Finite Group Databasebeta

← C61×#17516 #29520949

Subgroups — C61×#17516 #29520949

Order 15616.

948 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3480C211yesmaximal, characteristic
2C61×#2965C211yesmaximal, characteristic, complemented
3C61×#2925C211yesmaximal, characteristic, complemented
4C61×#1496C211yesmaximal, characteristic, complemented
5C61×#1495C211yesmaximal, characteristic, complemented
6C61×#1494C211yesmaximal, characteristic, complemented
7C61×#1491C211yesmaximal, characteristic, complemented
8C61×#1489C211yesmaximal, characteristic, complemented
9C61×#1488C211yesmaximal, characteristic, complemented
10C61×#1484C211yesmaximal, characteristic, complemented
11C61×#1483C211yesmaximal, characteristic, complemented
12C61×#1482C211yesmaximal, characteristic, complemented
13C61×#1479C211yesmaximal, characteristic, complemented
14C61×#1477C211yesmaximal, characteristic, complemented
15C61×#1476C211yesmaximal, characteristic, complemented
16C61×#559—21no—
17C61×#559C411yescharacteristic
18C61×#557C411yescharacteristic
19C61×#556—21no—
20C61×#556C411yescharacteristic
21C61×#553—21no—
22C61×#553—21no—
23C61×#553C411yescharacteristic
24C61×#553C411yescharacteristic
25C61×#550C411yescharacteristic
26C61×#548C411yescharacteristic
27C61×#548C411yescharacteristic
28C61×#532—21no—
29C61×#532C2211yescharacteristic
30C61×#529—21no—
31C61×#529—21no—
32C61×#529C2211yescharacteristic
33C61×#529C2211yescharacteristic
34C4×#41×C61—21no—
35C4×#41×C61C2211yescharacteristic
36C4×#41×C61C2211yescharacteristic
37C4×#41×C61C2211yescharacteristic
38C2×C4×Q8×C61C2211yescharacteristic
39C61×#446—21no—
40C61×#436—21no—
41C61×#435—21no—
42C61×#435—21no—
43C61×#433—21no—
44C61×#433—21no—
45C61×#432C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C61×#431C2211yescharacteristic
48C61×#431C2211yescharacteristic
49C61×#431C2211yescharacteristic
50C61×#431C2211yescharacteristic
51C61×#431C2211yescharacteristic
52C61×#423C2211yescharacteristic
53C2×C4⋊C8×C61C2211yescharacteristic
54C61×#408—21no—
55C61×#405—21no—
56C4×M16×C61C2211yescharacteristic
57C4×M16×C61C2211yescharacteristic
58C2×C4×C8×C61C2211yescharacteristic
59C61×Q8⋊C8C2211yescharacteristic
60C61×Q8⋊C8C2211yescharacteristic
61C61×Q8⋊C8C2211yescharacteristic
62C61×Q8⋊C8C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×Q8⋊C8C2211yescharacteristic
66C61×Q8⋊C8C2211yescharacteristic
67C61×D4⋊C8C2211yescharacteristic
68C61×D4⋊C8C2211yescharacteristic
69C61×D4⋊C8C2211yescharacteristic
70C61×D4⋊C8C2211yescharacteristic
71C61×D4⋊C8C2211yescharacteristic
72C61×D4⋊C8C2211yescharacteristic
73C61×D4⋊C8C2211yescharacteristic
74C61×D4⋊C8C2211yescharacteristic
75C2×#41×C61—21no—
76C2×#41×C61C2×C411yescharacteristic
77C2×#41×C61C2×C411yescharacteristic
78C2×#41×C61D411yescharacteristic
79C22×Q8×C61C2×C411yescharacteristic
80C2×M16×C61—21no—
81C2×M16×C61—21no—
82C2×M16×C61—21no—
83C22×C8×C61—21no—
84C22×C8×C61—21no—
85C4⋊Q8×C61—21no—
86C4⋊Q8×C61C2×C411yescharacteristic
