Finite Group Databasebeta

← C61×#23711 #29527144

Subgroups — C61×#23711 #29527144

Order 15616.

958 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×#440C211yesmaximal, characteristic, complemented
2C2×C61×#432C211yesmaximal, characteristic, complemented
3C4×C22⋊Q8×C61C211yesmaximal, characteristic, complemented
4C4×#121×C61C211yesmaximal, characteristic
5C61×#2086C211yesmaximal, characteristic, complemented
6C61×#2076C211yesmaximal, characteristic, complemented
7C61×#2067C211yesmaximal, characteristic, complemented
8C61×#2066C211yesmaximal, characteristic, complemented
9C61×#2055C211yesmaximal, characteristic, complemented
10C61×#2036C211yesmaximal, characteristic, complemented
11C61×#2034C211yesmaximal, characteristic
12C61×#2000C211yesmaximal, characteristic
13C61×#1776C211yesmaximal, characteristic, complemented
14C61×#1763C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C61C2211yescharacteristic
17C2×C22⋊Q8×C61C2211yescharacteristic
18C2×#121×C61C2211yescharacteristic
19C2×C4×Q8×C61C2211yescharacteristic
20C2×C4×D4×C61—21no—
21C2×C4×D4×C61C2211yescharacteristic
22C22×C42×C61C2211yescharacteristic
23C61×#440—24no—
24C61×#432—24no—
25C2×#107×C61C2211yescharacteristic
26C2×#107×C61C2211yescharacteristic
27C2×#106×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4⋊C8×C61C2211yescharacteristic
30C2×#103×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×C22⋊C8×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×#97×C61C2211yescharacteristic
39C2×#97×C61C2211yescharacteristic
40C61×#391C2211yescharacteristic
41C61×#390C2211yescharacteristic
42C61×#389C2211yescharacteristic
43C61×#389C2211yescharacteristic
44C61×#388—21no—
45C61×#387—21no—
46C61×#386—21no—
47C61×#385—21no—
48C61×#380C2211yescharacteristic
49C61×#380C2211yescharacteristic
50C4×C4⋊C4×C61—21no—
51C4×C4⋊C4×C61C2211yescharacteristic
52C4×C4⋊C4×C61C2211yescharacteristic
53C4×C22⋊C4×C61—21no—
54C4×C22⋊C4×C61—21no—
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×Q8×C61C2311yescharacteristic
62C22×D4×C61—21no—
63C22×D4×C61C2311yescharacteristic
64C23×C4×C61—21no—
65C23×C4×C61D411yescharacteristic
66C23×C4×C61D411yescharacteristic
67C23×C4×C61C2311yescharacteristic
68C2×SD16×C61—22no—
69C2×SD16×C61—22no—
70C2×SD16×C61—22no—
71C22×C8×C61C2311yescharacteristic
72C22×C8×C61C2311yescharacteristic
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75C22⋊Q8×C61—22no—
76C22⋊Q8×C61—22no—
77#121×C61—22no—
78#121×C61—22no—
79C4×Q8×C61—22no—
80C4×Q8×C61—22no—
81C4×D4×C61—22no—
82C4×D4×C61—22no—
83C4×D4×C61—44no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61C2311yescharacteristic
89C2×C4⋊C4×C61C2311yescharacteristic
90C2×C4⋊C4×C61C2311yescharacteristic
91C2×C4⋊C4×C61C2311yescharacteristic
92C2×C4⋊C4×C61C2311yescharacteristic
93C2×C4⋊C4×C61C2311yescharacteristic
94C2×C22⋊C4×C61—21no—
95C2×C22⋊C4×C61—21no—
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×C42×C61—22no—
102C2×C42×C61—22no—
103C2×C42×C61—21no—
104C2×C42×C61—21no—
105C2×C42×C61—21no—
106C2×C42×C61D411yescharacteristic
107C2×C42×C61D411yescharacteristic
108C2×C42×C61C2311yescharacteristic
109C2×C42×C61C2311yescharacteristic
110#107×C61—22no—
111#107×C61—22no—
112#106×C61—22no—
113C4⋊C8×C61—22no—
114C4⋊C8×C61—22no—
115#103×C61—22no—
116#103×C61—22no—
117#103×C61—22no—
118#102×C61—22no—
119#102×C61—22no—
120#102×C61—22no—
121C22⋊C8×C61—22no—
