Finite Group Databasebeta

← C61×#34294 #29537727

Subgroups — C61×#34294 #29537727

Order 15616.

3112 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#548C211yesmaximal, characteristic
2C2×C61×#520C211yesmaximal, characteristic, complemented
3C22×C4×Q8×C61C211yesmaximal, characteristic, complemented
4C61×#2367C213yesmaximal, complemented
5C61×#2361C213yesmaximal, complemented
6C61×#2360C213yesmaximal, complemented
7Q8×C4⋊C4×C61C211yesmaximal, characteristic, complemented
8D4×C4⋊C4×C61C213yesmaximal, complemented
9C61×#2341C211yesmaximal, characteristic, complemented
10Q8×C22⋊C4×C61C211yesmaximal, characteristic, complemented
11C61×#2326C213yesmaximal, complemented
12C61×#2323C213yesmaximal, complemented
13C4×#121×C61C213yesmaximal, complemented
14C61×#2290C213yesmaximal, complemented
15C61×#2276C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C23×Q8×C61C2211yescharacteristic
18C61×#548C4116yescomplemented
19C2×#124×C61C2213yes—
20C2×C22⋊Q8×C61C2213yes—
21C2×#121×C61C2213yes—
22C61×#520—28no—
23C2×C4×Q8×C61—28no—
24C2×C4×Q8×C61C2211yescharacteristic
25C2×C4×Q8×C61C2213yes—
26C2×C4×Q8×C61C2211yescharacteristic
27C2×C4×Q8×C61C2211yescharacteristic
28C2×C4×Q8×C61C2213yes—
29C2×C4×Q8×C61C2211yescharacteristic
30C2×C4×Q8×C61C2211yescharacteristic
31C2×C4×D4×C61C2213yes—
32C2×C4×D4×C61C2213yes—
33C2×C4×D4×C61C2216yes—
34C2×C4×D4×C61C2213yes—
35C2×#117×C61C2213yes—
36C22×C4⋊C4×C61C2213yes—
37C22×C4⋊C4×C61C2213yes—
38C22×C42×C61C2213yes—
39C61×#391C2213yes—
40C61×#391C2213yes—
41C61×#390C2213yes—
42C61×#390C2213yes—
43C61×#389C2213yes—
44C61×#389C2216yes—
45C61×#389C2213yes—
46C61×#388C2213yes—
47C61×#388C2213yes—
48C61×#388C2216yes—
49C61×#388C2216yes—
50C61×#387C2213yes—
51C61×#387C2213yes—
52C61×#386C2213yes—
53C61×#386C2213yes—
54C61×#385C2211yescharacteristic
55C61×#385C2213yes—
56C61×#385C2216yes—
57C61×#385C2216yes—
58C61×#384C2213yes—
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×C61C2×C418yescomplemented
72C22×Q8×C61—24no—
73C22×Q8×C61—24no—
74C22×Q8×C61C2×C418yescomplemented
75C22×Q8×C61C2313yes—
76C22×Q8×C61C2311yescharacteristic
77C22×D4×C61C2313yes—
78C22×D4×C61C2313yes—
79C23×C4×C61C2311yescharacteristic
80C23×C4×C61C2313yes—
81C23×C4×C61C2313yes—
82C23×C4×C61C2313yes—
83C23×C4×C61C2316yes—
84#124×C61C2×C4124yescomplemented
85C22⋊Q8×C61C2×C4124yescomplemented
86#121×C61C2×C4124yescomplemented
87C4×Q8×C61—24no—
88C4×Q8×C61—24no—
89C4×Q8×C61—24no—
90C4×Q8×C61—212no—
91C4×Q8×C61—212no—
92C4×Q8×C61C2×C418yescomplemented
93C4×Q8×C61D418yescomplemented
94C4×D4×C61—212no—
95C4×D4×C61—212no—
96C4×D4×C61—412no—
97C4×D4×C61C2×C4124yescomplemented
98#117×C61—212no—
99C2×C4⋊C4×C61—212no—
100C2×C4⋊C4×C61—212no—
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2313yes—
103C2×C4⋊C4×C61C2313yes—
104C2×C4⋊C4×C61C2313yes—
