Finite Group Databasebeta

← #29727397

Subgroups — #29727397

Order 15616.

1086 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839982C211yesmaximal, characteristic, complemented
2C2×#16839918C211yesmaximal, characteristic, complemented
3C2×#16839854C211yesmaximal, characteristic, complemented
4#21449381C211yesmaximal, characteristic
5Q8×C22⋊Dic61C211yesmaximal, characteristic, complemented
6#21447210C211yesmaximal, characteristic, complemented
7#21447016C211yesmaximal, characteristic, complemented
8#21446998C211yesmaximal, characteristic
9#21446911C211yesmaximal, characteristic, complemented
10#21446675C211yesmaximal, characteristic, complemented
11#21446422C211yesmaximal, characteristic, complemented
12#21446176C211yesmaximal, characteristic, complemented
13#21446157C211yesmaximal, characteristic, complemented
14#21446089C211yesmaximal, characteristic, complemented
15C2×C61×#448C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C2×#14519764C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×Q8×Dic61C2211yescharacteristic
21C2×Q8×Dic61C2211yescharacteristic
22C2×#14519742C2211yescharacteristic
23#16839982—24no—
24#16839918—24no—
25#16839854—24no—
26C2×#14519710C2211yescharacteristic
27C2×#14519709C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37#16839685—21no—
38#16839676—21no—
39#16839669—21no—
40#16839669—21no—
41#16839669C2211yescharacteristic
42#16839669C2211yescharacteristic
43#16839665—21no—
44#16839665C2211yescharacteristic
45#16839661C2211yescharacteristic
46#16839650—21no—
47#16839622—21no—
48#16839622C2211yescharacteristic
49C4×C22⋊Dic61—21no—
50C4×C22⋊Dic61C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C23×Q8×C61C2211yescharacteristic
56C22×SD16×C61C2211yescharacteristic
57C22×SD16×C61C2211yescharacteristic
58C2×#121×C61C2211yescharacteristic
59C61×#448—24no—
60C2×#103×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C2×#11758202—22no—
65C2×#11758202—22no—
66C2×#11758202—22no—
67C2×#11758202—22no—
68C2×#11758202—41no—
69C2×#11758202D414yescomplemented
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519764—22no—
73#14519764—41no—
74#14519756—22no—
75#14519756—41no—
76Q8×Dic61—22no—
77Q8×Dic61—22no—
78Q8×Dic61—41no—
79Q8×Dic61—41no—
80#14519742—22no—
81#14519742—41no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61D411yescharacteristic
97C2×C22⋊Dic61D411yescharacteristic
98C2×C4×Dic61—21no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61C2311yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103#14519710—22no—
104#14519709—41no—
105#14519706—22no—
106#14519702—22no—
107#14519702—22no—
108#14519701—22no—
109#14519701—22no—
110#14519698—22no—
111#14519698—41no—
112C22⋊#92418—22no—
113C8×Dic61—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684D411yescharacteristic
121#14519684D411yescharacteristic
122C22×Q8×C61—22no—
123C22×Q8×C61—22no—
124C22×Q8×C61—21no—
125C22×Q8×C61—22no—
126C22×Q8×C61—22no—
127C22×Q8×C61—41no—
128C22×Q8×C61—41no—
129C22×Q8×C61C2311yescharacteristic
130C22×Q8×C61C2311yescharacteristic
131C22×D4×C61—21no—
132C22×D4×C61C2311yescharacteristic
133C23×C4×C61—21no—
134C23×C4×C61C2311yescharacteristic
135C2×SD16×C61—22no—
136C2×SD16×C61—22no—
137C2×SD16×C61—22no—
138C2×SD16×C61—22no—
139C2×SD16×C61—22no—
140C2×SD16×C61—41no—
