Finite Group Databasebeta

← #29696850

Subgroups — #29696850

Order 15616.

1366 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840433C211yesmaximal, characteristic
2C2×#16839890C211yesmaximal, characteristic, complemented
3#21448777C211yesmaximal, characteristic, complemented
4#21446746C211yesmaximal, characteristic, complemented
5#21446744C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446643C211yesmaximal, characteristic, complemented
8#21446641C211yesmaximal, characteristic, complemented
9#21446623C211yesmaximal, characteristic, complemented
10#21445829C211yesmaximal, characteristic, complemented
11#21445828C211yesmaximal, characteristic, complemented
12#21445818C211yesmaximal, characteristic, complemented
13#21445643C211yesmaximal, characteristic, complemented
14#21445633C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C22×#11758222—21no—
17#16840433—24no—
18#16840433C418yescomplemented
19C2×#14519774C2211yescharacteristic
20C2×#14519773C2211yescharacteristic
21C2×#14519773C2211yescharacteristic
22C2×#14519751—21no—
23C2×#14519750—21no—
24C2×#14519750—21no—
25C2×C4×Dic122C2211yescharacteristic
26C2×#14519739C2211yescharacteristic
27C2×#14519739C2211yescharacteristic
28#16839890—24no—
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×#14519706C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519687C2211yescharacteristic
43C2×C8×Dic61C2211yescharacteristic
44#16839666—21no—
45#16839646—21no—
46#16839645—21no—
47#16839631C2211yescharacteristic
48#16839628C2211yescharacteristic
49#16839627C2211yescharacteristic
50C4⋊C4×Dic61C2211yescharacteristic
51C4⋊C4×Dic61C2211yescharacteristic
52C4×#11758196—21no—
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C4×C4⋊C4×C61C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C2×#11758222—28no—
63C2×#11758222—44no—
64C2×#11758222—44no—
65C22×Dic122D411yescharacteristic
66C22×D244—21no—
67C22×D244—21no—
68C22×D244C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C22×C22⋊D61—21no—
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C22×C22⋊D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78#14519774—22no—
79#14519774C2×C414yes—
80#14519773—22no—
81#14519773—22no—
82#14519773C2×C414yes—
83#14519773C2×C414yes—
84#14519751—28no—
85#14519750—28no—
86#14519750—28no—
87C4×Dic122C2×C414yes—
88C4×Dic122D414yes—
89#14519739—22no—
90#14519739—22no—
91#14519739C2×C414yes—
92#14519739C2×C414yes—
93C2×C4⋊Dic61D411yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196D411yescharacteristic
99C2×#11758196D411yescharacteristic
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61C2311yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106C4⋊#92418—22no—
107#14519706—22no—
108#14519706—22no—
109#14519699—22no—
110#14519699—22no—
111#14519699—41no—
112#14519699—41no—
113#14519698—41no—
114#14519698—41no—
115#14519697—22no—
116#14519697—22no—
117#14519697—41no—
118#14519697—41no—
119#14519687—22no—
120C8×Dic61—22no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127C22×D4×C61C2311yescharacteristic
128C23×C4×C61—21no—
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C4×D4×C61—22no—
132C4×D4×C61C2×C414yes—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C42×C61—21no—
138C2×C42×C61C2311yescharacteristic
139#102×C61—22no—
140#102×C61—22no—
141#97×C61—22no—
142#95×C61—21no—
143C24×C61—21no—
144C23×D61—21no—
145C23×D61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61C22×C412yes—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—24no—
155C22×C4×C61—21no—
156C22×C4×C61—42no—
157C22×C4×C61—42no—
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2411yescharacteristic
