Finite Group Databasebeta

← C4×C61×#471 #29524985

Subgroups — C4×C61×#471 #29524985

Order 15616.

914 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#471C211yesmaximal, characteristic
2C4×#137×C61C211yesmaximal, characteristic, complemented
3C4×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic
4C2×C4×SD16×C61C211yesmaximal, characteristic, complemented
5C4×#131×C61C211yesmaximal, characteristic, complemented
6C61×#1977C211yesmaximal, characteristic, complemented
7C61×#1951C211yesmaximal, characteristic, complemented
8C61×#1931C211yesmaximal, characteristic, complemented
9C61×#1930C211yesmaximal, characteristic, complemented
10C61×#1908C211yesmaximal, characteristic, complemented
11C61×#1907C211yesmaximal, characteristic
12C61×#1815C211yesmaximal, characteristic, complemented
13C4×#108×C61C211yesmaximal, characteristic, complemented
14C4×#101×C61C211yesmaximal, characteristic, complemented
15C4×#100×C61C211yesmaximal, characteristic, complemented
16C2×#137×C61C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic
19C2×#131×C61C2211yescharacteristic
20C2×#131×C61C2211yescharacteristic
21C4×#41×C61C2211yescharacteristic
22C2×C4×Q8×C61C2211yescharacteristic
23C2×C4×D4×C61C2211yescharacteristic
24C61×#471C418yesdirect product factor
25C61×#442—21no—
26C61×#441—21no—
27C61×#440—21no—
28C61×#440—21no—
29C4×Q16×C61—21no—
30C4×SD16×C61—21no—
31C4×SD16×C61—21no—
32C4×SD16×C61—21no—
33C4×SD16×C61—21no—
34C4×SD16×C61—21no—
35C4×SD16×C61—21no—
36C4×D8×C61—21no—
37C2×#108×C61C2211yescharacteristic
38C2×#108×C61C2211yescharacteristic
39C61×#428C2211yescharacteristic
40C61×#428C2211yescharacteristic
41C2×#106×C61C2211yescharacteristic
42C61×#419C2211yescharacteristic
43C61×#418C2211yescharacteristic
44C61×#417C2211yescharacteristic
45C61×#417C2211yescharacteristic
46C2×#103×C61C2211yescharacteristic
47C2×#102×C61C2211yescharacteristic
48C2×#101×C61C2211yescharacteristic
49C2×#101×C61C2211yescharacteristic
50C2×#100×C61C2211yescharacteristic
51C2×#100×C61C2211yescharacteristic
52C61×#405—21no—
53C61×#405—21no—
54C61×#405C2211yescharacteristic
55C61×#405C2211yescharacteristic
56C4×M16×C61—21no—
57C4×M16×C61C2211yescharacteristic
58C4×M16×C61C2211yescharacteristic
59C4×M16×C61C2211yescharacteristic
60C2×C4×C8×C61—21no—
61C2×C4×C8×C61C2211yescharacteristic
62C61×#343C2211yescharacteristic
63C61×#343C2211yescharacteristic
64C61×#343C2211yescharacteristic
65C61×#343C2211yescharacteristic
66C61×#341C2211yescharacteristic
67C61×#341C2211yescharacteristic
68C2×#41×C61C2311yescharacteristic
69C22×Q8×C61C2311yescharacteristic
70C22×D4×C61C2311yescharacteristic
71C23×C4×C61—21no—
72#137×C61—22no—
73#137×C61C2×C414yescomplemented
74AGL(1,ℤ/8)×C61—22no—
75AGL(1,ℤ/8)×C61C2×C414yes—
76C2×Q16×C61—21no—
77C2×SD16×C61—21no—
78C2×SD16×C61—21no—
79C2×SD16×C61—21no—
80C2×SD16×C61—21no—
81C2×SD16×C61—22no—
82C2×SD16×C61C2×C414yescomplemented
