Finite Group Databasebeta

← #29722420

Subgroups — #29722420

Order 15616.

1026 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×#16840008C211yesmaximal, characteristic, complemented
2C2×#16840008C211yesmaximal, characteristic, complemented
3C2×#16839804C211yesmaximal, characteristic, complemented
4#21449259C211yesmaximal, characteristic
5#21449248C211yesmaximal, characteristic, complemented
6#21447206C211yesmaximal, characteristic, complemented
7#21447199C211yesmaximal, characteristic, complemented
8#21447023C211yesmaximal, characteristic, complemented
9#21447009C211yesmaximal, characteristic, complemented
10#21446673C211yesmaximal, characteristic, complemented
11#21446552C211yesmaximal, characteristic, complemented
12#21446139C211yesmaximal, characteristic, complemented
13#21446124C211yesmaximal, characteristic, complemented
14#21445852C211yesmaximal, characteristic, complemented
15C2×C61×#436C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C2×#14519756C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519749—21no—
22C2×#14519736C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24#16840008—24no—
25#16840008—24no—
26#16839804—24no—
27C2×#14519711C2211yescharacteristic
28C2×#14519711C2211yescharacteristic
29C2×#14519711C2211yescharacteristic
30C2×#14519709C2211yescharacteristic
31C2×#14519709C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic
38#16839690—21no—
39#16839684—21no—
40#16839678—21no—
41#16839676—21no—
42#16839668C2211yescharacteristic
43#16839664C2211yescharacteristic
44#16839660C2211yescharacteristic
45#16839660C2211yescharacteristic
46#16839657—21no—
47#16839656—21no—
48#16839639—21no—
49#16839622C2211yescharacteristic
50#16839622C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C61×#436—24no—
59C2×C4⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C2×C4×C8×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×C22⋊D61—21no—
67C23×Dic61—21no—
68C2×#11758190—22no—
69C2×#11758190—22no—
70C2×#11758190—22no—
71#14519756—22no—
72#14519756—22no—
73#14519756—22no—
74#14519756—41no—
75#14519751—22no—
76#14519751—22no—
77#14519751—22no—
78#14519751—41no—
79#14519749—44no—
80#14519736—22no—
81#14519736—41no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—41no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×C4×Dic61—21no—
105#14519711—22no—
106#14519711—22no—
107#14519711D414yescomplemented
108#14519709—22no—
109#14519709—22no—
110#14519702—22no—
111#14519702—22no—
112#14519702—41no—
113#14519699—22no—
114#14519699—22no—
115#14519699—41no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122C22×D4×C61D411yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C2×M16×C61—22no—
126C2×M16×C61—22no—
127C2×M16×C61—22no—
128C2×M16×C61—22no—
129C2×M16×C61—22no—
130C2×M16×C61D414yescomplemented
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C4×D4×C61—22no—
136C4×D4×C61—22no—
137C2×C4⋊C4×C61D411yescharacteristic
138C2×C22⋊C4×C61D411yescharacteristic
139C2×C22⋊C4×C61D411yescharacteristic
140C2×C42×C61C2311yescharacteristic
141C4⋊C8×C61—22no—
142C22⋊C8×C61—22no—
143C22⋊C8×C61—22no—
144C4×C8×C61—22no—
145C24×C61C2×D411yescharacteristic
146C24×C61C2×D411yescharacteristic
147C23×D61—21no—
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C2×D4×C61—41no—
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—21no—
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D412yes—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61#4112yes—
167C22×C4×C61C2411yescharacteristic
168C2×C22⋊D61—42no—
169C2×C22⋊D61—42no—
170C2×C22⋊D61—42no—
171C2×C22⋊D61—42no—
172C2×C22⋊D61—42no—
173C2×C22⋊D61—81no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—42no—
182C22×Dic61—42no—
183C22×Dic61—81no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196M16×C61—28no—
197M16×C61—44no—
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×C61C2×D412yes—
207C2×C8×C61C2×D412yes—
208C2×C8×C61C2×D412yes—
209C2×C8×C61#4112yes—
210C4⋊C4×C61—22no—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—22no—
213C42×C61—21no—
214C42×C61—21no—
215C22⋊Dic61—42no—
216C22⋊Dic61—42no—
217C22⋊Dic61—42no—
218C22⋊Dic61—42no—
219C22⋊Dic61—42no—
220#11758198—42no—
221#11758198—42no—
222#11758198—42no—
223#11758198—81no—
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—21no—
234C4⋊Dic61—42no—
235C4⋊Dic61C2×D412yes—
236C4⋊Dic61C2×D412yes—
237#11758196—42no—
238#11758196—42no—
239#11758196—42no—
