Finite Group Databasebeta

← #35311357

Subgroups — #35311357

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×#14581714C211yesmaximal, characteristic
2C22×#14581712C211yesmaximal, characteristic
3C2×#19127602C211yesmaximal, characteristic
4C2×#19127570C211yesmaximal, characteristic, complemented
5C2×#19127463C211yesmaximal, characteristic, complemented
6C2×#19127455C211yesmaximal, characteristic, complemented
7C2×#340×C83C211yesmaximal, characteristic, complemented
8C23×D332C2211yescharacteristic
9C23×C83⋊C8C2211yescharacteristic
10C22×C4⋊Dic83C2211yescharacteristic
11C22×Dic83⋊C4—22no—
12C22×(C2×D83)⋊C4—22no—
13C22×C4×Dic83C2211yescharacteristic
14C2×#14581714—22no—
15C2×#14581714—22no—
16C2×#14581714—22no—
17C2×#14581712—22no—
18C2×#14581712—22no—
19C2×#14581712—22no—
20#19127602—22no—
21#19127602C414yescomplemented
22#19127570—22no—
23#19127570—22no—
24#19127463—22no—
25#19127455—22no—
26C23×C8×C83C2211yescharacteristic
27C22×C4⋊C4×C83C2211yescharacteristic
28C22×C4⋊C4×C83C2211yescharacteristic
29#340×C83—22no—
30C24×D83—21no—
31C22×D332—21no—
32C22×D332—21no—
33C22×D332—21no—
34C22×D332—21no—
35C22×D332—21no—
36C22×D332—21no—
37C22×D332—21no—
38C22×D332—21no—
39C22×D332—21no—
40C22×D332—21no—
41C22×D332—21no—
42C22×D332C2×C412yes—
43C22×D332D412yes—
44C22×D332Q812yes—
45C23×Dic83—21no—
46C23×Dic83D412yes—
47C22×C83⋊C8—21no—
48C22×C83⋊C8—21no—
49C22×C83⋊C8—21no—
50C22×C83⋊C8—21no—
51C22×C83⋊C8—21no—
52C22×C83⋊C8—21no—
53C22×C83⋊C8D412yes—
54C2×C4⋊Dic83—21no—
55C2×C4⋊Dic83—21no—
56C2×C4⋊Dic83—21no—
57C2×C4⋊Dic83—21no—
58C2×C4⋊Dic83—21no—
59C2×C4⋊Dic83D412yes—
60C2×Dic83⋊C4—28no—
61C2×Dic83⋊C4—44no—
62C2×Dic83⋊C4—44no—
63C2×(C2×D83)⋊C4—28no—
64C2×(C2×D83)⋊C4—44no—
65C2×(C2×D83)⋊C4—44no—
66C2×C4×Dic83—21no—
67C2×C4×Dic83—21no—
68C2×C4×Dic83—21no—
69C2×C4×Dic83—21no—
70C2×C4×Dic83C2×C412yes—
71C2×C4×Dic83D412yes—
72#14581714—28no—
73#14581712—28no—
74C23×C4×C83—21no—
75C23×C4×C83—21no—
76C23×C4×C83C2311yescharacteristic
77C22×C8×C83—21no—
78C22×C8×C83—21no—
79C22×C8×C83—21no—
80C22×C8×C83—21no—
81C22×C8×C83—21no—
82C22×C8×C83—21no—
83C22×C8×C83D412yes—
84C2×C4⋊C4×C83—21no—
85C2×C4⋊C4×C83—21no—
86C2×C4⋊C4×C83—21no—
87C2×C4⋊C4×C83—21no—
88C2×C4⋊C4×C83—21no—
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×C83C2×C412yes—
95C2×C4⋊C4×C83D412yes—
96C23×D83—22no—
97C23×D83—22no—
98C23×D83—22no—
99C23×D83—41no—
100C23×D83—41no—
101C23×D83—41no—
102C23×D83—41no—
103C23×D83—42no—
104C23×D83—42no—
105C23×D83—42no—
106C23×D83—42no—
107C2×D332—22no—
108C2×D332—22no—
109C2×D332—22no—
110C2×D332—22no—
111C2×D332—22no—
112C2×D332—22no—
113C2×D332—22no—
114C2×D332—22no—