141C22×C8×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143#121×C61—22no—
144#121×C61—41no—
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147#103×C61—22no—
148#103×C61D414yes—
149C22⋊C8×C61—22no—
150C24×C61—21no—
151C24×C61C2×D411yescharacteristic
152C2×Q8×C61—24no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—42no—
162C2×Q8×C61—42no—
163C2×Q8×C61—44no—
164C2×Q8×C61—44no—
165C2×Q8×C61—44no—
166C2×Q8×C61—44no—
167C2×Q8×C61C2×D412yes—
168C2×Q8×C61C2×D412yes—
169C2×Q8×C61#4112yes—
170C2×Q8×C61#4112yes—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—42no—
178C2×D4×C61—42no—
179C2×D4×C61—81no—
180C22×C4×C61—21no—
181C22×C4×C61—24no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—42no—
191C22×C4×C61—42no—
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2411yescharacteristic
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61C2×D411yescharacteristic
199C22×Dic61C2×D411yescharacteristic
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122C2×D412yes—
208SD16×C61—44no—
209SD16×C61—44no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61C2×D412yes—
216C4⋊C4×C61—21no—
217C4⋊C4×C61C2×D412yes—
218C22⋊C4×C61—42no—
219C22⋊Dic61—22no—
220C22⋊Dic61—22no—
221C22⋊Dic61—42no—
222C22⋊Dic61—42no—
223C22⋊Dic61—42no—
224C22⋊Dic61—42no—
225C22⋊Dic61—42no—
226C22⋊Dic61—81no—
227#11758202—28no—
228#11758202—44no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—42no—
236C4⋊Dic61—42no—
237C4⋊Dic61—81no—
238#11758196—42no—
239#11758196—42no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242C4×Dic61—21no—
243C4×Dic61—21no—
244C4×Dic61—42no—
245C4×Dic61—42no—
246C4×Dic61—42no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418C2×D412yes—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61#13512yes—
267C23×C61C22×D411yescharacteristic
268Q8×C61—22no—
269Q8×C61—22no—
270Q8×C61—22no—
271Q8×C61—22no—
272Q8×C61—22no—
273Q8×C61—48no—
274Q8×C61—41no—
275Q8×C61—41no—
276Q8×C61#12114yes—
277D4×C61—41no—
278D4×C61—41no—
279D4×C61—41no—
280D4×C61—41no—
281D4×C61—84no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—21no—
287C2×C4×C61—22no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—48no—
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×C61C22×D411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C2×C4×C61H(5,𝔽2)11yescharacteristic
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—22no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61#13712yes—
329Dic122—22no—
330Dic122—22no—
331Dic122—41no—
332Dic122—41no—
333C8×C61—22no—
334C8×C61—41no—
335#92418—22no—
336#92418—41no—
337#25149—611nomaximal, Sylow
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61#52511yescharacteristic
353C22×C61D4211yescharacteristic
354C22×C61D4211yescharacteristic
355C22×C61C2×#13511yescharacteristic
356C22×C61C2×#13711yescharacteristic
357C22×C61#57711yescharacteristic
358C22×C61#57811yescharacteristic
359C4×C61—24no—
360C4×C61—41no—
361C4×C61—42no—
362C4×C61—42no—
363C4×C61C2×#12111yescharacteristic
364C4×C61#53811yescharacteristic
365C4×C61#54611yescharacteristic
366C4×C61#54611yescharacteristic
367Dic61—22no—
368Dic61—42no—
369Dic61—41no—
370Dic61—41no—
371Dic61—41no—
372Dic61—81no—
373Dic61—81no—
374Dic61—81no—
375C2×#464—611no—
376C2×#451—611no—
377C2×#448D6111yescharacteristic
378C2×C4×Q16—611no—
379#2426—611no—