240#11758196—42no—
241C4×Dic61—42no—
242#11758190—44no—
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—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61#12112yes—
257C23×C61C22×D411yescharacteristic
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265D4×C61—44no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
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—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61#12112yes—
285C2×C4×C61AGL(1,ℤ/8)12yes—
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C612−1+411yescharacteristic
292C22⋊D61—84no—
293C22⋊D61—84no—
294C2×Dic61—22no—
295C2×Dic61—22no—
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—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—84no—
316D244—41no—
317D244—41no—
318D244—41no—
319D244—41no—
320Dic122—41no—
321Dic122—41no—
322Dic122—41no—
323Dic122—41no—
324C8×C61—22no—
325C8×C61—41no—
326C8×C61—41no—
327C8×C61#12114yescomplemented
328#24794—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—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61C2×#12111yescharacteristic
344C22×C61D4211yescharacteristic
345C22×C61#54711yescharacteristic
346C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C61#57511yescharacteristic
348C22×C61#57711yescharacteristic
349C22×C61#57811yescharacteristic
350C2×D61—81no—
351C2×D61—81no—
352C2×D61—81no—
353C2×D61—81no—
354C2×D61—81no—
355C2×D61—81no—
356C2×D61—81no—
357C4×C61—22no—
358C4×C61—22no—
359C4×C61—41no—
360C4×C61—41no—
361C4×C61C2×#12111yescharacteristic
362C4×C61#53711yescharacteristic
363C4×C61#54811yescharacteristic
364C4×C61#55311yescharacteristic
365Dic61—42no—
366Dic61—42no—
367Dic61—81no—
368Dic61—81no—
369Dic61—81no—
370Dic61—81no—
371Dic61—81no—
372C2×#468—611no—
373C2×#468—611no—
374C2×#436D6111yescharacteristic, complemented
375C2×#428—611no—
376#2416—611no—
377#2415—611no—
378#2067—611no—
379#2066—611no—
380#2036—611no—
381#2034—611no—
382#1968—611no—
383#1942—611no—
384#1875—611no—
385#1872—611no—
386#1809—611no—
387C2×C61—42no—
388C2×C61—81no—
389C2×C61#241611yescharacteristic
390C2×C61#305511yescharacteristic
391C2×C61#306311yescharacteristic
392C2×C61#327211yescharacteristic
393C2×C61#327711yescharacteristic
394C2×C61#335111yescharacteristic
395C2×C61#335311yescharacteristic
396D61—161no—
397C22×SD16—611no—
398C22×M16C2×D6111yescharacteristic
399C22×M16C2×D6111yescharacteristic
400C2×C22⋊Q8—611no—
401C2×C22⋊Q8—611no—
402C2×#121—611no—
403C2×#121—611no—
404C2×#121—1221no—
405C2×C4×D4C2×D6111yescharacteristic
406C2×#117—611no—
407C22×C4⋊C4—611no—
408#468—1224no—
409#468—1224no—
410#436—24no—
411#428—1224no—
412C2×#107—611no—
413C2×#107—611no—
414C2×#107—611no—
415C2×#106—611no—
416C2×#106—611no—
417C2×C4⋊C8C2×D6111yescharacteristic
418C2×#103—611no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×C22⋊C8C2×D6111yescharacteristic
425C2×C22⋊C8C2×D6111yescharacteristic
426C2×C4×C8C2×D6111yescharacteristic
427#397—1221no—
428#396—1221no—
429#394—1221no—
430#394—1221no—
431#391—611no—
432#390—611no—
433#389—611no—
434#389—611no—
435#389—1221no—
436#388—1221no—
437#386—1221no—
438#380—611no—
439#380—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444C61#2479411yescharacteristic, complemented, Sylow
445C22×Q8—611no—
446C22×D4—611no—
447C22×D4—1221no—
448C22×D4—1221no—
449C22×D4D24411yescharacteristic
450C23×C4—1221no—
451C23×C4C22×D6111yescharacteristic
452C23×C4C22×D6111yescharacteristic
453C2×SD16—1222no—
454C2×SD16—1222no—
455C2×SD16—1222no—
456C2×M16—22no—
457C2×M16—22no—
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—22no—
461C2×M16C22⋊D6114yescomplemented
462C22×C8C22×D6111yescharacteristic
463C22×C8C22×D6111yescharacteristic
464C22×C8C22×D6111yescharacteristic
465C22×C8C22×D6111yescharacteristic
466C22⋊Q8—1222no—
467C22⋊Q8—1222no—
468C22⋊Q8—1222no—
469C22⋊Q8—2441no—
470#121—1222no—
471#121—1222no—
472#121—1222no—
473#121—2441no—
474#121—2444no—
475C4×D4—22no—
476C4×D4—22no—
477#117—1222no—
478#117—2441no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—1222no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—2441no—
492C2×C4⋊C4D24411yescharacteristic
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4D24411yescharacteristic
503C2×C22⋊C4D24411yescharacteristic
504C2×C42—1221no—
505C2×C42C22×D6111yescharacteristic
506#107—614no—
507#107—1222no—
508#107—1222no—
509#106—1222no—
510#106—1222no—
511C4⋊C8—22no—
512#103—1222no—
