Finite Group Databasebeta

← C61×#25179 #29528612

Subgroups — C61×#25179 #29528612

Order 15616.

1206 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#460C211yesmaximal, characteristic, complemented
2C2×C61×#449C211yesmaximal, characteristic, complemented
3C2×C61×#449C211yesmaximal, characteristic, complemented
4C2×C61×#440C211yesmaximal, characteristic, complemented
5C61×#2428C211yesmaximal, characteristic, complemented
6C61×#2341C211yesmaximal, characteristic, complemented
7C61×#2067C211yesmaximal, characteristic, complemented
8C61×#2034C211yesmaximal, characteristic, complemented
9C61×#2033C211yesmaximal, characteristic, complemented
10C61×#2011C211yesmaximal, characteristic, complemented
11C61×#1972C211yesmaximal, characteristic, complemented
12C61×#1924C211yesmaximal, characteristic, complemented
13C61×#1880C211yesmaximal, characteristic, complemented
14C61×#1879C211yesmaximal, characteristic, complemented
15C61×#1865C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic
19C22×D8×C61C2211yescharacteristic
20C22×D8×C61C2211yescharacteristic
21C2×#127×C61C2211yescharacteristic
22C2×#121×C61—21no—
23C2×#121×C61C2211yescharacteristic
24C2×#121×C61C2211yescharacteristic
25C2×C4×Q8×C61C2211yescharacteristic
26C2×C4×Q8×C61C2211yescharacteristic
27C2×C4×D4×C61C2211yescharacteristic
28C61×#460—24no—
29C61×#449—24no—
30C61×#449—24no—
31C61×#440—24no—
32C2×#107×C61C2211yescharacteristic
33C2×#106×C61C2211yescharacteristic
34C2×C4⋊C8×C61C2211yescharacteristic
35C2×#103×C61C2211yescharacteristic
36C2×#103×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×C22⋊C8×C61C2211yescharacteristic
44C2×C22⋊C8×C61C2211yescharacteristic
45C2×#97×C61C2211yescharacteristic
46C61×#394—21no—
47C61×#392—21no—
48C61×#390—21no—
49C61×#390—21no—
50C61×#390C2211yescharacteristic
51C61×#390C2211yescharacteristic
52C61×#390C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#386—21no—
55C61×#380—21no—
56C61×#380C2211yescharacteristic
57C4×C22⋊C4×C61—21no—
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C2×#41×C61—22no—
64C2×#41×C61—22no—
65C2×#41×C61—22no—
66C2×#41×C61—22no—
67C2×#41×C61—41no—
68C2×#41×C61—41no—
69C22×Q8×C61C2311yescharacteristic
70C22×D4×C61—21no—
71C22×D4×C61—21no—
72C22×D4×C61—21no—
73C22×D4×C61—21no—
74C22×D4×C61—21no—
75C22×D4×C61C2311yescharacteristic
76C22×D4×C61C2311yescharacteristic
77C22×D4×C61C2311yescharacteristic
78C23×C4×C61—21no—
79C23×C4×C61—21no—
80C23×C4×C61C2311yescharacteristic
81C2×SD16×C61—22no—
82C2×SD16×C61—22no—
83C2×SD16×C61—22no—
84C2×SD16×C61—22no—
85C2×SD16×C61—22no—
86C2×SD16×C61D414yescomplemented
87C2×D8×C61—22no—
88C2×D8×C61—22no—
89C2×D8×C61—22no—
90C2×D8×C61—22no—
91C2×D8×C61—41no—
92C2×D8×C61—41no—
93C22×C8×C61C2311yescharacteristic
94C22×C8×C61C2311yescharacteristic
95C22×C8×C61C2311yescharacteristic
96C22×C8×C61C2311yescharacteristic
97#127×C61—22no—
98#127×C61—41no—
99#121×C61—22no—
100#121×C61—22no—
101#121×C61—44no—
102#121×C61—41no—
103#121×C61—41no—
104C4×Q8×C61—22no—
105C4×Q8×C61—22no—
106C4×Q8×C61—41no—
107C4×Q8×C61—41no—
108C4×D4×C61—22no—
109C4×D4×C61—41no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61D411yescharacteristic
128C2×C22⋊C4×C61D411yescharacteristic
129C2×C42×C61—21no—
130C2×C42×C61—21no—
131C2×C42×C61C2311yescharacteristic
132C2×C42×C61C2311yescharacteristic
133#107×C61—22no—
134#106×C61—41no—
135C4⋊C8×C61—22no—
136#103×C61—22no—
137#103×C61D414yescomplemented
138#102×C61—22no—
139#102×C61—22no—
140#102×C61—22no—
141#102×C61—22no—
142#102×C61—22no—
143#102×C61—41no—
144C22⋊C8×C61—22no—
145C22⋊C8×C61—22no—
146#97×C61—22no—
147#95×C61—21no—
148#95×C61—21no—
149#95×C61D411yescharacteristic
150#95×C61D411yescharacteristic
151C24×C61—21no—
152C24×C61—21no—
153C24×C61—21no—
154C24×C61C2×D411yescharacteristic
155#41×C61—44no—