115C2×D332—22no—
116C2×D332—22no—
117C2×D332—22no—
118C2×D332—22no—
119C2×D332—22no—
120C2×D332—22no—
121C2×D332—22no—
122C2×D332—41no—
123C2×D332—41no—
124C2×D332—41no—
125C2×D332—41no—
126C2×D332—41no—
127C2×D332—41no—
128C2×D332—41no—
129C2×D332—41no—
130C2×D332—41no—
131C2×D332—41no—
132C2×D332—41no—
133C2×D332—41no—
134C2×D332C4⋊C414yescomplemented
135C22×Dic83—22no—
136C22×Dic83—22no—
137C22×Dic83—22no—
138C22×Dic83—22no—
139C22×Dic83—22no—
140C22×Dic83—41no—
141C22×Dic83—41no—
142C22×Dic83—42no—
143C22×Dic83—42no—
144C22×Dic83C22⋊C414yes—
145C22×Dic83D814yes—
146C22×Dic83SD1614yes—
147C2×C83⋊C8—22no—
148C2×C83⋊C8—22no—
149C2×C83⋊C8—22no—
150C2×C83⋊C8—41no—
151C2×C83⋊C8—41no—
152C2×C83⋊C8—41no—
153C2×C83⋊C8—41no—
154C4⋊Dic83—22no—
155C4⋊Dic83—22no—
156C4⋊Dic83—41no—
157C4⋊Dic83—41no—
158Dic83⋊C4—416no—
159(C2×D83)⋊C4—416no—
160C4×Dic83—22no—
161C4×Dic83—22no—
162C4×Dic83—22no—
163C4×Dic83—22no—
164C24×C83C2×D411yescharacteristic
165C22×C4×C83—22no—
166C22×C4×C83—22no—
167C22×C4×C83—41no—
168C22×C4×C83—41no—
169C22×C4×C83—41no—
170C22×C4×C83—41no—
171C22×C4×C83—42no—
172C22×C4×C83—42no—
173C22×C4×C83—42no—
174C22×C4×C83—42no—
175C22×C4×C83C22×C411yescharacteristic
176C22×C4×C83C2×D411yescharacteristic
177C22×C4×C83C2×D411yescharacteristic
178C22×C4×C83C2×D411yescharacteristic
179C22×C4×C83C2×D411yescharacteristic
180C22×C4×C83C2×D411yescharacteristic
181C22×C4×C83C2×D411yescharacteristic
182C22×C4×C83C2×Q811yescharacteristic
183C22×C4×C83#4111yescharacteristic
184C22×C4×C83#4111yescharacteristic
185C22×C4×C83#4111yescharacteristic
186C22×C4×C83#4111yescharacteristic
187C22×C4×C83#4111yescharacteristic
188C22×C4×C83#4111yescharacteristic
189C2×C8×C83—22no—
190C2×C8×C83—22no—
191C2×C8×C83—22no—
192C2×C8×C83—41no—
193C2×C8×C83—41no—
194C2×C8×C83—41no—
195C2×C8×C83—41no—
196C4⋊C4×C83—22no—
197C4⋊C4×C83—22no—
198C4⋊C4×C83—22no—
199C4⋊C4×C83—22no—
200C4⋊C4×C83—41no—
201C4⋊C4×C83—41no—
202C4⋊C4×C83—41no—
203C4⋊C4×C83—41no—
204C23×C83C2×C22⋊C411yescharacteristic
205C23×C83#12011yescharacteristic
206C23×C83#12111yescharacteristic
207C23×C83C22⋊Q811yescharacteristic
208C23×C83#12311yescharacteristic
209C23×C83#12411yescharacteristic
210C23×C83#12711yescharacteristic
211C23×C83C2×D812yes—
212C23×C83C2×SD1612yes—
213C23×C83AGL(1,ℤ/8)12yes—
214C23×C83#13712yes—
215C22×D83—24no—
216C22×D83—42no—
217C22×D83—42no—
218C22×D83—42no—
219C22×D83—42no—
220C22×D83—42no—
221C22×D83—42no—
222C22×D83—44no—
223C22×D83—44no—
224C22×D83—44no—
225C22×D83—44no—
226C22×D83—44no—
227C22×D83—44no—
228C22×D83—82no—
229C22×D83—82no—
230C22×D83—82no—
231C22×D83—82no—
232C22×D83—82no—
233C22×D83—82no—