83C2×D8×C61—21no—
84#131×C61—22no—
85#131×C61—22no—
86#131×C61—22no—
87#131×C61C2×C414yescomplemented
88C2×M16×C61—21no—
89C2×M16×C61—21no—
90C2×M16×C61C2311yescharacteristic
91C2×M16×C61C2311yescharacteristic
92C2×M16×C61C2311yescharacteristic
93C2×M16×C61C2311yescharacteristic
94C2×M16×C61C2311yescharacteristic
95C2×M16×C61C2311yescharacteristic
96C22×C8×C61—21no—
97C22×C8×C61—21no—
98C22×C8×C61C2311yescharacteristic
99C22×C8×C61C2311yescharacteristic
100C4×Q8×C61—21no—
101C4×Q8×C61—21no—
102C4×Q8×C61—21no—
103C4×Q8×C61—21no—
104C4×Q8×C61D411yescharacteristic
105C4×Q8×C61D411yescharacteristic
106C4×D4×C61—21no—
107C4×D4×C61—21no—
108C4×D4×C61—21no—
109C4×D4×C61—21no—
110C4×D4×C61—21no—
111C4×D4×C61—21no—
112C4×D4×C61D411yescharacteristic
113C4×D4×C61D411yescharacteristic
114#117×C61—21no—
115#117×C61C2311yescharacteristic
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61—21no—
120C2×C42×C61—21no—
121C2×C42×C61—21no—
122C2×C42×C61C2311yescharacteristic
123#108×C61—22no—
124#108×C61C2×C414yescomplemented
125#107×C61—21no—
126#107×C61—21no—
127#106×C61—21no—
128#106×C61—21no—
129#106×C61—21no—
130#106×C61—21no—
131#103×C61—21no—
132#103×C61—21no—
133#103×C61—21no—
134#103×C61—21no—
135#103×C61—21no—
136#103×C61—21no—
137#102×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×C61—21no—
142#102×C61—21no—
143#101×C61—22no—
144#101×C61C2×C414yescomplemented
145#100×C61—22no—
146#100×C61C2×C414yescomplemented
147#97×C61—21no—
148#97×C61—21no—
149#97×C61—21no—
150#97×C61—21no—
151#97×C61—21no—
152C4×C8×C61—21no—
153C4×C8×C61—21no—
154C4×C8×C61—21no—
155C4×C8×C61—21no—
156C4×C8×C61—21no—
157C4×C8×C61D411yescharacteristic
158C4×C8×C61D411yescharacteristic
159C4×C8×C61D411yescharacteristic
160C4×C8×C61D411yescharacteristic
161C24×C61—21no—
162#41×C61—21no—
163#41×C61—21no—
164#41×C61C22×C412yes—
165#41×C61#4112yes—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61C22×C412yes—
172C2×Q8×C61C2×D411yescharacteristic
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×C61C22×C412yes—
180C2×D4×C61C2×D411yescharacteristic
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—41no—
188C22×C4×C61—41no—
189C22×C4×C61—82no—
190C22×C4×C61#4111yescharacteristic
191C22×C4×C61#4111yescharacteristic
192C22×C4×C61C2411yescharacteristic
193Q16×C61—24no—
194SD16×C61—24no—
195SD16×C61—24no—
196SD16×C61—24no—
197SD16×C61—24no—
198D8×C61—24no—
199M16×C61—24no—
200M16×C61—21no—
201M16×C61—21no—
202M16×C61—21no—
203M16×C61—21no—
204M16×C61—24no—
205M16×C61—21no—
206M16×C61—21no—
207M16×C61—21no—
208M16×C61—21no—
209M16×C61C22×C412yes—
210M16×C61C22×C412yes—
211M16×C61C22×C412yes—
212M16×C61#4112yes—
213C2×C8×C61—24no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—24no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61C22×C412yes—
224C2×C8×C61C2×D411yescharacteristic
225C2×C8×C61C2×D411yescharacteristic
226C2×C8×C61C2×D411yescharacteristic