156#41×C61—44no—
157#41×C61—44no—
158#41×C61—44no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61C2×D412yes—
163C2×Q8×C61C2×D412yes—
164C2×Q8×C61#4112yes—
165C2×D4×C61—24no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—42no—
183C2×D4×C61—42no—
184C2×D4×C61—42no—
185C2×D4×C61—42no—
186C2×D4×C61—42no—
187C2×D4×C61—42no—
188C2×D4×C61—42no—
189C2×D4×C61—42no—
190C2×D4×C61—42no—
191C2×D4×C61—42no—
192C2×D4×C61—81no—
193C2×D4×C61—81no—
194C2×D4×C61—81no—
195C2×D4×C61—81no—
196C2×D4×C61C2×D412yes—
197C2×D4×C61#4112yes—
198C22×C4×C61—21no—
199C22×C4×C61—24no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—42no—
211C22×C4×C61—42no—
212C22×C4×C61—42no—
213C22×C4×C61—42no—
214C22×C4×C61—81no—
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2411yescharacteristic
221SD16×C61—28no—
222SD16×C61—44no—
223D8×C61—44no—
224D8×C61—44no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61C2×D412yes—
236C2×C8×C61C2×D412yes—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—42no—
245C4⋊C4×C61—42no—
246C4⋊C4×C61—42no—
247C4⋊C4×C61C2×D412yes—
248C22⋊C4×C61—22no—
249C22⋊C4×C61—41no—
250C22⋊C4×C61—42no—
251C22⋊C4×C61—42no—
252C22⋊C4×C61—42no—
253C22⋊C4×C61—42no—
254C22⋊C4×C61—42no—
255C22⋊C4×C61—42no—
256C22⋊C4×C61—81no—
257C22⋊C4×C61—81no—
258C22⋊C4×C61—81no—
259C22⋊C4×C61—81no—
260C42×C61—21no—
261C42×C61—21no—
262C42×C61—21no—
263C42×C61—21no—
264C42×C61—42no—
265C42×C61—42no—
266C23×C61—21no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61C22×D411yescharacteristic
295Q8×C61—22no—
296Q8×C61—22no—
297Q8×C61—22no—
298Q8×C61#12114yescomplemented
299D4×C61—22no—
300D4×C61—22no—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—48no—
304D4×C61—41no—
305D4×C61—41no—
306D4×C61—41no—
307D4×C61—41no—
308D4×C61—41no—
309D4×C61—41no—
310D4×C61—41no—
311D4×C61—41no—
312D4×C61—84no—
313D4×C61—84no—
314D4×C61—84no—
315D4×C61—84no—
316C2×C4×C61—22no—
317C2×C4×C61—21no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—22no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—48no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—84no—
351C2×C4×C61AGL(1,ℤ/8)12yes—
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C2×#4111yescharacteristic
355C2×C4×C61C2×#4111yescharacteristic
356C2×C4×C61H(5,𝔽2)11yescharacteristic
357C2×C4×C61H(5,𝔽2)11yescharacteristic
358C8×C61—22no—
359C8×C61—22no—
360C8×C61—41no—
361C8×C61—41no—
362#25179C6111yesmaximal, characteristic, direct product factor, Sylow
363C22×C61—41no—
364C22×C61—42no—
365C22×C61—41no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—41no—
369C22×C61—42no—
370C22×C61—41no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—81no—
377C22×C61—81no—
378C22×C61—81no—
379C22×C61—81no—
380C22×C61—81no—
381C22×C61—81no—
382C22×C61—81no—
383C22×C61—81no—
384C22×C61—81no—
385C22×C61—81no—
386C22×C61—81no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61—81no—
391C22×C61#52511yescharacteristic
392C22×C61D4211yescharacteristic
393C22×C61D4211yescharacteristic
394C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C61#57511yescharacteristic
396C22×C61#57611yescharacteristic
397C22×C61#57711yescharacteristic
398C4×C61—24no—
399C4×C61—22no—
400C4×C61—41no—
401C4×C61—41no—
402C4×C61—41no—
403C4×C61—41no—
404C4×C61—42no—
405C4×C61—81no—
406C4×C61—81no—
407C4×C61—81no—
408C4×C61C2×#12111yescharacteristic
409C4×C61#53811yescharacteristic
410C4×C61#54611yescharacteristic
411C4×C61#54611yescharacteristic
412C2×#460C2×C6111yescharacteristic, complemented
413C2×#449C2×C6111yescharacteristic, complemented
414C2×#449C2×C6111yescharacteristic, complemented
415C2×#440C2×C6111yescharacteristic, complemented
416#2428C2×C6111yescharacteristic, complemented
417#2341C2×C6111yescharacteristic, complemented
418#2067C2×C6111yescharacteristic, complemented