87#127×C61—21no—
88#127×C61C2×C411yescharacteristic
89#126×C61—21no—
90#126×C61—21no—
91#126×C61—21no—
92#126×C61—21no—
93#126×C61—21no—
94#126×C61—21no—
95#125×C61—21no—
96#125×C61—21no—
97#125×C61C2×C411yescharacteristic
98#125×C61C2×C411yescharacteristic
99#124×C61—21no—
100#124×C61—21no—
101#124×C61—21no—
102#124×C61—21no—
103#124×C61—21no—
104#124×C61C2×C411yescharacteristic
105#124×C61C2×C411yescharacteristic
106#123×C61—21no—
107#123×C61—21no—
108#123×C61—21no—
109#123×C61—21no—
110#123×C61—21no—
111#123×C61—21no—
112C22⋊Q8×C61—21no—
113C22⋊Q8×C61—21no—
114C22⋊Q8×C61C2×C411yescharacteristic
115C22⋊Q8×C61C2×C411yescharacteristic
116#121×C61—21no—
117#121×C61—21no—
118#121×C61—21no—
119#121×C61—21no—
120#121×C61—21no—
121#121×C61—21no—
122#121×C61—21no—
123#121×C61C2×C411yescharacteristic
124#121×C61C2×C411yescharacteristic
125#121×C61C2×C411yescharacteristic
126#121×C61C2×C411yescharacteristic
127C4×Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C4×Q8×C61—21no—
131C4×Q8×C61C2×C411yescharacteristic
132C4×Q8×C61C2×C411yescharacteristic
133C4×Q8×C61C2×C411yescharacteristic
134C4×Q8×C61C2×C411yescharacteristic
135C4×Q8×C61C2×C411yescharacteristic
136C4×Q8×C61D411yescharacteristic
137C4×Q8×C61C2311yescharacteristic
138C4×Q8×C61C2311yescharacteristic
139C4×D4×C61—21no—
140C4×D4×C61—21no—
141C4×D4×C61—21no—
142C4×D4×C61—21no—
143C4×D4×C61—21no—
144C4×D4×C61—21no—
145C4×D4×C61—21no—
146C4×D4×C61—21no—
147C4×D4×C61—21no—
148C4×D4×C61—21no—
149C4×D4×C61—21no—
150C4×D4×C61—21no—
151C4×D4×C61—21no—
152C4×D4×C61C2×C411yescharacteristic
153C4×D4×C61C2×C411yescharacteristic
154C4×D4×C61C2×C411yescharacteristic
155C4×D4×C61C2×C411yescharacteristic
156C4×D4×C61C2×C411yescharacteristic
157C4×D4×C61D411yescharacteristic
158C4×D4×C61D411yescharacteristic
159C4×D4×C61D411yescharacteristic
160C4×D4×C61C2311yescharacteristic
161C4×D4×C61C2311yescharacteristic
162#117×C61—21no—
163#117×C61—21no—
164#117×C61—21no—
165#117×C61—21no—
166#117×C61C2×C411yescharacteristic
167#117×C61C2×C411yescharacteristic
168#117×C61D411yescharacteristic
169#117×C61D411yescharacteristic
170#117×C61D411yescharacteristic
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61C2×C411yescharacteristic
173C2×C42×C61—21no—
174C2×C42×C61—21no—
175C2×C42×C61—21no—
176C2×C42×C61C2311yescharacteristic
177C2×C42×C61C2311yescharacteristic
178C2×C42×C61C2311yescharacteristic
179C4⋊C8×C61—21no—
180C4⋊C8×C61—21no—
181C4⋊C8×C61—21no—
182C4⋊C8×C61—21no—
183C4⋊C8×C61—21no—
184C4⋊C8×C61C2311yescharacteristic
185C4⋊C8×C61C2311yescharacteristic
186C4⋊C8×C61C2311yescharacteristic
187C4⋊C8×C61C2311yescharacteristic
188C22⋊C8×C61—21no—
189C22⋊C8×C61—21no—
190C22⋊C8×C61—21no—
191C22⋊C8×C61—21no—
192C22⋊C8×C61—21no—
193C22⋊C8×C61—21no—
194C22⋊C8×C61—21no—
195#97×C61—21no—
196#97×C61—21no—
197#97×C61—21no—
198#97×C61—21no—
199C4×C8×C61—21no—
200C4×C8×C61—21no—
201C4×C8×C61—21no—
202C4×C8×C61C2311yescharacteristic
203C4×C8×C61C2311yescharacteristic
204C4×C8×C61C2311yescharacteristic
