Finite Group Databasebeta

← #29722317

Subgroups — #29722317

Order 15616.

1054 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840005C211yesmaximal, characteristic, complemented
2C2×#16839833C211yesmaximal, characteristic, complemented
3C22×#14519711C211yesmaximal, characteristic, complemented
4#21449271C211yesmaximal, characteristic, complemented
5#21449260C211yesmaximal, characteristic
6#21447212C211yesmaximal, characteristic, complemented
7#21447205C211yesmaximal, characteristic, complemented
8#21447021C211yesmaximal, characteristic, complemented
9#21447000C211yesmaximal, characteristic, complemented
10#21446702C211yesmaximal, characteristic, complemented
11#21446555C211yesmaximal, characteristic, complemented
12#21446137C211yesmaximal, characteristic, complemented
13#21446127C211yesmaximal, characteristic, complemented
14#21445849C211yesmaximal, characteristic, complemented
15C2×C61×#465C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C2×#14519753C2211yescharacteristic
18C2×#14519749—21no—
19C2×#14519748C2211yescharacteristic
20C2×C4×C22⋊D61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×C4⋊Dic61C2211yescharacteristic
23#16840005—24no—
24#16839833—24no—
25C2×#14519711—24no—
26C2×#14519711C2211yescharacteristic
27C2×#14519711C2211yescharacteristic
28C2×#14519711C2211yescharacteristic
29C2×#14519711C2211yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519687C2211yescharacteristic
38#16839695—21no—
39#16839685—21no—
40#16839684—21no—
41#16839678—21no—
42#16839669C2211yescharacteristic
43#16839665C2211yescharacteristic
44#16839658C2211yescharacteristic
45#16839658C2211yescharacteristic
46#16839642—21no—
47#16839639—21no—
48#16839620—21no—
49#16839619C2211yescharacteristic
50#16839619C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C22×SD16×C61C2211yescharacteristic
56C23×C8×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×#121×C61C2211yescharacteristic
59C61×#465—24no—
60C2×#106×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C22×C22⋊D61—21no—
64C22×C22⋊D61D411yescharacteristic
65C23×Dic61—21no—
66C23×Dic61—21no—
67C22×C4×D61C2311yescharacteristic
68C2×#11758189—22no—
69C2×#11758189—22no—
70C2×#11758189—22no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519753—22no—
74#14519753—41no—
75#14519749—44no—
76#14519748—22no—
77#14519748—41no—
78C4×C22⋊D61—22no—
79C4×C22⋊D61—22no—
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—41no—
85C2×C4⋊Dic61—41no—
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196D411yescharacteristic
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61D411yescharacteristic
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198D411yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103#14519711—22no—
104#14519711—22no—
105#14519711—22no—
106#14519711D414yescomplemented
107#14519706—22no—
108#14519701—22no—
109#14519701—41no—
110#14519698—22no—
111#14519698—41no—
112C22⋊#92418—22no—
113#14519689—22no—
114#14519687—22no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121C22×Q8×C61C2311yescharacteristic
122C22×D4×C61—21no—
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C2×SD16×C61—22no—
126C2×SD16×C61—22no—
127C2×SD16×C61—22no—
128C22×C8×C61—22no—
129C22×C8×C61—22no—
130C22×C8×C61D414yescomplemented
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22⋊Q8×C61—22no—
134C22⋊Q8×C61—22no—
135#121×C61—22no—
136#121×C61—22no—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142#106×C61—22no—
143#103×C61—22no—
144#102×C61—22no—
145C24×C61—21no—
146C24×C61C2×D411yescharacteristic
147C23×D61C2×D411yescharacteristic
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D412yes—
172C22×C4×C61#4112yes—
173C22×C4×C61C2411yescharacteristic
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—42no—
178C2×C22⋊D61—42no—
179C2×C22⋊D61—81no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—42no—
185C22×Dic61—42no—
186C22×Dic61—42no—
187C22×Dic61—42no—
188C22×Dic61—81no—
189C22×Dic61—81no—
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199SD16×C61—44no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—28no—
203C2×C8×C61C2×D412yes—
204C2×C8×C61C2×D412yes—
205C2×C8×C61C2×D412yes—
206C2×C8×C61#4112yes—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—42no—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—42no—
214C22⋊Dic61—22no—
215C22⋊Dic61—42no—
216C22⋊Dic61—42no—
217C22⋊Dic61—81no—
218#11758198—22no—
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—42no—
229C4⋊Dic61—42no—
230C4⋊Dic61C2×D412yes—
231C4⋊Dic61C2×D412yes—
232#11758196—22no—
233#11758196—42no—
