Finite Group Databasebeta

← C61×#8714 #29512147

Subgroups — C61×#8714 #29512147

Order 15616.

544 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2283C211yesmaximal, characteristic
2C61×#1817C211yesmaximal, characteristic
3C61×#1434C211yesmaximal, characteristic
4C61×#1294C212yesmaximal
5C61×#1294C212yesmaximal
6C22×C42×C61C2211yescharacteristic
7C2×C22⋊C8×C61C2212yes—
8C61×#383—21no—
9C61×#382C411yescharacteristic, complemented
10C61×#382C411yescharacteristic, complemented
11C61×#381—21no—
12C61×#380C2211yescharacteristic
13C61×#380C2211yescharacteristic
14C4×C4⋊C4×C61C411yescharacteristic, complemented
15C4×C4⋊C4×C61C411yescharacteristic, complemented
16C4×C22⋊C4×C61—21no—
17C61×#376—21no—
18C2×#95×C61—21no—
19C2×#95×C61—21no—
20C2×#95×C61C2212yes—
21C61×#336—21no—
22C61×#336—21no—
23C23×C4×C61—22no—
24C23×C4×C61D411yescharacteristic
25C23×C4×C61D411yescharacteristic
26C23×C4×C61C2311yescharacteristic
27C22×C8×C61—22no—
28C2×C4⋊C4×C61C2×C411yescharacteristic
29C2×C4⋊C4×C61C2×C411yescharacteristic
30C2×C4⋊C4×C61C2×C411yescharacteristic
31C2×C4⋊C4×C61C2×C411yescharacteristic
32C2×C22⋊C4×C61—21no—
33C2×C22⋊C4×C61—21no—
34C2×C42×C61—24no—
35C2×C42×C61—21no—
36C2×C42×C61—21no—
37C2×C42×C61C2×C411yescharacteristic
38C2×C42×C61C2×C411yescharacteristic
39C2×C42×C61D411yescharacteristic
40C2×C42×C61D411yescharacteristic
41C22⋊C8×C61—24no—
42#95×C61—24no—
43#95×C61—21no—
44#95×C61—21no—
45#95×C61—21no—
46#95×C61—21no—
47#95×C61—21no—
48#95×C61—21no—
49#95×C61—21no—
50#95×C61—21no—
51#95×C61—24no—
52#95×C61—42no—
53C24×C61C2×D411yescharacteristic
54C22×C4×C61—22no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—22no—
60C22×C4×C61—24no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—41no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61—42no—
69C22×C4×C61—42no—
70C22×C4×C61—42no—
71C22×C4×C61—42no—
72C22×C4×C61—42no—
73C22×C4×C61—42no—
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22×C411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61#4114yes—
81C2×C8×C61—42no—
82C2×C8×C61—42no—
83C2×C8×C61—42no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C22⋊C4×C61—42no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C42×C61—22no—
92C42×C61—22no—
93C42×C61—22no—
94C42×C61—22no—
95C42×C61—42no—
96C42×C61—42no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61C2×C22⋊C411yescharacteristic
102C23×C61#12312yes—
103C23×C61#13512yes—
104C23×C61AGL(1,ℤ/8)11yescharacteristic
105C23×C61#13711yescharacteristic
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—44no—
122C2×C4×C61—44no—
123C2×C4×C61—42no—
124C2×C4×C61—42no—
125C2×C4×C61—44no—
126C2×C4×C61—44no—
127C2×C4×C61—44no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—82no—
141C2×C4×C61—82no—
142C2×C4×C61—82no—
143C2×C4×C61—82no—
144C2×C4×C61#10412yes—
145C2×C4×C61#11712yes—
146C2×C4×C61#12312yes—
147C8×C61—82no—
148#8714C6111yesmaximal, characteristic, direct product factor, Sylow
149C22×C61—22no—
150C22×C61—22no—
151C22×C61—22no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—22no—
157C22×C61#38111yescharacteristic
158C22×C61#41011yescharacteristic
159C22×C61#41011yescharacteristic
160C22×C61#41611yescharacteristic
161C22×C61#41711yescharacteristic
162C22×C61C2×#10411yescharacteristic
163C22×C61#42111yescharacteristic
164C22×C61#48212yes—
165C22×C61#48512yes—
166C4×C61—22no—
167C4×C61—22no—
168C4×C61—22no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61—84no—
173C4×C61—81no—
174C4×C61—81no—
175C4×C61—81no—
176C4×C61—81no—
177#2283C2×C6111yescharacteristic
178#1817C2×C6111yescharacteristic
179#1434C2×C6111yescharacteristic
180#1294C2×C6112yes—
181#1294C2×C6112yes—
