Finite Group Databasebeta

← C61×#18447 #29521880

Subgroups — C61×#18447 #29521880

Order 15616.

982 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3534C211yesmaximal, characteristic
2C61×#3193C211yesmaximal, characteristic, complemented
3C61×#3190C211yesmaximal, characteristic, complemented
4C61×#2814C211yesmaximal, characteristic, complemented
5C61×#1612C211yesmaximal, characteristic, complemented
6C61×#1610C211yesmaximal, characteristic, complemented
7C61×#1609C211yesmaximal, characteristic, complemented
8C61×#1607C211yesmaximal, characteristic, complemented
9C61×#1606C211yesmaximal, characteristic, complemented
10C61×#1604C211yesmaximal, characteristic, complemented
11C61×#1603C211yesmaximal, characteristic, complemented
12C61×#1601C211yesmaximal, characteristic, complemented
13C61×#1519C211yesmaximal, characteristic, complemented
14C61×#1513C211yesmaximal, characteristic, complemented
15C61×#1468C211yesmaximal, characteristic, complemented
16C61×#562—21no—
17C61×#560—21no—
18C61×#553—21no—
19C61×#551—21no—
20C61×#546—21no—
21C61×#546—21no—
22C61×#546—21no—
23D42×C61—21no—
24C61×#540—21no—
25C61×#539—21no—
26C61×#539C2211yescharacteristic
27C61×#538—21no—
28C61×#538C2211yescharacteristic
29C61×#537C2211yescharacteristic
30C61×#534—21no—
31C61×#534C2211yescharacteristic
32C61×#525C2211yescharacteristic
33C2×#123×C61C2211yescharacteristic
34C2×C22⋊Q8×C61C2211yescharacteristic, complemented
35C2×#121×C61C2211yescharacteristic
36C61×#485—21no—
37C61×#484—21no—
38C61×#483C2211yescharacteristic, complemented
39C61×#480C2211yescharacteristic
40C61×#480C2211yescharacteristic, complemented
41C61×#480C2211yescharacteristic, complemented
42C61×#468—21no—
43C61×#468—21no—
44C61×#467—21no—
45C61×#465—21no—
46C61×#452—21no—
47C61×#451C2211yescharacteristic, complemented
48C61×#450—21no—
49C61×#448C2211yescharacteristic
50C61×#448C2211yescharacteristic, complemented
51C61×#448C2211yescharacteristic, complemented
52C61×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C61C2211yescharacteristic, complemented
54C61×#398—21no—
55C61×#398C2211yescharacteristic, complemented
56C61×#397—21no—
57C61×#397C2211yescharacteristic, complemented
58C61×#396—21no—
59C61×#395C2211yescharacteristic, complemented
60C61×#394—21no—
61C61×#393C2211yescharacteristic, complemented
62C61×#380C2211yescharacteristic, complemented
63C61×#328C2211yescharacteristic, complemented
64C61×#328C2211yescharacteristic, complemented
65C61×#327C2211yescharacteristic
66C61×#327C2211yescharacteristic
67C61×#327C2211yescharacteristic, complemented
68C61×#327C2211yescharacteristic, complemented
69C61×#327C2211yescharacteristic, complemented
70C61×#327C2211yescharacteristic, complemented
71C61×#324C2211yescharacteristic, complemented
72C61×#324C2211yescharacteristic, complemented
73C61×#323C2211yescharacteristic, complemented
74C61×#323C2211yescharacteristic, complemented
75C2×#41×C61—21no—
76C2×#41×C61D411yescharacteristic
77C22×Q8×C61C2311yescharacteristic
78C22×D4×C61—21no—
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61D411yescharacteristic
82C22×D4×C61D411yescharacteristic
83C23×C4×C61C2311yescharacteristic
84C2×Q16×C61—21no—
85C2×SD16×C61—21no—
86C2×SD16×C61—21no—
87C2×SD16×C61—21no—
88C2×M16×C61—21no—
89C22×C8×C61—21no—
90#127×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#124×C61—21no—
98#124×C61—21no—
99#124×C61—21no—
100#123×C61—21no—
101#123×C61—21no—
102#123×C61—21no—
103#123×C61—21no—
104#123×C61—21no—
105#123×C61—21no—
106#123×C61—21no—
107#123×C61—21no—
108#123×C61—21no—
109#123×C61—21no—
110#123×C61—21no—
111#123×C61—21no—
112#123×C61—21no—
113#123×C61—21no—
114C22⋊Q8×C61—21no—
