Finite Group Databasebeta

← C61×#14408 #29517841

Subgroups — C61×#14408 #29517841

Order 15616.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#389C211yesmaximal, characteristic, complemented
2C2×C61×#388C211yesmaximal, characteristic
3C2×C61×#388C211yesmaximal, characteristic
4C2×C61×#385C211yesmaximal, characteristic
5C2×C61×#380C211yesmaximal, characteristic
6C61×#1444C211yesmaximal, characteristic, complemented
7C61×#1442C211yesmaximal, characteristic, complemented
8C61×#1441C211yesmaximal, characteristic, complemented
9C61×#1441C211yesmaximal, characteristic, complemented
10C61×#1439C211yesmaximal, characteristic
11C61×#1439C211yesmaximal, characteristic
12C61×#1436C211yesmaximal, characteristic, complemented
13C61×#1436C211yesmaximal, characteristic, complemented
14C61×C4⋊#95C211yesmaximal, characteristic, complemented
15C61×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C61C2211yescharacteristic
17C22×C4⋊C4×C61C2211yescharacteristic
18C22×C4⋊C4×C61C2211yescharacteristic
19C22×C4⋊C4×C61C2211yescharacteristic
20C22×C4⋊C4×C61C2211yescharacteristic
21C22×C4⋊C4×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
24C22×C4⋊C4×C61C2211yescharacteristic
25C22×C22⋊C4×C61C2211yescharacteristic
26C22×C22⋊C4×C61C2211yescharacteristic
27C22×C22⋊C4×C61C2211yescharacteristic
28C22×C22⋊C4×C61C2211yescharacteristic
29C22×C22⋊C4×C61C2211yescharacteristic
30C22×C22⋊C4×C61C2211yescharacteristic
31C22×C42×C61C2211yescharacteristic
32C22×C42×C61C2211yescharacteristic
33C61×#389—24no—
34C61×#388—24no—
35C61×#388—24no—
36C61×#385C418yescomplemented
37C61×#380—24no—
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2211yescharacteristic
40C2×#95×C61C2211yescharacteristic
41C2×#95×C61C2211yescharacteristic
42C2×#95×C61C2211yescharacteristic
43C2×#95×C61C2211yescharacteristic
44C2×#95×C61C2211yescharacteristic
45C2×#95×C61C2211yescharacteristic
46C2×#95×C61C2211yescharacteristic
47C2×#95×C61C2211yescharacteristic
48C2×#95×C61C2211yescharacteristic
49C2×#95×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C2×#95×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C25×C61C2311yescharacteristic
57C23×C4×C61—22no—
58C23×C4×C61—22no—
59C23×C4×C61—41no—
60C23×C4×C61—41no—
61C23×C4×C61—41no—
62C23×C4×C61—41no—
63C23×C4×C61C2×C414yes—
64C23×C4×C61C2311yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C23×C4×C61C2311yescharacteristic
67C23×C4×C61C2311yescharacteristic
68C23×C4×C61C2311yescharacteristic
69C23×C4×C61C2311yescharacteristic
70C23×C4×C61C2311yescharacteristic
71C23×C4×C61C2311yescharacteristic
72C23×C4×C61C2311yescharacteristic
73C23×C4×C61C2311yescharacteristic
74C23×C4×C61C2311yescharacteristic
75C23×C4×C61C2311yescharacteristic
76C23×C4×C61C2311yescharacteristic
77C23×C4×C61C2311yescharacteristic
78C2×C4⋊C4×C61—22no—
79C2×C4⋊C4×C61—22no—
80C2×C4⋊C4×C61—22no—
81C2×C4⋊C4×C61—22no—
82C2×C4⋊C4×C61—22no—
83C2×C4⋊C4×C61—22no—
84C2×C4⋊C4×C61—22no—
85C2×C4⋊C4×C61—22no—
86C2×C4⋊C4×C61—22no—
87C2×C4⋊C4×C61—41no—
88C2×C4⋊C4×C61—41no—
89C2×C4⋊C4×C61—41no—
90C2×C4⋊C4×C61—41no—
91C2×C4⋊C4×C61—41no—
92C2×C4⋊C4×C61—41no—
93C2×C4⋊C4×C61—41no—
94C2×C4⋊C4×C61—41no—
95C2×C4⋊C4×C61—41no—
96C2×C4⋊C4×C61—41no—
97C2×C4⋊C4×C61—41no—
98C2×C4⋊C4×C61—41no—
