Finite Group Databasebeta

← #29691294

Subgroups — #29691294

Order 15616.

1080 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839913C211yesmaximal, characteristic
2#21448501C211yesmaximal, characteristic, complemented
3#21446699C211yesmaximal, characteristic, complemented
4#21446672C211yesmaximal, characteristic, complemented
5#21446519C211yesmaximal, characteristic, complemented
6#21446505C211yesmaximal, characteristic, complemented
7#21446443C211yesmaximal, characteristic, complemented
8#21446436C211yesmaximal, characteristic, complemented
9#21446177C211yesmaximal, characteristic, complemented
10#21446177C211yesmaximal, characteristic, complemented
11#21446131C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13#21445750C211yesmaximal, characteristic
14#21445585C211yesmaximal, characteristic, complemented
15C61×#2309C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19C2×C4×Dic122C2211yescharacteristic, complemented
20#16839913C418yescomplemented
21C2×#14519710C2211yescharacteristic, complemented
22C2×#14519708C2211yescharacteristic, complemented
23C2×#14519700C2211yescharacteristic, complemented
24C2×#14519700C2211yescharacteristic, complemented
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×#14519688C2211yescharacteristic, complemented
34C2×C4×#92418C2211yescharacteristic, complemented
35#16839668C2211yescharacteristic, complemented
36#16839660C2211yescharacteristic, complemented
37#16839657—21no—
38#16839656—21no—
39#16839650—21no—
40#16839643—21no—
41#16839622C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic, complemented
43#16839524C2211yescharacteristic, complemented
44#16839524C2211yescharacteristic, complemented
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839517C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49C23×D4×C61C2211yescharacteristic
50C2×#117×C61C2211yescharacteristic
51C2×#117×C61C2211yescharacteristic
52C61×#390—21no—
53C61×#390—21no—
54C61×#390C2211yescharacteristic
55C61×#390C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C61×#379—21no—
59C61×#379—21no—
60C22×Dic122C2311yescharacteristic
61C2×#11758200—41no—
62C2×#11758200—41no—
63C2×#11758200—41no—
64C2×#11758200—41no—
65C2×#11758200C2×C414yes—
66C2×#11758200C2×C414yes—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71#14519756—22no—
72#14519756C2×C414yes—
73C4×Dic122—41no—
74C4×Dic122—41no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85#14519710—41no—
86#14519708—41no—
87#14519700—41no—
88#14519700—41no—
89#14519698—41no—
90#14519698—41no—
91#14519698—41no—
92#14519698—41no—
93#14519698C2×C414yes—
94#14519698C2×C414yes—
95C22⋊#92418—22no—
96C22⋊#92418C2×C414yes—
97#14519688—41no—
98C4×#92418—41no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104C25×C61—21no—
105C22×D4×C61—21no—
106C22×D4×C61—22no—
107C22×D4×C61—41no—
108C22×D4×C61—41no—
109C22×D4×C61—41no—
110C22×D4×C61—41no—
111C22×D4×C61C2×C414yes—
112C22×D4×C61C2311yescharacteristic
113C22×D4×C61C2311yescharacteristic
114C23×C4×C61C2311yescharacteristic
115#117×C61—41no—
116#117×C61—41no—
117#117×C61—41no—
118#117×C61—41no—
119C2×C4⋊C4×C61D411yescharacteristic
120C2×C4⋊C4×C61D411yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61D411yescharacteristic
133C2×C22⋊C4×C61D411yescharacteristic
134C2×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C24×C61—21no—
138C24×C61—21no—
139C24×C61—24no—
140C24×C61—42no—
141C24×C61—42no—
142C24×C61—81no—
143C24×C61—81no—
144C24×C61—81no—
145C24×C61—81no—
146C24×C61C2×D411yescharacteristic
147C2×D4×C61—24no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—44no—
159C2×D4×C61—44no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—44no—
163C2×D4×C61—44no—
164C2×D4×C61C22×C412yes—
165C2×D4×C61C22×C412yes—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61C22×C412yes—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61#4112yes—
179C22×C4×C61C2411yescharacteristic
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122C22×C412yes—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—41no—
195C4⋊C4×C61—41no—
196C22⋊C4×C61—41no—
197C22⋊C4×C61—41no—
198C22⋊C4×C61—42no—
199C22⋊C4×C61—81no—
200C22⋊C4×C61—81no—
201C22⋊C4×C61—81no—
202C22⋊C4×C61—81no—
203C22⋊C4×C61—81no—
204C22⋊C4×C61—81no—
205C22⋊C4×C61—81no—
206C22⋊C4×C61—81no—
