Finite Group Databasebeta

← C61×#25241 #29528674

Subgroups — C61×#25241 #29528674

Order 15616.

850 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#485C211yesmaximal, characteristic, complemented
2C2×C61×#435C211yesmaximal, characteristic
3C61×#2485C211yesmaximal, characteristic
4C61×#2417C211yesmaximal, characteristic
5C61×#2086C211yesmaximal, characteristic, complemented
6C61×#2077C211yesmaximal, characteristic, complemented
7C61×#2068C211yesmaximal, characteristic, complemented
8C61×#2036C211yesmaximal, characteristic, complemented
9C61×#1943C211yesmaximal, characteristic, complemented
10C61×#1935C211yesmaximal, characteristic, complemented
11C61×#1894C211yesmaximal, characteristic, complemented
12C61×#1892C211yesmaximal, characteristic, complemented
13C61×#1852C211yesmaximal, characteristic, complemented
14C61×#1808C211yesmaximal, characteristic, complemented
15C61×#1736C211yesmaximal, characteristic, complemented
16C22×M16×C61C2211yescharacteristic
17C23×C8×C61C2211yescharacteristic
18C2×C22⋊Q8×C61C2211yescharacteristic
19C2×C22⋊Q8×C61C2211yescharacteristic
20C2×C4×D4×C61C2211yescharacteristic
21C2×#117×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C61×#485—24no—
24C61×#435—24no—
25C2×#107×C61C2211yescharacteristic
26C2×#107×C61C2211yescharacteristic
27C2×#107×C61C2211yescharacteristic
28C2×#106×C61C2211yescharacteristic
29C2×C4⋊C8×C61C2211yescharacteristic
30C2×#103×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C2×#103×C61C2211yescharacteristic
34C2×C22⋊C8×C61C2211yescharacteristic
35C2×C22⋊C8×C61C2211yescharacteristic
36C2×#97×C61C2211yescharacteristic
37C61×#398—21no—
38C61×#397—21no—
39C61×#396—21no—
40C61×#394—21no—
41C61×#391C2211yescharacteristic
42C61×#389C2211yescharacteristic
43C61×#389C2211yescharacteristic
44C61×#389C2211yescharacteristic
45C61×#388—21no—
46C61×#387—21no—
47C61×#386—21no—
48C61×#380—21no—
49C61×#380C2211yescharacteristic
50C61×#380C2211yescharacteristic
51C61×#380C2211yescharacteristic
52C61×#380C2211yescharacteristic
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×Q8×C61C2311yescharacteristic
62C22×D4×C61D411yescharacteristic
63C23×C4×C61—21no—
64C23×C4×C61C2311yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C2×M16×C61—22no—
67C2×M16×C61—22no—
68C2×M16×C61—41no—
69C22×C8×C61—22no—
70C22×C8×C61—22no—
71C22×C8×C61—41no—
72C22×C8×C61C2311yescharacteristic
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75C22×C8×C61C2311yescharacteristic
76C22⋊Q8×C61—22no—
77C22⋊Q8×C61—22no—
78C22⋊Q8×C61—22no—
79C22⋊Q8×C61—41no—
80C4×D4×C61—22no—
81C4×D4×C61—22no—
82#117×C61—22no—
83#117×C61—22no—
84C2×C4⋊C4×C61—22no—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—41no—
92C2×C4⋊C4×C61D411yescharacteristic
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×C4⋊C4×C61C2311yescharacteristic
100C2×C22⋊C4×C61—21no—
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—21no—
107C2×C22⋊C4×C61D411yescharacteristic
108C2×C22⋊C4×C61D411yescharacteristic
109C2×C42×C61—21no—
110C2×C42×C61C2311yescharacteristic
111#107×C61—22no—
112#107×C61—22no—
113#107×C61—41no—
114#106×C61—22no—
115C4⋊C8×C61—22no—
116#103×C61—22no—
117#103×C61—22no—
118#103×C61—22no—
119#103×C61—41no—
120C22⋊C8×C61—22no—
121C22⋊C8×C61D414yes—
122#97×C61—22no—