99C2×C4⋊C4×C61C2×C414yes—
100C2×C4⋊C4×C61C2×C414yes—
101C2×C4⋊C4×C61D414yes—
102C2×C22⋊C4×C61—22no—
103C2×C22⋊C4×C61—22no—
104C2×C22⋊C4×C61—22no—
105C2×C22⋊C4×C61—22no—
106C2×C22⋊C4×C61—22no—
107C2×C22⋊C4×C61—22no—
108C2×C22⋊C4×C61—22no—
109C2×C22⋊C4×C61—22no—
110C2×C22⋊C4×C61—41no—
111C2×C22⋊C4×C61—41no—
112C2×C22⋊C4×C61—41no—
113C2×C22⋊C4×C61—41no—
114C2×C22⋊C4×C61—41no—
115C2×C22⋊C4×C61—41no—
116C2×C22⋊C4×C61C2×C414yes—
117C2×C22⋊C4×C61C2×C414yes—
118C2×C22⋊C4×C61D414yes—
119C2×C22⋊C4×C61Q814yes—
120C2×C42×C61—22no—
121C2×C42×C61—22no—
122C2×C42×C61—22no—
123C2×C42×C61—22no—
124C2×C42×C61—41no—
125C2×C42×C61—41no—
126#95×C61—22no—
127#95×C61—22no—
128#95×C61—22no—
129#95×C61—22no—
130#95×C61—22no—
131#95×C61—22no—
132#95×C61—22no—
133#95×C61—22no—
134#95×C61—22no—
135#95×C61—22no—
136#95×C61—41no—
137#95×C61—41no—
138#95×C61—41no—
139#95×C61—41no—
140#95×C61—41no—
141#95×C61—41no—
142#95×C61C2×C414yes—
143#95×C61C2×C414yes—
144C24×C61—21no—
145C24×C61—21no—
146C24×C61—21no—
147C24×C61—21no—
148C24×C61—21no—
149C24×C61—21no—
150C24×C61—21no—
151C24×C61—21no—
152C24×C61—21no—
153C24×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61C22×C412yes—
157C24×C61C2×D412yes—
158C24×C61C2×Q812yes—
159C24×C61C2411yescharacteristic
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—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—28no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—44no—
244C22×C4×C61—44no—
245C22×C4×C61—44no—
246C22×C4×C61—44no—
247C22×C4×C61—44no—
248C22×C4×C61—44no—
249C22×C4×C61C22×C412yes—
250C22×C4×C61C22×C412yes—
251C22×C4×C61C22×C412yes—
252C22×C4×C61C22×C412yes—
253C22×C4×C61C22×C412yes—
254C22×C4×C61C22×C412yes—
255C22×C4×C61C2×D412yes—
256C22×C4×C61C2×D412yes—
257C22×C4×C61C2×D412yes—
258C22×C4×C61C2×D412yes—
259C22×C4×C61C2×D412yes—
260C22×C4×C61C2×Q812yes—
261C22×C4×C61C2×Q812yes—
262C22×C4×C61#4112yes—
263C22×C4×C61#4112yes—
264C22×C4×C61#4112yes—
265C4⋊C4×C61—28no—
266C4⋊C4×C61—44no—
267C4⋊C4×C61—44no—
268C4⋊C4×C61—44no—
269C4⋊C4×C61—44no—
270C4⋊C4×C61—44no—
271C4⋊C4×C61—44no—
272C4⋊C4×C61—44no—
273C22⋊C4×C61—44no—
274C22⋊C4×C61—44no—
275C22⋊C4×C61—44no—
276C22⋊C4×C61—44no—
277C22⋊C4×C61—44no—
278C22⋊C4×C61C4⋊C4116yescomplemented
279C42×C61—44no—
280C42×C61—44no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61C2×C4⋊C414yes—
316C23×C61C23×C411yescharacteristic
317C23×C61C22×D411yescharacteristic
318C23×C61C22×D411yescharacteristic
319C23×C61C22×Q811yescharacteristic
320C23×C61C2×#4111yescharacteristic
321C23×C61C2×#4111yescharacteristic
322C23×C61C2×#4111yescharacteristic
323C23×C61H(5,𝔽2)11yescharacteristic
324C23×C61H(5,𝔽2)11yescharacteristic
325C23×C61H(5,𝔽2)11yescharacteristic
326C23×C61H(5,𝔽2)11yescharacteristic
327C23×C61H(5,𝔽2)11yescharacteristic
328C23×C612−1+411yescharacteristic
329C23×C612−1+411yescharacteristic
330C23×C612−1+411yescharacteristic
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—416no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61C2×C4⋊C414yes—
428C2×C4×C61C2×C4⋊C414yes—
429C2×C4×C61C4×D414yes—
430#14408C6111yesmaximal, characteristic, direct product factor, Sylow
431C22×C61—24no—
432C22×C61—24no—
433C22×C61—24no—
434C22×C61—42no—
435C22×C61—42no—