105C2×C4⋊C4×C61C2316yes—
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2313yes—
108C2×C4⋊C4×C61C2313yes—
109C2×C4⋊C4×C61C2316yes—
110C2×C4⋊C4×C61C2313yes—
111C2×C4⋊C4×C61C2313yes—
112C2×C4⋊C4×C61C2313yes—
113C2×C22⋊C4×C61C2311yescharacteristic
114C2×C22⋊C4×C61C2313yes—
115C2×C22⋊C4×C61C2313yes—
116C2×C22⋊C4×C61C2313yes—
117C2×C22⋊C4×C61C2313yes—
118C2×C22⋊C4×C61C2313yes—
119C2×C22⋊C4×C61C2316yes—
120C2×C22⋊C4×C61C2316yes—
121C2×C22⋊C4×C61C2311yescharacteristic
122C2×C22⋊C4×C61C2313yes—
123C2×C42×C61—212no—
124C2×C42×C61C2313yes—
125C2×C42×C61C2313yes—
126C2×C42×C61C2313yes—
127C2×C42×C61C2313yes—
128C2×C42×C61C2313yes—
129C2×C42×C61C2316yes—
130C2×C42×C61C2313yes—
131C2×C42×C61C2313yes—
132#95×C61C2311yescharacteristic
133#95×C61C2313yes—
134#95×C61C2313yes—
135#95×C61C2313yes—
136#95×C61C2311yescharacteristic
137#95×C61C2313yes—
138#95×C61C2313yes—
139#95×C61C2316yes—
140#95×C61C2313yes—
141#95×C61C2313yes—
142#95×C61C2313yes—
143C24×C61C2413yes—
144C24×C61C2411yescharacteristic
145#41×C61—232no—
146C2×Q8×C61—232no—
147C2×Q8×C61—26no—
148C2×Q8×C61—26no—
149C2×Q8×C61C22×C4112yes—
150C2×Q8×C61C22×C414yes—
151C2×Q8×C61C2×D414yes—
152C2×Q8×C61#4114yes—
153C2×D4×C61—26no—
154C2×D4×C61—26no—
155C2×D4×C61—26no—
156C2×D4×C61—26no—
157C2×D4×C61C22×C4112yes—
158C2×D4×C61C22×C4112yes—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—26no—
162C22×C4×C61—26no—
163C22×C4×C61—26no—
164C22×C4×C61—26no—
165C22×C4×C61—22no—
166C22×C4×C61—26no—
167C22×C4×C61—26no—
168C22×C4×C61—212no—
169C22×C4×C61—43no—
170C22×C4×C61—46no—
171C22×C4×C61—46no—
172C22×C4×C61C22×C4112yes—
173C22×C4×C61C22×C4112yes—
174C22×C4×C61C2411yescharacteristic
175C22×C4×C61C2411yescharacteristic
176C22×C4×C61C2413yes—
177C22×C4×C61C2413yes—
178C22×C4×C61C2413yes—
179C22×C4×C61C2411yescharacteristic
180C22×C4×C61C2413yes—
181C22×C4×C61C2413yes—
182C22×C4×C61C2411yescharacteristic
183C22×C4×C61C2411yescharacteristic
184C22×C4×C61C2413yes—
185C22×C4×C61C2411yescharacteristic
186C22×C4×C61C2413yes—
187C4⋊C4×C61—26no—
188C4⋊C4×C61—26no—
189C4⋊C4×C61—212no—
190C4⋊C4×C61—26no—
191C4⋊C4×C61—22no—
192C4⋊C4×C61—26no—
193C4⋊C4×C61—22no—
194C4⋊C4×C61—43no—
195C4⋊C4×C61—46no—
196C4⋊C4×C61C22×C4112yes—
197C4⋊C4×C61C22×C4112yes—
198C4⋊C4×C61C2×D4112yes—
199C22⋊C4×C61—26no—
200C22⋊C4×C61—22no—
201C22⋊C4×C61—26no—
202C22⋊C4×C61—26no—
203C22⋊C4×C61—26no—
204C22⋊C4×C61—43no—
205C22⋊C4×C61—46no—
206C22⋊C4×C61C22×C414yes—
207C22⋊C4×C61C22×C4112yes—
208C22⋊C4×C61C22×C4124yes—
209C42×C61—26no—
210C42×C61—26no—
211C42×C61—26no—
212C42×C61—26no—
213C42×C61—26no—
214C42×C61—46no—
215C42×C61C22×C4112yes—
216C42×C61C2×D4112yes—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—23no—
222C23×C61—23no—
223C23×C61—23no—
224C23×C61—23no—
225C23×C61—23no—
226C23×C61—23no—