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×C61—21no—
131#95×C61—21no—
132C24×C61C2×D411yescharacteristic
133C24×C61C2×D411yescharacteristic
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×D4×C61—22no—
141C2×D4×C61—22no—
142C2×D4×C61—41no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—42no—
162C22×C4×C61—42no—
163C22×C4×C61—81no—
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D412yes—
169C22×C4×C61#4112yes—
170C22×C4×C61C2411yescharacteristic
171M16×C61—44no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—44no—
182C2×C8×C61C2×D412yes—
183C2×C8×C61C2×D412yes—
184C2×C8×C61#4112yes—
185C4⋊C4×C61—22no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
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—42no—
200C4⋊C4×C61—42no—
201C4⋊C4×C61—42no—
202C4⋊C4×C61—42no—
203C4⋊C4×C61—81no—
204C4⋊C4×C61—81no—
205C4⋊C4×C61#4112yes—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—42no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—42no—
212C22⋊C4×C61—81no—
213C22⋊C4×C61—81no—
214C22⋊C4×C61—81no—
215C42×C61—21no—
216C42×C61—21no—
217C42×C61—42no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61#12112yes—
231C23×C61#13712yes—
232C23×C61C22×D411yescharacteristic
233Q8×C61—41no—
234Q8×C61—41no—
235Q8×C61—41no—
236Q8×C61—41no—
237D4×C61—44no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—22no—
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—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
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—84no—
282C2×C4×C61#12112yes—
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61H(5,𝔽2)11yescharacteristic
288C2×C4×C612−1+411yescharacteristic
289C8×C61—22no—
290C8×C61—22no—
291C8×C61—22no—
292C8×C61—41no—
293#25241C6111yesmaximal, characteristic, direct product factor, Sylow
294C22×C61—22no—
295C22×C61—22no—
296C22×C61—22no—
297C22×C61—22no—
298C22×C61—22no—
299C22×C61—22no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61—41no—
303C22×C61—41no—
304C22×C61—41no—
305C22×C61—41no—
306C22×C61—41no—
307C22×C61—41no—
308C22×C61C2×#12111yescharacteristic
309C22×C61#54611yescharacteristic
310C22×C61#54711yescharacteristic
311C22×C61C2×#13711yescharacteristic
312C22×C61#57511yescharacteristic
313C22×C61#57611yescharacteristic
314C22×C61#57811yescharacteristic
315C4×C61—22no—
316C4×C61—41no—
317C4×C61—41no—
318C4×C61—41no—
319C4×C61—42no—
320C4×C61—81no—
321C4×C61—81no—
322C4×C61—81no—
323C4×C61—81no—
324C4×C61—81no—
325C4×C61—81no—
326C4×C61—81no—
327C4×C61#52911yescharacteristic
328C4×C61#53911yescharacteristic
329C4×C61#54611yescharacteristic
330C4×C61#54711yescharacteristic
331C2×#485C2×C6111yescharacteristic, complemented
332C2×#435C2×C6111yescharacteristic
333#2485C2×C6111yescharacteristic
334#2417C2×C6111yescharacteristic
335#2086C2×C6111yescharacteristic, complemented
336#2077C2×C6111yescharacteristic, complemented
337#2068C2×C6111yescharacteristic, complemented
338#2036C2×C6111yescharacteristic, complemented
339#1943C2×C6111yescharacteristic, complemented
340#1935C2×C6111yescharacteristic, complemented
341#1894C2×C6111yescharacteristic, complemented
342#1892C2×C6111yescharacteristic, complemented
343#1852C2×C6111yescharacteristic, complemented
344#1808C2×C6111yescharacteristic, complemented
