Finite Group Databasebeta

← C61×#14405 #29517838

Subgroups — C61×#14405 #29517838

Order 15616.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 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×#385C211yesmaximal, characteristic
6C2×C61×#385C211yesmaximal, characteristic
7C2×C61×#384C211yesmaximal, characteristic, complemented
8C61×#1444C211yesmaximal, characteristic, complemented
9C61×#1444C211yesmaximal, characteristic, complemented
10C61×#1442C211yesmaximal, characteristic, complemented
11C61×#1441C211yesmaximal, characteristic, complemented
12C61×#1439C211yesmaximal, characteristic
13C61×#1439C211yesmaximal, characteristic
14C61×#1436C211yesmaximal, characteristic, complemented
15C61×#1434C211yesmaximal, characteristic, complemented
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×C4⋊C4×C61C2211yescharacteristic
26C22×C4⋊C4×C61C2211yescharacteristic
27C22×C22⋊C4×C61C2211yescharacteristic
28C22×C22⋊C4×C61C2211yescharacteristic
29C22×C22⋊C4×C61C2211yescharacteristic
30C22×C22⋊C4×C61C2211yescharacteristic
31C22×C22⋊C4×C61C2211yescharacteristic
32C22×C22⋊C4×C61C2211yescharacteristic
33C22×C42×C61C2211yescharacteristic
34C22×C42×C61C2211yescharacteristic
35C61×#389—24no—
36C61×#388—24no—
37C61×#388C418yescomplemented
38C61×#385—24no—
39C61×#385—24no—
40C61×#385—24no—
41C61×#384—24no—
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
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C25×C61C2311yescharacteristic
59C23×C4×C61—22no—
60C23×C4×C61—22no—
61C23×C4×C61—22no—
62C23×C4×C61—41no—
63C23×C4×C61—41no—
64C23×C4×C61—41no—
65C23×C4×C61—41no—
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
78C23×C4×C61C2311yescharacteristic
79C23×C4×C61C2311yescharacteristic
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—22no—
88C2×C4⋊C4×C61—22no—
89C2×C4⋊C4×C61—22no—
90C2×C4⋊C4×C61—22no—
91C2×C4⋊C4×C61—22no—
92C2×C4⋊C4×C61—22no—
93C2×C4⋊C4×C61—22no—
94C2×C4⋊C4×C61—22no—
95C2×C4⋊C4×C61—22no—
96C2×C4⋊C4×C61—41no—
97C2×C4⋊C4×C61—41no—
98C2×C4⋊C4×C61—41no—
99C2×C4⋊C4×C61—41no—
100C2×C4⋊C4×C61—41no—
101C2×C4⋊C4×C61—41no—
102C2×C4⋊C4×C61—41no—
103C2×C4⋊C4×C61—41no—
104C2×C4⋊C4×C61—41no—
105C2×C4⋊C4×C61—41no—
106C2×C4⋊C4×C61—41no—
107C2×C4⋊C4×C61—41no—
108C2×C4⋊C4×C61C2×C414yescomplemented
109C2×C4⋊C4×C61D414yes—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61—22no—
114C2×C22⋊C4×C61—22no—
115C2×C22⋊C4×C61—22no—
116C2×C22⋊C4×C61—22no—
117C2×C22⋊C4×C61—22no—
118C2×C22⋊C4×C61—22no—
119C2×C22⋊C4×C61—41no—
120C2×C22⋊C4×C61—41no—
121C2×C22⋊C4×C61—41no—
122C2×C22⋊C4×C61—41no—
123C2×C22⋊C4×C61C2×C414yes—
124C2×C22⋊C4×C61C2×C414yes—
125C2×C22⋊C4×C61C2×C414yes—
126C2×C22⋊C4×C61D414yes—
127C2×C22⋊C4×C61Q814yes—
128C2×C42×C61—22no—
129C2×C42×C61—22no—
130C2×C42×C61—22no—
131C2×C42×C61—22no—
132C2×C42×C61—41no—
133C2×C42×C61C2×C414yescomplemented
134#95×C61—22no—
135#95×C61—22no—
136#95×C61—22no—
137#95×C61—22no—
138#95×C61—22no—
139#95×C61—22no—
140#95×C61—22no—
141#95×C61—22no—
142#95×C61—22no—
143#95×C61—22no—
144#95×C61—41no—
145#95×C61—41no—
146#95×C61—41no—
147#95×C61C2×C414yescomplemented
148#95×C61C2×C414yescomplemented
149#95×C61D414yes—
150C24×C61—21no—
151C24×C61—21no—
152C24×C61—21no—