161C2×C22⋊D61—24no—
162C2×C22⋊D61—24no—
163C2×C22⋊D61—24no—
164C2×C22⋊D61—24no—
165C2×C22⋊D61—42no—
166C2×C22⋊D61—42no—
167C2×C22⋊D61—42no—
168C2×C22⋊D61—42no—
169C2×C22⋊D61—81no—
170C2×C22⋊D61—81no—
171C2×C22⋊D61—81no—
172C2×C22⋊D61—81no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179#11758222—432no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—24no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—24no—
192C2×D244—42no—
193C2×D244—42no—
194C2×D244—81no—
195C2×D244—81no—
196C2×D244C22×C412yes—
197C2×D244C22×C412yes—
198C2×C4×D61—24no—
199C2×C4×D61—24no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×Dic122—22no—
205C2×Dic122—22no—
206C2×Dic122C22⋊C414yes—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61#4112yescomplemented
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61C22×C412yes—
218C4⋊C4×C61#4112yescomplemented
219C22⋊C4×C61—24no—
220C42×C61—81no—
221C42×C61C22×C412yes—
222C42×C61C2×D412yes—
223#11758198—24no—
224#11758198—24no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61C22⋊C414yes—
230#11758196—42no—
231#11758196—81no—
232#11758196C22⋊C414yes—
233#11758196C22⋊C414yes—
234C4×Dic61—42no—
235C4×Dic61—81no—
236C4×Dic61C22×C412yes—
237C4×Dic61C22×C412yes—
238C4×Dic61C2×D412yes—
239C4×Dic61C2×D412yes—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
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—22no—
255C22×D61—22no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268D4×C61—22no—
269D4×C61—22no—
270D4×C61—41no—
271D4×C61—41no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—48no—
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×C61C2×C22⋊C412yes—
287C2×C4×C61C2×C22⋊C412yes—
288C2×C4×C61C23×C411yescharacteristic
289C2×C4×C61C22×D411yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61H(5,𝔽2)11yescharacteristic
293C2×C4×C612−1+411yescharacteristic
294C22⋊D61—48no—
295C22⋊D61—48no—
296C22⋊D61—84no—
297C22⋊D61—84no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61C2×C22⋊C412yes—
311C2×Dic61C2×C22⋊C412yes—
312C2×Dic61C2×C22⋊C412yes—
313C2×Dic61C2×C22⋊C412yes—
314C2×Dic61AGL(1,ℤ/8)12yes—
315C2×Dic61AGL(1,ℤ/8)12yes—
316D244—22no—
317D244—22no—
318D244—22no—
319D244—22no—
320D244—48no—
321D244—41no—
322D244—41no—
323D244—41no—
324D244—41no—
325D244—84no—
326C4×D61—48no—
327C4×D61—48no—
328Dic122—28no—
329C8×C61—22no—
330C8×C61—41no—
331#92418—41no—
332#92418—41no—
333#22545—611nomaximal, Sylow
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61C22×C22⋊C411yescharacteristic
342C22×C61#54811yescharacteristic
343C22×C61#55011yescharacteristic
344C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
345C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C61#57611yescharacteristic
347C22×C61#57711yescharacteristic
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—42no—
354C2×D61—81no—
355C2×D61—81no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C2×D61—81no—
361C2×D61—81no—
362C4×C61—22no—
363C4×C61—22no—
364C4×C61—42no—
365C4×C61—42no—
366C4×C61—81no—
367C4×C61C4×#4111yescharacteristic
368C4×C61#52011yescharacteristic
369C4×C61#54811yescharacteristic
370C4×C61#55011yescharacteristic
371Dic61—22no—
372Dic61—22no—
373Dic61—22no—
374Dic61—81no—
375Dic61—81no—
376Dic61#41814yes—
377C2×#550—611no—
378C2×#446—611no—
379#2355—611no—
380#1982—611no—
381#1982—611no—
382#1982—611no—
383#1961—611no—
384#1961—611no—
385#1957—611no—
386#1804—611no—
387#1804—611no—
388#1802—611no—
389#1762—611no—
390#1762D6111yescharacteristic, complemented
391C4×#102—611no—
392C2×C61—82no—
393C2×C61#234111yescharacteristic
394C2×C61C2×#41811yescharacteristic
