Finite Group Databasebeta

← #35311356

Subgroups — #35311356

Order 21248.

1326 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581713C211yesmaximal, characteristic
2C2×#19127604C211yesmaximal, characteristic
3C2×#19127570C211yesmaximal, characteristic, complemented
4C2×#19127464C211yesmaximal, characteristic, complemented
5C2×#19127463C211yesmaximal, characteristic, complemented
6C2×#19127455C211yesmaximal, characteristic, complemented
7C22×#102×C83C211yesmaximal, characteristic
8C23×C83⋊C8C2211yescharacteristic
9C22×C4⋊Dic83C2211yescharacteristic
10C22×C4⋊Dic83C2211yescharacteristic
11C22×Dic83⋊C4—22no—
12C22×C22⋊Dic83—22no—
13C22×C4×Dic83C2211yescharacteristic
14C2×#14581713—22no—
15C2×#14581713—22no—
16C2×#14581713—22no—
17#19127604—22no—
18#19127604C414yescomplemented
19#19127570—22no—
20#19127570—22no—
21#19127464—22no—
22#19127463—22no—
23#19127455—22no—
24C23×D4×C83C2211yescharacteristic
25C23×C8×C83C2211yescharacteristic
26C22×C4⋊C4×C83C2211yescharacteristic
27C2×#102×C83—22no—
28C2×#102×C83—22no—
29C2×#102×C83—22no—
30C23×Dic83—21no—
31C23×Dic83—21no—
32C23×Dic83D412yes—
33C22×C83⋊C8—21no—
34C22×C83⋊C8—21no—
35C22×C83⋊C8—21no—
36C22×C83⋊C8—21no—
37C22×C83⋊C8—21no—
38C22×C83⋊C8—21no—
39C22×C83⋊C8D412yes—
40C2×C4⋊Dic83—21no—
41C2×C4⋊Dic83—21no—
42C2×C4⋊Dic83—21no—
43C2×C4⋊Dic83—21no—
44C2×C4⋊Dic83—21no—
45C2×C4⋊Dic83—21no—
46C2×C4⋊Dic83—21no—
47C2×C4⋊Dic83—21no—
48C2×C4⋊Dic83—21no—
49C2×C4⋊Dic83—21no—
50C2×C4⋊Dic83C2×C412yes—
51C2×C4⋊Dic83D412yes—
52C2×Dic83⋊C4—28no—
53C2×Dic83⋊C4—44no—
54C2×Dic83⋊C4—44no—
55C2×C22⋊Dic83—28no—
56C2×C22⋊Dic83—44no—
57C2×C22⋊Dic83—44no—
58C2×C4×Dic83—21no—
59C2×C4×Dic83—21no—
60C2×C4×Dic83—21no—
61C2×C4×Dic83—21no—
62C2×C4×Dic83C2×C412yes—
63C2×C4×Dic83D412yes—
64#14581713—28no—
65C25×C83—21no—
66C22×D4×C83—21no—
67C22×D4×C83—21no—
68C22×D4×C83—21no—
69C22×D4×C83—21no—
70C22×D4×C83—21no—
71C22×D4×C83—21no—
72C22×D4×C83—21no—
73C22×D4×C83—21no—
74C22×D4×C83—21no—
75C22×D4×C83—21no—
76C22×D4×C83—21no—
77C22×D4×C83C2×C412yes—
78C22×D4×C83D412yes—
79C22×D4×C83Q812yes—
80C23×C4×C83—21no—
81C23×C4×C83C2311yescharacteristic
82C22×C8×C83—21no—
83C22×C8×C83—21no—
84C22×C8×C83—21no—
85C22×C8×C83—21no—
86C22×C8×C83—21no—
87C22×C8×C83—21no—
88C22×C8×C83D412yes—
89C2×C4⋊C4×C83—21no—
90C2×C4⋊C4×C83—21no—
91C2×C4⋊C4×C83—21no—
92C2×C4⋊C4×C83—21no—
93C2×C4⋊C4×C83—21no—
94C2×C4⋊C4×C83D412yes—
95#102×C83—28no—
96C22×Dic83—22no—
97C22×Dic83—22no—
98C22×Dic83—22no—
99C22×Dic83—22no—
100C22×Dic83—22no—
101C22×Dic83—22no—
102C22×Dic83—41no—
103C22×Dic83—41no—
104C22×Dic83—41no—
105C22×Dic83—41no—
106C22×Dic83—42no—
107C22×Dic83—42no—
108C22×Dic83—42no—
109C22×Dic83—42no—
110C22×Dic83C22⋊C414yes—
111C22×Dic83D814yes—
