Finite Group Databasebeta

← C61×#18442 #29521875

Subgroups — C61×#18442 #29521875

Order 15616.

848 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3563C211yesmaximal, characteristic
2C61×#3238C211yesmaximal, characteristic
3C61×#3229C211yesmaximal, characteristic, complemented
4C61×#2660C211yesmaximal, characteristic, complemented
5C61×#1611C214yesmaximal, complemented
6C61×#1609C214yesmaximal
7C61×#1506C211yesmaximal, characteristic, complemented
8C61×#1500C211yesmaximal, characteristic
9C61×#1470C211yesmaximal, characteristic, complemented
10C61×#564—21no—
11C61×#563—21no—
12C61×#557—21no—
13C61×#554—21no—
14C61×#552—21no—
15C61×#552—21no—
16C61×#552—22no—
17C61×#544—21no—
18C61×#544C2212yes—
19C61×#541—21no—
20C61×#541—22no—
21C61×#539C2212yes—
22C61×#533C2211yescharacteristic
23C2×C4⋊Q8×C61C2211yescharacteristic
24C61×#529C2211yescharacteristic
25C2×#125×C61C2211yescharacteristic
26C61×#501—21no—
27C61×#498—21no—
28C61×#489—21no—
29C61×#487—21no—
30C61×#483C2214yes—
31C61×#483C2212yes—
32C61×#480C2212yes—
33C61×#477—21no—
34C61×#476—21no—
35C61×#475—22no—
36C61×#432C2211yescharacteristic
37C61×#431C2211yescharacteristic
38C61×#398C2214yes—
39C61×#395—22no—
40C61×#384—21no—
41C61×#382—21no—
42C61×#376C2211yescharacteristic
43C61×#328C2212yes—
44C61×#328C2214yes—
45C61×#327C2212yes—
46C61×#324C2214yes—
47C22×Q8×C61—21no—
48C4⋊Q8×C61—21no—
49C4⋊Q8×C61—22no—
50C4⋊Q8×C61—22no—
51C4⋊Q8×C61—21no—
52C4⋊Q8×C61—21no—
53C4⋊Q8×C61—21no—
54C4⋊Q8×C61—21no—
55C4⋊Q8×C61D411yescharacteristic
56C4⋊Q8×C61D411yescharacteristic
57#126×C61—22no—
58#126×C61—22no—
59#126×C61—22no—
60#126×C61—22no—
61#126×C61—21no—
62#125×C61—22no—
63#125×C61—22no—
64#125×C61—22no—
65#125×C61—22no—
66#125×C61—21no—
67#125×C61—22no—
68#125×C61—22no—
69#125×C61—22no—
70#125×C61—22no—
71#125×C61—21no—
72#125×C61—21no—
73#125×C61—21no—
74#125×C61—21no—
75#125×C61—21no—
76#125×C61D411yescharacteristic
77#124×C61D411yescharacteristic
78#123×C61—22no—
79#123×C61—22no—
80#123×C61—21no—
81C22⋊Q8×C61—21no—
82C22⋊Q8×C61—21no—
83C22⋊Q8×C61—22no—
84C22⋊Q8×C61—22no—
85C22⋊Q8×C61—22no—
86C22⋊Q8×C61—21no—
87C22⋊Q8×C61—22no—
88C22⋊Q8×C61C2312yes—
89C22⋊Q8×C61C2311yescharacteristic
90#121×C61C2311yescharacteristic
91C4×Q8×C61—21no—
92C4×Q8×C61—22no—
93C4×Q8×C61—21no—
94C4×Q8×C61—21no—
95C4×Q8×C61D412yes—
96C4×Q8×C61D411yescharacteristic
97C4×D4×C61—22no—
98C4×D4×C61—21no—
99C4×D4×C61D411yescharacteristic
100#117×C61—22no—
101#117×C61—21no—
102#117×C61—21no—
103#117×C61—22no—
104#117×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—24no—
108C2×C4⋊C4×C61D411yescharacteristic
109C2×C4⋊C4×C61D412yes—
110C2×C4⋊C4×C61D411yescharacteristic
111C2×C4⋊C4×C61C2312yes—
112C2×C4⋊C4×C61C2312yes—
113C2×C42×C61—21no—
114C2×C42×C61C2311yescharacteristic
115#107×C61—22no—
116#106×C61—24no—
117#106×C61—22no—
118C4⋊C8×C61—21no—
119C4⋊C8×C61—21no—
120#103×C61—24no—
121#103×C61—22no—
122#102×C61—22no—
123C22⋊C8×C61C2312yes—
124C22⋊C8×C61C2312yes—
125#97×C61—21no—
126C4×C8×C61—21no—
127#95×C61—21no—
128#95×C61—24no—
129#95×C61C2312yes—
130C2×Q8×C61—22no—
131C2×Q8×C61—21no—
132C2×Q8×C61—41no—
133C2×Q8×C61—41no—
134C2×Q8×C61—82no—
135C2×Q8×C61C2×D412yes—
136C2×Q8×C61C2×D411yescharacteristic
137C2×D4×C61—21no—
138C2×D4×C61C2×D411yescharacteristic
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—21no—
142C22×C4×C61—22no—
143C22×C4×C61C2×D412yes—
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D412yes—
147C22×C4×C61C2411yescharacteristic
148C2×C8×C61—22no—
149C2×C8×C61—22no—
150C4⋊C4×C61—22no—
151C4⋊C4×C61—22no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—22no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—22no—