122C22⋊C8×C61—22no—
123#97×C61—22no—
124#97×C61D414yescomplemented
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×C61—21no—
132#95×C61—21no—
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#4112yes—
141C2×D4×C61—24no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—42no—
148C2×D4×C61—42no—
149C2×D4×C61#4112yes—
150C22×C4×C61—22no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
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—21no—
167C22×C4×C61—41no—
168C22×C4×C61—41no—
169C22×C4×C61—42no—
170C22×C4×C61—42no—
171C22×C4×C61—42no—
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—28no—
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×C61C2×D412yes—
191C4⋊C4×C61—24no—
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—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—42no—
203C4⋊C4×C61—42no—
204C4⋊C4×C61—42no—
205C4⋊C4×C61#4112yes—
206C4⋊C4×C61#4112yes—
207C22⋊C4×C61—24no—
208C22⋊C4×C61—24no—
209C22⋊C4×C61—42no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—42no—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—42no—
214C42×C61—22no—
215C42×C61—22no—
216C42×C61—21no—
217C42×C61—21no—
218C42×C61—42no—
219C42×C61—42no—
220C42×C61—42no—
221C42×C61C2×D412yes—
222C42×C61#4112yes—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—22no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61#13712yes—
237C23×C61C22×D411yescharacteristic
238Q8×C61—22no—
239Q8×C61—22no—
240Q8×C61—41no—
241Q8×C61—41no—
242D4×C61—22no—
243D4×C61—22no—
244D4×C61—48no—
245D4×C61—41no—
246D4×C61—41no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
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—44no—
263C2×C4×C61—44no—
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—41no—
285C2×C4×C61—41no—
286C2×C4×C61—84no—
287C2×C4×C61#12112yes—
288C2×C4×C61#12112yes—
289C2×C4×C61AGL(1,ℤ/8)12yes—
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C8×C61—22no—
297C8×C61—22no—
298C8×C61—41no—
299C8×C61—41no—
300#23711C6111yesmaximal, characteristic, direct product factor, Sylow
301C22×C61—22no—
302C22×C61—22no—
303C22×C61—22no—
304C22×C61—41no—
305C22×C61—41no—
306C22×C61—41no—
307C22×C61—41no—
308C22×C61—42no—
309C22×C61—42no—
310C22×C61—42no—
311C22×C61—81no—
312C22×C61—81no—
313C22×C61—81no—
314C22×C61—81no—
315C22×C61C2×#12111yescharacteristic
316C22×C61#52511yescharacteristic
317C22×C61#52511yescharacteristic
318C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C61C2×#13711yescharacteristic
320C22×C61#57511yescharacteristic
321C22×C61#57511yescharacteristic
322C4×C61—22no—
323C4×C61—22no—
324C4×C61—22no—
325C4×C61—42no—
326C4×C61—42no—
327C4×C61—41no—
328C4×C61—42no—
329C4×C61—41no—
330C4×C61—81no—
331C4×C61—81no—
332C4×C61—81no—
333C4×C61—81no—
334C4×C61#52511yescharacteristic
335C4×C61#52911yescharacteristic
336C4×C61#52911yescharacteristic
337C4×C61#53211yescharacteristic
338C2×#440C2×C6111yescharacteristic, complemented
339C2×#432C2×C6111yescharacteristic, complemented
340C4×C22⋊Q8C2×C6111yescharacteristic, complemented
341C4×#121C2×C6111yescharacteristic
342#2086C2×C6111yescharacteristic, complemented
343#2076C2×C6111yescharacteristic, complemented
344#2067C2×C6111yescharacteristic, complemented
345#2066C2×C6111yescharacteristic, complemented
346#2055C2×C6111yescharacteristic, complemented
347#2036C2×C6111yescharacteristic, complemented
348#2034C2×C6111yescharacteristic
