Finite Group Databasebeta

← #29723719

Subgroups — #29723719

Order 15616.

1006 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840100C211yesmaximal, characteristic, complemented
2C2×#16839763C211yesmaximal, characteristic, complemented
3#21448748C211yesmaximal, characteristic, complemented
4#21447340C211yesmaximal, characteristic, complemented
5#21447237C211yesmaximal, characteristic, complemented
6#21447012C211yesmaximal, characteristic, complemented
7#21447005C211yesmaximal, characteristic, complemented
8#21446450C211yesmaximal, characteristic, complemented
9#21446443C211yesmaximal, characteristic, complemented
10#21446142C211yesmaximal, characteristic, complemented
11#21446117C211yesmaximal, characteristic, complemented
12#21446011C211yesmaximal, characteristic, complemented
13#21445850C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C61×#2407C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C2×#14519736C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19#16840100—24no—
20C2×#14519710C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24#16839763—24no—
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36#16839655—21no—
37#16839648—21no—
38#16839642—21no—
39#16839628C2211yescharacteristic
40#16839622C2211yescharacteristic
41#16839622C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43C22⋊C4×Dic61—21no—
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C22×#41×C61C2211yescharacteristic
51C2×C22⋊Q8×C61C2211yescharacteristic
52C2×#121×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C61×#394—21no—
55C61×#392—21no—
56C61×#391C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C61×#386—21no—
59C61×#385—21no—
60C61×#380C2211yescharacteristic
61C23×Dic61—21no—
62C2×#11758194—22no—
63C2×#11758194—22no—
64C2×#11758194—41no—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69#14519736—22no—
70#14519736—41no—
71C2×C4⋊Dic61—22no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—41no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83#14519710—22no—
84#14519708—22no—
85#14519708—41no—
86#14519708—41no—
87#14519701—22no—
88#14519701—22no—
89#14519701—41no—
90#14519701D414yescomplemented
91#14519698—22no—
92#14519698—22no—
93#14519698—22no—
94#14519698—41no—
95C22⋊#92418—22no—
96C22⋊#92418—22no—
97C22⋊#92418—41no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103C2×#41×C61—22no—
104C2×#41×C61—22no—
105C2×#41×C61—22no—
106C2×#41×C61—22no—
107C2×#41×C61—41no—
108C2×#41×C61—41no—
109C22×Q8×C61C2311yescharacteristic
110C22×D4×C61—21no—
111C22×D4×C61—21no—
112C22×D4×C61D411yescharacteristic
113C22×D4×C61C2311yescharacteristic
114C23×C4×C61—21no—
115C23×C4×C61C2311yescharacteristic
116C23×C4×C61C2311yescharacteristic
117C22⋊Q8×C61—22no—
118C22⋊Q8×C61—41no—
119#121×C61—22no—
120#121×C61—41no—
121C4×D4×C61—22no—
122C4×D4×C61—22no—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61D411yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
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×C61C2311yescharacteristic
135#95×C61—21no—
136#95×C61—21no—
137#95×C61—21no—
138C24×C61—21no—
139C24×C61C2×D411yescharacteristic
140C24×C61C2×D411yescharacteristic
141#41×C61—28no—
142#41×C61—44no—
143#41×C61—44no—
144#41×C61—44no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61C2×D412yes—
151C2×D4×C61—22no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—41no—
158C2×D4×C61—41no—
159C2×D4×C61—42no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61—42no—
164C2×D4×C61—81no—
165C2×D4×C61#4112yes—
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×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—42no—
180C22×C4×C61—42no—
181C22×C4×C61—42no—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61#4112yes—
187C22×C4×C61#4112yes—
188C22×C4×C61C2411yescharacteristic
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—42no—
194C22×Dic61—42no—
195C22×Dic61—81no—
196C4⋊C4×C61—22no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—42no—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—42no—
205C22⋊C4×C61—42no—
206C22⋊C4×C61—42no—
207C22⋊C4×C61—81no—
208C22⋊C4×C61—81no—
209C42×C61—21no—
210C42×C61—21no—
