Finite Group Databasebeta

← C61×#15263 #29518696

Subgroups — C61×#15263 #29518696

Order 15616.

3142 conjugacy classes of subgroups.

The subgroup lattice has 1548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C61C211yesmaximal, characteristic, complemented
2C22×#121×C61C211yesmaximal, characteristic, complemented
3C2×C61×#394C211yesmaximal, characteristic, complemented
4C2×C61×#392C211yesmaximal, characteristic, complemented
5C2×C61×#392C211yesmaximal, characteristic, complemented
6C2×C61×#386C211yesmaximal, characteristic, complemented
7C2×C61×#386C211yesmaximal, characteristic, complemented
8C2×C61×#385C211yesmaximal, characteristic, complemented
9C61×#1441C211yesmaximal, characteristic, complemented
10C61×#1439C211yesmaximal, characteristic, complemented
11C61×#1439C211yesmaximal, characteristic, complemented
12C61×#1438C211yesmaximal, characteristic, complemented
13C61×#1438C211yesmaximal, characteristic, complemented
14C61×#1438C211yesmaximal, characteristic, complemented
15C61×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C23×D4×C61C2211yescharacteristic
19C23×D4×C61C2211yescharacteristic
20C23×D4×C61C2211yescharacteristic
21C23×D4×C61C2211yescharacteristic
22C24×C4×C61C2211yescharacteristic
23C24×C4×C61C2211yescharacteristic
24C2×#121×C61—24no—
25C2×#121×C61—24no—
26C2×#121×C61—24no—
27C2×#121×C61—24no—
28C2×#121×C61—24no—
29C2×#121×C61—24no—
30C22×C4⋊C4×C61C2211yescharacteristic
31C22×C4⋊C4×C61C2211yescharacteristic
32C22×C4⋊C4×C61C2211yescharacteristic
33C22×C22⋊C4×C61C2211yescharacteristic
34C22×C22⋊C4×C61C2211yescharacteristic
35C22×C22⋊C4×C61C2211yescharacteristic
36C22×C22⋊C4×C61C2211yescharacteristic
37C22×C22⋊C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2211yescharacteristic
40C22×C22⋊C4×C61C2211yescharacteristic
41C22×C22⋊C4×C61C2211yescharacteristic
42C22×C22⋊C4×C61C2211yescharacteristic
43C22×C22⋊C4×C61C2211yescharacteristic
44C22×C22⋊C4×C61C2211yescharacteristic
45C22×C22⋊C4×C61C2211yescharacteristic
46C22×C22⋊C4×C61C2211yescharacteristic
47C61×#394—24no—
48C61×#392—24no—
49C61×#392—24no—
50C61×#386—24no—
51C61×#386—24no—
52C61×#385—24no—
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C2×#95×C61C2211yescharacteristic
61C2×#95×C61C2211yescharacteristic
62C2×#95×C61C2211yescharacteristic
63C25×C61C2311yescharacteristic
64C25×C61C2311yescharacteristic
65C25×C61C2311yescharacteristic
66C25×C61C2311yescharacteristic
67C22×D4×C61—22no—
68C22×D4×C61—22no—
69C22×D4×C61—22no—
70C22×D4×C61—22no—
71C22×D4×C61—22no—
72C22×D4×C61—22no—
73C22×D4×C61—22no—
74C22×D4×C61—22no—
75C22×D4×C61—22no—
76C22×D4×C61—22no—
77C22×D4×C61—22no—
78C22×D4×C61—22no—
79C22×D4×C61—22no—
80C22×D4×C61—22no—
81C22×D4×C61—22no—
82C22×D4×C61—22no—
83C22×D4×C61—22no—
84C22×D4×C61—22no—
85C22×D4×C61—22no—
86C22×D4×C61—22no—
87C22×D4×C61—22no—
88C22×D4×C61—22no—
89C22×D4×C61—22no—
90C22×D4×C61—22no—
91C22×D4×C61—22no—
92C22×D4×C61—22no—
93C22×D4×C61—22no—
94C22×D4×C61—22no—
95C22×D4×C61—41no—
96C22×D4×C61—41no—
97C22×D4×C61—41no—
98C22×D4×C61—41no—
99C22×D4×C61—41no—
100C22×D4×C61—41no—
101C22×D4×C61—41no—
102C22×D4×C61—41no—
103C22×D4×C61—41no—
104C22×D4×C61—41no—
105C22×D4×C61—41no—
106C22×D4×C61—41no—
107C22×D4×C61D414yescomplemented
108C22×D4×C61D414yescomplemented
109C23×C4×C61—22no—
110C23×C4×C61—22no—
111C23×C4×C61—22no—
112C23×C4×C61—22no—
113C23×C4×C61—22no—
114C23×C4×C61—22no—
115C23×C4×C61—22no—
116C23×C4×C61—22no—
117C23×C4×C61—22no—
118C23×C4×C61—22no—
119C23×C4×C61—41no—
120C23×C4×C61—41no—
121C23×C4×C61—41no—
122C23×C4×C61—41no—
123C23×C4×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134#121×C61—232no—
135#121×C61—232no—
136C2×C4⋊C4×C61—22no—
137C2×C4⋊C4×C61—22no—
138C2×C4⋊C4×C61—22no—
139C2×C4⋊C4×C61—22no—
140C2×C4⋊C4×C61—22no—
141C2×C4⋊C4×C61—22no—
142C2×C4⋊C4×C61—22no—
143C2×C4⋊C4×C61—41no—
144C2×C4⋊C4×C61D414yescomplemented
145C2×C22⋊C4×C61—22no—
146C2×C22⋊C4×C61—22no—
147C2×C22⋊C4×C61—22no—
148C2×C22⋊C4×C61—22no—
149C2×C22⋊C4×C61—22no—
150C2×C22⋊C4×C61—22no—
