Finite Group Databasebeta

← #35311460

Subgroups — #35311460

Order 21248.

1282 conjugacy classes of subgroups.

The subgroup lattice has 864 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×#19127597C211yesmaximal, 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—21no—
12C22×(C2×D83)⋊C4—21no—
13C22×(C2×D83)⋊C4—21no—
14C22×C4×Dic83C2211yescharacteristic
15C2×#14581714—22no—
16C2×#14581714—22no—
17C2×#14581714C414yescomplemented
18C2×#14581712—22no—
19C2×#14581712—22no—
20C2×#14581712—22no—
21#19127602—22no—
22#19127602—22no—
23#19127597—22no—
24#19127597—22no—
25C2×C83⋊#95—21no—
26#19127463—22no—
27#19127455—22no—
28C23×C8×C83C2211yescharacteristic
29C22×C4⋊C4×C83C2211yescharacteristic
30C22×C4⋊C4×C83C2211yescharacteristic
31#340×C83—22no—
32C24×D83—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×D332—21no—
43C22×D332—21no—
44C22×D332C2×C412yes—
45C22×D332D412yes—
46C22×D332Q812yes—
47C23×Dic83—21no—
48C23×Dic83D411yescharacteristic
49C23×Dic83D411yescharacteristic
50C22×C83⋊C8—21no—
51C22×C83⋊C8—21no—
52C22×C83⋊C8—21no—
53C22×C83⋊C8—21no—
54C22×C83⋊C8—21no—
55C22×C83⋊C8—21no—
56C22×C83⋊C8D412yes—
57C2×C4⋊Dic83—21no—
58C2×C4⋊Dic83—21no—
59C2×C4⋊Dic83—21no—
60C2×C4⋊Dic83C2×C412yes—
61C2×C4⋊Dic83D412yes—
62C2×C4⋊Dic83D412yes—
63C2×Dic83⋊C4—24no—
64C2×Dic83⋊C4—42no—
65C2×Dic83⋊C4—42no—
66C2×(C2×D83)⋊C4—24no—
67C2×(C2×D83)⋊C4—24no—
68C2×(C2×D83)⋊C4—42no—
69C2×(C2×D83)⋊C4—42no—
70C2×(C2×D83)⋊C4—42no—
71C2×(C2×D83)⋊C4—42no—
72C2×C4×Dic83—21no—
73C2×C4×Dic83—21no—
74C2×C4×Dic83—21no—
75C2×C4×Dic83—21no—
76C2×C4×Dic83—21no—
77C2×C4×Dic83—21no—
78#14581714—28no—
79#14581712—28no—
80C83⋊#95—24no—
81C23×C4×C83—21no—
82C23×C4×C83—21no—
83C23×C4×C83C2311yescharacteristic
84C22×C8×C83—21no—
85C22×C8×C83—21no—
86C22×C8×C83—21no—
87C22×C8×C83—21no—
88C22×C8×C83—21no—
89C22×C8×C83—21no—
90C22×C8×C83C2×C412yes—
91C2×C4⋊C4×C83—21no—
92C2×C4⋊C4×C83—21no—
93C2×C4⋊C4×C83—21no—
94C2×C4⋊C4×C83—21no—
95C2×C4⋊C4×C83—21no—
96C2×C4⋊C4×C83—21no—
97C2×C4⋊C4×C83—21no—
98C2×C4⋊C4×C83—21no—
99C2×C4⋊C4×C83—21no—
100C2×C4⋊C4×C83—21no—
101C2×C4⋊C4×C83D412yes—
102C2×C4⋊C4×C83D412yes—
103C23×D83—22no—
104C23×D83—22no—
105C23×D83—22no—
106C23×D83—41no—
107C23×D83—41no—
108C23×D83—41no—
109C23×D83—41no—
110C23×D83—41no—
111C23×D83—41no—
112C23×D83—41no—
113C23×D83—41no—
114C23×D83—41no—
115C23×D83—41no—
116C23×D83—41no—
117C23×D83—41no—
118C2×D332—22no—
119C2×D332—22no—
120C2×D332—22no—
121C2×D332—22no—
122C2×D332—22no—
123C2×D332—22no—
124C2×D332—22no—
125C2×D332—22no—
126C2×D332—22no—
127C2×D332—22no—
128C2×D332—22no—
129C2×D332—22no—
130C2×D332—22no—
131C2×D332—22no—
132C2×D332—22no—
133C2×D332—41no—
134C2×D332—41no—
135C2×D332—41no—