436C22×C61—42no—
437C22×C61—42no—
438C22×C61—42no—
439C22×C61—42no—
440C22×C61—42no—
441C22×C61—42no—
442C22×C61—42no—
443C22×C61—42no—
444C22×C61—42no—
445C22×C61—42no—
446C22×C61C22×C4⋊C411yescharacteristic
447C22×C61C2×C4×D411yescharacteristic
448C22×C61C4×#4111yescharacteristic
449C22×C61#51811yescharacteristic
450C22×C61#51811yescharacteristic
451C22×C61#51911yescharacteristic
452C22×C61#52011yescharacteristic
453C22×C61#53411yescharacteristic
454C22×C61#53511yescharacteristic
455C22×C61#53711yescharacteristic
456C22×C61#53711yescharacteristic
457C22×C61#53811yescharacteristic
458C22×C61#53811yescharacteristic
459C22×C61#53811yescharacteristic
460C22×C61#53911yescharacteristic
461C22×C61#54011yescharacteristic
462C22×C61#54211yescharacteristic
463C22×C61#54411yescharacteristic
464C22×C61#54411yescharacteristic
465C22×C61D4211yescharacteristic
466C22×C61#54611yescharacteristic
467C22×C61#54611yescharacteristic
468C22×C61#54711yescharacteristic
469C22×C61#54711yescharacteristic
470C22×C61#54811yescharacteristic
471C22×C61D4×Q811yescharacteristic
472C22×C61#55211yescharacteristic
473C22×C61#55411yescharacteristic
474C22×C61#55411yescharacteristic
475C22×C61#55411yescharacteristic
476C22×C61#55611yescharacteristic
477C22×C61#56211yescharacteristic
478C22×C61#56211yescharacteristic
479C22×C61#56311yescharacteristic
480C22×C61#56311yescharacteristic
481C4×C61—24no—
482C4×C61—24no—
483C4×C61—24no—
484C4×C61—42no—
485C4×C61—42no—
486C4×C61—42no—
487C4×C61—42no—
488C4×C61—42no—
489C4×C61—42no—
490C4×C61—42no—
491C4×C61—81no—
492C4×C61—81no—
493C4×C61—81no—
494C4×C61—81no—
495C2×#389C2×C6111yescharacteristic, complemented
496C2×#388C2×C6111yescharacteristic
497C2×#388C2×C6111yescharacteristic
498C2×#385C2×C6111yescharacteristic
499C2×#380C2×C6111yescharacteristic
500#1444C2×C6111yescharacteristic, complemented
501#1442C2×C6111yescharacteristic, complemented
502#1441C2×C6111yescharacteristic, complemented
503#1441C2×C6111yescharacteristic, complemented
504#1439C2×C6111yescharacteristic
505#1439C2×C6111yescharacteristic
506#1436C2×C6111yescharacteristic, complemented
507#1436C2×C6111yescharacteristic, complemented
508C4⋊#95C2×C6111yescharacteristic, complemented
509C22⋊#95C2×C6111yescharacteristic
510C2×C61—44no—
511C2×C61#231611yescharacteristic
512C2×C61#232111yescharacteristic
513C2×C61#233511yescharacteristic
514C2×C61D4×C4⋊C411yescharacteristic
515C2×C61#234911yescharacteristic
516C2×C61#236211yescharacteristic
517C2×C61#237811yescharacteristic
518C2×C61#267111yescharacteristic
519C2×C61#267611yescharacteristic
520C2×C61#269511yescharacteristic
521C2×C61#271511yescharacteristic
522C2×C61#272011yescharacteristic
523C2×C61#272911yescharacteristic
524C2×C61#276811yescharacteristic
525C2×C61#278811yescharacteristic
526C24×C4C22×C6111yescharacteristic
527C22×C4⋊C4C22×C6111yescharacteristic
528C22×C4⋊C4C22×C6111yescharacteristic
529C22×C4⋊C4C22×C6111yescharacteristic
530C22×C4⋊C4C22×C6111yescharacteristic
531C22×C4⋊C4C22×C6111yescharacteristic
532C22×C4⋊C4C22×C6111yescharacteristic
533C22×C4⋊C4C22×C6111yescharacteristic
534C22×C4⋊C4C22×C6111yescharacteristic
535C22×C22⋊C4C22×C6111yescharacteristic
536C22×C22⋊C4C22×C6111yescharacteristic