151C2×C22⋊C4×C61—22no—
152C2×C22⋊C4×C61—22no—
153C2×C22⋊C4×C61—22no—
154C2×C22⋊C4×C61—22no—
155C2×C22⋊C4×C61—22no—
156C2×C22⋊C4×C61—22no—
157C2×C22⋊C4×C61—22no—
158C2×C22⋊C4×C61—22no—
159C2×C22⋊C4×C61—22no—
160C2×C22⋊C4×C61—22no—
161C2×C22⋊C4×C61—22no—
162C2×C22⋊C4×C61—22no—
163C2×C22⋊C4×C61—22no—
164C2×C22⋊C4×C61—22no—
165C2×C22⋊C4×C61—22no—
166C2×C22⋊C4×C61—22no—
167C2×C22⋊C4×C61—22no—
168C2×C22⋊C4×C61—22no—
169C2×C22⋊C4×C61—22no—
170C2×C22⋊C4×C61—22no—
171C2×C22⋊C4×C61—22no—
172C2×C22⋊C4×C61—41no—
173C2×C22⋊C4×C61—41no—
174C2×C22⋊C4×C61—41no—
175C2×C22⋊C4×C61—41no—
176C2×C22⋊C4×C61—41no—
177C2×C22⋊C4×C61—41no—
178C2×C22⋊C4×C61—41no—
179C2×C22⋊C4×C61—41no—
180C2×C22⋊C4×C61—41no—
181C2×C22⋊C4×C61—41no—
182C2×C22⋊C4×C61—41no—
183C2×C22⋊C4×C61—41no—
184C2×C22⋊C4×C61D414yescomplemented
185C2×C22⋊C4×C61D414yescomplemented
186C2×C22⋊C4×C61D414yescomplemented
187#95×C61—22no—
188#95×C61—22no—
189#95×C61—22no—
190#95×C61—22no—
191#95×C61—22no—
192#95×C61—22no—
193#95×C61—22no—
194#95×C61—22no—
195#95×C61—22no—
196#95×C61—41no—
197C24×C61—21no—
198C24×C61—21no—
199C24×C61—21no—
200C24×C61—21no—
201C24×C61—21no—
202C24×C61—21no—
203C24×C61—21no—
204C24×C61—21no—
205C24×C61—21no—
206C24×C61—21no—
207C24×C61—21no—
208C24×C61—21no—
209C24×C61—21no—
210C24×C61—21no—
211C24×C61—21no—
212C24×C61—21no—
213C24×C61—21no—
214C24×C61—21no—
215C24×C61—21no—
216C24×C61—21no—
217C24×C61—21no—
218C24×C61—21no—
219C24×C61—21no—
220C24×C61—21no—
221C24×C61—21no—
222C24×C61—21no—
223C24×C61—21no—
224C24×C61—21no—
225C24×C61—21no—
226C24×C61—21no—
227C24×C61—21no—
228C24×C61—21no—
229C24×C61—21no—
230C24×C61—21no—
231C24×C61—21no—
232C24×C61—21no—
233C24×C61—21no—
234C24×C61—21no—
235C24×C61—21no—
236C24×C61—21no—
237C24×C61—21no—
238C24×C61—21no—
239C24×C61—21no—
240C24×C61—21no—
241C24×C61—21no—
242C24×C61—21no—
243C24×C61—21no—
244C24×C61—21no—
245C24×C61—21no—
246C24×C61—21no—
247C24×C61—21no—
248C24×C61—21no—
249C24×C61C2×D412yes—
250C24×C61C2×D412yes—
251C24×C61C2×D412yes—
252C24×C61C2×D412yes—
253C24×C61C2×D412yes—
254C24×C61C2×D412yes—
255C24×C61C2×D412yes—
256C24×C61#4112yes—
257C24×C61C2411yescharacteristic
258C2×D4×C61—28no—
259C2×D4×C61—28no—
260C2×D4×C61—28no—
261C2×D4×C61—28no—
262C2×D4×C61—28no—
263C2×D4×C61—28no—
264C2×D4×C61—28no—
265C2×D4×C61—28no—
266C2×D4×C61—44no—
267C2×D4×C61—44no—
268C2×D4×C61—44no—
269C2×D4×C61—44no—
270C2×D4×C61—44no—
271C2×D4×C61—44no—
272C2×D4×C61—44no—
273C2×D4×C61—44no—
274C2×D4×C61—44no—
275C2×D4×C61—44no—
276C2×D4×C61—44no—
277C2×D4×C61—44no—
278C2×D4×C61—44no—
279C2×D4×C61—44no—
280C2×D4×C61—44no—
281C2×D4×C61—44no—
282C2×D4×C61—44no—
283C2×D4×C61—44no—
284C2×D4×C61—44no—
285C2×D4×C61—44no—
286C2×D4×C61—44no—
287C2×D4×C61—44no—
288C2×D4×C61—44no—
289C2×D4×C61—44no—
290C2×D4×C61—44no—
291C2×D4×C61—44no—
292C2×D4×C61—44no—
293C2×D4×C61—44no—
294C2×D4×C61—44no—
295C2×D4×C61—44no—
296C2×D4×C61—44no—
297C2×D4×C61—44no—
298C2×D4×C61—44no—
299C2×D4×C61—44no—
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—28no—
309C22×C4×C61—28no—
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—21no—
326C22×C4×C61—21no—
327C22×C4×C61—21no—
328C22×C4×C61—21no—
329C22×C4×C61—21no—
330C22×C4×C61—21no—
331C22×C4×C61—21no—
332C22×C4×C61—21no—
333C22×C4×C61—21no—
334C22×C4×C61—21no—
335C22×C4×C61—21no—
336C22×C4×C61—21no—
337C22×C4×C61—21no—
338C22×C4×C61—21no—
339C22×C4×C61—21no—
340C22×C4×C61—21no—
341C22×C4×C61—21no—
342C22×C4×C61—21no—
343C22×C4×C61—21no—
344C22×C4×C61—21no—
345C22×C4×C61—21no—
346C22×C4×C61—21no—
347C22×C4×C61—21no—
348C22×C4×C61—21no—
349C22×C4×C61—21no—
350C22×C4×C61—21no—
351C22×C4×C61—21no—
352C22×C4×C61—21no—
353C22×C4×C61—21no—
354C22×C4×C61—21no—
355C22×C4×C61—21no—
356C22×C4×C61—21no—
357C22×C4×C61—21no—
358C22×C4×C61—21no—
359C22×C4×C61—21no—
360C22×C4×C61—21no—
361C22×C4×C61—21no—
362C22×C4×C61—21no—
363C22×C4×C61—21no—
364C22×C4×C61—21no—
365C22×C4×C61—21no—
366C22×C4×C61—44no—
367C22×C4×C61—44no—
368C22×C4×C61—44no—
369C22×C4×C61—44no—
370C22×C4×C61—44no—
