Finite Group Databasebeta

← C61×#22582 #29526015

Subgroups — C61×#22582 #29526015

Order 15616.

1038 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#417C211yesmaximal, characteristic
2C61×#2344C211yesmaximal, characteristic, complemented
3C61×#2339C211yesmaximal, characteristic
4C61×#1935C211yesmaximal, characteristic, complemented
5C61×#1933C211yesmaximal, characteristic, complemented
6C61×#1928C211yesmaximal, characteristic, complemented
7C61×#1927C211yesmaximal, characteristic, complemented
8C61×#1864C211yesmaximal, characteristic, complemented
9C61×#1862C211yesmaximal, characteristic, complemented
10C61×#1824C211yesmaximal, characteristic, complemented
11C61×#1809C211yesmaximal, characteristic, complemented
12C61×#1788C211yesmaximal, characteristic
13C61×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C61C211yesmaximal, characteristic, complemented
15C61×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×M16×C61C2211yescharacteristic
18C2×C4×D4×C61C2211yescharacteristic
19C2×C4×D4×C61C2211yescharacteristic
20C2×#117×C61—21no—
21C22×C4⋊C4×C61C2211yescharacteristic
22C2×#107×C61C2211yescharacteristic
23C2×#106×C61C2211yescharacteristic
24C61×#417C418yescomplemented
25C2×#103×C61C2211yescharacteristic
26C2×#103×C61C2211yescharacteristic
27C2×#103×C61C2211yescharacteristic
28C2×#103×C61C2211yescharacteristic
29C2×#102×C61C2211yescharacteristic
30C2×#102×C61C2211yescharacteristic
31C2×#102×C61C2211yescharacteristic
32C2×#102×C61C2211yescharacteristic
33C2×C22⋊C8×C61C2211yescharacteristic
34C2×#97×C61C2211yescharacteristic
35C2×C4×C8×C61C2211yescharacteristic
36C61×#391C2211yescharacteristic
37C61×#391C2211yescharacteristic
38C61×#389C2211yescharacteristic
39C61×#389C2211yescharacteristic
40C61×#387—21no—
41C61×#387—21no—
42C61×#386—21no—
43C61×#386—21no—
44C61×#381—21no—
45C61×#381—21no—
46C61×#380C2211yescharacteristic
47C61×#380C2211yescharacteristic
48C4×C4⋊C4×C61C2211yescharacteristic
49C4×C4⋊C4×C61C2211yescharacteristic
50C4×C22⋊C4×C61C2211yescharacteristic
51C2×#95×C61—21no—
52C61×#340C2211yescharacteristic
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C2×#41×C61—22no—
61C2×#41×C61—22no—
62C2×#41×C61—22no—
63C2×#41×C61—41no—
64C2×#41×C61—41no—
65C2×#41×C61C2×C414yes—
66C22×Q8×C61C2311yescharacteristic
67C22×D4×C61—21no—
68C22×D4×C61C2311yescharacteristic
69C23×C4×C61—21no—
70C23×C4×C61—21no—
71C23×C4×C61—21no—
72C23×C4×C61—21no—
73C23×C4×C61C2311yescharacteristic
74C2×M16×C61—41no—
75C2×M16×C61—41no—
76C2×M16×C61C2×C414yescomplemented
77C22×C8×C61C2311yescharacteristic
78C22×C8×C61C2311yescharacteristic
79C22×C8×C61C2311yescharacteristic
80C22×C8×C61C2311yescharacteristic
81C4×D4×C61—22no—
82C4×D4×C61—22no—
83C4×D4×C61—41no—
84C4×D4×C61—41no—
85#117×C61—44no—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61C2×C414yescomplemented
91C2×C4⋊C4×C61C2311yescharacteristic
92C2×C4⋊C4×C61C2311yescharacteristic
93C2×C4⋊C4×C61C2311yescharacteristic
94C2×C4⋊C4×C61C2311yescharacteristic
95C2×C4⋊C4×C61C2311yescharacteristic
96C2×C4⋊C4×C61C2311yescharacteristic
97C2×C22⋊C4×C61—21no—
98C2×C22⋊C4×C61—21no—
99C2×C22⋊C4×C61—21no—
100C2×C22⋊C4×C61—21no—
101C2×C22⋊C4×C61D411yescharacteristic
102C2×C22⋊C4×C61D411yescharacteristic
103C2×C42×C61—21no—
104C2×C42×C61—21no—
105C2×C42×C61C2311yescharacteristic
106C2×C42×C61C2311yescharacteristic
107#107×C61—41no—
108#106×C61—41no—
109#103×C61—41no—
110#103×C61—41no—
111#103×C61C2×C414yescomplemented
112#103×C61C2×C414yescomplemented
113#102×C61—22no—
114#102×C61—22no—
115#102×C61C2×C414yes—
116#102×C61C2×C414yes—
117C22⋊C8×C61—22no—
118#97×C61—41no—
119C4×C8×C61—41no—
120#95×C61—21no—
121#95×C61—21no—
122#95×C61—21no—
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×C61D411yescharacteristic
131#95×C61D411yescharacteristic
