Finite Group Databasebeta

← C61×#25693 #29529126

Subgroups — C61×#25693 #29529126

Order 15616.

1038 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3506C211yesmaximal, characteristic
2C61×#3165C211yesmaximal, characteristic, complemented
3C61×#3141C211yesmaximal, characteristic, complemented
4C61×#2563C211yesmaximal, characteristic, complemented
5C61×#2037C214yesmaximal, complemented
6C61×#1986C211yesmaximal, characteristic, complemented
7C61×#1980C211yesmaximal, characteristic, complemented
8C61×#1860C214yesmaximal, complemented
9C4×#100×C61C211yesmaximal, characteristic, complemented
10C61×#559—22no—
11C61×#556—21no—
12C61×#555—21no—
13C61×#553—22no—
14C61×#550—21no—
15C61×#547—21no—
16C61×#538—22no—
17C61×#535C2212yes—
18C61×#533C2211yescharacteristic
19C61×#532C2211yescharacteristic
20C2×C4⋊Q8×C61C2211yescharacteristic
21C61×#525—22no—
22C61×#520C2212yes—
23C2×C4×D4×C61C2211yescharacteristic
24C61×#501—22no—
25C61×#500—21no—
26C61×#498—21no—
27C61×#489—22no—
28C61×#487—21no—
29C61×#486—21no—
30C61×#428C2214yes—
31C2×#104×C61C2214yes—
32C61×#417C2214yes—
33C2×#100×C61C2212yes—
34C4×M16×C61C2211yescharacteristic
35C4×M16×C61C2211yescharacteristic
36C61×#393—22no—
37C61×#390C2212yes—
38C61×#382C2212yes—
39C61×#380—22no—
40C4×C4⋊C4×C61C2211yescharacteristic
41C61×#343C2212yes—
42C61×#339C2214yes—
43C2×#41×C61—22no—
44C2×#41×C61C2312yes—
45C22×Q8×C61—21no—
46C22×D4×C61C2311yescharacteristic
47C23×C4×C61D412yes—
48C2×M16×C61C2312yes—
49C2×M16×C61C2312yes—
50C4⋊Q8×C61—21no—
51C4⋊Q8×C61—21no—
52C4⋊Q8×C61—21no—
53C4⋊Q8×C61—21no—
54C4⋊Q8×C61D411yescharacteristic
55C4⋊Q8×C61D411yescharacteristic
56C4⋊Q8×C61D411yescharacteristic
57#127×C61—22no—
58#127×C61D411yescharacteristic
59#126×C61—24no—
60#125×C61D412yes—
61#124×C61—24no—
62#124×C61—22no—
63#124×C61D412yes—
64#123×C61—24no—
65#123×C61—24no—
66C22⋊Q8×C61—22no—
67C22⋊Q8×C61—21no—
68C22⋊Q8×C61—21no—
69#121×C61—24no—
70#121×C61—22no—
71#121×C61—21no—
72#121×C61—21no—
73#121×C61—22no—
74#121×C61—22no—
75#120×C61—24no—
76C4×Q8×C61—22no—
77C4×Q8×C61—21no—
78C4×Q8×C61—21no—
79C4×D4×C61—24no—
80C4×D4×C61—22no—
81C4×D4×C61—24no—
82C4×D4×C61—21no—
83C4×D4×C61—21no—
84C4×D4×C61—21no—
85C4×D4×C61—21no—
86C4×D4×C61—21no—
87C4×D4×C61—21no—
88#117×C61—22no—
89#117×C61—22no—
90#117×C61C2312yes—
91C2×C4⋊C4×C61—22no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61C2312yes—
95C2×C4⋊C4×C61C2311yescharacteristic
96C2×C22⋊C4×C61—24no—
97C2×C22⋊C4×C61D412yes—
98C2×C42×C61C2312yes—
99C2×C42×C61C2311yescharacteristic
100#107×C61—24no—
101#106×C61—24no—
102#104×C61—28no—
103#103×C61—24no—
104#102×C61—24no—
105#100×C61—24no—
106#97×C61—21no—
107#97×C61—21no—
108C4×C8×C61—21no—
109C4×C8×C61—21no—
110#95×C61—21no—
111#95×C61—24no—
112C24×C61C2×D412yes—
113#41×C61—24no—
114#41×C61—24no—
115#41×C61—84no—
116C2×Q8×C61—21no—
117C2×Q8×C61—21no—
118C2×Q8×C61—41no—
119C2×Q8×C61—41no—
120C2×Q8×C61—82no—
121C2×Q8×C61C2×D412yes—
122C2×D4×C61—22no—
123C2×D4×C61—24no—
124C2×D4×C61—24no—
125C2×D4×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61—22no—
130C2×D4×C61—22no—
131C2×D4×C61C2×D412yes—
132C22×C4×C61—24no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—44no—
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D412yes—
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2411yescharacteristic
143M16×C61—22no—
144M16×C61—22no—
145M16×C61—22no—
146M16×C61#4114yescomplemented
147C2×C8×C61—22no—
148C2×C8×C61—22no—
149C4⋊C4×C61—24no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—22no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—22no—
159C4⋊C4×C61—22no—
160C4⋊C4×C61—42no—
161C4⋊C4×C61—41no—
162C4⋊C4×C61—41no—
163C4⋊C4×C61C2×D412yes—
164C4⋊C4×C61C2×D412yes—
165C22⋊C4×C61—24no—