513#103—1222no—
514#103—2441no—
515#102—1222no—
516#102—1222no—
517#102—2441no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520C4×C8—22no—
521#95—1221no—
522#95—1221no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527C24—1221no—
528C24C2×D24411yescharacteristic
529C24C2×D24411yescharacteristic
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—41no—
539C2×D4—1221no—
540C2×D4—1221no—
541C2×D4—1221no—
542C2×D4—1221no—
543C2×D4—1221no—
544C2×D4—1221no—
545C2×D4—4881no—
546C2×D4—2442no—
547C2×D4—2442no—
548C2×D4—2442no—
549C2×D4—2442no—
550C2×D4—2442no—
551C22×C4—21no—
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—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—4881no—
569C22×C4—2442no—
570C22×C4—2442no—
571C22×C4C2×D24411yescharacteristic
572C22×C4C2×D24411yescharacteristic
573C22×C4C2×D24411yescharacteristic
574C22×C4C2×D24411yescharacteristic
575C22×C4#1175822212yes—
576C22×C4C2×C22⋊D6112yes—
577C22×C4C23×D6111yescharacteristic
578SD16—2444no—
579M16—28no—
580M16—44no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8D4×D6112yes—
590C2×C8#1175822412yes—
591C2×C8C2×C22⋊D6112yes—
592C2×C8C2×C22⋊D6112yes—
593C4⋊C4—22no—
594C4⋊C4—612no—
595C4⋊C4—612no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—2442no—
607C4⋊C4—2442no—
608C4⋊C4—2442no—
609C4⋊C4—2442no—
610C4⋊C4—2442no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—4881no—
614C22⋊C4—2442no—
615C22⋊C4—2442no—
616C22⋊C4—2442no—
617C22⋊C4—2442no—
618C22⋊C4—2442no—
619C22⋊C4—2442no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C42—21no—
623C42—21no—
624C42—2442no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645C23#1451975112yes—
646C23C22×D24411yescharacteristic
647Q8—2441no—
648Q8—2441no—
649Q8—2441no—
650Q8—2441no—
651D4—44no—
652D4—4884no—
653D4—4884no—
654D4—2441no—
655D4—2441no—
656D4—2441no—
657D4—2441no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
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—1222no—
677C2×C4—1222no—
678C2×C4—4884no—
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—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4#1451975112yes—
699C2×C4#1451980512yes—
700C2×C4C2×D4×D6111yescharacteristic
701C2×C4C22×C22⋊D6111yescharacteristic
702C2×C4C2×#1175822411yescharacteristic
703C2×C4C2×#1175822211yescharacteristic
704C2×C4#1451982311yescharacteristic
705C2×C4#1451982411yescharacteristic
706C8—22no—
707C8—41no—
708C8—41no—
709C8#1451974914yescomplemented
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—4881no—
725C22—4881no—
726C22—4881no—
727C22—4881no—
728C22—4881no—
729C22—4881no—
730C22—4881no—
731C22C2×#1451975111yescharacteristic
732C22D4×D24411yescharacteristic
733C22#1684041611yescharacteristic
734C22C2×#1451980511yescharacteristic
735C22#1684056211yescharacteristic
736C22#1684057411yescharacteristic
737C22#1684057911yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—41no—
742C4—4881no—
743C4—4881no—
744C4—4881no—
745C4—4881no—
746C4—4881no—
747C4—2442no—
748C4—2442no—
749C4C2×#1451974911yescharacteristic
750C4#1684034011yescharacteristic
751C4#1684042111yescharacteristic
752C4#1684045811yescharacteristic
753C2—42no—
754C2—81no—
755C2—9761no—
756C2#2144925911yescharacteristic
757C2#2145543811yescharacteristic
758C2#2145551011yescharacteristic
759C2#2145742111yescharacteristic
760C2#2145747711yescharacteristic
761C2#2145838111yescharacteristic
762C2#2145840411yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#436C2
socleC23×C61C22×D4
prime radical#21449259C2
hypercenterC2×#436D61
hypocenterC61#24794
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#16840008C2semidirect
2. C2×#16840008C2semidirect
3. C2×#16839804C2semidirect
5. #21449248C2semidirect
6. #21447206C2semidirect
7. #21447199C2semidirect
8. #21447023C2semidirect
9. #21447009C2semidirect
10. #21446673C2semidirect
11. #21446552C2semidirect
12. #21446139C2semidirect
13. #21446124C2semidirect
14. #21445852C2semidirect
15. C2×C61×#436C2semidirect
107. #14519711D4semidirect
130. C2×M16×C61D4semidirect
327. C8×C61#121semidirect
374. C2×#436D61semidirect
444. C61#24794semidirect
461. C2×M16C22⋊D61semidirect
709. C8#14519749semidirect

Maximal subgroups

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

subgroupindex
C2×#168400082
C2×#168398042
#214492592
#214492482
#214472062
#214471992
#214470232
#214470092
#214466732
#214465522
#214461392
#214461242
#214458522
C2×C61×#4362
#2479461