153C24×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61C22×C412yes—
163C24×C61C2×D412yes—
164C24×C61C2×Q812yes—
165C24×C61C2411yescharacteristic
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—21no—
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—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—44no—
247C22×C4×C61—44no—
248C22×C4×C61—44no—
249C22×C4×C61—44no—
250C22×C4×C61—44no—
251C22×C4×C61—44no—
252C22×C4×C61—44no—
253C22×C4×C61C22×C412yes—
254C22×C4×C61C22×C412yes—
255C22×C4×C61C22×C412yes—
256C22×C4×C61C22×C412yes—
257C22×C4×C61C22×C412yes—
258C22×C4×C61C22×C412yes—
259C22×C4×C61C2×D412yes—
260C22×C4×C61C2×D412yes—
261C22×C4×C61C2×D412yes—
262C22×C4×C61C2×D412yes—
263C22×C4×C61C2×D412yes—
264C22×C4×C61C2×D412yes—
265C22×C4×C61C2×D412yes—
266C22×C4×C61C2×D412yes—
267C22×C4×C61C2×Q812yes—
268C22×C4×C61C2×Q812yes—
269C22×C4×C61#4112yes—
270C22×C4×C61#4112yes—
271C4⋊C4×C61—28no—
272C4⋊C4×C61—44no—
273C4⋊C4×C61—44no—
274C4⋊C4×C61—44no—
275C4⋊C4×C61—44no—
276C4⋊C4×C61—44no—
277C4⋊C4×C61—44no—
278C4⋊C4×C61—44no—
279C4⋊C4×C61—44no—
280C4⋊C4×C61—44no—
281C22⋊C4×C61—28no—
282C22⋊C4×C61—28no—
283C22⋊C4×C61—44no—
284C22⋊C4×C61—44no—
285C22⋊C4×C61—44no—
286C22⋊C4×C61C4⋊C4116yescomplemented
287C42×C61—28no—
288C42×C61—44no—
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—22no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
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×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61C2×C4⋊C414yes—
324C23×C61C23×C411yescharacteristic
325C23×C61C22×D411yescharacteristic
326C23×C61C22×D411yescharacteristic
327C23×C61C22×D411yescharacteristic
328C23×C61C22×Q811yescharacteristic
329C23×C61C2×#4111yescharacteristic
330C23×C61C2×#4111yescharacteristic
331C23×C61H(5,𝔽2)11yescharacteristic
332C23×C61H(5,𝔽2)11yescharacteristic
333C23×C61H(5,𝔽2)11yescharacteristic
334C23×C61H(5,𝔽2)11yescharacteristic
335C23×C612−1+411yescharacteristic
336C23×C612−1+411yescharacteristic
337C23×C612−1+411yescharacteristic
338C23×C612−1+411yescharacteristic
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—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—22no—
379C2×C4×C61—22no—
380C2×C4×C61—22no—
381C2×C4×C61—416no—
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×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61C2×C4⋊C414yes—
435C2×C4×C61C2×C4⋊C414yes—
436C2×C4×C61C4×D414yes—
437C2×C4×C61C4×D414yes—
438#14405C6111yesmaximal, characteristic, direct product factor, Sylow
439C22×C61—24no—
440C22×C61—24no—
441C22×C61—24no—
442C22×C61—42no—
443C22×C61—42no—
444C22×C61—42no—
445C22×C61—42no—
446C22×C61—42no—
447C22×C61—42no—
448C22×C61—42no—
449C22×C61—42no—
450C22×C61—42no—
451C22×C61—42no—
452C22×C61—42no—
453C22×C61—42no—
454C22×C61C22×C4⋊C411yescharacteristic
455C22×C61C2×C4×D411yescharacteristic
456C22×C61C2×C4×D411yescharacteristic
457C22×C61#52011yescharacteristic
458C22×C61#52011yescharacteristic
459C22×C61#52011yescharacteristic
460C22×C61#52011yescharacteristic
461C22×C61#53411yescharacteristic
462C22×C61#53511yescharacteristic
463C22×C61#53511yescharacteristic
464C22×C61#53611yescharacteristic
465C22×C61#53611yescharacteristic
466C22×C61#53611yescharacteristic
467C22×C61#53911yescharacteristic