157C4⋊C4×C61—22no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—22no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—22no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—22no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61—22no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—22no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61—41no—
179C4⋊C4×C61—84no—
180C4⋊C4×C61C2×D411yescharacteristic
181C4⋊C4×C61C2×D412yes—
182C4⋊C4×C61C2×D411yescharacteristic
183C22⋊C4×C61—22no—
184C22⋊C4×C61—22no—
185C22⋊C4×C61—22no—
186C22⋊C4×C61—22no—
187C22⋊C4×C61—21no—
188C22⋊C4×C61—21no—
189C22⋊C4×C61—21no—
190C22⋊C4×C61—21no—
191C22⋊C4×C61—21no—
192C42×C61—24no—
193C42×C61—22no—
194C42×C61—22no—
195C42×C61—22no—
196C42×C61—22no—
197C42×C61—21no—
198C42×C61C2×D411yescharacteristic
199C42×C61C2×D411yescharacteristic
200C42×C61C2×D411yescharacteristic
201C42×C61C2×D411yescharacteristic
202C23×C61—21no—
203C23×C61C22×D411yescharacteristic
204Q8×C61—41no—
205Q8×C61—42no—
206Q8×C61—42no—
207Q8×C61—82no—
208Q8×C61—82no—
209Q8×C61—82no—
210D4×C61—41no—
211D4×C61—42no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—24no—
215C2×C4×C61—22no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—22no—
219C2×C4×C61—21no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—24no—
223C2×C4×C61—41no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—44no—
230C2×C4×C61—82no—
231C2×C4×C61#12011yescharacteristic
232C2×C4×C61#12011yescharacteristic
233C2×C4×C61#12011yescharacteristic
234C2×C4×C61#12011yescharacteristic
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61C22×D411yescharacteristic
237C8×C61—42no—
238C8×C61—42no—
239#18442C6111yesmaximal, characteristic, direct product factor, Sylow
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—41no—
243C22×C61—41no—
244C22×C61—41no—
245C22×C61C2×#12011yescharacteristic
246C22×C61#57712yes—
247C4×C61—21no—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61—21no—
251C4×C61—21no—
252C4×C61—44no—
253C4×C61—42no—
254C4×C61—41no—
255C4×C61—41no—
256C4×C61—42no—
257C4×C61—42no—
258C4×C61—42no—
259C4×C61—41no—
260C4×C61—82no—
261C4×C61#45612yes—
262#3563C2×C6111yescharacteristic
263#3238C2×C6111yescharacteristic
264#3229C2×C6111yescharacteristic, complemented
265#2660C2×C6111yescharacteristic, complemented
266#1611C2×C6114yescomplemented
267#1609C2×C6114yes—
268#1506C2×C6111yescharacteristic, complemented
269#1500C2×C6111yescharacteristic
270#1470C2×C6111yescharacteristic, complemented
271C2×C61—22no—
272C2×C61—81no—
273C2×C61#301011yescharacteristic
274C2×C61C2×#45611yescharacteristic
275C2×C61#302811yescharacteristic
276#564—21no—
277#563—21no—
278#557—21no—
279#554—21no—
280#552—21no—
281#552—21no—
282#552—22no—
283#544—21no—
284#544C22×C6112yes—
285#541—21no—
286#541—22no—
287#539C22×C6112yes—
288#533C22×C6111yescharacteristic
289C2×C4⋊Q8C22×C6111yescharacteristic
290#529C22×C6111yescharacteristic
291C2×#125C22×C6111yescharacteristic
292#501—21no—
293#498—21no—
294#489—21no—
295#487—21no—
296#483C22×C6114yes—
297#483C22×C6112yes—
298#480C22×C6112yes—
299#477—21no—
300#476—21no—
301#475—22no—
302#432C22×C6111yescharacteristic
303#431C22×C6111yescharacteristic
304#398C22×C6114yes—
305#395—22no—
306#384—21no—
307#382—21no—
308#376C22×C6111yescharacteristic
309#328C22×C6114yes—
310#328C22×C6112yes—
311#327C22×C6112yes—
312#324C22×C6114yes—
313C61#1844211yescharacteristic, direct product factor, Sylow
314C22×Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8D4×C6111yescharacteristic
323C4⋊Q8D4×C6111yescharacteristic
324#126—22no—
325#126—22no—
326#126—22no—
327#126—22no—
328#126—21no—
