Finite Group Databasebeta

← #29573644

Subgroups — #29573644

Order 15616.

480 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C4×#14519692C211yesmaximal, characteristic
2#21444157C211yesmaximal, characteristic
3#21443705C212yesmaximal, complemented
4#21443671C212yesmaximal, complemented
5C61×#2353C211yesmaximal, characteristic
6C2×#14519692—21no—
7#16839726C2212yes—
8C4×C22⋊Dic61C2212yes—
9#16839529—21no—
10#16839488—21no—
11#16839486—21no—
12C2×C4×D4×C61C2211yescharacteristic
13C61×#388—21no—
14C61×#387—21no—
15C61×#386—21no—
16C61×#383C411yescharacteristic, complemented
17C61×#381C2211yescharacteristic
18C61×#380C411yescharacteristic, complemented
19C4×C22⋊C4×C61—21no—
20C4×C22⋊C4×C61C2211yescharacteristic
21C61×#376C411yescharacteristic, complemented
22C2×#95×C61C411yescharacteristic, complemented
23C2×#11758194—22no—
24C2×C22⋊Dic61—22no—
25C2×C4×Dic61—22no—
26#14519692—24no—
27C22⋊#92418—22no—
28C22⋊#92418—22no—
29#14519684—22no—
30C22×D4×C61D411yescharacteristic
31C23×C4×C61—21no—
32C23×C4×C61C2×C411yescharacteristic
33C23×C4×C61C2311yescharacteristic
34C4×D4×C61—22no—
35C4×D4×C61—22no—
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61D411yescharacteristic
38C2×C22⋊C4×C61—21no—
39C2×C22⋊C4×C61—21no—
40C2×C22⋊C4×C61—21no—
41C2×C22⋊C4×C61D411yescharacteristic
42C2×C22⋊C4×C61D411yescharacteristic
43C2×C42×C61—21no—
44C2×C42×C61—21no—
45C2×C42×C61C2×C411yescharacteristic
46#95×C61—21no—
47#95×C61—21no—
48#95×C61—21no—
49#95×C61—21no—
50#95×C61—21no—
51#95×C61C2×C411yescharacteristic
52#95×C61C2×C411yescharacteristic
53#95×C61C2×C411yescharacteristic
54#95×C61C2×C411yescharacteristic
55C24×C61C22⋊C411yescharacteristic
56C24×C61C2×D411yescharacteristic
57C2×D4×C61—22no—
58C2×D4×C61—22no—
59C2×D4×C61—41no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—42no—
67C22×C4×C61—42no—
68C22×C4×C61—81no—
69C22×C4×C61—81no—
70C22×C4×C61—81no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61#4112yes—
77C22×C4×C61#4112yes—
78C22×Dic61—42no—
79C4⋊C4×C61—22no—
80C4⋊C4×C61—81no—
81C22⋊C4×C61—22no—
82C22⋊C4×C61—22no—
83C22⋊C4×C61—42no—
84C22⋊C4×C61—42no—
85C22⋊C4×C61—81no—
86C42×C61—21no—
87C42×C61—21no—
88C42×C61—42no—
89C42×C61—81no—
90C22⋊Dic61—24no—
91C22⋊Dic61—42no—
92C4×Dic61—82no—
93#11758194—82no—
94C2×#92418—42no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—41no—
100C23×C61—41no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61#10412yes—
104C23×C61C2×C22⋊C411yescharacteristic
105C23×C61#12312yes—
106D4×C61—44no—
107C2×C4×C61—22no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
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—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×C4×C61—84no—
133C2×C4×C61#11711yescharacteristic
134C2×C4×C61#11711yescharacteristic
135C2×C4×C61#12312yes—
136C2×Dic61—44no—
137C2×Dic61—82no—
138C2×Dic61—82no—
139#92418—82no—
140#8777—611nomaximal, Sylow
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—22no—
144C22×C61—22no—
145C22×C61—22no—
146C22×C61—22no—
147C22×C61—42no—
148C22×C61—42no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—81no—
152C22×C61—81no—
153C22×C61#38111yescharacteristic
154C22×C61C2×#10411yescharacteristic
155C22×C61#42111yescharacteristic
156C4×C61—22no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—42no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—81no—
164C4×C61—81no—
165C4×C61—81no—
166Dic61—84no—
167#2353D6111yescharacteristic
168C4×#99—611no—
169#1465—611no—
170#1297—612no—
171#1284—612no—
172C2×C61—21no—
173C2×C61—21no—
174C2×C61—42no—
175C2×C61—42no—
176C2×C61#182611yescharacteristic
177C2×C61#182711yescharacteristic
