Finite Group Databasebeta

← C61×#26786 #29530219

Subgroups — C61×#26786 #29530219

Order 15616.

904 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#483C211yesmaximal, characteristic, complemented
2C2×C61×#476C211yesmaximal, characteristic, complemented
3C61×#2492C211yesmaximal, characteristic, complemented
4C61×#2361C211yesmaximal, characteristic
5C61×#2066C211yesmaximal, characteristic, complemented
6C61×#2058C211yesmaximal, characteristic, complemented
7C61×#2034C211yesmaximal, characteristic
8C61×#2000C211yesmaximal, characteristic
9C61×#1968C211yesmaximal, characteristic, complemented
10C61×#1927C211yesmaximal, characteristic, complemented
11C61×#1926C211yesmaximal, characteristic, complemented
12C61×#1923C211yesmaximal, characteristic, complemented
13C61×#1877C211yesmaximal, characteristic, complemented
14C61×#1853C211yesmaximal, characteristic, complemented
15C4×#106×C61C211yesmaximal, characteristic, complemented
16C22×SD16×C61C2211yescharacteristic
17C2×C4⋊Q8×C61C2211yescharacteristic
18C2×C22⋊Q8×C61C2211yescharacteristic
19C2×#121×C61C2211yescharacteristic
20C2×C4×D4×C61—21no—
21C2×C4×D4×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C61×#483—24no—
24C61×#476—24no—
25C2×#106×C61C2211yescharacteristic
26C2×#106×C61C2211yescharacteristic
27C2×#106×C61C2211yescharacteristic
28C2×#106×C61C2211yescharacteristic
29C2×#106×C61C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C2×#103×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×#102×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C2×C4×C8×C61C2211yescharacteristic
40C61×#400—21no—
41C61×#393—21no—
42C61×#391—21no—
43C61×#391C2211yescharacteristic
44C61×#391C2211yescharacteristic
45C61×#390C2211yescharacteristic
46C61×#389C2211yescharacteristic
47C61×#388—21no—
48C61×#388—21no—
49C61×#386—21no—
50C61×#385—21no—
51C61×#380C2211yescharacteristic
52C4×C4⋊C4×C61C2211yescharacteristic
53C4×C4⋊C4×C61C2211yescharacteristic
54C4×C22⋊C4×C61C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Q8×C61—21no—
62C22×Q8×C61C2311yescharacteristic
63C22×D4×C61—21no—
64C22×D4×C61C2311yescharacteristic
65C23×C4×C61—21no—
66C23×C4×C61—21no—
67C23×C4×C61C2311yescharacteristic
68C2×SD16×C61—22no—
69C2×SD16×C61—22no—
70C2×SD16×C61—41no—
71C22×C8×C61C2311yescharacteristic
72C22×C8×C61C2311yescharacteristic
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75C4⋊Q8×C61—22no—
76C4⋊Q8×C61—41no—
77C22⋊Q8×C61—22no—
78C22⋊Q8×C61—41no—
79#121×C61—22no—
80#121×C61—22no—
81C4×D4×C61—22no—
82C4×D4×C61—41no—
83C4×D4×C61—44no—
84C2×C4⋊C4×C61—22no—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—41no—
90C2×C4⋊C4×C61C2311yescharacteristic
91C2×C4⋊C4×C61C2311yescharacteristic
92C2×C4⋊C4×C61C2311yescharacteristic
93C2×C4⋊C4×C61C2311yescharacteristic
94C2×C4⋊C4×C61C2311yescharacteristic
95C2×C4⋊C4×C61C2311yescharacteristic
96C2×C22⋊C4×C61—21no—
97C2×C22⋊C4×C61—21no—
98C2×C22⋊C4×C61—21no—
99C2×C22⋊C4×C61—21no—
100C2×C22⋊C4×C61—21no—
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61D411yescharacteristic
103C2×C22⋊C4×C61D411yescharacteristic
104C2×C42×C61—21no—
105C2×C42×C61—21no—
106C2×C42×C61C2311yescharacteristic
107C2×C42×C61C2311yescharacteristic
108#106×C61—22no—
109#106×C61—22no—
110#106×C61—22no—
111#106×C61—41no—
112#106×C61D414yescomplemented
113C4⋊C8×C61—22no—
114#103×C61—22no—
115#103×C61—22no—
116#103×C61—22no—
117#102×C61—22no—
118#102×C61—22no—
119#102×C61—22no—
120C22⋊C8×C61—22no—