115C22⋊Q8×C61—21no—
116C22⋊Q8×C61—21no—
117C22⋊Q8×C61—21no—
118C22⋊Q8×C61—21no—
119C22⋊Q8×C61—21no—
120C22⋊Q8×C61—21no—
121C22⋊Q8×C61—21no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61D411yescharacteristic
124C22⋊Q8×C61C2311yescharacteristic
125#121×C61—21no—
126#121×C61—21no—
127#121×C61—21no—
128#121×C61—21no—
129#121×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132#121×C61—21no—
133#121×C61—21no—
134#121×C61—21no—
135#121×C61—21no—
136#121×C61—21no—
137#121×C61—21no—
138#121×C61—21no—
139#121×C61—21no—
140#121×C61D411yescharacteristic
141#121×C61D411yescharacteristic
142#121×C61D411yescharacteristic
143#121×C61C2311yescharacteristic
144#121×C61C2311yescharacteristic
145#121×C61C2311yescharacteristic
146#120×C61—21no—
147#120×C61—21no—
148#120×C61—21no—
149#120×C61—21no—
150#120×C61—21no—
151#120×C61—21no—
152#120×C61—21no—
153#120×C61—21no—
154C4×D4×C61—21no—
155C4×D4×C61—21no—
156C4×D4×C61—21no—
157C4×D4×C61—21no—
158C4×D4×C61—21no—
159C4×D4×C61—21no—
160C4×D4×C61—21no—
161C4×D4×C61—21no—
162#117×C61—21no—
163#117×C61D411yescharacteristic
164C2×C4⋊C4×C61—21no—
165C2×C4⋊C4×C61—21no—
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61D411yescharacteristic
169C2×C4⋊C4×C61D411yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61D411yescharacteristic
180C2×C22⋊C4×C61D411yescharacteristic
181C2×C22⋊C4×C61C2311yescharacteristic
182#107×C61—21no—
183#107×C61—21no—
184#107×C61—21no—
185#106×C61—21no—
186#103×C61—21no—
187#103×C61—21no—
188#103×C61—21no—
189#103×C61—21no—
190#103×C61—21no—
191#102×C61—21no—
192#102×C61—21no—
193#102×C61—21no—
194C22⋊C8×C61—21no—
195C22⋊C8×C61—21no—
196C22⋊C8×C61C2311yescharacteristic
197C22⋊C8×C61C2311yescharacteristic
198C22⋊C8×C61C2311yescharacteristic
199C22⋊C8×C61C2311yescharacteristic
200#95×C61—21no—
201#95×C61—21no—
202#95×C61—21no—
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61—21no—
207C24×C61—21no—
208C24×C61C2×D411yescharacteristic
209C24×C61C2×D411yescharacteristic
210#41×C61—81no—
211#41×C61—81no—
212#41×C61—81no—
213C2×Q8×C61—21no—
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61—81no—
217C2×Q8×C61C2×D411yescharacteristic
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
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×C61—21no—
230C2×D4×C61—21no—
231C2×D4×C61—21no—
232C2×D4×C61—21no—
233C2×D4×C61—21no—
234C2×D4×C61—21no—
235C2×D4×C61—81no—
236C2×D4×C61—81no—
237C2×D4×C61—81no—
238C2×D4×C61—81no—
239C2×D4×C61—81no—
240C2×D4×C61—81no—
241C2×D4×C61—82no—
242C2×D4×C61C2×D411yescharacteristic
243C2×D4×C61C2×D411yescharacteristic
244C2×D4×C61C2×D411yescharacteristic
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—81no—
257C22×C4×C61C2×D411yescharacteristic
258C22×C4×C61C2×D411yescharacteristic
259C22×C4×C61C2×D411yescharacteristic
260C22×C4×C61C2×D411yescharacteristic
261C22×C4×C61C2×D411yescharacteristic
262C22×C4×C61C2×D411yescharacteristic
263C22×C4×C61C2×D411yescharacteristic
264C22×C4×C61C2×D411yescharacteristic
265C22×C4×C61C2411yescharacteristic
266Q16×C61—81no—
267SD16×C61—81no—
268SD16×C61—81no—
269SD16×C61—81no—
270M16×C61—81no—
271C2×C8×C61—21no—
272C2×C8×C61—21no—
273C2×C8×C61—21no—
274C2×C8×C61—21no—
275C2×C8×C61—81no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—21no—
285C4⋊C4×C61—21no—
286C4⋊C4×C61—21no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61—21no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61—21no—
291C4⋊C4×C61—41no—
292C4⋊C4×C61—41no—
293C4⋊C4×C61—81no—
294C4⋊C4×C61—81no—
295C4⋊C4×C61—81no—
296C4⋊C4×C61C2×D411yescharacteristic
297C4⋊C4×C61C2×D411yescharacteristic
298C4⋊C4×C61C2×D411yescharacteristic
299C4⋊C4×C61C2×D411yescharacteristic
300C22⋊C4×C61—21no—
