Finite Group Databasebeta

← #29589127

Subgroups — #29589127

Order 15616.

526 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 93 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#21448402C211yesmaximal, characteristic
2#21444132C212yesmaximal
3#21443753C211yesmaximal, characteristic, complemented
4#21443752C212yesmaximal, complemented
5C61×#1319C211yesmaximal, characteristic, complemented
6C22×Q8×D61C411yescharacteristic
7C2×#14519735C2211yescharacteristic
8C2×#14519734C411yescharacteristic
9#16839812—22no—
10#16839669C411yescharacteristic
11#16839668C411yescharacteristic
12#16839667C2211yescharacteristic
13#16839666—22no—
14#16839624—22no—
15#16839488C2212yes—
16#16839485—22no—
17C61×#391C2211yescharacteristic
18C61×#324C2212yes—
19C22×Dic122—21no—
20C22×Dic122C2×C411yescharacteristic
21C2×Q8×D61—22no—
22C2×Q8×D61—42no—
23C2×Q8×D61—42no—
24C2×Q8×D61C814yescomplemented
25C22×C4×D61—21no—
26C22×C4×D61C2×C411yescharacteristic
27#14519735—42no—
28#14519734—42no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×#11758196—21no—
31C2×#11758198—21no—
32C2×#11758198D412yes—
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61D412yes—
35#14519706—42no—
36C22⋊#92418—22no—
37C8×Dic61—42no—
38#14519684—22no—
39#14519684—22no—
40#14519684—22no—
41C22×Q8×C61C2×C411yescharacteristic
42C2×C4⋊C4×C61C2311yescharacteristic
43C2×C42×C61C2×C411yescharacteristic
44C22⋊C8×C61—22no—
45#95×C61—22no—
46C23×D61C22⋊C411yescharacteristic
47C2×Q8×C61—21no—
48C2×Q8×C61—41no—
49C2×Q8×C61—41no—
50C2×Q8×C61C2×C812yes—
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61C22×C411yescharacteristic
54C22×C4×C61C2×D412yes—
55C22×Dic61—21no—
56C22×Dic61—21no—
57C22×Dic61C22⋊C412yes—
58C22×Dic61C22⋊C411yescharacteristic
59Q8×D61—48no—
60Q8×D61—48no—
61C2×C4×D61—22no—
62C2×C4×D61—22no—
63C2×C4×D61—24no—
64C2×C4×D61—42no—
65C2×C4×D61—42no—
66C2×C4×D61C2×C812yes—
67C2×C4×D61M1612yes—
68C2×Dic122—21no—
69C2×Dic122—24no—
70C2×Dic122—42no—
71C2×Dic122—42no—
72C2×Dic122—41no—
73C2×Dic122—41no—
74C2×Dic122C2×C812yes—
75C2×C8×C61—42no—
76C4⋊C4×C61—41no—
77C42×C61—41no—
78#11758198—42no—
79#11758198—42no—
80C4⋊Dic61—41no—
81#11758196—42no—
82C4×Dic61—22no—
83C4×Dic61—22no—
84C4×Dic61—41no—
85C2×#92418—42no—
86C23×C61C2×C22⋊C411yescharacteristic
87C22×D61—21no—
88C22×D61—21no—
89C22×D61—41no—
90C22×D61—41no—
91C22×D61C22⋊C812yes—
92Q8×C61—42no—
93Q8×C61—42no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—42no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61C22×C811yescharacteristic
105C2×C4×C61C2×M1611yescharacteristic
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—42no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61C22⋊C812yes—
115C2×Dic61#9912yes—
116C2×Dic61#10012yes—
117C4×D61—24no—
118C4×D61—24no—
119C4×D61—48no—
120Dic122—42no—
121Dic122—48no—
122Dic122—42no—
123C8×C61—82no—
124#92418—82no—
125#11434—611nomaximal, Sylow
126C22×C61—21no—
127C22×C61—21no—
128C22×C61C2×C22⋊C811yescharacteristic
129C22×C61C2×#9911yescharacteristic
130C22×C61C2×#10011yescharacteristic
131C2×D61—22no—
132C2×D61—42no—
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—42no—
136C4×C61—21no—
137C4×C61—21no—
138C4×C61—42no—
139C4×C61—42no—
140C4×C61—81no—
141Dic61—42no—
142Dic61—42no—
143Dic61—81no—