112C22×Dic83SD1614yes—
113C2×C83⋊C8—22no—
114C2×C83⋊C8—22no—
115C2×C83⋊C8—22no—
116C2×C83⋊C8—41no—
117C2×C83⋊C8—41no—
118C2×C83⋊C8—41no—
119C2×C83⋊C8—41no—
120C4⋊Dic83—22no—
121C4⋊Dic83—22no—
122C4⋊Dic83—22no—
123C4⋊Dic83—22no—
124C4⋊Dic83—41no—
125C4⋊Dic83—41no—
126C4⋊Dic83—41no—
127C4⋊Dic83—41no—
128Dic83⋊C4—416no—
129C22⋊Dic83—416no—
130C4×Dic83—22no—
131C4×Dic83—22no—
132C4×Dic83—22no—
133C4×Dic83—22no—
134C24×C83—22no—
135C24×C83—22no—
136C24×C83—22no—
137C24×C83—41no—
138C24×C83—41no—
139C24×C83—41no—
140C24×C83—41no—
141C24×C83—42no—
142C24×C83—42no—
143C24×C83—42no—
144C24×C83—42no—
145C24×C83C2×D411yescharacteristic
146C2×D4×C83—22no—
147C2×D4×C83—22no—
148C2×D4×C83—22no—
149C2×D4×C83—22no—
150C2×D4×C83—22no—
151C2×D4×C83—22no—
152C2×D4×C83—22no—
153C2×D4×C83—22no—
154C2×D4×C83—22no—
155C2×D4×C83—22no—
156C2×D4×C83—22no—
157C2×D4×C83—22no—
158C2×D4×C83—22no—
159C2×D4×C83—22no—
160C2×D4×C83—22no—
161C2×D4×C83—41no—
162C2×D4×C83—41no—
163C2×D4×C83—41no—
164C2×D4×C83—41no—
165C2×D4×C83—41no—
166C2×D4×C83—41no—
167C2×D4×C83—41no—
168C2×D4×C83—41no—
169C2×D4×C83—41no—
170C2×D4×C83—41no—
171C2×D4×C83—41no—
172C2×D4×C83—41no—
173C2×D4×C83C4⋊C414yescomplemented
174C22×C4×C83—22no—
175C22×C4×C83—41no—
176C22×C4×C83—41no—
177C22×C4×C83—42no—
178C22×C4×C83—42no—
179C22×C4×C83C22×C411yescharacteristic
180C22×C4×C83C2×D411yescharacteristic
181C22×C4×C83C2×D411yescharacteristic
182C22×C4×C83C2×D411yescharacteristic
183C22×C4×C83C2×D411yescharacteristic
184C22×C4×C83C2×D411yescharacteristic
185C22×C4×C83C2×D411yescharacteristic
186C22×C4×C83C2×Q811yescharacteristic
187C22×C4×C83#4111yescharacteristic
188C22×C4×C83#4111yescharacteristic
189C22×C4×C83#4111yescharacteristic
190C22×C4×C83#4111yescharacteristic
191C22×C4×C83#4111yescharacteristic
192C22×C4×C83#4111yescharacteristic
193C2×C8×C83—22no—
194C2×C8×C83—22no—
195C2×C8×C83—22no—
196C2×C8×C83—41no—
197C2×C8×C83—41no—
198C2×C8×C83—41no—
199C2×C8×C83—41no—
200C4⋊C4×C83—22no—
201C4⋊C4×C83—22no—
202C4⋊C4×C83—41no—
203C4⋊C4×C83—41no—
204C23×C83—24no—
205C23×C83—42no—
206C23×C83—42no—
207C23×C83—42no—
208C23×C83—42no—
209C23×C83—42no—
210C23×C83—42no—
211C23×C83—44no—
212C23×C83—44no—
213C23×C83—44no—
214C23×C83—44no—
215C23×C83—44no—
216C23×C83—44no—
217C23×C83—82no—
218C23×C83—82no—
219C23×C83—82no—
220C23×C83—82no—
221C23×C83—82no—
222C23×C83—82no—
223C23×C83—81no—
224C23×C83—81no—
225C23×C83—81no—
226C23×C83—81no—
227C23×C83C2×C22⋊C411yescharacteristic
228C23×C83#12011yescharacteristic
229C23×C83#12111yescharacteristic
230C23×C83C22⋊Q811yescharacteristic
231C23×C83#12311yescharacteristic
232C23×C83#12411yescharacteristic
233C23×C83#12711yescharacteristic
234C23×C83C2×D812yes—
235C23×C83C2×SD1612yes—
