Finite Group Databasebeta

← #29734564

Subgroups — #29734564

Order 15616.

1298 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×#16840412C211yesmaximal, characteristic
2C2×#16840159C211yesmaximal, characteristic, complemented
3C2×#16840050C211yesmaximal, characteristic, complemented
4#21450989C211yesmaximal, characteristic, complemented
5#21447007C211yesmaximal, characteristic, complemented
6#21447006C211yesmaximal, characteristic, complemented
7#21447005C211yesmaximal, characteristic, complemented
8#21446769C211yesmaximal, characteristic, complemented
9#21446611C211yesmaximal, characteristic, complemented
10#21446014C211yesmaximal, characteristic, complemented
11#21446013C211yesmaximal, characteristic, complemented
12#21446011C211yesmaximal, characteristic, complemented
13#21446010C211yesmaximal, characteristic, complemented
14#102×Dic61C211yesmaximal, characteristic, complemented
15C61×#2034C211yesmaximal, characteristic, complemented
16C22×#11758224—21no—
17#16840412—24no—
18#16840412—24no—
19C2×#14519776C2211yescharacteristic
20C2×#14519776C2211yescharacteristic
21C2×#14519759—21no—
22C2×#14519758—21no—
23C2×#14519754—21no—
24C2×#14519748C2211yescharacteristic
25C2×D4×Dic61C2211yescharacteristic
26C2×C4×C22⋊D61C2211yescharacteristic
27C22×C4⋊Dic61C2211yescharacteristic
28C2×C4⋊C4×D61C2211yescharacteristic
29#16840159—24no—
30#16840050—24no—
31C2×#14519709C2211yescharacteristic
32C2×#14519709C2211yescharacteristic
33C2×#14519708C2211yescharacteristic
34C2×#14519708C2211yescharacteristic
35C2×#14519708C2211yescharacteristic
36C2×#14519706C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×C8×Dic61C2211yescharacteristic
43#16839675—21no—
44#16839674—21no—
45#16839662—21no—
46#16839626—21no—
47#16839622C2211yescharacteristic
48#16839619C2211yescharacteristic
49#16839619C2211yescharacteristic
50C4⋊C4×Dic61C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×#106×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C2×#11758224—28no—
64C2×#11758224—44no—
65C2×#11758224—44no—
66C22×Dic122—21no—
67C22×Dic122—21no—
68C22×C22⋊D61—21no—
69C22×C22⋊D61D411yescharacteristic
70C23×Dic61—21no—
71C23×Dic61—21no—
72C22×C4×D61—21no—
73C22×C4×D61C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76#14519776—22no—
77#14519776—22no—
78#14519776—22no—
79#14519776D414yes—
80#14519759—28no—
81#14519758—28no—
82#14519754—28no—
83#14519748—22no—
84#14519748—22no—
85D4×Dic61—22no—
86D4×Dic61D414yes—
87C4×C22⋊D61—22no—
88C4×C22⋊D61—22no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196D411yescharacteristic
100C4⋊C4×D61—22no—
101C4⋊C4×D61—22no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61D411yescharacteristic
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198D411yescharacteristic
109C2×C4×Dic61—21no—
110C2×C4×Dic61C2311yescharacteristic
111#14519709—22no—
112#14519709—22no—
113#14519708—22no—
114#14519708—22no—
115#14519708—22no—
116#14519706—22no—
117#14519698—22no—
118#14519698—22no—
119C22⋊#92418—22no—
120#14519689—22no—
121#14519689—22no—
122C8×Dic61—22no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127C22×D4×C61—21no—
128C22×D4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132#121×C61—22no—
133#121×C61—22no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139#106×C61—22no—
140#102×C61—22no—
141#102×C61—22no—
142C22⋊C8×C61—22no—
143#95×C61—21no—
144C24×C61—21no—
145C24×C61C2×D411yescharacteristic
146C23×D61C2×D411yescharacteristic
147C2×D4×C61—24no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—42no—
