Finite Group Databasebeta

← #29723840

Subgroups — #29723840

Order 15616.

1070 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839905C211yesmaximal, characteristic
2C2×C4×#11758199C211yesmaximal, characteristic, complemented
3#21448650C211yesmaximal, characteristic, complemented
4#21447358C211yesmaximal, characteristic, complemented
5#21447250C211yesmaximal, characteristic, complemented
6#21447136C211yesmaximal, characteristic, complemented
7#21446998C211yesmaximal, characteristic, complemented
8#21446494C211yesmaximal, characteristic, complemented
9#21446427C211yesmaximal, characteristic, complemented
10#21446170C211yesmaximal, characteristic, complemented
11#21446153C211yesmaximal, characteristic, complemented
12#21446065C211yesmaximal, characteristic, complemented
13#21445816C211yesmaximal, characteristic, complemented
14#21445757C211yesmaximal, characteristic, complemented
15C61×#2422C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21#16839905—24no—
22C4×#11758199—24no—
23C2×#14519710C2211yescharacteristic
24C2×#14519710C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519700C2211yescharacteristic
27C2×#14519700C2211yescharacteristic
28C2×#14519700C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C4×#92418C2211yescharacteristic
37#16839668C2211yescharacteristic
38#16839668C2211yescharacteristic
39#16839638—21no—
40#16839638—21no—
41#16839624—21no—
42#16839622C2211yescharacteristic
43#95×D61—21no—
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C2×#123×C61—21no—
51C2×#121×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C61×#397—21no—
54C61×#394—21no—
55C61×#390C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#385—21no—
58C61×#384C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C4×C22⋊C4×C61C2211yescharacteristic
61C2×#11758222—22no—
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C22×Dic122C2311yescharacteristic
68C22×D244C2311yescharacteristic
69C22×C22⋊D61—21no—
70C22×C4×D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C2×#11758200—22no—
74C2×#11758200—22no—
75C2×#11758200—41no—
76C2×#11758199—22no—
77C2×#11758199—22no—
78C2×#11758199D414yes—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C4×D244—22no—
84C4×D244—22no—
85C4×D244—41no—
86C4×D244—41no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C22⋊Dic61—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92#14519710—22no—
93#14519710—41no—
94C4⋊#92418—41no—
95#14519700—22no—
96#14519700—22no—
97#14519700—41no—
98#14519698—22no—
99#14519698—41no—
100#14519697—22no—
101#14519697—22no—
102#14519697—22no—
103C22⋊#92418—22no—
104C22⋊#92418—41no—
105C4×#92418—22no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111C22×D4×C61—21no—
112C22×D4×C61C2311yescharacteristic
113C23×C4×C61—21no—
114C23×C4×C61C2311yescharacteristic
115#123×C61—44no—
116#121×C61—22no—
117#121×C61—41no—
118C4×D4×C61—22no—
119C4×D4×C61—41no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61—21no—
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
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×C61D411yescharacteristic
132C2×C22⋊C4×C61D411yescharacteristic
133C2×C42×C61C2311yescharacteristic
134C2×C42×C61C2311yescharacteristic
135#95×C61—21no—
136#95×C61—21no—
137#95×C61D411yescharacteristic
138#95×C61D411yescharacteristic
139C24×C61—21no—
140C24×C61C2×D411yescharacteristic
141C23×D61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—42no—
148C2×D4×C61—42no—
149C2×D4×C61—81no—
150C2×D4×C61C2×D412yes—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—42no—
161C22×C4×C61—42no—
162C22×C4×C61—81no—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2411yescharacteristic
169C2×C22⋊D61—24no—
170C2×C22⋊D61—42no—
171C2×C22⋊D61—42no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175#11758222—44no—
176#11758222—44no—
177#11758222—44no—
178#11758222—44no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244C2×D412yes—
183C2×D244#4112yes—
184C2×D244#4112yes—
185C2×C4×D61—24no—
186C2×C4×D61—42no—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—81no—
193C2×C4×D61—81no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122#4112yes—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—42no—
207C4⋊C4×C61—42no—
208C4⋊C4×C61—81no—
209C22⋊C4×C61—22no—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—42no—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—42no—
216C42×C61—21no—
