Finite Group Databasebeta

← C61×#9180 #29512613

Subgroups — C61×#9180 #29512613

Order 15616.

544 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3037C211yesmaximal, characteristic
2C61×#2351C211yesmaximal, characteristic, complemented
3C61×#1517C211yesmaximal, characteristic
4C61×#1502C211yesmaximal, characteristic
5C61×#1479C211yesmaximal, characteristic, complemented
6C61×#1303C211yesmaximal, characteristic, complemented
7C61×#1286C211yesmaximal, characteristic, complemented
8C2×#137×C61—21no—
9C61×#532C2211yescharacteristic
10C2×C4×Q8×C61—21no—
11C2×C4×Q8×C61C2211yescharacteristic
12C61×#464—22no—
13C61×#462C412yescomplemented
14C61×#460C412yescomplemented
15C61×#431C2211yescharacteristic
16C61×#431C2211yescharacteristic
17C61×#423C2211yescharacteristic
18C61×#417—21no—
19C61×#389—21no—
20C61×#389—22no—
21C61×#382—21no—
22C61×#382C2211yescharacteristic
23C4×C4⋊C4×C61—21no—
24C4×C4⋊C4×C61C2211yescharacteristic
25C61×#327—21no—
26C61×#327—21no—
27C61×#327—22no—
28C61×Q8⋊C8—22no—
29C2×#41×C61—21no—
30C22×Q8×C61D411yescharacteristic
31#137×C61—42no—
32#137×C61—42no—
33C2×Q16×C61—22no—
34C2×SD16×C61—22no—
35C2×M16×C61—21no—
36C4⋊Q8×C61C2×C411yescharacteristic
37#127×C61C2×C411yescharacteristic
38#124×C61—21no—
39#121×C61—21no—
40#121×C61—21no—
41C4×Q8×C61—21no—
42C4×Q8×C61—21no—
43C4×Q8×C61—42no—
44C4×Q8×C61—42no—
45C4×Q8×C61C2×C412yes—
46C4×Q8×C61D412yes—
47C4×D4×C61—21no—
48C4×D4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—22no—
51C2×C4⋊C4×C61—22no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C42×C61—21no—
56C2×C42×C61—22no—
57C2×C42×C61—21no—
58C2×C42×C61C2311yescharacteristic
59C4⋊C8×C61—21no—
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C4⋊C8×C61C2×C412yes—
63#103×C61—22no—
64#102×C61—22no—
65C22⋊C8×C61—21no—
66C22⋊C8×C61—21no—
67C4×C8×C61—21no—
68C4×C8×C61—21no—
69#95×C61—22no—
70#95×C61—21no—
71#95×C61D411yescharacteristic
72#95×C61D411yescharacteristic
73#95×C61D412yes—
74#41×C61—41no—
75#41×C61—41no—
76#41×C61—41no—
77#41×C61—41no—
78C2×Q8×C61—21no—
79C2×Q8×C61—21no—
80C2×Q8×C61—21no—
81C2×Q8×C61—21no—
82C2×Q8×C61C22⋊C412yes—
83C2×Q8×C61D812yes—
84C2×Q8×C61SD1612yes—
85C2×D4×C61—21no—
86C2×D4×C61—21no—
87C2×D4×C61—21no—
88C2×D4×C61—41no—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—22no—
94C22×C4×C61—41no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98Q16×C61—44no—
99SD16×C61—44no—
100M16×C61—41no—
101M16×C61—41no—
102C2×C8×C61—22no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C4⋊C4×C61—22no—
106C4⋊C4×C61—22no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—42no—
111C4⋊C4×C61—44no—
112C4⋊C4×C61—44no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61C22⋊C412yes—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C42×C61—22no—
119C42×C61—22no—
120C42×C61—44no—
121C42×C61—41no—
122C42×C61—41no—
123C42×C61C22×C411yescharacteristic
124C42×C61C2×D411yescharacteristic
125C42×C61#4111yescharacteristic
126C42×C61#4111yescharacteristic
127C23×C61—41no—
128C23×C61#12011yescharacteristic
129Q8×C61—22no—
130Q8×C61—22no—