227C23×C61C23×C416yes—
228C23×C61C23×C412yes—
229C23×C61H(5,𝔽2)12yes—
230C23×C612−1+412yes—
231C23×C61C2511yescharacteristic
232Q8×C61—224no—
233Q8×C61C4×D4116yescomplemented
234D4×C61—224no—
235D4×C61—224no—
236C2×C4×C61—28no—
237C2×C4×C61—21no—
238C2×C4×C61—23no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—23no—
242C2×C4×C61—23no—
243C2×C4×C61—23no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—23no—
249C2×C4×C61—21no—
250C2×C4×C61—23no—
251C2×C4×C61—224no—
252C2×C4×C61—224no—
253C2×C4×C61—21no—
254C2×C4×C61—23no—
255C2×C4×C61—23no—
256C2×C4×C61—21no—
257C2×C4×C61—23no—
258C2×C4×C61—23no—
259C2×C4×C61—23no—
260C2×C4×C61—23no—
261C2×C4×C61—21no—
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—412no—
269C2×C4×C61—812no—
270C2×C4×C61C23×C412yes—
271C2×C4×C61C23×C416yes—
272C2×C4×C61C23×C416yes—
273C2×C4×C61C23×C412yes—
274C2×C4×C61C23×C416yes—
275C2×C4×C61C22×D412yes—
276C2×C4×C61C22×D416yes—
277C2×C4×C61C22×D416yes—
278C2×C4×C61C2×#4116yes—
279C2×C4×C612−1+412yes—
280#34294C6111yesmaximal, characteristic, direct product factor, Sylow
281C22×C61—22no—
282C22×C61—22no—
283C22×C61—22no—
284C22×C61—22no—
285C22×C61—22no—
286C22×C61—22no—
287C22×C61—26no—
288C22×C61—26no—
289C22×C61—26no—
290C22×C61—43no—
291C22×C61—43no—
292C22×C61—43no—
293C22×C61—43no—
294C22×C61#52014yescomplemented
295C22×C61C24×C411yescharacteristic
296C22×C61C23×D411yescharacteristic
297C22×C61C22×#4111yescharacteristic
298C22×C61C2×H(5,𝔽2)11yescharacteristic
299C22×C61C2×2−1+411yescharacteristic
300C22×C61C2×2−1+411yescharacteristic
301C22×C61#58511yescharacteristic
302C4×C61—22no—
303C4×C61—26no—
304C4×C61—26no—
305C4×C61—22no—
306C4×C61—22no—
307C4×C61—22no—
308C4×C61—26no—
309C4×C61—41no—
310C4×C61—43no—
311C4×C61—43no—
312C4×C61—41no—
313C4×C61—43no—
314C4×C61C2×C4×D4112yes—
315C2×#548C2×C6111yescharacteristic
316C2×#520C2×C6111yescharacteristic, complemented
317C22×C4×Q8C2×C6111yescharacteristic, complemented
318#2367C2×C6113yescomplemented
319#2361C2×C6113yescomplemented
320#2360C2×C6113yescomplemented
321Q8×C4⋊C4C2×C6111yescharacteristic, complemented
322D4×C4⋊C4C2×C6113yescomplemented
323#2341C2×C6111yescharacteristic, complemented
324Q8×C22⋊C4C2×C6111yescharacteristic, complemented
325#2326C2×C6113yescomplemented
326#2323C2×C6113yescomplemented
327C4×#121C2×C6113yescomplemented
328#2290C2×C6113yescomplemented
329#2276C2×C6111yescharacteristic, complemented
330C2×C61—24no—
331C2×C61—46no—
332C2×C61C22×C4×D411yescharacteristic
333C2×C61C2×#52011yescharacteristic
334C2×C61C4×2−1+411yescharacteristic
335C2×C61#348611yescharacteristic
336C2×C61#348811yescharacteristic
337C2×C61#351611yescharacteristic
338C2×C61#352211yescharacteristic
339C22×#41C22×C6111yescharacteristic
340C23×Q8C22×C6111yescharacteristic
341#548C4×C61116yescomplemented
