Finite Group Databasebeta

← #29700320

Subgroups — #29700320

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×#16839909C211yesmaximal, characteristic
2C2×#16839864C211yesmaximal, characteristic, complemented
3C2×#16839759C211yesmaximal, characteristic, complemented
4#21448855C211yesmaximal, characteristic, complemented
5#21448659C211yesmaximal, characteristic, complemented
6#21446695C211yesmaximal, characteristic, complemented
7#21446516C211yesmaximal, characteristic, complemented
8#21446440C211yesmaximal, characteristic, complemented
9#21446247C211yesmaximal, characteristic, complemented
10#21446173C211yesmaximal, characteristic, complemented
11#21446166C211yesmaximal, characteristic, complemented
12#21446090C211yesmaximal, characteristic, complemented
13#21446020C211yesmaximal, characteristic, complemented
14#21445650C211yesmaximal, characteristic, complemented
15C61×#1752C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×D488C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×#14519736C2211yescharacteristic
24#16839909C418yescomplemented
25#16839864—24no—
26C2×#14519711C2211yescharacteristic
27C2×#14519709C2211yescharacteristic
28#16839759—24no—
29C2×#14519702C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37#16839664C2211yescharacteristic
38#16839664C2211yescharacteristic
39#16839664C2211yescharacteristic
40#16839662—21no—
41#16839662—21no—
42#16839662—21no—
43#16839660C2211yescharacteristic
44#16839651—21no—
45#16839638—21no—
46#16839622C2211yescharacteristic
47#16839621—21no—
48C4×C4⋊Dic61C2211yescharacteristic
49#16839609—21no—
50#16839609—21no—
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C4×C22⋊C4×C61C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222C2×C414yescomplemented
68C22×Dic122C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C2×#11758190—22no—
76C2×#11758190—22no—
77C2×#11758190C2×C414yes—
78C2×D488—41no—
79C2×D488—41no—
80C2×D488C2×C414yes—
81#14519751—22no—
82#14519751C2×C414yes—
83C4×Dic122—22no—
84C4×Dic122—22no—
85C4×Dic122—41no—
86C4×Dic122—41no—
87C4×D244—22no—
88C4×D244—41no—
89#14519736—22no—
90#14519736—41no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61—21no—
113#14519711—22no—
114#14519709—41no—
115#14519702—22no—
116#14519702C2×C414yescomplemented
117#14519702D414yescomplemented
118#14519699—22no—
119#14519699—22no—
120#14519699—22no—
121#14519699—41no—
122#14519699C2×C414yescomplemented
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126C23×C4×C61C2311yescharacteristic
127C22×C8×C61—22no—
128C22×C8×C61—22no—
129C22×C8×C61—41no—
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C2×C22⋊C4×C61D411yescharacteristic
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C22⋊C8×C61C2×C414yescomplemented
139#97×C61—22no—
140#97×C61—41no—
141#95×C61D411yescharacteristic
142#95×C61D411yescharacteristic
143C24×C61C2×D411yescharacteristic
144C23×D61—21no—
145C23×D61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61C22×C412yes—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61#4112yes—
157C22×C4×C61C2411yescharacteristic
158C2×C22⋊D61—24no—
159C2×C22⋊D61—24no—
160C2×C22⋊D61—42no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61—81no—
163C2×C22⋊D61—81no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170#11758222—28no—
171#11758222—44no—
172#11758222—44no—
173#11758222—44no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244C22×C412yes—
185C2×D244C22×C412yes—
186C2×C4×D61—24no—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—81no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122C22×C412yes—
196C2×Dic122C2×D412yes—
197C2×Dic122#4112yes—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—44no—
208C2×C8×C61C22×C412yes—
209C2×C8×C61C22×C412yes—
210C2×C8×C61C2×D412yes—
211C22⋊C4×C61—41no—
212C22⋊C4×C61—41no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—21no—
216C42×C61—21no—
217C22⋊Dic61—42no—
218C22⋊Dic61—81no—
219#11758198—24no—
220#11758198—42no—
221#11758198—42no—
222#11758198—42no—
223#11758198—42no—
224#11758198—81no—
225#11758198—81no—
226#11758198—81no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61C22×C412yes—
236C4⋊Dic61C2×D412yes—
237#11758196—42no—
238#11758196—42no—
239#11758196—81no—
240C4×Dic61—42no—
241C4×Dic61—42no—
242C4×Dic61—42no—