132C24×C61—21no—
133C24×C61C2×D411yescharacteristic
134#41×C61—28no—
135#41×C61—44no—
136#41×C61—44no—
137#41×C61—44no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61C22×C412yes—
144C2×D4×C61—24no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—42no—
149C2×D4×C61—42no—
150C2×D4×C61C22×C412yes—
151C2×D4×C61#4112yes—
152C2×D4×C61#4112yes—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—24no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—24no—
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—42no—
171C22×C4×C61—42no—
172C22×C4×C61—42no—
173C22×C4×C61—42no—
174C22×C4×C61—81no—
175C22×C4×C61—81no—
176C22×C4×C61C22×C412yes—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61#4112yes—
183C22×C4×C61C2411yescharacteristic
184M16×C61—44no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61C22×C412yes—
196C2×C8×C61C22×C412yes—
197C4⋊C4×C61—24no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61—42no—
210C4⋊C4×C61C22×C412yes—
211C4⋊C4×C61C22×C412yes—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—41no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—81no—
218C42×C61—21no—
219C42×C61—21no—
220C42×C61—21no—
221C42×C61—21no—
222C42×C61—42no—
223C42×C61—42no—
224C23×C61—22no—
225C23×C61—22no—
226C23×C61—22no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61C4×D412yes—
238C23×C61C22×D411yescharacteristic
239Q8×C61—22no—
240Q8×C61—22no—
241Q8×C61—41no—
242Q8×C61—41no—
243D4×C61—22no—
244D4×C61—22no—
245D4×C61—22no—
246D4×C61—48no—
247D4×C61#11714yescomplemented
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—22no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—48no—
269C2×C4×C61—48no—
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—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—84no—
289C2×C4×C61—84no—
290C2×C4×C61C4×D412yes—
291C2×C4×C61AGL(1,ℤ/8)12yes—
292C2×C4×C61C23×C411yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61H(5,𝔽2)11yescharacteristic
297C2×C4×C61H(5,𝔽2)11yescharacteristic
298C8×C61—22no—
299C8×C61—22no—
300C8×C61—41no—
301C8×C61—41no—
302#22582C6111yesmaximal, characteristic, direct product factor, Sylow
303C22×C61—22no—
304C22×C61—24no—
305C22×C61—22no—
306C22×C61—22no—
307C22×C61—41no—
308C22×C61—42no—
309C22×C61—42no—
310C22×C61—42no—
311C22×C61—42no—
312C22×C61—41no—
313C22×C61—41no—
314C22×C61—42no—
315C22×C61—42no—
316C22×C61—41no—
317C22×C61C2×C4×D411yescharacteristic
318C22×C61#54611yescharacteristic
319C22×C61#54611yescharacteristic
320C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C61#57511yescharacteristic
322C22×C61#57711yescharacteristic
323C22×C61#57811yescharacteristic
324C4×C61—22no—
325C4×C61—22no—
326C4×C61—41no—
327C4×C61—42no—
328C4×C61—42no—
329C4×C61—42no—
330C4×C61—41no—
331C4×C61—41no—
332C4×C61—81no—
333C4×C61—81no—
334C4×C61—81no—
335C4×C61—81no—
336C4×C61C2×#11711yescharacteristic
337C4×C61#51811yescharacteristic
338C4×C61#55111yescharacteristic
339C4×C61#55111yescharacteristic
340C2×#417C2×C6111yescharacteristic
341#2344C2×C6111yescharacteristic, complemented
342#2339C2×C6111yescharacteristic
343#1935C2×C6111yescharacteristic, complemented
344#1933C2×C6111yescharacteristic, complemented
345#1928C2×C6111yescharacteristic, complemented
346#1927C2×C6111yescharacteristic, complemented
347#1864C2×C6111yescharacteristic, complemented
348#1862C2×C6111yescharacteristic, complemented
349#1824C2×C6111yescharacteristic, complemented
350#1809C2×C6111yescharacteristic, complemented
351#1788C2×C6111yescharacteristic
352#1762C2×C6111yescharacteristic, complemented
353C4×#102C2×C6111yescharacteristic, complemented
354#1753C2×C6111yescharacteristic, complemented
355C2×C61—42no—
356C2×C61—44no—
357C2×C61#234211yescharacteristic
358C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