380Q8×C22⋊C4—611no—
381#2068—611no—
382#2035—611no—
383#2033—611no—
384#2015—611no—
385#1968—611no—
386#1923—611no—
387#1880—611no—
388#1878—611no—
389#1865—611no—
390C2×C61—42no—
391C2×C61—161no—
392C2×C61#242411yescharacteristic
393C2×C61#310811yescharacteristic
394C2×C61#312111yescharacteristic
395C2×C61#327011yescharacteristic
396C2×C61#327811yescharacteristic
397C2×C61#328211yescharacteristic
398C2×C61#328511yescharacteristic
399C23×Q8C2×D6111yescharacteristic
400C22×Q16—611no—
401C22×Q16—611no—
402C22×SD16C2×D6111yescharacteristic
403C22×SD16C2×D6111yescharacteristic
404C2×#124—611no—
405C2×C22⋊Q8—611no—
406C2×#121C2×D6111yescharacteristic
407C2×C4×Q8—611no—
408C2×C4×Q8—611no—
409C2×C4×Q8—611no—
410#464—1224no—
411#451—1224no—
412#448—24no—
413C4×Q16—1224no—
414C2×#107—611no—
415C2×#106—611no—
416C2×C4⋊C8—611no—
417C2×#103—611no—
418C2×#103—611no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#103C2×D6111yescharacteristic
422C2×#103C2×D6111yescharacteristic
423C2×#102—611no—
424C2×#102—611no—
425C2×C22⋊C8—611no—
426C2×C22⋊C8C2×D6111yescharacteristic
427C2×C4×C8—611no—
428#396—1221no—
429#394—1221no—
430#391—611no—
431#391—611no—
432#391—1221no—
433#391—1221no—
434#390—611no—
435#390—1221no—
436#389—611no—
437#388—1221no—
438#380—611no—
439#380—1221no—
440C4×C22⋊C4—611no—
441C4×C22⋊C4—1221no—
442#340—611no—
443#340—611no—
444#336—611no—
445#336—611no—
446C61#2514911yescharacteristic, complemented, Sylow
447C22×Q8—22no—
448C22×Q8—22no—
449C22×Q8—21no—
450C22×Q8—22no—
451C22×Q8—22no—
452C22×Q8—41no—
453C22×Q8—41no—
454C22×Q8—611no—
455C22×Q8C22×D6111yescharacteristic
456C22×Q8C22×D6111yescharacteristic
457C22×D4—21no—
458C22×D4C22×D6111yescharacteristic
459C23×C4—21no—
460C23×C4C22×D6111yescharacteristic
461C2×Q16—614no—
462C2×Q16—1222no—
463C2×Q16—1222no—
464C2×Q16—1222no—
465C2×Q16—1222no—
466C2×Q16—2441no—
467C2×SD16—22no—
468C2×SD16—22no—
469C2×SD16—22no—
470C2×SD16—22no—
471C2×SD16—22no—
472C2×SD16—41no—
473C22×C8—611no—
474C22×C8—611no—
475C22×C8C22×D6111yescharacteristic
476C22×C8C22×D6111yescharacteristic
477#124—1222no—
478#124—2441no—
479C22⋊Q8—1222no—
480C22⋊Q8—2441no—
481#121—22no—
482#121—41no—
483C4×Q8—1222no—
484C4×Q8—1222no—
485C4×Q8—1222no—
486C4×Q8—2441no—
487C4×Q8—2441no—
488C4×Q8—2441no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4C22×D6111yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—611no—
500C2×C22⋊C4—611no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C42—611no—
508C2×C42—611no—
509C2×C42—1221no—
510C2×C42—1221no—
511C2×C42—1221no—
512#107—1222no—
513#106—2441no—
514C4⋊C8—1222no—
515#103—22no—
516#103—1222no—
517#103—1222no—
518#103—1222no—
519#103—1222no—
520#103C22⋊D6114yes—
521#102—1222no—
522#102—2441no—
523C22⋊C8—22no—
524C22⋊C8—1222no—
525C4×C8—1222no—
526#95—611no—
527#95—611no—
528#95—1221no—
529#95—1221no—
530#95—1221no—
531#95—1221no—
532#95—1221no—
533#95—1221no—
534C24—21no—
535C24D4×D6111yescharacteristic
536C2×Q8—24no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—42no—
546C2×Q8—42no—
547C2×Q8—44no—
548C2×Q8—44no—
549C2×Q8—44no—
550C2×Q8—44no—
551C2×Q8—612no—
552C2×Q8—1221no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8D4×D6112yes—
558C2×Q8#1175822412yes—
559C2×Q8#1175822412yes—
