612no—
173C4⋊C16—612no—
174#358—612no—
175#358C2×D6112yes—
176#357—612no—
177#357—612no—
178C61#3382911yescharacteristic, complemented, Sylow
179C2×Q16C22×D6112yes—
180C2×SD16—1222no—
181C2×D8—612no—
182C2×M16—611no—
183C22×C8C22×D6111yescharacteristic
184C4⋊Q8—1222no—
185#126—2442no—
186#124—1222no—
187#124—2442no—
188#123—2442no—
189C22⋊Q8—22no—
190C22⋊Q8—2442no—
191#121—1222no—
192C4×Q8—1222no—
193C4×D4—1222no—
194#117—611no—
195Q32—41no—
196SD32—2442no—
197D16—2441no—
198M32—41no—
199C2×C16—612no—
200C2×C16—2441no—
201C2×C16C22×D6111yescharacteristic
202C2×C16C22×D6111yescharacteristic
203#107—612no—
204#107—1222no—
205#107C22×D6112yes—
206#103—22no—
207#103—1222no—
208#102—1222no—
209#102—1222no—
210#97—612no—
211C4×C8—612no—
212C2×Q8—22no—
213C2×Q8—2442no—
214C2×D4—1222no—
215C2×D4—2442no—
216C22×C4—2442no—
217C22×C4D4×D6111yescharacteristic
218Q16—22no—
219Q16—22no—
220SD16—2444no—
221D8—1222no—
222D8—1222no—
223M16—2441no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—612no—
227C2×C8D4×D6111yescharacteristic
228C2×C8C23×D6111yescharacteristic
229C4⋊C4—22no—
230C4⋊C4—42no—
231C4⋊C4—612no—
232C4⋊C4—1222no—
233C4⋊C4—2442no—
234C4⋊C4—2442no—
235C22⋊C4—42no—
236C22⋊C4—611no—
237C22⋊C4—611no—
238C22⋊C4—2442no—
239C22⋊C4—2442no—
240C22⋊C4—2442no—
241C22⋊C4—2442no—
242C42—612no—
243C42—2442no—
244C16—21no—
245C16—21no—
246C16—1222no—
247C23—2442no—
248C23D8×D6111yescharacteristic
249Q8—42no—
250Q8—42no—
251Q8—9762no—
252D4—9762no—
253D4—2442no—
254D4—2442no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—612no—
260C2×C4—612no—
261C2×C4—9762no—
262C2×C4—2442no—
263C2×C4D8×D6111yescharacteristic
264C2×C4C2×D4×D6111yescharacteristic
265C8—21no—
266C8—1222no—
267C8#1451982211yescharacteristic
268C8#1451982411yescharacteristic
269C22—22no—
270C22—21no—
271C22—4882no—
272C22—4882no—
273C22—4882no—
274C22C2×D8×D6111yescharacteristic
275C4—21no—
276C4—82no—
277C4—82no—
278C4—1222no—
279C4—1222no—
280C4—4882no—
281C4#1684033911yescharacteristic
282C4#1684055911yescharacteristic
283C2—41no—
284C2—9762no—
285C2#2145712511yescharacteristic
286C2#2145896412yes—
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2219C2
socleC22×C61C22×D8
prime radical#21447922C2
hypercenter#2219D61
hypocenterC61#33829
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2219

Complements

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

NH ≅ G/Ntype
1. #21456459C2semidirect
2. #21447965C2semidirect
3. #21447959C2semidirect
5. #21447917C2semidirect
6. #21447883C2semidirect
7. #21447877C2semidirect
8. #21447579C2semidirect
9. C61×#2219C2semidirect
143. #2219D61semidirect
178. C61#33829semidirect

Maximal subgroups

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

subgroupindex
#214564592
#214479652
#214479592
#214479222
#214479172
#214478832
#214478772
#214475792
C61×#22192
#3382961