342C2×#124C22×C6113yes—
343C2×C22⋊Q8C22×C6113yes—
344C2×#121C22×C6113yes—
345#520—28no—
346C2×C4×Q8—28no—
347C2×C4×Q8C22×C6113yes—
348C2×C4×Q8C22×C6111yescharacteristic
349C2×C4×Q8C22×C6111yescharacteristic
350C2×C4×Q8C22×C6111yescharacteristic
351C2×C4×Q8C22×C6113yes—
352C2×C4×Q8C22×C6111yescharacteristic
353C2×C4×Q8C22×C6111yescharacteristic
354C2×C4×D4C22×C6113yes—
355C2×C4×D4C22×C6113yes—
356C2×C4×D4C22×C6116yes—
357C2×C4×D4C22×C6113yes—
358C2×#117C22×C6113yes—
359C22×C4⋊C4C22×C6113yes—
360C22×C4⋊C4C22×C6113yes—
361C22×C42C22×C6113yes—
362#391C22×C6113yes—
363#391C22×C6113yes—
364#390C22×C6113yes—
365#390C22×C6113yes—
366#389C22×C6116yes—
367#389C22×C6113yes—
368#389C22×C6113yes—
369#388C22×C6116yes—
370#388C22×C6116yes—
371#388C22×C6113yes—
372#388C22×C6113yes—
373#387C22×C6113yes—
374#387C22×C6113yes—
375#386C22×C6113yes—
376#386C22×C6113yes—
377#385C22×C6116yes—
378#385C22×C6116yes—
379#385C22×C6113yes—
380#385C22×C6111yescharacteristic
381#384C22×C6113yes—
382#380C22×C6113yes—
383#380C22×C6113yes—
384C4×C4⋊C4C22×C6113yes—
385C4×C4⋊C4C22×C6113yes—
386C4×C4⋊C4C22×C6113yes—
387C4×C4⋊C4C22×C6113yes—
388C4×C22⋊C4C22×C6113yes—
389C4×C22⋊C4C22×C6113yes—
390C4×C22⋊C4C22×C6116yes—
391#376C22×C6113yes—
392C61#3429411yescharacteristic, direct product factor, Sylow
393C2×#41—24no—
394C2×#41—24no—
395C2×#41C2×C4×C6118yescomplemented
396C22×Q8—24no—
397C22×Q8—24no—
398C22×Q8C2×C4×C6118yescomplemented
399C22×Q8C23×C6113yes—
400C22×Q8C23×C6111yescharacteristic
401C22×D4C23×C6113yes—
402C22×D4C23×C6113yes—
403C23×C4C23×C6111yescharacteristic
404C23×C4C23×C6113yes—
405C23×C4C23×C6113yes—
406C23×C4C23×C6113yes—
407C23×C4C23×C6116yes—
408#124C2×C4×C61124yescomplemented
409C22⋊Q8C2×C4×C61124yescomplemented
410#121C2×C4×C61124yescomplemented
411C4×Q8—24no—
412C4×Q8—24no—
413C4×Q8—24no—
414C4×Q8—212no—
415C4×Q8—212no—
416C4×Q8C2×C4×C6118yescomplemented
417C4×Q8D4×C6118yescomplemented
418C4×D4—212no—
419C4×D4—212no—
420C4×D4—412no—
421C4×D4C2×C4×C61124yescomplemented
422#117—212no—
423C2×C4⋊C4—212no—
424C2×C4⋊C4—212no—
425C2×C4⋊C4C23×C6113yes—
426C2×C4⋊C4C23×C6113yes—
427C2×C4⋊C4C23×C6113yes—
428C2×C4⋊C4C23×C6116yes—
429C2×C4⋊C4C23×C6111yescharacteristic
430C2×C4⋊C4C23×C6113yes—
431C2×C4⋊C4C23×C6111yescharacteristic
432C2×C4⋊C4C23×C6116yes—
433C2×C4⋊C4C23×C6113yes—
434C2×C4⋊C4C23×C6113yes—
435C2×C4⋊C4C23×C6113yes—
436C2×C4⋊C4C23×C6113yes—
437C2×C22⋊C4C23×C6113yes—
438C2×C22⋊C4C23×C6113yes—
439C2×C22⋊C4C23×C6113yes—
440C2×C22⋊C4C23×C6111yescharacteristic
441C2×C22⋊C4C23×C6113yes—
442C2×C22⋊C4C23×C6116yes—
443C2×C22⋊C4C23×C6113yes—
444C2×C22⋊C4C23×C6111yescharacteristic
445C2×C22⋊C4C23×C6113yes—
446C2×C22⋊C4C23×C6116yes—
447C2×C42—212no—
448C2×C42C23×C6113yes—
449C2×C42C23×C6113yes—
450C2×C42C23×C6113yes—
451C2×C42C23×C6113yes—
452C2×C42C23×C6113yes—