236C23×C83AGL(1,ℤ/8)12yes—
237C23×C83#13712yes—
238D4×C83—24no—
239D4×C83—24no—
240D4×C83—42no—
241D4×C83—42no—
242D4×C83—42no—
243D4×C83—42no—
244D4×C83—42no—
245D4×C83—42no—
246C2×C4×C83—42no—
247C2×C4×C83—44no—
248C2×C4×C83—82no—
249C2×C4×C83—81no—
250C2×C4×C83—81no—
251C2×C4×C83C2×C4⋊C411yescharacteristic
252C2×C4×C83#11711yescharacteristic
253C2×C4×C83C4×D411yescharacteristic
254C2×C4×C83C4×D411yescharacteristic
255C2×C4×C83C4×D411yescharacteristic
256C2×C4×C83C4×D411yescharacteristic
257C2×C4×C83#12011yescharacteristic
258C2×C4×C83#12011yescharacteristic
259C2×C4×C83#12111yescharacteristic
260C2×C4×C83#12111yescharacteristic
261C2×C4×C83#12111yescharacteristic
262C2×C4×C83#12111yescharacteristic
263C2×C4×C83#12111yescharacteristic
264C2×C4×C83#12111yescharacteristic
265C2×C4×C83#12111yescharacteristic
266C2×C4×C83C22⋊Q811yescharacteristic
267C2×C4×C83C22⋊Q811yescharacteristic
268C2×C4×C83C22⋊Q811yescharacteristic
269C2×C4×C83C22⋊Q811yescharacteristic
270C2×C4×C83C22⋊Q811yescharacteristic
271C2×C4×C83#12311yescharacteristic
272C2×C4×C83#12311yescharacteristic
273C2×C4×C83#12311yescharacteristic
274C2×C4×C83#12311yescharacteristic
275C2×C4×C83#12411yescharacteristic
276C2×C4×C83#12411yescharacteristic
277C2×C4×C83#12611yescharacteristic
278C2×C4×C83#12611yescharacteristic
279C2×Dic83—24no—
280C2×Dic83—24no—
281C2×Dic83—24no—
282C2×Dic83—24no—
283C2×Dic83—24no—
284C2×Dic83—24no—
285C2×Dic83—42no—
286C2×Dic83—42no—
287C2×Dic83—44no—
288C2×Dic83—44no—
289C2×Dic83—82no—
290C2×Dic83—82no—
291C2×Dic83—81no—
292C2×Dic83—81no—
293C2×Dic83—81no—
294C2×Dic83—81no—
295C2×Dic83#10218yescomplemented
296C8×C83—42no—
297C83⋊C8—42no—
298C22×C83—48no—
299C22×C83—44no—
300C22×C83—84no—
301C22×C83—82no—
302C22×C83—82no—
303C22×C83—84no—
304C22×C83—82no—
305C22×C83—82no—
306C22×C83—82no—
307C22×C83—82no—
308C22×C83—84no—
309C22×C83#38011yescharacteristic
310C22×C83#38611yescharacteristic
311C22×C83#39011yescharacteristic
312C22×C83#39211yescharacteristic
313C22×C83#39311yescharacteristic
314C22×C83#39711yescharacteristic
315C22×C83#39911yescharacteristic
316C22×C83C2×#10212yes—
317C22×C83#41712yes—
318C22×C83#44712yes—
319C22×C83#44812yes—
320C22×C83#45912yes—
321C22×C83#46112yes—
322C22×C83#47412yes—
323C22×C83#47612yes—
324C22×C83#48012yes—
325C22×C83#48112yes—
326C22×C83#48612yes—
327C22×C83#48912yes—
328C22×C83#49211yescharacteristic
329C22×C83#49311yescharacteristic
330C22×C83#49611yescharacteristic
331C22×C83#49711yescharacteristic
332C4×C83—82no—
333C4×C83#38511yescharacteristic
334C4×C83#38511yescharacteristic
335C4×C83#38811yescharacteristic
336C4×C83#38811yescharacteristic
337C4×C83#39411yescharacteristic
338C4×C83#39411yescharacteristic
