Finite Group Databasebeta

← #30604361

Subgroups — #30604361

Order 15616.

426 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 70 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#21461079C211yesmaximal, characteristic
2#21461055C211yesmaximal, characteristic
3#21460764C212yesmaximal, complemented
4#21460763C212yesmaximal, complemented
5#21451165C211yesmaximal, characteristic
6#16840782—21no—
7C2×C22⋊#92420—21no—
8#16840607—21no—
9#16840605—21no—
10#16840605C2212yes—
11#16840605C2212yes—
12C2×D4×Dic61C2211yescharacteristic
13C22×#11758196C411yescharacteristic
14#16839696—21no—
15#16839685—21no—
16#16839645—21no—
17#16839642C411yescharacteristic
18#16839637C2211yescharacteristic
19#16839635C2211yescharacteristic
20#16839634—21no—
21#16839620C411yescharacteristic
22C61×#386C411yescharacteristic
23C22×#92420—41no—
24#14519844—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27C22⋊#92420—41no—
28#14519832—41no—
29C23×Dic61C2×C411yescharacteristic
30C23×Dic61C2×C411yescharacteristic
31C23×Dic61D411yescharacteristic
32D4×Dic61—41no—
33D4×Dic61—41no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—41no—
41C2×#11758196—41no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61C2×C411yescharacteristic
44C2×C22⋊Dic61D411yescharacteristic
45C2×C22⋊Dic61C2311yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×D4×C61C2×C411yescharacteristic
52C23×C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61C2×C411yescharacteristic
55#95×C61—21no—
56C24×C61C22⋊C411yescharacteristic
57C24×C61C22×C411yescharacteristic
58C2×D4×C61—22no—
59C2×D4×C61—22no—
60C2×D4×C61—41no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—41no—
64C22×C4×C61—81no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—42no—
73C22×Dic61—41no—
74C22×Dic61—81no—
75C22×Dic61—81no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C2×D411yescharacteristic
79C22×Dic61C2×D411yescharacteristic
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—82no—
83C22⋊C4×C61—22no—
84C22⋊C4×C61—81no—
85C22⋊Dic61—22no—
86C22⋊Dic61—41no—
87C22⋊Dic61—41no—
88C22⋊Dic61—42no—
89C4⋊Dic61—41no—
90C4⋊Dic61—42no—
91#11758196—42no—
92#11758196—41no—
93#11758196—41no—
94#11758196—81no—
95#11758196—81no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61#10112yes—
107C23×C61C2×C22⋊C411yescharacteristic
108C23×C61#13112yes—
109D4×C61—44no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—82no—
120C2×Dic61—22no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—41no—
125C2×Dic61—42no—
126C2×Dic61—41no—
127C2×Dic61—42no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—42no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—81no—
137C2×Dic61—81no—
138C2×Dic61—81no—
139C2×Dic61#9911yescharacteristic
140C2×Dic61#9911yescharacteristic
141#92420—82no—
142#92420—82no—
143#11578—611nomaximal, Sylow
144C22×C61—21no—
145C22×C61—21no—
146C22×C61—22no—
147C22×C61—22no—
148C22×C61—42no—
149C22×C61—42no—
150C22×C61—42no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—81no—
156C22×C61#40811yescharacteristic
157C22×C61C2×#9911yescharacteristic
158C22×C61C2×#10111yescharacteristic
159C4×C61—41no—
160C4×C61—81no—
161C4×C61—81no—
162Dic61—21no—
163Dic61—21no—
164Dic61—41no—
165Dic61—42no—
166Dic61—41no—
167Dic61—41no—
168Dic61—81no—
169#2579—611no—
170#1466—611no—
171#1459—611no—
172#1326—612no—
173#1326—612no—
174C2×C61—21no—
175C2×C61—21no—
176C2×C61—42no—
177C2×C61—42no—
178C2×C61#147211yescharacteristic
179C2×C61#212011yescharacteristic
180C2×C61#212111yescharacteristic
181C2×C4×D4—611no—
182C22×C4⋊C4—611no—
183#432—1221no—
184C2×C22⋊C8—1221no—
185#398—1221no—
186#396—1221no—
187#387—1221no—
188#386—611no—
189#386#692311yescharacteristic
190#385—611no—
191#385—611no—
192#385—1221no—
193#380—611no—
194#324—1221no—
195#323—612no—
196#323—612no—
197#323—1221no—
198C61#1157811yescharacteristic, complemented, Sylow
199C22×D4C2×#692311yescharacteristic
200C23×C4—611no—
201C23×C4—611no—
202C23×C4—611no—
203C23×C4C2×#692311yescharacteristic
204C22×C8—2441no—
205C4×D4—2441no—
206C4×D4—2441no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—2441no—
214C2×C4⋊C4—2441no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—611no—
217C2×C22⋊C4—611no—
218C2×C22⋊C4—611no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4C2×#692311yescharacteristic
221C2×C42—611no—
222C4⋊C8—2441no—
223C22⋊C8—1222no—
224C22⋊C8—1222no—
225C22⋊C8—2441no—
226#97—2441no—
227#95—21no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232C24C22⋊#692311yescharacteristic
233C24C22×#692311yescharacteristic
234C2×D4—22no—
235C2×D4—22no—
236C2×D4—41no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—41no—
240C22×C4—81no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—4881no—
252C22×C4—4881no—
253C22×C4—2442no—
254C22×C4—2441no—
255C22×C4C22⋊#692311yescharacteristic
256C2×C8—4882no—
257C2×C8—2442no—
258C2×C8—2442no—
259C4⋊C4—4881no—
260C4⋊C4—4881no—
261C4⋊C4—2441no—
262C4⋊C4—2441no—
263C4⋊C4—2441no—
264C4⋊C4—2442no—
265C4⋊C4—2442no—
266C22⋊C4—22no—
267C22⋊C4—81no—
268C22⋊C4—1222no—
269C22⋊C4—2441no—
270C22⋊C4—2441no—
271C22⋊C4—2442no—
272C42—1221no—
273C42—1221no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23#1451983812yes—
283C23C2×C22⋊#692311yescharacteristic
284C23#1451986412yes—
285D4—44no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—82no—
296C2×C4—611no—
297C2×C4—611no—
298C2×C4—1222no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—4881no—
303C2×C4—4881no—
304C2×C4—4881no—
305C2×C4—2441no—
306C2×C4—2442no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2442no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2442no—
317C8—4882no—
318C8—4882no—
319C22—21no—
320C22—21no—
321C22—22no—
322C22—22no—
323C22—42no—
324C22—42no—
325C22—42no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22#1684073511yescharacteristic
332C22D61⋊#9911yescharacteristic
333C22C2×#1451983811yescharacteristic
334C4—41no—
335C4—81no—
336C4—81no—
337C4—1221no—
338C4—1221no—
339C4—4881no—
340C4—2441no—
341C4—2442no—
342C4—2441no—
343C4—2441no—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—42no—
348C2#2146109811yescharacteristic
349C2#2146207311yescharacteristic
350C2#2146207511yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#386C4
socleC22×C61C2×#99
prime radicalC22×D4×C61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenter#386#6923
hypocenterC61#11578
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #386

Complements

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

NH ≅ G/Ntype
3. #21460764C2semidirect
4. #21460763C2semidirect
198. C61#11578semidirect

Maximal subgroups

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

subgroupindex
#214610792
#214610552
#214607642
#214607632
#214511652
#1157861