227C2×C8×C61C2×D411yescharacteristic
228C2×C8×C61#4112yes—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—41no—
236C4⋊C4×C61—41no—
237C4⋊C4×C61C2×D411yescharacteristic
238C4⋊C4×C61C2×D411yescharacteristic
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C22⋊C4×C61—21no—
242C22⋊C4×C61—41no—
243C22⋊C4×C61—41no—
244C42×C61—21no—
245C42×C61—21no—
246C42×C61—21no—
247C42×C61—41no—
248C42×C61—41no—
249C42×C61C2×D411yescharacteristic
250C42×C61C2×D411yescharacteristic
251C42×C61C2×D411yescharacteristic
252C42×C61C2×D411yescharacteristic
253C23×C61—21no—
254C23×C61—22no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—81no—
258C23×C61—81no—
259C23×C61C2×#4111yescharacteristic
260Q8×C61—21no—
261Q8×C61—22no—
262Q8×C61—22no—
263Q8×C61—41no—
264Q8×C61—41no—
265Q8×C61C4×D412yes—
266D4×C61—22no—
267D4×C61—22no—
268D4×C61—22no—
269D4×C61—22no—
270D4×C61—21no—
271D4×C61—41no—
272D4×C61—41no—
273D4×C61C4×D412yes—
274C2×C4×C61—21no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—41no—
282C2×C4×C61—42no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—42no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—82no—
289C2×C4×C61—82no—
290C2×C4×C61—81no—
291C2×C4×C61—81no—
292C2×C4×C61#12111yescharacteristic
293C2×C4×C61#12111yescharacteristic
294C2×C4×C61#12111yescharacteristic
295C2×C4×C61#12111yescharacteristic
296C2×C4×C61C23×C411yescharacteristic
297C2×C4×C61C22×D411yescharacteristic
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C8×C61—22no—
303C8×C61—22no—
304C8×C61—22no—
305C8×C61—21no—
306C8×C61—22no—
307C8×C61—21no—
308C8×C61—41no—
309C8×C61—41no—
310C8×C61C4×D412yes—
311C8×C61C4×D412yes—
312C4×#471C6111yesmaximal, characteristic, direct product factor, Sylow
313C22×C61—21no—
314C22×C61—21no—
315C22×C61—22no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—42no—
319C22×C61—82no—
320C22×C61—82no—
321C22×C61—81no—
322C22×C61—81no—
323C22×C61C4×#4111yescharacteristic
324C22×C61C2×#12111yescharacteristic
325C22×C61#52911yescharacteristic
326C4×C61—21no—
327C4×C61—21no—
328C4×C61—21no—
329C4×C61—22no—
330C4×C61—41no—
331C4×C61—41no—
332C4×C61—42no—
333C4×C61—81no—
334C4×C61—81no—
335C4×C61#47112yesdirect product factor
336C4×C61C2×C4×D411yescharacteristic
337C4×C61C2×C4×D411yescharacteristic
338C4×C61#52511yescharacteristic
339C4×C61#53211yescharacteristic
340C2×#471C2×C6111yescharacteristic
341C4×#137C2×C6111yescharacteristic, complemented
342C4×AGL(1,ℤ/8)C2×C6111yescharacteristic
343C2×C4×SD16C2×C6111yescharacteristic, complemented
344C4×#131C2×C6111yescharacteristic, complemented
345#1977C2×C6111yescharacteristic, complemented
346#1951C2×C6111yescharacteristic, complemented
347#1931C2×C6111yescharacteristic, complemented
348#1930C2×C6111yescharacteristic, complemented
349#1908C2×C6111yescharacteristic, complemented
350#1907C2×C6111yescharacteristic
351#1815C2×C6111yescharacteristic, complemented
