Finite Group Databasebeta

← C61×#9564 #29512997

Subgroups — C61×#9564 #29512997

Order 15616.

466 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#1982C211yesmaximal, characteristic
2C61×#1957C211yesmaximal, characteristic
3C61×#1948C211yesmaximal, characteristic, complemented
4C8×C4⋊C4×C61C211yesmaximal, characteristic, complemented
5C2×C61×#331C211yesmaximal, characteristic
6C61×#1296C211yesmaximal, characteristic, complemented
7C61×#1277C211yesmaximal, characteristic, complemented
8C2×#127×C61C2211yescharacteristic
9C2×#106×C61—21no—
10C2×C4⋊C8×C61C2211yescharacteristic
11C2×C4⋊C8×C61C2211yescharacteristic
12C2×C4⋊C8×C61C2211yescharacteristic
13C2×#102×C61—21no—
14C2×#102×C61—21no—
15C2×#102×C61—21no—
16C2×#102×C61—21no—
17C2×C4×C8×C61—21no—
18C2×C4×C8×C61C2211yescharacteristic
19C61×#384C2211yescharacteristic
20C4×C4⋊C4×C61C2211yescharacteristic
21C61×#340—21no—
22C61×#336—21no—
23C61×#331C414yescomplemented
24C22×D4×C61—21no—
25C22×D4×C61—21no—
26C22×D4×C61—21no—
27C22×C8×C61—21no—
28C22×C8×C61—21no—
29C22×C8×C61—21no—
30C22×C8×C61D411yescharacteristic
31C22×C8×C61D411yescharacteristic
32#127×C61—21no—
33#127×C61—21no—
34#127×C61—21no—
35#127×C61C2×C412yes—
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61D411yescharacteristic
40C2×C4⋊C4×C61D411yescharacteristic
41C2×C42×C61—21no—
42C2×C42×C61C2311yescharacteristic
43#106×C61—42no—
44C4⋊C8×C61—21no—
45C4⋊C8×C61—21no—
46C4⋊C8×C61—21no—
47C4⋊C8×C61—21no—
48C4⋊C8×C61C2×C412yes—
49C4⋊C8×C61C2×C412yes—
50#102×C61—42no—
51#102×C61—42no—
52#102×C61—42no—
53#102×C61—42no—
54C4×C8×C61—21no—
55C4×C8×C61—21no—
56C4×C8×C61—42no—
57#95×C61—21no—
58C24×C61—41no—
59C2×D4×C61—22no—
60C2×D4×C61—22no—
61C2×D4×C61—22no—
62C2×D4×C61—41no—
63C2×D4×C61—41no—
64C2×D4×C61—41no—
65C2×D4×C61—41no—
66C2×D4×C61—41no—
67C2×D4×C61—41no—
68C2×D4×C61—41no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—81no—
74C2×D4×C61—81no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—41no—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C2×C8×C61—21no—
82C2×C8×C61—21no—
83C2×C8×C61—22no—
84C2×C8×C61—22no—
85C2×C8×C61—21no—
86C2×C8×C61—21no—
87C2×C8×C61—21no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61SD1612yes—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—81no—
103C4⋊C4×C61D812yes—
104C4⋊C4×C61SD1612yes—
105C42×C61—41no—
106C42×C61—41no—
107C42×C61C22×C411yescharacteristic
108C42×C61#4111yescharacteristic
109C42×C61#4111yescharacteristic
110C42×C61#4111yescharacteristic
111C23×C61—42no—
112C23×C61—81no—
113C23×C61—81no—
114C23×C61—81no—
115C23×C61—81no—
116C23×C61—81no—
117C23×C61—81no—
118C23×C61#12111yescharacteristic
119D4×C61—42no—
120D4×C61—42no—
121D4×C61—42no—
122D4×C61—42no—
123D4×C61—82no—
124D4×C61—82no—
125D4×C61—81no—
126D4×C61—81no—
127D4×C61—81no—
128D4×C61—81no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—22no—
132C2×C4×C61—22no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61#11711yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61#12311yescharacteristic
144C2×C4×C61#12411yescharacteristic
145C2×C4×C61#12611yescharacteristic
146C2×C4×C61C2×D811yescharacteristic
147C2×C4×C61C2×SD1611yescharacteristic
148C2×C4×C61C2×SD1611yescharacteristic
149C2×C4×C61#13511yescharacteristic
150C2×C4×C61#13511yescharacteristic
151C2×C4×C61#13511yescharacteristic
152C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
154C8×C61—22no—
155C8×C61—42no—
156C8×C61—42no—
157C8×C61—41no—
158C8×C61—81no—
159#9564C6111yesmaximal, characteristic, direct product factor, Sylow
160C22×C61—82no—
161C22×C61—82no—
162C22×C61—82no—
163C22×C61—161no—
164C22×C61—161no—
165C22×C61—161no—
166C22×C61—161no—
167C22×C61#38811yescharacteristic
168C22×C61#46011yescharacteristic
169C22×C61#46311yescharacteristic
170C22×C61#46511yescharacteristic
171C22×C61#46611yescharacteristic
172C22×C61#47111yescharacteristic
173C22×C61#47211yescharacteristic
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—42no—
177C4×C61—42no—
178C4×C61—161no—
179C4×C61C4×D811yescharacteristic
180C4×C61C4×SD1611yescharacteristic
181C4×C61C4×SD1611yescharacteristic
182C4×C61#44211yescharacteristic
183C4×C61#48111yescharacteristic
184C4×C61#48211yescharacteristic
185C4×C61#48611yescharacteristic
186C4×C61#48811yescharacteristic
187#1982C2×C6111yescharacteristic
188#1957C2×C6111yescharacteristic
189#1948C2×C6111yescharacteristic, complemented
190C8×C4⋊C4C2×C6111yescharacteristic, complemented
191C2×#331C2×C6111yescharacteristic