371C22×C4×C61—44no—
372C22×C4×C61—44no—
373C22×C4×C61—44no—
374C22×C4×C61—44no—
375C22×C4×C61—44no—
376C22×C4×C61—44no—
377C22×C4×C61—44no—
378C22×C4×C61C2×D412yes—
379C22×C4×C61C2×D412yes—
380C22×C4×C61C2×D412yes—
381C22×C4×C61C2×D412yes—
382C22×C4×C61C2×D412yes—
383C22×C4×C61C2×D412yes—
384C22×C4×C61C2×D412yes—
385C22×C4×C61C2×D412yes—
386C22×C4×C61C2×D412yes—
387C22×C4×C61C2×D412yes—
388C22×C4×C61C2×D412yes—
389C22×C4×C61#4112yes—
390C22×C4×C61#4112yes—
391C4⋊C4×C61—28no—
392C4⋊C4×C61—28no—
393C4⋊C4×C61—44no—
394C22⋊C4×C61—28no—
395C22⋊C4×C61—28no—
396C22⋊C4×C61—28no—
397C22⋊C4×C61—28no—
398C22⋊C4×C61—28no—
399C22⋊C4×C61—44no—
400C22⋊C4×C61—44no—
401C22⋊C4×C61—44no—
402C22⋊C4×C61—44no—
403C22⋊C4×C61—44no—
404C22⋊C4×C61—44no—
405C22⋊C4×C61—44no—
406C22⋊C4×C61—44no—
407C22⋊C4×C61—44no—
408C23×C61—22no—
409C23×C61—22no—
410C23×C61—22no—
411C23×C61—22no—
412C23×C61—22no—
413C23×C61—22no—
414C23×C61—22no—
415C23×C61—22no—
416C23×C61—22no—
417C23×C61—22no—
418C23×C61—22no—
419C23×C61—22no—
420C23×C61—22no—
421C23×C61—22no—
422C23×C61—22no—
423C23×C61—22no—
424C23×C61—22no—
425C23×C61—22no—
426C23×C61—22no—
427C23×C61—22no—
428C23×C61—22no—
429C23×C61—22no—
430C23×C61—22no—
431C23×C61—22no—
432C23×C61—22no—
433C23×C61—22no—
434C23×C61—22no—
435C23×C61—22no—
436C23×C61—22no—
437C23×C61—22no—
438C23×C61—22no—
439C23×C61—22no—
440C23×C61—22no—
441C23×C61—22no—
442C23×C61—22no—
443C23×C61—22no—
444C23×C61—22no—
445C23×C61—22no—
446C23×C61—22no—
447C23×C61—22no—
448C23×C61—22no—
449C23×C61—22no—
450C23×C61—22no—
451C23×C61—22no—
452C23×C61—22no—
453C23×C61—22no—
454C23×C61—22no—
455C23×C61—22no—
456C23×C61—22no—
457C23×C61—22no—
458C23×C61—41no—
459C23×C61—41no—
460C23×C61—41no—
461C23×C61—41no—
462C23×C61—41no—
463C23×C61—41no—
464C23×C61—41no—
465C23×C61—41no—
466C23×C61—41no—
467C23×C61—41no—
468C23×C61—41no—
469C23×C61—41no—
470C23×C61—41no—
471C23×C61—41no—
472C23×C61—41no—
473C23×C61—41no—
474C23×C61—41no—
475C23×C61—41no—
476C23×C61—41no—
477C23×C61—41no—
478C23×C61—41no—
479C23×C61—41no—
480C23×C61—41no—
481C23×C61—41no—
482C23×C61—41no—
483C23×C61—41no—
484C23×C61—41no—
485C23×C61—41no—
486C23×C61—41no—
487C23×C61—41no—
488C23×C61—41no—
489C23×C61—41no—
490C23×C61—41no—
491C23×C61—41no—
492C23×C61—41no—
493C23×C61—41no—
494C23×C61—41no—
495C23×C61—41no—
496C23×C61—41no—
497C23×C61—41no—
498C23×C61—41no—
499C23×C61—41no—
500C23×C61—41no—
501C23×C61—41no—
502C23×C61—41no—
503C23×C61—41no—
504C23×C61—41no—
505C23×C61—41no—
506C23×C61—41no—
507C23×C61—41no—
508C23×C61—41no—
509C23×C61—41no—
510C23×C61—41no—
511C23×C61—41no—
512C23×C61—41no—
513C23×C61—41no—
514C23×C61—41no—
515C23×C61—41no—
516C23×C61—41no—
517C23×C61—41no—
518C23×C61—41no—
519C23×C61—41no—
520C23×C61—41no—
521C23×C61—41no—
522C23×C61—41no—
523C23×C61—41no—
524C23×C61—41no—
525C23×C61—41no—
526C23×C61—41no—
527C23×C61—41no—
528C23×C61—41no—
529C23×C61—41no—
530C23×C61—41no—
531C23×C61—41no—
532C23×C61—41no—
533C23×C61—41no—
534C23×C61—41no—
535C23×C61—41no—
536C23×C61—41no—
537C23×C61—41no—
538C23×C61—41no—
539C23×C61—41no—
540C23×C61—41no—
541C23×C61—41no—
542C23×C61—41no—
543C23×C61—41no—
544C23×C61—41no—
545C23×C61—41no—
546C23×C61#12014yes—
547C23×C61#12114yescomplemented
548C23×C61C22×D411yescharacteristic
549C23×C61C22×D411yescharacteristic
550C23×C61C22×D411yescharacteristic
551C23×C61C22×D411yescharacteristic
552C23×C61C22×D411yescharacteristic
553C23×C61C22×D411yescharacteristic
554C23×C61C2×#4111yescharacteristic
555C23×C61C2×#4111yescharacteristic
556C23×C61C2×#4111yescharacteristic
557C23×C61H(5,𝔽2)11yescharacteristic
558C23×C61H(5,𝔽2)11yescharacteristic
559C23×C61H(5,𝔽2)11yescharacteristic
560C23×C61H(5,𝔽2)11yescharacteristic
561C23×C61H(5,𝔽2)11yescharacteristic
562C23×C612−1+411yescharacteristic
563D4×C61—416no—
564D4×C61—416no—
565D4×C61—416no—
566D4×C61—416no—
567D4×C61—416no—
568D4×C61—416no—
569C2×C4×C61—22no—
570C2×C4×C61—22no—
571C2×C4×C61—22no—
572C2×C4×C61—22no—
573C2×C4×C61—22no—
574C2×C4×C61—22no—