352C4×#108C2×C6111yescharacteristic, complemented
353C4×#101C2×C6111yescharacteristic, complemented
354C4×#100C2×C6111yescharacteristic, complemented
355C2×C61—21no—
356C2×C61—21no—
357C2×C61—42no—
358C2×C61—82no—
359C2×C61C4×#12111yescharacteristic
360C2×C61C2×#47111yescharacteristic
361C2×C61#306711yescharacteristic
362C2×#137C22×C6111yescharacteristic
363C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
364C22×SD16C22×C6111yescharacteristic
365C2×#131C22×C6111yescharacteristic
366C2×#131C22×C6111yescharacteristic
367C4×#41C22×C6111yescharacteristic
368C2×C4×Q8C22×C6111yescharacteristic
369C2×C4×D4C22×C6111yescharacteristic
370#471C4×C6118yesdirect product factor
371#442—21no—
372#441—21no—
373#440—21no—
374#440—21no—
375C4×Q16—21no—
376C4×SD16—21no—
377C4×SD16—21no—
378C4×SD16—21no—
379C4×SD16—21no—
380C4×SD16—21no—
381C4×SD16—21no—
382C4×D8—21no—
383C2×#108C22×C6111yescharacteristic
384C2×#108C22×C6111yescharacteristic
385#428C22×C6111yescharacteristic
386#428C22×C6111yescharacteristic
387C2×#106C22×C6111yescharacteristic
388#419C22×C6111yescharacteristic
389#418C22×C6111yescharacteristic
390#417C22×C6111yescharacteristic
391#417C22×C6111yescharacteristic
392C2×#103C22×C6111yescharacteristic
393C2×#102C22×C6111yescharacteristic
394C2×#101C22×C6111yescharacteristic
395C2×#101C22×C6111yescharacteristic
396C2×#100C22×C6111yescharacteristic
397C2×#100C22×C6111yescharacteristic
398#405—21no—
399#405—21no—
400#405C22×C6111yescharacteristic
401#405C22×C6111yescharacteristic
402C4×M16—21no—
403C4×M16C22×C6111yescharacteristic
404C4×M16C22×C6111yescharacteristic
405C4×M16C22×C6111yescharacteristic
406C2×C4×C8—21no—
407C2×C4×C8C22×C6111yescharacteristic
408#343C22×C6111yescharacteristic
409#343C22×C6111yescharacteristic
410#343C22×C6111yescharacteristic
411#343C22×C6111yescharacteristic
412#341C22×C6111yescharacteristic
413#341C22×C6111yescharacteristic
414C61C4×#47111yescharacteristic, direct product factor, Sylow
415C2×#41C23×C6111yescharacteristic
416C22×Q8C23×C6111yescharacteristic
417C22×D4C23×C6111yescharacteristic
418C23×C4—21no—
419#137—22no—
420#137C2×C4×C6114yescomplemented
421AGL(1,ℤ/8)—22no—
422AGL(1,ℤ/8)C2×C4×C6114yes—
423C2×Q16—21no—
424C2×SD16—21no—
425C2×SD16—21no—
426C2×SD16—21no—
427C2×SD16—21no—
428C2×SD16—22no—
429C2×SD16C2×C4×C6114yescomplemented
430C2×D8—21no—
431#131—22no—
432#131—22no—
433#131—22no—
434#131C2×C4×C6114yescomplemented
435C2×M16—21no—
436C2×M16—21no—
437C2×M16C23×C6111yescharacteristic
438C2×M16C23×C6111yescharacteristic
439C2×M16C23×C6111yescharacteristic
440C2×M16C23×C6111yescharacteristic
441C2×M16C23×C6111yescharacteristic
442C2×M16C23×C6111yescharacteristic
443C22×C8—21no—
444C22×C8—21no—
445C22×C8C23×C6111yescharacteristic
446C22×C8C23×C6111yescharacteristic
447C4×Q8—21no—
448C4×Q8—21no—
449C4×Q8—21no—
450C4×Q8—21no—
451C4×Q8D4×C6111yescharacteristic
452C4×Q8D4×C6111yescharacteristic
