Finite Group Databasebeta

← #29700309

Subgroups — #29700309

Order 15616.

1146 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×#16839906C211yesmaximal, characteristic
2C2×#16839757C211yesmaximal, characteristic, complemented
3#21448853C211yesmaximal, characteristic, complemented
4#21448657C211yesmaximal, characteristic, complemented
5#21446692C211yesmaximal, characteristic, complemented
6#21446516C211yesmaximal, characteristic, complemented
7#21446438C211yesmaximal, characteristic, complemented
8#21446244C211yesmaximal, characteristic, complemented
9#21446176C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446087C211yesmaximal, characteristic, complemented
12#21446015C211yesmaximal, characteristic, complemented
13#21445651C211yesmaximal, characteristic, complemented
14#21445596C211yesmaximal, characteristic, complemented
15C2×C61×#440C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519748C2211yescharacteristic
20C2×Q8×Dic61C2211yescharacteristic
21C2×#14519735C2211yescharacteristic
22#16839906C418yescomplemented
23C2×#14519708C2211yescharacteristic
24#16839757—24no—
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519687C2211yescharacteristic
33#16839665C2211yescharacteristic
34#16839664—21no—
35#16839664C2211yescharacteristic
36#16839663—21no—
37#16839663C2211yescharacteristic
38#16839662—21no—
39#16839660C2211yescharacteristic
40#16839650—21no—
41#16839641—21no—
42#16839619—21no—
43#16839619C2211yescharacteristic
44C4⋊C4×Dic61C2211yescharacteristic
45C4×#11758198—21no—
46C4×#11758198C2211yescharacteristic
47C4×C22⋊Dic61—21no—
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839517C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×SD16×C61C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C61×#440—24no—
58C2×#107×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#97×C61C2211yescharacteristic
62C2×#11758226—22no—
63C2×#11758226—22no—
64C2×#11758226—22no—
65C2×#11758226—41no—
66C2×#11758226—41no—
67C2×#11758226C2×C414yescomplemented
68C22×D244—21no—
69C22×D244C2311yescharacteristic
70C22×C22⋊D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61C2311yescharacteristic
73C2×#11758199—41no—
74C2×#11758199—41no—
75C2×#11758199C2×C414yes—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C2×C8×D61—22no—
79C2×C8×D61—22no—
80C2×C8×D61—41no—
81#14519748—22no—
82#14519748C2×C414yes—
83Q8×Dic61—22no—
84Q8×Dic61—41no—
85#14519735—22no—
86#14519735—41no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198D411yescharacteristic
102C2×#11758198D411yescharacteristic
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61C2311yescharacteristic
107#14519708—41no—
108#14519701—22no—
109#14519701C2×C414yescomplemented
110#14519699—22no—
111#14519699C2×C414yescomplemented
112#14519698—41no—
113#14519697—22no—
114#14519689C2×C414yescomplemented
115#14519687—41no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684D411yescharacteristic
120#14519684D411yescharacteristic
121C22×Q8×C61C2311yescharacteristic
122C22×D4×C61C2311yescharacteristic
123C23×C4×C61—21no—
124C2×SD16×C61—22no—
125C2×SD16×C61—22no—
126C2×SD16×C61C2×C414yes—
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C4×Q8×C61—22no—
130C4×Q8×C61—41no—
131C4×D4×C61—22no—
132C4×D4×C61—41no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C42×C61—21no—
138C2×C42×C61C2311yescharacteristic
139#107×C61—22no—
140#103×C61D414yescomplemented
141#102×C61—22no—
142#97×C61—22no—
143C24×C61—21no—
144C23×D61—21no—