453C2×C42C23×C6116yes—
454C2×C42C23×C6113yes—
455C2×C42C23×C6113yes—
456#95C23×C6111yescharacteristic
457#95C23×C6113yes—
458#95C23×C6113yes—
459#95C23×C6113yes—
460#95C23×C6111yescharacteristic
461#95C23×C6113yes—
462#95C23×C6113yes—
463#95C23×C6116yes—
464#95C23×C6113yes—
465#95C23×C6113yes—
466#95C23×C6113yes—
467C24C24×C6113yes—
468C24C24×C6111yescharacteristic
469#41—232no—
470C2×Q8—232no—
471C2×Q8—26no—
472C2×Q8—26no—
473C2×Q8C22×C4×C61112yes—
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×D4C22×C4×C61112yes—
482C2×D4C22×C4×C61112yes—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—26no—
486C22×C4—26no—
487C22×C4—26no—
488C22×C4—26no—
489C22×C4—22no—
490C22×C4—26no—
491C22×C4—26no—
492C22×C4—212no—
493C22×C4—43no—
494C22×C4—46no—
495C22×C4—46no—
496C22×C4C22×C4×C61112yes—
497C22×C4C22×C4×C61112yes—
498C22×C4C24×C6111yescharacteristic
499C22×C4C24×C6111yescharacteristic
500C22×C4C24×C6113yes—
501C22×C4C24×C6113yes—
502C22×C4C24×C6113yes—
503C22×C4C24×C6111yescharacteristic
504C22×C4C24×C6113yes—
505C22×C4C24×C6113yes—
506C22×C4C24×C6111yescharacteristic
507C22×C4C24×C6111yescharacteristic
508C22×C4C24×C6113yes—
509C22×C4C24×C6111yescharacteristic
510C22×C4C24×C6113yes—
511C4⋊C4—26no—
512C4⋊C4—26no—
513C4⋊C4—212no—
514C4⋊C4—26no—
515C4⋊C4—22no—
516C4⋊C4—26no—
517C4⋊C4—22no—
518C4⋊C4—46no—
519C4⋊C4—43no—
520C4⋊C4C22×C4×C61112yes—
521C4⋊C4C22×C4×C61112yes—
522C4⋊C4C2×D4×C61112yes—
523C22⋊C4—26no—
524C22⋊C4—22no—
525C22⋊C4—26no—
526C22⋊C4—26no—
527C22⋊C4—26no—
528C22⋊C4—46no—
529C22⋊C4—43no—
530C22⋊C4C22×C4×C6114yes—
531C22⋊C4C22×C4×C61112yes—
532C22⋊C4C22×C4×C61124yes—
533C42—26no—
534C42—26no—
535C42—26no—
536C42—26no—
537C42—26no—
538C42—46no—
539C42C22×C4×C61112yes—
540C42C2×D4×C61112yes—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—23no—
546C23—23no—
547C23—23no—
548C23—23no—
549C23—23no—
550C23—23no—
551C23C23×C4×C6116yes—
552C23C23×C4×C6112yes—
553C23H(5,𝔽2)×C6112yes—
554C232−1+4×C6112yes—
555C23C25×C6111yescharacteristic
556Q8—224no—
557Q8C4×D4×C61116yescomplemented
558D4—224no—
559D4—224no—
560C2×C4—28no—
561C2×C4—21no—
562C2×C4—23no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—23no—
566C2×C4—23no—
567C2×C4—23no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—23no—
573C2×C4—21no—
574C2×C4—23no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—21no—
578C2×C4—23no—
579C2×C4—23no—
580C2×C4—21no—
581C2×C4—23no—
582C2×C4—23no—
583C2×C4—23no—
584C2×C4—23no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—23no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—23no—
591C2×C4—23no—
592C2×C4—412no—
593C2×C4—812no—
594C2×C4C23×C4×C6112yes—
595C2×C4C23×C4×C6116yes—
596C2×C4C23×C4×C6116yes—
597C2×C4C23×C4×C6112yes—
598C2×C4C23×C4×C6116yes—
599C2×C4C22×D4×C6112yes—
600C2×C4C22×D4×C6116yes—