395C2×C61#289711yescharacteristic
396C2×C61#336611yescharacteristic
397C2×C61#336811yescharacteristic
398C2×C61#339711yescharacteristic
399C2×C61#339911yescharacteristic
400D61—82no—
401D61—82no—
402C22×#41—1221no—
403#550—618no—
404#550—1224no—
405C2×#127—611no—
406C2×#127—611no—
407C2×#127—611no—
408C2×#121—1221no—
409C2×#121—1221no—
410C2×#121—1221no—
411C2×C4×Q8—611no—
412C2×C4×D4—611no—
413C2×C4×D4—611no—
414C2×C4×D4C2×D6111yescharacteristic
415#446—1224no—
416C2×C4⋊C8—611no—
417C2×C4⋊C8—611no—
418C2×C4⋊C8—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×#102—611no—
427C2×#102—611no—
428C2×#102—611no—
429C2×#102C2×D6111yescharacteristic
430C2×#102C2×D6111yescharacteristic
431C2×#97—611no—
432C2×#97C2×D6111yescharacteristic
433C2×C4×C8—611no—
434#391—1221no—
435#387—1221no—
436#387—1221no—
437#384—611no—
438#382—611no—
439#382—611no—
440C4×C4⋊C4—611no—
441C4×C4⋊C4—611no—
442C4×C4⋊C4—1221no—
443C4×C4⋊C4C2×D6111yescharacteristic
444#340—611no—
445#340—611no—
446#340C2×D6111yescharacteristic
447#340C2×D6111yescharacteristic
448C61#2254511yescharacteristic, complemented, Sylow
449C2×#41—1228no—
450C2×#41—2444no—
451C2×#41—2444no—
452C22×Q8—611no—
453C22×D4—611no—
454C22×D4—611no—
455C22×D4—1221no—
456C22×D4—1221no—
457C22×D4—1221no—
458C22×D4—1221no—
459C22×D4—1221no—
460C22×D4—1221no—
461C22×D4C22×D6111yescharacteristic
462C23×C4—21no—
463C23×C4—1221no—
464C23×C4—1221no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8C22×D6111yescharacteristic
468C22×C8C22×D6111yescharacteristic
469#127—614no—
470#127—614no—
471#127—614no—
472#127—1222no—
473#127—1222no—
474#127—1222no—
475#121—1228no—
476#121—1228no—
477#121—1228no—
478C4×Q8—614no—
479C4×Q8—614no—
480C4×D4—22no—
481C4×D4—614no—
482C4×D4—614no—
483C4×D4—1222no—
484C4×D4—1222no—
485C4×D4C4×D6114yes—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4C22×D6111yescharacteristic
494C2×C4⋊C4C22×D6111yescharacteristic
495C2×C4⋊C4C22×D6111yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C42—21no—
500C2×C42—611no—
501C2×C42—611no—
502C2×C42—1221no—
503C2×C42—1221no—
504C2×C42C22×D6111yescharacteristic
505C4⋊C8—1222no—
506C4⋊C8—1222no—
507C4⋊C8—1222no—
508#102—22no—
509#102—22no—
510#102—1222no—
511#102—1222no—
512#102—1222no—
513#102—1222no—
514#102—2441no—
515#102—2441no—
516#102—2441no—
517#102—2441no—
518#102—2441no—
519#102—2441no—
520#97—22no—
521#97—1222no—
522C4×C8—1222no—
523#95—21no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528#95—1221no—
529#95—1221no—
530C24—21no—
531C24—1221no—
532C24—1221no—
533#41—24432no—
534C2×Q8—614no—
535C2×Q8—1222no—
536C2×Q8—1222no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—612no—
543C2×D4—612no—
544C2×D4—1224no—
545C2×D4—1224no—
546C2×D4—1224no—
547C2×D4—1224no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—1221no—
551C2×D4—1221no—
552C2×D4—1221no—
553C2×D4—1221no—
554C2×D4—1221no—
555C2×D4—1221no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—1224no—
559C2×D4—1224no—
560C2×D4—4881no—
561C2×D4—4881no—
562C2×D4—4881no—
563C2×D4—4881no—
564C2×D4—4881no—
565C2×D4—4881no—
566C2×D4—2442no—
567C2×D4—2442no—
568C2×D4—2442no—
569C2×D4—2442no—
570C2×D4—2442no—
571C2×D4—2442no—
572C2×D4C2×C4×D6112yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—21no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—1224no—
584C22×C4—1224no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—2442no—
588C22×C4—2442no—
589C22×C4—2442no—
590C22×C4—2442no—
591C22×C4D4×D6111yescharacteristic
592C22×C4D4×D6111yescharacteristic
593C22×C4C23×D6111yescharacteristic
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8#1175822212yescomplemented