234C22×D83—81no—
235C22×D83—81no—
236C22×D83—81no—
237C22×D83—81no—
238C2×C4×C83—42no—
239C2×C4×C83—42no—
240C2×C4×C83—44no—
241C2×C4×C83—44no—
242C2×C4×C83—82no—
243C2×C4×C83—82no—
244C2×C4×C83—81no—
245C2×C4×C83—81no—
246C2×C4×C83—81no—
247C2×C4×C83—81no—
248C2×C4×C83C2×C4⋊C411yescharacteristic
249C2×C4×C83#11711yescharacteristic
250C2×C4×C83C4×D411yescharacteristic
251C2×C4×C83C4×D411yescharacteristic
252C2×C4×C83C4×D411yescharacteristic
253C2×C4×C83C4×D411yescharacteristic
254C2×C4×C83#12011yescharacteristic
255C2×C4×C83#12011yescharacteristic
256C2×C4×C83#12111yescharacteristic
257C2×C4×C83#12111yescharacteristic
258C2×C4×C83#12111yescharacteristic
259C2×C4×C83#12111yescharacteristic
260C2×C4×C83#12111yescharacteristic
261C2×C4×C83#12111yescharacteristic
262C2×C4×C83#12111yescharacteristic
263C2×C4×C83C22⋊Q811yescharacteristic
264C2×C4×C83C22⋊Q811yescharacteristic
265C2×C4×C83C22⋊Q811yescharacteristic
266C2×C4×C83C22⋊Q811yescharacteristic
267C2×C4×C83C22⋊Q811yescharacteristic
268C2×C4×C83#12311yescharacteristic
269C2×C4×C83#12311yescharacteristic
270C2×C4×C83#12311yescharacteristic
271C2×C4×C83#12311yescharacteristic
272C2×C4×C83#12411yescharacteristic
273C2×C4×C83#12411yescharacteristic
274C2×C4×C83#12611yescharacteristic
275C2×C4×C83#12611yescharacteristic
276C2×Dic83—24no—
277C2×Dic83—24no—
278C2×Dic83—24no—
279C2×Dic83—24no—
280C2×Dic83—24no—
281C2×Dic83—24no—
282C2×Dic83—42no—
283C2×Dic83—44no—
284C2×Dic83—82no—
285C2×Dic83—81no—
286C2×Dic83—81no—
287C2×Dic83#10218yescomplemented
288D332—24no—
289D332—24no—
290D332—42no—
291D332—42no—
292D332—42no—
293D332—42no—
294D332—42no—
295D332—42no—
296C8×C83—42no—
297C83⋊C8—42no—
298C22×C83#38011yescharacteristic
299C22×C83#38611yescharacteristic
300C22×C83#39011yescharacteristic
301C22×C83#39211yescharacteristic
302C22×C83#39311yescharacteristic
303C22×C83#39711yescharacteristic
304C22×C83#39911yescharacteristic
305C22×C83C2×#10212yes—
306C22×C83#41712yes—
307C22×C83#44712yes—
308C22×C83#44812yes—
309C22×C83#45912yes—
310C22×C83#46112yes—
311C22×C83#47412yes—
312C22×C83#47612yes—
313C22×C83#48012yes—
314C22×C83#48112yes—
315C22×C83#48612yes—
316C22×C83#48912yes—
317C22×C83#49211yescharacteristic
318C22×C83#49311yescharacteristic
319C22×C83#49611yescharacteristic
320C22×C83#49711yescharacteristic
321C2×D83—48no—
322C2×D83—44no—
323C2×D83—84no—
324C2×D83—82no—
325C2×D83—82no—
326C2×D83—84no—
327C2×D83—82no—
328C2×D83—82no—
329C2×D83—82no—
330C2×D83—82no—
331C2×D83—84no—
332C4×C83—82no—
333C4×C83—82no—
334C4×C83#38511yescharacteristic
335C4×C83#38511yescharacteristic
336C4×C83#38811yescharacteristic