131Q8×C61—22no—
132Q8×C61—41no—
133Q8×C61—41no—
134Q8×C61#10214yes—
135D4×C61—41no—
136D4×C61—41no—
137D4×C61—81no—
138D4×C61—81no—
139D4×C61—81no—
140D4×C61—81no—
141C2×C4×C61—22no—
142C2×C4×C61—22no—
143C2×C4×C61—22no—
144C2×C4×C61—22no—
145C2×C4×C61—22no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—42no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—42no—
153C2×C4×C61—41no—
154C2×C4×C61—42no—
155C2×C4×C61—41no—
156C2×C4×C61—42no—
157C2×C4×C61—41no—
158C2×C4×C61—81no—
159C2×C4×C61—81no—
160C2×C4×C61C2×C22⋊C411yescharacteristic
161C2×C4×C61C4×D411yescharacteristic
162C2×C4×C61C4×D411yescharacteristic
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61#12111yescharacteristic
165C2×C4×C61#12311yescharacteristic
166C2×C4×C61C2×D811yescharacteristic
167C2×C4×C61C2×SD1611yescharacteristic
168C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C61#13711yescharacteristic
170C8×C61—42no—
171C8×C61—81no—
172C8×C61—81no—
173#9180C6111yesmaximal, characteristic, direct product factor, Sylow
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61—81no—
179C22×C61#38611yescharacteristic
180C22×C61#44711yescharacteristic
181C22×C61#44811yescharacteristic
182C4×C61—24no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—42no—
188C4×C61—42no—
189C4×C61—82no—
190C4×C61—81no—
191C4×C61—81no—
192C4×C61C2×#10211yescharacteristic
193C4×C61#41711yescharacteristic
194C4×C61#48011yescharacteristic
195C4×C61#48111yescharacteristic
196#3037C2×C6111yescharacteristic
197#2351C2×C6111yescharacteristic, complemented
198#1517C2×C6111yescharacteristic
199#1502C2×C6111yescharacteristic
200#1479C2×C6111yescharacteristic, complemented
201#1303C2×C6111yescharacteristic, complemented
202#1286C2×C6111yescharacteristic, complemented
203C2×C61—21no—
204C2×C61—21no—
205C2×C61—161no—
206C2×C61#187411yescharacteristic
207C2×C61#190511yescharacteristic
208C2×C61#190611yescharacteristic
209C2×#137—21no—
210#532C22×C6111yescharacteristic
211C2×C4×Q8—21no—
212C2×C4×Q8C22×C6111yescharacteristic
213#464—22no—
214#462C4×C6112yescomplemented
215#460C4×C6112yescomplemented
216#431C22×C6111yescharacteristic
217#431C22×C6111yescharacteristic
218#423C22×C6111yescharacteristic
219#417—21no—
220#389—21no—
221#389—22no—
222#382—21no—
223#382C22×C6111yescharacteristic
224C4×C4⋊C4—21no—
225C4×C4⋊C4C22×C6111yescharacteristic
226#327—21no—
227#327—21no—
228#327—22no—
229Q8⋊C8—22no—
230C61#918011yescharacteristic, direct product factor, Sylow
231C2×#41—21no—
232C22×Q8D4×C6111yescharacteristic
233#137—42no—
234#137—42no—
235C2×Q16—22no—
236C2×SD16—22no—
237C2×M16—21no—
238C4⋊Q8C2×C4×C6111yescharacteristic
239#127C2×C4×C6111yescharacteristic
240#124—21no—
241#121—21no—
242#121—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—42no—
246C4×Q8—42no—
247C4×Q8C2×C4×C6112yes—
248C4×Q8D4×C6112yes—
249C4×D4—21no—
250C4×D4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4D4×C6111yescharacteristic
257C2×C42—21no—
258C2×C42—22no—
259C2×C42—21no—
260C2×C42C23×C6111yescharacteristic
