Finite Group Databasebeta

← #29723721

Subgroups — #29723721

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×#16840104C211yesmaximal, characteristic, complemented
2C2×#16839764C211yesmaximal, characteristic, complemented
3#21449164C211yesmaximal, characteristic
4#21448748C211yesmaximal, characteristic, complemented
5#21447339C211yesmaximal, characteristic, complemented
6#21447239C211yesmaximal, characteristic, complemented
7#21447016C211yesmaximal, characteristic, complemented
8#21447009C211yesmaximal, characteristic, complemented
9#21446454C211yesmaximal, characteristic, complemented
10#21446447C211yesmaximal, characteristic, complemented
11#21446139C211yesmaximal, characteristic, complemented
12#21446014C211yesmaximal, characteristic, complemented
13#21445852C211yesmaximal, characteristic, complemented
14#21445760C211yesmaximal, characteristic, complemented
15C61×#1870C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519756C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21#16840104—24no—
22C2×#14519711C2211yescharacteristic
23C2×#14519709C2211yescharacteristic
24C2×#14519709C2211yescharacteristic
25C2×#14519709C2211yescharacteristic
26#16839764—24no—
27C2×#14519702C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35#16839677—21no—
36#16839670—21no—
37#16839668C2211yescharacteristic
38#16839664C2211yescharacteristic
39#16839655—21no—
40#16839648—21no—
41#16839642—21no—
42#16839638—21no—
43#16839633—21no—
44#16839628C2211yescharacteristic
45#16839622C2211yescharacteristic
46#16839622C2211yescharacteristic
47#16839622C2211yescharacteristic
48C4×C4⋊Dic61C2211yescharacteristic
49C22⋊C4×Dic61—21no—
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
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×C22⋊D61—21no—
71C23×Dic61—21no—
72C22×C4×D61—21no—
73#14519756—22no—
74#14519756—41no—
75#14519751—22no—
76#14519751—41no—
77#14519736—22no—
78#14519736—41no—
79C2×C4⋊Dic61—22no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61—41no—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×#11758196—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—21no—
99#14519711—22no—
100#14519709—22no—
101#14519709—41no—
102#14519709—41no—
103#14519702—22no—
104#14519702—22no—
105#14519702—41no—
106#14519702D414yescomplemented
107#14519699—22no—
108#14519699—22no—
109#14519699—22no—
110#14519699—41no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C22×D4×C61D411yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C2×M16×C61—22no—
123C2×M16×C61—22no—
124C2×M16×C61—41no—
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C4×D4×C61—22no—
130C4×D4×C61—22no—
131C2×C4⋊C4×C61D411yescharacteristic
132C2×C22⋊C4×C61D411yescharacteristic
133C2×C22⋊C4×C61D411yescharacteristic
134C2×C42×C61C2311yescharacteristic
135C22⋊C8×C61—22no—
136C22⋊C8×C61—22no—
137C22⋊C8×C61—41no—
138C24×C61C2×D411yescharacteristic
139C24×C61C2×D411yescharacteristic
140C23×D61—21no—
141C2×D4×C61—22no—
142C2×D4×C61—41no—
143C2×D4×C61—41no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
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—21no—
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61#4112yes—
159C22×C4×C61#4112yes—
160C22×C4×C61C2411yescharacteristic
161C2×C22⋊D61—42no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—42no—
164C2×C22⋊D61—42no—
165C2×C22⋊D61—42no—
166C2×C22⋊D61—81no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—42no—
175C22×Dic61—42no—
176C22×Dic61—81no—
177#11758222—28no—
178#11758222—44no—
179#11758222—44no—
180#11758222—44no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244#4112yes—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122C2×D412yes—
196M16×C61—44no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61C2×D412yes—
209C4⋊C4×C61—22no—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—22no—
212C42×C61—21no—
213C42×C61—21no—
214C22⋊Dic61—42no—
215C22⋊Dic61—42no—
216C22⋊Dic61—42no—
217C22⋊Dic61—81no—
218C22⋊Dic61—81no—
219#11758198—42no—
220#11758198—42no—