339C4×C83#39611yescharacteristic
340C4×C83#39611yescharacteristic
341Dic83—28no—
342Dic83—82no—
343Dic83—82no—
344#11049—831nomaximal, Sylow
345C2×C83—84no—
346C2×C83#143911yescharacteristic
347C2×C83#180212yes—
348C2×C83#187412yes—
349C2×C83#195711yescharacteristic
350C2×C83#195911yescharacteristic
351C2×C83#201111yescharacteristic
352C2×C83#201311yescharacteristic
353C2×C83#202312yes—
354C2×C83#207112yes—
355C2×C83#209311yescharacteristic
356C2×C83#209411yescharacteristic
357C22×#102—831no—
358C22×#102D8311yescharacteristic
359C2×#390—831no—
360C2×#384—831no—
361C2×#340—831no—
362C2×#340—831no—
363C2×#336—831no—
364C83#1104911yescharacteristic, complemented, Sylow
365C23×D4C2×D8311yescharacteristic
366C23×C8—831no—
367C23×C8C2×D8311yescharacteristic
368C22×C4⋊C4—831no—
369C22×C4⋊C4—831no—
370C22×C4⋊C4—1662no—
371C22×C4⋊C4C2×D8311yescharacteristic
372C22×C22⋊C4—1662no—
373C22×C42—831no—
374C2×#102—22no—
375C2×#102—22no—
376C2×#102—22no—
377C2×#102—1662no—
378C2×#102—1662no—
379C2×#102—1662no—
380#390—834no—
381#390—1662no—
382#384—1662no—
383#384—1662no—
384#340—1662no—
385#340—1662no—
386#336—1662no—
387C25—21no—
388C22×D4—21no—
389C22×D4—21no—
390C22×D4—21no—
391C22×D4—21no—
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—21no—
397C22×D4—21no—
398C22×D4—21no—
399C22×D4Dic16612yes—
400C22×D4C4×D8312yes—
401C22×D4C22⋊D8312yes—
402C23×C4—21no—
403C23×C4—832no—
404C23×C4—1661no—
405C23×C4—1661no—
406C23×C4C22×D8311yescharacteristic
407C22×C8—21no—
408C22×C8—21no—
409C22×C8—21no—
410C22×C8—21no—
411C22×C8—21no—
412C22×C8—21no—
413C22×C8—832no—
414C22×C8—1661no—
415C22×C8—1661no—
416C22×C8—1661no—
417C22×C8—1661no—
418C22×C8—1661no—
419C22×C8—1661no—
420C22×C8C22⋊D8312yes—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—3324no—
427C2×C4⋊C4—3324no—
428C2×C4⋊C4—832no—
429C2×C4⋊C4—832no—
430C2×C4⋊C4—1668no—
431C2×C4⋊C4—1661no—
432C2×C4⋊C4—1661no—
433C2×C4⋊C4—1661no—
434C2×C4⋊C4—1661no—
435C2×C4⋊C4—1661no—
436C2×C4⋊C4—1661no—
437C2×C4⋊C4—1661no—
438C2×C4⋊C4—1661no—
439C2×C4⋊C4—1661no—
440C2×C4⋊C4—1661no—
441C2×C4⋊C4C22⋊D8312yes—
442C2×C22⋊C4—3324no—
443C2×C22⋊C4—3324no—
444C2×C22⋊C4—1668no—
445C2×C42—832no—
446C2×C42—832no—
447C2×C42—1661no—
448C2×C42—1661no—
449C2×C42—1661no—
450C2×C42—1661no—
451#102—28no—
452#102—1668no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—41no—
457C24—41no—
458C24—41no—
459C24—41no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24D4×D8311yescharacteristic
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4Dic83⋊C414yescomplemented
493C22×C4—22no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—3321no—
499C22×C4—3321no—
500C22×C4—3321no—
501C22×C4—3321no—
502C22×C4—3322no—
503C22×C4—3322no—
504C22×C4—3322no—