207C42×C61—21no—
208C42×C61—21no—
209C42×C61—21no—
210C42×C61—21no—
211C42×C61—42no—
212C22⋊Dic61—24no—
213C22⋊Dic61—81no—
214#11758200—44no—
215#11758200—44no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61C22×C412yes—
222#11758196—24no—
223#11758196—42no—
224#11758196—81no—
225C4×Dic61—42no—
226C4×Dic61—81no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418C22×C412yes—
238C2×#92418C22×C412yes—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—48no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—84no—
261C23×C61—84no—
262C23×C61—84no—
263C23×C61—84no—
264C23×C61—84no—
265C23×C61—84no—
266C23×C61C4×D412yes—
267C23×C61C22×D411yescharacteristic
268D4×C61—22no—
269D4×C61—22no—
270D4×C61—22no—
271D4×C61—22no—
272D4×C61—48no—
273D4×C61—41no—
274D4×C61—41no—
275D4×C61—41no—
276D4×C61—41no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61C4×D412yes—
302C2×C4×C61C23×C411yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61H(5,𝔽2)11yescharacteristic
305C2×C4×C61H(5,𝔽2)11yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×C4×C61H(5,𝔽2)11yescharacteristic
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320Dic122—22no—
321Dic122—22no—
322Dic122—41no—
323Dic122—41no—
324#92418—22no—
325#92418—22no—
326#92418—41no—
327#92418—41no—
328#22052—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—816no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61C2×C4×D411yescharacteristic
352C22×C61#53411yescharacteristic
353C22×C61#53511yescharacteristic
354C22×C61#57611yescharacteristic
355C22×C61#57711yescharacteristic
356C22×C61#57711yescharacteristic
357C22×C61#57711yescharacteristic
358C4×C61—22no—
359C4×C61—41no—
360C4×C61—41no—
361C4×C61—41no—
362C4×C61—41no—
363C4×C61—81no—
364C4×C61—81no—
365C4×C61#51811yescharacteristic
366C4×C61#51811yescharacteristic
367C4×C61#53811yescharacteristic
368C4×C61#53811yescharacteristic
369Dic61—42no—
370Dic61—42no—
371Dic61—81no—
372Dic61—81no—
373C2×#450—611no—
374#2323—611no—
375#2309D6111yescharacteristic
376#1973—611no—
377#1968—611no—
378#1936—611no—
379#1934—611no—
380#1926—611no—
381#1925—611no—
382#1880—611no—
383#1880—611no—
384#1873—611no—
385#1854—611no—
386#1786—611no—
387#1750—611no—
388C2×C61—42no—
389C2×C61—82no—
390C2×C61—82no—
391C2×C61#232111yescharacteristic
392C2×C61#294611yescharacteristic
393C2×C61#294911yescharacteristic
394C2×C61#319811yescharacteristic
395C2×C61#320011yescharacteristic
396C2×C61#322211yescharacteristic
397C2×C61#322411yescharacteristic
398C23×D4C2×D6111yescharacteristic
399C22×SD16—611no—
400C22×SD16—611no—
401C2×C22⋊Q8—611no—
402C2×C4×Q8—611no—
403C2×#117C2×D6111yescharacteristic
404C2×#117C2×D6111yescharacteristic
405#450—618no—
406C2×#107—611no—
407C2×#106—611no—
408C2×#103—611no—
409C2×#103—611no—
410C2×#102—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×C22⋊C8—611no—
417C2×C22⋊C8—611no—
418C2×#97—611no—
419C2×C4×C8—611no—
420#391—611no—
421#390—21no—
422#390—21no—
423#390C2×D6111yescharacteristic
424#390C2×D6111yescharacteristic
425#390C2×D6111yescharacteristic
426#390C2×D6111yescharacteristic
427#389—611no—
428#389—1221no—
429#388—1221no—
430#388—1221no—
431#387—1221no—
432#380—611no—
433#379—21no—
434#379—21no—
435C4×C4⋊C4—611no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#336—611no—
441#336—611no—
442C61#2205211yescharacteristic, complemented, Sylow
443C25—21no—
444C22×Q8—611no—
445C22×D4—22no—
446C22×D4—21no—
447C22×D4—41no—
448C22×D4—41no—
449C22×D4—41no—
450C22×D4—41no—
451C22×D4C4×D6114yes—
452C22×D4C22×D6111yescharacteristic
453C22×D4C22×D6111yescharacteristic
454C23×C4C22×D6111yescharacteristic
455C2×SD16—614no—
456C2×SD16—614no—
457C2×SD16—2441no—
458C2×SD16—2441no—
459C2×SD16—2441no—
460C2×SD16—2441no—
461C22×C8—611no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—611no—
465C22⋊Q8—614no—
466C22⋊Q8—1222no—
467C4×Q8—2441no—
468C4×Q8—2441no—
469#117—41no—
470#117—41no—
471#117—41no—
472#117—41no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4C22⋊D6111yescharacteristic
480C2×C4⋊C4C22⋊D6111yescharacteristic
481C2×C4⋊C4C22×D6111yescharacteristic
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4C22⋊D6111yescharacteristic
495C2×C22⋊C4C22⋊D6111yescharacteristic
496C2×C42—21no—
497C2×C42—1221no—
498C2×C42—1221no—
499C2×C42C22×D6111yescharacteristic