154C2×D4×C61—42no—
155C2×D4×C61C2×D412yes—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2411yescharacteristic
167C2×C22⋊D61—24no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—42no—
171C2×C22⋊D61—42no—
172C2×C22⋊D61SD1614yes—
173C22×Dic61—24no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—24no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—42no—
180C22×Dic61—42no—
181C22×Dic61—42no—
182C22×Dic61—42no—
183C22×Dic61C2×D411yescharacteristic
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186#11758224—432no—
187C2×C4×D61—24no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—42no—
195C2×C4×D61—42no—
196C2×Dic122—24no—
197C2×Dic122—42no—
198C2×Dic122—42no—
199C2×Dic122—42no—
200C2×Dic122—81no—
201C2×Dic122—81no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61#4112yescomplemented
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61C2×D412yes—
214C22⋊C4×C61—24no—
215C22⋊C4×C61—81no—
216C22⋊Dic61—24no—
217C22⋊Dic61—24no—
218C22⋊Dic61—22no—
219C22⋊Dic61—81no—
220#11758198—22no—
221#11758198—81no—
222#11758198—81no—
223C4⋊Dic61—24no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61C2×D412yes—
231C4⋊Dic61C2×D412yes—
232#11758196—24no—
233#11758196—24no—
234#11758196—22no—
235#11758196—42no—
236C4×Dic61—42no—
237C4×Dic61C2×D412yes—
238C4×Dic61C2×D412yes—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418#4112yescomplemented
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—22no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61C2×SD1612yes—
259C23×C61C22×D411yescharacteristic
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61C2×SD1612yes—
267D4×C61—22no—
268D4×C61—22no—
269D4×C61—48no—
270D4×C61—41no—
271D4×C61—41no—
272C2×C4×C61—22no—
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—41no—
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×C61C22×D411yescharacteristic
289C2×C4×C61C22×D411yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C612−1+411yescharacteristic
293C2×C4×C612−1+411yescharacteristic
294C22⋊D61—28no—
295C22⋊D61—48no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—48no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—48no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61#12012yes—
316C2×Dic61#12012yes—
317C2×Dic61C2×SD1612yes—
318C2×Dic61AGL(1,ℤ/8)12yes—
319C4×D61—48no—
320C4×D61—41no—
321C4×D61—41no—
322C4×D61—41no—
323C4×D61—41no—
324Dic122—48no—
325Dic122—84no—
326C8×C61—22no—
327C8×C61—41no—
328#92418—22no—
329#92418—41no—
330#25699—611nomaximal, Sylow
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—81no—
342C22×C61—81no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61C2×#12011yescharacteristic
346C22×C61#54711yescharacteristic
347C22×C61#54711yescharacteristic
348C22×C61C22×SD1611yescharacteristic
349C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C61#57711yescharacteristic
351C22×C61#57711yescharacteristic
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—41no—
356C2×D61—41no—
357C2×D61—41no—
358C2×D61—41no—
359C4×C61—41no—
360C4×C61—42no—
361C4×C61—81no—
362C4×C61—81no—
363C4×C61#53211yescharacteristic
364C4×C61#53611yescharacteristic
365C4×C61#54811yescharacteristic
366C4×C61#54811yescharacteristic
367Dic61—22no—
368Dic61—41no—
369Dic61—42no—
370Dic61—42no—
371Dic61—81no—
372Dic61—81no—
373Dic61#45014yes—
374C2×#547—611no—
375C2×#498—611no—
376C2×#476—611no—
377#2563—611no—
378#2034—611no—
379#2034—611no—
380#2034—611no—
381#2034D6111yescharacteristic, complemented
382#1988—611no—
383#1954—611no—