575C2×C4×C61—22no—
576C2×C4×C61—22no—
577C2×C4×C61—22no—
578C2×C4×C61—22no—
579C2×C4×C61—22no—
580C2×C4×C61—22no—
581C2×C4×C61—22no—
582C2×C4×C61—22no—
583C2×C4×C61—22no—
584C2×C4×C61—22no—
585C2×C4×C61—22no—
586C2×C4×C61—22no—
587C2×C4×C61—22no—
588C2×C4×C61—22no—
589C2×C4×C61—22no—
590C2×C4×C61—22no—
591C2×C4×C61—22no—
592C2×C4×C61—22no—
593C2×C4×C61—22no—
594C2×C4×C61—22no—
595C2×C4×C61—22no—
596C2×C4×C61—22no—
597C2×C4×C61—22no—
598C2×C4×C61—22no—
599C2×C4×C61—22no—
600C2×C4×C61—22no—
601C2×C4×C61—22no—
602C2×C4×C61—416no—
603C2×C4×C61—416no—
604C2×C4×C61—41no—
605C2×C4×C61—41no—
606C2×C4×C61—41no—
607C2×C4×C61—41no—
608C2×C4×C61—41no—
609C2×C4×C61—41no—
610C2×C4×C61—41no—
611C2×C4×C61—41no—
612C2×C4×C61—41no—
613C2×C4×C61—41no—
614C2×C4×C61—41no—
615C2×C4×C61—41no—
616C2×C4×C61—41no—
617C2×C4×C61—41no—
618C2×C4×C61—41no—
619C2×C4×C61—41no—
620C2×C4×C61—41no—
621C2×C4×C61—41no—
622C2×C4×C61—41no—
623C2×C4×C61—41no—
624C2×C4×C61—41no—
625C2×C4×C61—41no—
626C2×C4×C61—41no—
627C2×C4×C61—41no—
628C2×C4×C61—41no—
629C2×C4×C61—41no—
630C2×C4×C61—41no—
631C2×C4×C61—41no—
632C2×C4×C61—41no—
633C2×C4×C61—41no—
634C2×C4×C61—41no—
635C2×C4×C61—41no—
636C2×C4×C61—41no—
637C2×C4×C61—41no—
638C2×C4×C61—41no—
639C2×C4×C61—41no—
640C2×C4×C61—41no—
641C2×C4×C61—41no—
642C2×C4×C61—41no—
643C2×C4×C61—41no—
644C2×C4×C61—41no—
645C2×C4×C61—41no—
646C2×C4×C61#12014yes—
647C2×C4×C61#12114yescomplemented
648#15263C6111yesmaximal, characteristic, direct product factor, Sylow
649C22×C61—24no—
650C22×C61—24no—
651C22×C61—24no—
652C22×C61—24no—
653C22×C61—24no—
654C22×C61—24no—
655C22×C61—42no—
656C22×C61—42no—
657C22×C61—42no—
658C22×C61—42no—
659C22×C61—42no—
660C22×C61—42no—
661C22×C61—42no—
662C22×C61—42no—
663C22×C61—42no—
664C22×C61—42no—
665C22×C61—42no—
666C22×C61—42no—
667C22×C61—42no—
668C22×C61—42no—
669C22×C61—42no—
670C22×C61—42no—
671C22×C61—42no—
672C22×C61—42no—
673C22×C61—42no—
674C22×C61—42no—
675C22×C61—42no—
676C22×C61—42no—
677C22×C61—42no—
678C22×C61—42no—
679C22×C61—42no—
680C22×C61—42no—
681C22×C61—42no—
682C22×C61—42no—
683C22×C61—42no—
684C22×C61—42no—
685C22×C61—42no—
686C22×C61—42no—
687C22×C61—42no—
688C22×C61—42no—
689C22×C61—42no—
690C22×C61—42no—
691C22×C61—42no—
692C22×C61—42no—
693C22×C61—81no—
694C22×C61—81no—
695C22×C61—81no—
696C22×C61—81no—
697C22×C61—81no—
698C22×C61—81no—
699C22×C61—81no—
700C22×C61—81no—
701C22×C61—81no—
702C22×C61—81no—
703C22×C61—81no—
704C22×C61—81no—
705C22×C61—81no—
706C22×C61—81no—
707C22×C61—81no—
708C22×C61—81no—
709C22×C61C2×#12011yescharacteristic
710C22×C61C2×#12011yescharacteristic
711C22×C61C2×#12111yescharacteristic
712C22×C61C2×#12111yescharacteristic
713C22×C61#52511yescharacteristic
714C22×C61#53211yescharacteristic
715C22×C61#53411yescharacteristic
716C22×C61#53411yescharacteristic
717C22×C61#53511yescharacteristic
718C22×C61#53711yescharacteristic
719C22×C61#53711yescharacteristic
720C22×C61#53711yescharacteristic
721C22×C61#53811yescharacteristic
722C22×C61#54011yescharacteristic
723C22×C61#54011yescharacteristic
724C22×C61D4211yescharacteristic
725C22×C61D4211yescharacteristic
726C22×C61D4211yescharacteristic
727C22×C61D4211yescharacteristic
728C22×C61D4211yescharacteristic
729C22×C61D4211yescharacteristic
730C22×C61D4211yescharacteristic
731C22×C61#54611yescharacteristic
732C22×C61#54611yescharacteristic
733C22×C61#54611yescharacteristic
734C22×C61#54611yescharacteristic
735C22×C61#54611yescharacteristic
736C22×C61#54611yescharacteristic
737C22×C61#54711yescharacteristic
738C22×C61#54711yescharacteristic
739C22×C61#54811yescharacteristic
740C22×C61#55011yescharacteristic
741C22×C61#55311yescharacteristic
742C22×C61#56011yescharacteristic
743C22×C61#56211yescharacteristic
744C4×C61—24no—
745C4×C61—24no—
746C4×C61—42no—
747C4×C61—42no—
748C4×C61—42no—
749C4×C61—42no—
750C4×C61—42no—
751C4×C61—42no—
752C4×C61—42no—
753C4×C61—81no—
754C4×C61—81no—
755C22×#121C2×C6111yescharacteristic, complemented
756C22×#121C2×C6111yescharacteristic, complemented