136C2×D332—41no—
137C2×D332—41no—
138C2×D332—41no—
139C2×D332—41no—
140C2×D332—41no—
141C2×D332—41no—
142C2×D332—41no—
143C2×D332—41no—
144C2×D332—41no—
145C2×D332C4⋊C414yescomplemented
146C22×Dic83—22no—
147C22×Dic83—22no—
148C22×Dic83—21no—
149C22×Dic83—21no—
150C22×Dic83—21no—
151C22×Dic83—21no—
152C22×Dic83—22no—
153C22×Dic83—21no—
154C22×Dic83—21no—
155C22×Dic83—21no—
156C22×Dic83—21no—
157C22×Dic83—21no—
158C22×Dic83—21no—
159C22×Dic83—21no—
160C22×Dic83—21no—
161C22×Dic83—41no—
162C22×Dic83—41no—
163C22×Dic83—41no—
164C22×Dic83—41no—
165C22×Dic83D812yes—
166C22×Dic83SD1612yes—
167C2×C83⋊C8—22no—
168C2×C83⋊C8—22no—
169C2×C83⋊C8—22no—
170C2×C83⋊C8—41no—
171C2×C83⋊C8—41no—
172C2×C83⋊C8—41no—
173C2×C83⋊C8—41no—
174C4⋊Dic83—22no—
175C4⋊Dic83—22no—
176C4⋊Dic83—22no—
177C4⋊Dic83C22⋊C414yescomplemented
178Dic83⋊C4—48no—
179(C2×D83)⋊C4—48no—
180(C2×D83)⋊C4—48no—
181C4×Dic83—41no—
182C4×Dic83—41no—
183C4×Dic83—41no—
184C4×Dic83—41no—
185C24×C83C2×D411yescharacteristic
186C22×C4×C83—22no—
187C22×C4×C83—22no—
188C22×C4×C83—41no—
189C22×C4×C83—41no—
190C22×C4×C83—41no—
191C22×C4×C83—41no—
192C22×C4×C83—41no—
193C22×C4×C83—41no—
194C22×C4×C83—41no—
195C22×C4×C83—41no—
196C22×C4×C83—41no—
197C22×C4×C83—41no—
198C22×C4×C83—41no—
199C22×C4×C83—41no—
200C22×C4×C83C22×C411yescharacteristic
201C22×C4×C83C2×D411yescharacteristic
202C22×C4×C83C2×D411yescharacteristic
203C22×C4×C83C2×D411yescharacteristic
204C22×C4×C83C2×D411yescharacteristic
205C22×C4×C83C2×D411yescharacteristic
206C22×C4×C83C2×D411yescharacteristic
207C22×C4×C83C2×Q811yescharacteristic
208C22×C4×C83#4111yescharacteristic
209C22×C4×C83#4111yescharacteristic
210C22×C4×C83#4111yescharacteristic
211C22×C4×C83#4111yescharacteristic
212C22×C4×C83#4111yescharacteristic
213C22×C4×C83#4111yescharacteristic
214C2×C8×C83—22no—
215C2×C8×C83—22no—
216C2×C8×C83—22no—
217C2×C8×C83—41no—
218C2×C8×C83—41no—
219C2×C8×C83—41no—
220C2×C8×C83—41no—
221C4⋊C4×C83—22no—
222C4⋊C4×C83—22no—
223C4⋊C4×C83—22no—
224C4⋊C4×C83—22no—
225C4⋊C4×C83—41no—
226C4⋊C4×C83—41no—
227C4⋊C4×C83—41no—
228C4⋊C4×C83—41no—
229C23×C83C4×D411yescharacteristic
230C23×C83#12011yescharacteristic
231C23×C83#12011yescharacteristic
232C23×C83#12111yescharacteristic
233C23×C83#12111yescharacteristic
234C23×C83C22⋊Q811yescharacteristic
235C23×C83#12411yescharacteristic
236C23×C83C2×D811yescharacteristic
237C23×C83C2×SD1611yescharacteristic
238C23×C83#13511yescharacteristic
239C23×C83#13511yescharacteristic
240C23×C83AGL(1,ℤ/8)11yescharacteristic
241C23×C83AGL(1,ℤ/8)11yescharacteristic
242C23×C83AGL(1,ℤ/8)11yescharacteristic
243C23×C83#13711yescharacteristic
244C22×D83—24no—
245C22×D83—42no—
246C22×D83—42no—
247C22×D83—42no—