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—614no—
611C4⋊C4—614no—
612C4⋊C4—614no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—4881no—
618C4⋊C4—2442no—
619C4⋊C4C2×C4×D6112yes—
620C4⋊C4#1175822212yescomplemented
621C22⋊C4—24no—
622C22⋊C4—1224no—
623C22⋊C4—1224no—
624C42—81no—
625C42—612no—
626C42—612no—
627C42—612no—
628C42—612no—
629C42—4881no—
630C42—2442no—
631C42C2×C4×D6112yes—
632C42D4×D6112yes—
633C23—22no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—1222no—
641C23—1222no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23C2×D4×D6111yescharacteristic
655Q8—1228no—
656D4—22no—
657D4—22no—
658D4—41no—
659D4—41no—
660D4—1222no—
661D4—1222no—
662D4—1222no—
663D4—1222no—
664D4—4884no—
665D4—4884no—
666D4—4884no—
667D4—2448no—
668D4—2448no—
669D4—2448no—
670D4—2441no—
671D4—2441no—
672D4—2441no—
673D4—2441no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—48no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—612no—
689C2×C4—612no—
690C2×C4—612no—
691C2×C4—612no—
692C2×C4—612no—
693C2×C4—612no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—2448no—
701C2×C4—2448no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4C22⋊C4×D6112yes—
709C2×C4C22⋊C4×D6112yes—
710C2×C4C22×C4×D6111yescharacteristic
711C2×C4C2×D4×D6111yescharacteristic
712C2×C4C2×#1175822211yescharacteristic
713C2×C4C2×#1175822211yescharacteristic
714C2×C4#1451982311yescharacteristic
715C2×C4#1451982411yescharacteristic
716C8—22no—
717C8—41no—
718C8—2441no—
719C8—2441no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—4881no—
728C22—4881no—
729C22—4881no—
730C22—4881no—
731C22—4881no—
732C22—4881no—
733C22—4881no—
734C22—4881no—
735C22—2442no—
736C22—2442no—
737C22—2442no—
738C22—2442no—
739C22—2442no—
740C22—2442no—
741C22C2×C22⋊C4×D6111yescharacteristic
742C22#1684042111yescharacteristic
743C22#1684043311yescharacteristic
744C22AGL(1,ℤ/8)×D6111yescharacteristic
745C22AGL(1,ℤ/8)×D6111yescharacteristic
746C22#1684056611yescharacteristic
747C22#1684057111yescharacteristic
748C4—22no—
749C4—22no—
750C4—42no—
751C4—42no—
752C4—81no—
753C4—614no—
754C4—1222no—
755C4—1222no—
756C4—1222no—
757C4—4881no—
758C4—4881no—
759C4C4×#1175822211yescharacteristic
760C4#1684024211yescharacteristic
761C4#1684042111yescharacteristic
762C4#1684043311yescharacteristic
763C2—82no—
764C2—4882no—
765C2—4882no—
766C2#2144865911yescharacteristic
767C2#418×D6111yescharacteristic
768C2#2145434311yescharacteristic
769C2#2145852711yescharacteristic
770C2#2145854911yescharacteristic
771C2#2145884011yescharacteristic
772C2#2145886211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1762C2
socleC23×C61C22×D4
prime radicalC2×#16840433C2
cosocleC22×C4×C61C24
hypercenter#1762D61
hypocenterC61#22545
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#16839890C2semidirect
3. #21448777C2semidirect
4. #21446746C2semidirect
5. #21446744C2semidirect
6. #21446744C2semidirect
7. #21446643C2semidirect
8. #21446641C2semidirect
9. #21446623C2semidirect
10. #21445829C2semidirect
11. #21445828C2semidirect
12. #21445818C2semidirect
13. #21445643C2semidirect
14. #21445633C2semidirect
15. C61×#1762C2semidirect
18. #16840433C4semidirect
212. C2×C8×C61#41semidirect
218. C4⋊C4×C61#41semidirect
390. #1762D61semidirect
448. C61#22545semidirect
605. C2×C8#11758222semidirect
620. C4⋊C4#11758222semidirect

Maximal subgroups

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

subgroupindex
C2×#168404332
C2×#168398902
#214487772
#214467462
#214467442
#214466432
#214466412
#214466232
#214458292
#214458282
#214458182
#214456432
#214456332
C61×#17622
#2254561