757C2×#394C2×C6111yescharacteristic, complemented
758C2×#392C2×C6111yescharacteristic, complemented
759C2×#392C2×C6111yescharacteristic, complemented
760C2×#386C2×C6111yescharacteristic, complemented
761C2×#386C2×C6111yescharacteristic, complemented
762C2×#385C2×C6111yescharacteristic, complemented
763#1441C2×C6111yescharacteristic, complemented
764#1439C2×C6111yescharacteristic, complemented
765#1439C2×C6111yescharacteristic, complemented
766#1438C2×C6111yescharacteristic, complemented
767#1438C2×C6111yescharacteristic, complemented
768#1438C2×C6111yescharacteristic, complemented
769C22⋊#95C2×C6111yescharacteristic, complemented
770C2×C61—44no—
771C2×C61—44no—
772C2×C61—82no—
773C2×C61—82no—
774C2×C61#240311yescharacteristic
775C2×C61#240711yescharacteristic
776C2×C61#240811yescharacteristic
777C2×C61#241011yescharacteristic
778C2×C61#241611yescharacteristic
779C2×C61#242411yescharacteristic
780C2×C61#242811yescharacteristic
781C2×C61#243011yescharacteristic
782C2×C61#246411yescharacteristic
783C2×C61#267111yescharacteristic
784C2×C61#267111yescharacteristic
785C2×C61#267311yescharacteristic
786C2×C61#267511yescharacteristic
787C2×C61#267611yescharacteristic
788C2×C61#268811yescharacteristic
789C23×D4C22×C6111yescharacteristic
790C23×D4C22×C6111yescharacteristic
791C23×D4C22×C6111yescharacteristic
792C23×D4C22×C6111yescharacteristic
793C23×D4C22×C6111yescharacteristic
794C23×D4C22×C6111yescharacteristic
795C24×C4C22×C6111yescharacteristic
796C24×C4C22×C6111yescharacteristic
797C2×#121—24no—
798C2×#121—24no—
799C2×#121—24no—
800C2×#121—24no—
801C2×#121—24no—
802C2×#121—24no—
803C22×C4⋊C4C22×C6111yescharacteristic
804C22×C4⋊C4C22×C6111yescharacteristic
805C22×C4⋊C4C22×C6111yescharacteristic
806C22×C22⋊C4C22×C6111yescharacteristic
807C22×C22⋊C4C22×C6111yescharacteristic
808C22×C22⋊C4C22×C6111yescharacteristic
809C22×C22⋊C4C22×C6111yescharacteristic
810C22×C22⋊C4C22×C6111yescharacteristic
811C22×C22⋊C4C22×C6111yescharacteristic
812C22×C22⋊C4C22×C6111yescharacteristic
813C22×C22⋊C4C22×C6111yescharacteristic
814C22×C22⋊C4C22×C6111yescharacteristic
815C22×C22⋊C4C22×C6111yescharacteristic
816C22×C22⋊C4C22×C6111yescharacteristic
817C22×C22⋊C4C22×C6111yescharacteristic
818C22×C22⋊C4C22×C6111yescharacteristic
819C22×C22⋊C4C22×C6111yescharacteristic
820#394—24no—
821#392—24no—
822#392—24no—
823#386—24no—
824#386—24no—
825#385—24no—
826C2×#95C22×C6111yescharacteristic
827C2×#95C22×C6111yescharacteristic
828C2×#95C22×C6111yescharacteristic
829C2×#95C22×C6111yescharacteristic
830C2×#95C22×C6111yescharacteristic
831C2×#95C22×C6111yescharacteristic
832C2×#95C22×C6111yescharacteristic
833C2×#95C22×C6111yescharacteristic
834C2×#95C22×C6111yescharacteristic
835C2×#95C22×C6111yescharacteristic
836C61#1526311yescharacteristic, direct product factor, Sylow
837C25C23×C6111yescharacteristic
838C25C23×C6111yescharacteristic
839C25C23×C6111yescharacteristic
840C25C23×C6111yescharacteristic
841C22×D4—22no—
842C22×D4—22no—
843C22×D4—22no—
844C22×D4—22no—
845C22×D4—22no—
846C22×D4—22no—
847C22×D4—22no—
848C22×D4—22no—
849C22×D4—22no—
850C22×D4—22no—
851C22×D4—22no—
852C22×D4—22no—
853C22×D4—22no—
854C22×D4—22no—
855C22×D4—22no—
856C22×D4—22no—
857C22×D4—22no—
858C22×D4—22no—
859C22×D4—22no—
860C22×D4—22no—
861C22×D4—22no—
862C22×D4—22no—
863C22×D4—22no—
864C22×D4—22no—
865C22×D4—22no—
866C22×D4—22no—
867C22×D4—22no—
868C22×D4—22no—
869C22×D4—41no—
870C22×D4—41no—
871C22×D4—41no—
872C22×D4—41no—
873C22×D4—41no—
874C22×D4—41no—
875C22×D4—41no—
876C22×D4—41no—
877C22×D4—41no—
878C22×D4—41no—
879C22×D4—41no—
880C22×D4—41no—
881C22×D4D4×C6114yescomplemented
882C22×D4D4×C6114yescomplemented
883C23×C4—22no—
884C23×C4—22no—
885C23×C4—22no—
886C23×C4—22no—
887C23×C4—22no—
888C23×C4—22no—
889C23×C4—22no—
890C23×C4—22no—
891C23×C4—22no—
892C23×C4—22no—
893C23×C4—41no—
894C23×C4—41no—
895C23×C4—41no—
896C23×C4—41no—
897C23×C4C23×C6111yescharacteristic
898C23×C4C23×C6111yescharacteristic
899C23×C4C23×C6111yescharacteristic