205C4×C8×C61C2311yescharacteristic
206#41×C61—22no—
207#41×C61—22no—
208#41×C61—41no—
209#41×C61—41no—
210#41×C61—41no—
211#41×C61—41no—
212#41×C61—42no—
213#41×C61—42no—
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61—22no—
217C2×Q8×C61—41no—
218C2×Q8×C61C22⋊C411yescharacteristic
219C2×Q8×C61C22×C411yescharacteristic
220C2×Q8×C61C22×C411yescharacteristic
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—21no—
229C2×D4×C61C22⋊C411yescharacteristic
230C2×D4×C61C22⋊C411yescharacteristic
231C2×D4×C61C22⋊C411yescharacteristic
232C2×D4×C61C22×C411yescharacteristic
233C2×D4×C61C22×C411yescharacteristic
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×C61C22×C411yescharacteristic
243C22×C4×C61C22×C411yescharacteristic
244C22×C4×C61C22×C411yescharacteristic
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251M16×C61—42no—
252M16×C61—42no—
253M16×C61—42no—
254C2×C8×C61—21no—
255C2×C8×C61—21no—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—42no—
263C2×C8×C61—42no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61C22⋊C411yescharacteristic
279C4⋊C4×C61C22⋊C411yescharacteristic
280C4⋊C4×C61C22⋊C411yescharacteristic
281C4⋊C4×C61C22⋊C411yescharacteristic
282C4⋊C4×C61C22⋊C411yescharacteristic
283C4⋊C4×C61C22⋊C411yescharacteristic
284C4⋊C4×C61C22×C411yescharacteristic
285C4⋊C4×C61C22×C411yescharacteristic
286C4⋊C4×C61C22×C411yescharacteristic
287C4⋊C4×C61C22×C411yescharacteristic
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C22⋊C4×C61—21no—
292C22⋊C4×C61—21no—
293C22⋊C4×C61—21no—
294C22⋊C4×C61—21no—
295C22⋊C4×C61—21no—
296C22⋊C4×C61—21no—
297C22⋊C4×C61—21no—
298C22⋊C4×C61—21no—
299C22⋊C4×C61—21no—
300C22⋊C4×C61—21no—
301C22⋊C4×C61—21no—
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61C22⋊C411yescharacteristic
305C22⋊C4×C61C22⋊C411yescharacteristic
306C22⋊C4×C61C22⋊C411yescharacteristic
307C22⋊C4×C61C22⋊C411yescharacteristic
308C22⋊C4×C61C22⋊C411yescharacteristic
309C22⋊C4×C61C22⋊C411yescharacteristic
310C42×C61—21no—
311C42×C61—21no—
312C42×C61—21no—
313C42×C61—21no—
314C42×C61—21no—
315C42×C61—21no—
316C42×C61—21no—
317C42×C61—21no—
318C42×C61C22×C411yescharacteristic
319C42×C61C22×C411yescharacteristic
320C42×C61C22×C411yescharacteristic
321C42×C61C2×D411yescharacteristic
322C42×C61C2×D411yescharacteristic
323C42×C61C2×D411yescharacteristic
324C42×C61C2×D411yescharacteristic
325C42×C61C2×D411yescharacteristic
326C42×C61C2×D411yescharacteristic
327C42×C61C2411yescharacteristic
328C23×C61—21no—
329C23×C61—21no—
330C23×C61C2×C22⋊C411yescharacteristic
331C23×C61C2×C22⋊C411yescharacteristic
332C23×C61C2×C22⋊C411yescharacteristic
333Q8×C61—21no—
334Q8×C61—21no—
335Q8×C61—21no—
336Q8×C61—41no—
337Q8×C61—42no—
338Q8×C61—42no—
339Q8×C61#13112yes—
340D4×C61—21no—
341D4×C61—21no—
342D4×C61—21no—
343D4×C61—21no—
344D4×C61—41no—
345D4×C61—41no—
346D4×C61—41no—
347D4×C61—42no—
348D4×C61—42no—
349D4×C61—42no—
350D4×C61—42no—
351D4×C61—42no—
352D4×C61—81no—
353D4×C61—81no—
