Finite Group Databasebeta

← #30604762

Subgroups — #30604762

Order 15616.

552 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 88 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#21461524C211yesmaximal, characteristic, complemented
2#21461052C211yesmaximal, characteristic, complemented
3#21460802C214yesmaximal, complemented
4#21451572C211yesmaximal, characteristic
5C2×D61⋊M16—21no—
6#16840778—21no—
7#16840642—21no—
8#16840642C2212yes—
9#16840608C2212yes—
10#16840606—21no—
11C2×#14519774C411yescharacteristic
12C2×#14519752—21no—
13C2×#14519734C2211yescharacteristic
14#16839680—21no—
15#16839680C2212yes—
16#16839672—21no—
17#16839672C412yes—
18#16839663—21no—
19C61×#382C411yescharacteristic
20C2×#11758213—41no—
21D61⋊M16—24no—
22D61⋊M16—42no—
23C2×#11758217—22no—
24C2×D61⋊C8—41no—
25C4⋊#92420—41no—
26C22⋊#92420—22no—
27C4×#92420—41no—
28C22×D244—21no—
29C22×D244—22no—
30C22×D244—21no—
31C22×D244C2×C412yes—
32C22×C4×D61D411yescharacteristic
33#14519774—41no—
34#14519774—41no—
35#14519752—42no—
36#14519752—42no—
37#14519734—41no—
38#14519734—41no—
39C2×#11758196D411yescharacteristic
40C2×#11758196C2311yescharacteristic
41C2×#11758198—22no—
42C2×#11758198—22no—
43C2×#11758198—22no—
44C2×#11758198C2×C411yescharacteristic
45C2×#11758198D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4⋊C4×C61—21no—
48C2×C42×C61C2×C411yescharacteristic
49#95×C61—21no—
50#95×C61C2×C412yes—
51C23×D61—22no—
52C23×D61C22⋊C411yescharacteristic
53C22×C4×C61—22no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22×C411yescharacteristic
57C22×Dic61C22⋊C411yescharacteristic
58C22×Dic61C2×D411yescharacteristic
59C22×Dic61C2×D411yescharacteristic
60C2×D244—42no—
61C2×D244—42no—
62C2×D244—44no—
63C2×D244—41no—
64C2×D244—41no—
65C2×D244—42no—
66C2×D244—42no—
67C2×D244—82no—
68C2×D244—82no—
69C2×D244—82no—
70C2×D244—82no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—22no—
74C2×C4×D61D812yes—
75C2×C4×D61SD1612yes—
76#11758217—24no—
77#11758217—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80#11758213—44no—
81D61⋊C8—44no—
82C4⋊C4×C61—42no—
83C42×C61—21no—
84C42×C61—21no—
85#11758198—41no—
86#11758198—41no—
87#11758198—42no—
88#11758198—42no—
89#11758198—82no—
90#11758198—82no—
91#11758196—41no—
92#11758196—41no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C23×C61C2×C22⋊C411yescharacteristic
96C22×D61—21no—
97C22×D61—21no—
98C22×D61—41no—
99C22×D61—41no—
100C22×D61—42no—
101C22×D61—42no—
102C22×D61—42no—
103C22×D61—42no—
104C22×D61—42no—
105C22×D61—42no—
106C22×D61—42no—
107C22×D61#10212yes—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—42no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61#9911yescharacteristic
116C2×C4×C61#9911yescharacteristic
117C2×C4×C61#10212yes—
118C2×C4×C61#10412yes—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61C2×D811yescharacteristic
126C2×Dic61C2×SD1611yescharacteristic
127D244—84no—
128D244—84no—
129D244—88no—
130D244—82no—
131D244—82no—
132C4×D61—22no—
133C4×D61—22no—
134C4×D61—22no—
135C4×D61—22no—
136#92420—44no—
137#92420—82no—
138#11699—611nomaximal, Sylow
139C22×C61—21no—
140C22×C61—21no—
141C22×C61C2×#9911yescharacteristic
142C22×C61C2×#10211yescharacteristic
143C22×C61C2×#10411yescharacteristic
144C2×D61—22no—
145C2×D61—41no—
146C2×D61—41no—
147C2×D61—42no—
148C2×D61—81no—
149C2×D61—82no—
150C2×D61—82no—
151C2×D61—82no—
152C2×D61—82no—
153C2×D61—82no—
154C2×D61—82no—
155C2×D61—82no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61—82no—
159C4×C61#32712yes—
160C4×C61#32712yes—
161Dic61—21no—
162Dic61—21no—
163Dic61—41no—