166C22⋊C4×C61—24no—
167C22⋊C4×C61—24no—
168C22⋊C4×C61—22no—
169C22⋊C4×C61—22no—
170C22⋊C4×C61—22no—
171C22⋊C4×C61—22no—
172C22⋊C4×C61—22no—
173C22⋊C4×C61—84no—
174C42×C61—24no—
175C42×C61—22no—
176C42×C61—24no—
177C42×C61C2×D411yescharacteristic
178C42×C61C2×D411yescharacteristic
179C42×C61C2×D411yescharacteristic
180C42×C61C2×D411yescharacteristic
181C23×C61—22no—
182C23×C61—22no—
183C23×C61—22no—
184C23×C61—22no—
185C23×C61—42no—
186C23×C61—42no—
187C23×C61C22×D411yescharacteristic
188Q8×C61—24no—
189Q8×C61—42no—
190Q8×C61—81no—
191Q8×C61—82no—
192Q8×C61—82no—
193D4×C61—24no—
194D4×C61—42no—
195D4×C61—42no—
196D4×C61—42no—
197D4×C61—42no—
198D4×C61—42no—
199D4×C61—81no—
200D4×C61—84no—
201D4×C61—84no—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—41no—
208C2×C4×C61—44no—
209C2×C4×C61—44no—
210C2×C4×C61—42no—
211C2×C4×C61—42no—
212C2×C4×C61—44no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61—82no—
217C2×C4×C61—84no—
218C2×C4×C61#12011yescharacteristic
219C2×C4×C61#12011yescharacteristic
220C2×C4×C61#12011yescharacteristic
221C2×C4×C61#12011yescharacteristic
222C2×C4×C61C22×D411yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C2×#4112yes—
225C2×C4×C612−1+412yes—
226C8×C61—24no—
227C8×C61—42no—
228#25693C6111yesmaximal, characteristic, direct product factor, Sylow
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—44no—
232C22×C61—42no—
233C22×C61—42no—
234C22×C61—42no—
235C22×C61—42no—
236C22×C61—42no—
237C22×C61—42no—
238C22×C61—82no—
239C22×C61C2×#12011yescharacteristic
240C22×C61#53211yescharacteristic
241C22×C61#53611yescharacteristic
242C4×C61—21no—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—42no—
246C4×C61—42no—
247C4×C61—42no—
248C4×C61—42no—
249C4×C61—82no—
250C4×C61—82no—
251C4×C61#45512yes—
252C4×C61#54712yes—
253C4×C61#54812yes—
254#3506C2×C6111yescharacteristic
255#3165C2×C6111yescharacteristic, complemented
256#3141C2×C6111yescharacteristic, complemented
257#2563C2×C6111yescharacteristic, complemented
258#2037C2×C6114yescomplemented
259#1986C2×C6111yescharacteristic, complemented
260#1980C2×C6111yescharacteristic, complemented
261#1860C2×C6114yescomplemented
262C4×#100C2×C6111yescharacteristic, complemented
263C2×C61—21no—
264C2×C61—21no—
265C2×C61—82no—
266C2×C61—82no—
267C2×C61#243211yescharacteristic
268C2×C61C2×#45511yescharacteristic
269C2×C61#302111yescharacteristic
270#559—22no—
271#556—21no—
272#555—21no—
273#553—22no—
274#550—21no—
275#547—21no—
276#538—22no—
277#535C22×C6112yes—
278#533C22×C6111yescharacteristic
279#532C22×C6111yescharacteristic
280C2×C4⋊Q8C22×C6111yescharacteristic
281#525—22no—
282#520C22×C6112yes—
283C2×C4×D4C22×C6111yescharacteristic
284#501—22no—
285#500—21no—
286#498—21no—
287#489—22no—
288#487—21no—
289#486—21no—
290#428C22×C6114yes—
291C2×#104C22×C6114yes—
292#417C22×C6114yes—
293C2×#100C22×C6112yes—
294C4×M16C22×C6111yescharacteristic
295C4×M16C22×C6111yescharacteristic
296#393—22no—
297#390C22×C6112yes—
298#382C22×C6112yes—
299#380—22no—
300C4×C4⋊C4C22×C6111yescharacteristic
301#343C22×C6112yes—
302#339C22×C6114yes—
303C61#2569311yescharacteristic, direct product factor, Sylow
304C2×#41—22no—
305C2×#41C23×C6112yes—
306C22×Q8—21no—
307C22×D4C23×C6111yescharacteristic
308C23×C4D4×C6112yes—
309C2×M16C23×C6112yes—
310C2×M16C23×C6112yes—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8D4×C6111yescharacteristic
316C4⋊Q8D4×C6111yescharacteristic
317C4⋊Q8D4×C6111yescharacteristic
318#127—22no—
319#127D4×C6111yescharacteristic
320#126—24no—
321#125D4×C6112yes—
322#124—24no—
323#124—22no—
324#124D4×C6112yes—
325#123—24no—
326#123—24no—
327C22⋊Q8—22no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330#121—22no—
331#121—24no—