359C2×C61#294711yescharacteristic
360C2×C61#330611yescharacteristic
361C2×C61#331511yescharacteristic
362C2×C61#332311yescharacteristic
363C2×C61#333011yescharacteristic
364C22×#41C22×C6111yescharacteristic
365C22×M16C22×C6111yescharacteristic
366C2×C4×D4C22×C6111yescharacteristic
367C2×C4×D4C22×C6111yescharacteristic
368C2×#117—21no—
369C22×C4⋊C4C22×C6111yescharacteristic
370C2×#107C22×C6111yescharacteristic
371C2×#106C22×C6111yescharacteristic
372#417C4×C6118yescomplemented
373C2×#103C22×C6111yescharacteristic
374C2×#103C22×C6111yescharacteristic
375C2×#103C22×C6111yescharacteristic
376C2×#103C22×C6111yescharacteristic
377C2×#102C22×C6111yescharacteristic
378C2×#102C22×C6111yescharacteristic
379C2×#102C22×C6111yescharacteristic
380C2×#102C22×C6111yescharacteristic
381C2×C22⋊C8C22×C6111yescharacteristic
382C2×#97C22×C6111yescharacteristic
383C2×C4×C8C22×C6111yescharacteristic
384#391C22×C6111yescharacteristic
385#391C22×C6111yescharacteristic
386#389C22×C6111yescharacteristic
387#389C22×C6111yescharacteristic
388#387—21no—
389#387—21no—
390#386—21no—
391#386—21no—
392#381—21no—
393#381—21no—
394#380C22×C6111yescharacteristic
395#380C22×C6111yescharacteristic
396C4×C4⋊C4C22×C6111yescharacteristic
397C4×C4⋊C4C22×C6111yescharacteristic
398C4×C22⋊C4C22×C6111yescharacteristic
399C2×#95—21no—
400#340C22×C6111yescharacteristic
401#340C22×C6111yescharacteristic
402#340C22×C6111yescharacteristic
403#340C22×C6111yescharacteristic
404#340C22×C6111yescharacteristic
405#340C22×C6111yescharacteristic
406#336C22×C6111yescharacteristic
407#336C22×C6111yescharacteristic
408C61#2258211yescharacteristic, direct product factor, Sylow
409C2×#41—22no—
410C2×#41—22no—
411C2×#41—22no—
412C2×#41—41no—
413C2×#41—41no—
414C2×#41C2×C4×C6114yes—
415C22×Q8C23×C6111yescharacteristic
416C22×D4—21no—
417C22×D4C23×C6111yescharacteristic
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—21no—
421C23×C4—21no—
422C23×C4C23×C6111yescharacteristic
423C2×M16—41no—
424C2×M16—41no—
425C2×M16C2×C4×C6114yescomplemented
426C22×C8C23×C6111yescharacteristic
427C22×C8C23×C6111yescharacteristic
428C22×C8C23×C6111yescharacteristic
429C22×C8C23×C6111yescharacteristic
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—41no—
433C4×D4—41no—
434#117—44no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4C2×C4×C6114yescomplemented
440C2×C4⋊C4C23×C6111yescharacteristic
441C2×C4⋊C4C23×C6111yescharacteristic
442C2×C4⋊C4C23×C6111yescharacteristic
443C2×C4⋊C4C23×C6111yescharacteristic
444C2×C4⋊C4C23×C6111yescharacteristic
445C2×C4⋊C4C23×C6111yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4D4×C6111yescharacteristic
451C2×C22⋊C4D4×C6111yescharacteristic
452C2×C42—21no—
453C2×C42—21no—
454C2×C42C23×C6111yescharacteristic
455C2×C42C23×C6111yescharacteristic
456#107—41no—
457#106—41no—
458#103—41no—
459#103—41no—
460#103C2×C4×C6114yescomplemented
461#103C2×C4×C6114yescomplemented
462#102—22no—
463#102—22no—
464#102C2×C4×C6114yes—
465#102C2×C4×C6114yes—
466C22⋊C8—22no—
467#97—41no—
468C4×C8—41no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95D4×C6111yescharacteristic
480#95D4×C6111yescharacteristic
481C24—21no—
482C24C2×D4×C6111yescharacteristic
483#41—28no—
484#41—44no—
485#41—44no—
486#41—44no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8C22×C4×C6112yes—
493C2×D4—24no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4C22×C4×C6112yes—
500C2×D4#41×C6112yes—
501C2×D4#41×C6112yes—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—24no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—24no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4C22×C4×C6112yes—
526C22×C4C2×D4×C6111yescharacteristic
527C22×C4C2×D4×C6111yescharacteristic
528C22×C4C2×D4×C6111yescharacteristic
529C22×C4C2×D4×C6111yescharacteristic