345#1736C2×C6111yescharacteristic, complemented
346C2×C61—42no—
347C2×C61—42no—
348C2×C61#242511yescharacteristic
349C2×C61#305611yescharacteristic
350C2×C61#306111yescharacteristic
351C2×C61#331211yescharacteristic
352C2×C61#331911yescharacteristic
353C2×C61#334611yescharacteristic
354C2×C61#334911yescharacteristic
355C22×M16C22×C6111yescharacteristic
356C23×C8C22×C6111yescharacteristic
357C2×C22⋊Q8C22×C6111yescharacteristic
358C2×C22⋊Q8C22×C6111yescharacteristic
359C2×C4×D4C22×C6111yescharacteristic
360C2×#117C22×C6111yescharacteristic
361C22×C4⋊C4C22×C6111yescharacteristic
362#485—24no—
363#435—24no—
364C2×#107C22×C6111yescharacteristic
365C2×#107C22×C6111yescharacteristic
366C2×#107C22×C6111yescharacteristic
367C2×#106C22×C6111yescharacteristic
368C2×C4⋊C8C22×C6111yescharacteristic
369C2×#103C22×C6111yescharacteristic
370C2×#103C22×C6111yescharacteristic
371C2×#103C22×C6111yescharacteristic
372C2×#103C22×C6111yescharacteristic
373C2×C22⋊C8C22×C6111yescharacteristic
374C2×C22⋊C8C22×C6111yescharacteristic
375C2×#97C22×C6111yescharacteristic
376#398—21no—
377#397—21no—
378#396—21no—
379#394—21no—
380#391C22×C6111yescharacteristic
381#389C22×C6111yescharacteristic
382#389C22×C6111yescharacteristic
383#389C22×C6111yescharacteristic
384#388—21no—
385#387—21no—
386#386—21no—
387#380—21no—
388#380C22×C6111yescharacteristic
389#380C22×C6111yescharacteristic
390#380C22×C6111yescharacteristic
391#380C22×C6111yescharacteristic
392#340C22×C6111yescharacteristic
393#340C22×C6111yescharacteristic
394#340C22×C6111yescharacteristic
395#340C22×C6111yescharacteristic
396#340C22×C6111yescharacteristic
397#340C22×C6111yescharacteristic
398#340C22×C6111yescharacteristic
399#340C22×C6111yescharacteristic
400C61#2524111yescharacteristic, direct product factor, Sylow
401C22×Q8C23×C6111yescharacteristic
402C22×D4D4×C6111yescharacteristic
403C23×C4—21no—
404C23×C4C23×C6111yescharacteristic
405C23×C4C23×C6111yescharacteristic
406C2×M16—22no—
407C2×M16—22no—
408C2×M16—41no—
409C22×C8—22no—
410C22×C8—22no—
411C22×C8—41no—
412C22×C8C23×C6111yescharacteristic
413C22×C8C23×C6111yescharacteristic
414C22×C8C23×C6111yescharacteristic
415C22×C8C23×C6111yescharacteristic
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—41no—
420C4×D4—22no—
421C4×D4—22no—
422#117—22no—
423#117—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—41no—
432C2×C4⋊C4D4×C6111yescharacteristic
433C2×C4⋊C4C23×C6111yescharacteristic
434C2×C4⋊C4C23×C6111yescharacteristic
435C2×C4⋊C4C23×C6111yescharacteristic
436C2×C4⋊C4C23×C6111yescharacteristic
437C2×C4⋊C4C23×C6111yescharacteristic
438C2×C4⋊C4C23×C6111yescharacteristic
439C2×C4⋊C4C23×C6111yescharacteristic
440C2×C22⋊C4—21no—
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⋊C4D4×C6111yescharacteristic
448C2×C22⋊C4D4×C6111yescharacteristic
449C2×C42—21no—
450C2×C42C23×C6111yescharacteristic
451#107—22no—
452#107—22no—
453#107—41no—
454#106—22no—
455C4⋊C8—22no—
456#103—22no—
457#103—22no—
458#103—22no—
459#103—41no—
460C22⋊C8—22no—
461C22⋊C8D4×C6114yes—
462#97—22no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472C24C2×D4×C6111yescharacteristic
473C24C2×D4×C6111yescharacteristic
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—41no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—81no—