329#125—22no—
330#125—22no—
331#125—22no—
332#125—22no—
333#125—21no—
334#125—22no—
335#125—22no—
336#125—22no—
337#125—22no—
338#125—21no—
339#125—21no—
340#125—21no—
341#125—21no—
342#125—21no—
343#125D4×C6111yescharacteristic
344#124D4×C6111yescharacteristic
345#123—22no—
346#123—21no—
347#123—22no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—21no—
354C22⋊Q8—22no—
355C22⋊Q8C23×C6111yescharacteristic
356C22⋊Q8C23×C6112yes—
357#121C23×C6111yescharacteristic
358C4×Q8—21no—
359C4×Q8—22no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8D4×C6111yescharacteristic
363C4×Q8D4×C6112yes—
364C4×D4—21no—
365C4×D4—22no—
366C4×D4D4×C6111yescharacteristic
367#117—22no—
368#117—21no—
369#117—21no—
370#117—22no—
371#117—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4D4×C6111yescharacteristic
376C2×C4⋊C4D4×C6112yes—
377C2×C4⋊C4D4×C6111yescharacteristic
378C2×C4⋊C4C23×C6112yes—
379C2×C4⋊C4C23×C6112yes—
380C2×C42—21no—
381C2×C42C23×C6111yescharacteristic
382#107—22no—
383#106—24no—
384#106—22no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387#103—24no—
388#103—22no—
389#102—22no—
390C22⋊C8C23×C6112yes—
391C22⋊C8C23×C6112yes—
392#97—21no—
393C4×C8—21no—
394#95—21no—
395#95—24no—
396#95C23×C6112yes—
397C2×Q8—22no—
398C2×Q8—21no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8—82no—
402C2×Q8C2×D4×C6112yes—
403C2×Q8C2×D4×C6111yescharacteristic
404C2×D4—21no—
405C2×D4C2×D4×C6111yescharacteristic
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4C2×D4×C6112yes—
411C22×C4C2×D4×C6111yescharacteristic
412C22×C4C2×D4×C6111yescharacteristic
413C22×C4C2×D4×C6112yes—
414C22×C4C24×C6111yescharacteristic
415C2×C8—22no—
416C2×C8—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4—84no—
447C4⋊C4C2×D4×C6111yescharacteristic
448C4⋊C4C2×D4×C6112yes—
449C4⋊C4C2×D4×C6111yescharacteristic
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—21no—
455C22⋊C4—21no—
456C22⋊C4—21no—
457C22⋊C4—21no—
458C22⋊C4—21no—
459C42—24no—
460C42—22no—
461C42—22no—
462C42—22no—
463C42—22no—
464C42—21no—
465C42C2×D4×C6111yescharacteristic
466C42C2×D4×C6111yescharacteristic
467C42C2×D4×C6111yescharacteristic
468C42C2×D4×C6111yescharacteristic
469C23—21no—
470C23C22×D4×C6111yescharacteristic
471Q8—41no—
472Q8—42no—
473Q8—42no—
474Q8—82no—
475Q8—82no—
476Q8—82no—
477D4—41no—
478D4—42no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—44no—
496C2×C4—42no—
497C2×C4—82no—
498C2×C4#120×C6111yescharacteristic
499C2×C4#120×C6111yescharacteristic
500C2×C4#120×C6111yescharacteristic
501C2×C4#120×C6111yescharacteristic
502C2×C4C22×D4×C6111yescharacteristic
503C2×C4C22×D4×C6111yescharacteristic
504C8—42no—
505C8—42no—
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22C2×#120×C6111yescharacteristic
512C22C61×#57712yes—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—44no—
519C4—42no—
520C4—41no—
521C4—41no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—41no—
526C4—82no—
527C4C61×#45612yes—
528C2—22no—
529C2—81no—
530C2C61×#301011yescharacteristic
531C2C2×C61×#45611yescharacteristic
532C2C61×#302811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radical#121×C61C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#3229C2semidirect
4. C61×#2660C2semidirect
5. C61×#1611C2semidirect
7. C61×#1506C2semidirect
9. C61×#1470C2semidirect
239. #18442C61direct (N × H)
264. #3229C2×C61semidirect
265. #2660C2×C61semidirect
266. #1611C2×C61semidirect
268. #1506C2×C61semidirect
270. #1470C2×C61semidirect
313. C61#18442direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35632
C61×#32382
C61×#32292
C61×#26602
C61×#16112
C61×#16092
C61×#15062
C61×#15002
C61×#14702
#1844261