221#11758198—81no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—42no—
234C4⋊Dic61C2×D412yes—
235#11758196—42no—
236C4×Dic61—42no—
237C4×Dic61—81no—
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—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61#12312yes—
252C23×C61C22×D411yescharacteristic
253C22×D61—22no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260D4×C61—44no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—21no—
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—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61#12312yes—
281C2×C4×C61C22×D411yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61H(5,𝔽2)11yescharacteristic
286C2×C4×C61H(5,𝔽2)11yescharacteristic
287C22⋊D61—48no—
288C22⋊D61—84no—
289C2×Dic61—22no—
290C2×Dic61—22no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—84no—
311D244—22no—
312D244—22no—
313D244—41no—
314D244—41no—
315C4×D61—48no—
316Dic122—22no—
317Dic122—22no—
318Dic122—41no—
319Dic122—41no—
320C8×C61—22no—
321C8×C61—41no—
322C8×C61—41no—
323C8×C61—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—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61C2×#12311yescharacteristic
340C22×C61D4211yescharacteristic
341C22×C61#54611yescharacteristic
342C22×C61#57511yescharacteristic
343C22×C61#57511yescharacteristic
344C22×C61#57711yescharacteristic
345C22×C61#57711yescharacteristic
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—81no—
350C2×D61—81no—
351C2×D61—81no—
352C2×D61—81no—
353C4×C61—22no—
354C4×C61—41no—
355C4×C61—41no—
356C4×C61—41no—
357C4×C61#52511yescharacteristic
358C4×C61#53811yescharacteristic
359C4×C61#54611yescharacteristic
360C4×C61#55111yescharacteristic
361Dic61—42no—
362Dic61—42no—
363Dic61—81no—
364Dic61—81no—
365Dic61—81no—
366Dic61—81no—
367Dic61—81no—
368C2×#485—611no—
369C2×#417—611no—
370#2407—611no—
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#1870D6111yescharacteristic, complemented
380#1853—611no—
381#1809—611no—
382#1788—611no—
383C2×C61—42no—
384C2×C61—81no—
385C2×C61#241811yescharacteristic
386C2×C61#309311yescharacteristic
387C2×C61#309911yescharacteristic
388C2×C61#327111yescharacteristic
389C2×C61#327511yescharacteristic
390C2×C61#330711yescharacteristic
391C2×C61#332311yescharacteristic
392D61—82no—
393C22×#41—611no—
394C22×M16C2×D6111yescharacteristic
395C2×C22⋊Q8—611no—
396C2×#121—611no—
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⋊C8C2×D6111yescharacteristic
415C2×C22⋊C8C2×D6111yescharacteristic
416C2×C22⋊C8C2×D6111yescharacteristic
417#394—1221no—
418#392—1221no—
419#391—611no—
420#390—611no—
421#388—1221no—
422#387—1221no—
423#386—1221no—
424#386—1221no—
425#385—1221no—
426#382—611no—
427#380—611no—
428#380—611no—
429#380—611no—
430C4×C4⋊C4—611no—
431C4×C22⋊C4—1221no—
432#340—611no—
433#340—611no—
434#340—611no—
435#340—611no—
436#336C2×D6111yescharacteristic
437#336C2×D6111yescharacteristic
438C61#2489111yescharacteristic, complemented, Sylow
439C2×#41—1222no—
440C2×#41—1222no—
441C2×#41—1222no—
442C2×#41—1222no—
443C2×#41—2441no—
444C2×#41—2441no—
445C22×Q8—611no—
446C22×D4—611no—
447C22×D4—1221no—
448C22×D4—1221no—
449C22×D4D24411yescharacteristic
450C23×C4—1221no—
451C23×C4—1221no—
452C23×C4C22×D6111yescharacteristic
453C23×C4C22×D6111yescharacteristic
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C22×C8C22×D6111yescharacteristic
458C22×C8C22×D6111yescharacteristic
459C22×C8C22×D6111yescharacteristic
460C22×C8C22×D6111yescharacteristic
461C22⋊Q8—1222no—
462C22⋊Q8—2441no—
463#121—1222no—
464#121—2441no—
465C4×D4—22no—
466C4×D4—22no—
467#117—1222no—
468#117—2441no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—1222no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—2441no—
479C2×C4⋊C4D24411yescharacteristic
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4D24411yescharacteristic
489C2×C22⋊C4D24411yescharacteristic
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—22no—
506C22⋊C8—22no—
507C22⋊C8—41no—
508#95—1221no—
509#95—1221no—
510#95—1221no—
511#95—1221no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516C24—1221no—