900C23×C4C23×C6111yescharacteristic
901C23×C4C23×C6111yescharacteristic
902C23×C4C23×C6111yescharacteristic
903C23×C4C23×C6111yescharacteristic
904C23×C4C23×C6111yescharacteristic
905C23×C4C23×C6111yescharacteristic
906C23×C4C23×C6111yescharacteristic
907C23×C4C23×C6111yescharacteristic
908#121—232no—
909#121—232no—
910C2×C4⋊C4—22no—
911C2×C4⋊C4—22no—
912C2×C4⋊C4—22no—
913C2×C4⋊C4—22no—
914C2×C4⋊C4—22no—
915C2×C4⋊C4—22no—
916C2×C4⋊C4—22no—
917C2×C4⋊C4—41no—
918C2×C4⋊C4D4×C6114yescomplemented
919C2×C22⋊C4—22no—
920C2×C22⋊C4—22no—
921C2×C22⋊C4—22no—
922C2×C22⋊C4—22no—
923C2×C22⋊C4—22no—
924C2×C22⋊C4—22no—
925C2×C22⋊C4—22no—
926C2×C22⋊C4—22no—
927C2×C22⋊C4—22no—
928C2×C22⋊C4—22no—
929C2×C22⋊C4—22no—
930C2×C22⋊C4—22no—
931C2×C22⋊C4—22no—
932C2×C22⋊C4—22no—
933C2×C22⋊C4—22no—
934C2×C22⋊C4—22no—
935C2×C22⋊C4—22no—
936C2×C22⋊C4—22no—
937C2×C22⋊C4—22no—
938C2×C22⋊C4—22no—
939C2×C22⋊C4—22no—
940C2×C22⋊C4—22no—
941C2×C22⋊C4—22no—
942C2×C22⋊C4—22no—
943C2×C22⋊C4—22no—
944C2×C22⋊C4—22no—
945C2×C22⋊C4—22no—
946C2×C22⋊C4—41no—
947C2×C22⋊C4—41no—
948C2×C22⋊C4—41no—
949C2×C22⋊C4—41no—
950C2×C22⋊C4—41no—
951C2×C22⋊C4—41no—
952C2×C22⋊C4—41no—
953C2×C22⋊C4—41no—
954C2×C22⋊C4—41no—
955C2×C22⋊C4—41no—
956C2×C22⋊C4—41no—
957C2×C22⋊C4—41no—
958C2×C22⋊C4D4×C6114yescomplemented
959C2×C22⋊C4D4×C6114yescomplemented
960C2×C22⋊C4D4×C6114yescomplemented
961#95—22no—
962#95—22no—
963#95—22no—
964#95—22no—
965#95—22no—
966#95—22no—
967#95—22no—
968#95—22no—
969#95—22no—
970#95—41no—
971C24—21no—
972C24—21no—
973C24—21no—
974C24—21no—
975C24—21no—
976C24—21no—
977C24—21no—
978C24—21no—
979C24—21no—
980C24—21no—
981C24—21no—
982C24—21no—
983C24—21no—
984C24—21no—
985C24—21no—
986C24—21no—
987C24—21no—
988C24—21no—
989C24—21no—
990C24—21no—
991C24—21no—
992C24—21no—
993C24—21no—
994C24—21no—
995C24—21no—
996C24—21no—
997C24—21no—
998C24—21no—
999C24—21no—
1000C24—21no—
1001C24—21no—
1002C24—21no—
1003C24—21no—
1004C24—21no—
1005C24—21no—
1006C24—21no—
1007C24—21no—
1008C24—21no—
1009C24—21no—
1010C24—21no—
1011C24—21no—
1012C24—21no—
1013C24—21no—
1014C24—21no—
1015C24—21no—
1016C24—21no—
1017C24—21no—
1018C24—21no—
1019C24—21no—
1020C24—21no—
1021C24—21no—
1022C24—21no—
1023C24C2×D4×C6112yes—
1024C24C2×D4×C6112yes—
1025C24C2×D4×C6112yes—
1026C24C2×D4×C6112yes—
1027C24C2×D4×C6112yes—
1028C24C2×D4×C6112yes—
1029C24C2×D4×C6112yes—
1030C24#41×C6112yes—
1031C24C24×C6111yescharacteristic
1032C2×D4—28no—
1033C2×D4—28no—
1034C2×D4—28no—
1035C2×D4—28no—
1036C2×D4—28no—
1037C2×D4—28no—
1038C2×D4—28no—
1039C2×D4—28no—
1040C2×D4—44no—
1041C2×D4—44no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—44no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—44no—
1056C2×D4—44no—
1057C2×D4—44no—
1058C2×D4—44no—
1059C2×D4—44no—
1060C2×D4—44no—
1061C2×D4—44no—
1062C2×D4—44no—
1063C2×D4—44no—
1064C2×D4—44no—
1065C2×D4—44no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C22×C4—21no—
1075C22×C4—21no—
1076C22×C4—21no—
1077C22×C4—21no—
1078C22×C4—21no—
1079C22×C4—21no—
1080C22×C4—21no—
1081C22×C4—21no—
1082C22×C4—28no—
1083C22×C4—28no—
1084C22×C4—21no—
1085C22×C4—21no—
1086C22×C4—21no—
1087C22×C4—21no—
1088C22×C4—21no—
1089C22×C4—21no—
1090C22×C4—21no—
1091C22×C4—21no—
1092C22×C4—21no—
1093C22×C4—21no—
1094C22×C4—21no—
1095C22×C4—21no—
1096C22×C4—21no—
1097C22×C4—21no—
1098C22×C4—21no—
1099C22×C4—21no—
1100C22×C4—21no—
1101C22×C4—21no—
1102C22×C4—21no—
1103C22×C4—21no—
1104C22×C4—21no—
1105C22×C4—21no—
1106C22×C4—21no—
1107C22×C4—21no—
1108C22×C4—21no—
1109C22×C4—21no—
1110C22×C4—21no—
1111C22×C4—21no—
1112C22×C4—21no—
1113C22×C4—21no—
1114C22×C4—21no—
1115C22×C4—21no—
1116C22×C4—21no—
1117C22×C4—21no—
1118C22×C4—21no—
1119C22×C4—21no—
1120C22×C4—21no—
1121C22×C4—21no—
1122C22×C4—21no—
1123C22×C4—21no—
1124C22×C4—21no—
1125C22×C4—21no—
1126C22×C4—21no—
1127C22×C4—21no—
1128C22×C4—21no—
1129C22×C4—21no—
1130C22×C4—21no—
1131C22×C4—21no—
1132C22×C4—21no—
1133C22×C4—21no—
1134C22×C4—21no—
1135C22×C4—21no—
1136C22×C4—21no—
1137C22×C4—21no—
1138C22×C4—21no—
