Finite Group Databasebeta

← C61×#25979 #29529412

Subgroups — C61×#25979 #29529412

Order 15616.

928 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#477C211yesmaximal, characteristic, complemented
2C2×C61×#419C211yesmaximal, characteristic
3C61×#2439C211yesmaximal, characteristic
4Q8×C22⋊C4×C61C211yesmaximal, characteristic
5C61×#2097C211yesmaximal, characteristic, complemented
6C61×#2068C211yesmaximal, characteristic, complemented
7C61×#2066C211yesmaximal, characteristic, complemented
8C61×#2024C211yesmaximal, characteristic, complemented
9C61×#1865C211yesmaximal, characteristic, complemented
10C61×#1865C211yesmaximal, characteristic, complemented
11C61×#1854C211yesmaximal, characteristic
12C61×#1851C211yesmaximal, characteristic
13C61×#1809C211yesmaximal, characteristic
14C61×#1805C211yesmaximal, characteristic, complemented
15C61×#1787C211yesmaximal, characteristic
16C23×Q8×C61C2211yescharacteristic
17C22×M16×C61C2211yescharacteristic
18C2×C4⋊Q8×C61C2211yescharacteristic
19C2×C4×Q8×C61C2211yescharacteristic
20C2×C4×Q8×C61C2211yescharacteristic
21C2×#117×C61C2211yescharacteristic
22C61×#477—24no—
23C2×#107×C61C2211yescharacteristic
24C2×#107×C61C2211yescharacteristic
25C2×#106×C61C2211yescharacteristic
26C2×#106×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C61×#419—24no—
30C2×#103×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C2×#103×C61C2211yescharacteristic
34C2×#103×C61C2211yescharacteristic
35C2×#103×C61C2211yescharacteristic
36C2×#103×C61C2211yescharacteristic
37C2×#103×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C61×#396—21no—
40C61×#393—21no—
41C61×#391—21no—
42C61×#391—21no—
43C61×#391—21no—
44C61×#391C2211yescharacteristic
45C61×#391C2211yescharacteristic
46C61×#389C2211yescharacteristic
47C61×#389C2211yescharacteristic
48C61×#387—21no—
49C61×#382C2211yescharacteristic
50C61×#380—21no—
51C61×#380C2211yescharacteristic
52C61×#380C2211yescharacteristic
53C4×C22⋊C4×C61—21no—
54C4×C22⋊C4×C61C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Q8×C61—21no—
62C22×Q8×C61—21no—
63C22×Q8×C61—22no—
64C22×Q8×C61—22no—
65C22×Q8×C61—22no—
66C22×Q8×C61—41no—
67C22×Q8×C61—41no—
68C22×Q8×C61Q814yescomplemented
69C22×Q8×C61C2311yescharacteristic
70C22×Q8×C61C2311yescharacteristic
71C23×C4×C61—21no—
72C23×C4×C61C2311yescharacteristic
73C2×M16×C61—22no—
74C2×M16×C61—22no—
75C2×M16×C61—41no—
76C22×C8×C61C2311yescharacteristic
77C22×C8×C61C2311yescharacteristic
78C22×C8×C61C2311yescharacteristic
79C22×C8×C61C2311yescharacteristic
80C4⋊Q8×C61—22no—
81C4⋊Q8×C61—41no—
82C4×Q8×C61—22no—
83C4×Q8×C61—22no—
84C4×Q8×C61—41no—
85C4×Q8×C61—41no—
86#117×C61—22no—
87#117×C61—41no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61C2311yescharacteristic
94C2×C4⋊C4×C61C2311yescharacteristic
95C2×C4⋊C4×C61C2311yescharacteristic
96C2×C4⋊C4×C61C2311yescharacteristic
97C2×C4⋊C4×C61C2311yescharacteristic
98C2×C4⋊C4×C61C2311yescharacteristic
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×C61—21no—
107C2×C42×C61C2311yescharacteristic
108C2×C42×C61C2311yescharacteristic
109#107×C61—22no—
110#107×C61—22no—
111#106×C61—41no—
112#106×C61—41no—
113C4⋊C8×C61—22no—
114C4⋊C8×C61—41no—
115#103×C61—22no—
116#103×C61—22no—
117#103×C61—22no—
118#103×C61—22no—
119#103×C61—22no—
120#103×C61—41no—
121#103×C61—41no—
122#103×C61D414yes—
123C22⋊C8×C61—22no—
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×C61—21no—