537C22×C22⋊C4C22×C6111yescharacteristic
538C22×C22⋊C4C22×C6111yescharacteristic
539C22×C22⋊C4C22×C6111yescharacteristic
540C22×C22⋊C4C22×C6111yescharacteristic
541C22×C42C22×C6111yescharacteristic
542C22×C42C22×C6111yescharacteristic
543#389—24no—
544#388—24no—
545#388—24no—
546#385C4×C6118yescomplemented
547#380—24no—
548C2×#95C22×C6111yescharacteristic
549C2×#95C22×C6111yescharacteristic
550C2×#95C22×C6111yescharacteristic
551C2×#95C22×C6111yescharacteristic
552C2×#95C22×C6111yescharacteristic
553C2×#95C22×C6111yescharacteristic
554C2×#95C22×C6111yescharacteristic
555C2×#95C22×C6111yescharacteristic
556C2×#95C22×C6111yescharacteristic
557C2×#95C22×C6111yescharacteristic
558C2×#95C22×C6111yescharacteristic
559C2×#95C22×C6111yescharacteristic
560C2×#95C22×C6111yescharacteristic
561C2×#95C22×C6111yescharacteristic
562C2×#95C22×C6111yescharacteristic
563C2×#95C22×C6111yescharacteristic
564C2×#95C22×C6111yescharacteristic
565C2×#95C22×C6111yescharacteristic
566C61#1440811yescharacteristic, direct product factor, Sylow
567C25C23×C6111yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—41no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4C2×C4×C6114yes—
575C23×C4C23×C6111yescharacteristic
576C23×C4C23×C6111yescharacteristic
577C23×C4C23×C6111yescharacteristic
578C23×C4C23×C6111yescharacteristic
579C23×C4C23×C6111yescharacteristic
580C23×C4C23×C6111yescharacteristic
581C23×C4C23×C6111yescharacteristic
582C23×C4C23×C6111yescharacteristic
583C23×C4C23×C6111yescharacteristic
584C23×C4C23×C6111yescharacteristic
585C23×C4C23×C6111yescharacteristic
586C23×C4C23×C6111yescharacteristic
587C23×C4C23×C6111yescharacteristic
588C23×C4C23×C6111yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4C2×C4×C6114yes—
611C2×C4⋊C4C2×C4×C6114yes—
612C2×C4⋊C4D4×C6114yes—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4—41no—
627C2×C22⋊C4C2×C4×C6114yes—
628C2×C22⋊C4C2×C4×C6114yes—
629C2×C22⋊C4D4×C6114yes—
630C2×C22⋊C4Q8×C6114yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—22no—
635C2×C42—41no—
636C2×C42—41no—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—41no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95—41no—
653#95C2×C4×C6114yes—
654#95C2×C4×C6114yes—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C6112yes—
668C24C2×D4×C6112yes—
669C24C2×Q8×C6112yes—
670C24C24×C6111yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—28no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4C22×C4×C6112yes—
761C22×C4C22×C4×C6112yes—
762C22×C4C22×C4×C6112yes—
763C22×C4C22×C4×C6112yes—
764C22×C4C22×C4×C6112yes—
765C22×C4C22×C4×C6112yes—
766C22×C4C2×D4×C6112yes—
767C22×C4C2×D4×C6112yes—
768C22×C4C2×D4×C6112yes—
769C22×C4C2×D4×C6112yes—
770C22×C4C2×D4×C6112yes—
771C22×C4C2×Q8×C6112yes—
772C22×C4C2×Q8×C6112yes—
773C22×C4#41×C6112yes—
774C22×C4#41×C6112yes—
775C22×C4#41×C6112yes—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4C4⋊C4×C61116yescomplemented
790C42—44no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊C4×C6114yes—
827C23C23×C4×C6111yescharacteristic
828C23C22×D4×C6111yescharacteristic
829C23C22×D4×C6111yescharacteristic
830C23C22×Q8×C6111yescharacteristic
831C23C2×#41×C6111yescharacteristic
832C23C2×#41×C6111yescharacteristic