505C22×C4—3322no—
506C22×C4—834no—
507C22×C4—834no—
508C22×C4—834no—
509C22×C4—1662no—
510C22×C4—1662no—
511C22×C4—1662no—
512C22×C4—1662no—
513C22×C4—1662no—
514C22×C4—1662no—
515C22×C4C2×C4×D8311yescharacteristic
516C22×C4D4×D8311yescharacteristic
517C22×C4D4×D8311yescharacteristic
518C22×C4D4×D8311yescharacteristic
519C22×C4C2×C22⋊D8311yescharacteristic
520C22×C4C2×C22⋊D8311yescharacteristic
521C22×C4C2×C22⋊D8311yescharacteristic
522C22×C4C2×Dic16611yescharacteristic
523C22×C4#1305058911yescharacteristic
524C22×C4#1305058911yescharacteristic
525C22×C4#1305058911yescharacteristic
526C22×C4#1305058911yescharacteristic
527C22×C4#1305059011yescharacteristic
528C22×C4#1305059011yescharacteristic
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—3321no—
537C2×C8—3321no—
538C2×C8—3321no—
539C2×C8—3321no—
540C2×C8—1662no—
541C2×C8—1662no—
542C2×C8—1662no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—33216no—
548C4⋊C4—3321no—
549C4⋊C4—3321no—
550C4⋊C4—3321no—
551C4⋊C4—3321no—
552C4⋊C4—1662no—
553C4⋊C4—1662no—
554C4⋊C4—1662no—
555C4⋊C4—1662no—
556C22⋊C4—33216no—
557C42—1662no—
558C42—1662no—
559C42—1662no—
560C42—1662no—
561C23—24no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—44no—
569C23—44no—
570C23—44no—
571C23—44no—
572C23—44no—
573C23—44no—
574C23—81no—
575C23—81no—
576C23—82no—
577C23—81no—
578C23—81no—
579C23—82no—
580C23—82no—
581C23—82no—
582C23—82no—
583C23—82no—
584C23C22⋊C4×D8311yescharacteristic
585C23#1458176011yescharacteristic
586C23#1458176411yescharacteristic
587C23#1458176911yescharacteristic
588C23#1458177411yescharacteristic
589C23#1458177811yescharacteristic
590C23#1458178811yescharacteristic
591C23D8×D8312yes—
592C23SD16×D8312yes—
593C23#1458181612yes—
594C23#1458182112yes—
595D4—24no—
596D4—24no—
597D4—42no—
598D4—42no—
599D4—42no—
600D4—42no—
601D4—42no—
602D4—42no—
603C2×C4—44no—
604C2×C4—42no—
605C2×C4—81no—
606C2×C4—81no—
607C2×C4—82no—
608C2×C4—3324no—
609C2×C4—3322no—
610C2×C4—3322no—
611C2×C4—3324no—
612C2×C4—838no—
613C2×C4—6641no—
614C2×C4—6641no—
615C2×C4—6641no—
616C2×C4—6641no—
617C2×C4—6642no—
618C2×C4—6642no—
619C2×C4—1664no—
620C2×C4—1664no—
621C2×C4—1664no—
622C2×C4—1664no—
623C2×C4—1664no—
624C2×C4—1664no—
625C2×C4C2×Dic83⋊C411yescharacteristic
626C2×C4#1458174811yescharacteristic
627C2×C4(C22⋊D83)⋊C411yescharacteristic
628C2×C4(C22⋊D83)⋊C411yescharacteristic
629C2×C4C4×C22⋊D8311yescharacteristic
630C2×C4C4×C22⋊D8311yescharacteristic
631C2×C4#1458176011yescharacteristic
632C2×C4#1458176111yescharacteristic
633C2×C4#1458176311yescharacteristic
634C2×C4#1458176311yescharacteristic
635C2×C4#1458176411yescharacteristic
636C2×C4#1458176411yescharacteristic
637C2×C4#1458176411yescharacteristic
