Finite Group Databasebeta

← C61×#24722 #29528155

Subgroups — C61×#24722 #29528155

Order 15616.

674 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3079C211yesmaximal, characteristic
2C2×C61×#477C211yesmaximal, characteristic, complemented
3C4×#137×C61C211yesmaximal, characteristic
4C61×#2925C211yesmaximal, characteristic
5C61×#2078C212yesmaximal
6C61×#2052C212yesmaximal
7C61×#1997C211yesmaximal, characteristic, complemented
8C61×#1952C212yesmaximal, complemented
9C61×#1950C211yesmaximal, characteristic, complemented
10C61×#1930C212yesmaximal, complemented
11C61×#1801C211yesmaximal, characteristic, complemented
12C2×#137×C61C2211yescharacteristic
13C2×C4⋊Q8×C61C2211yescharacteristic
14C4×#41×C61C2211yescharacteristic
15C2×C4×Q8×C61C2211yescharacteristic
16C61×#477—21no—
17C61×#477—21no—
18C61×#477—21no—
19C61×#477—22no—
20C61×#476—21no—
21C61×#475—21no—
22C61×#474—21no—
23C61×#441—21no—
24C61×#440—21no—
25C4×Q16×C61—21no—
26C4×SD16×C61—21no—
27C61×#433—22no—
28C61×#432—21no—
29C61×#431—21no—
30C2×#108×C61C2212yes—
31C61×#428C2212yes—
32C61×#428C2211yescharacteristic
33C2×#107×C61C2212yes—
34C61×#423C2211yescharacteristic
35C61×#423C2211yescharacteristic
36C2×C4⋊C8×C61C2211yescharacteristic
37C61×#419C2211yescharacteristic
38C61×#417C2212yes—
39C61×#417C2211yescharacteristic
40C2×#103×C61C2212yes—
41C2×#101×C61C2212yes—
42C61×#408C2212yes—
43C61×#405C2212yes—
44C4×M16×C61C2211yescharacteristic
45C61×#343C2212yes—
46C61×#343C2212yes—
47C61×#343C2212yes—
48C61×#341C2212yes—
49C2×#41×C61C2311yescharacteristic
50C22×Q8×C61—21no—
51C22×Q8×C61C2311yescharacteristic
52#137×C61—22no—
53#137×C61—22no—
54C2×Q16×C61—21no—
55C2×SD16×C61—21no—
56C2×M16×C61C2311yescharacteristic
57C2×M16×C61C2312yes—
58C2×M16×C61C2312yes—
59C2×M16×C61C2311yescharacteristic
60C22×C8×C61C2312yes—
61C4⋊Q8×C61—21no—
62C4⋊Q8×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61—21no—
65C4×Q8×C61—21no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61D411yescharacteristic
70C4×Q8×C61D411yescharacteristic
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C4×D4×C61D411yescharacteristic
74C4×D4×C61D411yescharacteristic
75#117×C61—21no—
76#117×C61C2311yescharacteristic
77C2×C4⋊C4×C61—21no—
78C2×C4⋊C4×C61—21no—
79C2×C4⋊C4×C61C2312yes—
80C2×C4⋊C4×C61C2311yescharacteristic
81C2×C42×C61—21no—
82C2×C42×C61—21no—
83C2×C42×C61C2311yescharacteristic
84#108×C61—24no—
85#107×C61—22no—
86#107×C61—22no—
87#107×C61—21no—
88#107×C61—22no—
89#106×C61—21no—
90#106×C61—22no—
91C4⋊C8×C61—21no—
92C4⋊C8×C61—21no—
93C4⋊C8×C61—21no—
94C4⋊C8×C61—21no—
95C4⋊C8×C61D411yescharacteristic
96C4⋊C8×C61D411yescharacteristic
97C4⋊C8×C61D412yes—
98#103×C61—21no—
99#103×C61—22no—
100#103×C61—22no—
101#103×C61—22no—
102#103×C61—21no—
103#103×C61—21no—
104#102×C61—21no—
105#102×C61—22no—
106#101×C61—24no—
107C22⋊C8×C61—22no—
108C22⋊C8×C61—22no—
109#97×C61—22no—