182C2×C61—22no—
183C2×C61—22no—
184C2×C61#150011yescharacteristic
185C2×C61#150911yescharacteristic
186C2×C61#151211yescharacteristic
187C2×C61#152111yescharacteristic
188C2×C61#182011yescharacteristic
189C2×C61#182511yescharacteristic
190C2×C61#182611yescharacteristic
191C22×C42C22×C6111yescharacteristic
192C2×C22⋊C8C22×C6112yes—
193#383—21no—
194#382C4×C6111yescharacteristic, complemented
195#382C4×C6111yescharacteristic, complemented
196#381—21no—
197#380C22×C6111yescharacteristic
198#380C22×C6111yescharacteristic
199C4×C4⋊C4C4×C6111yescharacteristic, complemented
200C4×C4⋊C4C4×C6111yescharacteristic, complemented
201C4×C22⋊C4—21no—
202#376—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95C22×C6112yes—
206#336—21no—
207#336—21no—
208C61#871411yescharacteristic, direct product factor, Sylow
209C23×C4—22no—
210C23×C4D4×C6111yescharacteristic
211C23×C4D4×C6111yescharacteristic
212C23×C4C23×C6111yescharacteristic
213C22×C8—22no—
214C2×C4⋊C4C2×C4×C6111yescharacteristic
215C2×C4⋊C4C2×C4×C6111yescharacteristic
216C2×C4⋊C4C2×C4×C6111yescharacteristic
217C2×C4⋊C4C2×C4×C6111yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C42—24no—
221C2×C42—21no—
222C2×C42—21no—
223C2×C42C2×C4×C6111yescharacteristic
224C2×C42C2×C4×C6111yescharacteristic
225C2×C42D4×C6111yescharacteristic
226C2×C42D4×C6111yescharacteristic
227C22⋊C8—24no—
228#95—24no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—24no—
238#95—42no—
239C24C2×D4×C6111yescharacteristic
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—24no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4C22⋊C4×C6111yescharacteristic
261C22×C4C22⋊C4×C6111yescharacteristic
262C22×C4C22⋊C4×C6111yescharacteristic
263C22×C4C22⋊C4×C6111yescharacteristic
264C22×C4C22×C4×C6111yescharacteristic
265C22×C4C2×D4×C6111yescharacteristic
266C22×C4#41×C6114yes—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C22⋊C4—42no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—22no—
281C42—42no—
282C42—42no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23C2×C22⋊C4×C6111yescharacteristic
288C23#123×C6112yes—
289C23#135×C6112yes—
290C23AGL(1,ℤ/8)×C6111yescharacteristic
291C23#137×C6111yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4#104×C6112yes—
331C2×C4#117×C6112yes—
332C2×C4#123×C6112yes—
333C8—82no—
334C22—22no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22C61×#38111yescharacteristic
343C22C61×#41011yescharacteristic
344C22C61×#41011yescharacteristic
345C22C61×#41611yescharacteristic
346C22C61×#41711yescharacteristic
347C22C2×#104×C6111yescharacteristic
348C22C61×#42111yescharacteristic
349C22C61×#48212yes—
350C22C61×#48512yes—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—84no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—81no—
362C2—22no—
363C2—22no—
364C2C61×#150011yescharacteristic
365C2C61×#150911yescharacteristic
366C2C61×#151211yescharacteristic
367C2C61×#152111yescharacteristic
368C2C61×#182011yescharacteristic
369C2C61×#182511yescharacteristic
370C2C61×#182611yescharacteristic
subgroupG/H
center, socleC23×C61C2×C22⋊C4
commutatorC22×C4C22×C4×C61
Frattini, cosocleC23×C4C23×C61
prime radicalC24×C61C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C61 ◁ C22×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
9. C61×#382C4semidirect
10. C61×#382C4semidirect
14. C4×C4⋊C4×C61C4semidirect
15. C4×C4⋊C4×C61C4semidirect
148. #8714C61direct (N × H)
194. #382C4×C61semidirect
195. #382C4×C61semidirect
199. C4×C4⋊C4C4×C61semidirect
200. C4×C4⋊C4C4×C61semidirect
208. C61#8714direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#22832
C61×#18172
C61×#14342
C61×#12942
#871461