145C23×D61C2×D411yescharacteristic
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61C22×C412yes—
150C2×Q8×C61C2×D412yes—
151C2×Q8×C61#4112yes—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61C22×C412yes—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—42no—
162C22×C4×C61—42no—
163C22×C4×C61—81no—
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2411yescharacteristic
167C2×C22⋊D61—24no—
168C2×C22⋊D61—81no—
169C2×C22⋊D61—81no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176#11758226—28no—
177#11758226—44no—
178#11758226—44no—
179#11758226—44no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—24no—
185C2×D244—21no—
186C2×D244—42no—
187C2×D244—42no—
188C2×D244C22×C412yes—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—24no—
194C2×C4×D61—42no—
195C2×C4×D61—42no—
196C2×C4×D61C22×C412yes—
197C2×C4×D61#4112yes—
198SD16×C61—28no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61C22×C412yes—
204C2×C8×C61C2×D412yes—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61C2×D412yes—
210C22⋊C4×C61—42no—
211C42×C61—21no—
212C42×C61—21no—
213C42×C61—42no—
214C22⋊Dic61—24no—
215C22⋊Dic61—42no—
216C22⋊Dic61—81no—
217#11758199—44no—
218#11758198—41no—
219#11758198—41no—
220#11758198—42no—
221#11758198—42no—
222#11758198—42no—
223#11758198—81no—
224#11758198—81no—
225#11758198—81no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—42no—
232C4⋊Dic61C22×C412yes—
233#11758196—81no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—42no—
237C4×Dic61—42no—
238C4×Dic61—81no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418C22×C412yes—
245C8×D61—44no—
246C23×C61—22no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61C22×D411yescharacteristic
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—22no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61C4×D412yes—
268Q8×C61—22no—
269Q8×C61—22no—
270Q8×C61—22no—
271Q8×C61C4×D414yes—
272D4×C61—22no—
273D4×C61—22no—
274D4×C61—41no—
275D4×C61—41no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—84no—
292C2×C4×C61C23×C411yescharacteristic
293C2×C4×C61C22×D411yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61H(5,𝔽2)11yescharacteristic
297C2×C4×C61H(5,𝔽2)11yescharacteristic
298C22⋊D61—84no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—22no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61C4×D412yes—
317D244—22no—
318D244—22no—
319D244—48no—
320D244—41no—
321D244—41no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—48no—
327C8×C61—22no—
328C8×C61—22no—
329#92418—22no—
330#92418—41no—
331#22857—611nomaximal, Sylow
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61C2×C4×D411yescharacteristic
340C22×C61D4211yescharacteristic
341C22×C61#54611yescharacteristic
342C22×C61#57511yescharacteristic
343C22×C61#57511yescharacteristic
344C22×C61#57611yescharacteristic
345C22×C61#57711yescharacteristic
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C4×C61—24no—
361C4×C61—41no—
362C4×C61—42no—
363C4×C61—41no—
364C4×C61—81no—
365C4×C61C2×C4×D411yescharacteristic
366C4×C61#51811yescharacteristic
367C4×C61#54611yescharacteristic
368C4×C61#55111yescharacteristic
369Dic61—22no—
370Dic61—42no—
371Dic61—41no—
372Dic61—41no—
373Dic61—81no—
374Dic61—81no—
375C2×#449—611no—
376C2×#440D6111yescharacteristic, complemented
377C2×#416—611no—
378#2363—611no—
379#2341—611no—
380#1972—611no—
381#1936—611no—
382#1925—611no—
383#1893—611no—
384#1880—611no—
385#1879—611no—
386#1865—611no—
387#1854—611no—
388#1763—611no—