121C22⋊C8×C61—22no—
122C4×C8×C61—22no—
123#95×C61—21no—
124#95×C61—21no—
125#95×C61—21no—
126#95×C61—21no—
127#95×C61—21no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61D411yescharacteristic
132#95×C61D411yescharacteristic
133C24×C61—21no—
134C24×C61C2×D411yescharacteristic
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61—21no—
141C2×Q8×C61—42no—
142C2×Q8×C61—42no—
143C2×Q8×C61—81no—
144C2×D4×C61—24no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—42no—
151C2×D4×C61—42no—
152C2×D4×C61#4112yes—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—42no—
167C22×C4×C61—42no—
168C22×C4×C61—42no—
169C22×C4×C61—42no—
170C22×C4×C61—81no—
171C22×C4×C61—81no—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2411yescharacteristic
178SD16×C61—44no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61C2×D412yes—
190C2×C8×C61#4112yes—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—42no—
201C4⋊C4×C61—42no—
202C4⋊C4×C61—42no—
203C4⋊C4×C61—42no—
204C4⋊C4×C61C2×D412yes—
205C4⋊C4×C61C2×D412yes—
206C4⋊C4×C61#4112yes—
207C22⋊C4×C61—24no—
208C22⋊C4×C61—41no—
209C22⋊C4×C61—42no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—42no—
212C22⋊C4×C61—81no—
213C22⋊C4×C61—81no—
214C22⋊C4×C61SD1614yescomplemented
215C42×C61—21no—
216C42×C61—21no—
217C42×C61—21no—
218C42×C61—21no—
219C42×C61—42no—
220C42×C61—81no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—22no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61C2×SD1612yes—
235C23×C61C22×D411yescharacteristic
236Q8×C61—41no—
237Q8×C61—41no—
238Q8×C61—41no—
239Q8×C61—41no—
240Q8×C61—84no—
241D4×C61—22no—
242D4×C61—22no—
243D4×C61—48no—
244D4×C61—41no—
245D4×C61—41no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—22no—
252C2×C4×C61—21no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—84no—
285C2×C4×C61—84no—
286C2×C4×C61C2×SD1612yes—
287C2×C4×C61C2×SD1612yes—
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61H(5,𝔽2)11yescharacteristic
293C2×C4×C612−1+411yescharacteristic
294C8×C61—22no—
295C8×C61—22no—
296C8×C61—41no—
297C8×C61—41no—
298#26786C6111yesmaximal, characteristic, direct product factor, Sylow
299C22×C61—22no—
300C22×C61—22no—
301C22×C61—22no—
302C22×C61—41no—
303C22×C61—41no—
304C22×C61—41no—
305C22×C61—41no—
306C22×C61—42no—
307C22×C61—42no—
308C22×C61—42no—
309C22×C61—81no—
310C22×C61—81no—
311C22×C61—81no—
312C22×C61—81no—
313C22×C61#52511yescharacteristic
314C22×C61D4211yescharacteristic
315C22×C61#54711yescharacteristic
316C22×C61C22×SD1611yescharacteristic
317C22×C61#57511yescharacteristic
318C22×C61#57711yescharacteristic
319C22×C61#57711yescharacteristic
320C4×C61—22no—
321C4×C61—22no—
322C4×C61—41no—
323C4×C61—42no—
324C4×C61—41no—
325C4×C61—41no—
326C4×C61—42no—
327C4×C61—42no—
328C4×C61—81no—
329C4×C61—81no—
330C4×C61—81no—
331C4×C61—81no—
332C4×C61#53211yescharacteristic
333C4×C61#54211yescharacteristic
334C4×C61#54811yescharacteristic
335C4×C61#55111yescharacteristic
336C2×#483C2×C6111yescharacteristic, complemented
337C2×#476C2×C6111yescharacteristic, complemented
338#2492C2×C6111yescharacteristic, complemented
339#2361C2×C6111yescharacteristic
340#2066C2×C6111yescharacteristic, complemented
341#2058C2×C6111yescharacteristic, complemented
342#2034C2×C6111yescharacteristic
343#2000C2×C6111yescharacteristic
344#1968C2×C6111yescharacteristic, complemented
345#1927C2×C6111yescharacteristic, complemented
346#1926C2×C6111yescharacteristic, complemented
