Finite Group Databasebeta

← C61×#10376 #29513809

Subgroups — C61×#10376 #29513809

Order 15616.

464 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2569C211yesmaximal, characteristic, complemented
2C61×#1964C211yesmaximal, characteristic
3C61×#1519C211yesmaximal, characteristic
4C2×C61×#327C211yesmaximal, characteristic
5C61×#1294C211yesmaximal, characteristic, complemented
6C61×#1289C211yesmaximal, characteristic, complemented
7C61×#1282C211yesmaximal, characteristic, complemented
8C2×#121×C61C2211yescharacteristic
9C2×#99×C61—21no—
10C2×#99×C61—21no—
11C2×C22⋊C8×C61C2211yescharacteristic
12C2×C22⋊C8×C61C2211yescharacteristic
13C61×#400—21no—
14C61×#398—21no—
15C61×#387—21no—
16C61×#387—21no—
17C61×#385—21no—
18C61×#380—21no—
19C61×#380C2211yescharacteristic
20C61×#380C2211yescharacteristic
21C4×C22⋊C4×C61C2211yescharacteristic
22C2×#95×C61C2211yescharacteristic
23C61×#327—21no—
24C61×#327—21no—
25C61×#327—21no—
26C61×#327—21no—
27C22×D4×C61—21no—
28C22×D4×C61Q811yescharacteristic
29C23×C4×C61—21no—
30C23×C4×C61C2311yescharacteristic
31C22×C8×C61—21no—
32C22×C8×C61—21no—
33#121×C61—21no—
34#121×C61—21no—
35#121×C61—21no—
36#121×C61—21no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61—21no—
41C2×C4⋊C4×C61—21no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61Q811yescharacteristic
44C2×C22⋊C4×C61—21no—
45C2×C22⋊C4×C61—21no—
46C2×C22⋊C4×C61—21no—
47C2×C22⋊C4×C61D411yescharacteristic
48C2×C22⋊C4×C61D411yescharacteristic
49C2×C42×C61—21no—
50#99×C61—42no—
51#99×C61—42no—
52C22⋊C8×C61—21no—
53C22⋊C8×C61—21no—
54C22⋊C8×C61—21no—
55C22⋊C8×C61—21no—
56#95×C61—21no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61D411yescharacteristic
64#95×C61D411yescharacteristic
65#95×C61D411yescharacteristic
66#95×C61D411yescharacteristic
67C24×C61—21no—
68C24×C61C2×D411yescharacteristic
69C2×D4×C61—21no—
70C2×D4×C61—21no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C2×D4×C61—81no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—42no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—81no—
90C22×C4×C61—81no—
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×Q811yescharacteristic
94C22×C4×C61#4111yescharacteristic
95C22×C4×C61#4111yescharacteristic
96C22×C4×C61#4111yescharacteristic
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—81no—
100C2×C8×C61—81no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—42no—
104C4⋊C4×C61—42no—
105C4⋊C4×C61—81no—
106C4⋊C4×C61—81no—
107C4⋊C4×C61—81no—
108C4⋊C4×C61—81no—
109C22⋊C4×C61—21no—
110C22⋊C4×C61—21no—
111C22⋊C4×C61—21no—
112C22⋊C4×C61—21no—
113C22⋊C4×C61—41no—
114C22⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C22⋊C4×C61—41no—
119C42×C61—81no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—81no—
126C23×C61—81no—
127C23×C61#12011yescharacteristic
128C23×C61C22⋊Q811yescharacteristic
129C23×C61#12411yescharacteristic
130C23×C61#13511yescharacteristic
131C23×C61#13511yescharacteristic
132C23×C61AGL(1,ℤ/8)11yescharacteristic
133C23×C61AGL(1,ℤ/8)11yescharacteristic
134D4×C61—81no—
135D4×C61—81no—
136D4×C61—81no—
137D4×C61—81no—
138D4×C61—81no—
139D4×C61—81no—
140C2×C4×C61—22no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—82no—
168C2×C4×C61—82no—
169C2×C4×C61—81no—
170C2×C4×C61—81no—
171C2×C4×C61—81no—
172C2×C4×C61C22⋊Q811yescharacteristic
173C2×C4×C61C22⋊Q811yescharacteristic
174C2×C4×C61#12411yescharacteristic
175C2×C4×C61#12411yescharacteristic
176C8×C61—81no—
177C8×C61—81no—
178#10376C6111yesmaximal, characteristic, direct product factor, Sylow
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61—161no—
193C22×C61—161no—
194C22×C61#39311yescharacteristic
195C22×C61#44911yescharacteristic
196C22×C61#44911yescharacteristic
197C22×C61#47811yescharacteristic
198C22×C61#47811yescharacteristic
199C22×C61#48811yescharacteristic
200C22×C61#49011yescharacteristic
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—21no—
205C4×C61—42no—
206C4×C61—81no—
207C4×C61—81no—
208C4×C61—81no—
209C4×C61—81no—
210C4×C61—81no—
211C4×C61—81no—
212C4×C61—161no—
213#2569C2×C6111yescharacteristic, complemented