468C22×C61#53911yescharacteristic
469C22×C61#54211yescharacteristic
470C22×C61#54211yescharacteristic
471C22×C61#54411yescharacteristic
472C22×C61#54411yescharacteristic
473C22×C61D4211yescharacteristic
474C22×C61D4211yescharacteristic
475C22×C61D4211yescharacteristic
476C22×C61#54711yescharacteristic
477C22×C61#54711yescharacteristic
478C22×C61#54711yescharacteristic
479C22×C61#54811yescharacteristic
480C22×C61D4×Q811yescharacteristic
481C22×C61D4×Q811yescharacteristic
482C22×C61#55311yescharacteristic
483C22×C61#55411yescharacteristic
484C22×C61#55411yescharacteristic
485C22×C61#56011yescharacteristic
486C22×C61#56311yescharacteristic
487C22×C61#56311yescharacteristic
488C22×C61#56311yescharacteristic
489C4×C61—24no—
490C4×C61—24no—
491C4×C61—24no—
492C4×C61—24no—
493C4×C61—42no—
494C4×C61—42no—
495C4×C61—42no—
496C4×C61—42no—
497C4×C61—42no—
498C4×C61—42no—
499C4×C61—81no—
500C4×C61—81no—
501C4×C61—81no—
502C4×C61—81no—
503C2×#389C2×C6111yescharacteristic, complemented
504C2×#388C2×C6111yescharacteristic
505C2×#388C2×C6111yescharacteristic
506C2×#385C2×C6111yescharacteristic
507C2×#385C2×C6111yescharacteristic
508C2×#385C2×C6111yescharacteristic
509C2×#384C2×C6111yescharacteristic, complemented
510#1444C2×C6111yescharacteristic, complemented
511#1444C2×C6111yescharacteristic, complemented
512#1442C2×C6111yescharacteristic, complemented
513#1441C2×C6111yescharacteristic, complemented
514#1439C2×C6111yescharacteristic
515#1439C2×C6111yescharacteristic
516#1436C2×C6111yescharacteristic, complemented
517#1434C2×C6111yescharacteristic, complemented
518C2×C61—44no—
519C2×C61#231711yescharacteristic
520C2×C61#232211yescharacteristic
521C2×C61#232611yescharacteristic
522C2×C61D4×C4⋊C411yescharacteristic
523C2×C61D4×C4⋊C411yescharacteristic
524C2×C61#236111yescharacteristic
525C2×C61#238311yescharacteristic
526C2×C61#266911yescharacteristic
527C2×C61#267411yescharacteristic
528C2×C61#267711yescharacteristic
529C2×C61#268011yescharacteristic
530C2×C61#271811yescharacteristic
531C2×C61#272011yescharacteristic
532C2×C61#272911yescharacteristic
533C2×C61#279011yescharacteristic
534C24×C4C22×C6111yescharacteristic
535C22×C4⋊C4C22×C6111yescharacteristic
536C22×C4⋊C4C22×C6111yescharacteristic
537C22×C4⋊C4C22×C6111yescharacteristic
538C22×C4⋊C4C22×C6111yescharacteristic
539C22×C4⋊C4C22×C6111yescharacteristic
540C22×C4⋊C4C22×C6111yescharacteristic
541C22×C4⋊C4C22×C6111yescharacteristic
542C22×C4⋊C4C22×C6111yescharacteristic
543C22×C4⋊C4C22×C6111yescharacteristic
544C22×C4⋊C4C22×C6111yescharacteristic
545C22×C22⋊C4C22×C6111yescharacteristic
546C22×C22⋊C4C22×C6111yescharacteristic
547C22×C22⋊C4C22×C6111yescharacteristic
548C22×C22⋊C4C22×C6111yescharacteristic
549C22×C22⋊C4C22×C6111yescharacteristic
550C22×C22⋊C4C22×C6111yescharacteristic
551C22×C42C22×C6111yescharacteristic
552C22×C42C22×C6111yescharacteristic
553#389—24no—
554#388—24no—
555#388C4×C6118yescomplemented
556#385—24no—
557#385—24no—
558#385—24no—
559#384—24no—
560C2×#95C22×C6111yescharacteristic
561C2×#95C22×C6111yescharacteristic
562C2×#95C22×C6111yescharacteristic
563C2×#95C22×C6111yescharacteristic
564C2×#95C22×C6111yescharacteristic
565C2×#95C22×C6111yescharacteristic