337C4×C83#38811yescharacteristic
338C4×C83#39411yescharacteristic
339C4×C83#39411yescharacteristic
340C4×C83#39611yescharacteristic
341C4×C83#39611yescharacteristic
342Dic83—28no—
343Dic83—82no—
344#11049—831nomaximal, Sylow
345C2×C83#143911yescharacteristic
346C2×C83#180212yes—
347C2×C83#187412yes—
348C2×C83#195711yescharacteristic
349C2×C83#195911yescharacteristic
350C2×C83#201111yescharacteristic
351C2×C83#201311yescharacteristic
352C2×C83#202312yes—
353C2×C83#207112yes—
354C2×C83#209311yescharacteristic
355C2×C83#209411yescharacteristic
356D83—84no—
357C22×#102—831no—
358C22×#102—831no—
359C2×#390—831no—
360C2×#384—831no—
361C2×#340—831no—
362C2×#340D8311yescharacteristic, complemented
363C2×#336—831no—
364C83#1104911yescharacteristic, complemented, Sylow
365C23×D4—831no—
366C23×C8—831no—
367C23×C8C2×D8311yescharacteristic
368C22×C4⋊C4—831no—
369C22×C4⋊C4—1662no—
370C22×C4⋊C4C2×D8311yescharacteristic
371C22×C4⋊C4C2×D8311yescharacteristic
372C22×C22⋊C4—1662no—
373C22×C42—831no—
374C2×#102—1662no—
375C2×#102—1662no—
376C2×#102—1662no—
377C2×#102—1662no—
378C2×#102—1662no—
379C2×#102—1662no—
380#390—834no—
381#390—1662no—
382#384—1662no—
383#384—1662no—
384#340—22no—
385#340—1662no—
386#336—1662no—
387C25—1661no—
388C22×D4—832no—
389C22×D4—832no—
390C22×D4—832no—
391C22×D4—1661no—
392C22×D4—1661no—
393C22×D4—1661no—
394C22×D4—1661no—
395C22×D4—1661no—
396C22×D4—1661no—
397C22×D4—1661no—
398C22×D4—1661no—
399C22×D4—1661no—
400C22×D4—1661no—
401C22×D4—1661no—
402C23×C4—21no—
403C23×C4—21no—
404C23×C4—832no—
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—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—3324no—
432C2×C4⋊C4—3324no—
433C2×C4⋊C4—832no—
434C2×C4⋊C4—1668no—
435C2×C4⋊C4—1661no—
436C2×C4⋊C4—1661no—
437C2×C4⋊C4—1661no—
438C2×C4⋊C4—1661no—
439C2×C4⋊C4—1661no—
440C2×C4⋊C4C4×D8312yes—
441C2×C4⋊C4D33212yes—
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—1668no—
452#102—1668no—
453C24—3321no—
454C24—3321no—
455C24—3321no—
456C24—3321no—
457C24—3322no—
458C24—3322no—
459C24—3322no—
460C24—3322no—
461C24—1662no—
462C24—1662no—
463C24—1662no—
464C24D4×D8311yescharacteristic
465C2×D4—3321no—
466C2×D4—3321no—
467C2×D4—3321no—
468C2×D4—3321no—
469C2×D4—3321no—
470C2×D4—3321no—
471C2×D4—3321no—
472C2×D4—3321no—
473C2×D4—3321no—
474C2×D4—3321no—
475C2×D4—3321no—
476C2×D4—3321no—
477C2×D4—834no—
478C2×D4—1662no—
479C2×D4—1662no—
480C2×D4—1662no—
481C2×D4—1662no—
482C2×D4—1662no—
483C2×D4—1662no—
484C2×D4—1662no—
485C2×D4—1662no—
486C2×D4—1662no—
487C2×D4—1662no—
488C2×D4—1662no—
489C2×D4—1662no—
490C2×D4—1662no—
491C2×D4—1662no—
492C2×D4—1662no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—3321no—