192#1296C2×C6111yescharacteristic, complemented
193#1277C2×C6111yescharacteristic, complemented
194C2×C61—162no—
195C2×C61#166611yescharacteristic
196C2×C61#166811yescharacteristic
197C2×C61#167711yescharacteristic
198C2×C61#168111yescharacteristic
199C2×C61#192611yescharacteristic
200C2×C61#193111yescharacteristic
201C2×C61#193411yescharacteristic
202C2×#127C22×C6111yescharacteristic
203C2×#106—21no—
204C2×C4⋊C8C22×C6111yescharacteristic
205C2×C4⋊C8C22×C6111yescharacteristic
206C2×C4⋊C8C22×C6111yescharacteristic
207C2×#102—21no—
208C2×#102—21no—
209C2×#102—21no—
210C2×#102—21no—
211C2×C4×C8—21no—
212C2×C4×C8C22×C6111yescharacteristic
213#384C22×C6111yescharacteristic
214C4×C4⋊C4C22×C6111yescharacteristic
215#340—21no—
216#336—21no—
217#331C4×C6114yescomplemented
218C61#956411yescharacteristic, direct product factor, Sylow
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8D4×C6111yescharacteristic
226C22×C8D4×C6111yescharacteristic
227#127—21no—
228#127—21no—
229#127—21no—
230#127C2×C4×C6112yes—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4D4×C6111yescharacteristic
235C2×C4⋊C4D4×C6111yescharacteristic
236C2×C42—21no—
237C2×C42C23×C6111yescharacteristic
238#106—42no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8C2×C4×C6112yes—
244C4⋊C8C2×C4×C6112yes—
245#102—42no—
246#102—42no—
247#102—42no—
248#102—42no—
249C4×C8—21no—
250C4×C8—21no—
251C4×C8—42no—
252#95—21no—
253C24—41no—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—81no—
269C2×D4—81no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4C2×D4×C6111yescharacteristic
274C22×C4C2×D4×C6111yescharacteristic
275C22×C4#41×C6111yescharacteristic
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8SD16×C6112yes—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—81no—
298C4⋊C4D8×C6112yes—
299C4⋊C4SD16×C6112yes—
300C42—41no—
301C42—41no—
302C42C22×C4×C6111yescharacteristic
303C42#41×C6111yescharacteristic
304C42#41×C6111yescharacteristic
305C42#41×C6111yescharacteristic
306C23—42no—
307C23—81no—
308C23—81no—
309C23—81no—
310C23—81no—
311C23—81no—
312C23—81no—
313C23#121×C6111yescharacteristic
314D4—42no—
315D4—42no—
316D4—42no—
317D4—42no—
318D4—82no—
319D4—82no—
320D4—81no—
321D4—81no—
322D4—81no—
323D4—81no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4#117×C6111yescharacteristic
336C2×C4C4×D4×C6111yescharacteristic
337C2×C4C4×D4×C6111yescharacteristic
338C2×C4#123×C6111yescharacteristic
339C2×C4#124×C6111yescharacteristic
340C2×C4#126×C6111yescharacteristic
341C2×C4C2×D8×C6111yescharacteristic
342C2×C4C2×SD16×C6111yescharacteristic
343C2×C4C2×SD16×C6111yescharacteristic
344C2×C4#135×C6111yescharacteristic
345C2×C4#135×C6111yescharacteristic
346C2×C4#135×C6111yescharacteristic
347C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
348C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
349C8—22no—
350C8—42no—
351C8—42no—
352C8—41no—
353C8—81no—
354C22—82no—
355C22—82no—
356C22—82no—
357C22—161no—
358C22—161no—
359C22—161no—
360C22—161no—
361C22C61×#38811yescharacteristic
362C22C61×#46011yescharacteristic
363C22C61×#46311yescharacteristic
364C22C61×#46511yescharacteristic
365C22C61×#46611yescharacteristic
366C22C61×#47111yescharacteristic
367C22C61×#47211yescharacteristic
368C4—21no—
369C4—21no—
370C4—42no—
371C4—42no—
372C4—161no—
373C4C4×D8×C6111yescharacteristic
374C4C4×SD16×C6111yescharacteristic
375C4C4×SD16×C6111yescharacteristic
376C4C61×#44211yescharacteristic
377C4C61×#48111yescharacteristic
378C4C61×#48211yescharacteristic
379C4C61×#48611yescharacteristic
380C4C61×#48811yescharacteristic
381C2—162no—
382C2C61×#166611yescharacteristic
383C2C61×#166811yescharacteristic
384C2C61×#167711yescharacteristic
385C2C61×#168111yescharacteristic
386C2C61×#192611yescharacteristic
387C2C61×#193111yescharacteristic
388C2C61×#193411yescharacteristic
subgroupG/H
center, socleC23×C61#121
commutatorC42C22×C4×C61
Frattini, cosocleC2×C42C23×C61
prime radicalC2×#127×C61C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#1948C2semidirect
4. C8×C4⋊C4×C61C2semidirect
6. C61×#1296C2semidirect
7. C61×#1277C2semidirect
23. C61×#331C4semidirect
159. #9564C61direct (N × H)
189. #1948C2×C61semidirect
190. C8×C4⋊C4C2×C61semidirect
192. #1296C2×C61semidirect
193. #1277C2×C61semidirect
217. #331C4×C61semidirect
218. C61#9564direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#19822
C61×#19572
C61×#19482
C8×C4⋊C4×C612
C2×C61×#3312
C61×#12962
C61×#12772
#956461