110#97×C61—21no—
111C4×C8×C61—22no—
112C4×C8×C61—21no—
113#41×C61—21no—
114#41×C61—21no—
115#41×C61—21no—
116#41×C61—21no—
117C2×Q8×C61—21no—
118C2×Q8×C61—21no—
119C2×Q8×C61—21no—
120C2×Q8×C61—21no—
121C2×Q8×C61—21no—
122C2×Q8×C61—41no—
123C2×Q8×C61—41no—
124C2×Q8×C61—82no—
125C2×Q8×C61C2×D411yescharacteristic
126C2×Q8×C61#4112yes—
127C2×D4×C61—21no—
128C2×D4×C61C2×D411yescharacteristic
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—22no—
135C22×C4×C61#4111yescharacteristic
136C22×C4×C61#4111yescharacteristic
137C22×C4×C61C2411yescharacteristic
138Q16×C61—24no—
139SD16×C61—24no—
140M16×C61—21no—
141M16×C61—22no—
142M16×C61—22no—
143M16×C61—22no—
144M16×C61—21no—
145M16×C61—21no—
146M16×C61—22no—
147M16×C61#4112yes—
148C2×C8×C61—21no—
149C2×C8×C61—22no—
150C2×C8×C61—22no—
151C2×C8×C61—22no—
152C2×C8×C61—21no—
153C2×C8×C61—22no—
154C2×C8×C61C2×D412yes—
155C2×C8×C61C2×D412yes—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—22no—
160C4⋊C4×C61—22no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—41no—
163C4⋊C4×C61—41no—
164C4⋊C4×C61—41no—
165C4⋊C4×C61—41no—
166C4⋊C4×C61C2×D411yescharacteristic
167C4⋊C4×C61C2×D411yescharacteristic
168C22⋊C4×C61—21no—
169C22⋊C4×C61—21no—
170C22⋊C4×C61—21no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61—21no—
174C42×C61—41no—
175C42×C61—41no—
176C42×C61C2×D411yescharacteristic
177C42×C61C2×D411yescharacteristic
178C42×C61C2×D411yescharacteristic
179C42×C61C2×D411yescharacteristic
180C23×C61—21no—
181C23×C61C2×#4111yescharacteristic
182Q8×C61—22no—
183Q8×C61—21no—
184Q8×C61—21no—
185Q8×C61—22no—
186Q8×C61—41no—
187Q8×C61—41no—
188Q8×C61—82no—
189Q8×C61—82no—
190D4×C61—21no—
191D4×C61—21no—
192D4×C61—41no—
193D4×C61—41no—
194C2×C4×C61—22no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—22no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—42no—
205C2×C4×C61—41no—
206C2×C4×C61—42no—
207C2×C4×C61—81no—
208C2×C4×C61—81no—
209C2×C4×C61—82no—
210C2×C4×C61#12111yescharacteristic
211C2×C4×C61#12111yescharacteristic
212C2×C4×C61#12111yescharacteristic
213C2×C4×C61#12111yescharacteristic
214C2×C4×C61C22×D411yescharacteristic
215C2×C4×C61C22×D411yescharacteristic
216C2×C4×C61C2×#4111yescharacteristic
217C2×C4×C61C2×#4111yescharacteristic
218C2×C4×C612−1+411yescharacteristic
219C2×C4×C612−1+411yescharacteristic
220C8×C61—22no—
221C8×C61—22no—
222C8×C61—22no—
223C8×C61—42no—
224C8×C61—41no—
225C8×C61—42no—
226#24722C6111yesmaximal, characteristic, direct product factor, Sylow
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—41no—
230C22×C61—41no—
231C22×C61—41no—
232C22×C61C2×#12111yescharacteristic
233C22×C61#55211yescharacteristic
234C22×C61#55611yescharacteristic
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—21no—
238C4×C61—41no—
239C4×C61—42no—
240C4×C61—41no—
241C4×C61—41no—
242C4×C61—81no—
243C4×C61—82no—
244C4×C61#47312yes—