419#2034C2×C6111yescharacteristic, complemented
420#2033C2×C6111yescharacteristic, complemented
421#2011C2×C6111yescharacteristic, complemented
422#1972C2×C6111yescharacteristic, complemented
423#1924C2×C6111yescharacteristic, complemented
424#1880C2×C6111yescharacteristic, complemented
425#1879C2×C6111yescharacteristic, complemented
426#1865C2×C6111yescharacteristic, complemented
427C2×C61—81no—
428C2×C61—82no—
429C2×C61—82no—
430C2×C61—161no—
431C2×C61#242411yescharacteristic
432C2×C61#311511yescharacteristic
433C2×C61#311911yescharacteristic
434C2×C61#326511yescharacteristic
435C2×C61#326811yescharacteristic
436C2×C61#327111yescharacteristic
437C2×C61#327411yescharacteristic
438C22×#41C22×C6111yescharacteristic
439C22×SD16C22×C6111yescharacteristic
440C22×SD16C22×C6111yescharacteristic
441C22×D8C22×C6111yescharacteristic
442C22×D8C22×C6111yescharacteristic
443C2×#127C22×C6111yescharacteristic
444C2×#121—21no—
445C2×#121C22×C6111yescharacteristic
446C2×#121C22×C6111yescharacteristic
447C2×C4×Q8C22×C6111yescharacteristic
448C2×C4×Q8C22×C6111yescharacteristic
449C2×C4×D4C22×C6111yescharacteristic
450#460—24no—
451#449—24no—
452#449—24no—
453#440—24no—
454C2×#107C22×C6111yescharacteristic
455C2×#106C22×C6111yescharacteristic
456C2×C4⋊C8C22×C6111yescharacteristic
457C2×#103C22×C6111yescharacteristic
458C2×#103C22×C6111yescharacteristic
459C2×#102C22×C6111yescharacteristic
460C2×#102C22×C6111yescharacteristic
461C2×#102C22×C6111yescharacteristic
462C2×#102C22×C6111yescharacteristic
463C2×#102C22×C6111yescharacteristic
464C2×#102C22×C6111yescharacteristic
465C2×C22⋊C8C22×C6111yescharacteristic
466C2×C22⋊C8C22×C6111yescharacteristic
467C2×#97C22×C6111yescharacteristic
468#394—21no—
469#392—21no—
470#390—21no—
471#390—21no—
472#390C22×C6111yescharacteristic
473#390C22×C6111yescharacteristic
474#390C22×C6111yescharacteristic
475#389C22×C6111yescharacteristic
476#386—21no—
477#380—21no—
478#380C22×C6111yescharacteristic
479C4×C22⋊C4—21no—
480C4×C22⋊C4C22×C6111yescharacteristic
481#340C22×C6111yescharacteristic
482#340C22×C6111yescharacteristic
483#336C22×C6111yescharacteristic
484#336C22×C6111yescharacteristic
485C61#2517911yescharacteristic, direct product factor, Sylow
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—41no—
491C2×#41—41no—
492C22×Q8C23×C6111yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C23×C6111yescharacteristic
499C22×D4C23×C6111yescharacteristic
500C22×D4C23×C6111yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C23×C6111yescharacteristic
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16D4×C6114yescomplemented
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—41no—
515C2×D8—41no—
516C22×C8C23×C6111yescharacteristic
517C22×C8C23×C6111yescharacteristic
518C22×C8C23×C6111yescharacteristic
519C22×C8C23×C6111yescharacteristic
520#127—22no—
521#127—41no—
522#121—22no—
523#121—22no—
524#121—44no—
525#121—41no—
526#121—41no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—41no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4C23×C6111yescharacteristic
537C2×C4⋊C4C23×C6111yescharacteristic
538C2×C4⋊C4C23×C6111yescharacteristic
539C2×C4⋊C4C23×C6111yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C6111yescharacteristic
551C2×C22⋊C4D4×C6111yescharacteristic
552C2×C42—21no—
553C2×C42—21no—
554C2×C42C23×C6111yescharacteristic
555C2×C42C23×C6111yescharacteristic
556#107—22no—
557#106—41no—
558C4⋊C8—22no—
559#103—22no—
560#103D4×C6114yescomplemented
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569#97—22no—
570#95—21no—
571#95—21no—
572#95D4×C6111yescharacteristic
573#95D4×C6111yescharacteristic
574C24—21no—
575C24—21no—
576C24—21no—
577C24C2×D4×C6111yescharacteristic
578#41—44no—
579#41—44no—
580#41—44no—
581#41—44no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C6112yes—
