Finite Group Databasebeta

← C61×#11089 #29514522

Subgroups — C61×#11089 #29514522

Order 15616.

1154 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#99×C61C211yesmaximal, characteristic
2C22×#99×C61C211yesmaximal, characteristic
3C22×#99×C61C211yesmaximal, characteristic
4C61×#2315C211yesmaximal, characteristic, complemented
5C2×C61×#342C211yesmaximal, characteristic, complemented
6C2×C61×#342C211yesmaximal, characteristic, complemented
7C2×C61×#342C211yesmaximal, characteristic, complemented
8C23×D4×C61C2211yescharacteristic
9C22×C22⋊C4×C61C2211yescharacteristic
10C22×C22⋊C4×C61C2211yescharacteristic
11C22×C22⋊C4×C61C2211yescharacteristic
12C22×C22⋊C4×C61C2211yescharacteristic
13C22×C22⋊C4×C61C2211yescharacteristic
14C22×C22⋊C4×C61C2211yescharacteristic
15C2×#99×C61—22no—
16C2×#99×C61—22no—
17C2×#99×C61—22no—
18C2×#99×C61—22no—
19C2×#99×C61—22no—
20C2×#99×C61—22no—
21C2×#99×C61—22no—
22C2×#99×C61—22no—
23C2×#99×C61C414yescomplemented
24C61×#385—22no—
25C61×#385—22no—
26C61×#380—22no—
27C61×#342—22no—
28C61×#342—22no—
29C61×#342—22no—
30C25×C61Q811yescharacteristic
31C25×C61C2311yescharacteristic
32C22×D4×C61—21no—
33C22×D4×C61—21no—
34C22×D4×C61—21no—
35C22×D4×C61—21no—
36C22×D4×C61—21no—
37C22×D4×C61—21no—
38C22×D4×C61—21no—
39C22×D4×C61—21no—
40C22×D4×C61—21no—
41C22×D4×C61—21no—
42C22×D4×C61—21no—
43C22×D4×C61—21no—
44C22×D4×C61C2×C412yes—
45C22×D4×C61D412yes—
46C23×C4×C61—21no—
47C23×C4×C61—21no—
48C23×C4×C61—21no—
49C23×C4×C61—21no—
50C23×C4×C61—21no—
51C23×C4×C61—21no—
52C23×C4×C61Q811yescharacteristic
53C2×C4⋊C4×C61—24no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C2×C22⋊C4×C61—21no—
64C2×C22⋊C4×C61—21no—
65C2×C22⋊C4×C61—21no—
66C2×C22⋊C4×C61—21no—
67C2×C22⋊C4×C61—21no—
68C2×C22⋊C4×C61—21no—
69C2×C22⋊C4×C61—21no—
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—21no—
76C2×C22⋊C4×C61—21no—
77C2×C22⋊C4×C61—21no—
78C2×C22⋊C4×C61—21no—
79C2×C22⋊C4×C61—21no—
80C2×C22⋊C4×C61—21no—
81C2×C22⋊C4×C61—21no—
82C2×C22⋊C4×C61C2×C412yes—
83C2×C22⋊C4×C61C2×C412yes—
84C2×C22⋊C4×C61D412yes—
85C2×C22⋊C4×C61D412yes—
86C2×C22⋊C4×C61D412yes—
87C2×C22⋊C4×C61D412yes—
88C2×C22⋊C4×C61D412yes—
89C2×C22⋊C4×C61D412yes—
90#99×C61—28no—
91#99×C61—28no—
92#99×C61—28no—
93#95×C61—24no—
94C24×C61—21no—
95C24×C61—21no—
96C24×C61—21no—
97C24×C61—21no—
98C24×C61—21no—
99C24×C61—21no—
100C24×C61—82no—
101C24×C61—82no—
102C24×C61C4⋊C412yescomplemented
103C24×C61C22×C411yescharacteristic
104C24×C61C2×D411yescharacteristic
105C24×C61C2×D411yescharacteristic
106C24×C61C2×D411yescharacteristic
107C24×C61C2×D411yescharacteristic
108C24×C61C2×D411yescharacteristic
109C24×C61C2×D411yescharacteristic
110C24×C61C2×D411yescharacteristic
111C24×C61C2×Q811yescharacteristic
112C24×C61#4111yescharacteristic
113C24×C61#4111yescharacteristic
114C24×C61#4111yescharacteristic