144Dic61#32314yes—
145#2310—611no—
146#1458—612no—
147#1319—611no—
148#1319—612no—
149#1319D6111yescharacteristic, complemented
150C2×C61—21no—
151C2×C61—21no—
152C2×C61C2×#32311yescharacteristic
153C2×C61#212911yescharacteristic
154C2×C61#213511yescharacteristic
155D61—42no—
156C23×Q8—611no—
157C2×#117—611no—
158C2×#117—611no—
159#431—1222no—
160#391—611no—
161#391—611no—
162#391—611no—
163#391—1222no—
164#391C2×D6111yescharacteristic
165#381—1222no—
166#324—612no—
167#324C2×D6112yes—
168#323—1222no—
169C61#1143411yescharacteristic, complemented, Sylow
170C22×Q8—614no—
171C22×Q8—611no—
172C22×Q8—1221no—
173C22×Q8—1222no—
174C22×Q8—2442no—
175C22×Q8—2442no—
176C22×Q8C4×D6111yescharacteristic
177C23×C4—611no—
178C23×C4—1221no—
179#117—2442no—
180#117—2442no—
181C2×C4⋊C4—611no—
182C2×C4⋊C4—1221no—
183C2×C4⋊C4C22×D6111yescharacteristic
184C2×C22⋊C4—612no—
185C2×C22⋊C4—1221no—
186C2×C42—612no—
187C2×C42—611no—
188C2×C42C4×D6111yescharacteristic
189C4⋊C8—2442no—
190C22⋊C8—22no—
191C22⋊C8—1222no—
192C4×C8—2442no—
193#95—22no—
194#95—1222no—
195#95—1222no—
196#95—1222no—
197C24—611no—
198C2×Q8—21no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8—612no—
202C2×Q8—1224no—
203C2×Q8—1221no—
204C2×Q8—2441no—
205C2×Q8—2441no—
206C2×Q8—2442no—
207C2×Q8—2442no—
208C2×Q8—2448no—
209C2×Q8—2448no—
210C2×Q8C8×D6112yes—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—611no—
214C22×C4—612no—
215C22×C4—612no—
216C22×C4—612no—
217C22×C4—1222no—
218C22×C4—1222no—
219C22×C4—1224no—
220C22×C4—1221no—
221C22×C4—1221no—
222C22×C4—2442no—
223C22×C4—2442no—
224C22×C4C2×C4×D6111yescharacteristic
225C22×C4D4×D6112yes—
226C2×C8—42no—
227C2×C8—2442no—
228C4⋊C4—41no—
229C4⋊C4—2441no—
230C4⋊C4—2442no—
231C22⋊C4—2442no—
232C22⋊C4—2442no—
233C42—41no—
234C42—1222no—
235C42—1222no—
236C42—2441no—
237C23—612no—
238C23—1221no—
239C23—1221no—
240C23—2441no—
241C23—2441no—
242C23C22⋊C4×D6111yescharacteristic
243Q8—42no—
244Q8—42no—
245Q8—2442no—
246Q8—2442no—
247Q8—2448no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—612no—
259C2×C4—612no—
260C2×C4—612no—
261C2×C4—1224no—
262C2×C4—1224no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—2448no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4—2442no—
272C2×C4C2×C8×D6111yescharacteristic
273C2×C4M16×D6111yescharacteristic
274C8—82no—
275C8—4882no—
276C22—21no—
277C22—21no—
278C22—1222no—
279C22—2442no—
280C22—2442no—
281C22—2441no—
282C22—2441no—
283C22C22⋊C8×D6111yescharacteristic
284C22#99×D6111yescharacteristic
285C22#100×D6111yescharacteristic
286C4—21no—
287C4—21no—
288C4—42no—
289C4—42no—
290C4—81no—
291C4—614no—
292C4—4881no—
293C4—2442no—
294C4—2442no—
295C2—21no—
296C2—21no—
297C2—2442no—
298C2#323×D6111yescharacteristic
299C2#2144749211yescharacteristic
300C2#2144751211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1319C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1319D61
hypocenterC61#11434
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
3. #21443753C2semidirect
4. #21443752C2semidirect
5. C61×#1319C2semidirect
24. C2×Q8×D61C8semidirect
149. #1319D61semidirect
169. C61#11434semidirect

Maximal subgroups

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

subgroupindex
#214484022
#214441322
#214437532
#214437522
C61×#13192
#1143461