530C22×C4C2×D4×C6111yescharacteristic
531C22×C4#41×C6112yes—
532C22×C4C24×C6111yescharacteristic
533M16—44no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8C22×C4×C6112yes—
545C2×C8C22×C4×C6112yes—
546C4⋊C4—24no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4C22×C4×C6112yes—
560C4⋊C4C22×C4×C6112yes—
561C22⋊C4—22no—
562C22⋊C4—41no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—81no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C42—42no—
573C23—22no—
574C23—22no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—22no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23C4×D4×C6112yes—
587C23C22×D4×C6111yescharacteristic
588Q8—22no—
589Q8—22no—
590Q8—41no—
591Q8—41no—
592D4—22no—
593D4—22no—
594D4—22no—
595D4—48no—
596D4#117×C6114yescomplemented
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—48no—
618C2×C4—48no—
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—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—84no—
638C2×C4—84no—
639C2×C4C4×D4×C6112yes—
640C2×C4AGL(1,ℤ/8)×C6112yes—
641C2×C4C23×C4×C6111yescharacteristic
642C2×C4C2×#41×C6111yescharacteristic
643C2×C4C2×#41×C6111yescharacteristic
644C2×C4C2×#41×C6111yescharacteristic
645C2×C4H(5,𝔽2)×C6111yescharacteristic
646C2×C4H(5,𝔽2)×C6111yescharacteristic
647C8—22no—
648C8—22no—
649C8—41no—
650C8—41no—
651C22—22no—
652C22—24no—
653C22—22no—
654C22—22no—
655C22—42no—
656C22—41no—
657C22—41no—
658C22—42no—
659C22—42no—
660C22—41no—
661C22—41no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22C2×C4×D4×C6111yescharacteristic
666C22C61×#54611yescharacteristic
667C22C61×#54611yescharacteristic
668C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
669C22C61×#57511yescharacteristic
670C22C61×#57711yescharacteristic
671C22C61×#57811yescharacteristic
672C4—22no—
673C4—22no—
674C4—41no—
675C4—41no—
676C4—41no—
677C4—42no—
678C4—42no—
679C4—42no—
680C4—81no—
681C4—81no—
682C4—81no—
683C4—81no—
684C4C2×#117×C6111yescharacteristic
685C4C61×#51811yescharacteristic
686C4C61×#55111yescharacteristic
687C4C61×#55111yescharacteristic
688C2—42no—
689C2—44no—
690C2C61×#234211yescharacteristic
691C2C4×AGL(1,ℤ/8)×C6111yescharacteristic
692C2C61×#294711yescharacteristic
693C2C61×#330611yescharacteristic
694C2C61×#331511yescharacteristic
695C2C61×#332311yescharacteristic
696C2C61×#333011yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutatorC2×C4C23×C4×C61
Frattini, cosocleC22×C4C24×C61
prime radicalC22×#41×C61C22
LCSG ▷ C2×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
2. C61×#2344C2semidirect
4. C61×#1935C2semidirect
5. C61×#1933C2semidirect
6. C61×#1928C2semidirect
7. C61×#1927C2semidirect
8. C61×#1864C2semidirect
9. C61×#1862C2semidirect
10. C61×#1824C2semidirect
11. C61×#1809C2semidirect
13. C61×#1762C2semidirect
14. C4×#102×C61C2semidirect
15. C61×#1753C2semidirect
24. C61×#417C4semidirect
76. C2×M16×C61C2×C4semidirect
90. C2×C4⋊C4×C61C2×C4semidirect
111. #103×C61C2×C4semidirect
112. #103×C61C2×C4semidirect
247. D4×C61#117semidirect
302. #22582C61direct (N × H)
341. #2344C2×C61semidirect
343. #1935C2×C61semidirect
344. #1933C2×C61semidirect
345. #1928C2×C61semidirect
346. #1927C2×C61semidirect
347. #1864C2×C61semidirect
348. #1862C2×C61semidirect
349. #1824C2×C61semidirect
350. #1809C2×C61semidirect
352. #1762C2×C61semidirect
353. C4×#102C2×C61semidirect
354. #1753C2×C61semidirect
372. #417C4×C61semidirect
408. C61#22582direct (N × H)
425. C2×M16C2×C4×C61semidirect
439. C2×C4⋊C4C2×C4×C61semidirect
460. #103C2×C4×C61semidirect
461. #103C2×C4×C61semidirect
596. D4#117×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4172
C61×#23442
C61×#23392
C61×#19352
C61×#19332
C61×#19282
C61×#19272
C61×#18642
C61×#18622
C61×#18242
C61×#18092
C61×#17882
C61×#17622
C4×#102×C612
C61×#17532
#2258261