349#2000C2×C6111yescharacteristic
350#1776C2×C6111yescharacteristic, complemented
351#1763C2×C6111yescharacteristic, complemented
352#1762C2×C6111yescharacteristic, complemented
353C2×C61—42no—
354C2×C61—82no—
355C2×C61#239211yescharacteristic
356C2×C61#305511yescharacteristic
357C2×C61#305611yescharacteristic
358C2×C61#311011yescharacteristic
359C2×C61#311111yescharacteristic
360C2×C61#311511yescharacteristic
361C2×C61#311711yescharacteristic
362C22×SD16C22×C6111yescharacteristic
363C2×C22⋊Q8C22×C6111yescharacteristic
364C2×#121C22×C6111yescharacteristic
365C2×C4×Q8C22×C6111yescharacteristic
366C2×C4×D4—21no—
367C2×C4×D4C22×C6111yescharacteristic
368C22×C42C22×C6111yescharacteristic
369#440—24no—
370#432—24no—
371C2×#107C22×C6111yescharacteristic
372C2×#107C22×C6111yescharacteristic
373C2×#106C22×C6111yescharacteristic
374C2×C4⋊C8C22×C6111yescharacteristic
375C2×C4⋊C8C22×C6111yescharacteristic
376C2×#103C22×C6111yescharacteristic
377C2×#103C22×C6111yescharacteristic
378C2×#103C22×C6111yescharacteristic
379C2×#102C22×C6111yescharacteristic
380C2×#102C22×C6111yescharacteristic
381C2×#102C22×C6111yescharacteristic
382C2×C22⋊C8C22×C6111yescharacteristic
383C2×C22⋊C8C22×C6111yescharacteristic
384C2×#97C22×C6111yescharacteristic
385C2×#97C22×C6111yescharacteristic
386#391C22×C6111yescharacteristic
387#390C22×C6111yescharacteristic
388#389C22×C6111yescharacteristic
389#389C22×C6111yescharacteristic
390#388—21no—
391#387—21no—
392#386—21no—
393#385—21no—
394#380C22×C6111yescharacteristic
395#380C22×C6111yescharacteristic
396C4×C4⋊C4—21no—
397C4×C4⋊C4C22×C6111yescharacteristic
398C4×C4⋊C4C22×C6111yescharacteristic
399C4×C22⋊C4—21no—
400C4×C22⋊C4—21no—
401#340C22×C6111yescharacteristic
402#340C22×C6111yescharacteristic
403#340C22×C6111yescharacteristic
404#340C22×C6111yescharacteristic
405#340C22×C6111yescharacteristic
406#340C22×C6111yescharacteristic
407C61#2371111yescharacteristic, direct product factor, Sylow
408C22×Q8C23×C6111yescharacteristic
409C22×D4—21no—
410C22×D4C23×C6111yescharacteristic
411C23×C4—21no—
412C23×C4D4×C6111yescharacteristic
413C23×C4D4×C6111yescharacteristic
414C23×C4C23×C6111yescharacteristic
415C2×SD16—22no—
416C2×SD16—22no—
417C2×SD16—22no—
418C22×C8C23×C6111yescharacteristic
419C22×C8C23×C6111yescharacteristic
420C22×C8C23×C6111yescharacteristic
421C22×C8C23×C6111yescharacteristic
422C22⋊Q8—22no—
423C22⋊Q8—22no—
424#121—22no—
425#121—22no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—44no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
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⋊C4—21no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42D4×C6111yescharacteristic
454C2×C42D4×C6111yescharacteristic
455C2×C42C23×C6111yescharacteristic
456C2×C42C23×C6111yescharacteristic
457#107—22no—
458#107—22no—
459#106—22no—
460C4⋊C8—22no—
461C4⋊C8—22no—
462#103—22no—
463#103—22no—
464#103—22no—
465#102—22no—
466#102—22no—
467#102—22no—
468C22⋊C8—22no—
469C22⋊C8—22no—
470#97—22no—
471#97D4×C6114yescomplemented
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480C24—21no—
481C24C2×D4×C6111yescharacteristic
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8#41×C6112yes—
488C2×D4—24no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4#41×C6112yes—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4C2×D4×C6111yescharacteristic
