Finite Group Databasebeta

← #29836453

Subgroups — #29836453

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#21447969C212yesmaximal, complemented
3#21447955C212yesmaximal, complemented
4#21447934C212yesmaximal, complemented
5#21447905C211yesmaximal, characteristic
6#21447883C212yesmaximal, complemented
7#21447877C212yesmaximal, complemented
8#21447577C211yesmaximal, characteristic, complemented
9C61×#2216C211yesmaximal, characteristic, complemented
10#16840385—22no—
11C2×#14519720C2212yes—
12C2×D976C2211yescharacteristic
13C2×#14519717C2211yescharacteristic
14#16840166C2212yes—
15#16840147C2212yes—
16#16840123—22no—
17#16840010—22no—
18#16839998C2212yes—
19#16839865—22no—
20Q16×Dic61C2212yes—
21#16839844C2212yes—
22#16839717C2211yescharacteristic
23#16839588C2211yescharacteristic
24#16839587C2212yes—
25#16839580C2212yes—
26#16839580C2212yes—
27#16839566C2212yes—
28#16839564C2212yes—
29#16839562C2212yes—
30C2×Q32×C61C2211yescharacteristic
31C22×C16×C61C2211yescharacteristic
32C61×#467C2212yes—
33C61×#366C2211yescharacteristic
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—
50#14519717—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—
63C2×C16×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⋊Dic61D812yes—
84#11758201—44no—
85#11758198—42no—
86#11758198—42no—
87#11758198—42no—
88#11758198—42no—
89C4⋊Dic61—22no—
90C4⋊Dic61—42no—
91C4⋊Dic61D811yescharacteristic
92C4⋊Dic61D811yescharacteristic
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#33828—611nomaximal, Sylow
126C22×C61—21no—
127C22×C61—21no—
128C22×C61—21no—
129C22×C61C22×D811yescharacteristic
130C2×D61—82no—
131C2×D61—82no—
132C2×D61—82no—
133C4×C61—21no—
134C4×C61—82no—
135C4×C61—82no—
136C4×C61#53711yescharacteristic
137C4×C61#57511yescharacteristic
138Dic61—22no—
139Dic61—22no—
140Dic61—82no—
141#3175—612no—
142#2227—612no—
143#2224—612no—
144#2220—612no—
145#2216D6111yescharacteristic, complemented
146#2215—611no—
147#2211—612no—
148#2210—612no—
149#2151—611no—
150C2×C61—41no—
151C2×C61#324511yescharacteristic
152C2×C61#341511yescharacteristic
153C2×C61#341711yescharacteristic
154D61—162no—
155#542—1222no—
156C2×Q32C2×D6111yescharacteristic
157C2×SD32—612no—
158C2×D16—611no—
159C2×M32—611no—
160C22×C16C2×D6111yescharacteristic
161#500—612no—
162#495—612no—
163#489—1222no—
164#468—1222no—
165#467C2×D6112yes—
166#466—612no—
167#440—1222no—
168C4×Q16—612no—
169C4×D8—612no—
170#405—611no—
171#366—611no—
172#366—612no—
173#366C2×D6111yescharacteristic
174C4⋊C16—612no—
175C4⋊C16—612no—
176#358—612no—
177#358C2×D6112yes—
178#357—612no—
179#357—612no—
180C61#3382811yescharacteristic, complemented, Sylow
181C2×Q16C22×D6112yes—
182C2×SD16—1222no—
183C2×D8—612no—
184C2×M16—611no—
185C22×C8C22×D6111yescharacteristic
186C4⋊Q8—1222no—
187#126—2442no—
188#124—1222no—
189#124—2442no—
190#123—2442no—
191C22⋊Q8—22no—
192C22⋊Q8—2442no—
193#121—1222no—
194C4×Q8—1222no—
195C4×D4—1222no—
196#117—611no—
197Q32—41no—
198SD32—2442no—
199D16—2441no—
200M32—2441no—
201C2×C16—41no—
202C2×C16—612no—
203C2×C16C22×D6111yescharacteristic
204C2×C16C22×D6111yescharacteristic
205#107—612no—
206#107—1222no—
207#107C22×D6112yes—
208#103—22no—
209#103—1222no—
210#102—1222no—
211#102—1222no—
212#97—612no—
213C4×C8—612no—
214C2×Q8—22no—
215C2×Q8—2442no—
216C2×D4—1222no—
217C2×D4—2442no—
218C22×C4—2442no—
219C22×C4D4×D6111yescharacteristic
220Q16—22no—
221Q16—22no—
222SD16—2444no—
223D8—1222no—
224D8—1222no—
225M16—2441no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—612no—
229C2×C8D4×D6111yescharacteristic
230C2×C8C23×D6111yescharacteristic
231C4⋊C4—22no—
232C4⋊C4—42no—
233C4⋊C4—611no—
234C4⋊C4—611no—
235C4⋊C4—1222no—
236C4⋊C4—2442no—
237C4⋊C4—2442no—
238C22⋊C4—42no—
239C22⋊C4—612no—
240C22⋊C4—2442no—
241C22⋊C4—2442no—
242C22⋊C4—2442no—
243C22⋊C4—2442no—
244C42—612no—
245C42—2442no—
246C16—21no—
247C16—21no—
248C16—1222no—
249C23—2442no—
250C23D8×D6111yescharacteristic
251Q8—42no—
252Q8—42no—
253Q8—9762no—
254D4—9762no—
255D4—2442no—
256D4—2442no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—612no—
262C2×C4—612no—
263C2×C4—9762no—
264C2×C4—2442no—
265C2×C4D8×D6111yescharacteristic
266C2×C4C2×D4×D6111yescharacteristic
267C8—21no—
268C8—1222no—
269C8#1451982211yescharacteristic
270C8#1451982411yescharacteristic
271C22—21no—
272C22—21no—
273C22—21no—
274C22—4882no—
275C22—4882no—
276C22—4882no—
277C22C2×D8×D6111yescharacteristic
278C4—21no—
279C4—82no—
280C4—82no—
281C4—1222no—
282C4—1222no—
283C4—4882no—
284C4#1684033911yescharacteristic
285C4#1684055911yescharacteristic
286C2—41no—
287C2—9762no—
288C2#2145712511yescharacteristic
289C2#2145895711yescharacteristic
290C2#2145896811yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2216C2
socleC22×C61C22×D8
prime radical#21447905C2
hypercenter#2216D61
hypocenterC61#33828
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2216

Complements

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

NH ≅ G/Ntype
1. #21456459C2semidirect
2. #21447969C2semidirect
3. #21447955C2semidirect
4. #21447934C2semidirect
6. #21447883C2semidirect
7. #21447877C2semidirect
8. #21447577C2semidirect
9. C61×#2216C2semidirect
145. #2216D61semidirect
180. C61#33828semidirect

Maximal subgroups

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

subgroupindex
#214564592
#214479692
#214479552
#214479342
#214479052
#214478832
#214478772
#214475772
C61×#22162
#3382861