301C22⋊C4×C61—21no—
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61—21no—
307C22⋊C4×C61—21no—
308C22⋊C4×C61—21no—
309C22⋊C4×C61—21no—
310C22⋊C4×C61—21no—
311C22⋊C4×C61—21no—
312C22⋊C4×C61—21no—
313C22⋊C4×C61—21no—
314C22⋊C4×C61—21no—
315C22⋊C4×C61—21no—
316C22⋊C4×C61—21no—
317C22⋊C4×C61—21no—
318C22⋊C4×C61—21no—
319C22⋊C4×C61—21no—
320C22⋊C4×C61—21no—
321C22⋊C4×C61—21no—
322C22⋊C4×C61—21no—
323C22⋊C4×C61—21no—
324C22⋊C4×C61—21no—
325C22⋊C4×C61—41no—
326C22⋊C4×C61—41no—
327C22⋊C4×C61—81no—
328C22⋊C4×C61—81no—
329C22⋊C4×C61—81no—
330C42×C61—21no—
331C42×C61—21no—
332C42×C61—21no—
333C23×C61—21no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—21no—
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—42no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—81no—
347C23×C61—81no—
348C23×C61—81no—
349C23×C61—81no—
350C23×C61—81no—
351C23×C61#12011yescharacteristic
352C23×C61#12011yescharacteristic
353C23×C61C22×D411yescharacteristic
354Q8×C61—41no—
355Q8×C61—41no—
356Q8×C61—41no—
357Q8×C61—41no—
358Q8×C61—41no—
359Q8×C61—81no—
360D4×C61—41no—
361D4×C61—41no—
362D4×C61—41no—
363D4×C61—42no—
364D4×C61—42no—
365D4×C61—41no—
366D4×C61—41no—
367D4×C61—41no—
368D4×C61—41no—
369D4×C61—41no—
370D4×C61—41no—
371D4×C61—81no—
372D4×C61—81no—
373D4×C61—81no—
374D4×C61—81no—
375D4×C61—81no—
376D4×C61—81no—
377D4×C61—81no—
378D4×C61—81no—
379D4×C61—81no—
380D4×C61—81no—
381D4×C61—81no—
382D4×C61—81no—
383C2×C4×C61—21no—
384C2×C4×C61—21no—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61—21no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
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—81no—
414C2×C4×C61—81no—
415C2×C4×C61—81no—
416C2×C4×C61—81no—
417C2×C4×C61—81no—
418C2×C4×C61—81no—
419C2×C4×C61—81no—
420C2×C4×C61#12011yescharacteristic
421C2×C4×C61#12011yescharacteristic
422C2×C4×C61C22×D411yescharacteristic
423C2×C4×C61C22×D411yescharacteristic
424C8×C61—41no—
425C8×C61—41no—
426C8×C61—41no—
427C8×C61—41no—
428#18447C6111yesmaximal, characteristic, direct product factor, Sylow
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61—41no—
442C22×C61—41no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—41no—
446C22×C61—41no—
447C22×C61—41no—
448C22×C61—41no—
449C22×C61—81no—
450C22×C61—81no—
451C22×C61—81no—
452C22×C61—81no—
453C22×C61—162no—
454C22×C61—162no—
455C22×C61C2×#12011yescharacteristic
456C22×C61#57611yescharacteristic
457C22×C61#57711yescharacteristic
458C4×C61—21no—
459C4×C61—21no—
460C4×C61—21no—
461C4×C61—21no—
462C4×C61—41no—
463C4×C61—41no—
464C4×C61—41no—
465C4×C61—41no—
466C4×C61—41no—
467C4×C61—41no—
468C4×C61—41no—
469C4×C61—41no—
470C4×C61—81no—
471C4×C61—81no—
472C4×C61—81no—
473C4×C61—81no—
474#3534C2×C6111yescharacteristic
475#3193C2×C6111yescharacteristic, complemented
476#3190C2×C6111yescharacteristic, complemented
477#2814C2×C6111yescharacteristic, complemented
478#1612C2×C6111yescharacteristic, complemented
479#1610C2×C6111yescharacteristic, complemented
480#1609C2×C6111yescharacteristic, complemented
481#1607C2×C6111yescharacteristic, complemented
482#1606C2×C6111yescharacteristic, complemented
483#1604C2×C6111yescharacteristic, complemented
484#1603C2×C6111yescharacteristic, complemented
485#1601C2×C6111yescharacteristic, complemented
486#1519C2×C6111yescharacteristic, complemented
487#1513C2×C6111yescharacteristic, complemented
488#1468C2×C6111yescharacteristic, complemented
489C2×C61—21no—
490C2×C61—21no—
491C2×C61—41no—
492C2×C61—41no—
493C2×C61—81no—
494C2×C61—81no—
495C2×C61—81no—
496C2×C61—81no—
497C2×C61#301211yescharacteristic
498C2×C61#302211yescharacteristic
499C2×C61#302611yescharacteristic
500#562—21no—