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8C2×C4×C6112yes—
265#103—22no—
266#102—22no—
267C22⋊C8—21no—
268C22⋊C8—21no—
269C4×C8—21no—
270C4×C8—21no—
271#95—22no—
272#95—21no—
273#95D4×C6111yescharacteristic
274#95D4×C6111yescharacteristic
275#95D4×C6112yes—
276#41—41no—
277#41—41no—
278#41—41no—
279#41—41no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8C22⋊C4×C6112yes—
285C2×Q8D8×C6112yes—
286C2×Q8SD16×C6112yes—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—41no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—41no—
297C22×C4C2×D4×C6111yescharacteristic
298C22×C4C2×D4×C6111yescharacteristic
299C22×C4C2×D4×C6111yescharacteristic
300Q16—44no—
301SD16—44no—
302M16—41no—
303M16—41no—
304C2×C8—22no—
305C2×C8—41no—
306C2×C8—41no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—44no—
313C4⋊C4—42no—
314C4⋊C4—44no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4C22⋊C4×C6112yes—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C42—22no—
321C42—22no—
322C42—44no—
323C42—41no—
324C42—41no—
325C42C22×C4×C6111yescharacteristic
326C42C2×D4×C6111yescharacteristic
327C42#41×C6111yescharacteristic
328C42#41×C6111yescharacteristic
329C23—41no—
330C23#120×C6111yescharacteristic
331Q8—22no—
332Q8—22no—
333Q8—22no—
334Q8—41no—
335Q8—41no—
336Q8#102×C6114yes—
337D4—41no—
338D4—41no—
339D4—81no—
340D4—81no—
341D4—81no—
342D4—81no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4C2×C22⋊C4×C6111yescharacteristic
363C2×C4C4×D4×C6111yescharacteristic
364C2×C4C4×D4×C6111yescharacteristic
365C2×C4#121×C6111yescharacteristic
366C2×C4#121×C6111yescharacteristic
367C2×C4#123×C6111yescharacteristic
368C2×C4C2×D8×C6111yescharacteristic
369C2×C4C2×SD16×C6111yescharacteristic
370C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
371C2×C4#137×C6111yescharacteristic
372C8—42no—
373C8—81no—
374C8—81no—
375C22—21no—
376C22—21no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22C61×#38611yescharacteristic
381C22C61×#44711yescharacteristic
382C22C61×#44811yescharacteristic
383C4—24no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—42no—
389C4—42no—
390C4—82no—
391C4—81no—
392C4—81no—
393C4C2×#102×C6111yescharacteristic
394C4C61×#41711yescharacteristic
395C4C61×#48011yescharacteristic
396C4C61×#48111yescharacteristic
397C2—21no—
398C2—21no—
399C2—161no—
400C2C61×#187411yescharacteristic
401C2C61×#190511yescharacteristic
402C2C61×#190611yescharacteristic
subgroupG/H
center, socleC22×C61#386
commutatorC42C22×C4×C61
Frattini, cosocleC2×C42C23×C61
prime radicalC61×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2351C2semidirect
5. C61×#1479C2semidirect
6. C61×#1303C2semidirect
7. C61×#1286C2semidirect
13. C61×#462C4semidirect
14. C61×#460C4semidirect
173. #9180C61direct (N × H)
197. #2351C2×C61semidirect
200. #1479C2×C61semidirect
201. #1303C2×C61semidirect
202. #1286C2×C61semidirect
214. #462C4×C61semidirect
215. #460C4×C61semidirect
230. C61#9180direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#30372
C61×#23512
C61×#15172
C61×#15022
C61×#14792
C61×#13032
C61×#12862
#918061