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—21no—
456C4×D4—21no—
457C4×D4—21no—
458C4×D4—21no—
459C4×D4D4×C6111yescharacteristic
460C4×D4D4×C6111yescharacteristic
461#117—21no—
462#117C23×C6111yescharacteristic
463C2×C4⋊C4—21no—
464C2×C4⋊C4C23×C6111yescharacteristic
465C2×C4⋊C4C23×C6111yescharacteristic
466C2×C22⋊C4—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42C23×C6111yescharacteristic
470#108—22no—
471#108C2×C4×C6114yescomplemented
472#107—21no—
473#107—21no—
474#106—21no—
475#106—21no—
476#106—21no—
477#106—21no—
478#103—21no—
479#103—21no—
480#103—21no—
481#103—21no—
482#103—21no—
483#103—21no—
484#102—21no—
485#102—21no—
486#102—21no—
487#102—21no—
488#102—21no—
489#102—21no—
490#101—22no—
491#101C2×C4×C6114yescomplemented
492#100—22no—
493#100C2×C4×C6114yescomplemented
494#97—21no—
495#97—21no—
496#97—21no—
497#97—21no—
498#97—21no—
499C4×C8—21no—
500C4×C8—21no—
501C4×C8—21no—
502C4×C8—21no—
503C4×C8—21no—
504C4×C8D4×C6111yescharacteristic
505C4×C8D4×C6111yescharacteristic
506C4×C8D4×C6111yescharacteristic
507C4×C8D4×C6111yescharacteristic
508C24—21no—
509#41—21no—
510#41—21no—
511#41C22×C4×C6112yes—
512#41#41×C6112yes—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8C22×C4×C6112yes—
519C2×Q8C2×D4×C6111yescharacteristic
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4C22×C4×C6112yes—
527C2×D4C2×D4×C6111yescharacteristic
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—82no—
537C22×C4#41×C6111yescharacteristic
538C22×C4#41×C6111yescharacteristic
539C22×C4C24×C6111yescharacteristic
540Q16—24no—
541SD16—24no—
542SD16—24no—
543SD16—24no—
544SD16—24no—
545D8—24no—
546M16—24no—
547M16—21no—
548M16—21no—
549M16—21no—
550M16—21no—
551M16—24no—
552M16—21no—
553M16—21no—
554M16—21no—
555M16—21no—
556M16C22×C4×C6112yes—
557M16C22×C4×C6112yes—
558M16C22×C4×C6112yes—
559M16#41×C6112yes—
560C2×C8—24no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—24no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8C22×C4×C6112yes—
571C2×C8C2×D4×C6111yescharacteristic
572C2×C8C2×D4×C6111yescharacteristic
573C2×C8C2×D4×C6111yescharacteristic
574C2×C8C2×D4×C6111yescharacteristic
575C2×C8#41×C6112yes—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4C2×D4×C6111yescharacteristic
585C4⋊C4C2×D4×C6111yescharacteristic
586C22⋊C4—21no—
587C22⋊C4—21no—
588C22⋊C4—21no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—41no—
595C42—41no—
596C42C2×D4×C6111yescharacteristic
597C42C2×D4×C6111yescharacteristic
598C42C2×D4×C6111yescharacteristic
599C42C2×D4×C6111yescharacteristic
600C23—21no—
601C23—22no—
602C23—41no—
603C23—41no—
604C23—81no—
605C23—81no—
606C23C2×#41×C6111yescharacteristic
607Q8—21no—
608Q8—22no—
609Q8—22no—
610Q8—41no—
611Q8—41no—
612Q8C4×D4×C6112yes—
613D4—22no—
614D4—22no—
615D4—21no—
616D4—22no—
617D4—22no—
618D4—41no—
619D4—41no—
620D4C4×D4×C6112yes—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—82no—