384#1853—611no—
385#1853—611no—
386#1853—611no—
387#1853—611no—
388C4×#102—611no—
389C2×C61—42no—
390C2×C61—82no—
391C2×C61#243211yescharacteristic
392C2×C61C2×#45011yescharacteristic
393C2×C61#301011yescharacteristic
394C2×C61#333511yescharacteristic
395C2×C61#333511yescharacteristic
396C2×C61#335411yescharacteristic
397C2×C61#335411yescharacteristic
398D61—42no—
399C22×#41—1221no—
400#547—1224no—
401#547—1224no—
402C2×C4⋊Q8—611no—
403C2×C4⋊Q8—611no—
404C2×#123—1221no—
405C2×#123—1221no—
406C2×C22⋊Q8—1221no—
407C2×#121—611no—
408C2×#121C2×D6111yescharacteristic
409C2×C4×D4—611no—
410C2×C4×D4—611no—
411C22×C4⋊C4—611no—
412C22×C4⋊C4—611no—
413#498—1224no—
414#476—1224no—
415C2×#106—611no—
416C2×#106—611no—
417C2×#106—611no—
418C2×#106—611no—
419C2×#106—611no—
420C2×#106C2×D6111yescharacteristic
421C2×C4⋊C8—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#102C2×D6111yescharacteristic
425C2×#102C2×D6111yescharacteristic
426C2×C22⋊C8—611no—
427C2×C22⋊C8—611no—
428C2×C22⋊C8—611no—
429C2×C22⋊C8C2×D6111yescharacteristic
430C2×C4×C8—611no—
431#393—1221no—
432#393—1221no—
433#390—1221no—
434#382—1221no—
435#380—611no—
436#380—611no—
437#380—611no—
438#380C2×D6111yescharacteristic
439C4×C4⋊C4—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340C2×D6111yescharacteristic
446C61#2569911yescharacteristic, complemented, Sylow
447C2×#41—1228no—
448C2×#41—2444no—
449C2×#41—2444no—
450C22×Q8—1221no—
451C22×Q8—1221no—
452C22×D4—21no—
453C22×D4—611no—
454C22×D4—1221no—
455C22×D4C22×D6111yescharacteristic
456C23×C4—611no—
457C23×C4—1221no—
458C23×C4—1221no—
459C23×C4—1221no—
460C23×C4C22×D6111yescharacteristic
461C22×C8—611no—
462C22×C8—611no—
463C22×C8C22×D6111yescharacteristic
464C22×C8C22×D6111yescharacteristic
465C4⋊Q8—614no—
466C4⋊Q8—1222no—
467C4⋊Q8—1222no—
468C4⋊Q8—1222no—
469#123—1228no—
470#123—1228no—
471C22⋊Q8—1228no—
472#121—22no—
473#121—22no—
474#121—1222no—
475#121—1222no—
476C4×D4—614no—
477C4×D4—1222no—
478C4×D4—1222no—
479C4×D4—1222no—
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—1222no—
487C2×C4⋊C4—1222no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1222no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4C22×D6111yescharacteristic
494C2×C4⋊C4C22×D6111yescharacteristic
495C2×C4⋊C4C22×D6111yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—611no—
499C2×C22⋊C4—611no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C42—611no—
506C2×C42—1221no—
507#106—22no—
508#106—1222no—
509#106—1222no—
510#106—1222no—
511#106—1222no—
512#106—1222no—
513C4⋊C8—1222no—
514#102—22no—
515#102—22no—
516#102—1222no—
517#102—1222no—
518C22⋊C8—22no—
519C22⋊C8—1222no—
520C22⋊C8—1222no—
521C22⋊C8—1222no—
522C4×C8—1222no—
523#95—21no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528C24—21no—
529C24—611no—
530C24D4×D6111yescharacteristic
531#41—24432no—
532C2×Q8—1224no—
533C2×Q8—4881no—
534C2×Q8—4881no—
535C2×Q8—2442no—
536C2×Q8—2442no—
537C2×Q8—2442no—
538C2×D4—24no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—614no—
547C2×D4—1222no—
548C2×D4—1222no—
549C2×D4—1224no—
550C2×D4—2442no—
551C2×D4—2442no—
552C2×D4D4×D6112yes—
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—21no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—1224no—
566C22×C4—1224no—
567C22×C4—1224no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—2442no—
579C22×C4—2442no—
580C22×C4—2442no—
581C22×C4—2442no—
582C22×C4—2442no—
583C22×C4—2442no—
584C22×C4D4×D6111yescharacteristic
585C22×C4C23×D6111yescharacteristic
