Finite Group Databasebeta

← #30604263

Subgroups — #30604263

Order 15616.

408 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461073C211yesmaximal, characteristic, complemented
2#21461053C211yesmaximal, characteristic, complemented
3#21460760C212yesmaximal, complemented
4#21460748C212yesmaximal, complemented
5#21450278C211yesmaximal, characteristic
6#16840783—21no—
7#16840779—21no—
8#16840607C2212yes—
9#16840607C2212yes—
10#16840606—21no—
11#16840606—21no—
12C2×#14519752C411yescharacteristic
13C2×#14519735C2211yescharacteristic
14#16839679—21no—
15#16839679—21no—
16#16839664C2211yescharacteristic
17#16839663C411yescharacteristic
18#16839652—21no—
19#16839652—21no—
20#16839627C2211yescharacteristic
21C4×#11758198C411yescharacteristic
22C61×#384C411yescharacteristic
23#14519844—41no—
24C4⋊#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27#14519832—41no—
28C4×#92420—41no—
29C22×D244—21no—
30C22×D244C2×C411yescharacteristic
31C22×C4×D61C2×C411yescharacteristic
32#14519752—41no—
33#14519752—41no—
34#14519735—41no—
35#14519735—41no—
36C2×C4⋊Dic61C2311yescharacteristic
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198D411yescharacteristic
44C2×#11758198D411yescharacteristic
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C42×C61C2×C411yescharacteristic
56C23×D61—21no—
57C23×D61C22⋊C411yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C2×D244—22no—
68C2×D244—41no—
69C2×D244—41no—
70C2×D244—42no—
71C2×D244—81no—
72C2×D244—81no—
73C2×C4×D61—22no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—41no—
77C2×#92420—42no—
78C2×#92420—42no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—81no—
82C4⋊C4×C61—81no—
83C42×C61—41no—
84#11758198—41no—
85#11758198—41no—
86#11758198—42no—
87#11758198—42no—
88#11758198—42no—
89#11758198—41no—
90#11758198—41no—
91#11758198—81no—
92#11758198—81no—
93C4⋊Dic61—41no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—22no—
99C23×C61C2×C22⋊C411yescharacteristic
100C22×D61—21no—
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—41no—
104C22×D61—41no—
105C22×D61—41no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61—41no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—22no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61#13112yes—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61#9911yescharacteristic
135C2×Dic61#9911yescharacteristic
136D244—82no—
137D244—84no—
138C4×D61—42no—
139C4×D61—42no—
140#92420—82no—
141#92420—82no—
142#11550—611nomaximal, Sylow
143C22×C61—21no—
144C22×C61—21no—
145C22×C61#40811yescharacteristic
146C22×C61C2×#9911yescharacteristic
147C22×C61#41311yescharacteristic
148C2×D61—41no—
149C2×D61—41no—
150C2×D61—41no—
151C2×D61—81no—
152C2×D61—81no—
153C2×D61—81no—
154C2×D61—81no—
155C2×D61—81no—
156C2×D61—81no—
157C2×D61—81no—
158C2×D61—81no—
159C2×D61—81no—
160C4×C61—22no—
161C4×C61—42no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—81no—
165Dic61—21no—
166Dic61—21no—
167Dic61—41no—
168Dic61—41no—
169Dic61—81no—
170#2500—611no—
171#1464—611no—
172#1458—611no—
173#1324—612no—
174#1318—612no—
175C2×C61—21no—
176C2×C61—21no—
177C2×C61#146811yescharacteristic
178C2×C61#212611yescharacteristic
179C2×C61#213411yescharacteristic
180D61—81no—
181D61—161no—
182C2×#121—611no—
183C2×#117—611no—
184#432—1221no—
185#431—1221no—
186#394—1221no—
187#394—1221no—
188#390—611no—
189#390—611no—
190#388—1221no—
191#388—1221no—
192#384#692311yescharacteristic
193#382—611no—
194C4×C22⋊C4—611no—
195#324—612no—
196#324—612no—
197#323—1221no—
198#323—1221no—
199C61#1155011yescharacteristic, complemented, Sylow
200C22×D4—611no—
201C22×D4—1221no—
202C23×C4—611no—
203#121—2441no—
204#121—2441no—
205#117—2441no—
206#117—2441no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4C2×#692311yescharacteristic
211C2×C4⋊C4C2×#692311yescharacteristic
212C2×C22⋊C4—611no—
213C2×C22⋊C4—611no—
214C2×C22⋊C4—1221no—
215C2×C22⋊C4—1221no—
216C2×C22⋊C4—1221no—
217C2×C22⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42C2×#692311yescharacteristic
224C4⋊C8—2441no—
225C4⋊C8—2441no—
226C22⋊C8—1222no—
227C22⋊C8—1222no—
228#97—2441no—
229C4×C8—2441no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233C24—611no—
234C24—1221no—
235C2×D4—1222no—
236C2×D4—4881no—
237C2×D4—4881no—
238C2×D4—2441no—
239C2×D4—2441no—
240C2×D4—2442no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1222no—
249C22×C4—1221no—
250C22×C4—2441no—
251C22×C4C22⋊#692311yescharacteristic
252C22×C4C22⋊#692311yescharacteristic
253C22×C4C22×#692311yescharacteristic
254C2×C8—2442no—
255C2×C8—2442no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—81no—
259C4⋊C4—81no—
260C4⋊C4—2441no—
261C22⋊C4—4881no—
262C22⋊C4—4881no—
263C22⋊C4—2441no—
264C22⋊C4—2441no—
265C22⋊C4—2442no—
266C22⋊C4—2442no—
267C22⋊C4—2442no—
268C22⋊C4—2441no—
269C22⋊C4—2441no—
270C42—41no—
271C42—1221no—
272C42—1221no—
273C42—1221no—
274C42—1221no—
275C42—1222no—
276C23—1221no—
277C23—1221no—
278C23—1221no—
279C23—2441no—
280C23—2441no—
281C23—2441no—
282C23—2441no—
283C23—2441no—
284C23—2441no—
285C23—2441no—
286C23—2441no—
287C23—2441no—
288C23C2×C22⋊#692311yescharacteristic
289D4—4882no—
290D4—4884no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—2442no—
310C2×C4—2442no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4#1451986512yes—
317C8—4882no—
318C8—4882no—
319C22—21no—
320C22—21no—
321C22—4881no—
322C22—4881no—
323C22—4881no—
324C22—4881no—
325C22—4881no—
326C22—4881no—
327C22—4881no—
328C22—4881no—
329C22—4881no—
330C22—2441no—
331C22—2441no—
332C22—2441no—
333C22#1684073711yescharacteristic
334C22D61⋊#9911yescharacteristic
335C22#1684074811yescharacteristic
336C4—22no—
337C4—42no—
338C4—41no—
339C4—41no—
340C4—81no—
341C4—1221no—
342C4—1221no—
343C4—4881no—
344C4—2441no—
345C4—2441no—
346C2—21no—
347C2—21no—
348C2—9761no—
349C2—4881no—
350C2#2146108711yescharacteristic
351C2#2146209311yescharacteristic
352C2#2146211911yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socleC22×C61C2×#99
prime radicalC2×#14519752C4
cosocleC2×C4⋊Dic61C23
hypercenter#384#6923
hypocenterC61#11550
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #384

Complements

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

NH ≅ G/Ntype
1. #21461073C2semidirect
2. #21461053C2semidirect
3. #21460760C2semidirect
4. #21460748C2semidirect
199. C61#11550semidirect

Maximal subgroups

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

subgroupindex
#214610732
#214610532
#214607602
#214607482
#214502782
#1155061