501#560—21no—
502#553—21no—
503#551—21no—
504#546—21no—
505#546—21no—
506#546—21no—
507D42—21no—
508#540—21no—
509#539—21no—
510#539C22×C6111yescharacteristic
511#538—21no—
512#538C22×C6111yescharacteristic
513#537C22×C6111yescharacteristic
514#534—21no—
515#534C22×C6111yescharacteristic
516#525C22×C6111yescharacteristic
517C2×#123C22×C6111yescharacteristic
518C2×C22⋊Q8C22×C6111yescharacteristic, complemented
519C2×#121C22×C6111yescharacteristic
520#485—21no—
521#484—21no—
522#483C22×C6111yescharacteristic, complemented
523#480C22×C6111yescharacteristic
524#480C22×C6111yescharacteristic, complemented
525#480C22×C6111yescharacteristic, complemented
526#468—21no—
527#468—21no—
528#467—21no—
529#465—21no—
530#452—21no—
531#451C22×C6111yescharacteristic, complemented
532#450—21no—
533#448C22×C6111yescharacteristic
534#448C22×C6111yescharacteristic, complemented
535#448C22×C6111yescharacteristic, complemented
536#407C22×C6111yescharacteristic, complemented
537C2×C22⋊C8C22×C6111yescharacteristic, complemented
538#398—21no—
539#398C22×C6111yescharacteristic, complemented
540#397—21no—
541#397C22×C6111yescharacteristic, complemented
542#396—21no—
543#395C22×C6111yescharacteristic, complemented
544#394—21no—
545#393C22×C6111yescharacteristic, complemented
546#380C22×C6111yescharacteristic, complemented
547#328C22×C6111yescharacteristic, complemented
548#328C22×C6111yescharacteristic, complemented
549#327C22×C6111yescharacteristic
550#327C22×C6111yescharacteristic
551#327C22×C6111yescharacteristic, complemented
552#327C22×C6111yescharacteristic, complemented
553#327C22×C6111yescharacteristic, complemented
554#327C22×C6111yescharacteristic, complemented
555#324C22×C6111yescharacteristic, complemented
556#324C22×C6111yescharacteristic, complemented
557#323C22×C6111yescharacteristic, complemented
558#323C22×C6111yescharacteristic, complemented
559C61#1844711yescharacteristic, direct product factor, Sylow
560C2×#41—21no—
561C2×#41D4×C6111yescharacteristic
562C22×Q8C23×C6111yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C6111yescharacteristic
567C22×D4D4×C6111yescharacteristic
568C23×C4C23×C6111yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8D4×C6111yescharacteristic
609C22⋊Q8C23×C6111yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121D4×C6111yescharacteristic
626#121D4×C6111yescharacteristic
627#121D4×C6111yescharacteristic
628#121C23×C6111yescharacteristic
629#121C23×C6111yescharacteristic
630#121C23×C6111yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C6111yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4D4×C6111yescharacteristic
654C2×C4⋊C4D4×C6111yescharacteristic
655C2×C4⋊C4C23×C6111yescharacteristic
656C2×C4⋊C4C23×C6111yescharacteristic
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4D4×C6111yescharacteristic
665C2×C22⋊C4D4×C6111yescharacteristic
666C2×C22⋊C4C23×C6111yescharacteristic
667#107—21no—
668#107—21no—
669#107—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C6111yescharacteristic
682C22⋊C8C23×C6111yescharacteristic
683C22⋊C8C23×C6111yescharacteristic
684C22⋊C8C23×C6111yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C6111yescharacteristic
690#95C23×C6111yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C6111yescharacteristic
694C24C2×D4×C6111yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C6111yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C6111yescharacteristic
728C2×D4C2×D4×C6111yescharacteristic
729C2×D4C2×D4×C6111yescharacteristic
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—81no—
742C22×C4C2×D4×C6111yescharacteristic
743C22×C4C2×D4×C6111yescharacteristic
744C22×C4C2×D4×C6111yescharacteristic
