Finite Group Databasebeta

← #30604136

Subgroups — #30604136

Order 15616.

446 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461071C211yesmaximal, characteristic
2#21461071C211yesmaximal, characteristic
3#21460764C212yesmaximal
4#21460763C212yesmaximal
5#21448298C211yesmaximal, characteristic
6#16840783—21no—
7#16840783—21no—
8#16840608—21no—
9#16840608—21no—
10#16840605C2212yes—
11#16840605C2212yes—
12C2×#14519733C411yescharacteristic
13C2×#14519733C2211yescharacteristic
14C22×C4×Dic61C411yescharacteristic
15#16839659—21no—
16#16839657—21no—
17#16839637C2211yescharacteristic
18#16839635C2211yescharacteristic
19#16839634C411yescharacteristic
20C4⋊C4×Dic61—21no—
21#16839613—21no—
22C61×#385C411yescharacteristic
23C4⋊#92420—41no—
24C4⋊#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27#14519832—41no—
28#14519832—41no—
29C23×Dic61C2×C411yescharacteristic
30C23×Dic61C2×C411yescharacteristic
31#14519733—22no—
32#14519733—22no—
33#14519733—41no—
34#14519733—41no—
35C2×C4⋊Dic61—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196D411yescharacteristic
40C2×#11758196D411yescharacteristic
41C2×C22⋊Dic61C2×C411yescharacteristic
42C2×C22⋊Dic61C2311yescharacteristic
43C2×C4×Dic61—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61—41no—
47C2×C4×Dic61—41no—
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C23×C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61—21no—
55C2×C22⋊C4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61C2×C411yescharacteristic
57#95×C61—21no—
58C24×C61C22×C411yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—42no—
62C22×C4×C61—41no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—22no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—42no—
73C22×Dic61—41no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C2×#92420—42no—
79C2×#92420—42no—
80C4⋊C4×C61—42no—
81C22⋊C4×C61—21no—
82C22⋊C4×C61—41no—
83C22⋊C4×C61M1612yes—
84C22⋊Dic61—21no—
85C22⋊Dic61—41no—
86C22⋊Dic61M1612yes—
87C4⋊Dic61—42no—
88#11758196—24no—
89#11758196—41no—
90#11758196—41no—
91#11758196—42no—
92#11758196—42no—
93C4×Dic61—24no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—42no—
99C4×Dic61—41no—
100C4×Dic61—41no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61C2×C22⋊C411yescharacteristic
106C23×C61C2×M1611yescharacteristic
107C23×C61C2×M1611yescharacteristic
108C2×C4×C61—22no—
109C2×C4×C61—22no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—42no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—42no—
120C2×Dic61—22no—
121C2×Dic61—22no—
122C2×Dic61—22no—
123C2×Dic61—22no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—22no—
129C2×Dic61—22no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—42no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—42no—
140C2×Dic61#9911yescharacteristic
141C2×Dic61#9911yescharacteristic
142C2×Dic61#10112yes—
143#92420—82no—
144#92420—82no—
145#11518—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—42no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61#40711yescharacteristic
156C22×C61C2×#9911yescharacteristic
157C22×C61C2×#10111yescharacteristic
158C4×C61—42no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61—42no—
162Dic61—21no—
163Dic61—21no—
164Dic61—22no—
165Dic61—42no—
166Dic61—41no—
167Dic61—41no—
168Dic61—42no—
169#2296—611no—
170#1464—611no—
171#1464—611no—
172#1326—612no—
173#1326—612no—
174C2×C61—21no—
175C2×C61—21no—
176C2×C61—41no—
177C2×C61—41no—
178C2×C61#146311yescharacteristic
179C2×C61#212011yescharacteristic
180C2×C61#212011yescharacteristic
181C2×#117—611no—
182C2×#117—611no—
183C22×C42—611no—
184#432—1221no—
185#432—1221no—
186#389—1221no—
187#389—1221no—
188#385—611no—
189#385—611no—
190#385—611no—
191#385#692311yescharacteristic
192C4×C4⋊C4—1221no—
193C4×C4⋊C4—1221no—
194#324—1221no—
195#324—1221no—
196#323—612no—
197#323—612no—
198C61#1151811yescharacteristic, complemented, Sylow
199C23×C4—611no—
200C23×C4—611no—
201C23×C4C2×#692311yescharacteristic
202#117—1222no—
203#117—1222no—
204#117—2441no—
205#117—2441no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C22⋊C4—611no—
214C2×C22⋊C4—611no—
215C2×C22⋊C4C2×#692311yescharacteristic
216C2×C22⋊C4C2×#692311yescharacteristic
217C2×C42—611no—
218C2×C42—611no—
219C2×C42—1221no—
220C2×C42—1221no—
221C2×C42—1221no—
222C2×C42—2441no—
223C2×C42—2441no—
224C4⋊C8—2441no—
225C4⋊C8—2441no—
226C22⋊C8—1222no—
227C22⋊C8—1222no—
228#97—2441no—
229#97—2441no—
230#95—21no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234C24C22×#692311yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—42no—
238C22×C4—41no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1222no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—2442no—
251C22×C4—2441no—
252C22×C4C22⋊#692311yescharacteristic
253C22×C4C22⋊#692311yescharacteristic
254C2×C8—2442no—
255C2×C8—2442no—
256C4⋊C4—42no—
257C4⋊C4—1224no—
258C4⋊C4—2441no—
259C4⋊C4—2441no—
260C4⋊C4—2442no—
261C4⋊C4—2442no—
262C4⋊C4—2442no—
263C22⋊C4—21no—
264C22⋊C4—41no—
265C22⋊C4—612no—
266C22⋊C4—1221no—
267C22⋊C4—2441no—
268C22⋊C4#1175821312yes—
269C42—1221no—
270C42—1221no—
271C42—1221no—
272C42—1221no—
273C42—1224no—
274C42—2441no—
275C42—2441no—
276C42—2442no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23C2×C22⋊#692311yescharacteristic
282C23D61⋊M1611yescharacteristic
283C23C2×#1175821311yescharacteristic
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—611no—
297C2×C4—611no—
298C2×C4—612no—
299C2×C4—1222no—
300C2×C4—1222no—
301C2×C4—1222no—
302C2×C4—1222no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1222no—
308C2×C4—1222no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2442no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2442no—
319C8—4882no—
320C8—4882no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—41no—
326C22—41no—
327C22—42no—
328C22—41no—
329C22—41no—
330C22#1684073311yescharacteristic
331C22D61⋊#9911yescharacteristic
332C22D61⋊#10111yescharacteristic
333C4—42no—
334C4—41no—
335C4—42no—
336C4—41no—
337C4—1221no—
338C4—1221no—
339C4—1222no—
340C4—2442no—
341C4—2441no—
342C4—2441no—
343C4—2442no—
344C2—21no—
345C2—21no—
346C2—41no—
347C2—41no—
348C2#2146106811yescharacteristic
349C2#2146207111yescharacteristic
350C2#2146207311yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#385C4
socleC22×C61C2×#99
cosocleC2×C22⋊Dic61C23
hypercenter#385#6923
hypocenterC61#11518
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #385

Complements

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

NH ≅ G/Ntype
198. C61#11518semidirect

Maximal subgroups

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

subgroupindex
#214610712
#214607642
#214607632
#214482982
#1151861