245C4×C61#52511yescharacteristic
246C4×C61#53611yescharacteristic
247C4×C61#54711yescharacteristic
248C4×C61#54811yescharacteristic
249#3079C2×C6111yescharacteristic
250C2×#477C2×C6111yescharacteristic, complemented
251C4×#137C2×C6111yescharacteristic
252#2925C2×C6111yescharacteristic
253#2078C2×C6112yes—
254#2052C2×C6112yes—
255#1997C2×C6111yescharacteristic, complemented
256#1952C2×C6112yescomplemented
257#1950C2×C6111yescharacteristic, complemented
258#1930C2×C6112yescomplemented
259#1801C2×C6111yescharacteristic, complemented
260C2×C61—21no—
261C2×C61—21no—
262C2×C61—81no—
263C2×C61#241511yescharacteristic
264C2×C61C2×#47311yescharacteristic
265C2×C61#306811yescharacteristic
266C2×#137C22×C6111yescharacteristic
267C2×C4⋊Q8C22×C6111yescharacteristic
268C4×#41C22×C6111yescharacteristic
269C2×C4×Q8C22×C6111yescharacteristic
270#477—21no—
271#477—21no—
272#477—21no—
273#477—22no—
274#476—21no—
275#475—21no—
276#474—21no—
277#441—21no—
278#440—21no—
279C4×Q16—21no—
280C4×SD16—21no—
281#433—22no—
282#432—21no—
283#431—21no—
284C2×#108C22×C6112yes—
285#428C22×C6112yes—
286#428C22×C6111yescharacteristic
287C2×#107C22×C6112yes—
288#423C22×C6111yescharacteristic
289#423C22×C6111yescharacteristic
290C2×C4⋊C8C22×C6111yescharacteristic
291#419C22×C6111yescharacteristic
292#417C22×C6112yes—
293#417C22×C6111yescharacteristic
294C2×#103C22×C6112yes—
295C2×#101C22×C6112yes—
296#408C22×C6112yes—
297#405C22×C6112yes—
298C4×M16C22×C6111yescharacteristic
299#343C22×C6112yes—
300#343C22×C6112yes—
301#343C22×C6112yes—
302#341C22×C6112yes—
303C61#2472211yescharacteristic, direct product factor, Sylow
304C2×#41C23×C6111yescharacteristic
305C22×Q8—21no—
306C22×Q8C23×C6111yescharacteristic
307#137—22no—
308#137—22no—
309C2×Q16—21no—
310C2×SD16—21no—
311C2×M16C23×C6111yescharacteristic
312C2×M16C23×C6112yes—
313C2×M16C23×C6112yes—
314C2×M16C23×C6111yescharacteristic
315C22×C8C23×C6112yes—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8D4×C6111yescharacteristic
325C4×Q8D4×C6111yescharacteristic
326C4×D4—21no—
327C4×D4—21no—
328C4×D4D4×C6111yescharacteristic
329C4×D4D4×C6111yescharacteristic
330#117—21no—
331#117C23×C6111yescharacteristic
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4C23×C6111yescharacteristic
335C2×C4⋊C4C23×C6112yes—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42C23×C6111yescharacteristic
339#108—24no—
340#107—22no—
341#107—22no—
342#107—21no—
343#107—22no—
344#106—21no—
345#106—22no—
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8D4×C6111yescharacteristic
351C4⋊C8D4×C6111yescharacteristic
352C4⋊C8D4×C6112yes—
353#103—21no—
354#103—22no—
355#103—22no—
356#103—22no—
357#103—21no—
358#103—21no—
359#102—21no—
360#102—22no—
361#101—24no—
362C22⋊C8—22no—
363C22⋊C8—22no—
364#97—22no—
365#97—21no—
366C4×C8—22no—
367C4×C8—21no—
368#41—21no—
369#41—21no—
370#41—21no—
371#41—21no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—41no—