132#95×C61—21no—
133#95×C61—21no—
134#95×C61D411yescharacteristic
135#95×C61D411yescharacteristic
136C24×C61C2×D411yescharacteristic
137C2×Q8×C61—24no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—28no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—42no—
148C2×Q8×C61—42no—
149C2×Q8×C61—42no—
150C2×Q8×C61—44no—
151C2×Q8×C61—44no—
152C2×Q8×C61—44no—
153C2×Q8×C61—42no—
154C2×Q8×C61—81no—
155C2×Q8×C61C2×D412yes—
156C2×Q8×C61C2×Q812yes—
157C2×Q8×C61C2×Q812yes—
158C2×Q8×C61#4112yes—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—24no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—42no—
173C22×C4×C61—42no—
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×Q812yes—
180C22×C4×C61#4112yes—
181C22×C4×C61C2411yescharacteristic
182M16×C61—44no—
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×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61C2×D412yes—
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—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—42no—
207C4⋊C4×C61—42no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61—42no—
210C4⋊C4×C61—81no—
211C4⋊C4×C61C2×D412yes—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—41no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—81no—
217C42×C61—21no—
218C42×C61—21no—
219C42×C61—21no—
220C42×C61—21no—
221C42×C61—42no—
222C42×C61—42no—
223C42×C61—42no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61C22⋊Q812yes—
231C23×C61C22×D411yescharacteristic
232Q8×C61—22no—
233Q8×C61—22no—
234Q8×C61—22no—
235Q8×C61—22no—
236Q8×C61—22no—
237Q8×C61—48no—
238Q8×C61—41no—
239Q8×C61—41no—
240Q8×C61—84no—
241Q8×C61C22⋊Q814yes—
242C2×C4×C61—22no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—22no—
254C2×C4×C61—21no—
255C2×C4×C61—22no—
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—21no—
263C2×C4×C61—21no—
264C2×C4×C61—48no—
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×C61C22⋊Q812yes—
285C2×C4×C61#13712yes—
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C22×Q811yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C61H(5,𝔽2)11yescharacteristic
292C8×C61—22no—
293C8×C61—41no—
294C8×C61—41no—
295C8×C61—41no—
296#25979C6111yesmaximal, characteristic, direct product factor, Sylow
297C22×C61—22no—
298C22×C61—22no—
299C22×C61—22no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61—41no—
303C22×C61—41no—
304C22×C61C2×C22⋊Q811yescharacteristic
305C22×C61D4211yescharacteristic
306C22×C61#54611yescharacteristic
307C22×C61C2×#13711yescharacteristic
308C22×C61#57511yescharacteristic
309C22×C61#57711yescharacteristic
310C22×C61#57811yescharacteristic
311C4×C61—22no—
312C4×C61—24no—
313C4×C61—22no—
314C4×C61—41no—
315C4×C61—42no—
316C4×C61—41no—
317C4×C61—42no—
318C4×C61—41no—
319C4×C61—81no—
320C4×C61—81no—
321C4×C61—81no—
322C4×C61—81no—
323C4×C61—81no—
324C4×C61C2×C22⋊Q811yescharacteristic
325C4×C61#54311yescharacteristic
326C4×C61#54611yescharacteristic
327C4×C61#55111yescharacteristic
328C2×#477C2×C6111yescharacteristic, complemented
329C2×#419C2×C6111yescharacteristic
330#2439C2×C6111yescharacteristic
331Q8×C22⋊C4C2×C6111yescharacteristic
332#2097C2×C6111yescharacteristic, complemented
333#2068C2×C6111yescharacteristic, complemented
334#2066C2×C6111yescharacteristic, complemented
335#2024C2×C6111yescharacteristic, complemented
336#1865C2×C6111yescharacteristic, complemented