504C22×C4C2×D4×C6111yescharacteristic
505C22×C4C2×D4×C6111yescharacteristic
506C22×C4C2×D4×C6111yescharacteristic
507C22×C4C2×D4×C6111yescharacteristic
508C22×C4C2×D4×C6112yes—
509C22×C4#41×C6112yes—
510C22×C4C24×C6111yescharacteristic
511M16—44no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—44no—
522C2×C8C2×D4×C6112yes—
523C2×C8C2×D4×C6112yes—
524C2×C8#41×C6112yes—
525C4⋊C4—22no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
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—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—81no—
544C4⋊C4—81no—
545C4⋊C4#41×C6112yes—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—81no—
553C22⋊C4—81no—
554C22⋊C4—81no—
555C42—21no—
556C42—21no—
557C42—42no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23#121×C6112yes—
571C23#137×C6112yes—
572C23C22×D4×C6111yescharacteristic
573Q8—41no—
574Q8—41no—
575Q8—41no—
576Q8—41no—
577D4—44no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
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×C4—41no—
621C2×C4—84no—
622C2×C4#121×C6112yes—
623C2×C4C22×D4×C6111yescharacteristic
624C2×C4C2×#41×C6111yescharacteristic
625C2×C4C2×#41×C6111yescharacteristic
626C2×C4C2×#41×C6111yescharacteristic
627C2×C4H(5,𝔽2)×C6111yescharacteristic
628C2×C42−1+4×C6111yescharacteristic
629C8—22no—
630C8—22no—
631C8—22no—
632C8—41no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22C2×#121×C6111yescharacteristic
648C22C61×#54611yescharacteristic
649C22C61×#54711yescharacteristic
650C22C2×#137×C6111yescharacteristic
651C22C61×#57511yescharacteristic
652C22C61×#57611yescharacteristic
653C22C61×#57811yescharacteristic
654C4—22no—
655C4—41no—
656C4—41no—
657C4—42no—
658C4—41no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—81no—
666C4C61×#52911yescharacteristic
667C4C61×#53911yescharacteristic
668C4C61×#54611yescharacteristic
669C4C61×#54711yescharacteristic
670C2—42no—
671C2—42no—
672C2C61×#242511yescharacteristic
673C2C61×#305611yescharacteristic
674C2C61×#306111yescharacteristic
675C2C61×#331211yescharacteristic
676C2C61×#331911yescharacteristic
677C2C61×#334611yescharacteristic
678C2C61×#334911yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC22×D4×C61D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C4×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#485C2semidirect
5. C61×#2086C2semidirect
6. C61×#2077C2semidirect
7. C61×#2068C2semidirect
8. C61×#2036C2semidirect
9. C61×#1943C2semidirect
10. C61×#1935C2semidirect
11. C61×#1894C2semidirect
12. C61×#1892C2semidirect
13. C61×#1852C2semidirect
14. C61×#1808C2semidirect
15. C61×#1736C2semidirect
293. #25241C61direct (N × H)
331. C2×#485C2×C61semidirect
335. #2086C2×C61semidirect
336. #2077C2×C61semidirect
337. #2068C2×C61semidirect
338. #2036C2×C61semidirect
339. #1943C2×C61semidirect
340. #1935C2×C61semidirect
341. #1894C2×C61semidirect
342. #1892C2×C61semidirect
343. #1852C2×C61semidirect
344. #1808C2×C61semidirect
345. #1736C2×C61semidirect
400. C61#25241direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4852
C2×C61×#4352
C61×#24852
C61×#24172
C61×#20862
C61×#20772
C61×#20682
C61×#20362
C61×#19432
C61×#19352
C61×#18942
C61×#18922
C61×#18522
C61×#18082
C61×#17362
#2524161