378C2×Q8—41no—
379C2×Q8—82no—
380C2×Q8C2×D4×C6111yescharacteristic
381C2×Q8#41×C6112yes—
382C2×D4—21no—
383C2×D4C2×D4×C6111yescharacteristic
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4#41×C6111yescharacteristic
391C22×C4#41×C6111yescharacteristic
392C22×C4C24×C6111yescharacteristic
393Q16—24no—
394SD16—24no—
395M16—21no—
396M16—22no—
397M16—22no—
398M16—22no—
399M16—21no—
400M16—21no—
401M16—22no—
402M16#41×C6112yes—
403C2×C8—21no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—21no—
408C2×C8—22no—
409C2×C8C2×D4×C6112yes—
410C2×C8C2×D4×C6112yes—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4C2×D4×C6111yescharacteristic
422C4⋊C4C2×D4×C6111yescharacteristic
423C22⋊C4—21no—
424C22⋊C4—21no—
425C22⋊C4—21no—
426C42—21no—
427C42—21no—
428C42—21no—
429C42—41no—
430C42—41no—
431C42C2×D4×C6111yescharacteristic
432C42C2×D4×C6111yescharacteristic
433C42C2×D4×C6111yescharacteristic
434C42C2×D4×C6111yescharacteristic
435C23—21no—
436C23C2×#41×C6111yescharacteristic
437Q8—21no—
438Q8—22no—
439Q8—22no—
440Q8—21no—
441Q8—41no—
442Q8—41no—
443Q8—82no—
444Q8—82no—
445D4—21no—
446D4—21no—
447D4—41no—
448D4—41no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4—82no—
465C2×C4#121×C6111yescharacteristic
466C2×C4#121×C6111yescharacteristic
467C2×C4#121×C6111yescharacteristic
468C2×C4#121×C6111yescharacteristic
469C2×C4C22×D4×C6111yescharacteristic
470C2×C4C22×D4×C6111yescharacteristic
471C2×C4C2×#41×C6111yescharacteristic
472C2×C4C2×#41×C6111yescharacteristic
473C2×C42−1+4×C6111yescharacteristic
474C2×C42−1+4×C6111yescharacteristic
475C8—22no—
476C8—22no—
477C8—22no—
478C8—41no—
479C8—42no—
480C8—42no—
481C22—21no—
482C22—21no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22C2×#121×C6111yescharacteristic
487C22C61×#55211yescharacteristic
488C22C61×#55611yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—42no—
496C4—81no—
497C4—82no—
498C4C61×#47312yes—
499C4C61×#52511yescharacteristic
500C4C61×#53611yescharacteristic
501C4C61×#54711yescharacteristic
502C4C61×#54811yescharacteristic
503C2—21no—
504C2—21no—
505C2—81no—
506C2C61×#241511yescharacteristic
507C2C2×C61×#47311yescharacteristic
508C2C61×#306811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×#41×C61C23
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
2. C2×C61×#477C2semidirect
7. C61×#1997C2semidirect
8. C61×#1952C2semidirect
9. C61×#1950C2semidirect
10. C61×#1930C2semidirect
11. C61×#1801C2semidirect
226. #24722C61direct (N × H)
250. C2×#477C2×C61semidirect
255. #1997C2×C61semidirect
256. #1952C2×C61semidirect
257. #1950C2×C61semidirect
258. #1930C2×C61semidirect
259. #1801C2×C61semidirect
303. C61#24722direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#30792
C2×C61×#4772
C4×#137×C612
C61×#29252
C61×#20782
C61×#20522
C61×#19972
C61×#19522
C61×#19502
C61×#19302
C61×#18012
#2472261