Finite Group Databasebeta

← #29596037

Subgroups — #29596037

Order 15616.

428 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 89 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#21454527C211yesmaximal, characteristic
2#21447482C212yesmaximal
3#21445863C212yesmaximal, complemented
4#21443940C211yesmaximal, characteristic, complemented
5C61×#1391C211yesmaximal, characteristic, complemented
6C2×#14519785C411yescharacteristic, complemented
7C2×#14519784C2211yescharacteristic
8#16840308C2211yescharacteristic
9#16839837—22no—
10#16839825—22no—
11#16839798—22no—
12#16839785C411yescharacteristic, complemented
13#16839736C2212yes—
14#16839728C411yescharacteristic, complemented
15C2×C8×Dic61C411yescharacteristic, complemented
16#16839556—22no—
17#16839554—22no—
18#16839518—22no—
19C61×#410C2212yes—
20C61×#408C2211yescharacteristic
21C2×#11758222C2×C411yescharacteristic
22#14519785—41no—
23#14519785—41no—
24#14519784—41no—
25#14519784—41no—
26C2×#11758194C2×C411yescharacteristic
27C2×#11758194D412yes—
28C2×#11758189—21no—
29C22×#92418C2×C411yescharacteristic
30C22×#92418D412yes—
31C2×C8×D61—21no—
32#14519775Q811yescharacteristic
33#14519773D411yescharacteristic
34#14519766Q811yescharacteristic
35#14519764D411yescharacteristic
36#14519749—22no—
37C4×C22⋊D61—22no—
38#14519736—22no—
39C2×C4×Dic61C2×C411yescharacteristic
40#14519710—42no—
41#14519708—42no—
42#14519706—22no—
43#14519692—22no—
44#14519692—22no—
45#14519689—22no—
46C8×Dic61—21no—
47C8×Dic61—21no—
48C2×#41×C61C2311yescharacteristic
49C2×M16×C61C2×C411yescharacteristic
50C22×C8×C61C2×C411yescharacteristic
51#117×C61—22no—
52#99×C61—22no—
53#99×C61—22no—
54C22⋊C8×C61—22no—
55#41×C61—41no—
56#41×C61—41no—
57C2×Q8×C61C2×Q811yescharacteristic
58C2×D4×C61C2×D411yescharacteristic
59C2×D4×C61#4112yes—
60C22×C4×C61C22×C411yescharacteristic
61C22×C4×C61C2×D412yes—
62C2×C22⋊D61—21no—
63C2×C22⋊D61—22no—
64C22×Dic61—21no—
65#11758222—41no—
66#11758222—41no—
67C2×D244C4⋊C411yescharacteristic
68C2×C4×D61—21no—
69C2×Dic122C4⋊C411yescharacteristic
70M16×C61—41no—
71C2×C8×C61—21no—
72C2×C8×C61—21no—
73C2×C8×C61—41no—
74C4⋊C4×C61—42no—
75C22⋊C4×C61—42no—
76C42×C61—42no—
77C22⋊Dic61—22no—
78C22⋊Dic61—42no—
79#11758198—22no—
80C4⋊Dic61—42no—
81#11758196—22no—
82C4×Dic61—21no—
83C4×Dic61—42no—
84C4×Dic61C4⋊C411yescharacteristic
85C4×Dic61C4⋊C411yescharacteristic
86#11758194—41no—
87#11758194—42no—
88C2×#92418—22no—
89C2×#92418—22no—
90C2×#92418—21no—
91C2×#92418—21no—
92C2×#92418C22⋊C411yescharacteristic
93C2×#92418C22⋊C412yes—
94C2×#92418C22⋊C411yescharacteristic
95#11758189—42no—
96C8×D61—41no—
97C8×D61—41no—
98C23×C61#11711yescharacteristic
99C23×C61#12112yes—
100C22×D61—21no—
101Q8×C61—41no—
102D4×C61—41no—
103D4×C61—42no—
104C2×C4×C61—22no—
105C2×C4×C61—21no—
106C2×C4×C61—22no—
107C2×C4×C61—21no—
108C2×C4×C61—82no—
109C2×C4×C61C2×C22⋊C411yescharacteristic
110C2×C4×C61C2×C4⋊C411yescharacteristic
111C2×C4×C61C22⋊Q812yes—
112C22⋊D61—44no—
113C22⋊D61—42no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—42no—
118C2×Dic61—82no—
119D244—41no—
120C4×D61—41no—
121C4×D61—41no—
122Dic122—41no—
123C8×C61—41no—
124C8×C61—41no—
125#92418—21no—
126#92418—22no—
127#92418#9911yescharacteristic
128#92418#9911yescharacteristic
129#12807—611nomaximal, Sylow
130C22×C61—22no—
131C22×C61—21no—
132C22×C61—41no—
133C22×C61—42no—
134C22×C61#38011yescharacteristic
135C2×D61—42no—
136C2×D61—41no—
137C4×C61—21no—
138C4×C61—22no—
139C4×C61—162no—
140C4×C61C2×#9911yescharacteristic
141C4×C61#41011yescharacteristic
142Dic61—22no—
143Dic61—41no—