217C42×C61—21no—
218C42×C61—21no—
219C42×C61—21no—
220C22⋊Dic61—81no—
221#11758200—44no—
222#11758199—28no—
223#11758198—42no—
224#11758198—42no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—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×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418C2×D412yes—
241C23×C61—21no—
242C23×C61—22no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61C22×D411yescharacteristic
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263D4×C61—22no—
264D4×C61—22no—
265D4×C61—41no—
266D4×C61—41no—
267D4×C61—84no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
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—84no—
295C2×C4×C61#13512yes—
296C2×C4×C61AGL(1,ℤ/8)12yes—
297C2×C4×C61C22×D411yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61H(5,𝔽2)11yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C22⋊D61—48no—
304C2×Dic61—22no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313D244—22no—
314D244—22no—
315D244—22no—
316D244#12314yescomplemented
317C4×D61—48no—
318C4×D61—84no—
319C4×D61—84no—
320Dic122—22no—
321Dic122—22no—
322Dic122—41no—
323Dic122—41no—
324#92418—22no—
325#92418—41no—
326#92418—41no—
327#92418—41no—
328#24899—611nomaximal, Sylow
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—42no—
338C22×C61—41no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61—81no—
342C22×C61—81no—
343C22×C61#52511yescharacteristic
344C22×C61D4211yescharacteristic
345C22×C61#54611yescharacteristic
346C22×C61C2×#13511yescharacteristic
347C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
348C22×C61#57611yescharacteristic
349C22×C61#57811yescharacteristic
350C2×D61—24no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—42no—
357C4×C61—22no—
358C4×C61—22no—
359C4×C61—41no—
360C4×C61—41no—
361C4×C61—41no—
362C4×C61—81no—
363C4×C61—81no—
364C4×C61—81no—
365C4×C61C2×#12311yescharacteristic
366C4×C61#53811yescharacteristic
367C4×C61#54611yescharacteristic
368C4×C61#55111yescharacteristic
369Dic61—42no—
370Dic61—81no—
371Dic61—81no—
372C2×#449—611no—
373C2×C4×D8—611no—
374#2422D6111yescharacteristic, complemented
375#2339—611no—
376#2095—611no—
377#2076—611no—
378#2055—611no—
379#2033—611no—
380#1933—611no—
381#1923—611no—
382#1879—611no—
383#1877—611no—
384#1862—611no—
385#1802—611no—
386#1788—611no—
387C2×C61—81no—
388C2×C61—82no—
389C2×C61#241811yescharacteristic
390C2×C61#310611yescharacteristic
391C2×C61#312411yescharacteristic
392C2×C61#326411yescharacteristic
393C2×C61#328311yescharacteristic
394C2×C61#329711yescharacteristic
395C2×C61#333011yescharacteristic
396D61—44no—
397C22×#41—611no—
398C22×SD16—611no—
399C22×D8—611no—
400C2×#123—21no—
401C2×#121C2×D6111yescharacteristic
402C2×C4×D4—611no—
403C2×C4×D4—611no—
404C2×C4×D4C2×D6111yescharacteristic
405#449—1224no—
406C4×D8—1224no—
407C2×#107—611no—
408C2×#107—611no—
409C2×C4⋊C8—611no—
410C2×#103—611no—
411C2×#103—611no—
412C2×#103—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×#102—611no—
418C2×C22⋊C8—611no—
419C2×C22⋊C8—611no—
420C2×C4×C8—611no—
421#397—21no—
422#394—21no—
423#391—611no—
424#391—611no—
425#390C2×D6111yescharacteristic
426#389C2×D6111yescharacteristic
427#386—1221no—
428#386—1221no—
429#385—21no—
430#384C2×D6111yescharacteristic
431#381—1221no—
432#380—611no—
433#380C2×D6111yescharacteristic
434C4×C22⋊C4C2×D6111yescharacteristic
435C2×#95—1221no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#336—611no—
441#336—611no—
442C61#2489911yescharacteristic, complemented, Sylow
443C2×#41—1222no—
444C2×#41—1222no—
445C2×#41—1222no—
446C2×#41—1222no—
447C2×#41—2441no—
448C2×#41—2441no—
449C22×Q8—611no—
450C22×D4—21no—
451C22×D4—611no—
452C22×D4—1221no—
453C22×D4C22×D6111yescharacteristic
454C23×C4—21no—
455C23×C4—1221no—
456C23×C4—1221no—
457C23×C4—1221no—
458C23×C4C22×D6111yescharacteristic
459C2×SD16—1222no—
460C2×SD16—1222no—
461C2×SD16—2441no—
462C2×D8—614no—
463C2×D8—1222no—
464C2×D8—1222no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8—611no—
468C22×C8—611no—
469#123—44no—
470#121—22no—
471#121—41no—
472C4×D4—22no—
473C4×D4—41no—
474C4×D4—1222no—
475C4×D4—1222no—
476C4×D4—2441no—
477C4×D4—2441no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C4⋊C4C22×D6111yescharacteristic
485C2×C4⋊C4C22×D6111yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4C22⋊D6111yescharacteristic
495C2×C22⋊C4C22⋊D6111yescharacteristic