601C2×C4C22×D4×C6116yes—
602C2×C4C2×#41×C6116yes—
603C2×C42−1+4×C6112yes—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—26no—
611C22—26no—
612C22—26no—
613C22—43no—
614C22—43no—
615C22—43no—
616C22—43no—
617C22C61×#52014yescomplemented
618C22C24×C4×C6111yescharacteristic
619C22C23×D4×C6111yescharacteristic
620C22C22×#41×C6111yescharacteristic
621C22C2×H(5,𝔽2)×C6111yescharacteristic
622C22C2×2−1+4×C6111yescharacteristic
623C22C2×2−1+4×C6111yescharacteristic
624C22C61×#58511yescharacteristic
625C4—22no—
626C4—26no—
627C4—26no—
628C4—22no—
629C4—22no—
630C4—22no—
631C4—26no—
632C4—41no—
633C4—43no—
634C4—43no—
635C4—41no—
636C4—43no—
637C4C2×C4×D4×C61112yes—
638C2—24no—
639C2—46no—
640C2C22×C4×D4×C6111yescharacteristic
641C2C2×C61×#52011yescharacteristic
642C2C4×2−1+4×C6111yescharacteristic
643C2C61×#348611yescharacteristic
644C2C61×#348811yescharacteristic
645C2C61×#351611yescharacteristic
646C2C61×#352211yescharacteristic
subgroupG/H
center, socleC23×C61C25
commutatorC22C24×C4×C61
Frattini, cosocleC23C25×C61
prime radicalC2×C61×#548C2
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. C22×C4×Q8×C61C2semidirect
4. C61×#2367C2semidirect
5. C61×#2361C2semidirect
6. C61×#2360C2semidirect
7. Q8×C4⋊C4×C61C2semidirect
8. D4×C4⋊C4×C61C2semidirect
9. C61×#2341C2semidirect
10. Q8×C22⋊C4×C61C2semidirect
11. C61×#2326C2semidirect
12. C61×#2323C2semidirect
13. C4×#121×C61C2semidirect
14. C61×#2290C2semidirect
15. C61×#2276C2semidirect
18. C61×#548C4semidirect
71. C2×#41×C61C2×C4semidirect
74. C22×Q8×C61C2×C4semidirect
84. #124×C61C2×C4semidirect
85. C22⋊Q8×C61C2×C4semidirect
86. #121×C61C2×C4semidirect
92. C4×Q8×C61C2×C4semidirect
93. C4×Q8×C61D4semidirect
97. C4×D4×C61C2×C4semidirect
233. Q8×C61C4×D4semidirect
280. #34294C61direct (N × H)
294. C22×C61#520semidirect
316. C2×#520C2×C61semidirect
317. C22×C4×Q8C2×C61semidirect
318. #2367C2×C61semidirect
319. #2361C2×C61semidirect
320. #2360C2×C61semidirect
321. Q8×C4⋊C4C2×C61semidirect
322. D4×C4⋊C4C2×C61semidirect
323. #2341C2×C61semidirect
324. Q8×C22⋊C4C2×C61semidirect
325. #2326C2×C61semidirect
326. #2323C2×C61semidirect
327. C4×#121C2×C61semidirect
328. #2290C2×C61semidirect
329. #2276C2×C61semidirect
341. #548C4×C61semidirect
392. C61#34294direct (N × H)
395. C2×#41C2×C4×C61semidirect
398. C22×Q8C2×C4×C61semidirect
408. #124C2×C4×C61semidirect
409. C22⋊Q8C2×C4×C61semidirect
410. #121C2×C4×C61semidirect
416. C4×Q8C2×C4×C61semidirect
417. C4×Q8D4×C61semidirect
421. C4×D4C2×C4×C61semidirect
557. Q8C4×D4×C61semidirect
617. C22C61×#520semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5482
C2×C61×#5202
C22×C4×Q8×C612
C61×#23672
C61×#23612
C61×#23602
Q8×C4⋊C4×C612
D4×C4⋊C4×C612
C61×#23412
Q8×C22⋊C4×C612
C61×#23262
C61×#23232
C4×#121×C612
C61×#22902
C61×#22762
#3429461