586C2×Q8C2×D4×C6112yes—
587C2×Q8#41×C6112yes—
588C2×D4—24no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C6112yes—
620C2×D4#41×C6112yes—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4C2×D4×C6111yescharacteristic
639C22×C4C2×D4×C6111yescharacteristic
640C22×C4C2×D4×C6111yescharacteristic
641C22×C4C2×D4×C6111yescharacteristic
642C22×C4C2×D4×C6111yescharacteristic
643C22×C4C24×C6111yescharacteristic
644SD16—28no—
645SD16—44no—
646D8—44no—
647D8—44no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8C2×D4×C6112yes—
659C2×C8C2×D4×C6112yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C2×D4×C6112yes—
671C22⋊C4—22no—
672C22⋊C4—41no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—42no—
688C42—42no—
689C23—22no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—22no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23C22×D4×C6111yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8#121×C6114yescomplemented
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—48no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—84no—
736D4—84no—
737D4—84no—
738D4—84no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—48no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4AGL(1,ℤ/8)×C6112yes—
775C2×C4C22×D4×C6111yescharacteristic
776C2×C4C22×D4×C6111yescharacteristic
777C2×C4C2×#41×C6111yescharacteristic
778C2×C4C2×#41×C6111yescharacteristic
779C2×C4H(5,𝔽2)×C6111yescharacteristic
780C2×C4H(5,𝔽2)×C6111yescharacteristic
781C8—22no—
782C8—22no—
783C8—41no—
784C8—41no—
785C22—41no—
786C22—42no—
787C22—41no—
788C22—42no—
789C22—42no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—42no—
794C22—42no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22C61×#52511yescharacteristic
814C22D42×C6111yescharacteristic
815C22D42×C6111yescharacteristic
816C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
817C22C61×#57511yescharacteristic
818C22C61×#57611yescharacteristic
819C22C61×#57711yescharacteristic
820C4—24no—
821C4—22no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4C2×#121×C6111yescharacteristic
831C4C61×#53811yescharacteristic
832C4C61×#54611yescharacteristic
833C4C61×#54611yescharacteristic
834C2—81no—
835C2—82no—
836C2—82no—
837C2—161no—
838C2C61×#242411yescharacteristic
839C2C61×#311511yescharacteristic
840C2C61×#311911yescharacteristic
841C2C61×#326511yescharacteristic
842C2C61×#326811yescharacteristic
843C2C61×#327111yescharacteristic
844C2C61×#327411yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
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×#460C2semidirect
2. C2×C61×#449C2semidirect
3. C2×C61×#449C2semidirect
4. C2×C61×#440C2semidirect
5. C61×#2428C2semidirect
6. C61×#2341C2semidirect
7. C61×#2067C2semidirect
8. C61×#2034C2semidirect
9. C61×#2033C2semidirect
10. C61×#2011C2semidirect
11. C61×#1972C2semidirect
12. C61×#1924C2semidirect
13. C61×#1880C2semidirect
14. C61×#1879C2semidirect
15. C61×#1865C2semidirect
86. C2×SD16×C61D4semidirect
137. #103×C61D4semidirect
298. Q8×C61#121semidirect
362. #25179C61direct (N × H)
412. C2×#460C2×C61semidirect
413. C2×#449C2×C61semidirect
414. C2×#449C2×C61semidirect
415. C2×#440C2×C61semidirect
416. #2428C2×C61semidirect
417. #2341C2×C61semidirect
418. #2067C2×C61semidirect
419. #2034C2×C61semidirect
420. #2033C2×C61semidirect
421. #2011C2×C61semidirect
422. #1972C2×C61semidirect
423. #1924C2×C61semidirect
424. #1880C2×C61semidirect
425. #1879C2×C61semidirect
426. #1865C2×C61semidirect
485. C61#25179direct (N × H)
509. C2×SD16D4×C61semidirect
560. #103D4×C61semidirect
721. Q8#121×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4602
C2×C61×#4492
C2×C61×#4402
C61×#24282
C61×#23412
C61×#20672
C61×#20342
C61×#20332
C61×#20112
C61×#19722
C61×#19242
C61×#18802
C61×#18792
C61×#18652
#2517961