354D4×C61—81no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—42no—
377C2×C4×C61—42no—
378C2×C4×C61—42no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—81no—
384C2×C4×C61—81no—
385C2×C4×C61—81no—
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C2×C22⋊C411yescharacteristic
389C2×C4×C61C2×C22⋊C411yescharacteristic
390C2×C4×C61C2×C22⋊C411yescharacteristic
391C2×C4×C61C2×C22⋊C411yescharacteristic
392C2×C4×C61C2×C22⋊C411yescharacteristic
393C2×C4×C61C2×C22⋊C411yescharacteristic
394C2×C4×C61C2×C22⋊C411yescharacteristic
395C2×C4×C61C23×C411yescharacteristic
396C2×C4×C61C22×D411yescharacteristic
397C2×C4×C61C22×D411yescharacteristic
398C8×C61—22no—
399C8×C61—41no—
400C8×C61—41no—
401C8×C61—41no—
402C8×C61—41no—
403C8×C61—41no—
404C8×C61—41no—
405C8×C61—41no—
406#17516C6111yesmaximal, characteristic, direct product factor, Sylow
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—21no—
411C22×C61—21no—
412C22×C61—21no—
413C22×C61—21no—
414C22×C61—21no—
415C22×C61—21no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61—41no—
421C22×C61—41no—
422C22×C61C22×C22⋊C411yescharacteristic
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—22no—
427C4×C61—21no—
428C4×C61—21no—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—21no—
432C4×C61—21no—
433C4×C61—21no—
434C4×C61—41no—
435C4×C61—41no—
436C4×C61—41no—
437C4×C61—41no—
438C4×C61—41no—
439C4×C61C2×#13111yescharacteristic
440C4×C61#56811yescharacteristic
441C4×C61#57511yescharacteristic
442C4×C61#57511yescharacteristic
443#3480C2×C6111yescharacteristic
444#2965C2×C6111yescharacteristic, complemented
445#2925C2×C6111yescharacteristic, complemented
446#1496C2×C6111yescharacteristic, complemented
447#1495C2×C6111yescharacteristic, complemented
448#1494C2×C6111yescharacteristic, complemented
449#1491C2×C6111yescharacteristic, complemented
450#1489C2×C6111yescharacteristic, complemented
451#1488C2×C6111yescharacteristic, complemented
452#1484C2×C6111yescharacteristic, complemented
453#1483C2×C6111yescharacteristic, complemented
454#1482C2×C6111yescharacteristic, complemented
455#1479C2×C6111yescharacteristic, complemented
456#1477C2×C6111yescharacteristic, complemented
457#1476C2×C6111yescharacteristic, complemented
458C2×C61—41no—
459C2×C61—41no—
460C2×C61—41no—
461C2×C61—81no—
462C2×C61—81no—
463C2×C61#288011yescharacteristic
464C2×C61#289611yescharacteristic
465C2×C61#290111yescharacteristic
466#559—21no—
467#559C4×C6111yescharacteristic
468#557C4×C6111yescharacteristic
469#556—21no—
470#556C4×C6111yescharacteristic
471#553—21no—
472#553—21no—
473#553C4×C6111yescharacteristic
474#553C4×C6111yescharacteristic
475#550C4×C6111yescharacteristic
476#548C4×C6111yescharacteristic
477#548C4×C6111yescharacteristic
478#532—21no—
479#532C22×C6111yescharacteristic
480#529—21no—
481#529—21no—
482#529C22×C6111yescharacteristic
483#529C22×C6111yescharacteristic
484C4×#41—21no—
485C4×#41C22×C6111yescharacteristic
486C4×#41C22×C6111yescharacteristic