638C2×C4#1458176511yescharacteristic
639C2×C4#1458176511yescharacteristic
640C2×C4#1458176911yescharacteristic
641C2×C4#1458176911yescharacteristic
642C2×C4#1458176911yescharacteristic
643C2×C4#1458177111yescharacteristic
644C2×C4#1458177111yescharacteristic
645C2×C4#1458177311yescharacteristic
646C2×C4#1458177311yescharacteristic
647C2×C4#1458177411yescharacteristic
648C2×C4#1458177511yescharacteristic
649C2×C4#1458177811yescharacteristic
650C2×C4#1458177911yescharacteristic
651C2×C4#1458178511yescharacteristic
652C2×C4#1458178511yescharacteristic
653C8—42no—
654C8—3322no—
655C22—48no—
656C22—44no—
657C22—82no—
658C22—84no—
659C22—84no—
660C22—84no—
661C22—82no—
662C22—82no—
663C22—82no—
664C22—82no—
665C22—82no—
666C22#1912755911yescharacteristic
667C22#1912757711yescharacteristic
668C22#1912760111yescharacteristic
669C22#1912760911yescharacteristic
670C22#1912761311yescharacteristic
671C22#1912762911yescharacteristic
672C22#1912763711yescharacteristic
673C22#102×D8312yes—
674C22#1912769912yes—
675C22#1912783312yes—
676C22#1912783812yes—
677C22#1912789412yes—
678C22#1912790412yes—
679C22#1912797912yes—
680C22#1912798912yes—
681C22#1912801312yes—
682C22#1912801812yes—
683C22#1912804612yes—
684C22#1912805912yes—
685C22#1912807211yescharacteristic
686C22#1912807611yescharacteristic
687C22#1912808911yescharacteristic
688C22#1912809211yescharacteristic
689C4—82no—
690C4—6642no—
691C4—6642no—
692C4—1668no—
693C4#1912757311yescharacteristic
694C4#1912757411yescharacteristic
695C4#1912758911yescharacteristic
696C4#1912759511yescharacteristic
697C4#1912761511yescharacteristic
698C4#1912761611yescharacteristic
699C4#1912762411yescharacteristic
700C4#1912762411yescharacteristic
701C2—84no—
702C2#2490570611yescharacteristic
703C2#2490746112yes—
704C2#2490777712yes—
705C2#2490826711yescharacteristic
706C2#2490827811yescharacteristic
707C2#2490853211yescharacteristic
708C2#2490854411yescharacteristic
709C2#2490859712yes—
710C2#2490886912yes—
711C2#2490898911yescharacteristic
712C2#2490899411yescharacteristic
subgroupG/H
centerC24D4×D83
commutatorC22×C4×C83C22×C4
FrattiniC23×C4C22×D83
FittingC22×#102×C83C2
socleC24×C83C2×D4
prime radicalC23×D4×C83C22
cosocleC23×C4×C83C23
hypercenterC22×#102D83
hypocenterC83#11049
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
3. C2×#19127570C2semidirect
4. C2×#19127464C2semidirect
5. C2×#19127463C2semidirect
6. C2×#19127455C2semidirect
18. #19127604C4semidirect
173. C2×D4×C83C4⋊C4semidirect
295. C2×Dic83#102semidirect
364. C83#11049semidirect
492. C2×D4Dic83⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#145817132
C2×#191276042
C2×#191275702
C2×#191274642
C2×#191274632
C2×#191274552
C22×#102×C832
#1104983