1139C22×C4—21no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4C2×D4×C6112yes—
1153C22×C4C2×D4×C6112yes—
1154C22×C4C2×D4×C6112yes—
1155C22×C4C2×D4×C6112yes—
1156C22×C4C2×D4×C6112yes—
1157C22×C4C2×D4×C6112yes—
1158C22×C4C2×D4×C6112yes—
1159C22×C4C2×D4×C6112yes—
1160C22×C4C2×D4×C6112yes—
1161C22×C4C2×D4×C6112yes—
1162C22×C4C2×D4×C6112yes—
1163C22×C4#41×C6112yes—
1164C22×C4#41×C6112yes—
1165C4⋊C4—28no—
1166C4⋊C4—28no—
1167C4⋊C4—44no—
1168C22⋊C4—28no—
1169C22⋊C4—28no—
1170C22⋊C4—28no—
1171C22⋊C4—28no—
1172C22⋊C4—28no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C23—22no—
1183C23—22no—
1184C23—22no—
1185C23—22no—
1186C23—22no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—22no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—22no—
1202C23—22no—
1203C23—22no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—22no—
1228C23—22no—
1229C23—22no—
1230C23—22no—
1231C23—22no—
1232C23—41no—
1233C23—41no—
1234C23—41no—
1235C23—41no—
1236C23—41no—
1237C23—41no—
1238C23—41no—
1239C23—41no—
1240C23—41no—
1241C23—41no—
1242C23—41no—
1243C23—41no—
1244C23—41no—
1245C23—41no—
1246C23—41no—
1247C23—41no—
1248C23—41no—
1249C23—41no—
1250C23—41no—
1251C23—41no—
1252C23—41no—
1253C23—41no—
1254C23—41no—
1255C23—41no—
1256C23—41no—
1257C23—41no—
1258C23—41no—
1259C23—41no—
1260C23—41no—
1261C23—41no—
1262C23—41no—
1263C23—41no—
1264C23—41no—
1265C23—41no—
1266C23—41no—
1267C23—41no—
1268C23—41no—
1269C23—41no—
1270C23—41no—
1271C23—41no—
1272C23—41no—
1273C23—41no—
1274C23—41no—
1275C23—41no—
1276C23—41no—
1277C23—41no—
1278C23—41no—
1279C23—41no—
1280C23—41no—
1281C23—41no—
1282C23—41no—
1283C23—41no—
1284C23—41no—
1285C23—41no—
1286C23—41no—
1287C23—41no—
1288C23—41no—
1289C23—41no—
1290C23—41no—
1291C23—41no—
1292C23—41no—
1293C23—41no—
1294C23—41no—
1295C23—41no—
1296C23—41no—
1297C23—41no—
1298C23—41no—
1299C23—41no—
1300C23—41no—
1301C23—41no—
1302C23—41no—
1303C23—41no—
1304C23—41no—
1305C23—41no—
1306C23—41no—
1307C23—41no—
1308C23—41no—
1309C23—41no—
1310C23—41no—
1311C23—41no—
1312C23—41no—
1313C23—41no—
1314C23—41no—
1315C23—41no—
1316C23—41no—
1317C23—41no—
1318C23—41no—
1319C23—41no—
1320C23#120×C6114yes—
1321C23#121×C6114yescomplemented
1322C23C22×D4×C6111yescharacteristic
1323C23C22×D4×C6111yescharacteristic
1324C23C22×D4×C6111yescharacteristic
1325C23C22×D4×C6111yescharacteristic
1326C23C22×D4×C6111yescharacteristic
1327C23C22×D4×C6111yescharacteristic
1328C23C2×#41×C6111yescharacteristic
1329C23C2×#41×C6111yescharacteristic
1330C23C2×#41×C6111yescharacteristic
1331C23H(5,𝔽2)×C6111yescharacteristic
1332C23H(5,𝔽2)×C6111yescharacteristic
1333C23H(5,𝔽2)×C6111yescharacteristic
1334C23H(5,𝔽2)×C6111yescharacteristic
1335C23H(5,𝔽2)×C6111yescharacteristic
1336C232−1+4×C6111yescharacteristic
1337D4—416no—
1338D4—416no—
1339D4—416no—
1340D4—416no—
1341D4—416no—
1342D4—416no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—416no—
1377C2×C4—416no—
1378C2×C4—41no—
1379C2×C4—41no—
1380C2×C4—41no—
1381C2×C4—41no—
1382C2×C4—41no—
1383C2×C4—41no—
1384C2×C4—41no—
1385C2×C4—41no—
1386C2×C4—41no—
1387C2×C4—41no—
1388C2×C4—41no—
1389C2×C4—41no—
1390C2×C4—41no—
1391C2×C4—41no—
1392C2×C4—41no—
1393C2×C4—41no—
1394C2×C4—41no—
1395C2×C4—41no—
1396C2×C4—41no—
1397C2×C4—41no—
1398C2×C4—41no—
1399C2×C4—41no—
1400C2×C4—41no—
1401C2×C4—41no—
1402C2×C4—41no—
1403C2×C4—41no—
1404C2×C4—41no—
1405C2×C4—41no—
1406C2×C4—41no—
1407C2×C4—41no—
1408C2×C4—41no—
1409C2×C4—41no—
1410C2×C4—41no—
1411C2×C4—41no—
1412C2×C4—41no—
1413C2×C4—41no—
1414C2×C4—41no—
1415C2×C4—41no—
1416C2×C4—41no—
1417C2×C4—41no—
1418C2×C4—41no—
1419C2×C4—41no—
1420C2×C4#120×C6114yes—
1421C2×C4#121×C6114yescomplemented
1422C22—24no—
1423C22—24no—
1424C22—24no—
1425C22—24no—
1426C22—24no—
1427C22—24no—
1428C22—42no—
1429C22—42no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22—42no—
1437C22—42no—
1438C22—42no—
1439C22—42no—
1440C22—42no—
1441C22—42no—
1442C22—42no—
1443C22—42no—
1444C22—42no—
1445C22—42no—
1446C22—42no—
1447C22—42no—