566C2×#95C22×C6111yescharacteristic
567C2×#95C22×C6111yescharacteristic
568C2×#95C22×C6111yescharacteristic
569C2×#95C22×C6111yescharacteristic
570C2×#95C22×C6111yescharacteristic
571C2×#95C22×C6111yescharacteristic
572C2×#95C22×C6111yescharacteristic
573C2×#95C22×C6111yescharacteristic
574C2×#95C22×C6111yescharacteristic
575C2×#95C22×C6111yescharacteristic
576C61#1440511yescharacteristic, direct product factor, Sylow
577C25C23×C6111yescharacteristic
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—41no—
582C23×C4—41no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4C23×C6111yescharacteristic
586C23×C4C23×C6111yescharacteristic
587C23×C4C23×C6111yescharacteristic
588C23×C4C23×C6111yescharacteristic
589C23×C4C23×C6111yescharacteristic
590C23×C4C23×C6111yescharacteristic
591C23×C4C23×C6111yescharacteristic
592C23×C4C23×C6111yescharacteristic
593C23×C4C23×C6111yescharacteristic
594C23×C4C23×C6111yescharacteristic
595C23×C4C23×C6111yescharacteristic
596C23×C4C23×C6111yescharacteristic
597C23×C4C23×C6111yescharacteristic
598C23×C4C23×C6111yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4C2×C4×C6114yescomplemented
628C2×C4⋊C4D4×C6114yes—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—41no—
639C2×C22⋊C4—41no—
640C2×C22⋊C4—41no—
641C2×C22⋊C4—41no—
642C2×C22⋊C4C2×C4×C6114yes—
643C2×C22⋊C4C2×C4×C6114yes—
644C2×C22⋊C4C2×C4×C6114yes—
645C2×C22⋊C4D4×C6114yes—
646C2×C22⋊C4Q8×C6114yes—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—22no—
650C2×C42—22no—
651C2×C42—41no—
652C2×C42C2×C4×C6114yescomplemented
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—41no—
664#95—41no—
665#95—41no—
666#95C2×C4×C6114yescomplemented
667#95C2×C4×C6114yescomplemented
668#95D4×C6114yes—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C22×C4×C6112yes—
682C24C2×D4×C6112yes—
683C24C2×Q8×C6112yes—
684C24C24×C6111yescharacteristic
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—21no—
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—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4C22×C4×C6112yes—
773C22×C4C22×C4×C6112yes—
774C22×C4C22×C4×C6112yes—
775C22×C4C22×C4×C6112yes—
776C22×C4C22×C4×C6112yes—
777C22×C4C22×C4×C6112yes—
778C22×C4C2×D4×C6112yes—
779C22×C4C2×D4×C6112yes—
780C22×C4C2×D4×C6112yes—
781C22×C4C2×D4×C6112yes—
782C22×C4C2×D4×C6112yes—
783C22×C4C2×D4×C6112yes—
784C22×C4C2×D4×C6112yes—
785C22×C4C2×D4×C6112yes—
786C22×C4C2×Q8×C6112yes—
787C22×C4C2×Q8×C6112yes—
788C22×C4#41×C6112yes—
789C22×C4#41×C6112yes—
790C4⋊C4—28no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4C4⋊C4×C61116yescomplemented
806C42—28no—
807C42—44no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×C4⋊C4×C6114yes—
843C23C23×C4×C6111yescharacteristic
844C23C22×D4×C6111yescharacteristic
845C23C22×D4×C6111yescharacteristic
846C23C22×D4×C6111yescharacteristic
847C23C22×Q8×C6111yescharacteristic
848C23C2×#41×C6111yescharacteristic
849C23C2×#41×C6111yescharacteristic
850C23H(5,𝔽2)×C6111yescharacteristic
851C23H(5,𝔽2)×C6111yescharacteristic
852C23H(5,𝔽2)×C6111yescharacteristic
853C23H(5,𝔽2)×C6111yescharacteristic
854C232−1+4×C6111yescharacteristic
855C232−1+4×C6111yescharacteristic
856C232−1+4×C6111yescharacteristic
