Finite Group Databasebeta

← #30599368

Subgroups — #30599368

Order 15616.

438 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461069C211yesmaximal, characteristic
2#21461069C211yesmaximal, characteristic
3#21460720C212yesmaximal
4#21460720C212yesmaximal
5#21448436C211yesmaximal, characteristic
6#16840732C2212yes—
7#16840732C2212yes—
8#16840608—21no—
9#16840608—21no—
10#16840608—21no—
11#16840608—21no—
12C2×#14519733C411yescharacteristic
13C2×#14519733C411yescharacteristic
14C22×#11758196C2211yescharacteristic
15#16839659—21no—
16#16839659—21no—
17#16839657—21no—
18#16839657—21no—
19#16839622C411yescharacteristic
20#16839620C2211yescharacteristic
21#16839620C2211yescharacteristic
22C61×#380C411yescharacteristic
23C2×#11758217—22no—
24C2×#11758217—22no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27C22⋊#92420—22no—
28C22⋊#92420—22no—
29C23×Dic61C2×C411yescharacteristic
30C23×Dic61C2311yescharacteristic
31#14519733—42no—
32#14519733—42no—
33C2×C4⋊Dic61—21no—
34C2×#11758196—22no—
35C2×#11758196—22no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196D411yescharacteristic
41C2×#11758196D411yescharacteristic
42C2×#11758196D411yescharacteristic
43C2×#11758196D411yescharacteristic
44C2×C22⋊Dic61C2×C411yescharacteristic
45C2×C22⋊Dic61C2×C411yescharacteristic
46C2×C4×Dic61—21no—
47C2×C4×Dic61—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C23×C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61—21no—
53C2×C22⋊C4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61C2×C411yescharacteristic
55#95×C61—21no—
56C24×C61C22×C411yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—81no—
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—22no—
67C22×Dic61—22no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—81no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61#4112yes—
76C22×Dic61#4112yes—
77#11758217—82no—
78#11758217—82no—
79C2×#92420—42no—
80C2×#92420—42no—
81C4⋊C4×C61—81no—
82C22⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C22⋊Dic61—41no—
85C22⋊Dic61—41no—
86C4⋊Dic61—81no—
87#11758196—22no—
88#11758196—22no—
89#11758196—22no—
90#11758196—22no—
91#11758196—42no—
92#11758196—42no—
93#11758196—81no—
94#11758196—81no—
95C4×Dic61—42no—
96C4×Dic61—42no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—41no—
100C23×C61—41no—
101C23×C61C2×C22⋊C411yescharacteristic
102C23×C61#11711yescharacteristic
103C23×C61#11711yescharacteristic
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—81no—
115C2×C4×C61—81no—
116C2×Dic61—24no—
117C2×Dic61—24no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—42no—
125C2×Dic61—42no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61#10012yes—
133C2×Dic61#10112yes—
134C2×Dic61#12312yes—
135C2×Dic61#12312yes—
136#92420—82no—
137#92420—82no—
138#8757—611nomaximal, Sylow
139C22×C61—21no—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—21no—
144C22×C61—21no—
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—42no—
148C22×C61—42no—
149C22×C61#38111yescharacteristic
150C22×C61C2×#10011yescharacteristic
151C22×C61C2×#10111yescharacteristic
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—81no—
155C4×C61—81no—
156Dic61—22no—
157Dic61—22no—
158Dic61—22no—
159Dic61—22no—
160Dic61—81no—
161Dic61—81no—
162#2316—611no—
163#1463—611no—
164#1463—611no—
165#1305—612no—
166#1305—612no—
167C2×C61—21no—
168C2×C61—21no—
169C2×C61—41no—
170C2×C61—41no—
171C2×C61#182111yescharacteristic
172C2×C61#182811yescharacteristic
173C2×C61#183011yescharacteristic
174C2×#117—611no—
175C2×#117—611no—
176C22×C4⋊C4—611no—
177#407—612no—
178#407—612no—
179#389—1221no—
180#389—1221no—
181#389—1221no—
182#389—1221no—
183#380—611no—
184#380—611no—
185#380—611no—
186#380#692311yescharacteristic
187#324—1221no—
188#324—1221no—
189#324—1221no—
190#324—1221no—
191C61#875711yescharacteristic, complemented, Sylow
192C23×C4—611no—
193C23×C4—611no—
194C23×C4C2×#692311yescharacteristic
195C2×M16—1222no—
196C2×M16—1222no—
197#117—2442no—
198#117—2442no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—1222no—
205C2×C4⋊C4—1222no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C22⋊C4—611no—
212C2×C22⋊C4—611no—
213C2×C22⋊C4C2×#692311yescharacteristic
214C2×C22⋊C4C2×#692311yescharacteristic
215C2×C42—1221no—
216C2×C42—1221no—
217C22⋊C8—1222no—
218C22⋊C8—1222no—
219C22⋊C8—1222no—
220C22⋊C8—1222no—
221#95—21no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225C24C22×#692311yescharacteristic
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—81no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—612no—
236C22×C4—612no—
237C22×C4—1222no—
238C22×C4—1222no—
239C22×C4—1221no—
240C22×C4—1221no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—4881no—
244C22×C4C22⋊#692311yescharacteristic
245C22×C4C22⋊#692311yescharacteristic
246M16—4882no—
247M16—4882no—
248C2×C8—2442no—
249C2×C8—2442no—
250C4⋊C4—81no—
251C4⋊C4—1222no—
252C4⋊C4—1222no—
253C4⋊C4—1222no—
254C4⋊C4—1222no—
255C4⋊C4—4881no—
256C4⋊C4—4881no—
257C4⋊C4—4881no—
258C4⋊C4—2442no—
259C4⋊C4—2442no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—2441no—
263C22⋊C4—2441no—
264C42—2442no—
265C42—2442no—
266C23—21no—
267C23—21no—
268C23—41no—
269C23—41no—
270C23C2×C22⋊#692311yescharacteristic
271C23#1451985611yescharacteristic
272C23#1451985611yescharacteristic
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—612no—
286C2×C4—612no—
287C2×C4—612no—
288C2×C4—612no—
289C2×C4—1224no—
290C2×C4—1224no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2442no—
298C2×C4—2442no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C8—4882no—
306C8—4882no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—42no—
316C22—42no—
317C22#1684070511yescharacteristic
318C22D61⋊#10011yescharacteristic
319C22D61⋊#10111yescharacteristic
320C4—41no—
321C4—41no—
322C4—81no—
323C4—81no—
324C4—1222no—
325C4—1222no—
326C4—1222no—
327C4—1222no—
328C4—4881no—
329C4—4881no—
330C2—21no—
331C2—21no—
332C2—41no—
333C2—41no—
334C2#2146171911yescharacteristic
335C2#2146173011yescharacteristic
336C2#2146173311yescharacteristic
subgroupG/H
centerC22#16840705
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#380C4
socleC22×C61#381
cosocleC23×Dic61C23
hypercenter#380#6923
hypocenterC61#8757
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #380

Complements

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

NH ≅ G/Ntype
191. C61#8757semidirect

Maximal subgroups

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

subgroupindex
#214610692
#214607202
#214484362
#875761