144Dic61—41no—
145Dic61—162no—
146#2931—611no—
147#2126—612no—
148#1812—612no—
149#1391—611no—
150#1391D6111yescharacteristic, complemented
151C2×C61—21no—
152C2×C61—42no—
153C2×C61—41no—
154C2×C61#179911yescharacteristic
155D61—81no—
156C2×#131—611no—
157C2×#131—611no—
158#532—611no—
159#436—1222no—
160C8×D4—1222no—
161#427—1222no—
162#423—611no—
163#410—612no—
164#410C2×D6112yes—
165#408—611no—
166#408C2×D6111yescharacteristic
167C2×C4×C8—611no—
168#354—1222no—
169#353—1222no—
170H(3,ℤ/4)—1222no—
171C61#1280711yescharacteristic, complemented, Sylow
172C2×#41—611no—
173C2×#41C22×D6111yescharacteristic
174#131—2441no—
175#131—2441no—
176#131—2441no—
177#131—2441no—
178C2×M16—611no—
179C2×M16—612no—
180C2×M16—1221no—
181C2×M16C4×D6111yescharacteristic
182C22×C8—611no—
183C22×C8—612no—
184C22×C8—1221no—
185C22×C8C4×D6111yescharacteristic
186C4⋊Q8—611no—
187#127—611no—
188#124—611no—
189#124—611no—
190#121—1222no—
191C4×D4—1222no—
192#117—22no—
193#117—1222no—
194C2×C42—611no—
195#107—2442no—
196#106—2442no—
197C4⋊C8—1222no—
198#99—22no—
199#99—22no—
200#99—1222no—
201#99—1222no—
202C22⋊C8—22no—
203C22⋊C8—1222no—
204C4×C8—1221no—
205C4×C8—1221no—
206#41—41no—
207#41—41no—
208#41—2441no—
209#41—2441no—
210C2×Q8—611no—
211C2×Q8Q8×D6111yescharacteristic
212C2×D4—611no—
213C2×D4—1221no—
214C2×D4—1222no—
215C2×D4#1175822212yes—
216C2×D4D4×D6111yescharacteristic
217C22×C4—1221no—
218C22×C4—1221no—
219C22×C4C2×C4×D6111yescharacteristic
220C22×C4D4×D6112yes—
221M16—41no—
222M16—2442no—
223M16—2441no—
224M16—2442no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—41no—
228C2×C8—611no—
229C2×C8—611no—
230C2×C8—612no—
231C2×C8—1222no—
232C2×C8—1222no—
233C2×C8—1221no—
234C2×C8—1221no—
235C2×C8—2441no—
236C2×C8—2441no—
237C4⋊C4—42no—
238C4⋊C4—1222no—
239C4⋊C4—2442no—
240C22⋊C4—42no—
241C22⋊C4—1222no—
242C22⋊C4—1222no—
243C22⋊C4—2442no—
244C42—42no—
245C42—611no—
246C42—611no—
247C42—1221no—
248C42—2442no—
249C23—1221no—
250C23#1451973411yescharacteristic
251C23#1451975012yes—
252Q8—41no—
253Q8—2441no—
254D4—42no—
255D4—41no—
256D4—2441no—
257D4—2444no—
258D4—2442no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—82no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—4882no—
268C2×C4—2442no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4C22⋊C4×D6111yescharacteristic
272C2×C4C4⋊C4×D6111yescharacteristic
273C2×C4#1451975512yes—
274C8—41no—
275C8—41no—
276C8—611no—
277C8—611no—
278C8—1222no—
279C8—1221no—
280C22—22no—
281C22—21no—
282C22—41no—
283C22—42no—
284C22—2442no—
285C22—2441no—
286C22#1683962111yescharacteristic
287C4—21no—
288C4—22no—
289C4—162no—
290C4—1222no—
291C4—9762no—
292C4—2441no—
293C4—2441no—
294C4#99×D6111yescharacteristic
295C4#1683973411yescharacteristic
296C2—21no—
297C2—42no—
298C2—41no—
299C2—4881no—
300C2#2144580611yescharacteristic
subgroupG/H
centerC4#16839734
commutatorC22×C4×C61C22×C4
FrattiniC2×#41C22×D61
FittingC61×#1391C2
socleC2×C61#1799
prime radical#16840308C22
cosocleC2×#41×C61C23
hypercenter#1391D61
hypocenterC61#12807
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1391

Complements

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

NH ≅ G/Ntype
3. #21445863C2semidirect
4. #21443940C2semidirect
5. C61×#1391C2semidirect
6. C2×#14519785C4semidirect
12. #16839785C4semidirect
14. #16839728C4semidirect
15. C2×C8×Dic61C4semidirect
150. #1391D61semidirect
171. C61#12807semidirect

Maximal subgroups

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

subgroupindex
#214545272
#214474822
#214458632
#214439402
C61×#13912
#1280761