500C2×C42C22×D6111yescharacteristic
501#107—2441no—
502#106—2441no—
503#103—2441no—
504#103—2441no—
505#102—614no—
506#102—614no—
507#102—2441no—
508#102—2441no—
509#102—2441no—
510#102—2441no—
511C22⋊C8—614no—
512C22⋊C8—1222no—
513#97—2441no—
514C4×C8—2441no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519#95—1221no—
520C24—21no—
521C24—21no—
522C24—24no—
523C24—42no—
524C24—42no—
525C24—81no—
526C24—81no—
527C24—81no—
528C24—81no—
529C24C2×C22⋊D6111yescharacteristic
530C2×Q8—612no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—24no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4C2×C4×D6112yes—
554C2×D4C2×C4×D6112yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4C2×C4×D6112yes—
566C22×C4#1175822212yes—
567C22×C4C2×C22⋊D6111yescharacteristic
568C22×C4C2×C22⋊D6111yescharacteristic
569C22×C4C2×C22⋊D6111yescharacteristic
570C22×C4C2×C22⋊D6111yescharacteristic
571C22×C4C2×C22⋊D6111yescharacteristic
572C22×C4C23×D6111yescharacteristic
573SD16—2444no—
574SD16—2444no—
575C2×C8—612no—
576C2×C8—612no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—612no—
594C4⋊C4—1221no—
595C4⋊C4—1224no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—4881no—
601C4⋊C4—2442no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—42no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—1224no—
614C22⋊C4—4881no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—42no—
620C42—4881no—
621C42—2442no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—22no—
629C23—22no—
630C23—48no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23C4×C22⋊D6112yes—
650C23C22×C22⋊D6111yescharacteristic
651Q8—1222no—
652Q8—1222no—
653Q8—2441no—
654Q8—2441no—
655D4—22no—
656D4—22no—
657D4—22no—
658D4—22no—
659D4—48no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4C4×C22⋊D6112yes—
701C2×C4C22×C4×D6111yescharacteristic
702C2×C4C2×#1175822211yescharacteristic
703C2×C4#1451982211yescharacteristic
704C2×C4#1451982211yescharacteristic
705C2×C4#1451982211yescharacteristic
706C2×C4#1451982211yescharacteristic
707C8—1222no—
708C8—1222no—
709C8—2441no—
710C8—2441no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—816no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22C2×C4×C22⋊D6111yescharacteristic
734C22#1684032111yescharacteristic
735C22#1684032911yescharacteristic
736C22#1684056511yescharacteristic
737C22#1684057311yescharacteristic
738C22#1684057311yescharacteristic
739C22#1684057311yescharacteristic
740C4—22no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—81no—
746C4—81no—
747C4—4881no—
748C4—4881no—
749C4—2442no—
750C4—2442no—
751C4#1684023511yescharacteristic
752C4#1684023511yescharacteristic
753C4#1684035011yescharacteristic
754C4#1684035011yescharacteristic
755C2—42no—
756C2—82no—
757C2—82no—
758C2#2144847711yescharacteristic
759C2#2145465111yescharacteristic
760C2#2145467611yescharacteristic
761C2#2145667111yescharacteristic
762C2#2145669111yescharacteristic
763C2#2145689111yescharacteristic
764C2#2145691311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2309C2
socleC23×C61C22×D4
prime radicalC23×D4×C61C22
cosocleC22×C4×C61C24
hypercenter#2309D61
hypocenterC61#22052
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. #21448501C2semidirect
3. #21446699C2semidirect
4. #21446672C2semidirect
5. #21446519C2semidirect
6. #21446505C2semidirect
7. #21446443C2semidirect
8. #21446436C2semidirect
9. #21446177C2semidirect
10. #21446177C2semidirect
11. #21446131C2semidirect
12. #21446018C2semidirect
14. #21445585C2semidirect
19. C2×C4×Dic122C22semidirect
20. #16839913C4semidirect
21. C2×#14519710C22semidirect
22. C2×#14519708C22semidirect
23. C2×#14519700C22semidirect
24. C2×#14519700C22semidirect
33. C2×#14519688C22semidirect
34. C2×C4×#92418C22semidirect
35. #16839668C22semidirect
36. #16839660C22semidirect
42. C4×C4⋊Dic61C22semidirect
43. #16839524C22semidirect
44. #16839524C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839517C22semidirect
48. #16839517C22semidirect
442. C61#22052semidirect

Maximal subgroups

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

subgroupindex
C2×#168399132
#214485012
#214466992
#214466722
#214465192
#214465052
#214464432
#214464362
#214461772
#214461312
#214460182
#214457502
#214455852
C61×#23092
#2205261