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—612no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8#1175822412yescomplemented
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—612no—
604C4⋊C4—612no—
605C4⋊C4—1222no—
606C4⋊C4—1224no—
607C4⋊C4—1224no—
608C4⋊C4—1224no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—2442no—
616C4⋊C4D4×D6112yes—
617C22⋊C4—24no—
618C22⋊C4—81no—
619C22⋊C4—1222no—
620C22⋊C4—1222no—
621C22⋊C4—1224no—
622C22⋊C4—1224no—
623C22⋊C4—4881no—
624C22⋊C4—4881no—
625C22⋊C4—4881no—
626C42—612no—
627C42—612no—
628C42—2442no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—22no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—612no—
643C23—1221no—
644C23—1221no—
645C23—1221no—
646C23—1221no—
647C23—1221no—
648C23—1221no—
649C23SD16×D6112yes—
650C23C2×D4×D6111yescharacteristic
651Q8—4884no—
652Q8—2448no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—41no—
657D4—41no—
658D4—1228no—
659D4—2448no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—612no—
677C2×C4—612no—
678C2×C4—612no—
679C2×C4—612no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—2448no—
688C2×C4—2448no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2448no—
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×C4C2×D4×D6111yescharacteristic
705C2×C4C2×D4×D6111yescharacteristic
706C2×C4#41×D6111yescharacteristic
707C2×C4C2×#1175822411yescharacteristic
708C2×C4#1451982411yescharacteristic
709C2×C4#1451982411yescharacteristic
710C8—22no—
711C8—41no—
712C8—1222no—
713C8—2441no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—1222no—
729C22—1222no—
730C22—1222no—
731C22—2441no—
732C22—2441no—
733C22—2441no—
734C22—2441no—
735C22#120×D6111yescharacteristic
736C22#1684041011yescharacteristic
737C22#1684041211yescharacteristic
738C22C2×SD16×D6111yescharacteristic
739C22AGL(1,ℤ/8)×D6111yescharacteristic
740C22#1684056911yescharacteristic
741C22#1684057211yescharacteristic
742C4—42no—
743C4—41no—
744C4—81no—
745C4—81no—
746C4—614no—
747C4—1222no—
748C4—4881no—
749C4—4881no—
750C4—2442no—
751C4—2442no—
752C4—2441no—
753C4#1684030711yescharacteristic
754C4#1684033411yescharacteristic
755C4#1684041811yescharacteristic
756C4#1684042011yescharacteristic
757C2—42no—
758C2—82no—
759C2—2442no—
760C2#2144944211yescharacteristic
761C2#450×D6111yescharacteristic
762C2#2145510211yescharacteristic
763C2#2145817111yescharacteristic
764C2#2145817411yescharacteristic
765C2#2145840911yescharacteristic
766C2#2145841211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2034C2
socleC23×C61C22×D4
prime radicalC2×#16840412C2
hypercenter#2034D61
hypocenterC61#25699
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

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

NH ≅ G/Ntype
2. C2×#16840159C2semidirect
3. C2×#16840050C2semidirect
4. #21450989C2semidirect
5. #21447007C2semidirect
6. #21447006C2semidirect
7. #21447005C2semidirect
8. #21446769C2semidirect
9. #21446611C2semidirect
10. #21446014C2semidirect
11. #21446013C2semidirect
12. #21446011C2semidirect
13. #21446010C2semidirect
14. #102×Dic61C2semidirect
15. C61×#2034C2semidirect
207. C2×C8×C61#41semidirect
244. C2×#92418#41semidirect
381. #2034D61semidirect
446. C61#25699semidirect
597. C2×C8#11758224semidirect

Maximal subgroups

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

subgroupindex
C2×#168404122
C2×#168401592
C2×#168400502
#214509892
#214470072
#214470062
#214470052
#214467692
#214466112
#214460142
#214460132
#214460112
#214460102
#102×Dic612
C61×#20342
#2569961