Finite Group Databasebeta

← C61×#34295 #29537728

Subgroups — C61×#34295 #29537728

Order 15616.

3200 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#550C211yesmaximal, characteristic
2C2×C61×#520C211yesmaximal, characteristic, complemented
3C2×C4×#41×C61C211yesmaximal, characteristic, complemented
4C61×#2366C213yesmaximal, complemented
5C61×#2363C213yesmaximal, complemented
6C61×#2361C213yesmaximal, complemented
7C61×#2352C213yesmaximal, complemented
8C61×#2351C211yesmaximal, characteristic, complemented
9C61×#2341C211yesmaximal, characteristic, complemented
10C61×#2341C211yesmaximal, characteristic, complemented
11C61×#2328C213yesmaximal, complemented
12C61×#2324C213yesmaximal, complemented
13C4×#121×C61C213yesmaximal, complemented
14C61×#2290C213yesmaximal, complemented
15C61×#2276C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×#41×C61C2211yescharacteristic
18C61×#550C4116yescomplemented
19C2×#127×C61C2213yes—
20C2×#121×C61C2213yes—
21C2×#121×C61C2213yes—
22C61×#520—28no—
23C4×#41×C61—28no—
24C2×C4×Q8×C61C2211yescharacteristic
25C2×C4×Q8×C61C2211yescharacteristic
26C2×C4×Q8×C61C2211yescharacteristic
27C2×C4×Q8×C61C2211yescharacteristic
28C2×C4×Q8×C61C2211yescharacteristic
29C2×C4×D4×C61C2213yes—
30C2×C4×D4×C61C2213yes—
31C2×C4×D4×C61C2213yes—
32C2×C4×D4×C61C2213yes—
33C2×C4×D4×C61C2216yes—
34C2×C4×D4×C61C2213yes—
35C2×#117×C61C2213yes—
36C2×#117×C61C2213yes—
37C22×C4⋊C4×C61C2213yes—
38C22×C42×C61C2213yes—
39C61×#390C2213yes—
40C61×#390C2213yes—
41C61×#390C2216yes—
42C61×#390C2213yes—
43C61×#390C2213yes—
44C61×#389C2213yes—
45C61×#389C2213yes—
46C61×#388C2213yes—
47C61×#388C2213yes—
48C61×#388C2216yes—
49C61×#387C2211yescharacteristic
50C61×#387C2213yes—
51C61×#386C2213yes—
52C61×#386C2213yes—
53C61×#386C2216yes—
54C61×#386C2216yes—
55C61×#386C2216yes—
56C61×#385C2213yes—
57C61×#385C2213yes—
58C61×#382C2213yes—
59C61×#380C2213yes—
60C61×#380C2213yes—
61C4×C4⋊C4×C61C2213yes—
62C4×C4⋊C4×C61C2213yes—
63C4×C4⋊C4×C61C2213yes—
64C4×C4⋊C4×C61C2213yes—
65C4×C22⋊C4×C61C2213yes—
66C4×C22⋊C4×C61C2213yes—
67C4×C22⋊C4×C61C2216yes—
68C61×#376C2213yes—
69C2×#41×C61—24no—
70C2×#41×C61—24no—
71C2×#41×C61—24no—
72C2×#41×C61—24no—
73C2×#41×C61C2×C418yescomplemented
74C2×#41×C61C2×C418yescomplemented
75C22×Q8×C61C2311yescharacteristic
76C22×D4×C61C2313yes—
77C22×D4×C61C2313yes—
78C22×D4×C61C2313yes—
79C22×D4×C61C2316yes—
80C23×C4×C61C2313yes—
81C23×C4×C61C2313yes—
82C23×C4×C61C2313yes—
83C23×C4×C61C2316yes—
84C23×C4×C61C2313yes—
85#127×C61C2×C4124yescomplemented
86#121×C61C2×C4124yescomplemented
87#121×C61C2×C4124yescomplemented
88C4×Q8×C61—24no—
89C4×Q8×C61—24no—
90C4×Q8×C61—24no—
91C4×Q8×C61C2×C418yescomplemented
92C4×Q8×C61D418yescomplemented
93C4×D4×C61—212no—
94C4×D4×C61—212no—
95C4×D4×C61—212no—
96C4×D4×C61—212no—
97C4×D4×C61—412no—
98C4×D4×C61C2×C4124yescomplemented