517C24C2×D24411yescharacteristic
518C24C2×D24411yescharacteristic
519#41—1228no—
520#41—2444no—
521#41—2444no—
522#41—2444no—
523C2×Q8—612no—
524C2×Q8—1221no—
525C2×Q8—1221no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×D4—22no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—612no—
533C2×D4—1221no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—4881no—
539C2×D4—2442no—
540C2×D4—2442no—
541C2×D4—2442no—
542C2×D4—2442no—
543C2×D4—2442no—
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—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—4881no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4—2442no—
565C22×C4—2442no—
566C22×C4—2442no—
567C22×C4C2×D24411yescharacteristic
568C22×C4C2×D24411yescharacteristic
569C22×C4C2×D24411yescharacteristic
570C22×C4C2×D24411yescharacteristic
571C22×C4#1175822412yes—
572C22×C4#1175822412yes—
573C22×C4C23×D6111yescharacteristic
574M16—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8D4×D6112yes—
587C4⋊C4—22no—
588C4⋊C4—612no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—2442no—
601C4⋊C4—2442no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—4881no—
605C22⋊C4—4881no—
606C22⋊C4—4881no—
607C22⋊C4—2442no—
608C22⋊C4—2442no—
609C22⋊C4—2442no—
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—21no—
629C23—1222no—
630C23—2441no—
631C23—2441no—
632C23—2441no—
633C23—2441no—
634C23—2441no—
635C23—2441no—
636C23#1451976112yes—
637C23C22×D24411yescharacteristic
638Q8—1222no—
639Q8—1222no—
640Q8—2441no—
641Q8—2441no—
642D4—44no—
643D4—1222no—
644D4—1222no—
645D4—4884no—
646D4—2448no—
647D4—2441no—
648D4—2441no—
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—21no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—4884no—
671C2×C4—2448no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
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#1451976112yes—
692C2×C4C2×D4×D6111yescharacteristic
693C2×C4#41×D6111yescharacteristic
694C2×C4C2×#1175822411yescharacteristic
695C2×C4C2×#1175822411yescharacteristic
696C2×C4#1451982211yescharacteristic
697C2×C4#1451982311yescharacteristic
698C8—22no—
699C8—41no—
700C8—41no—
701C8—41no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—4881no—
717C22—4881no—
718C22—4881no—
719C22—4881no—
720C22—2442no—
721C22—2442no—
722C22—2442no—
723C22C2×#1451976111yescharacteristic
724C22D4×D24411yescharacteristic
725C22#1684040711yescharacteristic
726C22#1684056211yescharacteristic
727C22#1684056211yescharacteristic
728C22#1684057411yescharacteristic
729C22#1684057411yescharacteristic
730C4—22no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—4881no—
735C4—4881no—
736C4—4881no—
737C4—4881no—
738C4—4881no—
739C4—2442no—
740C4—2442no—
741C4#1684027211yescharacteristic
742C4#1684034911yescharacteristic
743C4#1684039911yescharacteristic
744C4#1684043511yescharacteristic
745C2—42no—
746C2—81no—
747C2—4882no—
748C2#2144927911yescharacteristic
749C2#2145575211yescharacteristic
750C2#2145581011yescharacteristic
751C2#2145740911yescharacteristic
752C2#2145745511yescharacteristic
753C2#2145779711yescharacteristic
754C2#2145803711yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1870C2
socleC23×C61C22×D4
prime radical#21449164C2
hypercenter#1870D61
hypocenterC61#24891
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×#16840104C2semidirect
2. C2×#16839764C2semidirect
4. #21448748C2semidirect
5. #21447339C2semidirect
6. #21447239C2semidirect
7. #21447016C2semidirect
8. #21447009C2semidirect
9. #21446454C2semidirect
10. #21446447C2semidirect
11. #21446139C2semidirect
12. #21446014C2semidirect
13. #21445852C2semidirect
14. #21445760C2semidirect
15. C61×#1870C2semidirect
106. #14519702D4semidirect
379. #1870D61semidirect
438. C61#24891semidirect

Maximal subgroups

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

subgroupindex
C2×#168401042
C2×#168397642
#214491642
#214487482
#214473392
#214472392
#214470162
#214470092
#214464542
#214464472
#214461392
#214460142
#214458522
#214457602
C61×#18702
#2489161