560C2×Q8C2×C22⋊D6112yes—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—81no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4D4×D6111yescharacteristic
591C22×C4C23×D6111yescharacteristic
592Q16—1228no—
593Q16—2444no—
594SD16—44no—
595SD16—44no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—612no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8C2×C22⋊D6112yes—
608C4⋊C4—21no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—4881no—
616C4⋊C4—2442no—
617C4⋊C4—2442no—
618C4⋊C4—2442no—
619C4⋊C4—2442no—
620C4⋊C4C2×C22⋊D6112yes—
621C22⋊C4—42no—
622C22⋊C4—1222no—
623C22⋊C4—1222no—
624C22⋊C4—4881no—
625C22⋊C4—2442no—
626C22⋊C4—2442no—
627C22⋊C4—2442no—
628C22⋊C4—2442no—
629C22⋊C4—2442no—
630C42—1221no—
631C42—1221no—
632C42—1221no—
633C42—1221no—
634C42—2442no—
635C42—2442no—
636C42—2442no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23#1451979812yes—
651C23C2×D4×D6111yescharacteristic
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—22no—
657Q8—48no—
658Q8—41no—
659Q8—41no—
660Q8—1222no—
661Q8—1222no—
662Q8—2441no—
663Q8—2441no—
664Q8#1451974814yes—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—84no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—48no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—612no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1222no—
699C2×C4—1221no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4C2×D4×D6111yescharacteristic
712C2×C4C22×C22⋊D6111yescharacteristic
713C2×C4C2×#1175822411yescharacteristic
714C2×C4C2×#1175822411yescharacteristic
715C2×C4#1451982211yescharacteristic
716C2×C4#1451982211yescharacteristic
717C8—22no—
718C8—41no—
719C8—1222no—
720C8—2441no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22#1684026811yescharacteristic
736C22#1684039411yescharacteristic
737C22D4×C22⋊D6111yescharacteristic
738C22C2×#1451979811yescharacteristic
739C22#137×D6111yescharacteristic
740C22#1684056811yescharacteristic
741C22#1684057811yescharacteristic
742C4—24no—
743C4—42no—
744C4—41no—
745C4—42no—
746C4—1222no—
747C4—4881no—
748C4—4881no—
749C4—4881no—
750C4—2441no—
751C4—2441no—
752C4—2442no—
753C4—2441no—
754C4C2×#1451974811yescharacteristic
755C4#1684034711yescharacteristic
756C4#1684039911yescharacteristic
757C4#1684040611yescharacteristic
758C2—42no—
759C2—161no—
760C2#2144935111yescharacteristic
761C2#2145589411yescharacteristic
762C2#2145604111yescharacteristic
763C2#2145738311yescharacteristic
764C2#2145748311yescharacteristic
765C2#2145752611yescharacteristic
766C2#2145755311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#448C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
hypercenterC2×#448D61
hypocenterC61#25149
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×#16839982C2semidirect
2. C2×#16839918C2semidirect
3. C2×#16839854C2semidirect
5. Q8×C22⋊Dic61C2semidirect
6. #21447210C2semidirect
7. #21447016C2semidirect
9. #21446911C2semidirect
10. #21446675C2semidirect
11. #21446422C2semidirect
12. #21446176C2semidirect
13. #21446157C2semidirect
14. #21446089C2semidirect
69. C2×#11758202D4semidirect
446. C61#25149semidirect

Maximal subgroups

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

subgroupindex
C2×#168399822
C2×#168399182
C2×#168398542
#214493812
Q8×C22⋊Dic612
#214472102
#214470162
#214469982
#214469112
#214466752
#214464222
#214461762
#214461572
#214460892
C2×C61×#4482
#2514961