211C22⋊Dic61—42no—
212C22⋊Dic61—42no—
213C22⋊Dic61—81no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—42no—
222C4⋊Dic61C2×D412yes—
223C4×Dic61—42no—
224C4×Dic61—81no—
225#11758194—44no—
226C2×#92418—21no—
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×#92418C2×D412yes—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—22no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61#12312yes—
259C23×C61C22×D411yescharacteristic
260Q8×C61—22no—
261Q8×C61—22no—
262Q8×C61—41no—
263Q8×C61—41no—
264D4×C61—22no—
265D4×C61—22no—
266D4×C61—44no—
267D4×C61—48no—
268D4×C61—41no—
269D4×C61—41no—
270D4×C61—84no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—22no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—48no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61#12312yes—
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61H(5,𝔽2)11yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×Dic61—22no—
308C2×Dic61—41no—
309C2×Dic61—41no—
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—84no—
320#92418—22no—
321#92418—41no—
322#92418—41no—
323#92418—41no—
324#24891—611nomaximal, Sylow
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—42no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—42no—
340C22×C61—41no—
341C22×C61—42no—
342C22×C61—81no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61—81no—
346C22×C61C2×#12311yescharacteristic
347C22×C61D4211yescharacteristic
348C22×C61#54611yescharacteristic
349C22×C61#57511yescharacteristic
350C22×C61#57511yescharacteristic
351C22×C61#57711yescharacteristic
352C22×C61#57711yescharacteristic
353C4×C61—22no—
354C4×C61—41no—
355C4×C61—41no—
356C4×C61—41no—
357C4×C61—42no—
358C4×C61—81no—
359C4×C61—81no—
360C4×C61#52511yescharacteristic
361C4×C61#53811yescharacteristic
362C4×C61#54611yescharacteristic
363C4×C61#55111yescharacteristic
364Dic61—42no—
365Dic61—81no—
366Dic61—81no—
367Dic61—81no—
368C2×#485—611no—
369C2×#417—611no—
370#2407D6111yescharacteristic
371#2352—611no—
372#2092—611no—
373#2074—611no—
374#2035—611no—
375#2034—611no—
376#1927—611no—
377#1926—611no—
378#1875—611no—
379#1870—611no—
380#1853—611no—
381#1809—611no—
382#1788—611no—
383C2×C61—42no—
384C2×C61—81no—
385C2×C61—82no—
386C2×C61#241811yescharacteristic
387C2×C61#309311yescharacteristic
388C2×C61#309911yescharacteristic
389C2×C61#327111yescharacteristic
390C2×C61#327511yescharacteristic
391C2×C61#330711yescharacteristic
392C2×C61#332311yescharacteristic
393C22×#41C2×D6111yescharacteristic
394C22×M16—611no—
395C2×C22⋊Q8C2×D6111yescharacteristic
396C2×#121C2×D6111yescharacteristic
397C2×C4×D4C2×D6111yescharacteristic
398C2×#117—611no—
399C22×C4⋊C4—611no—
400#485—1224no—
401C2×#107—611no—
402C2×#106—611no—
403C2×#106—611no—
404C2×#106—611no—
405#417—1224no—
406C2×#103—611no—
407C2×#103—611no—
408C2×#103—611no—
409C2×#103—611no—
410C2×#102—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×C22⋊C8—611no—
417#394—21no—
418#392—21no—
419#391C2×D6111yescharacteristic
420#390C2×D6111yescharacteristic
421#388—1221no—
422#387—1221no—
423#386—21no—
424#386—1221no—
425#385—21no—
426#382—611no—
427#380—611no—
428#380—611no—
429#380C2×D6111yescharacteristic
430C4×C4⋊C4—611no—
431C4×C22⋊C4—1221no—
432#340—611no—
433#340—611no—
434#340—611no—
435#340—611no—
436#336—611no—
437#336—611no—
438C61#2489111yescharacteristic, complemented, Sylow
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—41no—
444C2×#41—41no—
445C22×Q8C22×D6111yescharacteristic
446C22×D4—21no—
447C22×D4—21no—
448C22×D4C22⋊D6111yescharacteristic
449C22×D4C22×D6111yescharacteristic
450C23×C4—21no—
451C23×C4—1221no—
452C23×C4C22×D6111yescharacteristic
453C23×C4C22×D6111yescharacteristic
454C2×M16—1222no—
455C2×M16—1222no—
456C2×M16—2441no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—611no—
461C22⋊Q8—22no—
462C22⋊Q8—41no—
463#121—22no—
464#121—41no—
465C4×D4—22no—
466C4×D4—22no—
467#117—1222no—
468#117—2441no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—1222no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—2441no—
477C2×C4⋊C4C22⋊D6111yescharacteristic
478C2×C4⋊C4C22×D6111yescharacteristic