487C4×#41C22×C6111yescharacteristic
488C2×C4×Q8C22×C6111yescharacteristic
489#446—21no—
490#436—21no—
491#435—21no—
492#435—21no—
493#433—21no—
494#433—21no—
495#432C22×C6111yescharacteristic
496#432C22×C6111yescharacteristic
497#431C22×C6111yescharacteristic
498#431C22×C6111yescharacteristic
499#431C22×C6111yescharacteristic
500#431C22×C6111yescharacteristic
501#431C22×C6111yescharacteristic
502#423C22×C6111yescharacteristic
503C2×C4⋊C8C22×C6111yescharacteristic
504#408—21no—
505#405—21no—
506C4×M16C22×C6111yescharacteristic
507C4×M16C22×C6111yescharacteristic
508C2×C4×C8C22×C6111yescharacteristic
509Q8⋊C8C22×C6111yescharacteristic
510Q8⋊C8C22×C6111yescharacteristic
511Q8⋊C8C22×C6111yescharacteristic
512Q8⋊C8C22×C6111yescharacteristic
513Q8⋊C8C22×C6111yescharacteristic
514Q8⋊C8C22×C6111yescharacteristic
515Q8⋊C8C22×C6111yescharacteristic
516Q8⋊C8C22×C6111yescharacteristic
517D4⋊C8C22×C6111yescharacteristic
518D4⋊C8C22×C6111yescharacteristic
519D4⋊C8C22×C6111yescharacteristic
520D4⋊C8C22×C6111yescharacteristic
521D4⋊C8C22×C6111yescharacteristic
522D4⋊C8C22×C6111yescharacteristic
523D4⋊C8C22×C6111yescharacteristic
524D4⋊C8C22×C6111yescharacteristic
525C61#1751611yescharacteristic, direct product factor, Sylow
526C2×#41—21no—
527C2×#41C2×C4×C6111yescharacteristic
528C2×#41C2×C4×C6111yescharacteristic
529C2×#41D4×C6111yescharacteristic
530C22×Q8C2×C4×C6111yescharacteristic
531C2×M16—21no—
532C2×M16—21no—
533C2×M16—21no—
534C22×C8—21no—
535C22×C8—21no—
536C4⋊Q8—21no—
537C4⋊Q8C2×C4×C6111yescharacteristic
538#127—21no—
539#127C2×C4×C6111yescharacteristic
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#125—21no—
547#125—21no—
548#125C2×C4×C6111yescharacteristic
549#125C2×C4×C6111yescharacteristic
550#124—21no—
551#124—21no—
552#124—21no—
553#124—21no—
554#124—21no—
555#124C2×C4×C6111yescharacteristic
556#124C2×C4×C6111yescharacteristic
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8C2×C4×C6111yescharacteristic
566C22⋊Q8C2×C4×C6111yescharacteristic
567#121—21no—
568#121—21no—
569#121—21no—
570#121—21no—
571#121—21no—
572#121—21no—
573#121—21no—
574#121C2×C4×C6111yescharacteristic
575#121C2×C4×C6111yescharacteristic
576#121C2×C4×C6111yescharacteristic
577#121C2×C4×C6111yescharacteristic
578C4×Q8—21no—
579C4×Q8—21no—
580C4×Q8—21no—
581C4×Q8—21no—
582C4×Q8C2×C4×C6111yescharacteristic
583C4×Q8C2×C4×C6111yescharacteristic
584C4×Q8C2×C4×C6111yescharacteristic
585C4×Q8C2×C4×C6111yescharacteristic
586C4×Q8C2×C4×C6111yescharacteristic
587C4×Q8D4×C6111yescharacteristic
588C4×Q8C23×C6111yescharacteristic
589C4×Q8C23×C6111yescharacteristic
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4—21no—
600C4×D4—21no—
601C4×D4—21no—
602C4×D4—21no—
603C4×D4C2×C4×C6111yescharacteristic
604C4×D4C2×C4×C6111yescharacteristic
605C4×D4C2×C4×C6111yescharacteristic
606C4×D4C2×C4×C6111yescharacteristic
607C4×D4C2×C4×C6111yescharacteristic
608C4×D4D4×C6111yescharacteristic
609C4×D4D4×C6111yescharacteristic
610C4×D4D4×C6111yescharacteristic