234#11758196—42no—
235#11758196—81no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244#11758189—44no—
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×C61—41no—
256C23×C61#12112yes—
257C23×C61AGL(1,ℤ/8)12yes—
258C23×C61#13712yes—
259C23×C61C22×D411yescharacteristic
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267Q8×C61—41no—
268Q8×C61—41no—
269Q8×C61—41no—
270Q8×C61—41no—
271D4×C61—41no—
272D4×C61—41no—
273D4×C61—41no—
274D4×C61—41no—
275D4×C61—84no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
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#12112yes—
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61C22×D411yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61H(5,𝔽2)11yescharacteristic
297C2×C4×C612−1+411yescharacteristic
298C22⋊D61—44no—
299C22⋊D61—84no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
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—
320C2×Dic61—41no—
321C2×Dic61—84no—
322C2×Dic61—84no—
323C4×D61—41no—
324C4×D61—41no—
325C4×D61—41no—
326C4×D61—41no—
327C8×C61—22no—
328C8×C61#12114yescomplemented
329#92418—41no—
330#92418—41no—
331#24787—611nomaximal, Sylow
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61—81no—
342C22×C61—81no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61#46814yescomplemented
346C22×C61C2×#12111yescharacteristic
347C22×C61D4211yescharacteristic
348C22×C61#54711yescharacteristic
349C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C61C2×#13711yescharacteristic
351C22×C61#57611yescharacteristic
352C22×C61#57811yescharacteristic
353C2×D61—41no—
354C2×D61—41no—
355C2×D61—41no—
356C2×D61—41no—
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—41no—
360C4×C61—22no—
361C4×C61—81no—
362C4×C61—81no—
363C4×C61—81no—
364C4×C61C2×#12111yescharacteristic
365C4×C61#53711yescharacteristic
366C4×C61#54811yescharacteristic
367C4×C61#55311yescharacteristic
368Dic61—41no—
369Dic61—42no—
370Dic61—42no—
371Dic61—41no—
372Dic61—41no—
373Dic61—81no—
374Dic61—81no—
375C2×#468—611no—
376C2×#465D6111yescharacteristic, complemented
377C2×#435—611no—
378C22×#107—611no—
379#2417—611no—
380#2416—611no—
381#2068—611no—
382#2067—611no—
383#2036—611no—
384#2033—611no—
385#1973—611no—
386#1943—611no—
387#1874—611no—
388#1872—611no—
389#1809—611no—
390C2×C61—24no—
391C2×C61—161no—
392C2×C61#241611yescharacteristic
393C2×C61C2×#46811yescharacteristic
394C2×C61#306111yescharacteristic
395C2×C61#326411yescharacteristic
396C2×C61#327011yescharacteristic
397C2×C61#334311yescharacteristic
398C2×C61#334611yescharacteristic
399D61—81no—
400C22×SD16C2×D6111yescharacteristic
401C22×M16—611no—
402C23×C8C2×D6111yescharacteristic
403C2×C22⋊Q8—611no—
404C2×C22⋊Q8C2×D6111yescharacteristic
405C2×#121—611no—
406C2×#121—1221no—
407C2×#121C2×D6111yescharacteristic
408C2×C4×D4—611no—
409C22×C4⋊C4—611no—
410C22×C4⋊C4—611no—
411#468—1224no—
412#465—24no—
413#435—1224no—
414C2×#107—611no—
415C2×#107—611no—
416C2×#107—611no—
417C2×#107—611no—
418C2×#107—1224no—
419C2×#106C2×D6111yescharacteristic
420C2×C4⋊C8—611no—
421C2×#103—611no—
422C2×#103—611no—
423C2×#103C2×D6111yescharacteristic
424C2×#102—611no—
425C2×#102—611no—
426C2×#102C2×D6111yescharacteristic
427C2×C22⋊C8—611no—
428C2×C22⋊C8—611no—
429C2×#97—611no—
430#398—1221no—
431#396—1221no—
432#396—1221no—
433#394—1221no—
434#391—611no—
435#390—611no—
436#389—611no—
437#389—611no—
438#386—1221no—
439#386—1221no—
440#380—611no—
441#380—611no—
442#380—1221no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447C61#2478711yescharacteristic, complemented, Sylow
448C22×Q8C22×D6111yescharacteristic
449C22×D4—21no—
450C22×D4—611no—
451C22×D4—1221no—
452C22×D4C22×D6111yescharacteristic
453C23×C4—611no—
454C23×C4—1221no—
455C23×C4—1221no—
456C23×C4C22×D6111yescharacteristic
457C2×SD16—22no—
458C2×SD16—22no—
459C2×SD16—22no—
460C2×M16—1222no—
461C2×M16—1222no—
462C2×M16—1222no—
463C22×C8—22no—
464C22×C8—22no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8C22⋊D6114yescomplemented
468C22×C8C22×D6111yescharacteristic
469C22×C8C22×D6111yescharacteristic
470C22⋊Q8—22no—
471C22⋊Q8—22no—
472C22⋊Q8—1222no—
473C22⋊Q8—2441no—
474#121—22no—
475#121—22no—
476#121—1222no—
477#121—2441no—
478#121—2444no—
479C4×D4—1222no—
480C4×D4—1222no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—1222no—
488C2×C4⋊C4—1222no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—2441no—
495C2×C4⋊C4—2441no—
496C2×C4⋊C4C22×D6111yescharacteristic
497C2×C4⋊C4C22×D6111yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—611no—