115C24×C61#4111yescharacteristic
116C24×C61#4111yescharacteristic
117C24×C61#4111yescharacteristic
118C2×D4×C61—22no—
119C2×D4×C61—22no—
120C2×D4×C61—22no—
121C2×D4×C61—22no—
122C2×D4×C61—22no—
123C2×D4×C61—22no—
124C2×D4×C61—22no—
125C2×D4×C61—22no—
126C2×D4×C61—22no—
127C2×D4×C61—22no—
128C2×D4×C61—22no—
129C2×D4×C61—22no—
130C2×D4×C61—41no—
131C2×D4×C61—41no—
132C2×D4×C61—41no—
133C2×D4×C61—41no—
134C2×D4×C61—41no—
135C2×D4×C61—41no—
136C2×D4×C61—41no—
137C2×D4×C61—41no—
138C2×D4×C61—41no—
139C2×D4×C61—41no—
140C2×D4×C61—41no—
141C2×D4×C61—41no—
142C2×D4×C61—41no—
143C2×D4×C61—41no—
144C2×D4×C61—41no—
145C2×D4×C61—41no—
146C22×C4×C61—22no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—41no—
161C22×C4×C61—41no—
162C22×C4×C61—41no—
163C22×C4×C61—41no—
164C22×C4×C61—41no—
165C22×C4×C61—41no—
166C22×C4×C61—41no—
167C22×C4×C61—41no—
168C22×C4×C61—41no—
169C22×C4×C61—41no—
170C22×C4×C61—82no—
171C22×C4×C61—82no—
172C22×C4×C61—82no—
173C22×C4×C61—82no—
174C22×C4×C61—82no—
175C22×C4×C61—82no—
176C22×C4×C61C4⋊C412yescomplemented
177C4⋊C4×C61—84no—
178C22⋊C4×C61—22no—
179C22⋊C4×C61—22no—
180C22⋊C4×C61—22no—
181C22⋊C4×C61—22no—
182C22⋊C4×C61—22no—
183C22⋊C4×C61—22no—
184C22⋊C4×C61—22no—
185C22⋊C4×C61—22no—
186C22⋊C4×C61—22no—
187C22⋊C4×C61—22no—
188C22⋊C4×C61—22no—
189C22⋊C4×C61—22no—
190C22⋊C4×C61—22no—
191C22⋊C4×C61—41no—
192C22⋊C4×C61—41no—
193C22⋊C4×C61—41no—
194C22⋊C4×C61—41no—
195C22⋊C4×C61—41no—
196C22⋊C4×C61—41no—
197C22⋊C4×C61—41no—
198C22⋊C4×C61—41no—
199C22⋊C4×C61—41no—
200C22⋊C4×C61—41no—
201C22⋊C4×C61C22⋊C414yes—
202C23×C61—22no—
203C23×C61—22no—
204C23×C61—22no—
205C23×C61—42no—
206C23×C61—42no—
207C23×C61—42no—
208C23×C61—42no—
209C23×C61—42no—
210C23×C61—42no—
211C23×C61—42no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61—41no—
216C23×C61—82no—
217C23×C61—82no—
218C23×C61—82no—
219C23×C61—81no—
220C23×C61—81no—
221C23×C61—81no—
222C23×C61—81no—
223C23×C61—81no—
224C23×C61—81no—
225C23×C61—81no—
226C23×C61—81no—
227C23×C61—82no—
228C23×C61—82no—
229C23×C61—82no—
230C23×C61—82no—
231C23×C61C2×C22⋊C411yescharacteristic
232C23×C61C2×C4⋊C411yescharacteristic
233C23×C61#11711yescharacteristic
234C23×C61C4×D411yescharacteristic
235C23×C61C4×D411yescharacteristic
236C23×C61C4×D411yescharacteristic
237C23×C61C4×D411yescharacteristic
238C23×C61#12011yescharacteristic
239C23×C61#12011yescharacteristic
240C23×C61#12011yescharacteristic
241C23×C61#12111yescharacteristic
242C23×C61#12111yescharacteristic
243C23×C61#12111yescharacteristic
244C23×C61#12111yescharacteristic
245C23×C61#12111yescharacteristic
246C23×C61#12111yescharacteristic
247C23×C61#12111yescharacteristic
248C23×C61#12111yescharacteristic
249C23×C61C22⋊Q811yescharacteristic
250C23×C61C22⋊Q811yescharacteristic
251C23×C61C22⋊Q811yescharacteristic
252C23×C61C22⋊Q811yescharacteristic