164Dic61—41no—
165#2619—611no—
166#1742—611no—
167#1458—611no—
168#1345—614no—
169C2×C61—21no—
170C2×C61—21no—
171C2×C61C2×#32711yescharacteristic
172C2×C61#212211yescharacteristic
173C2×C61#213411yescharacteristic
174D61—42no—
175D61—162no—
176C22×M16—1221no—
177C2×#127—611no—
178C2×#121—1221no—
179C2×#117—611no—
180#431—1221no—
181#394—612no—
182#394—1221no—
183#392—612no—
184#392—1221no—
185#390—1221no—
186#382#692311yescharacteristic
187#343—612no—
188#343—1221no—
189#324—612no—
190#323—1221no—
191C61#1169911yescharacteristic, complemented, Sylow
192C22×D4—612no—
193C22×D4—1222no—
194C22×D4—1221no—
195C22×D4—1221no—
196C23×C4—611no—
197C2×M16—1222no—
198C2×M16—1224no—
199C2×M16—2442no—
200C2×M16—2441no—
201C22×C8—2441no—
202#127—2441no—
203#127—2441no—
204#121—2442no—
205#121—2442no—
206#117—2441no—
207#117—2441no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—611no—
211C2×C22⋊C4—611no—
212C2×C22⋊C4—611no—
213C2×C22⋊C4—1222no—
214C2×C22⋊C4—1222no—
215C2×C22⋊C4—1222no—
216C2×C42—611no—
217C2×C42C2×#692311yescharacteristic
218C4⋊C8—2441no—
219C22⋊C8—1222no—
220C4×C8—2441no—
221#95—21no—
222#95C2×#692312yes—
223C24—611no—
224C24—1222no—
225C2×D4—4882no—
226C2×D4—4882no—
227C2×D4—4882no—
228C2×D4—4882no—
229C2×D4—2442no—
230C2×D4—2442no—
231C2×D4—2444no—
232C2×D4—2441no—
233C2×D4—2441no—
234C2×D4—2442no—
235C2×D4—2442no—
236C22×C4—22no—
237C22×C4—611no—
238C22×C4—612no—
239C22×C4—612no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4—1222no—
245C22×C4C22⋊#692311yescharacteristic
246C22×C4C22⋊#692311yescharacteristic
247C22×C4C22×#692311yescharacteristic
248M16—1224no—
249M16—2442no—
250M16—2444no—
251C2×C8—2442no—
252C2×C8—2444no—
253C2×C8—2442no—
254C4⋊C4—42no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C22⋊C4—4882no—
258C22⋊C4—4882no—
259C22⋊C4—2441no—
260C22⋊C4—2441no—
261C22⋊C4—2442no—
262C22⋊C4—2442no—
263C42—21no—
264C42—21no—
265C42—1221no—
266C42—1221no—
267C23—612no—
268C23—1221no—
269C23—1221no—
270C23—2442no—
271C23—2442no—
272C23—2442no—
273C23—2442no—
274C23—2441no—
275C23—2441no—
276C23—2442no—
277C23—2442no—
278C23—2442no—
279C23C2×C22⋊#692311yescharacteristic
280D4—4884no—
281D4—4884no—
282D4—4888no—
283D4—4882no—
284D4—4882no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1222no—
297C2×C4—1222no—
298C2×C4—1222no—
299C2×C4—1222no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4#1451983611yescharacteristic
305C2×C4#1451983611yescharacteristic
306C2×C4#1451983912yes—
307C2×C4#1451984212yes—
308C8—4882no—
309C8—2444no—
310C22—21no—
311C22—21no—
312C22—1222no—
313C22—4882no—
314C22—4882no—
315C22—4882no—
316C22—4882no—
317C22—4881no—
318C22—4882no—
319C22—4882no—
320C22—4882no—
321C22—2442no—
322C22—2441no—
323C22—2441no—
324C22C2×#1451983611yescharacteristic
325C22C2×#1451983911yescharacteristic
326C22C2×#1451984211yescharacteristic
327C4—41no—
328C4—41no—
329C4—82no—
330C4—1221no—
331C4—1221no—
332C4—2441no—
333C4—2441no—
334C4#1684061412yes—
335C4#1684061412yes—
336C2—21no—
337C2—21no—
338C2—9762no—
339C2—2442no—
340C2C2×#1684061411yescharacteristic
341C2#2146208011yescharacteristic
342C2#2146212011yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC22×C61C2×#99
prime radical#21451572C2
cosocleC2×#11758196C23
hypercenter#382#6923
hypocenterC61#11699
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
1. #21461524C2semidirect
2. #21461052C2semidirect
3. #21460802C2semidirect
191. C61#11699semidirect

Maximal subgroups

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

subgroupindex
#214615242
#214610522
#214608022
#214515722
#1169961