520C22×C4C2×D4×C6111yescharacteristic
521C22×C4C2×D4×C6111yescharacteristic
522C22×C4C2×D4×C6111yescharacteristic
523C22×C4C2×D4×C6111yescharacteristic
524C22×C4C24×C6111yescharacteristic
525SD16—28no—
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×C8—21no—
535C2×C8—21no—
536C2×C8C2×D4×C6112yes—
537C2×C8C2×D4×C6112yes—
538C4⋊C4—24no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4#41×C6112yes—
553C4⋊C4#41×C6112yes—
554C22⋊C4—24no—
555C22⋊C4—24no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C42—22no—
562C42—22no—
563C42—21no—
564C42—21no—
565C42—42no—
566C42—42no—
567C42—42no—
568C42C2×D4×C6112yes—
569C42#41×C6112yes—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23#137×C6112yes—
584C23C22×D4×C6111yescharacteristic
585Q8—22no—
586Q8—22no—
587Q8—41no—
588Q8—41no—
589D4—22no—
590D4—22no—
591D4—48no—
592D4—41no—
593D4—41no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—44no—
610C2×C4—44no—
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—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—84no—
634C2×C4#121×C6112yes—
635C2×C4#121×C6112yes—
636C2×C4AGL(1,ℤ/8)×C6112yes—
637C2×C4C22×D4×C6111yescharacteristic
638C2×C4C2×#41×C6111yescharacteristic
639C2×C4C2×#41×C6111yescharacteristic
640C2×C4C2×#41×C6111yescharacteristic
641C2×C4C2×#41×C6111yescharacteristic
642C2×C4C2×#41×C6111yescharacteristic
643C8—22no—
644C8—22no—
645C8—41no—
646C8—41no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22C2×#121×C6111yescharacteristic
662C22C61×#52511yescharacteristic
663C22C61×#52511yescharacteristic
664C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
665C22C2×#137×C6111yescharacteristic
666C22C61×#57511yescharacteristic
667C22C61×#57511yescharacteristic
668C4—22no—
669C4—22no—
670C4—22no—
671C4—41no—
672C4—42no—
673C4—42no—
674C4—41no—
675C4—42no—
676C4—81no—
677C4—81no—
678C4—81no—
679C4—81no—
680C4C61×#52511yescharacteristic
681C4C61×#52911yescharacteristic
682C4C61×#52911yescharacteristic
683C4C61×#53211yescharacteristic
684C2—42no—
685C2—82no—
686C2C61×#239211yescharacteristic
687C2C61×#305511yescharacteristic
688C2C61×#305611yescharacteristic
689C2C61×#311011yescharacteristic
690C2C61×#311111yescharacteristic
691C2C61×#311511yescharacteristic
692C2C61×#311711yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×#121×C61C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C22×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#440C2semidirect
2. C2×C61×#432C2semidirect
3. C4×C22⋊Q8×C61C2semidirect
5. C61×#2086C2semidirect
6. C61×#2076C2semidirect
7. C61×#2067C2semidirect
8. C61×#2066C2semidirect
9. C61×#2055C2semidirect
10. C61×#2036C2semidirect
13. C61×#1776C2semidirect
14. C61×#1763C2semidirect
15. C61×#1762C2semidirect
124. #97×C61D4semidirect
300. #23711C61direct (N × H)
338. C2×#440C2×C61semidirect
339. C2×#432C2×C61semidirect
340. C4×C22⋊Q8C2×C61semidirect
342. #2086C2×C61semidirect
343. #2076C2×C61semidirect
344. #2067C2×C61semidirect
345. #2066C2×C61semidirect
346. #2055C2×C61semidirect
347. #2036C2×C61semidirect
350. #1776C2×C61semidirect
351. #1763C2×C61semidirect
352. #1762C2×C61semidirect
407. C61#23711direct (N × H)
471. #97D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4402
C2×C61×#4322
C4×C22⋊Q8×C612
C4×#121×C612
C61×#20862
C61×#20762
C61×#20672
C61×#20662
C61×#20552
C61×#20362
C61×#20342
C61×#20002
C61×#17762
C61×#17632
C61×#17622
#2371161