243C4×Dic61—81no—
244D488—44no—
245#11758190—28no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61C4×D412yes—
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—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
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×C61C4×D412yes—
287C2×C4×C61C23×C411yescharacteristic
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61H(5,𝔽2)11yescharacteristic
292C2×C4×C61H(5,𝔽2)11yescharacteristic
293C22⋊D61—48no—
294C22⋊D61—84no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313D244—22no—
314D244—22no—
315D244—22no—
316D244—22no—
317D244—41no—
318D244—41no—
319D244—41no—
320D244—41no—
321C4×D61—48no—
322C4×D61—84no—
323Dic122—22no—
324Dic122—22no—
325Dic122—22no—
326Dic122C4×D414yes—
327C8×C61—22no—
328C8×C61—22no—
329C8×C61—22no—
330C8×C61—41no—
331#22857—611nomaximal, Sylow
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61C2×C4×D411yescharacteristic
340C22×C61D4211yescharacteristic
341C22×C61#54611yescharacteristic
342C22×C61#57511yescharacteristic
343C22×C61#57511yescharacteristic
344C22×C61#57611yescharacteristic
345C22×C61#57711yescharacteristic
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—81no—
353C2×D61—81no—
354C2×D61—81no—
355C2×D61—81no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C4×C61—22no—
361C4×C61—41no—
362C4×C61—41no—
363C4×C61—41no—
364C4×C61—41no—
365C4×C61C2×C4×D411yescharacteristic
366C4×C61#51811yescharacteristic
367C4×C61#54611yescharacteristic
368C4×C61#55111yescharacteristic
369Dic61—24no—
370Dic61—42no—
371Dic61—42no—
372Dic61—81no—
373Dic61—81no—
374Dic61—81no—
375C2×#449—611no—
376C2×#440—611no—
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#1752D6111yescharacteristic, complemented
390C2×C61—42no—
391C2×C61#235811yescharacteristic
392C2×C61#294311yescharacteristic
393C2×C61#294611yescharacteristic
394C2×C61#326811yescharacteristic
395C2×C61#327111yescharacteristic
396C2×C61#330911yescharacteristic
397C2×C61#332111yescharacteristic
398D61—82no—
399D61—82no—
400C22×#41—611no—
401C22×SD16—611no—
402C22×D8—611no—
403C23×C8C2×D6111yescharacteristic
404C2×#121—611no—
405C2×C4×Q8—611no—
406C2×C4×Q8—611no—
407C2×C4×D4—611no—
408C2×#117—611no—
409#449—618no—
410#440—1224no—
411C2×#107—611no—
412C2×#106—611no—
413#416—1224no—
414C2×#103—611no—
415C2×#103—611no—
416C2×#103—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×C22⋊C8C2×D6111yescharacteristic
423C2×#97C2×D6111yescharacteristic
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—1221no—
438C4×C22⋊C4—1221no—
439C4×C22⋊C4C2×D6111yescharacteristic
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#336C2×D6111yescharacteristic
445#336C2×D6111yescharacteristic
446C61#2285711yescharacteristic, complemented, Sylow
447C2×#41—614no—
448C2×#41—1222no—
449C2×#41—1222no—
450C2×#41—1222no—
451C2×#41—2441no—
452C2×#41—2441no—
453C22×Q8—611no—
454C22×D4—611no—
455C22×D4—611no—
456C22×D4—1221no—
457C22×D4—1221no—
458C23×C4—1221no—
459C23×C4—1221no—
460C23×C4C22×D6111yescharacteristic
461C2×SD16—614no—
462C2×SD16—1222no—
463C2×SD16—1222no—
464C2×D8—614no—
465C2×D8—2441no—
466C2×D8—2441no—
467C22×C8—22no—
468C22×C8—22no—
469C22×C8—41no—
470C22×C8C22×D6111yescharacteristic
471C22×C8C22×D6111yescharacteristic
472C22×C8C22×D6111yescharacteristic
473C22×C8C22×D6111yescharacteristic
474#121—614no—
475#121—1222no—
476C4×Q8—1222no—
477C4×Q8—1222no—
478C4×Q8—2441no—
479C4×Q8—2441no—
480C4×D4—1222no—
481C4×D4—2441no—
482#117—1222no—
483#117—2441no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
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⋊C4D24411yescharacteristic
503C2×C22⋊C4D24411yescharacteristic
504C2×C42—1221no—
505C2×C42—1221no—
506C2×C42—1221no—
507C2×C42—1221no—
508C2×C42C22×D6111yescharacteristic
509C2×C42C22×D6111yescharacteristic
510#107—1222no—
511#106—2441no—
512#103—614no—
513#103—614no—
514#103—1222no—
515#102—614no—
516#102—1222no—
517#102—1222no—
518#102—1222no—
519#102—2441no—
520C22⋊C8C4×D6114yescomplemented
521#97—22no—
522#97—41no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526#95D24411yescharacteristic
527#95D24411yescharacteristic
528C24—1221no—
529C24—1221no—
530C24C2×D24411yescharacteristic
531#41—1228no—
532#41—2444no—
533#41—2444no—
534#41—2444no—
535C2×Q8—612no—