745C22×C4C2×D4×C6111yescharacteristic
746C22×C4C2×D4×C6111yescharacteristic
747C22×C4C2×D4×C6111yescharacteristic
748C22×C4C2×D4×C6111yescharacteristic
749C22×C4C2×D4×C6111yescharacteristic
750C22×C4C24×C6111yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—41no—
777C4⋊C4—41no—
778C4⋊C4—81no—
779C4⋊C4—81no—
780C4⋊C4—81no—
781C4⋊C4C2×D4×C6111yescharacteristic
782C4⋊C4C2×D4×C6111yescharacteristic
783C4⋊C4C2×D4×C6111yescharacteristic
784C4⋊C4C2×D4×C6111yescharacteristic
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—41no—
811C22⋊C4—41no—
812C22⋊C4—81no—
813C22⋊C4—81no—
814C22⋊C4—81no—
815C42—21no—
816C42—21no—
817C42—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C6111yescharacteristic
837C23#120×C6111yescharacteristic
838C23C22×D4×C6111yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
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—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C6111yescharacteristic
906C2×C4#120×C6111yescharacteristic
907C2×C4C22×D4×C6111yescharacteristic
908C2×C4C22×D4×C6111yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C6111yescharacteristic
940C22C61×#57611yescharacteristic
941C22C61×#57711yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C61×#301211yescharacteristic
967C2C61×#302211yescharacteristic
968C2C61×#302611yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3193C2semidirect
3. C61×#3190C2semidirect
4. C61×#2814C2semidirect
5. C61×#1612C2semidirect
6. C61×#1610C2semidirect
7. C61×#1609C2semidirect
8. C61×#1607C2semidirect
9. C61×#1606C2semidirect
10. C61×#1604C2semidirect
11. C61×#1603C2semidirect
12. C61×#1601C2semidirect
13. C61×#1519C2semidirect
14. C61×#1513C2semidirect
15. C61×#1468C2semidirect
34. C2×C22⋊Q8×C61C22semidirect
38. C61×#483C22semidirect
40. C61×#480C22semidirect
41. C61×#480C22semidirect
47. C61×#451C22semidirect
50. C61×#448C22semidirect
51. C61×#448C22semidirect
52. C61×#407C22semidirect
53. C2×C22⋊C8×C61C22semidirect
55. C61×#398C22semidirect
57. C61×#397C22semidirect
59. C61×#395C22semidirect
61. C61×#393C22semidirect
62. C61×#380C22semidirect
63. C61×#328C22semidirect
64. C61×#328C22semidirect
67. C61×#327C22semidirect
68. C61×#327C22semidirect
69. C61×#327C22semidirect
70. C61×#327C22semidirect
71. C61×#324C22semidirect
72. C61×#324C22semidirect
73. C61×#323C22semidirect
74. C61×#323C22semidirect
428. #18447C61direct (N × H)
475. #3193C2×C61semidirect
476. #3190C2×C61semidirect
477. #2814C2×C61semidirect
478. #1612C2×C61semidirect
479. #1610C2×C61semidirect
480. #1609C2×C61semidirect
481. #1607C2×C61semidirect
482. #1606C2×C61semidirect
483. #1604C2×C61semidirect
484. #1603C2×C61semidirect
485. #1601C2×C61semidirect
486. #1519C2×C61semidirect
487. #1513C2×C61semidirect
488. #1468C2×C61semidirect
518. C2×C22⋊Q8C22×C61semidirect
522. #483C22×C61semidirect
524. #480C22×C61semidirect
525. #480C22×C61semidirect
531. #451C22×C61semidirect
534. #448C22×C61semidirect
535. #448C22×C61semidirect
536. #407C22×C61semidirect
537. C2×C22⋊C8C22×C61semidirect
539. #398C22×C61semidirect
541. #397C22×C61semidirect
543. #395C22×C61semidirect
545. #393C22×C61semidirect
546. #380C22×C61semidirect
547. #328C22×C61semidirect
548. #328C22×C61semidirect
551. #327C22×C61semidirect
552. #327C22×C61semidirect
553. #327C22×C61semidirect
554. #327C22×C61semidirect
555. #324C22×C61semidirect
556. #324C22×C61semidirect
557. #323C22×C61semidirect
558. #323C22×C61semidirect
559. C61#18447direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35342
C61×#31932
C61×#31902
C61×#28142
C61×#16122
C61×#16102
C61×#16092
C61×#16072
C61×#16062
C61×#16042
C61×#16032
C61×#16012
C61×#15192
C61×#15132
C61×#14682
#1844761