Finite Group Databasebeta

← C61×#29863 #29533296

Subgroups — C61×#29863 #29533296

Order 15616.

686 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#489C211yesmaximal, characteristic, complemented
2C61×#3079C211yesmaximal, characteristic, complemented
3C61×#3040C211yesmaximal, characteristic
4C61×#2923C211yesmaximal, characteristic, complemented
5C61×#2064C212yesmaximal, complemented
6C61×#2063C212yesmaximal, complemented
7C61×#2052C212yesmaximal, complemented
8C61×#2051C212yesmaximal
9C61×#1997C211yesmaximal, characteristic, complemented
10C61×#1967C211yesmaximal, characteristic, complemented
11C61×#1849C211yesmaximal, characteristic, complemented
12C2×#137×C61C2211yescharacteristic
13C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
14C2×C4⋊Q8×C61C2211yescharacteristic
15C2×#124×C61C2211yescharacteristic
16C4×#41×C61C2211yescharacteristic
17C61×#489—22no—
18C61×#489—22no—
19C61×#477—21no—
20C61×#476—21no—
21C61×#475—21no—
22C61×#474—21no—
23C61×#464—21no—
24C61×#464—21no—
25C61×#463—21no—
26C61×#463—21no—
27C61×#433—22no—
28C61×#432—22no—
29C2×#108×C61C2212yes—
30C2×#108×C61C2212yes—
31C61×#428C2212yes—
32C61×#424C2212yes—
33C61×#423C2211yescharacteristic
34C61×#423C2211yescharacteristic
35C61×#419C2211yescharacteristic
36C61×#418C2211yescharacteristic
37C61×#417C2212yes—
38C2×#103×C61C2212yes—
39C2×#102×C61C2212yes—
40C2×#101×C61C2212yes—
41C2×#100×C61C2212yes—
42C61×#408C2212yes—
43C4×M16×C61C2211yescharacteristic
44C2×#97×C61C2211yescharacteristic
45C61×#343C2212yes—
46C61×#343C2212yes—
47C2×#41×C61C2311yescharacteristic
48C22×Q8×C61—21no—
49C22×Q8×C61C2311yescharacteristic
50C22×D4×C61C2311yescharacteristic
51#137×C61—42no—
52AGL(1,ℤ/8)×C61—42no—
53C2×Q16×C61—21no—
54C2×SD16×C61—21no—
55C2×SD16×C61—21no—
56C2×D8×C61—21no—
57C2×M16×C61C2311yescharacteristic
58C2×M16×C61C2311yescharacteristic
59C2×M16×C61C2312yes—
60C2×M16×C61C2312yes—
61C22×C8×C61C2312yes—
62C4⋊Q8×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66#124×C61—21no—
67#124×C61—21no—
68#124×C61—21no—
69#124×C61—21no—
70C4×Q8×C61D411yescharacteristic
71C4×Q8×C61D411yescharacteristic
72C4×D4×C61—21no—
73C4×D4×C61—21no—
74C4×D4×C61D411yescharacteristic
75C4×D4×C61D411yescharacteristic
76#117×C61—21no—
77#117×C61C2311yescharacteristic
78C2×C4⋊C4×C61—21no—
79C2×C4⋊C4×C61C2312yes—
80C2×C22⋊C4×C61—21no—
81C2×C22⋊C4×C61—21no—
82C2×C42×C61—21no—
83C2×C42×C61C2311yescharacteristic
84#108×C61—42no—
85#108×C61—42no—
86#107×C61—22no—
87#106×C61—22no—
88C4⋊C8×C61—24no—
89C4⋊C8×C61—21no—
90C4⋊C8×C61—21no—
91C4⋊C8×C61—21no—
92C4⋊C8×C61—21no—
93#103×C61—22no—
94#103×C61—24no—
95#103×C61—21no—
96#103×C61—21no—
97#102×C61—22no—
98#102×C61—24no—
99#102×C61—21no—
100#102×C61—21no—
101#101×C61—42no—
102#100×C61—42no—
103C22⋊C8×C61—24no—
104#97×C61—21no—
105#97×C61D412yes—