833C23C2×#41×C6111yescharacteristic
834C23H(5,𝔽2)×C6111yescharacteristic
835C23H(5,𝔽2)×C6111yescharacteristic
836C23H(5,𝔽2)×C6111yescharacteristic
837C23H(5,𝔽2)×C6111yescharacteristic
838C23H(5,𝔽2)×C6111yescharacteristic
839C232−1+4×C6111yescharacteristic
840C232−1+4×C6111yescharacteristic
841C232−1+4×C6111yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—416no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4C2×C4⋊C4×C6114yes—
939C2×C4C2×C4⋊C4×C6114yes—
940C2×C4C4×D4×C6114yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊C4×C6111yescharacteristic
957C22C2×C4×D4×C6111yescharacteristic
958C22C4×#41×C6111yescharacteristic
959C22C61×#51811yescharacteristic
960C22C61×#51811yescharacteristic
961C22C61×#51911yescharacteristic
962C22C61×#52011yescharacteristic
963C22C61×#53411yescharacteristic
964C22C61×#53511yescharacteristic
965C22C61×#53711yescharacteristic
966C22C61×#53711yescharacteristic
967C22C61×#53811yescharacteristic
968C22C61×#53811yescharacteristic
969C22C61×#53811yescharacteristic
970C22C61×#53911yescharacteristic
971C22C61×#54011yescharacteristic
972C22C61×#54211yescharacteristic
973C22C61×#54411yescharacteristic
974C22C61×#54411yescharacteristic
975C22D42×C6111yescharacteristic
976C22C61×#54611yescharacteristic
977C22C61×#54611yescharacteristic
978C22C61×#54711yescharacteristic
979C22C61×#54711yescharacteristic
980C22C61×#54811yescharacteristic
981C22D4×Q8×C6111yescharacteristic
982C22C61×#55211yescharacteristic
983C22C61×#55411yescharacteristic
984C22C61×#55411yescharacteristic
985C22C61×#55411yescharacteristic
986C22C61×#55611yescharacteristic
987C22C61×#56211yescharacteristic
988C22C61×#56211yescharacteristic
989C22C61×#56311yescharacteristic
990C22C61×#56311yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C61×#231611yescharacteristic
1007C2C61×#232111yescharacteristic
1008C2C61×#233511yescharacteristic
1009C2D4×C4⋊C4×C6111yescharacteristic
1010C2C61×#234911yescharacteristic
1011C2C61×#236211yescharacteristic
1012C2C61×#237811yescharacteristic
1013C2C61×#267111yescharacteristic
1014C2C61×#267611yescharacteristic
1015C2C61×#269511yescharacteristic
1016C2C61×#271511yescharacteristic
1017C2C61×#272011yescharacteristic
1018C2C61×#272911yescharacteristic
1019C2C61×#276811yescharacteristic
1020C2C61×#278811yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutatorC23C23×C4×C61
Frattini, cosocleC24C24×C61
prime radicalC25×C61C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#389C2semidirect
6. C61×#1444C2semidirect
7. C61×#1442C2semidirect
8. C61×#1441C2semidirect
9. C61×#1441C2semidirect
12. C61×#1436C2semidirect
13. C61×#1436C2semidirect
14. C61×C4⋊#95C2semidirect
36. C61×#385C4semidirect
278. C22⋊C4×C61C4⋊C4semidirect
430. #14408C61direct (N × H)
495. C2×#389C2×C61semidirect
500. #1444C2×C61semidirect
501. #1442C2×C61semidirect
502. #1441C2×C61semidirect
503. #1441C2×C61semidirect
506. #1436C2×C61semidirect
507. #1436C2×C61semidirect
508. C4⋊#95C2×C61semidirect
546. #385C4×C61semidirect
566. C61#14408direct (N × H)
789. C22⋊C4C4⋊C4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#3892
C2×C61×#3882
C2×C61×#3852
C2×C61×#3802
C61×#14442
C61×#14422
C61×#14412
C61×#14392
C61×#14362
C61×C4⋊#952
C61×C22⋊#952
#1440861