Finite Group Databasebeta

← #30603819

Subgroups — #30603819

Order 15616.

678 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 90 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#21461051C212yesmaximal, complemented
2#21460745C212yesmaximal, complemented
3#21460744C212yesmaximal
4#21448199C211yesmaximal, characteristic
5#16840779—22no—
6#16840608—22no—
7#16840605C2214yes—
8C23×C4×D61C411yescharacteristic
9C2×#14519733C411yescharacteristic
10C2×#14519733C2211yescharacteristic
11#16839625C2211yescharacteristic
12#16839621—22no—
13#16839617C411yescharacteristic
14#16839617C2211yescharacteristic
15#16839609—22no—
16C61×#381C411yescharacteristic
17#14519844—42no—
18C22⋊#92420—24no—
19C4×#92420—42no—
20C24×D61C2×C411yescharacteristic
21C23×Dic61C2×C411yescharacteristic
22C22×C4×D61—21no—
23C22×C4×D61—21no—
24C22×C4×D61—22no—
25C22×C4×D61—41no—
26C22×C4×D61—41no—
27C22×C4×D61—42no—
28C22×C4×D61C814yescomplemented
29#14519733—41no—
30#14519733—41no—
31#14519733—42no—
32C2×#11758196—21no—
33C2×#11758196D412yes—
34C2×C22⋊Dic61C2×C411yescharacteristic
35C2×C22⋊Dic61C2311yescharacteristic
36C2×#11758198—22no—
37C2×#11758198—22no—
38C2×C4×Dic61—21no—
39C2×C4×Dic61D412yes—
40#14519684—22no—
41C23×C4×C61C2×C411yescharacteristic
42C2×C22⋊C4×C61C2×C411yescharacteristic
43C2×C22⋊C4×C61C2×C411yescharacteristic
44#95×C61—22no—
45C24×C61C22×C411yescharacteristic
46C23×D61—21no—
47C23×D61—21no—
48C23×D61—44no—
49C23×D61—41no—
50C23×D61—41no—
51C23×D61C2×C812yes—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61—41no—
56C22×C4×C61—41no—
57C22×C4×C61C22⋊C412yes—
58C22×C4×C61C2×C812yes—
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61—22no—
62C22×Dic61—21no—
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C2×C812yes—
66C22×Dic61M1612yes—
67C22×Dic61C2×D412yes—
68C2×C4×D61—24no—
69C2×C4×D61—24no—
70C2×C4×D61—42no—
71C2×C4×D61—42no—
72C2×C4×D61—44no—
73C2×C4×D61—44no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61—42no—
77C2×C4×D61—44no—
78C2×C4×D61—44no—
79C2×#92420—44no—
80C22⋊C4×C61—41no—
81C22⋊C4×C61—41no—
82C22⋊Dic61—41no—
83C22⋊Dic61—41no—
84#11758198—44no—
85#11758198—44no—
86#11758196—42no—
87#11758196—42no—
88C4×Dic61—22no—
89C4×Dic61—22no—
90C4×Dic61—42no—
91C23×C61—21no—
92C23×C61—21no—
93C23×C61—42no—
94C23×C61C2×C22⋊C411yescharacteristic
95C23×C61C22×C811yescharacteristic
96C23×C61C2×M1611yescharacteristic
97C22×D61—24no—
98C22×D61—22no—
99C22×D61—44no—
100C22×D61—44no—
101C22×D61—42no—
102C22×D61—42no—
103C22×D61—48no—
104C22×D61—44no—
105C22×D61—41no—
106C22×D61—41no—
107C22×D61—42no—
108C22×D61—44no—
109C2×C4×C61—22no—
110C2×C4×C61—22no—
111C2×C4×C61—42no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—42no—
115C2×C4×C61—42no—
116C2×C4×C61—42no—
117C2×C4×C61—41no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—22no—
121C2×Dic61—22no—
122C2×Dic61—22no—
123C2×Dic61—22no—
124C2×Dic61—22no—
125C2×Dic61—42no—
126C2×Dic61—42no—
127C2×Dic61—41no—
128C2×Dic61C22⋊C812yes—
129C2×Dic61C22⋊C812yes—
130C2×Dic61#9911yescharacteristic
131C2×Dic61#9911yescharacteristic
132C2×Dic61#10012yes—
133C4×D61—48no—
134C4×D61—44no—
135C4×D61—44no—
136#92420—84no—
137#11425—611nomaximal, Sylow
138C22×C61—22no—
139C22×C61—21no—
140C22×C61—21no—
141C22×C61—41no—
142C22×C61—41no—
143C22×C61—42no—
144C22×C61—42no—
145C22×C61C2×C22⋊C811yescharacteristic
146C22×C61C2×#9911yescharacteristic
147C22×C61C2×#10011yescharacteristic
148C2×D61—24no—
149C2×D61—44no—
150C2×D61—42no—
151C2×D61—48no—
152C2×D61—44no—
153C2×D61—44no—
154C2×D61—42no—
155C2×D61—44no—
156C4×C61—42no—
157C4×C61—42no—
158C4×C61—81no—
159Dic61—22no—
160Dic61—42no—
161Dic61—81no—
162Dic61#32312yes—