106#97×C61D412yes—
107C4×C8×C61—21no—
108C24×C61—21no—
109#41×C61—22no—
110#41×C61—22no—
111C2×Q8×C61—21no—
112C2×Q8×C61—21no—
113C2×Q8×C61—22no—
114C2×Q8×C61—22no—
115C2×Q8×C61—41no—
116C2×Q8×C61—41no—
117C2×Q8×C61—82no—
118C2×Q8×C61C2×D411yescharacteristic
119C2×D4×C61—21no—
120C2×D4×C61—21no—
121C2×D4×C61—21no—
122C2×D4×C61—22no—
123C2×D4×C61—22no—
124C2×D4×C61C2×D411yescharacteristic
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—22no—
130C22×C4×C61#4111yescharacteristic
131C22×C4×C61#4111yescharacteristic
132C22×C4×C61C2411yescharacteristic
133Q16×C61—42no—
134SD16×C61—42no—
135SD16×C61—42no—
136D8×C61—42no—
137M16×C61—22no—
138M16×C61—22no—
139M16×C61—22no—
140M16×C61—22no—
141M16×C61—22no—
142M16×C61—22no—
143C2×C8×C61—22no—
144C2×C8×C61—22no—
145C2×C8×C61—22no—
146C2×C8×C61—21no—
147C2×C8×C61—22no—
148C2×C8×C61—21no—
149C2×C8×C61C2×D414yes—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—41no—
155C4⋊C4×C61—41no—
156C4⋊C4×C61C2×D411yescharacteristic
157C4⋊C4×C61C2×D411yescharacteristic
158C22⋊C4×C61—21no—
159C22⋊C4×C61—21no—
160C22⋊C4×C61—21no—
161C22⋊C4×C61—41no—
162C22⋊C4×C61—41no—
163C22⋊C4×C61—41no—
164C22⋊C4×C61—41no—
165C42×C61—21no—
166C42×C61—21no—
167C42×C61—21no—
168C42×C61C2×D411yescharacteristic
169C42×C61C2×D411yescharacteristic
170C42×C61C2×D411yescharacteristic
171C42×C61C2×D411yescharacteristic
172C23×C61—21no—
173C23×C61—41no—
174C23×C61—42no—
175C23×C61—81no—
176C23×C61—81no—
177C23×C61C2×#4111yescharacteristic
178Q8×C61—21no—
179Q8×C61—21no—
180Q8×C61—41no—
181Q8×C61—41no—
182Q8×C61—42no—
183Q8×C61—82no—
184Q8×C61—82no—
185D4×C61—21no—
186D4×C61—21no—
187D4×C61—42no—
188D4×C61—41no—
189D4×C61—41no—
190D4×C61—42no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—42no—
197C2×C4×C61—41no—
198C2×C4×C61—42no—
199C2×C4×C61—42no—
200C2×C4×C61—81no—
201C2×C4×C61—81no—
202C2×C4×C61—82no—
203C2×C4×C61#12111yescharacteristic
204C2×C4×C61#12111yescharacteristic
205C2×C4×C61#12111yescharacteristic
206C2×C4×C61#12111yescharacteristic
207C2×C4×C61C22×D411yescharacteristic
208C2×C4×C61C22×D411yescharacteristic
209C2×C4×C61H(5,𝔽2)12yes—
210C2×C4×C612−1+412yes—
211C8×C61—24no—
212C8×C61—42no—
213C8×C61—41no—
214C8×C61—41no—
215C8×C61—42no—
216#29863C6111yesmaximal, characteristic, direct product factor, Sylow
217C22×C61—21no—
218C22×C61—21no—
219C22×C61—41no—
220C22×C61—41no—
221C22×C61—41no—
222C22×C61—81no—
223C22×C61—81no—
224C22×C61—81no—
225C22×C61—162no—
226C22×C61C2×#12111yescharacteristic
227C22×C61#54212yes—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—41no—
233C4×C61—41no—
234C4×C61—41no—
235C4×C61—81no—
236C4×C61—82no—
237C4×C61#53511yescharacteristic
238C4×C61#53611yescharacteristic
239C4×C61#53712yes—
240C2×#489C2×C6111yescharacteristic, complemented
241#3079C2×C6111yescharacteristic, complemented