611C4×D4C23×C6111yescharacteristic
612C4×D4C23×C6111yescharacteristic
613#117—21no—
614#117—21no—
615#117—21no—
616#117—21no—
617#117C2×C4×C6111yescharacteristic
618#117C2×C4×C6111yescharacteristic
619#117D4×C6111yescharacteristic
620#117D4×C6111yescharacteristic
621#117D4×C6111yescharacteristic
622C2×C4⋊C4—21no—
623C2×C4⋊C4C2×C4×C6111yescharacteristic
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42C23×C6111yescharacteristic
628C2×C42C23×C6111yescharacteristic
629C2×C42C23×C6111yescharacteristic
630C4⋊C8—21no—
631C4⋊C8—21no—
632C4⋊C8—21no—
633C4⋊C8—21no—
634C4⋊C8—21no—
635C4⋊C8C23×C6111yescharacteristic
636C4⋊C8C23×C6111yescharacteristic
637C4⋊C8C23×C6111yescharacteristic
638C4⋊C8C23×C6111yescharacteristic
639C22⋊C8—21no—
640C22⋊C8—21no—
641C22⋊C8—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644C22⋊C8—21no—
645C22⋊C8—21no—
646#97—21no—
647#97—21no—
648#97—21no—
649#97—21no—
650C4×C8—21no—
651C4×C8—21no—
652C4×C8—21no—
653C4×C8C23×C6111yescharacteristic
654C4×C8C23×C6111yescharacteristic
655C4×C8C23×C6111yescharacteristic
656C4×C8C23×C6111yescharacteristic
657#41—22no—
658#41—22no—
659#41—41no—
660#41—41no—
661#41—41no—
662#41—41no—
663#41—42no—
664#41—42no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C22⋊C4×C6111yescharacteristic
670C2×Q8C22×C4×C6111yescharacteristic
671C2×Q8C22×C4×C6111yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4C22⋊C4×C6111yescharacteristic
681C2×D4C22⋊C4×C6111yescharacteristic
682C2×D4C22⋊C4×C6111yescharacteristic
683C2×D4C22×C4×C6111yescharacteristic
684C2×D4C22×C4×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×C4C22×C4×C6111yescharacteristic
694C22×C4C22×C4×C6111yescharacteristic
695C22×C4C22×C4×C6111yescharacteristic
696C22×C4C2×D4×C6111yescharacteristic
697C22×C4C2×D4×C6111yescharacteristic
698C22×C4C2×D4×C6111yescharacteristic
699C22×C4C2×D4×C6111yescharacteristic
700C22×C4C2×D4×C6111yescharacteristic
701C22×C4C2×D4×C6111yescharacteristic
702M16—42no—
703M16—42no—
704M16—42no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—42no—
714C2×C8—42no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4C22⋊C4×C6111yescharacteristic
730C4⋊C4C22⋊C4×C6111yescharacteristic
731C4⋊C4C22⋊C4×C6111yescharacteristic
732C4⋊C4C22⋊C4×C6111yescharacteristic
733C4⋊C4C22⋊C4×C6111yescharacteristic
734C4⋊C4C22⋊C4×C6111yescharacteristic
735C4⋊C4C22×C4×C6111yescharacteristic
736C4⋊C4C22×C4×C6111yescharacteristic
737C4⋊C4C22×C4×C6111yescharacteristic
738C4⋊C4C22×C4×C6111yescharacteristic
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⋊C4C22⋊C4×C6111yescharacteristic
756C22⋊C4C22⋊C4×C6111yescharacteristic
757C22⋊C4C22⋊C4×C6111yescharacteristic
758C22⋊C4C22⋊C4×C6111yescharacteristic
759C22⋊C4C22⋊C4×C6111yescharacteristic
760C22⋊C4C22⋊C4×C6111yescharacteristic
761C42—21no—
762C42—21no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42—21no—
769C42C22×C4×C6111yescharacteristic
770C42C22×C4×C6111yescharacteristic
771C42C22×C4×C6111yescharacteristic