214#1964C2×C6111yescharacteristic
215#1519C2×C6111yescharacteristic
216C2×#327C2×C6111yescharacteristic
217#1294C2×C6111yescharacteristic, complemented
218#1289C2×C6111yescharacteristic, complemented
219#1282C2×C6111yescharacteristic, complemented
220C2×C61—21no—
221C2×C61—21no—
222C2×C61—21no—
223C2×C61—21no—
224C2×C61—21no—
225C2×C61—21no—
226C2×C61—161no—
227C2×C61#202511yescharacteristic
228C2×C61#203111yescharacteristic
229C2×C61#203211yescharacteristic
230C2×#121C22×C6111yescharacteristic
231C2×#99—21no—
232C2×#99—21no—
233C2×C22⋊C8C22×C6111yescharacteristic
234C2×C22⋊C8C22×C6111yescharacteristic
235#400—21no—
236#398—21no—
237#387—21no—
238#387—21no—
239#385—21no—
240#380—21no—
241#380C22×C6111yescharacteristic
242#380C22×C6111yescharacteristic
243C4×C22⋊C4C22×C6111yescharacteristic
244C2×#95C22×C6111yescharacteristic
245#327—21no—
246#327—21no—
247#327—21no—
248#327—21no—
249C61#1037611yescharacteristic, direct product factor, Sylow
250C22×D4—21no—
251C22×D4Q8×C6111yescharacteristic
252C23×C4—21no—
253C23×C4C23×C6111yescharacteristic
254C22×C8—21no—
255C22×C8—21no—
256#121—21no—
257#121—21no—
258#121—21no—
259#121—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4Q8×C6111yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4D4×C6111yescharacteristic
271C2×C22⋊C4D4×C6111yescharacteristic
272C2×C42—21no—
273#99—42no—
274#99—42no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—21no—
284#95—21no—
285#95—21no—
286#95D4×C6111yescharacteristic
287#95D4×C6111yescharacteristic
288#95D4×C6111yescharacteristic
289#95D4×C6111yescharacteristic
290C24—21no—
291C24C2×D4×C6111yescharacteristic
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—81no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—42no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—81no—
313C22×C4—81no—
314C22×C4C2×D4×C6111yescharacteristic
315C22×C4C2×D4×C6111yescharacteristic
316C22×C4C2×Q8×C6111yescharacteristic
317C22×C4#41×C6111yescharacteristic
318C22×C4#41×C6111yescharacteristic
319C22×C4#41×C6111yescharacteristic
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—81no—
323C2×C8—81no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—81no—
329C4⋊C4—81no—
330C4⋊C4—81no—
331C4⋊C4—81no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—81no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—81no—
349C23—81no—
350C23#120×C6111yescharacteristic
351C23C22⋊Q8×C6111yescharacteristic
352C23#124×C6111yescharacteristic
353C23#135×C6111yescharacteristic
354C23#135×C6111yescharacteristic
355C23AGL(1,ℤ/8)×C6111yescharacteristic
356C23AGL(1,ℤ/8)×C6111yescharacteristic
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—81no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4C22⋊Q8×C6111yescharacteristic
396C2×C4C22⋊Q8×C6111yescharacteristic
397C2×C4#124×C6111yescharacteristic
398C2×C4#124×C6111yescharacteristic
399C8—81no—
400C8—81no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—161no—
415C22—161no—
416C22C61×#39311yescharacteristic
417C22C61×#44911yescharacteristic
418C22C61×#44911yescharacteristic
419C22C61×#47811yescharacteristic
420C22C61×#47811yescharacteristic
421C22C61×#48811yescharacteristic
422C22C61×#49011yescharacteristic
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—42no—
428C4—81no—
429C4—81no—
430C4—81no—
431C4—81no—
432C4—81no—
433C4—81no—
434C4—161no—
435C2—21no—
436C2—21no—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—161no—
442C2C61×#202511yescharacteristic
443C2C61×#203111yescharacteristic
444C2C61×#203211yescharacteristic
subgroupG/H
center, socleC22×C61#393
commutator, Frattini, cosocleC23×C4C23×C61
prime radicalC2×#121×C61C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#2569C2semidirect
5. C61×#1294C2semidirect
6. C61×#1289C2semidirect
7. C61×#1282C2semidirect
178. #10376C61direct (N × H)
213. #2569C2×C61semidirect
217. #1294C2×C61semidirect
218. #1289C2×C61semidirect
219. #1282C2×C61semidirect
249. C61#10376direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#25692
C61×#19642
C61×#15192
C2×C61×#3272
C61×#12942
C61×#12892
C61×#12822
#1037661