Finite Group Databasebeta

← C61×#25688 #29529121

Subgroups — C61×#25688 #29529121

Order 15616.

964 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3509C211yesmaximal, characteristic
2C61×#3165C211yesmaximal, characteristic, complemented
3C61×#3079C211yesmaximal, characteristic
4C61×#2862C211yesmaximal, characteristic, complemented
5C61×#2038C214yesmaximal
6C61×#1994C211yesmaximal, characteristic, complemented
7C61×#1966C211yesmaximal, characteristic, complemented
8C61×#1857C214yesmaximal, complemented
9C4×#104×C61C211yesmaximal, characteristic
10C61×#557—21no—
11C61×#557—21no—
12C61×#556—21no—
13C61×#556—21no—
14C61×#552—22no—
15C61×#552—22no—
16C61×#541—22no—
17C61×#536C2212yes—
18C61×#533—21no—
19C61×#533—21no—
20C61×#533C2211yescharacteristic
21C2×C4⋊Q8×C61C2211yescharacteristic
22C2×C4⋊Q8×C61C2211yescharacteristic
23C61×#519C2212yes—
24C4×#41×C61C2211yescharacteristic
25C61×#501—22no—
26C61×#500—21no—
27C61×#498—21no—
28C61×#477—21no—
29C61×#476—21no—
30C61×#475—21no—
31C61×#474—21no—
32C61×#428C2214yes—
33C61×#428C2212yes—
34C61×#423C2211yescharacteristic
35C2×#104×C61C2212yes—
36C61×#417C2212yes—
37C2×#101×C61C2214yes—
38C4×M16×C61C2211yescharacteristic
39C61×#391—22no—
40C61×#391C2214yes—
41C61×#382—22no—
42C43×C61C2211yescharacteristic
43C61×#339C2212yes—
44C61×#339C2214yes—
45C2×#41×C61C2311yescharacteristic
46C22×Q8×C61—21no—
47C22×Q8×C61C2312yes—
48C2×M16×C61C2312yes—
49C2×M16×C61C2312yes—
50C4⋊Q8×C61—22no—
51C4⋊Q8×C61—21no—
52C4⋊Q8×C61—21no—
53C4⋊Q8×C61—21no—
54C4⋊Q8×C61—21no—
55C4⋊Q8×C61—21no—
56C4⋊Q8×C61—21no—
57C4⋊Q8×C61—21no—
58C4⋊Q8×C61—21no—
59C4⋊Q8×C61D411yescharacteristic
60C4⋊Q8×C61D411yescharacteristic
61#126×C61—24no—
62#126×C61—24no—
63#125×C61—22no—
64#125×C61—22no—
65#125×C61—24no—
66#125×C61—24no—
67#125×C61D412yes—
68#124×C61—22no—
69#123×C61—24no—
70C22⋊Q8×C61—22no—
71C22⋊Q8×C61—22no—
72C22⋊Q8×C61—21no—
73C22⋊Q8×C61—21no—
74C22⋊Q8×C61—22no—
75C22⋊Q8×C61—22no—
76C4×Q8×C61—22no—
77C4×Q8×C61—22no—
78C4×Q8×C61—22no—
79C4×Q8×C61—22no—
80C4×Q8×C61—22no—
81C4×Q8×C61—22no—
82C4×Q8×C61—21no—
83C4×Q8×C61—21no—
84C4×Q8×C61D411yescharacteristic
85C4×Q8×C61D411yescharacteristic
86C4×D4×C61—21no—
87C4×D4×C61—21no—
88C4×D4×C61D411yescharacteristic
89C4×D4×C61D411yescharacteristic
90#117×C61—22no—
91#117×C61—22no—
92#117×C61—24no—
93#117×C61—21no—
94#117×C61C2312yes—
95#117×C61C2311yescharacteristic
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61D412yes—
98C2×C4⋊C4×C61D412yes—
99C2×C4⋊C4×C61C2312yes—
100C2×C42×C61—21no—
101C2×C42×C61—21no—
102C2×C42×C61—21no—
103C2×C42×C61C2312yes—
104C2×C42×C61C2311yescharacteristic
105#107×C61—22no—
106#107×C61—24no—
107#106×C61—22no—
108#106×C61—24no—
109C4⋊C8×C61—21no—
110C4⋊C8×C61—21no—
111#104×C61—24no—
112#103×C61—22no—
113#102×C61—22no—
114#101×C61—28no—
115#97×C61—21no—
116C4×C8×C61—21no—
117#95×C61—28no—
118#41×C61—22no—
119#41×C61—22no—
120C2×Q8×C61—21no—
121C2×Q8×C61—21no—
122C2×Q8×C61—22no—
123C2×Q8×C61—22no—
124C2×Q8×C61—24no—
125C2×Q8×C61—24no—
126C2×Q8×C61—44no—
127C2×Q8×C61—41no—
128C2×Q8×C61—41no—
129C2×Q8×C61C2×D411yescharacteristic
130C2×D4×C61—21no—
131C2×D4×C61C2×D411yescharacteristic
132C22×C4×C61—22no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—22no—
137C22×C4×C61C2×D414yes—
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2411yescharacteristic
141M16×C61—22no—
142M16×C61—24no—
143M16×C61#4114yes—
144C2×C8×C61—22no—
145C2×C8×C61—22no—
146C4⋊C4×C61—24no—
147C4⋊C4×C61—24no—
148C4⋊C4×C61—24no—
149C4⋊C4×C61—24no—
150C4⋊C4×C61—22no—
151C4⋊C4×C61—22no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—22no—