389#1752—611no—
390C2×C61—82no—
391C2×C61#235811yescharacteristic
392C2×C61#294311yescharacteristic
393C2×C61#294611yescharacteristic
394C2×C61#326811yescharacteristic
395C2×C61#327111yescharacteristic
396C2×C61#330911yescharacteristic
397C2×C61#332111yescharacteristic
398D61—42no—
399D61—82no—
400C22×#41—611no—
401C22×SD16C2×D6111yescharacteristic
402C22×D8—611no—
403C23×C8—611no—
404C2×#121—611no—
405C2×C4×Q8—611no—
406C2×C4×Q8C2×D6111yescharacteristic
407C2×C4×D4C2×D6111yescharacteristic
408C2×#117—611no—
409#449—618no—
410#440—24no—
411C2×#107C2×D6111yescharacteristic
412C2×#106—611no—
413#416—1224no—
414C2×#103—611no—
415C2×#103—611no—
416C2×#103C2×D6111yescharacteristic
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102C2×D6111yescharacteristic
422C2×C22⋊C8—611no—
423C2×#97—611no—
424C2×#97C2×D6111yescharacteristic
425#390—611no—
426#390—611no—
427#390—611no—
428#390—1221no—
429#390—1221no—
430#390—1221no—
431#389—611no—
432#388—1221no—
433#386—1221no—
434#380—611no—
435#380—1221no—
436C4×C4⋊C4—611no—
437C4×C22⋊C4—611no—
438C4×C22⋊C4—1221no—
439C4×C22⋊C4—1221no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#336—611no—
445#336—611no—
446C61#2285711yescharacteristic, complemented, Sylow
447C2×#41—614no—
448C2×#41—1222no—
449C2×#41—1222no—
450C2×#41—1222no—
451C2×#41—2441no—
452C2×#41—2441no—
453C22×Q8C22×D6111yescharacteristic
454C22×D4—611no—
455C22×D4—1221no—
456C22×D4—1221no—
457C22×D4C22×D6111yescharacteristic
458C23×C4—21no—
459C23×C4—611no—
460C23×C4—1221no—
461C2×SD16—22no—
462C2×SD16—22no—
463C2×SD16C4×D6114yes—
464C2×D8—614no—
465C2×D8—2441no—
466C2×D8—2441no—
467C22×C8—611no—
468C22×C8—611no—
469C22×C8—1222no—
470C22×C8—1222no—
471C22×C8—2441no—
472C22×C8C22×D6111yescharacteristic
473C22×C8C22×D6111yescharacteristic
474#121—614no—
475#121—1222no—
476C4×Q8—22no—
477C4×Q8—41no—
478C4×Q8—1222no—
479C4×Q8—2441no—
480C4×D4—22no—
481C4×D4—41no—
482#117—1222no—
483#117—2441no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—611no—
494C2×C22⋊C4—611no—
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⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C42—21no—
505C2×C42—611no—
506C2×C42—1221no—
507C2×C42—1221no—
508C2×C42—1221no—
509C2×C42C22×D6111yescharacteristic
510#107—22no—
511#106—2441no—
512#103—614no—
513#103—1222no—
514#103C22⋊D6114yescomplemented
515#102—22no—
516#102—614no—
517#102—1222no—
518#102—1222no—
519#102—2441no—
520C22⋊C8—614no—
521#97—22no—
522#97—2441no—
523#95—611no—
524#95—611no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528C24—21no—
529C24—611no—
530C24—1221no—
531#41—1228no—
532#41—2444no—
533#41—2444no—
534#41—2444no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8C2×C4×D6112yes—
539C2×Q8#1175822212yes—
540C2×Q8C2×C22⋊D6112yes—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—612no—
547C2×D4—1224no—
548C2×D4—1224no—
549C2×D4—1221no—
550C2×D4—1221no—
551C2×D4—1221no—
552C2×D4—1221no—
553C2×D4—1221no—
554C2×D4—4881no—
555C2×D4—4881no—
556C2×D4—2442no—
557C2×D4—2442no—
558C2×D4C2×C4×D6112yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—81no—
565C22×C4—611no—
566C22×C4—612no—
567C22×C4—612no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—1224no—
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×C4D4×D6111yescharacteristic
581C22×C4D4×D6111yescharacteristic
582C22×C4C23×D6111yescharacteristic
583SD16—28no—
584D8—2444no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—612no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—2444no—