242#3040C2×C6111yescharacteristic
243#2923C2×C6111yescharacteristic, complemented
244#2064C2×C6112yescomplemented
245#2063C2×C6112yescomplemented
246#2052C2×C6112yescomplemented
247#2051C2×C6112yes—
248#1997C2×C6111yescharacteristic, complemented
249#1967C2×C6111yescharacteristic, complemented
250#1849C2×C6111yescharacteristic, complemented
251C2×C61—22no—
252C2×C61—81no—
253C2×C61—161no—
254C2×C61#262011yescharacteristic
255C2×C61#306811yescharacteristic
256C2×C61#306911yescharacteristic
257C2×#137C22×C6111yescharacteristic
258C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
259C2×C4⋊Q8C22×C6111yescharacteristic
260C2×#124C22×C6111yescharacteristic
261C4×#41C22×C6111yescharacteristic
262#489—22no—
263#489—22no—
264#477—21no—
265#476—21no—
266#475—21no—
267#474—21no—
268#464—21no—
269#464—21no—
270#463—21no—
271#463—21no—
272#433—22no—
273#432—22no—
274C2×#108C22×C6112yes—
275C2×#108C22×C6112yes—
276#428C22×C6112yes—
277#424C22×C6112yes—
278#423C22×C6111yescharacteristic
279#423C22×C6111yescharacteristic
280#419C22×C6111yescharacteristic
281#418C22×C6111yescharacteristic
282#417C22×C6112yes—
283C2×#103C22×C6112yes—
284C2×#102C22×C6112yes—
285C2×#101C22×C6112yes—
286C2×#100C22×C6112yes—
287#408C22×C6112yes—
288C4×M16C22×C6111yescharacteristic
289C2×#97C22×C6111yescharacteristic
290#343C22×C6112yes—
291#343C22×C6112yes—
292C61#2986311yescharacteristic, direct product factor, Sylow
293C2×#41C23×C6111yescharacteristic
294C22×Q8—21no—
295C22×Q8C23×C6111yescharacteristic
296C22×D4C23×C6111yescharacteristic
297#137—42no—
298AGL(1,ℤ/8)—42no—
299C2×Q16—21no—
300C2×SD16—21no—
301C2×SD16—21no—
302C2×D8—21no—
303C2×M16C23×C6111yescharacteristic
304C2×M16C23×C6111yescharacteristic
305C2×M16C23×C6112yes—
306C2×M16C23×C6112yes—
307C22×C8C23×C6112yes—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312#124—21no—
313#124—21no—
314#124—21no—
315#124—21no—
316C4×Q8D4×C6111yescharacteristic
317C4×Q8D4×C6111yescharacteristic
318C4×D4—21no—
319C4×D4—21no—
320C4×D4D4×C6111yescharacteristic
321C4×D4D4×C6111yescharacteristic
322#117—21no—
323#117C23×C6111yescharacteristic
324C2×C4⋊C4—21no—
325C2×C4⋊C4C23×C6112yes—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C42—21no—
329C2×C42C23×C6111yescharacteristic
330#108—42no—
331#108—42no—
332#107—22no—
333#106—22no—
334C4⋊C8—24no—
335C4⋊C8—21no—
336C4⋊C8—21no—
337C4⋊C8—21no—
338C4⋊C8—21no—
339#103—22no—
340#103—24no—
341#103—21no—
342#103—21no—
343#102—22no—
344#102—24no—
345#102—21no—
346#102—21no—
347#101—42no—
348#100—42no—
349C22⋊C8—24no—
350#97—21no—
351#97D4×C6112yes—
352#97D4×C6112yes—
353C4×C8—21no—
354C24—21no—
355#41—22no—
356#41—22no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—41no—
362C2×Q8—41no—
363C2×Q8—82no—
364C2×Q8C2×D4×C6111yescharacteristic