159C4⋊C4×C61—22no—
160C4⋊C4×C61—22no—
161C4⋊C4×C61—22no—
162C4⋊C4×C61—41no—
163C4⋊C4×C61—41no—
164C4⋊C4×C61C2×D411yescharacteristic
165C4⋊C4×C61C2×D412yes—
166C4⋊C4×C61C2×D411yescharacteristic
167C4⋊C4×C61C2×D412yes—
168C22⋊C4×C61—24no—
169C22⋊C4×C61—24no—
170C22⋊C4×C61—21no—
171C22⋊C4×C61—22no—
172C22⋊C4×C61—21no—
173C22⋊C4×C61—21no—
174C42×C61—24no—
175C42×C61—24no—
176C42×C61—24no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61—21no—
180C42×C61—22no—
181C42×C61—22no—
182C42×C61—22no—
183C42×C61—42no—
184C42×C61C2×D411yescharacteristic
185C42×C61C2×D411yescharacteristic
186C42×C61C2×D411yescharacteristic
187C42×C61C2×D411yescharacteristic
188C23×C61—21no—
189C23×C61C22×D411yescharacteristic
190Q8×C61—21no—
191Q8×C61—21no—
192Q8×C61—42no—
193Q8×C61—42no—
194Q8×C61—44no—
195Q8×C61—42no—
196Q8×C61—42no—
197Q8×C61—82no—
198Q8×C61—82no—
199D4×C61—21no—
200D4×C61—21no—
201D4×C61—42no—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—24no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—24no—
210C2×C4×C61—21no—
211C2×C4×C61—28no—
212C2×C4×C61—42no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—44no—
218C2×C4×C61—42no—
219C2×C4×C61#12011yescharacteristic
220C2×C4×C61#12011yescharacteristic
221C2×C4×C61#12011yescharacteristic
222C2×C4×C61#12011yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C22×D411yescharacteristic
225C2×C4×C61C2×#4112yes—
226C2×C4×C612−1+412yes—
227C8×C61—24no—
228C8×C61—42no—
229#25688C6111yesmaximal, characteristic, direct product factor, Sylow
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—41no—
233C22×C61—41no—
234C22×C61—41no—
235C22×C61C2×#12011yescharacteristic
236C22×C61#54712yes—
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—44no—
240C4×C61—44no—
241C4×C61—41no—
242C4×C61—41no—
243C4×C61—42no—
244C4×C61—41no—
245C4×C61—42no—
246C4×C61—82no—
247C4×C61#45412yes—
248C4×C61#45612yes—
249C4×C61#53211yescharacteristic
250C4×C61#53611yescharacteristic
251C4×C61#54812yes—
252#3509C2×C6111yescharacteristic
253#3165C2×C6111yescharacteristic, complemented
254#3079C2×C6111yescharacteristic
255#2862C2×C6111yescharacteristic, complemented
256#2038C2×C6114yes—
257#1994C2×C6111yescharacteristic, complemented
258#1966C2×C6111yescharacteristic, complemented
259#1857C2×C6114yescomplemented
260C4×#104C2×C6111yescharacteristic
261C2×C61—22no—
262C2×C61—81no—
263C2×C61#243211yescharacteristic
264C2×C61C2×#45411yescharacteristic
265C2×C61C2×#45611yescharacteristic
266#557—21no—
267#557—21no—
268#556—21no—
269#556—21no—
270#552—22no—
271#552—22no—
272#541—22no—
273#536C22×C6112yes—
274#533—21no—
275#533—21no—
276#533C22×C6111yescharacteristic
277C2×C4⋊Q8C22×C6111yescharacteristic
278C2×C4⋊Q8C22×C6111yescharacteristic
279#519C22×C6112yes—
280C4×#41C22×C6111yescharacteristic
281#501—22no—
282#500—21no—
283#498—21no—
284#477—21no—
285#476—21no—
286#475—21no—
287#474—21no—
288#428C22×C6112yes—
289#428C22×C6114yes—
290#423C22×C6111yescharacteristic
291C2×#104C22×C6112yes—
292#417C22×C6112yes—
293C2×#101C22×C6114yes—
294C4×M16C22×C6111yescharacteristic
295#391—22no—
296#391C22×C6114yes—
297#382—22no—
298C43C22×C6111yescharacteristic
299#339C22×C6112yes—
300#339C22×C6114yes—
301C61#2568811yescharacteristic, direct product factor, Sylow
302C2×#41C23×C6111yescharacteristic
303C22×Q8—21no—
304C22×Q8C23×C6112yes—
305C2×M16C23×C6112yes—
306C2×M16C23×C6112yes—
307C4⋊Q8—22no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8D4×C6111yescharacteristic
317C4⋊Q8D4×C6111yescharacteristic
318#126—24no—
319#126—24no—
320#125—22no—
321#125—22no—