99#117×C61—212no—
100#117×C61—212no—
101C2×C4⋊C4×C61—212no—
102C2×C4⋊C4×C61C2313yes—
103C2×C4⋊C4×C61C2313yes—
104C2×C4⋊C4×C61C2313yes—
105C2×C4⋊C4×C61C2313yes—
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2313yes—
108C2×C4⋊C4×C61C2313yes—
109C2×C4⋊C4×C61C2313yes—
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2313yes—
112C2×C22⋊C4×C61C2313yes—
113C2×C22⋊C4×C61C2313yes—
114C2×C22⋊C4×C61C2316yes—
115C2×C22⋊C4×C61C2313yes—
116C2×C22⋊C4×C61C2316yes—
117C2×C22⋊C4×C61C2313yes—
118C2×C22⋊C4×C61C2313yes—
119C2×C22⋊C4×C61C2313yes—
120C2×C22⋊C4×C61C2316yes—
121C2×C22⋊C4×C61C2313yes—
122C2×C22⋊C4×C61C2313yes—
123C2×C42×C61—212no—
124C2×C42×C61C2313yes—
125C2×C42×C61C2313yes—
126C2×C42×C61C2313yes—
127C2×C42×C61C2313yes—
128C2×C42×C61C2311yescharacteristic
129C2×C42×C61C2316yes—
130C2×C42×C61C2313yes—
131C2×C42×C61C2313yes—
132#95×C61C2311yescharacteristic
133#95×C61C2313yes—
134#95×C61C2313yes—
135#95×C61C2313yes—
136#95×C61C2313yes—
137#95×C61C2311yescharacteristic
138#95×C61C2311yescharacteristic
139#95×C61C2313yes—
140#95×C61C2316yes—
141#95×C61C2311yescharacteristic
142#95×C61C2313yes—
143C24×C61C2413yes—
144C24×C61C2413yes—
145#41×C61—232no—
146#41×C61—232no—
147C2×Q8×C61C22×C414yes—
148C2×Q8×C61C2×D414yes—
149C2×Q8×C61#4114yes—
150C2×D4×C61—26no—
151C2×D4×C61—26no—
152C2×D4×C61—26no—
153C2×D4×C61—26no—
154C2×D4×C61—46no—
155C2×D4×C61—46no—
156C2×D4×C61—43no—
157C2×D4×C61—43no—
158C2×D4×C61C22×C4112yes—
159C2×D4×C61C22×C4112yes—
160C2×D4×C61C22×C4112yes—
161C2×D4×C61C22×C4124yes—
162C22×C4×C61—26no—
163C22×C4×C61—26no—
164C22×C4×C61—26no—
165C22×C4×C61—26no—
166C22×C4×C61—26no—
167C22×C4×C61—26no—
168C22×C4×C61—26no—
169C22×C4×C61—212no—
170C22×C4×C61—43no—
171C22×C4×C61—43no—
172C22×C4×C61—43no—
173C22×C4×C61—46no—
174C22×C4×C61—46no—
175C22×C4×C61C22×C4112yes—
176C22×C4×C61C22×C4112yes—
177C22×C4×C61C2411yescharacteristic
178C22×C4×C61C2413yes—
179C22×C4×C61C2413yes—
180C22×C4×C61C2413yes—
181C22×C4×C61C2411yescharacteristic
182C22×C4×C61C2411yescharacteristic
183C22×C4×C61C2411yescharacteristic
184C22×C4×C61C2413yes—
185C22×C4×C61C2411yescharacteristic
186C22×C4×C61C2411yescharacteristic
187C22×C4×C61C2413yes—
188C22×C4×C61C2411yescharacteristic
189C22×C4×C61C2413yes—
190C4⋊C4×C61—26no—
191C4⋊C4×C61—26no—
192C4⋊C4×C61—22no—
193C4⋊C4×C61—26no—
194C4⋊C4×C61—26no—
195C4⋊C4×C61—26no—
196C4⋊C4×C61—43no—
197C4⋊C4×C61C22×C414yes—
198C4⋊C4×C61C22×C4112yes—
199C4⋊C4×C61C2×D4112yes—
200C22⋊C4×C61—26no—
201C22⋊C4×C61—212no—
202C22⋊C4×C61—26no—
203C22⋊C4×C61—26no—
204C22⋊C4×C61—43no—
205C22⋊C4×C61—46no—
206C22⋊C4×C61—43no—
207C22⋊C4×C61—43no—
208C22⋊C4×C61—46no—
209C22⋊C4×C61C22×C4112yes—
210C22⋊C4×C61C22×C4112yes—
211C42×C61—22no—
212C42×C61—26no—
213C42×C61—26no—
214C42×C61—26no—
215C42×C61—26no—
216C42×C61—46no—
217C42×C61C22×C4112yes—