496C2×C42C22×D6111yescharacteristic
497C2×C42C22×D6111yescharacteristic
498#107—1222no—
499#107—2441no—
500C4⋊C8—2441no—
501#103—1222no—
502#103—1222no—
503#103—2441no—
504#102—1222no—
505#102—1222no—
506#102—1222no—
507#102—1222no—
508#102—2441no—
509C22⋊C8—1222no—
510C22⋊C8—2441no—
511C4×C8—1222no—
512#95—21no—
513#95—21no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519#95C22⋊D6111yescharacteristic
520#95C22⋊D6111yescharacteristic
521C24—21no—
522C24—1221no—
523C24C2×C22⋊D6111yescharacteristic
524#41—2444no—
525#41—2444no—
526#41—2444no—
527#41—2444no—
528C2×Q8—612no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—81no—
542C2×D4—612no—
543C2×D4—612no—
544C2×D4—612no—
545C2×D4—1224no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4—2442no—
550C2×D4—2442no—
551C2×D4D4×D6112yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—81no—
564C22×C4—1224no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—4881no—
569C22×C4—4881no—
570C22×C4—2442no—
571C22×C4—2442no—
572C22×C4—2442no—
573C22×C4—2442no—
574C22×C4—2442no—
575C22×C4—2442no—
576C22×C4C2×C22⋊D6111yescharacteristic
577C22×C4C2×C22⋊D6111yescharacteristic
578C22×C4C2×C22⋊D6111yescharacteristic
579C22×C4C2×C22⋊D6111yescharacteristic
580C22×C4C2×C22⋊D6111yescharacteristic
581C22×C4C23×D6111yescharacteristic
582SD16—2444no—
583D8—1228no—
584C2×C8—612no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—81no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—4881no—
617C22⋊C4—2442no—
618C22⋊C4—2442no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—22no—
629C23—21no—
630C23—21no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—1222no—
638C23—1222no—
639C23—1222no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23C22×C22⋊D6111yescharacteristic
645Q8—1222no—
646Q8—1222no—
647Q8—2441no—
648Q8—2441no—
649D4—22no—
650D4—22no—
651D4—41no—
652D4—41no—
653D4—84no—
654D4—614no—
655D4—1222no—
656D4—1222no—
657D4—1222no—
658D4—2448no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—84no—
686C2×C4—1222no—
687C2×C4—4884no—
688C2×C4—4884no—
689C2×C4—2448no—
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#1451979712yes—
699C2×C4#1451980312yes—
700C2×C4C2×D4×D6111yescharacteristic
701C2×C4#41×D6111yescharacteristic
702C2×C4#41×D6111yescharacteristic
703C2×C4#41×D6111yescharacteristic
704C2×C4#1451982211yescharacteristic
705C2×C4#1451982311yescharacteristic
706C8—1222no—
707C8—2441no—
708C8—2441no—
709C8—2441no—
710C22—41no—
711C22—41no—
712C22—42no—
713C22—41no—
714C22—42no—
715C22—42no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—1224no—
725C22—2442no—
726C22—2442no—
727C22—2442no—
728C22—2442no—
729C22—2442no—
730C22—2442no—
731C22#1684026911yescharacteristic
732C22D4×C22⋊D6111yescharacteristic
733C22#1684040011yescharacteristic
734C22C2×#1451979711yescharacteristic
735C22C2×#1451980311yescharacteristic
736C22#1684056511yescharacteristic
737C22#1684057711yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4—81no—
745C4—81no—
746C4—4881no—
747C4—4881no—
748C4—2442no—
749C4#123×D6111yescharacteristic
750C4#1684034811yescharacteristic
751C4#1684040411yescharacteristic
752C4#1684044011yescharacteristic
753C2—81no—
754C2—82no—
755C2—2444no—
756C2#2144927811yescharacteristic
757C2#2145587311yescharacteristic
758C2#2145607511yescharacteristic
759C2#2145729511yescharacteristic
760C2#2145753711yescharacteristic
761C2#2145766311yescharacteristic
762C2#2145811811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2422C2
socleC23×C61C22×D4
prime radicalC2×#16839905C2
hypercenter#2422D61
hypocenterC61#24899
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2422

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758199C2semidirect
3. #21448650C2semidirect
4. #21447358C2semidirect
5. #21447250C2semidirect
6. #21447136C2semidirect
7. #21446998C2semidirect
8. #21446494C2semidirect
9. #21446427C2semidirect
10. #21446170C2semidirect
11. #21446153C2semidirect
12. #21446065C2semidirect
13. #21445816C2semidirect
14. #21445757C2semidirect
15. C61×#2422C2semidirect
316. D244#123semidirect
374. #2422D61semidirect
442. C61#24899semidirect

Maximal subgroups

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

subgroupindex
C2×#168399052
C2×C4×#117581992
#214486502
#214473582
#214472502
#214471362
#214469982
#214464942
#214464272
#214461702
#214461532
#214460652
#214458162
#214457572
C61×#24222
#2489961