253C23×C61C22⋊Q811yescharacteristic
254C23×C61C22⋊Q811yescharacteristic
255C23×C61#12311yescharacteristic
256C23×C61#12311yescharacteristic
257C23×C61#12311yescharacteristic
258C23×C61#12311yescharacteristic
259C23×C61#12311yescharacteristic
260C23×C61#12411yescharacteristic
261C23×C61#12411yescharacteristic
262C23×C61#12411yescharacteristic
263C23×C61#12611yescharacteristic
264C23×C61#12611yescharacteristic
265C23×C61#12711yescharacteristic
266D4×C61—42no—
267D4×C61—42no—
268D4×C61—42no—
269D4×C61—42no—
270D4×C61—42no—
271D4×C61—42no—
272D4×C61—42no—
273D4×C61—42no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—24no—
278C2×C4×C61—44no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—44no—
284C2×C4×C61—44no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—82no—
291C2×C4×C61—82no—
292C2×C4×C61—82no—
293C2×C4×C61—82no—
294C2×C4×C61—82no—
295C2×C4×C61—82no—
296C2×C4×C61—82no—
297C2×C4×C61—82no—
298C2×C4×C61—82no—
299C2×C4×C61—82no—
300C2×C4×C61—82no—
301C2×C4×C61—82no—
302C2×C4×C61—82no—
303C2×C4×C61—82no—
304C2×C4×C61—82no—
305#11089C6111yesmaximal, characteristic, direct product factor, Sylow
306C22×C61—22no—
307C22×C61—22no—
308C22×C61—22no—
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—42no—
342C22×C61—82no—
343C22×C61—82no—
344C22×C61—82no—
345C22×C61—82no—
346C22×C61—82no—
347C22×C61—82no—
348C22×C61—82no—
349C22×C61#38011yescharacteristic
350C22×C61#38511yescharacteristic
351C22×C61#38511yescharacteristic
352C22×C61#38611yescharacteristic
353C22×C61#38811yescharacteristic
354C22×C61#38811yescharacteristic
355C22×C61#39011yescharacteristic
356C22×C61#39211yescharacteristic
357C22×C61#39311yescharacteristic
358C22×C61#39411yescharacteristic
359C22×C61#39411yescharacteristic
360C22×C61#39611yescharacteristic
361C22×C61#39611yescharacteristic
362C22×C61#39711yescharacteristic
363C22×C61#39911yescharacteristic
364C4×C61—44no—
365C4×C61—42no—
366C4×C61—82no—
367C4×C61—82no—
368C4×C61—82no—
369C4×C61—82no—
370C4×C61—82no—
371C22×#99C2×C6111yescharacteristic
372C22×#99C2×C6111yescharacteristic
373C22×#99C2×C6111yescharacteristic
374#2315C2×C6111yescharacteristic, complemented
375C2×#342C2×C6111yescharacteristic, complemented
376C2×#342C2×C6111yescharacteristic, complemented
377C2×#342C2×C6111yescharacteristic, complemented
378C2×C61—21no—
379C2×C61—21no—
380C2×C61—21no—
381C2×C61—21no—
382C2×C61—21no—
383C2×C61—21no—
384C2×C61—21no—
385C2×C61—21no—
386C2×C61—21no—
387C2×C61—21no—
388C2×C61—21no—
389C2×C61—21no—
390C2×C61—21no—
391C2×C61—21no—
392C2×C61—82no—
393C2×C61#143911yescharacteristic
394C2×C61#203212yes—
395C23×D4C22×C6111yescharacteristic
396C22×C22⋊C4C22×C6111yescharacteristic
397C22×C22⋊C4C22×C6111yescharacteristic
398C22×C22⋊C4C22×C6111yescharacteristic
399C22×C22⋊C4C22×C6111yescharacteristic