347#1923C2×C6111yescharacteristic, complemented
348#1877C2×C6111yescharacteristic, complemented
349#1853C2×C6111yescharacteristic, complemented
350C4×#106C2×C6111yescharacteristic, complemented
351C2×C61—42no—
352C2×C61—82no—
353C2×C61#246111yescharacteristic
354C2×C61#310111yescharacteristic
355C2×C61#312511yescharacteristic
356C2×C61#327511yescharacteristic
357C2×C61D4×SD1611yescharacteristic
358C2×C61#333511yescharacteristic
359C2×C61#335011yescharacteristic
360C22×SD16C22×C6111yescharacteristic
361C2×C4⋊Q8C22×C6111yescharacteristic
362C2×C22⋊Q8C22×C6111yescharacteristic
363C2×#121C22×C6111yescharacteristic
364C2×C4×D4—21no—
365C2×C4×D4C22×C6111yescharacteristic
366C22×C4⋊C4C22×C6111yescharacteristic
367#483—24no—
368#476—24no—
369C2×#106C22×C6111yescharacteristic
370C2×#106C22×C6111yescharacteristic
371C2×#106C22×C6111yescharacteristic
372C2×#106C22×C6111yescharacteristic
373C2×#106C22×C6111yescharacteristic
374C2×C4⋊C8C22×C6111yescharacteristic
375C2×#103C22×C6111yescharacteristic
376C2×#103C22×C6111yescharacteristic
377C2×#103C22×C6111yescharacteristic
378C2×#102C22×C6111yescharacteristic
379C2×#102C22×C6111yescharacteristic
380C2×#102C22×C6111yescharacteristic
381C2×C22⋊C8C22×C6111yescharacteristic
382C2×C22⋊C8C22×C6111yescharacteristic
383C2×C4×C8C22×C6111yescharacteristic
384#400—21no—
385#393—21no—
386#391—21no—
387#391C22×C6111yescharacteristic
388#391C22×C6111yescharacteristic
389#390C22×C6111yescharacteristic
390#389C22×C6111yescharacteristic
391#388—21no—
392#388—21no—
393#386—21no—
394#385—21no—
395#380C22×C6111yescharacteristic
396C4×C4⋊C4C22×C6111yescharacteristic
397C4×C4⋊C4C22×C6111yescharacteristic
398C4×C22⋊C4C22×C6111yescharacteristic
399#340C22×C6111yescharacteristic
400#340C22×C6111yescharacteristic
401#340C22×C6111yescharacteristic
402#340C22×C6111yescharacteristic
403#336C22×C6111yescharacteristic
404#336C22×C6111yescharacteristic
405C61#2678611yescharacteristic, direct product factor, Sylow
406C22×Q8—21no—
407C22×Q8C23×C6111yescharacteristic
408C22×D4—21no—
409C22×D4C23×C6111yescharacteristic
410C23×C4—21no—
411C23×C4—21no—
412C23×C4C23×C6111yescharacteristic
413C2×SD16—22no—
414C2×SD16—22no—
415C2×SD16—41no—
416C22×C8C23×C6111yescharacteristic
417C22×C8C23×C6111yescharacteristic
418C22×C8C23×C6111yescharacteristic
419C22×C8C23×C6111yescharacteristic
420C4⋊Q8—22no—
421C4⋊Q8—41no—
422C22⋊Q8—22no—
423C22⋊Q8—41no—
424#121—22no—
425#121—22no—
426C4×D4—22no—
427C4×D4—41no—
428C4×D4—44no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4C23×C6111yescharacteristic
436C2×C4⋊C4C23×C6111yescharacteristic
437C2×C4⋊C4C23×C6111yescharacteristic
438C2×C4⋊C4C23×C6111yescharacteristic
439C2×C4⋊C4C23×C6111yescharacteristic
440C2×C4⋊C4C23×C6111yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4D4×C6111yescharacteristic
448C2×C22⋊C4D4×C6111yescharacteristic
449C2×C42—21no—
450C2×C42—21no—
451C2×C42C23×C6111yescharacteristic
452C2×C42C23×C6111yescharacteristic
453#106—22no—
454#106—22no—
455#106—22no—
456#106—41no—
457#106D4×C6114yescomplemented
458C4⋊C8—22no—
459#103—22no—
460#103—22no—
461#103—22no—
462#102—22no—
463#102—22no—
464#102—22no—
465C22⋊C8—22no—
466C22⋊C8—22no—
467C4×C8—22no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95D4×C6111yescharacteristic
477#95D4×C6111yescharacteristic
478C24—21no—
479C24C2×D4×C6111yescharacteristic
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—81no—