501C2×C22⋊C4—611no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C42—611no—
509#107—614no—
510#107—1222no—
511#107—1222no—
512#107—1222no—
513#106—22no—
514C4⋊C8—1222no—
515#103—22no—
516#103—1222no—
517#103—2441no—
518#102—22no—
519#102—1222no—
520#102—2441no—
521C22⋊C8—1222no—
522C22⋊C8—1222no—
523#97—1222no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528#95—1221no—
529#95—1221no—
530C24—21no—
531C24—611no—
532C24D4×D6111yescharacteristic
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—1222no—
549C2×D4—1222no—
550C2×D4—1222no—
551C2×D4—4881no—
552C2×D4—2442no—
553C2×D4—2442no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—4881no—
575C22×C4—4881no—
576C22×C4—2442no—
577C22×C4—2442no—
578C22×C4—2442no—
579C22×C4—2442no—
580C22×C4D4×D6111yescharacteristic
581C22×C4#1175822412yes—
582C22×C4C2×C22⋊D6112yes—
583C22×C4C23×D6111yescharacteristic
584SD16—44no—
585M16—2444no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—28no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8D4×D6112yes—
596C2×C8#1175822412yes—
597C2×C8C2×C22⋊D6112yes—
598C2×C8C2×C22⋊D6112yes—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—612no—
605C4⋊C4—612no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1222no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—4881no—
614C4⋊C4—2442no—
615C4⋊C4—2442no—
616C4⋊C4—2442no—
617C4⋊C4—2442no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—1222no—
621C22⋊C4—1222no—
622C22⋊C4—4881no—
623C22⋊C4—4881no—
624C22⋊C4—2442no—
625C22⋊C4—2442no—
626C22⋊C4—2442no—
627C22⋊C4—2442no—
628C42—1221no—
629C42—1221no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23—1221no—
646C23—1221no—
647C23—1221no—
648C23#1451974812yes—
649C23#1451980412yes—
650C23#1451980612yes—
651C23C2×D4×D6111yescharacteristic
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—84no—
661D4—4884no—
662D4—2444no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
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—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1221no—
689C2×C4—4884no—
690C2×C4—4884no—
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×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4#1451974812yes—
706C2×C4C2×D4×D6111yescharacteristic
707C2×C4C22×C22⋊D6111yescharacteristic
708C2×C4C2×#1175822411yescharacteristic
709C2×C4C2×#1175822411yescharacteristic
710C2×C4#1451982311yescharacteristic
711C2×C4#1451982411yescharacteristic
712C8—22no—
713C8—2441no—
714C8—2441no—
715C8#1451974914yescomplemented
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—2441no—
730C22—2441no—
731C22—2441no—
732C22—2441no—
733C22—2441no—
734C22—2441no—
735C22—2441no—
736C22#1684000514yescomplemented
737C22C2×#1451974811yescharacteristic
738C22#1684039611yescharacteristic
739C22#1684041211yescharacteristic
740C22C2×#1451980411yescharacteristic
741C22C2×#1451980611yescharacteristic
742C22#1684056411yescharacteristic
743C22#1684057611yescharacteristic
744C4—22no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—4881no—
749C4—4881no—
750C4—2441no—
751C4—2441no—
752C4—2441no—
753C4—2442no—
754C4—2442no—
755C4C2×#1451974911yescharacteristic
756C4#1684034011yescharacteristic
757C4#1684041811yescharacteristic
758C4#1684046411yescharacteristic
759C2—24no—
760C2—161no—
761C2—4881no—
762C2#2144926011yescharacteristic
763C2C2×#1684000511yescharacteristic
764C2#2145548511yescharacteristic
765C2#2145729611yescharacteristic
766C2#2145738611yescharacteristic
767C2#2145826511yescharacteristic
768C2#2145831011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#465C2
socleC23×C61C22×D4
prime radical#21449260C2
hypercenterC2×#465D61
hypocenterC61#24787
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#16840005C2semidirect
2. C2×#16839833C2semidirect
3. C22×#14519711C2semidirect
4. #21449271C2semidirect
6. #21447212C2semidirect
7. #21447205C2semidirect
8. #21447021C2semidirect
9. #21447000C2semidirect
10. #21446702C2semidirect
11. #21446555C2semidirect
12. #21446137C2semidirect
13. #21446127C2semidirect
14. #21445849C2semidirect
15. C2×C61×#465C2semidirect
106. #14519711D4semidirect
130. C22×C8×C61D4semidirect
328. C8×C61#121semidirect
345. C22×C61#468semidirect
376. C2×#465D61semidirect
447. C61#24787semidirect
467. C22×C8C22⋊D61semidirect
715. C8#14519749semidirect
736. C22#16840005semidirect

Maximal subgroups

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

subgroupindex
C2×#168400052
C2×#168398332
C22×#145197112
#214492712
#214492602
#214472122
#214472052
#214470212
#214470002
#214467022
#214465552
#214461372
#214461272
#214458492
C2×C61×#4652
#2478761