400C22×C22⋊C4C22×C6111yescharacteristic
401C22×C22⋊C4C22×C6111yescharacteristic
402C2×#99—22no—
403C2×#99—22no—
404C2×#99—22no—
405C2×#99—22no—
406C2×#99—22no—
407C2×#99—22no—
408C2×#99—22no—
409C2×#99—22no—
410C2×#99C4×C6114yescomplemented
411#385—22no—
412#385—22no—
413#380—22no—
414#342—22no—
415#342—22no—
416#342—22no—
417C61#1108911yescharacteristic, direct product factor, Sylow
418C25Q8×C6111yescharacteristic
419C25C23×C6111yescharacteristic
420C22×D4—21no—
421C22×D4—21no—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—21no—
427C22×D4—21no—
428C22×D4—21no—
429C22×D4—21no—
430C22×D4—21no—
431C22×D4—21no—
432C22×D4C2×C4×C6112yes—
433C22×D4D4×C6112yes—
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—21no—
439C23×C4—21no—
440C23×C4Q8×C6111yescharacteristic
441C2×C4⋊C4—24no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4C2×C4×C6112yes—
471C2×C22⋊C4C2×C4×C6112yes—
472C2×C22⋊C4D4×C6112yes—
473C2×C22⋊C4D4×C6112yes—
474C2×C22⋊C4D4×C6112yes—
475C2×C22⋊C4D4×C6112yes—
476C2×C22⋊C4D4×C6112yes—
477C2×C22⋊C4D4×C6112yes—
478#99—28no—
479#99—28no—
480#99—28no—
481#95—24no—
482C24—21no—
483C24—21no—
484C24—21no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—82no—
489C24—82no—
490C24C4⋊C4×C6112yescomplemented
491C24C22×C4×C6111yescharacteristic
492C24C2×D4×C6111yescharacteristic
493C24C2×D4×C6111yescharacteristic
494C24C2×D4×C6111yescharacteristic
495C24C2×D4×C6111yescharacteristic
496C24C2×D4×C6111yescharacteristic
497C24C2×D4×C6111yescharacteristic
498C24C2×D4×C6111yescharacteristic
499C24C2×Q8×C6111yescharacteristic
500C24#41×C6111yescharacteristic
501C24#41×C6111yescharacteristic
502C24#41×C6111yescharacteristic
503C24#41×C6111yescharacteristic
504C24#41×C6111yescharacteristic
505C24#41×C6111yescharacteristic
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—41no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—82no—
559C22×C4—82no—
560C22×C4—82no—
561C22×C4—82no—
562C22×C4—82no—
563C22×C4—82no—
564C22×C4C4⋊C4×C6112yescomplemented
565C4⋊C4—84no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—41no—
587C22⋊C4—41no—
588C22⋊C4—41no—
589C22⋊C4C22⋊C4×C6114yes—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—82no—
605C23—82no—
606C23—82no—
607C23—81no—
608C23—81no—
609C23—81no—
610C23—81no—
611C23—81no—
612C23—81no—
613C23—81no—
614C23—81no—
615C23—82no—
616C23—82no—
617C23—82no—
618C23—82no—
619C23C2×C22⋊C4×C6111yescharacteristic
620C23C2×C4⋊C4×C6111yescharacteristic
621C23#117×C6111yescharacteristic
622C23C4×D4×C6111yescharacteristic
623C23C4×D4×C6111yescharacteristic
624C23C4×D4×C6111yescharacteristic
625C23C4×D4×C6111yescharacteristic
626C23#120×C6111yescharacteristic
627C23#120×C6111yescharacteristic
628C23#120×C6111yescharacteristic
629C23#121×C6111yescharacteristic
630C23#121×C6111yescharacteristic
631C23#121×C6111yescharacteristic