178C2×C61#182811yescharacteristic
179C2×C4×D4C2×D6111yescharacteristic
180C2×#99—1221no—
181#407—612no—
182#388—21no—
183#387—21no—
184#386—21no—
185#383Dic6111yescharacteristic, complemented
186#381C2×D6111yescharacteristic
187#380Dic6111yescharacteristic, complemented
188C4×C22⋊C4—21no—
189C4×C22⋊C4—612no—
190C4×C22⋊C4C2×D6111yescharacteristic
191#376Dic6111yescharacteristic, complemented
192C2×#95Dic6111yescharacteristic, complemented
193#342—1221no—
194#324—1221no—
195#323—1221no—
196C61#877711yescharacteristic, complemented, Sylow
197C22×D4C22⋊D6111yescharacteristic
198C23×C4—21no—
199C23×C4C2×Dic6111yescharacteristic
200C23×C4C22×D6111yescharacteristic
201C2×M16—1222no—
202C4×D4—22no—
203C4×D4—22no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C22⋊D6111yescharacteristic
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—1222no—
210C2×C22⋊C4C22⋊D6111yescharacteristic
211C2×C22⋊C4C22⋊D6111yescharacteristic
212C2×C42—21no—
213C2×C42—21no—
214C2×C42—1222no—
215C2×C42C2×Dic6111yescharacteristic
216#99—1224no—
217C22⋊C8—1222no—
218C22⋊C8—1222no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—1222no—
225#95C2×Dic6111yescharacteristic
226#95C2×Dic6111yescharacteristic
227#95C2×Dic6111yescharacteristic
228#95C2×Dic6111yescharacteristic
229C24C22⋊Dic6111yescharacteristic
230C24C2×C22⋊D6111yescharacteristic
231C2×D4—22no—
232C2×D4—22no—
233C2×D4—41no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—81no—
243C22×C4—81no—
244C22×C4—81no—
245C22×C4—2442no—
246C22×C4C22⋊Dic6111yescharacteristic
247C22×C4C22⋊Dic6111yescharacteristic
248C22×C4C22⋊Dic6111yescharacteristic
249C22×C4#1175822212yes—
250C22×C4#1175822212yes—
251C22×C4C22×Dic6111yescharacteristic
252C22×C4C2×C22⋊D6111yescharacteristic
253M16—4882no—
254C2×C8—2442no—
255C4⋊C4—22no—
256C4⋊C4—81no—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C22⋊C4—81no—
262C22⋊C4—1224no—
263C22⋊C4—2442no—
264C42—21no—
265C42—21no—
266C42—42no—
267C42—81no—
268C42—4882no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23#1451970412yes—
278C23C2×C22⋊Dic6111yescharacteristic
279C23#1451976012yes—
280D4—44no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—84no—
307C2×C4—4882no—
308C2×C4—4882no—
309C2×C4—2444no—
310C2×C4#1451973611yescharacteristic
311C2×C4#1451973611yescharacteristic
312C2×C4#1451976012yes—
313C8—4882no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—42no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22#1683962511yescharacteristic
327C22C2×#1451970411yescharacteristic
328C22#1683977911yescharacteristic
329C4—22no—
330C4—21no—
331C4—21no—
332C4—42no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—4884no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—42no—
344C2#2144591811yescharacteristic
345C2#2144592311yescharacteristic
346C2#2144592711yescharacteristic
subgroupG/H
centerC22#16839625
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#2353C2
socleC22×C61#381
prime radicalC22×D4×C61D4
cosocleC23×C4×C61C23
hypercenter#2353D61
hypocenterC61#8777
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2353

Complements

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

NH ≅ G/Ntype
3. #21443705C2semidirect
4. #21443671C2semidirect
16. C61×#383C4semidirect
18. C61×#380C4semidirect
21. C61×#376C4semidirect
22. C2×#95×C61C4semidirect
185. #383Dic61semidirect
187. #380Dic61semidirect
191. #376Dic61semidirect
192. C2×#95Dic61semidirect
196. C61#8777semidirect

Maximal subgroups

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

subgroupindex
C4×#145196922
#214441572
#214437052
#214436712
C61×#23532
#877761