218C42×C61C2×D4112yes—
219C23×C61—23no—
220C23×C61—23no—
221C23×C61—23no—
222C23×C61—23no—
223C23×C61—23no—
224C23×C61—23no—
225C23×C61—23no—
226C23×C61—23no—
227C23×C61—23no—
228C23×C61—23no—
229C23×C61—23no—
230C23×C61—23no—
231C23×C61C23×C416yes—
232C23×C61C23×C416yes—
233C23×C61C2511yescharacteristic
234Q8×C61C4×D4116yescomplemented
235D4×C61—224no—
236D4×C61—224no—
237D4×C61—412no—
238D4×C61—424no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—23no—
245C2×C4×C61—23no—
246C2×C4×C61—23no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—23no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—224no—
254C2×C4×C61—224no—
255C2×C4×C61—21no—
256C2×C4×C61—23no—
257C2×C4×C61—23no—
258C2×C4×C61—21no—
259C2×C4×C61—23no—
260C2×C4×C61—23no—
261C2×C4×C61—23no—
262C2×C4×C61—21no—
263C2×C4×C61—23no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—23no—
267C2×C4×C61—23no—
268C2×C4×C61—23no—
269C2×C4×C61—21no—
270C2×C4×C61—412no—
271C2×C4×C61—412no—
272C2×C4×C61—812no—
273C2×C4×C61C23×C412yes—
274C2×C4×C61C23×C416yes—
275C2×C4×C61C23×C412yes—
276C2×C4×C61C23×C412yes—
277C2×C4×C61C23×C416yes—
278C2×C4×C61C22×D412yes—
279C2×C4×C61C22×D416yes—
280C2×C4×C61C22×D416yes—
281C2×C4×C61C2×#4116yes—
282C2×C4×C61H(5,𝔽2)12yes—
283#34295C6111yesmaximal, characteristic, direct product factor, Sylow
284C22×C61—26no—
285C22×C61—26no—
286C22×C61—26no—
287C22×C61—26no—
288C22×C61—26no—
289C22×C61—26no—
290C22×C61—43no—
291C22×C61—43no—
292C22×C61—43no—
293C22×C61—43no—
294C22×C61—43no—
295C22×C61—43no—
296C22×C61—43no—
297C22×C61—43no—
298C22×C61C24×C411yescharacteristic
299C22×C61C23×D411yescharacteristic
300C22×C61C22×#4111yescharacteristic
301C22×C61C2×H(5,𝔽2)11yescharacteristic
302C22×C61#58511yescharacteristic
303C22×C61#58511yescharacteristic
304C22×C61#58511yescharacteristic
305C4×C61—22no—
306C4×C61—22no—
307C4×C61—22no—
308C4×C61—26no—
309C4×C61—22no—
310C4×C61—22no—
311C4×C61—26no—
312C4×C61—41no—
313C4×C61—43no—
314C4×C61—43no—
315C4×C61—43no—
316C4×C61—41no—
317C4×C61C2×C4×D4112yes—
318C2×#550C2×C6111yescharacteristic
319C2×#520C2×C6111yescharacteristic, complemented
320C2×C4×#41C2×C6111yescharacteristic, complemented
321#2366C2×C6113yescomplemented
322#2363C2×C6113yescomplemented
323#2361C2×C6113yescomplemented
324#2352C2×C6113yescomplemented
325#2351C2×C6111yescharacteristic, complemented
326#2341C2×C6111yescharacteristic, complemented
327#2341C2×C6111yescharacteristic, complemented
328#2328C2×C6113yescomplemented
329#2324C2×C6113yescomplemented
330C4×#121C2×C6113yescomplemented
331#2290C2×C6113yescomplemented
332#2276C2×C6111yescharacteristic, complemented
333C2×C61—46no—
334C2×C61—46no—
335C2×C61C22×C4×D411yescharacteristic
336C2×C61#342811yescharacteristic
337C2×C61C4×H(5,𝔽2)11yescharacteristic
338C2×C61#348711yescharacteristic
339C2×C61#348811yescharacteristic