632C23#121×C6111yescharacteristic
633C23#121×C6111yescharacteristic
634C23#121×C6111yescharacteristic
635C23#121×C6111yescharacteristic
636C23#121×C6111yescharacteristic
637C23C22⋊Q8×C6111yescharacteristic
638C23C22⋊Q8×C6111yescharacteristic
639C23C22⋊Q8×C6111yescharacteristic
640C23C22⋊Q8×C6111yescharacteristic
641C23C22⋊Q8×C6111yescharacteristic
642C23C22⋊Q8×C6111yescharacteristic
643C23#123×C6111yescharacteristic
644C23#123×C6111yescharacteristic
645C23#123×C6111yescharacteristic
646C23#123×C6111yescharacteristic
647C23#123×C6111yescharacteristic
648C23#124×C6111yescharacteristic
649C23#124×C6111yescharacteristic
650C23#124×C6111yescharacteristic
651C23#126×C6111yescharacteristic
652C23#126×C6111yescharacteristic
653C23#127×C6111yescharacteristic
654D4—42no—
655D4—42no—
656D4—42no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—44no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4—82no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4—82no—
684C2×C4—82no—
685C2×C4—82no—
686C2×C4—82no—
687C2×C4—82no—
688C2×C4—82no—
689C2×C4—82no—
690C2×C4—82no—
691C2×C4—82no—
692C2×C4—82no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—82no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—82no—
735C22—82no—
736C22C61×#38011yescharacteristic
737C22C61×#38511yescharacteristic
738C22C61×#38511yescharacteristic
739C22C61×#38611yescharacteristic
740C22C61×#38811yescharacteristic
741C22C61×#38811yescharacteristic
742C22C61×#39011yescharacteristic
743C22C61×#39211yescharacteristic
744C22C61×#39311yescharacteristic
745C22C61×#39411yescharacteristic
746C22C61×#39411yescharacteristic
747C22C61×#39611yescharacteristic
748C22C61×#39611yescharacteristic
749C22C61×#39711yescharacteristic
750C22C61×#39911yescharacteristic
751C4—44no—
752C4—42no—
753C4—82no—
754C4—82no—
755C4—82no—
756C4—82no—
757C4—82no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—82no—
773C2C61×#143911yescharacteristic
774C2C61×#203212yes—
subgroupG/H
center, socleC22×C61#393
commutatorC24C22×C4×C61
Frattini, cosocleC25C23×C61
prime radicalC23×D4×C61C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C25×C61 ◁ G

Complements

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

NH ≅ G/Ntype
4. C61×#2315C2semidirect
5. C2×C61×#342C2semidirect
6. C2×C61×#342C2semidirect
7. C2×C61×#342C2semidirect
23. C2×#99×C61C4semidirect
102. C24×C61C4⋊C4semidirect
176. C22×C4×C61C4⋊C4semidirect
305. #11089C61direct (N × H)
374. #2315C2×C61semidirect
375. C2×#342C2×C61semidirect
376. C2×#342C2×C61semidirect
377. C2×#342C2×C61semidirect
410. C2×#99C4×C61semidirect
417. C61#11089direct (N × H)
490. C24C4⋊C4×C61semidirect
564. C22×C4C4⋊C4×C61semidirect

Maximal subgroups

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

subgroupindex
C22×#99×C612
C61×#23152
C2×C61×#3422
#1108961