248C22×D83—42no—
249C22×D83—42no—
250C22×D83—42no—
251C22×D83—42no—
252C22×D83—42no—
253C22×D83—42no—
254C22×D83—42no—
255C22×D83—42no—
256C22×D83—42no—
257C22×D83—42no—
258C22×D83—42no—
259C22×D83—42no—
260C22×D83—42no—
261C22×D83—42no—
262C22×D83—42no—
263C22×D83—81no—
264C22×D83—81no—
265C22×D83—81no—
266C22×D83—81no—
267C22×D83—81no—
268C22×D83—81no—
269C22×D83—81no—
270C22×D83—81no—
271C22×D83—81no—
272C22×D83—81no—
273C22×D83—81no—
274C22×D83—81no—
275C22×D83—81no—
276C22×D83—81no—
277C22×D83—81no—
278C22×D83—81no—
279C2×C4×C83—42no—
280C2×C4×C83—42no—
281C2×C4×C83—42no—
282C2×C4×C83—42no—
283C2×C4×C83—42no—
284C2×C4×C83—42no—
285C2×C4×C83—81no—
286C2×C4×C83—81no—
287C2×C4×C83—81no—
288C2×C4×C83—81no—
289C2×C4×C83—81no—
290C2×C4×C83—81no—
291C2×C4×C83—81no—
292C2×C4×C83—81no—
293C2×C4×C83C2×C22⋊C411yescharacteristic
294C2×C4×C83C2×C4⋊C411yescharacteristic
295C2×C4×C83#11711yescharacteristic
296C2×C4×C83C4×D411yescharacteristic
297C2×C4×C83C4×D411yescharacteristic
298C2×C4×C83C4×D411yescharacteristic
299C2×C4×C83#12011yescharacteristic
300C2×C4×C83#12111yescharacteristic
301C2×C4×C83#12111yescharacteristic
302C2×C4×C83#12111yescharacteristic
303C2×C4×C83#12111yescharacteristic
304C2×C4×C83#12111yescharacteristic
305C2×C4×C83#12111yescharacteristic
306C2×C4×C83C22⋊Q811yescharacteristic
307C2×C4×C83C22⋊Q811yescharacteristic
308C2×C4×C83C22⋊Q811yescharacteristic
309C2×C4×C83C22⋊Q811yescharacteristic
310C2×C4×C83C22⋊Q811yescharacteristic
311C2×C4×C83#12311yescharacteristic
312C2×C4×C83#12311yescharacteristic
313C2×C4×C83#12311yescharacteristic
314C2×C4×C83#12311yescharacteristic
315C2×C4×C83#12311yescharacteristic
316C2×C4×C83#12411yescharacteristic
317C2×C4×C83#12411yescharacteristic
318C2×C4×C83#12611yescharacteristic
319C2×C4×C83#12611yescharacteristic
320C2×C4×C83#12711yescharacteristic
321C2×Dic83—24no—
322C2×Dic83—22no—
323C2×Dic83—22no—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—22no—
327C2×Dic83—22no—
328C2×Dic83—41no—
329C2×Dic83—41no—
330C2×Dic83—42no—
331C2×Dic83—42no—
332C2×Dic83—42no—
333C2×Dic83—41no—
334C2×Dic83—41no—
335C2×Dic83—41no—
336C2×Dic83—42no—
337C2×Dic83—41no—
338C2×Dic83—42no—
339C2×Dic83—42no—
340C2×Dic83—41no—
341C2×Dic83—41no—
342D332—24no—
343D332—24no—
344D332—42no—
345D332—42no—
346D332—42no—
347D332—42no—
348D332—42no—
349D332—42no—
350C8×C83—42no—
351C83⋊C8—42no—
352C22×C83#38511yescharacteristic
353C22×C83#38611yescharacteristic
354C22×C83#38811yescharacteristic
355C22×C83#39211yescharacteristic
356C22×C83#39311yescharacteristic
357C22×C83#39411yescharacteristic
358C22×C83#39611yescharacteristic
359C22×C83C4×D811yescharacteristic
360C22×C83C4×SD1611yescharacteristic