489C2×D4—24no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4#41×C6112yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—81no—
516C22×C4—81no—
517C22×C4C2×D4×C6111yescharacteristic
518C22×C4C2×D4×C6111yescharacteristic
519C22×C4C2×D4×C6111yescharacteristic
520C22×C4C2×D4×C6111yescharacteristic
521C22×C4C2×D4×C6111yescharacteristic
522C22×C4C24×C6111yescharacteristic
523SD16—44no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8C2×D4×C6112yes—
535C2×C8#41×C6112yes—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4C2×D4×C6112yes—
550C4⋊C4C2×D4×C6112yes—
551C4⋊C4#41×C6112yes—
552C22⋊C4—24no—
553C22⋊C4—41no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—81no—
558C22⋊C4—81no—
559C22⋊C4SD16×C6114yescomplemented
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—42no—
565C42—81no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23C2×SD16×C6112yes—
580C23C22×D4×C6111yescharacteristic
581Q8—41no—
582Q8—41no—
583Q8—41no—
584Q8—41no—
585Q8—84no—
586D4—22no—
587D4—22no—
588D4—48no—
589D4—41no—
590D4—41no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—84no—
630C2×C4—84no—
631C2×C4C2×SD16×C6112yes—
632C2×C4C2×SD16×C6112yes—
633C2×C4C22×D4×C6111yescharacteristic
634C2×C4C2×#41×C6111yescharacteristic
635C2×C4C2×#41×C6111yescharacteristic
636C2×C4C2×#41×C6111yescharacteristic
637C2×C4H(5,𝔽2)×C6111yescharacteristic
638C2×C42−1+4×C6111yescharacteristic
639C8—22no—
640C8—22no—
641C8—41no—
642C8—41no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22C61×#52511yescharacteristic
658C22D42×C6111yescharacteristic
659C22C61×#54711yescharacteristic
660C22C22×SD16×C6111yescharacteristic
661C22C61×#57511yescharacteristic
662C22C61×#57711yescharacteristic
663C22C61×#57711yescharacteristic
664C4—22no—
665C4—22no—
666C4—41no—
667C4—42no—
668C4—41no—
669C4—41no—
670C4—42no—
671C4—42no—
672C4—81no—
673C4—81no—
674C4—81no—
675C4—81no—
676C4C61×#53211yescharacteristic
677C4C61×#54211yescharacteristic
678C4C61×#54811yescharacteristic
679C4C61×#55111yescharacteristic
680C2—42no—
681C2—82no—
682C2C61×#246111yescharacteristic
683C2C61×#310111yescharacteristic
684C2C61×#312511yescharacteristic
685C2C61×#327511yescharacteristic
686C2D4×SD16×C6111yescharacteristic
687C2C61×#333511yescharacteristic
688C2C61×#335011yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×#121×C61C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C4×C22⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#483C2semidirect
2. C2×C61×#476C2semidirect
3. C61×#2492C2semidirect
5. C61×#2066C2semidirect
6. C61×#2058C2semidirect
9. C61×#1968C2semidirect
10. C61×#1927C2semidirect
11. C61×#1926C2semidirect
12. C61×#1923C2semidirect
13. C61×#1877C2semidirect
14. C61×#1853C2semidirect
15. C4×#106×C61C2semidirect
112. #106×C61D4semidirect
214. C22⋊C4×C61SD16semidirect
298. #26786C61direct (N × H)
336. C2×#483C2×C61semidirect
337. C2×#476C2×C61semidirect
338. #2492C2×C61semidirect
340. #2066C2×C61semidirect
341. #2058C2×C61semidirect
344. #1968C2×C61semidirect
345. #1927C2×C61semidirect
346. #1926C2×C61semidirect
347. #1923C2×C61semidirect
348. #1877C2×C61semidirect
349. #1853C2×C61semidirect
350. C4×#106C2×C61semidirect
405. C61#26786direct (N × H)
457. #106D4×C61semidirect
559. C22⋊C4SD16×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4832
C2×C61×#4762
C61×#24922
C61×#23612
C61×#20662
C61×#20582
C61×#20342
C61×#20002
C61×#19682
C61×#19272
C61×#19262
C61×#19232
C61×#18772
C61×#18532
C4×#106×C612
#2678661