596C2×C8C2×C4×D6112yes—
597C2×C8C2×C22⋊D6112yes—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—42no—
602C4⋊C4—612no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—4881no—
609C4⋊C4—2442no—
610C4⋊C4C2×C22⋊D6112yes—
611C22⋊C4—42no—
612C22⋊C4—1224no—
613C22⋊C4—4881no—
614C22⋊C4—4881no—
615C22⋊C4—4881no—
616C22⋊C4—4881no—
617C22⋊C4—2441no—
618C22⋊C4—2441no—
619C22⋊C4—2442no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C42—21no—
624C42—21no—
625C42—42no—
626C42—1221no—
627C42—1221no—
628C42—4881no—
629C42—2442no—
630C42—2442no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—612no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23—1222no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23C2×D4×D6111yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8C4×C22⋊D6114yes—
657D4—22no—
658D4—22no—
659D4—41no—
660D4—41no—
661D4—1222no—
662D4—1222no—
663D4—4884no—
664D4—2448no—
665D4—2441no—
666D4—2441no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—84no—
683C2×C4—612no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—2448no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4C22×C4×D6111yescharacteristic
707C2×C4C22×C22⋊D6111yescharacteristic
708C2×C4#41×D6111yescharacteristic
709C2×C4C2×#1175822211yescharacteristic
710C2×C4#1451982211yescharacteristic
711C2×C4#1451982311yescharacteristic
712C8—22no—
713C8—22no—
714C8—1222no—
715C8—2441no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—1222no—
724C22—1222no—
725C22—1222no—
726C22—4881no—
727C22—4881no—
728C22—4881no—
729C22—4881no—
730C22—2442no—
731C22—2442no—
732C22—2442no—
733C22—2441no—
734C22—2441no—
735C22—2441no—
736C22—2441no—
737C22C4×D4×D6111yescharacteristic
738C22D4×C22⋊D6111yescharacteristic
739C22#1684040811yescharacteristic
740C22#1684055811yescharacteristic
741C22#1684056111yescharacteristic
742C22#1684056611yescharacteristic
743C22#1684057111yescharacteristic
744C4—24no—
745C4—41no—
746C4—42no—
747C4—41no—
748C4—81no—
749C4—1222no—
750C4—4881no—
751C4—4881no—
752C4—2442no—
753C4—2441no—
754C4—2441no—
755C4C2×C4×C22⋊D6111yescharacteristic
756C4#1684023411yescharacteristic
757C4#1684040011yescharacteristic
758C4#1684044111yescharacteristic
759C2—82no—
760C2—4882no—
761C2—2442no—
762C2#2144879611yescharacteristic
763C2#2145461411yescharacteristic
764C2#2145465011yescharacteristic
765C2#2145735311yescharacteristic
766C2#2145739811yescharacteristic
767C2#2145783011yescharacteristic
768C2#2145801011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC2×#16839906C2
cosocleC22×C4×C61C24
hypercenterC2×#440D61
hypocenterC61#22857
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#16839757C2semidirect
3. #21448853C2semidirect
4. #21448657C2semidirect
5. #21446692C2semidirect
6. #21446516C2semidirect
7. #21446438C2semidirect
8. #21446244C2semidirect
9. #21446176C2semidirect
10. #21446167C2semidirect
11. #21446087C2semidirect
12. #21446015C2semidirect
13. #21445651C2semidirect
14. #21445596C2semidirect
15. C2×C61×#440C2semidirect
22. #16839906C4semidirect
67. C2×#11758226C2×C4semidirect
109. #14519701C2×C4semidirect
111. #14519699C2×C4semidirect
114. #14519689C2×C4semidirect
140. #103×C61D4semidirect
376. C2×#440D61semidirect
446. C61#22857semidirect
514. #103C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399062
C2×#168397572
#214488532
#214486572
#214466922
#214465162
#214464382
#214462442
#214461762
#214461672
#214460872
#214460152
#214456512
#214455962
C2×C61×#4402
#2285761