361C22×C83#44011yescharacteristic
362C22×C83#44211yescharacteristic
363C22×C83#44711yescharacteristic
364C22×C83#44711yescharacteristic
365C22×C83#44811yescharacteristic
366C22×C83#44911yescharacteristic
367C22×C83#44911yescharacteristic
368C22×C83#44911yescharacteristic
369C22×C83#45011yescharacteristic
370C22×C83#45211yescharacteristic
371C22×C83#45911yescharacteristic
372C22×C83#46011yescharacteristic
373C22×C83#46311yescharacteristic
374C22×C83#46411yescharacteristic
375C22×C83#46511yescharacteristic
376C22×C83#46611yescharacteristic
377C22×C83#46811yescharacteristic
378C22×C83#46911yescharacteristic
379C22×C83#47411yescharacteristic
380C22×C83#47611yescharacteristic
381C22×C83#47811yescharacteristic
382C22×C83#47811yescharacteristic
383C22×C83#48611yescharacteristic
384C22×C83#48811yescharacteristic
385C22×C83#48911yescharacteristic
386C22×C83#49011yescharacteristic
387C2×D83—44no—
388C2×D83—44no—
389C2×D83—44no—
390C2×D83—82no—
391C2×D83—82no—
392C2×D83—82no—
393C2×D83—82no—
394C2×D83—82no—
395C2×D83—82no—
396C2×D83—82no—
397C2×D83—82no—
398C2×D83—82no—
399C2×D83—82no—
400C2×D83—82no—
401C2×D83—82no—
402C4×C83—82no—
403C4×C83—82no—
404C4×C83#38011yescharacteristic
405C4×C83#38511yescharacteristic
406C4×C83#38811yescharacteristic
407C4×C83#39011yescharacteristic
408C4×C83#39411yescharacteristic
409C4×C83#39611yescharacteristic
410C4×C83#39711yescharacteristic
411C4×C83#39911yescharacteristic
412Dic83—44no—
413Dic83—42no—
414Dic83—42no—
415#11066—831nomaximal, Sylow
416C2×C83#143911yescharacteristic
417C2×C83#186211yescharacteristic
418C2×C83#186411yescharacteristic
419C2×C83#187911yescharacteristic
420C2×C83#188011yescharacteristic
421C2×C83#193411yescharacteristic
422C2×C83#193611yescharacteristic
423C2×C83#199911yescharacteristic
424C2×C83#200011yescharacteristic
425C2×C83#202311yescharacteristic
426C2×C83#202511yescharacteristic
427C2×C83#204111yescharacteristic
428C2×C83#204211yescharacteristic
429C2×C83#206511yescharacteristic
430C2×C83#206711yescharacteristic
431D83—84no—
432C22×#102—831no—
433C22×#102—831no—
434C2×#390—831no—
435C2×#389—831no—
436C2×#340—831no—
437C2×#340D8311yescharacteristic, complemented
438C2×#336—831no—
439C83#1106611yescharacteristic, complemented, Sylow
440C23×D4—831no—
441C23×C8—831no—
442C23×C8C2×D8311yescharacteristic
443C22×C4⋊C4—831no—
444C22×C4⋊C4—1661no—
445C22×C4⋊C4C2×D8311yescharacteristic
446C22×C4⋊C4C2×D8311yescharacteristic
447C22×C22⋊C4—1661no—
448C22×C22⋊C4—1661no—
449C22×C42—831no—
450C2×#102—834no—
451C2×#102—1662no—
452C2×#102—1662no—
453C2×#102—1662no—
454C2×#102—1662no—
455C2×#102—1662no—
456#390—1662no—
457#390—1662no—
458#389—1662no—
459#389—1662no—
460C2×#95—1661no—
461#340—22no—