340C2×C61#351711yescharacteristic
341C2×C61#352411yescharacteristic
342C22×#41C22×C6111yescharacteristic
343C22×#41C22×C6111yescharacteristic
344#550C4×C61116yescomplemented
345C2×#127C22×C6113yes—
346C2×#121C22×C6113yes—
347C2×#121C22×C6113yes—
348#520—28no—
349C4×#41—28no—
350C2×C4×Q8C22×C6111yescharacteristic
351C2×C4×Q8C22×C6111yescharacteristic
352C2×C4×Q8C22×C6111yescharacteristic
353C2×C4×Q8C22×C6111yescharacteristic
354C2×C4×Q8C22×C6111yescharacteristic
355C2×C4×D4C22×C6113yes—
356C2×C4×D4C22×C6113yes—
357C2×C4×D4C22×C6113yes—
358C2×C4×D4C22×C6113yes—
359C2×C4×D4C22×C6116yes—
360C2×C4×D4C22×C6113yes—
361C2×#117C22×C6113yes—
362C2×#117C22×C6113yes—
363C22×C4⋊C4C22×C6113yes—
364C22×C42C22×C6113yes—
365#390C22×C6113yes—
366#390C22×C6116yes—
367#390C22×C6113yes—
368#390C22×C6113yes—
369#390C22×C6113yes—
370#389C22×C6113yes—
371#389C22×C6113yes—
372#388C22×C6116yes—
373#388C22×C6113yes—
374#388C22×C6113yes—
375#387C22×C6113yes—
376#387C22×C6111yescharacteristic
377#386C22×C6116yes—
378#386C22×C6113yes—
379#386C22×C6116yes—
380#386C22×C6116yes—
381#386C22×C6113yes—
382#385C22×C6113yes—
383#385C22×C6113yes—
384#382C22×C6113yes—
385#380C22×C6113yes—
386#380C22×C6113yes—
387C4×C4⋊C4C22×C6113yes—
388C4×C4⋊C4C22×C6113yes—
389C4×C4⋊C4C22×C6113yes—
390C4×C4⋊C4C22×C6113yes—
391C4×C22⋊C4C22×C6113yes—
392C4×C22⋊C4C22×C6113yes—
393C4×C22⋊C4C22×C6116yes—
394#376C22×C6113yes—
395C61#3429511yescharacteristic, direct product factor, Sylow
396C2×#41—24no—
397C2×#41—24no—
398C2×#41—24no—
399C2×#41—24no—
400C2×#41C2×C4×C6118yescomplemented
401C2×#41C2×C4×C6118yescomplemented
402C22×Q8C23×C6111yescharacteristic
403C22×D4C23×C6113yes—
404C22×D4C23×C6113yes—
405C22×D4C23×C6116yes—
406C22×D4C23×C6113yes—
407C23×C4C23×C6113yes—
408C23×C4C23×C6113yes—
409C23×C4C23×C6113yes—
410C23×C4C23×C6116yes—
411C23×C4C23×C6113yes—
412#127C2×C4×C61124yescomplemented
413#121C2×C4×C61124yescomplemented
414#121C2×C4×C61124yescomplemented
415C4×Q8—24no—
416C4×Q8—24no—
417C4×Q8—24no—
418C4×Q8C2×C4×C6118yescomplemented
419C4×Q8D4×C6118yescomplemented
420C4×D4—212no—
421C4×D4—212no—
422C4×D4—212no—
423C4×D4—212no—
424C4×D4—412no—
425C4×D4C2×C4×C61124yescomplemented
426#117—212no—
427#117—212no—
428C2×C4⋊C4—212no—
429C2×C4⋊C4C23×C6113yes—
430C2×C4⋊C4C23×C6113yes—
431C2×C4⋊C4C23×C6111yescharacteristic
432C2×C4⋊C4C23×C6113yes—
433C2×C4⋊C4C23×C6113yes—
434C2×C4⋊C4C23×C6113yes—
435C2×C4⋊C4C23×C6113yes—
436C2×C4⋊C4C23×C6111yescharacteristic
437C2×C4⋊C4C23×C6113yes—
438C2×C4⋊C4C23×C6113yes—
439C2×C22⋊C4C23×C6113yes—
440C2×C22⋊C4C23×C6116yes—
441C2×C22⋊C4C23×C6113yes—
442C2×C22⋊C4C23×C6113yes—
443C2×C22⋊C4C23×C6116yes—
444C2×C22⋊C4C23×C6116yes—
445C2×C22⋊C4C23×C6113yes—
446C2×C22⋊C4C23×C6113yes—
447C2×C22⋊C4C23×C6113yes—
448C2×C22⋊C4C23×C6113yes—
449C2×C22⋊C4C23×C6113yes—
450C2×C42—212no—