504C22×C4—3321no—
505C22×C4—3322no—
506C22×C4—3322no—
507C22×C4—834no—
508C22×C4—834no—
509C22×C4—834no—
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×C4D4×D8311yescharacteristic
520C22×C4C2×C22⋊D8311yescharacteristic
521C22×C4C2×D33211yescharacteristic
522C22×C4Q8×D8311yescharacteristic
523C22×C4#1305058911yescharacteristic
524C22×C4#1305059011yescharacteristic
525C22×C4#1305059011yescharacteristic
526C22×C4#1305059011yescharacteristic
527C22×C4#1305059011yescharacteristic
528C22×C4#1305059111yescharacteristic
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—22no—
546C4⋊C4—22no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—33216no—
552C4⋊C4—3321no—
553C4⋊C4—3321no—
554C4⋊C4—1662no—
555C4⋊C4—1662no—
556C22⋊C4—33216no—
557C42—1662no—
558C42—1662no—
559C42—1662no—
560C42—1662no—
561C23—3322no—
562C23—3322no—
563C23—3322no—
564C23—3322no—
565C23—3322no—
566C23—3322no—
567C23—3324no—
568C23—3324no—
569C23—3324no—
570C23—3324no—
571C23—3324no—
572C23—3324no—
573C23—6641no—
574C23—6641no—
575C23—6641no—
576C23—6642no—
577C23—6641no—
578C23—6642no—
579C23—6642no—
580C23—6642no—
581C23—6642no—
582C23—6642no—
583C23—1664no—
584C23C22⋊C4×D8311yescharacteristic
585C23#1458176211yescharacteristic
586C23#1458176511yescharacteristic
587C23#1458177011yescharacteristic
588C23#1458177711yescharacteristic
589C23#1458177811yescharacteristic
590C23#1458178811yescharacteristic
591C23D8×D8312yes—
592C23SD16×D8312yes—
593C23#1458181912yes—
594C23#1458182412yes—
595D4—3322no—
596D4—3322no—
597D4—3322no—
598D4—3322no—
599D4—3322no—
600D4—3322no—
601D4—1664no—
602D4—1664no—
603C2×C4—44no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—44no—
607C2×C4—81no—
608C2×C4—81no—
609C2×C4—81no—
610C2×C4—81no—
611C2×C4—82no—
612C2×C4—82no—
613C2×C4—3324no—
614C2×C4—3322no—
615C2×C4—838no—
616C2×C4—6641no—
617C2×C4—6641no—
618C2×C4—6642no—
619C2×C4—1664no—
620C2×C4—1664no—
621C2×C4—1664no—
622C2×C4—1664no—
623C2×C4—1664no—
624C2×C4—1664no—
625C2×C4C4⋊C4×D8311yescharacteristic
626C2×C4#1458174911yescharacteristic
627C2×C4(C22⋊D83)⋊C411yescharacteristic
628C2×C4C4×C22⋊D8311yescharacteristic
629C2×C4#1458175411yescharacteristic
630C2×C4C4×D33211yescharacteristic
631C2×C4#1458176011yescharacteristic
632C2×C4#1458176211yescharacteristic
633C2×C4#1458176411yescharacteristic
634C2×C4#1458176511yescharacteristic
635C2×C4#1458176511yescharacteristic
636C2×C4#1458176511yescharacteristic
637C2×C4#1458176511yescharacteristic
638C2×C4#1458176611yescharacteristic
639C2×C4#1458176711yescharacteristic
640C2×C4#1458176811yescharacteristic
641C2×C4#1458177011yescharacteristic