462#340—1662no—
463#336—1662no—
464C25—1661no—
465C22×D4—832no—
466C22×D4—832no—
467C22×D4—832no—
468C22×D4—1661no—
469C22×D4—1661no—
470C22×D4—1661no—
471C22×D4—1661no—
472C22×D4—1661no—
473C22×D4—1661no—
474C22×D4—1661no—
475C22×D4—1661no—
476C22×D4—1661no—
477C22×D4—1661no—
478C22×D4—1661no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—831no—
482C23×C4—831no—
483C23×C4—1661no—
484C23×C4C22×D8311yescharacteristic
485C22×C8—21no—
486C22×C8—21no—
487C22×C8—21no—
488C22×C8—21no—
489C22×C8—21no—
490C22×C8—21no—
491C22×C8—832no—
492C22×C8—1661no—
493C22×C8—1661no—
494C22×C8—1661no—
495C22×C8—1661no—
496C22×C8—1661no—
497C22×C8—1661no—
498C22×C8C4×D8312yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—3322no—
510C2×C4⋊C4—3322no—
511C2×C4⋊C4—832no—
512C2×C4⋊C4—832no—
513C2×C4⋊C4—832no—
514C2×C4⋊C4—1664no—
515C2×C4⋊C4—1661no—
516C2×C4⋊C4—1661no—
517C2×C4⋊C4—1661no—
518C2×C4⋊C4D33212yes—
519C2×C4⋊C4C22⋊D8312yes—
520C2×C22⋊C4—3322no—
521C2×C22⋊C4—3322no—
522C2×C22⋊C4—3322no—
523C2×C22⋊C4—3322no—
524C2×C22⋊C4—1664no—
525C2×C22⋊C4—1664no—
526C2×C42—1661no—
527C2×C42—1661no—
528C2×C42—1661no—
529C2×C42—1661no—
530C2×C42—1661no—
531C2×C42—1661no—
532#102—1668no—
533#102—1668no—
534#95—1664no—
535C24—3321no—
536C24—3321no—
537C24—3321no—
538C24—3321no—
539C24—3321no—
540C24—3321no—
541C24—3321no—
542C24—3321no—
543C24—3321no—
544C24—3321no—
545C24—3321no—
546C24—3321no—
547C24—1662no—
548C24—1662no—
549C24—1662no—
550C24D4×D8311yescharacteristic
551C2×D4—3321no—
552C2×D4—3321no—
553C2×D4—3321no—
554C2×D4—3321no—
555C2×D4—3321no—
556C2×D4—3321no—
557C2×D4—3321no—
558C2×D4—3321no—
559C2×D4—3321no—
560C2×D4—3321no—
561C2×D4—3321no—
562C2×D4—3321no—
563C2×D4—834no—
564C2×D4—1662no—
565C2×D4—1662no—
566C2×D4—1662no—
567C2×D4—1662no—
568C2×D4—1662no—
569C2×D4—1662no—
570C2×D4—1662no—
571C2×D4—1662no—
572C2×D4—1662no—
573C2×D4—1662no—
574C2×D4—1662no—
575C2×D4—1662no—
576C2×D4—1662no—
577C2×D4—1662no—
578C2×D4—1662no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—3321no—
594C22×C4—3321no—
595C22×C4—3321no—
596C22×C4—3321no—
597C22×C4—832no—
598C22×C4—832no—
599C22×C4—1661no—
600C22×C4—1661no—
601C22×C4—1661no—
602C22×C4—1662no—
603C22×C4—1661no—
604C22×C4—1661no—
605C22×C4—1661no—
606C22×C4—1662no—
607C22×C4—1661no—
608C22×C4—1661no—
609C22×C4—1661no—
610C22×C4—1661no—
611C22×C4—1661no—
612C22×C4—1661no—
613C22×C4—1662no—
614C22×C4C2×C4×D8311yescharacteristic
615C22×C4D4×D8311yescharacteristic
616C22×C4D4×D8311yescharacteristic
617C22×C4D4×D8311yescharacteristic
618C22×C4D4×D8311yescharacteristic
619C22×C4C2×C22⋊D8311yescharacteristic
620C22×C4C2×D33211yescharacteristic
621C22×C4Q8×D8311yescharacteristic