337#1865C2×C6111yescharacteristic, complemented
338#1854C2×C6111yescharacteristic
339#1851C2×C6111yescharacteristic
340#1809C2×C6111yescharacteristic
341#1805C2×C6111yescharacteristic, complemented
342#1787C2×C6111yescharacteristic
343C2×C61—42no—
344C2×C61#243711yescharacteristic
345C2×C61#307811yescharacteristic
346C2×C61#308211yescharacteristic
347C2×C61#327011yescharacteristic
348C2×C61#327511yescharacteristic
349C2×C61#331311yescharacteristic
350C2×C61#332911yescharacteristic
351C23×Q8C22×C6111yescharacteristic
352C22×M16C22×C6111yescharacteristic
353C2×C4⋊Q8C22×C6111yescharacteristic
354C2×C4×Q8C22×C6111yescharacteristic
355C2×C4×Q8C22×C6111yescharacteristic
356C2×#117C22×C6111yescharacteristic
357#477—24no—
358C2×#107C22×C6111yescharacteristic
359C2×#107C22×C6111yescharacteristic
360C2×#106C22×C6111yescharacteristic
361C2×#106C22×C6111yescharacteristic
362C2×C4⋊C8C22×C6111yescharacteristic
363C2×C4⋊C8C22×C6111yescharacteristic
364#419—24no—
365C2×#103C22×C6111yescharacteristic
366C2×#103C22×C6111yescharacteristic
367C2×#103C22×C6111yescharacteristic
368C2×#103C22×C6111yescharacteristic
369C2×#103C22×C6111yescharacteristic
370C2×#103C22×C6111yescharacteristic
371C2×#103C22×C6111yescharacteristic
372C2×#103C22×C6111yescharacteristic
373C2×C22⋊C8C22×C6111yescharacteristic
374#396—21no—
375#393—21no—
376#391—21no—
377#391—21no—
378#391—21no—
379#391C22×C6111yescharacteristic
380#391C22×C6111yescharacteristic
381#389C22×C6111yescharacteristic
382#389C22×C6111yescharacteristic
383#387—21no—
384#382C22×C6111yescharacteristic
385#380—21no—
386#380C22×C6111yescharacteristic
387#380C22×C6111yescharacteristic
388C4×C22⋊C4—21no—
389C4×C22⋊C4C22×C6111yescharacteristic
390#340C22×C6111yescharacteristic
391#340C22×C6111yescharacteristic
392#340C22×C6111yescharacteristic
393#340C22×C6111yescharacteristic
394#336C22×C6111yescharacteristic
395#336C22×C6111yescharacteristic
396C61#2597911yescharacteristic, direct product factor, Sylow
397C22×Q8—21no—
398C22×Q8—21no—
399C22×Q8—22no—
400C22×Q8—22no—
401C22×Q8—22no—
402C22×Q8—41no—
403C22×Q8—41no—
404C22×Q8Q8×C6114yescomplemented
405C22×Q8C23×C6111yescharacteristic
406C22×Q8C23×C6111yescharacteristic
407C23×C4—21no—
408C23×C4C23×C6111yescharacteristic
409C2×M16—22no—
410C2×M16—22no—
411C2×M16—41no—
412C22×C8C23×C6111yescharacteristic
413C22×C8C23×C6111yescharacteristic
414C22×C8C23×C6111yescharacteristic
415C22×C8C23×C6111yescharacteristic
416C4⋊Q8—22no—
417C4⋊Q8—41no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×Q8—41no—
421C4×Q8—41no—
422#117—22no—
423#117—41no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4C23×C6111yescharacteristic
430C2×C4⋊C4C23×C6111yescharacteristic
431C2×C4⋊C4C23×C6111yescharacteristic
432C2×C4⋊C4C23×C6111yescharacteristic
433C2×C4⋊C4C23×C6111yescharacteristic
434C2×C4⋊C4C23×C6111yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4D4×C6111yescharacteristic
439C2×C22⋊C4D4×C6111yescharacteristic
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42C23×C6111yescharacteristic
444C2×C42C23×C6111yescharacteristic
445#107—22no—
446#107—22no—
447#106—41no—
448#106—41no—
449C4⋊C8—22no—
450C4⋊C8—41no—
451#103—22no—
452#103—22no—
453#103—22no—
454#103—22no—
455#103—22no—
456#103—41no—
457#103—41no—
458#103D4×C6114yes—
459C22⋊C8—22no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95D4×C6111yescharacteristic
471#95D4×C6111yescharacteristic