536C2×Q8—612no—
537C2×Q8—612no—
538C2×Q8—1221no—
539C2×Q8—1221no—
540C2×Q8—1221no—
541C2×D4—612no—
542C2×D4—612no—
543C2×D4—1224no—
544C2×D4—1224no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—1221no—
551C2×D4—1221no—
552C2×D4—1221no—
553C2×D4—1221no—
554C2×D4—1221no—
555C2×D4—4881no—
556C2×D4—4881no—
557C2×D4—2442no—
558C2×D4—2442no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1224no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—4881no—
571C22×C4—2442no—
572C22×C4—2442no—
573C22×C4—2442no—
574C22×C4—2442no—
575C22×C4C2×C4×D6112yes—
576C22×C4C2×D24411yescharacteristic
577C22×C4C2×D24411yescharacteristic
578C22×C4C2×D24411yescharacteristic
579C22×C4C2×D24411yescharacteristic
580C22×C4C2×D24411yescharacteristic
581C22×C4#1175822212yes—
582C22×C4C23×D6111yescharacteristic
583SD16—1228no—
584D8—2444no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—44no—
595C2×C8C2×C4×D6112yes—
596C2×C8C2×C4×D6112yes—
597C2×C8D4×D6112yes—
598C4⋊C4—612no—
599C4⋊C4—612no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—4881no—
609C4⋊C4—2442no—
610C4⋊C4—2442no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C22⋊C4—1224no—
614C22⋊C4—4881no—
615C22⋊C4—4881no—
616C22⋊C4—4881no—
617C22⋊C4—4881no—
618C22⋊C4—2442no—
619C22⋊C4—2442no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—4881no—
628C42—2442no—
629C42—2442no—
630C42—2442no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—1222no—
638C23—1222no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23C4×D24412yes—
652C23C22×D24411yescharacteristic
653Q8—614no—
654Q8—1222no—
655Q8—1222no—
656Q8—1222no—
657D4—1222no—
658D4—1222no—
659D4—1222no—
660D4—1222no—
661D4—4884no—
662D4—2448no—
663D4—2441no—
664D4—2441no—
665D4—2441no—
666D4—2441no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—4884no—
691C2×C4—2448no—
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×C4C4×D24412yes—
706C2×C4C22×C4×D6111yescharacteristic
707C2×C4C2×D4×D6111yescharacteristic
708C2×C4#41×D6111yescharacteristic
709C2×C4C2×#1175822211yescharacteristic
710C2×C4#1451982211yescharacteristic
711C2×C4#1451982311yescharacteristic
712C8—22no—
713C8—22no—
714C8—22no—
715C8—41no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—4881no—
724C22—4881no—
725C22—4881no—
726C22—4881no—
727C22—4881no—
728C22—4881no—
729C22—4881no—
730C22—4881no—
731C22—2442no—
732C22—2442no—
733C22—2442no—
734C22—2442no—
735C22—2442no—
736C22—2442no—
737C22C2×C4×D24411yescharacteristic
738C22D4×D24411yescharacteristic
739C22#1684040711yescharacteristic
740C22#1684056211yescharacteristic
741C22#1684056211yescharacteristic
742C22#1684056711yescharacteristic
743C22#1684057411yescharacteristic
744C4—22no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—1224no—
750C4—4881no—
751C4—4881no—
752C4—4881no—
753C4—2442no—
754C4—2442no—
755C4C4×D4×D6111yescharacteristic
756C4#1684023411yescharacteristic
757C4#1684040211yescharacteristic
758C4#1684043611yescharacteristic
759C2—42no—
760C2—4882no—
761C2—4882no—
762C2#2144880111yescharacteristic
763C2#2145462111yescharacteristic
764C2#2145465311yescharacteristic
765C2#2145736411yescharacteristic
766C2#2145740911yescharacteristic
767C2#2145782711yescharacteristic
768C2#2145800711yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1752C2
socleC23×C61C22×D4
prime radicalC2×#16839909C2
cosocleC22×C4×C61C24
hypercenter#1752D61
hypocenterC61#22857
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
2. C2×#16839864C2semidirect
3. C2×#16839759C2semidirect
4. #21448855C2semidirect
5. #21448659C2semidirect
6. #21446695C2semidirect
7. #21446516C2semidirect
8. #21446440C2semidirect
9. #21446247C2semidirect
10. #21446173C2semidirect
11. #21446166C2semidirect
12. #21446090C2semidirect
13. #21446020C2semidirect
14. #21445650C2semidirect
15. C61×#1752C2semidirect
24. #16839909C4semidirect
67. C2×#11758222C2×C4semidirect
116. #14519702C2×C4semidirect
117. #14519702D4semidirect
122. #14519699C2×C4semidirect
138. C22⋊C8×C61C2×C4semidirect
389. #1752D61semidirect
446. C61#22857semidirect
520. C22⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399092
C2×#168398642
C2×#168397592
#214488552
#214486592
#214466952
#214465162
#214464402
#214462472
#214461732
#214461662
#214460902
#214460202
#214456502
C61×#17522
#2285761