1448C22—42no—
1449C22—42no—
1450C22—42no—
1451C22—42no—
1452C22—42no—
1453C22—42no—
1454C22—42no—
1455C22—42no—
1456C22—42no—
1457C22—42no—
1458C22—42no—
1459C22—42no—
1460C22—42no—
1461C22—42no—
1462C22—42no—
1463C22—42no—
1464C22—42no—
1465C22—42no—
1466C22—81no—
1467C22—81no—
1468C22—81no—
1469C22—81no—
1470C22—81no—
1471C22—81no—
1472C22—81no—
1473C22—81no—
1474C22—81no—
1475C22—81no—
1476C22—81no—
1477C22—81no—
1478C22—81no—
1479C22—81no—
1480C22—81no—
1481C22—81no—
1482C22C2×#120×C6111yescharacteristic
1483C22C2×#120×C6111yescharacteristic
1484C22C2×#121×C6111yescharacteristic
1485C22C2×#121×C6111yescharacteristic
1486C22C61×#52511yescharacteristic
1487C22C61×#53211yescharacteristic
1488C22C61×#53411yescharacteristic
1489C22C61×#53411yescharacteristic
1490C22C61×#53511yescharacteristic
1491C22C61×#53711yescharacteristic
1492C22C61×#53711yescharacteristic
1493C22C61×#53711yescharacteristic
1494C22C61×#53811yescharacteristic
1495C22C61×#54011yescharacteristic
1496C22C61×#54011yescharacteristic
1497C22D42×C6111yescharacteristic
1498C22D42×C6111yescharacteristic
1499C22D42×C6111yescharacteristic
1500C22D42×C6111yescharacteristic
1501C22D42×C6111yescharacteristic
1502C22D42×C6111yescharacteristic
1503C22D42×C6111yescharacteristic
1504C22C61×#54611yescharacteristic
1505C22C61×#54611yescharacteristic
1506C22C61×#54611yescharacteristic
1507C22C61×#54611yescharacteristic
1508C22C61×#54611yescharacteristic
1509C22C61×#54611yescharacteristic
1510C22C61×#54711yescharacteristic
1511C22C61×#54711yescharacteristic
1512C22C61×#54811yescharacteristic
1513C22C61×#55011yescharacteristic
1514C22C61×#55311yescharacteristic
1515C22C61×#56011yescharacteristic
1516C22C61×#56211yescharacteristic
1517C4—24no—
1518C4—24no—
1519C4—42no—
1520C4—42no—
1521C4—42no—
1522C4—42no—
1523C4—42no—
1524C4—42no—
1525C4—42no—
1526C4—81no—
1527C4—81no—
1528C2—44no—
1529C2—44no—
1530C2—82no—
1531C2—82no—
1532C2C61×#240311yescharacteristic
1533C2C61×#240711yescharacteristic
1534C2C61×#240811yescharacteristic
1535C2C61×#241011yescharacteristic
1536C2C61×#241611yescharacteristic
1537C2C61×#242411yescharacteristic
1538C2C61×#242811yescharacteristic
1539C2C61×#243011yescharacteristic
1540C2C61×#246411yescharacteristic
1541C2C61×#267111yescharacteristic
1542C2C61×#267111yescharacteristic
1543C2C61×#267311yescharacteristic
1544C2C61×#267511yescharacteristic
1545C2C61×#267611yescharacteristic
1546C2C61×#268811yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C61C2semidirect
2. C22×#121×C61C2semidirect
3. C2×C61×#394C2semidirect
4. C2×C61×#392C2semidirect
5. C2×C61×#392C2semidirect
6. C2×C61×#386C2semidirect
7. C2×C61×#386C2semidirect
8. C2×C61×#385C2semidirect
9. C61×#1441C2semidirect
10. C61×#1439C2semidirect
11. C61×#1439C2semidirect
12. C61×#1438C2semidirect
13. C61×#1438C2semidirect
14. C61×#1438C2semidirect
15. C61×C22⋊#95C2semidirect
107. C22×D4×C61D4semidirect
108. C22×D4×C61D4semidirect
144. C2×C4⋊C4×C61D4semidirect
184. C2×C22⋊C4×C61D4semidirect
185. C2×C22⋊C4×C61D4semidirect
186. C2×C22⋊C4×C61D4semidirect
547. C23×C61#121semidirect
647. C2×C4×C61#121semidirect
648. #15263C61direct (N × H)
755. C22×#121C2×C61semidirect
756. C22×#121C2×C61semidirect
757. C2×#394C2×C61semidirect
758. C2×#392C2×C61semidirect
759. C2×#392C2×C61semidirect
760. C2×#386C2×C61semidirect
761. C2×#386C2×C61semidirect
762. C2×#385C2×C61semidirect
763. #1441C2×C61semidirect
764. #1439C2×C61semidirect
765. #1439C2×C61semidirect
766. #1438C2×C61semidirect
767. #1438C2×C61semidirect
768. #1438C2×C61semidirect
769. C22⋊#95C2×C61semidirect
836. C61#15263direct (N × H)
881. C22×D4D4×C61semidirect
882. C22×D4D4×C61semidirect
918. C2×C4⋊C4D4×C61semidirect
958. C2×C22⋊C4D4×C61semidirect
959. C2×C22⋊C4D4×C61semidirect
960. C2×C22⋊C4D4×C61semidirect
1321. C23#121×C61semidirect
1421. C2×C4#121×C61semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C612
C2×C61×#3942
C2×C61×#3922
C2×C61×#3862
C2×C61×#3852
C61×#14412
C61×#14392
C61×#14382
C61×C22⋊#952
#1526361