479C2×C4⋊C4C22×D6111yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4C22⋊D6111yescharacteristic
489C2×C22⋊C4C22⋊D6111yescharacteristic
490C2×C42—1221no—
491C2×C42—1221no—
492C2×C42C22×D6111yescharacteristic
493#107—1222no—
494#106—1222no—
495#106—2441no—
496#106—2441no—
497#103—614no—
498#103—1222no—
499#103—1222no—
500#103—2441no—
501#102—1222no—
502#102—1222no—
503#102—1222no—
504#102—2441no—
505C22⋊C8—1222no—
506C22⋊C8—1222no—
507C22⋊C8—2441no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—1221no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516C24—21no—
517C24C2×C22⋊D6111yescharacteristic
518C24C2×C22⋊D6111yescharacteristic
519#41—28no—
520#41—44no—
521#41—44no—
522#41—44no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8D4×D6112yes—
529C2×D4—22no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—81no—
543C2×D4#1175822412yes—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—4881no—
565C22×C4—2442no—
566C22×C4—2442no—
567C22×C4#1175822412yes—
568C22×C4#1175822412yes—
569C22×C4C2×C22⋊D6111yescharacteristic
570C22×C4C2×C22⋊D6111yescharacteristic
571C22×C4C2×C22⋊D6111yescharacteristic
572C22×C4C2×C22⋊D6111yescharacteristic
573C22×C4C23×D6111yescharacteristic
574M16—2444no—
575C2×C8—612no—
576C2×C8—1221no—
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—22no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—612no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—2442no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—4881no—
610C22⋊C4—2442no—
611C22⋊C4—2442no—
612C42—21no—
613C42—21no—
614C42—4881no—
615C42—2442no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—22no—
629C23—21no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23#1451975812yes—
637C23C22×C22⋊D6111yescharacteristic
638Q8—22no—
639Q8—22no—
640Q8—41no—
641Q8—41no—
642D4—22no—
643D4—22no—
644D4—44no—
645D4—48no—
646D4—41no—
647D4—41no—
648D4—84no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—48no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—1222no—
679C2×C4—4884no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4#1451975812yes—
692C2×C4C2×D4×D6111yescharacteristic
693C2×C4C2×#1175822411yescharacteristic
694C2×C4C2×#1175822411yescharacteristic
695C2×C4C2×#1175822411yescharacteristic
696C2×C4#1451982211yescharacteristic
697C2×C4#1451982211yescharacteristic
698C8—1222no—
699C8—2441no—
700C8—2441no—
701C8—2441no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—42no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22C2×#1451975811yescharacteristic
724C22D4×C22⋊D6111yescharacteristic
725C22#1684040611yescharacteristic
726C22#1684056011yescharacteristic
727C22#1684056011yescharacteristic
728C22#1684057011yescharacteristic
729C22#1684057311yescharacteristic
730C4—22no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—41no—
735C4—81no—
736C4—81no—
737C4—4881no—
738C4—4881no—
739C4—4881no—
740C4—2442no—
741C4#1684026811yescharacteristic
742C4#1684034711yescharacteristic
743C4#1684039911yescharacteristic
744C4#1684044311yescharacteristic
745C2—42no—
746C2—81no—
747C2—82no—
748C2#2144927711yescharacteristic
749C2#2145574811yescharacteristic
750C2#2145580411yescharacteristic
751C2#2145740011yescharacteristic
752C2#2145745111yescharacteristic
753C2#2145779511yescharacteristic
754C2#2145803511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#2407C2
socleC23×C61C22×D4
hypercenter#2407D61
hypocenterC61#24891
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C2×#16840100C2semidirect
2. C2×#16839763C2semidirect
3. #21448748C2semidirect
4. #21447340C2semidirect
5. #21447237C2semidirect
6. #21447012C2semidirect
7. #21447005C2semidirect
8. #21446450C2semidirect
9. #21446443C2semidirect
10. #21446142C2semidirect
11. #21446117C2semidirect
12. #21446011C2semidirect
13. #21445850C2semidirect
14. #21445759C2semidirect
90. #14519701D4semidirect
438. C61#24891semidirect

Maximal subgroups

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

subgroupindex
C2×#168401002
C2×#168397632
#214487482
#214473402
#214472372
#214470122
#214470052
#214464502
#214464432
#214461422
#214461172
#214460112
#214458502
#214457592
C61×#24072
#2489161