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4C2×D4×C6111yescharacteristic
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4#41×C6111yescharacteristic
377C22×C4#41×C6111yescharacteristic
378C22×C4C24×C6111yescharacteristic
379Q16—42no—
380SD16—42no—
381SD16—42no—
382D8—42no—
383M16—22no—
384M16—22no—
385M16—22no—
386M16—22no—
387M16—22no—
388M16—22no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—21no—
393C2×C8—22no—
394C2×C8—21no—
395C2×C8C2×D4×C6114yes—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4C2×D4×C6111yescharacteristic
403C4⋊C4C2×D4×C6111yescharacteristic
404C22⋊C4—21no—
405C22⋊C4—21no—
406C22⋊C4—21no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C42—21no—
412C42—21no—
413C42—21no—
414C42C2×D4×C6111yescharacteristic
415C42C2×D4×C6111yescharacteristic
416C42C2×D4×C6111yescharacteristic
417C42C2×D4×C6111yescharacteristic
418C23—21no—
419C23—41no—
420C23—42no—
421C23—81no—
422C23—81no—
423C23C2×#41×C6111yescharacteristic
424Q8—21no—
425Q8—21no—
426Q8—41no—
427Q8—41no—
428Q8—42no—
429Q8—82no—
430Q8—82no—
431D4—21no—
432D4—21no—
433D4—42no—
434D4—41no—
435D4—41no—
436D4—42no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—82no—
449C2×C4#121×C6111yescharacteristic
450C2×C4#121×C6111yescharacteristic
451C2×C4#121×C6111yescharacteristic
452C2×C4#121×C6111yescharacteristic
453C2×C4C22×D4×C6111yescharacteristic
454C2×C4C22×D4×C6111yescharacteristic
455C2×C4H(5,𝔽2)×C6112yes—
456C2×C42−1+4×C6112yes—
457C8—24no—
458C8—42no—
459C8—41no—
460C8—41no—
461C8—42no—
462C22—21no—
463C22—21no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—162no—
471C22C2×#121×C6111yescharacteristic
472C22C61×#54212yes—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—41no—
478C4—41no—
479C4—41no—
480C4—82no—
481C4—81no—
482C4C61×#53511yescharacteristic
483C4C61×#53611yescharacteristic
484C4C61×#53712yes—
485C2—22no—
486C2—81no—
487C2—161no—
488C2C61×#262011yescharacteristic
489C2C61×#306811yescharacteristic
490C2C61×#306911yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×AGL(1,ℤ/8)×C61C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#489C2semidirect
2. C61×#3079C2semidirect
4. C61×#2923C2semidirect
5. C61×#2064C2semidirect
6. C61×#2063C2semidirect
7. C61×#2052C2semidirect
9. C61×#1997C2semidirect
10. C61×#1967C2semidirect
11. C61×#1849C2semidirect
216. #29863C61direct (N × H)
240. C2×#489C2×C61semidirect
241. #3079C2×C61semidirect
243. #2923C2×C61semidirect
244. #2064C2×C61semidirect
245. #2063C2×C61semidirect
246. #2052C2×C61semidirect
248. #1997C2×C61semidirect
249. #1967C2×C61semidirect
250. #1849C2×C61semidirect
292. C61#29863direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4892
C61×#30792
C61×#30402
C61×#29232
C61×#20642
C61×#20632
C61×#20522
C61×#20512
C61×#19972
C61×#19672
C61×#18492
#2986361