322#125—24no—
323#125—24no—
324#125D4×C6112yes—
325#124—22no—
326#123—24no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8D4×C6111yescharacteristic
342C4×Q8D4×C6111yescharacteristic
343C4×D4—21no—
344C4×D4—21no—
345C4×D4D4×C6111yescharacteristic
346C4×D4D4×C6111yescharacteristic
347#117—22no—
348#117—22no—
349#117—24no—
350#117—21no—
351#117C23×C6111yescharacteristic
352#117C23×C6112yes—
353C2×C4⋊C4—21no—
354C2×C4⋊C4D4×C6112yes—
355C2×C4⋊C4D4×C6112yes—
356C2×C4⋊C4C23×C6112yes—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42C23×C6112yes—
361C2×C42C23×C6111yescharacteristic
362#107—22no—
363#107—24no—
364#106—22no—
365#106—24no—
366C4⋊C8—21no—
367C4⋊C8—21no—
368#104—24no—
369#103—22no—
370#102—22no—
371#101—28no—
372#97—21no—
373C4×C8—21no—
374#95—28no—
375#41—22no—
376#41—22no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—24no—
382C2×Q8—24no—
383C2×Q8—44no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8C2×D4×C6111yescharacteristic
387C2×D4—21no—
388C2×D4C2×D4×C6111yescharacteristic
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4C2×D4×C6114yes—
395C22×C4C2×D4×C6111yescharacteristic
396C22×C4C2×D4×C6111yescharacteristic
397C22×C4C24×C6111yescharacteristic
398M16—22no—
399M16—24no—
400M16#41×C6114yes—
401C2×C8—22no—
402C2×C8—22no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4C2×D4×C6111yescharacteristic
422C4⋊C4C2×D4×C6112yes—
423C4⋊C4C2×D4×C6111yescharacteristic
424C4⋊C4C2×D4×C6112yes—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—21no—
428C22⋊C4—22no—
429C22⋊C4—21no—
430C22⋊C4—21no—
431C42—24no—
432C42—24no—
433C42—24no—
434C42—21no—
435C42—21no—
436C42—21no—
437C42—22no—
438C42—22no—
439C42—22no—
440C42—42no—
441C42C2×D4×C6111yescharacteristic
442C42C2×D4×C6111yescharacteristic
443C42C2×D4×C6111yescharacteristic
444C42C2×D4×C6111yescharacteristic
445C23—21no—
446C23C22×D4×C6111yescharacteristic
447Q8—21no—
448Q8—21no—
449Q8—42no—
450Q8—42no—
451Q8—44no—
452Q8—42no—
453Q8—42no—
454Q8—82no—
455Q8—82no—
456D4—21no—
457D4—21no—
458D4—42no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—28no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—21no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—42no—
476C2×C4#120×C6111yescharacteristic
477C2×C4#120×C6111yescharacteristic
478C2×C4#120×C6111yescharacteristic
479C2×C4#120×C6111yescharacteristic
480C2×C4C22×D4×C6111yescharacteristic
481C2×C4C22×D4×C6111yescharacteristic
482C2×C4C2×#41×C6112yes—
483C2×C42−1+4×C6112yes—
484C8—24no—
485C8—42no—
486C22—21no—
487C22—21no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22C2×#120×C6111yescharacteristic
492C22C61×#54712yes—
493C4—21no—
494C4—21no—
495C4—44no—
496C4—44no—
497C4—41no—
498C4—41no—
499C4—42no—
500C4—41no—
501C4—42no—
502C4—82no—
503C4C61×#45412yes—
504C4C61×#45612yes—
505C4C61×#53211yescharacteristic
506C4C61×#53611yescharacteristic
507C4C61×#54812yes—
508C2—22no—
509C2—81no—
510C2C61×#243211yescharacteristic
511C2C2×C61×#45411yescharacteristic
512C2C2×C61×#45611yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
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. C61×#3165C2semidirect
4. C61×#2862C2semidirect
6. C61×#1994C2semidirect
7. C61×#1966C2semidirect
8. C61×#1857C2semidirect
229. #25688C61direct (N × H)
253. #3165C2×C61semidirect
255. #2862C2×C61semidirect
257. #1994C2×C61semidirect
258. #1966C2×C61semidirect
259. #1857C2×C61semidirect
301. C61#25688direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35092
C61×#31652
C61×#30792
C61×#28622
C61×#20382
C61×#19942
C61×#19662
C61×#18572
C4×#104×C612
#2568861