636C2×C4—82no—
637C2×C4—81no—
638C2×C4—81no—
639C2×C4#121×C6111yescharacteristic
640C2×C4#121×C6111yescharacteristic
641C2×C4#121×C6111yescharacteristic
642C2×C4#121×C6111yescharacteristic
643C2×C4C23×C4×C6111yescharacteristic
644C2×C4C22×D4×C6111yescharacteristic
645C2×C4C22×D4×C6111yescharacteristic
646C2×C4C2×#41×C6111yescharacteristic
647C2×C4C2×#41×C6111yescharacteristic
648C2×C4C2×#41×C6111yescharacteristic
649C8—22no—
650C8—22no—
651C8—22no—
652C8—21no—
653C8—22no—
654C8—21no—
655C8—41no—
656C8—41no—
657C8C4×D4×C6112yes—
658C8C4×D4×C6112yes—
659C22—21no—
660C22—21no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—42no—
665C22—82no—
666C22—82no—
667C22—81no—
668C22—81no—
669C22C4×#41×C6111yescharacteristic
670C22C2×#121×C6111yescharacteristic
671C22C61×#52911yescharacteristic
672C4—21no—
673C4—21no—
674C4—21no—
675C4—22no—
676C4—41no—
677C4—41no—
678C4—42no—
679C4—81no—
680C4—81no—
681C4C61×#47112yesdirect product factor
682C4C2×C4×D4×C6111yescharacteristic
683C4C2×C4×D4×C6111yescharacteristic
684C4C61×#52511yescharacteristic
685C4C61×#53211yescharacteristic
686C2—21no—
687C2—21no—
688C2—42no—
689C2—82no—
690C2C4×#121×C6111yescharacteristic
691C2C2×C61×#47111yescharacteristic
692C2C61×#306711yescharacteristic
subgroupG/H
centerC2×C4×C61#121
commutatorC2×C4C23×C4×C61
Frattini, cosocleC22×C4C24×C61
socleC22×C61C2×#121
prime radicalC2×AGL(1,ℤ/8)×C61C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#137×C61C2semidirect
4. C2×C4×SD16×C61C2semidirect
5. C4×#131×C61C2semidirect
6. C61×#1977C2semidirect
7. C61×#1951C2semidirect
8. C61×#1931C2semidirect
9. C61×#1930C2semidirect
10. C61×#1908C2semidirect
12. C61×#1815C2semidirect
13. C4×#108×C61C2semidirect
14. C4×#101×C61C2semidirect
15. C4×#100×C61C2semidirect
24. C61×#471C4direct (N × H)
73. #137×C61C2×C4semidirect
82. C2×SD16×C61C2×C4semidirect
87. #131×C61C2×C4semidirect
124. #108×C61C2×C4semidirect
144. #101×C61C2×C4semidirect
146. #100×C61C2×C4semidirect
312. C4×#471C61direct (N × H)
335. C4×C61#471direct (N × H)
341. C4×#137C2×C61semidirect
343. C2×C4×SD16C2×C61semidirect
344. C4×#131C2×C61semidirect
345. #1977C2×C61semidirect
346. #1951C2×C61semidirect
347. #1931C2×C61semidirect
348. #1930C2×C61semidirect
349. #1908C2×C61semidirect
351. #1815C2×C61semidirect
352. C4×#108C2×C61semidirect
353. C4×#101C2×C61semidirect
354. C4×#100C2×C61semidirect
370. #471C4×C61direct (N × H)
414. C61C4×#471direct (N × H)
420. #137C2×C4×C61semidirect
429. C2×SD16C2×C4×C61semidirect
434. #131C2×C4×C61semidirect
471. #108C2×C4×C61semidirect
491. #101C2×C4×C61semidirect
493. #100C2×C4×C61semidirect
681. C4C61×#471direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4712
C4×#137×C612
C4×AGL(1,ℤ/8)×C612
C2×C4×SD16×C612
C4×#131×C612
C61×#19772
C61×#19512
C61×#19312
C61×#19302
C61×#19082
C61×#19072
C61×#18152
C4×#108×C612
C4×#101×C612
C4×#100×C612
C4×#47161