Finite Group Databasebeta

← #30604340

Subgroups — #30604340

Order 15616.

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

normal subgroups only

This group has 416 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#21461076C211yesmaximal, characteristic
2#21461056C211yesmaximal, characteristic
3#21460762C212yesmaximal, complemented
4#21460760C212yesmaximal, complemented
5#21451020C211yesmaximal, characteristic
6#16840733—21no—
7D61⋊(C22⋊C8)—21no—
8#16840607C2212yes—
9#16840607C2212yes—
10#16840606—21no—
11#16840606—21no—
12C2×C4×D244C2211yescharacteristic
13#16839684—21no—
14#16839684—21no—
15#16839663C411yescharacteristic
16#16839663C411yescharacteristic
17#16839633—21no—
18#16839633—21no—
19#16839631C2211yescharacteristic
20#16839627C2211yescharacteristic
21C4×C4⋊Dic61C411yescharacteristic
22C2×#125×C61C411yescharacteristic
23C2×#11758213—41no—
24C2×D61⋊C8—41no—
25#14519834—41no—
26#14519834—41no—
27C22⋊#92420—22no—
28C22⋊#92420—22no—
29C22×D244C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C4×D244—41no—
33C4×D244—41no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2311yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198D411yescharacteristic
43C2×#11758198D411yescharacteristic
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61C2×C411yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#125×C61—41no—
50#125×C61—41no—
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×D61C22⋊C411yescharacteristic
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×Dic61—21no—
65C22×Dic61C2×D411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C2×D244—22no—
68C2×D244—22no—
69C2×D244—41no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—81no—
75C2×C4×D61—81no—
76C2×#92420—42no—
77C2×#92420—42no—
78#11758213—82no—
79D61⋊C8—82no—
80C4⋊C4×C61—42no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C42×C61—21no—
86C42×C61—21no—
87#11758198—41no—
88#11758198—41no—
89#11758198—42no—
90#11758198—42no—
91#11758198—81no—
92#11758198—81no—
93C4⋊Dic61—41no—
94C4⋊Dic61—42no—
95#11758196—81no—
96#11758196—81no—
97C4×Dic61—22no—
98C4×Dic61—22no—
99C23×C61C2×C22⋊C411yescharacteristic
100C22×D61—21no—
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—41no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61#10112yes—
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—41no—
120C2×C4×C61—41no—
121C2×C4×C61#9911yescharacteristic
122C2×C4×C61#9911yescharacteristic
123C2×C4×C61#13112yes—
124C2×Dic61—22no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134D244—44no—
135C4×D61—42no—
136C4×D61—42no—
137C4×D61—81no—
138C4×D61—81no—
139#92420—82no—
140#92420—82no—
141#11572—611nomaximal, Sylow
142C22×C61—21no—
143C22×C61—21no—
144C22×C61#40811yescharacteristic
145C22×C61C2×#9911yescharacteristic
146C22×C61C2×#10111yescharacteristic
147C2×D61—22no—
148C2×D61—41no—
149C2×D61—41no—
150C2×D61—42no—
151C2×D61—42no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—81no—
156C2×D61—81no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—22no—
160C4×C61—41no—
161C4×C61—81no—
162C4×C61—81no—
163Dic61—42no—
164Dic61—41no—
165Dic61—41no—
166Dic61—81no—
167#2566—611no—
168#1465—611no—
169#1459—611no—
170#1325—612no—
171#1324—612no—
172C2×C61—21no—
173C2×C61—21no—
174C2×C61#147211yescharacteristic
175C2×C61#212711yescharacteristic
176C2×C61#213211yescharacteristic
177D61—42no—
178D61—81no—
179C2×#125#692311yescharacteristic
180C2×C4×D4—611no—
181#407—1221no—
182C2×C22⋊C8—1221no—
183#396—1221no—
184#396—1221no—
185#390—611no—
186#390—611no—
187#385—1221no—
188#385—1221no—
189#384—611no—
190#382—611no—
191C4×C4⋊C4—611no—
192#324—612no—
193#324—612no—
194#323—1221no—
195#323—1221no—
196C61#1157211yescharacteristic, complemented, Sylow
197C22×D4—611no—
198C23×C4—611no—
199C23×C4—611no—
200C2×M16—2441no—
201C22×C8—2441no—
202#125—41no—
203#125—41no—
204C4×D4—2441no—
205C4×D4—2441no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4C2×#692311yescharacteristic
213C2×C4⋊C4C2×#692311yescharacteristic
214C2×C22⋊C4—611no—
215C2×C22⋊C4—611no—
216C2×C22⋊C4—1221no—
217C2×C22⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42C2×#692311yescharacteristic
223C22⋊C8—1222no—
224C22⋊C8—1222no—
225C22⋊C8—2441no—
226C22⋊C8—2441no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230C24—611no—
231C24—611no—
232C2×D4—1222no—
233C2×D4—1222no—
234C2×D4—2441no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—1221no—
240C22×C4—1221no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—4881no—
246C22×C4—4881no—
247C22×C4C22⋊#692311yescharacteristic
248C22×C4C22⋊#692311yescharacteristic
249C22×C4C22×#692311yescharacteristic
250M16—4882no—
251C2×C8—4882no—
252C2×C8—2442no—
253C2×C8—2442no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—4881no—
260C4⋊C4—4881no—
261C4⋊C4—2441no—
262C4⋊C4—2442no—
263C22⋊C4—4881no—
264C22⋊C4—4881no—
265C22⋊C4—2441no—
266C22⋊C4—2441no—
267C22⋊C4—2442no—
268C22⋊C4—2442no—
269C42—21no—
270C42—21no—
271C42—1222no—
272C42—1222no—
273C23—612no—
274C23—1221no—
275C23—1221no—
276C23—1221no—
277C23—1221no—
278C23—1221no—
279C23—2441no—
280C23—2441no—
281C23—2441no—
282C23—2441no—
283C23C2×C22⋊#692311yescharacteristic
284D4—2444no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—1222no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—4881no—
300C2×C4—4881no—
301C2×C4—2442no—
302C2×C4—2442no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4#1451983511yescharacteristic
311C2×C4#1451983511yescharacteristic
312C2×C4#1451986512yes—
313C8—4882no—
314C8—4882no—
315C22—21no—
316C22—21no—
317C22—1222no—
318C22—4881no—
319C22—4881no—
320C22—2442no—
321C22—2442no—
322C22—2441no—
323C22—2441no—
324C22—2441no—
325C22—2441no—
326C22—2441no—
327C22#1684073711yescharacteristic
328C22C2×#1451983511yescharacteristic
329C22D61⋊#10111yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—81no—
335C4—81no—
336C4—4881no—
337C4—2442no—
338C4—2441no—
339C4—2441no—
340C2—21no—
341C2—21no—
342C2—4881no—
343C2—2442no—
344C2#2146109911yescharacteristic
345C2#2146209411yescharacteristic
346C2#2146211011yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#125×C61C4
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC2×C4⋊Dic61C23
hypercenterC2×#125#6923
hypocenterC61#11572
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
3. #21460762C2semidirect
4. #21460760C2semidirect
196. C61#11572semidirect

Maximal subgroups

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

subgroupindex
#214610762
#214610562
#214607622
#214607602
#214510202
#1157261