451C2×C42C23×C6113yes—
452C2×C42C23×C6113yes—
453C2×C42C23×C6113yes—
454C2×C42C23×C6113yes—
455C2×C42C23×C6111yescharacteristic
456C2×C42C23×C6116yes—
457C2×C42C23×C6113yes—
458C2×C42C23×C6113yes—
459#95C23×C6111yescharacteristic
460#95C23×C6113yes—
461#95C23×C6113yes—
462#95C23×C6113yes—
463#95C23×C6113yes—
464#95C23×C6111yescharacteristic
465#95C23×C6111yescharacteristic
466#95C23×C6113yes—
467#95C23×C6116yes—
468#95C23×C6111yescharacteristic
469#95C23×C6113yes—
470C24C24×C6113yes—
471C24C24×C6113yes—
472#41—232no—
473#41—232no—
474C2×Q8C22×C4×C6114yes—
475C2×Q8C2×D4×C6114yes—
476C2×Q8#41×C6114yes—
477C2×D4—26no—
478C2×D4—26no—
479C2×D4—26no—
480C2×D4—26no—
481C2×D4—46no—
482C2×D4—46no—
483C2×D4—43no—
484C2×D4—43no—
485C2×D4C22×C4×C61112yes—
486C2×D4C22×C4×C61112yes—
487C2×D4C22×C4×C61112yes—
488C2×D4C22×C4×C61124yes—
489C22×C4—26no—
490C22×C4—26no—
491C22×C4—26no—
492C22×C4—26no—
493C22×C4—26no—
494C22×C4—26no—
495C22×C4—26no—
496C22×C4—212no—
497C22×C4—43no—
498C22×C4—43no—
499C22×C4—43no—
500C22×C4—46no—
501C22×C4—46no—
502C22×C4C22×C4×C61112yes—
503C22×C4C22×C4×C61112yes—
504C22×C4C24×C6111yescharacteristic
505C22×C4C24×C6113yes—
506C22×C4C24×C6113yes—
507C22×C4C24×C6113yes—
508C22×C4C24×C6111yescharacteristic
509C22×C4C24×C6111yescharacteristic
510C22×C4C24×C6111yescharacteristic
511C22×C4C24×C6113yes—
512C22×C4C24×C6111yescharacteristic
513C22×C4C24×C6111yescharacteristic
514C22×C4C24×C6113yes—
515C22×C4C24×C6111yescharacteristic
516C22×C4C24×C6113yes—
517C4⋊C4—26no—
518C4⋊C4—26no—
519C4⋊C4—22no—
520C4⋊C4—26no—
521C4⋊C4—26no—
522C4⋊C4—26no—
523C4⋊C4—43no—
524C4⋊C4C22×C4×C6114yes—
525C4⋊C4C22×C4×C61112yes—
526C4⋊C4C2×D4×C61112yes—
527C22⋊C4—26no—
528C22⋊C4—212no—
529C22⋊C4—26no—
530C22⋊C4—26no—
531C22⋊C4—46no—
532C22⋊C4—43no—
533C22⋊C4—46no—
534C22⋊C4—43no—
535C22⋊C4—43no—
536C22⋊C4C22×C4×C61112yes—
537C22⋊C4C22×C4×C61112yes—
538C42—22no—
539C42—26no—
540C42—26no—
541C42—26no—
542C42—26no—
543C42—46no—
544C42C22×C4×C61112yes—
545C42C2×D4×C61112yes—
546C23—23no—
547C23—23no—
548C23—23no—
549C23—23no—
550C23—23no—
551C23—23no—
552C23—23no—
553C23—23no—
554C23—23no—
555C23—23no—
556C23—23no—
557C23—23no—
558C23C23×C4×C6116yes—
559C23C23×C4×C6116yes—
560C23C25×C6111yescharacteristic
561Q8C4×D4×C61116yescomplemented
562D4—224no—
563D4—224no—
564D4—412no—
565D4—424no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—23no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—23no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—21no—
583C2×C4—23no—
584C2×C4—23no—
585C2×C4—21no—
586C2×C4—23no—
587C2×C4—23no—
588C2×C4—23no—
589C2×C4—21no—
590C2×C4—23no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—23no—
594C2×C4—23no—
595C2×C4—23no—
596C2×C4—21no—
597C2×C4—412no—
598C2×C4—412no—
599C2×C4—812no—
600C2×C4C23×C4×C6112yes—
601C2×C4C23×C4×C6116yes—