163Dic61#32312yes—
164#2280—611no—
165#1458—612no—
166#1317—612no—
167#1316—612no—
168C2×C61—21no—
169C2×C61—21no—
170C2×C61—41no—
171C2×C61—41no—
172C2×C61C2×#32311yescharacteristic
173C2×C61#212012yes—
174D61—44no—
175C24×C4—611no—
176C2×#117—611no—
177C2×#117—611no—
178#431—1222no—
179#381—611no—
180#381#692311yescharacteristic
181#380—1222no—
182#379—611no—
183#379—611no—
184C4×C22⋊C4—1222no—
185#324—1222no—
186#323—614no—
187C61#1142511yescharacteristic, complemented, Sylow
188C25—611no—
189C23×C4—611no—
190C23×C4—614no—
191C23×C4—1222no—
192C23×C4—1221no—
193C23×C4—1221no—
194C23×C4—2441no—
195C23×C4—2441no—
196C23×C4—2442no—
197C23×C4C2×#692311yescharacteristic
198#117—2441no—
199#117—2441no—
200#117—2442no—
201C2×C4⋊C4—612no—
202C2×C4⋊C4—1221no—
203C2×C22⋊C4—611no—
204C2×C22⋊C4—611no—
205C2×C22⋊C4—1222no—
206C2×C22⋊C4—1222no—
207C2×C22⋊C4C2×#692311yescharacteristic
208C2×C22⋊C4C2×#692311yescharacteristic
209C2×C42—612no—
210C2×C42—1221no—
211C4⋊C8—2442no—
212C22⋊C8—1224no—
213C4×C8—2442no—
214#95—22no—
215#95—1222no—
216C24—612no—
217C24—1221no—
218C24—1221no—
219C24—2441no—
220C24—2441no—
221C24—2444no—
222C24C22×#692311yescharacteristic
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—612no—
231C22×C4—612no—
232C22×C4—612no—
233C22×C4—1224no—
234C22×C4—1224no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4—1222no—
238C22×C4—1221no—
239C22×C4—2441no—
240C22×C4—2441no—
241C22×C4—2442no—
242C22×C4—2444no—
243C22×C4—2444no—
244C22×C4—2442no—
245C22×C4—2442no—
246C22×C4—2444no—
247C22×C4—2444no—
248C22×C4D61⋊C812yes—
249C22×C4C22⋊#692312yes—
250C2×C8—2444no—
251C4⋊C4—2442no—
252C4⋊C4—2442no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—2444no—
256C22⋊C4—2444no—
257C22⋊C4—2441no—
258C22⋊C4—2441no—
259C42—1222no—
260C42—1222no—
261C42—2442no—
262C23—21no—
263C23—21no—
264C23—42no—
265C23—1224no—
266C23—1222no—
267C23—2442no—
268C23—2442no—
269C23—2442no—
270C23—2444no—
271C23—2444no—
272C23—2444no—
273C23—2448no—
274C23—2444no—
275C23—2441no—
276C23—2441no—
277C23C2×C22⋊#692311yescharacteristic
278C23C2×D61⋊C811yescharacteristic
279C23D61⋊M1611yescharacteristic
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—612no—
290C2×C4—611no—
291C2×C4—611no—
292C2×C4—612no—
293C2×C4—612no—
294C2×C4—1222no—
295C2×C4—1222no—
296C2×C4—1222no—
297C2×C4—1222no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1222no—
301C2×C4—2444no—
302C2×C4—2444no—
303C2×C4—2448no—
304C2×C4—2442no—
305C2×C4—2441no—
306C2×C4—2442no—
307C8—4884no—
308C22—22no—
309C22—21no—
310C22—21no—
311C22—41no—
312C22—41no—
313C22—42no—
314C22—42no—
315C22—1224no—
316C22—2444no—
317C22—2442no—
318C22—2444no—
319C22—2444no—
320C22—2448no—
321C22—2442no—
322C22—2444no—
323C22D61⋊(C22⋊C8)11yescharacteristic
324C22D61⋊#9911yescharacteristic
325C22D61⋊#10011yescharacteristic
326C4—42no—
327C4—42no—
328C4—81no—
329C4—612no—
330C4—612no—
331C4—1222no—
332C4—4881no—
333C4—2442no—
334C2—21no—
335C2—21no—
336C2—41no—
337C2—41no—
338C2—2444no—
339C2D61⋊#32311yescharacteristic
340C2#2146207312yes—
subgroupG/H
centerC22D61⋊#99
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC61×#381C4
socleC22×C61C2×#99
prime radicalC24×D61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenter#381#6923
hypocenterC61#11425
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #381

Complements

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

NH ≅ G/Ntype
1. #21461051C2semidirect
2. #21460745C2semidirect
28. C22×C4×D61C8semidirect
187. C61#11425semidirect

Maximal subgroups

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

subgroupindex
#214610512
#214607452
#214607442
#214481992
#1142561