772C42C2×D4×C6111yescharacteristic
773C42C2×D4×C6111yescharacteristic
774C42C2×D4×C6111yescharacteristic
775C42C2×D4×C6111yescharacteristic
776C42C2×D4×C6111yescharacteristic
777C42C2×D4×C6111yescharacteristic
778C42C24×C6111yescharacteristic
779C23—21no—
780C23—21no—
781C23C2×C22⋊C4×C6111yescharacteristic
782C23C2×C22⋊C4×C6111yescharacteristic
783C23C2×C22⋊C4×C6111yescharacteristic
784Q8—21no—
785Q8—21no—
786Q8—21no—
787Q8—41no—
788Q8—42no—
789Q8—42no—
790Q8#131×C6112yes—
791D4—21no—
792D4—21no—
793D4—21no—
794D4—21no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—42no—
799D4—42no—
800D4—42no—
801D4—42no—
802D4—42no—
803D4—81no—
804D4—81no—
805D4—81no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4C2×C22⋊C4×C6111yescharacteristic
838C2×C4C2×C22⋊C4×C6111yescharacteristic
839C2×C4C2×C22⋊C4×C6111yescharacteristic
840C2×C4C2×C22⋊C4×C6111yescharacteristic
841C2×C4C2×C22⋊C4×C6111yescharacteristic
842C2×C4C2×C22⋊C4×C6111yescharacteristic
843C2×C4C2×C22⋊C4×C6111yescharacteristic
844C2×C4C2×C22⋊C4×C6111yescharacteristic
845C2×C4C2×C22⋊C4×C6111yescharacteristic
846C2×C4C23×C4×C6111yescharacteristic
847C2×C4C22×D4×C6111yescharacteristic
848C2×C4C22×D4×C6111yescharacteristic
849C8—22no—
850C8—41no—
851C8—41no—
852C8—41no—
853C8—41no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22C22×C22⋊C4×C6111yescharacteristic
873C4—21no—
874C4—21no—
875C4—21no—
876C4—22no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4C2×#131×C6111yescharacteristic
890C4C61×#56811yescharacteristic
891C4C61×#57511yescharacteristic
892C4C61×#57511yescharacteristic
893C2—41no—
894C2—41no—
895C2—41no—
896C2—81no—
897C2—81no—
898C2C61×#288011yescharacteristic
899C2C61×#289611yescharacteristic
900C2C61×#290111yescharacteristic
subgroupG/H
centerC2×C4×C61C22×D4
commutatorC2×C4C23×C4×C61
Frattini, cosocleC42C24×C61
socleC22×C61C22×C22⋊C4
prime radicalC61×#3480C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C4×#41×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2965C2semidirect
3. C61×#2925C2semidirect
4. C61×#1496C2semidirect
5. C61×#1495C2semidirect
6. C61×#1494C2semidirect
7. C61×#1491C2semidirect
8. C61×#1489C2semidirect
9. C61×#1488C2semidirect
10. C61×#1484C2semidirect
11. C61×#1483C2semidirect
12. C61×#1482C2semidirect
13. C61×#1479C2semidirect
14. C61×#1477C2semidirect
15. C61×#1476C2semidirect
406. #17516C61direct (N × H)
444. #2965C2×C61semidirect
445. #2925C2×C61semidirect
446. #1496C2×C61semidirect
447. #1495C2×C61semidirect
448. #1494C2×C61semidirect
449. #1491C2×C61semidirect
450. #1489C2×C61semidirect
451. #1488C2×C61semidirect
452. #1484C2×C61semidirect
453. #1483C2×C61semidirect
454. #1482C2×C61semidirect
455. #1479C2×C61semidirect
456. #1477C2×C61semidirect
457. #1476C2×C61semidirect
525. C61#17516direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#34802
C61×#29652
C61×#29252
C61×#14962
C61×#14952
C61×#14942
C61×#14912
C61×#14892
C61×#14882
C61×#14842
C61×#14832
C61×#14822
C61×#14792
C61×#14772
C61×#14762
#1751661