642C2×C4#1458177011yescharacteristic
643C2×C4#1458177011yescharacteristic
644C2×C4#1458177211yescharacteristic
645C2×C4#1458177411yescharacteristic
646C2×C4#1458177511yescharacteristic
647C2×C4#1458177711yescharacteristic
648C2×C4#1458177711yescharacteristic
649C2×C4#1458177811yescharacteristic
650C2×C4#1458178011yescharacteristic
651C2×C4#1458178611yescharacteristic
652C2×C4#1458178711yescharacteristic
653C8—42no—
654C8—3322no—
655C22—3328no—
656C22—3324no—
657C22—6644no—
658C22—6642no—
659C22—6644no—
660C22—6644no—
661C22—6642no—
662C22—6642no—
663C22—6642no—
664C22—6642no—
665C22—6642no—
666C22#1912756011yescharacteristic
667C22#1912757911yescharacteristic
668C22#1912760111yescharacteristic
669C22#1912761011yescharacteristic
670C22#1912761411yescharacteristic
671C22#1912763011yescharacteristic
672C22#1912763611yescharacteristic
673C22#102×D8312yes—
674C22#1912770112yes—
675C22#1912783612yes—
676C22#1912784112yes—
677C22#1912789512yes—
678C22#1912790512yes—
679C22#1912798012yes—
680C22#1912799012yes—
681C22#1912801612yes—
682C22#1912802112yes—
683C22#1912804612yes—
684C22#1912806212yes—
685C22#1912807211yescharacteristic
686C22#1912807611yescharacteristic
687C22#1912808711yescharacteristic
688C22#1912809411yescharacteristic
689C4—82no—
690C4—82no—
691C4—6642no—
692C4—1668no—
693C4#1912757211yescharacteristic
694C4#1912757511yescharacteristic
695C4#1912759011yescharacteristic
696C4#1912759211yescharacteristic
697C4#1912761611yescharacteristic
698C4#1912761911yescharacteristic
699C4#1912762311yescharacteristic
700C4#1912762511yescharacteristic
701C2—6644no—
702C2#2490570711yescharacteristic
703C2#2490746212yes—
704C2#2490777912yes—
705C2#2490826711yescharacteristic
706C2#2490827611yescharacteristic
707C2#2490853511yescharacteristic
708C2#2490854711yescharacteristic
709C2#2490859812yes—
710C2#2490887012yes—
711C2#2490898811yescharacteristic
712C2#2490899311yescharacteristic
subgroupG/H
centerC24D4×D83
commutatorC22×C4×C83C22×C4
FrattiniC23×C4C22×D83
FittingC2×#340×C83C2
socleC24×C83C2×D4
prime radicalC23×D332C22
cosocleC23×C4×C83C23
hypercenterC2×#340D83
hypocenterC83#11049
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×#19127570C2semidirect
5. C2×#19127463C2semidirect
6. C2×#19127455C2semidirect
7. C2×#340×C83C2semidirect
21. #19127602C4semidirect
134. C2×D332C4⋊C4semidirect
287. C2×Dic83#102semidirect
362. C2×#340D83semidirect
364. C83#11049semidirect

Maximal subgroups

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

subgroupindex
C22×#145817142
C22×#145817122
C2×#191276022
C2×#191275702
C2×#191274632
C2×#191274552
C2×#340×C832
#1104983