622C22×C4#1305058911yescharacteristic
623C22×C4#1305059011yescharacteristic
624C22×C4#1305059011yescharacteristic
625C22×C4#1305059011yescharacteristic
626C22×C4#1305059011yescharacteristic
627C22×C4#1305059111yescharacteristic
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—3321no—
636C2×C8—3321no—
637C2×C8—3321no—
638C2×C8—3321no—
639C2×C8—1662no—
640C2×C8—1662no—
641C2×C8—1662no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—3328no—
651C4⋊C4—834no—
652C4⋊C4—1662no—
653C4⋊C4—1662no—
654C4⋊C4—1662no—
655C22⋊C4—3328no—
656C22⋊C4—3328no—
657C42—3321no—
658C42—3321no—
659C42—3321no—
660C42—3321no—
661C23—3322no—
662C23—3322no—
663C23—3322no—
664C23—3322no—
665C23—3322no—
666C23—3322no—
667C23—3322no—
668C23—3322no—
669C23—3322no—
670C23—3322no—
671C23—3322no—
672C23—3322no—
673C23—3322no—
674C23—3322no—
675C23—3322no—
676C23—3322no—
677C23—3322no—
678C23—3322no—
679C23—6641no—
680C23—6641no—
681C23—6641no—
682C23—6641no—
683C23—6641no—
684C23—6641no—
685C23—6641no—
686C23—6641no—
687C23—6641no—
688C23—6641no—
689C23—6641no—
690C23—6641no—
691C23—6641no—
692C23—6641no—
693C23—6641no—
694C23—6641no—
695C23—1664no—
696C23#1458175411yescharacteristic
697C23#1458176011yescharacteristic
698C23#1458176211yescharacteristic
699C23#1458176511yescharacteristic
700C23#1458176511yescharacteristic
701C23#1458177011yescharacteristic
702C23#1458177811yescharacteristic
703C23D8×D8311yescharacteristic
704C23SD16×D8311yescharacteristic
705C23#1458181311yescharacteristic
706C23#1458181511yescharacteristic
707C23#1458181611yescharacteristic
708C23#1458181911yescharacteristic
709C23#1458181911yescharacteristic
710C23#1458182411yescharacteristic
711D4—3322no—
712D4—3322no—
713D4—3322no—
714D4—3322no—
715D4—3322no—
716D4—3322no—
717D4—1664no—
718D4—1664no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—3322no—
734C2×C4—3322no—
735C2×C4—3321no—
736C2×C4—3321no—
737C2×C4—3322no—
738C2×C4—3321no—
739C2×C4—3321no—
740C2×C4—3321no—
741C2×C4—3321no—
742C2×C4—3322no—
743C2×C4—3322no—
744C2×C4—3321no—
745C2×C4—3321no—
746C2×C4—3322no—
747C2×C4—1662no—
748C2×C4—1664no—
749C2×C4—1662no—
750C2×C4—1662no—
751C2×C4—1662no—
752C2×C4—1662no—
753C2×C4—1662no—
754C2×C4C22⋊C4×D8311yescharacteristic
755C2×C4C4⋊C4×D8311yescharacteristic
756C2×C4#1458174911yescharacteristic
757C2×C4(C22⋊D83)⋊C411yescharacteristic
758C2×C4C4×C22⋊D8311yescharacteristic
759C2×C4C4×D33211yescharacteristic
760C2×C4#1458176211yescharacteristic
761C2×C4#1458176411yescharacteristic
762C2×C4#1458176511yescharacteristic
763C2×C4#1458176511yescharacteristic
764C2×C4#1458176511yescharacteristic
765C2×C4#1458176611yescharacteristic
766C2×C4#1458176711yescharacteristic
767C2×C4#1458176811yescharacteristic