602C2×C4C23×C4×C6112yes—
603C2×C4C23×C4×C6112yes—
604C2×C4C23×C4×C6116yes—
605C2×C4C22×D4×C6112yes—
606C2×C4C22×D4×C6116yes—
607C2×C4C22×D4×C6116yes—
608C2×C4C2×#41×C6116yes—
609C2×C4H(5,𝔽2)×C6112yes—
610C22—26no—
611C22—26no—
612C22—26no—
613C22—26no—
614C22—26no—
615C22—26no—
616C22—43no—
617C22—43no—
618C22—43no—
619C22—43no—
620C22—43no—
621C22—43no—
622C22—43no—
623C22—43no—
624C22C24×C4×C6111yescharacteristic
625C22C23×D4×C6111yescharacteristic
626C22C22×#41×C6111yescharacteristic
627C22C2×H(5,𝔽2)×C6111yescharacteristic
628C22C61×#58511yescharacteristic
629C22C61×#58511yescharacteristic
630C22C61×#58511yescharacteristic
631C4—22no—
632C4—22no—
633C4—22no—
634C4—26no—
635C4—22no—
636C4—22no—
637C4—26no—
638C4—41no—
639C4—43no—
640C4—43no—
641C4—43no—
642C4—41no—
643C4C2×C4×D4×C61112yes—
644C2—46no—
645C2—46no—
646C2C22×C4×D4×C6111yescharacteristic
647C2C61×#342811yescharacteristic
648C2C4×H(5,𝔽2)×C6111yescharacteristic
649C2C61×#348711yescharacteristic
650C2C61×#348811yescharacteristic
651C2C61×#351711yescharacteristic
652C2C61×#352411yescharacteristic
subgroupG/H
center, socleC23×C61C25
commutatorC22C24×C4×C61
Frattini, cosocleC23C25×C61
prime radicalC2×C61×#550C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#520C2semidirect
3. C2×C4×#41×C61C2semidirect
4. C61×#2366C2semidirect
5. C61×#2363C2semidirect
6. C61×#2361C2semidirect
7. C61×#2352C2semidirect
8. C61×#2351C2semidirect
9. C61×#2341C2semidirect
10. C61×#2341C2semidirect
11. C61×#2328C2semidirect
12. C61×#2324C2semidirect
13. C4×#121×C61C2semidirect
14. C61×#2290C2semidirect
15. C61×#2276C2semidirect
18. C61×#550C4semidirect
73. C2×#41×C61C2×C4semidirect
74. C2×#41×C61C2×C4semidirect
85. #127×C61C2×C4semidirect
86. #121×C61C2×C4semidirect
87. #121×C61C2×C4semidirect
91. C4×Q8×C61C2×C4semidirect
92. C4×Q8×C61D4semidirect
98. C4×D4×C61C2×C4semidirect
234. Q8×C61C4×D4semidirect
283. #34295C61direct (N × H)
319. C2×#520C2×C61semidirect
320. C2×C4×#41C2×C61semidirect
321. #2366C2×C61semidirect
322. #2363C2×C61semidirect
323. #2361C2×C61semidirect
324. #2352C2×C61semidirect
325. #2351C2×C61semidirect
326. #2341C2×C61semidirect
327. #2341C2×C61semidirect
328. #2328C2×C61semidirect
329. #2324C2×C61semidirect
330. C4×#121C2×C61semidirect
331. #2290C2×C61semidirect
332. #2276C2×C61semidirect
344. #550C4×C61semidirect
395. C61#34295direct (N × H)
400. C2×#41C2×C4×C61semidirect
401. C2×#41C2×C4×C61semidirect
412. #127C2×C4×C61semidirect
413. #121C2×C4×C61semidirect
414. #121C2×C4×C61semidirect
418. C4×Q8C2×C4×C61semidirect
419. C4×Q8D4×C61semidirect
425. C4×D4C2×C4×C61semidirect
561. Q8C4×D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5502
C2×C61×#5202
C2×C4×#41×C612
C61×#23662
C61×#23632
C61×#23612
C61×#23522
C61×#23512
C61×#23412
C61×#23282
C61×#23242
C4×#121×C612
C61×#22902
C61×#22762
#3429561