472C24C2×D4×C6111yescharacteristic
473C2×Q8—24no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—28no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—42no—
490C2×Q8—81no—
491C2×Q8C2×D4×C6112yes—
492C2×Q8C2×Q8×C6112yes—
493C2×Q8C2×Q8×C6112yes—
494C2×Q8#41×C6112yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—24no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4C2×D4×C6111yescharacteristic
511C22×C4C2×D4×C6111yescharacteristic
512C22×C4C2×D4×C6111yescharacteristic
513C22×C4C2×D4×C6111yescharacteristic
514C22×C4C2×D4×C6111yescharacteristic
515C22×C4C2×Q8×C6112yes—
516C22×C4#41×C6112yes—
517C22×C4C24×C6111yescharacteristic
518M16—44no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8C2×D4×C6112yes—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—81no—
547C4⋊C4C2×D4×C6112yes—
548C22⋊C4—22no—
549C22⋊C4—41no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—81no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—42no—
558C42—42no—
559C42—42no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23C22⋊Q8×C6112yes—
567C23C22×D4×C6111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—22no—
571Q8—22no—
572Q8—22no—
573Q8—48no—
574Q8—41no—
575Q8—41no—
576Q8—84no—
577Q8C22⋊Q8×C6114yes—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—48no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
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×C4C22⋊Q8×C6112yes—
621C2×C4#137×C6112yes—
622C2×C4C22×D4×C6111yescharacteristic
623C2×C4C22×Q8×C6111yescharacteristic
624C2×C4C2×#41×C6111yescharacteristic
625C2×C4C2×#41×C6111yescharacteristic
626C2×C4H(5,𝔽2)×C6111yescharacteristic
627C2×C4H(5,𝔽2)×C6111yescharacteristic
628C8—22no—
629C8—41no—
630C8—41no—
631C8—41no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22C2×C22⋊Q8×C6111yescharacteristic
640C22D42×C6111yescharacteristic
641C22C61×#54611yescharacteristic
642C22C2×#137×C6111yescharacteristic
643C22C61×#57511yescharacteristic
644C22C61×#57711yescharacteristic
645C22C61×#57811yescharacteristic
646C4—22no—
647C4—24no—
648C4—22no—
649C4—41no—
650C4—41no—
651C4—42no—
652C4—41no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4C2×C22⋊Q8×C6111yescharacteristic
660C4C61×#54311yescharacteristic
661C4C61×#54611yescharacteristic
662C4C61×#55111yescharacteristic
663C2—42no—
664C2C61×#243711yescharacteristic
665C2C61×#307811yescharacteristic
666C2C61×#308211yescharacteristic
667C2C61×#327011yescharacteristic
668C2C61×#327511yescharacteristic
669C2C61×#331311yescharacteristic
670C2C61×#332911yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC24×C61C2×D4
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×#477C2semidirect
5. C61×#2097C2semidirect
6. C61×#2068C2semidirect
7. C61×#2066C2semidirect
8. C61×#2024C2semidirect
9. C61×#1865C2semidirect
10. C61×#1865C2semidirect
14. C61×#1805C2semidirect
68. C22×Q8×C61Q8semidirect
296. #25979C61direct (N × H)
328. C2×#477C2×C61semidirect
332. #2097C2×C61semidirect
333. #2068C2×C61semidirect
334. #2066C2×C61semidirect
335. #2024C2×C61semidirect
336. #1865C2×C61semidirect
337. #1865C2×C61semidirect
341. #1805C2×C61semidirect
396. C61#25979direct (N × H)
404. C22×Q8Q8×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4772
C2×C61×#4192
C61×#24392
Q8×C22⋊C4×C612
C61×#20972
C61×#20682
C61×#20662
C61×#20242
C61×#18652
C61×#18542
C61×#18512
C61×#18092
C61×#18052
C61×#17872
#2597961