857C232−1+4×C6111yescharacteristic
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—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—416no—
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×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4C2×C4⋊C4×C6114yes—
954C2×C4C2×C4⋊C4×C6114yes—
955C2×C4C4×D4×C6114yes—
956C2×C4C4×D4×C6114yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C4⋊C4×C6111yescharacteristic
973C22C2×C4×D4×C6111yescharacteristic
974C22C2×C4×D4×C6111yescharacteristic
975C22C61×#52011yescharacteristic
976C22C61×#52011yescharacteristic
977C22C61×#52011yescharacteristic
978C22C61×#52011yescharacteristic
979C22C61×#53411yescharacteristic
980C22C61×#53511yescharacteristic
981C22C61×#53511yescharacteristic
982C22C61×#53611yescharacteristic
983C22C61×#53611yescharacteristic
984C22C61×#53611yescharacteristic
985C22C61×#53911yescharacteristic
986C22C61×#53911yescharacteristic
987C22C61×#54211yescharacteristic
988C22C61×#54211yescharacteristic
989C22C61×#54411yescharacteristic
990C22C61×#54411yescharacteristic
991C22D42×C6111yescharacteristic
992C22D42×C6111yescharacteristic
993C22D42×C6111yescharacteristic
994C22C61×#54711yescharacteristic
995C22C61×#54711yescharacteristic
996C22C61×#54711yescharacteristic
997C22C61×#54811yescharacteristic
998C22D4×Q8×C6111yescharacteristic
999C22D4×Q8×C6111yescharacteristic
1000C22C61×#55311yescharacteristic
1001C22C61×#55411yescharacteristic
1002C22C61×#55411yescharacteristic
1003C22C61×#56011yescharacteristic
1004C22C61×#56311yescharacteristic
1005C22C61×#56311yescharacteristic
1006C22C61×#56311yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—81no—
1018C4—81no—
1019C4—81no—
1020C4—81no—
1021C2—44no—
1022C2C61×#231711yescharacteristic
1023C2C61×#232211yescharacteristic
1024C2C61×#232611yescharacteristic
1025C2D4×C4⋊C4×C6111yescharacteristic
1026C2D4×C4⋊C4×C6111yescharacteristic
1027C2C61×#236111yescharacteristic
1028C2C61×#238311yescharacteristic
1029C2C61×#266911yescharacteristic
1030C2C61×#267411yescharacteristic
1031C2C61×#267711yescharacteristic
1032C2C61×#268011yescharacteristic
1033C2C61×#271811yescharacteristic
1034C2C61×#272011yescharacteristic
1035C2C61×#272911yescharacteristic
1036C2C61×#279011yescharacteristic
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
7. C2×C61×#384C2semidirect
8. C61×#1444C2semidirect
9. C61×#1444C2semidirect
10. C61×#1442C2semidirect
11. C61×#1441C2semidirect
14. C61×#1436C2semidirect
15. C61×#1434C2semidirect
37. C61×#388C4semidirect
108. C2×C4⋊C4×C61C2×C4semidirect
133. C2×C42×C61C2×C4semidirect
147. #95×C61C2×C4semidirect
148. #95×C61C2×C4semidirect
286. C22⋊C4×C61C4⋊C4semidirect
438. #14405C61direct (N × H)
503. C2×#389C2×C61semidirect
509. C2×#384C2×C61semidirect
510. #1444C2×C61semidirect
511. #1444C2×C61semidirect
512. #1442C2×C61semidirect
513. #1441C2×C61semidirect
516. #1436C2×C61semidirect
517. #1434C2×C61semidirect
555. #388C4×C61semidirect
576. C61#14405direct (N × H)
627. C2×C4⋊C4C2×C4×C61semidirect
652. C2×C42C2×C4×C61semidirect
666. #95C2×C4×C61semidirect
667. #95C2×C4×C61semidirect
805. 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×#3842
C61×#14442
C61×#14422
C61×#14412
C61×#14392
C61×#14362
C61×#14342
#1440561