332#121—21no—
333#121—21no—
334#121—22no—
335#121—22no—
336#120—24no—
337C4×Q8—22no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×D4—24no—
341C4×D4—22no—
342C4×D4—24no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4—21no—
349#117—22no—
350#117—22no—
351#117C23×C6112yes—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4C23×C6112yes—
356C2×C4⋊C4C23×C6111yescharacteristic
357C2×C22⋊C4—24no—
358C2×C22⋊C4D4×C6112yes—
359C2×C42C23×C6112yes—
360C2×C42C23×C6111yescharacteristic
361#107—24no—
362#106—24no—
363#104—28no—
364#103—24no—
365#102—24no—
366#100—24no—
367#97—21no—
368#97—21no—
369C4×C8—21no—
370C4×C8—21no—
371#95—21no—
372#95—24no—
373C24C2×D4×C6112yes—
374#41—24no—
375#41—24no—
376#41—84no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—41no—
380C2×Q8—41no—
381C2×Q8—82no—
382C2×Q8C2×D4×C6112yes—
383C2×D4—22no—
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4C2×D4×C6112yes—
393C22×C4—24no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—44no—
400C22×C4C2×D4×C6111yescharacteristic
401C22×C4C2×D4×C6112yes—
402C22×C4C2×D4×C6111yescharacteristic
403C22×C4C24×C6111yescharacteristic
404M16—22no—
405M16—22no—
406M16—22no—
407M16#41×C6114yescomplemented
408C2×C8—22no—
409C2×C8—22no—
410C4⋊C4—24no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—42no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4C2×D4×C6112yes—
425C4⋊C4C2×D4×C6112yes—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—84no—
435C42—24no—
436C42—22no—
437C42—24no—
438C42C2×D4×C6111yescharacteristic
439C42C2×D4×C6111yescharacteristic
440C42C2×D4×C6111yescharacteristic
441C42C2×D4×C6111yescharacteristic
442C23—22no—
443C23—22no—
444C23—22no—
445C23—22no—
446C23—42no—
447C23—42no—
448C23C22×D4×C6111yescharacteristic
449Q8—24no—
450Q8—42no—
451Q8—81no—
452Q8—82no—
453Q8—82no—
454D4—24no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—42no—
459D4—42no—
460D4—81no—
461D4—84no—
462D4—84no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—44no—
470C2×C4—44no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—44no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—82no—
478C2×C4—84no—
479C2×C4#120×C6111yescharacteristic
480C2×C4#120×C6111yescharacteristic
481C2×C4#120×C6111yescharacteristic
482C2×C4#120×C6111yescharacteristic
483C2×C4C22×D4×C6111yescharacteristic
484C2×C4C22×D4×C6111yescharacteristic
485C2×C4C2×#41×C6112yes—
486C2×C42−1+4×C6112yes—
487C8—24no—
488C8—42no—
489C22—21no—
490C22—21no—
491C22—44no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—82no—
499C22C2×#120×C6111yescharacteristic
500C22C61×#53211yescharacteristic
501C22C61×#53611yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—42no—
506C4—42no—
507C4—42no—
508C4—42no—
509C4—82no—
510C4—82no—
511C4C61×#45512yes—
512C4C61×#54712yes—
513C4C61×#54812yes—
514C2—21no—
515C2—21no—
516C2—82no—
517C2—82no—
518C2C61×#243211yescharacteristic
519C2C2×C61×#45511yescharacteristic
520C2C61×#302111yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3506C2
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
3. C61×#3141C2semidirect
4. C61×#2563C2semidirect
5. C61×#2037C2semidirect
6. C61×#1986C2semidirect
7. C61×#1980C2semidirect
8. C61×#1860C2semidirect
9. C4×#100×C61C2semidirect
146. M16×C61#41semidirect
228. #25693C61direct (N × H)
255. #3165C2×C61semidirect
256. #3141C2×C61semidirect
257. #2563C2×C61semidirect
258. #2037C2×C61semidirect
259. #1986C2×C61semidirect
260. #1980C2×C61semidirect
261. #1860C2×C61semidirect
262. C4×#100C2×C61semidirect
303. C61#25693direct (N × H)
407. M16#41×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35062
C61×#31652
C61×#31412
C61×#25632
C61×#20372
C61×#19862
C61×#19802
C61×#18602
C4×#100×C612
#2569361