768C2×C4#1458177011yescharacteristic
769C2×C4#1458177011yescharacteristic
770C2×C4#1458177011yescharacteristic
771C2×C4#1458177211yescharacteristic
772C2×C4#1458177411yescharacteristic
773C2×C4#1458177511yescharacteristic
774C2×C4#1458177711yescharacteristic
775C2×C4#1458177711yescharacteristic
776C2×C4#1458177711yescharacteristic
777C2×C4#1458177811yescharacteristic
778C2×C4#1458178011yescharacteristic
779C2×C4#1458178611yescharacteristic
780C2×C4#1458178711yescharacteristic
781C2×C4#1458178811yescharacteristic
782C8—42no—
783C8—3322no—
784C22—3324no—
785C22—3324no—
786C22—3324no—
787C22—6642no—
788C22—6642no—
789C22—6642no—
790C22—6642no—
791C22—6642no—
792C22—6642no—
793C22—6642no—
794C22—6642no—
795C22—6642no—
796C22—6642no—
797C22—6642no—
798C22—6642no—
799C22#1912757211yescharacteristic
800C22#1912757911yescharacteristic
801C22#1912759011yescharacteristic
802C22#1912761011yescharacteristic
803C22#1912761411yescharacteristic
804C22#1912761611yescharacteristic
805C22#1912762511yescharacteristic
806C22#1912778311yescharacteristic
807C22#1912778811yescharacteristic
808C22#1912780011yescharacteristic
809C22#1912781211yescharacteristic
810C22#1912783311yescharacteristic
811C22#1912783611yescharacteristic
812C22#1912784111yescharacteristic
813C22#1912784511yescharacteristic
814C22#1912784711yescharacteristic
815C22#1912784911yescharacteristic
816C22#1912785011yescharacteristic
817C22#1912786211yescharacteristic
818C22#1912789511yescharacteristic
819C22#1912790011yescharacteristic
820C22#1912791911yescharacteristic
821C22#1912792611yescharacteristic
822C22#1912793311yescharacteristic
823C22#1912793611yescharacteristic
824C22#1912795011yescharacteristic
825C22#1912795311yescharacteristic
826C22#1912798011yescharacteristic
827C22#1912799011yescharacteristic
828C22#1912800011yescharacteristic
829C22#1912800411yescharacteristic
830C22#1912804611yescharacteristic
831C22#1912805711yescharacteristic
832C22#1912806211yescharacteristic
833C22#1912806411yescharacteristic
834C4—82no—
835C4—82no—
836C4—3324no—
837C4—3322no—
838C4—3322no—
839C4#1912756011yescharacteristic
840C4#1912757511yescharacteristic
841C4#1912759211yescharacteristic
842C4#1912760111yescharacteristic
843C4#1912761911yescharacteristic
844C4#1912762311yescharacteristic
845C4#1912763011yescharacteristic
846C4#1912763611yescharacteristic
847C2—6644no—
848C2#2490570711yescharacteristic
849C2#2490770711yescharacteristic
850C2#2490772111yescharacteristic
851C2#2490781211yescharacteristic
852C2#2490781911yescharacteristic
853C2#2490814411yescharacteristic
854C2#2490815811yescharacteristic
855C2#2490846011yescharacteristic
856C2#2490846511yescharacteristic
857C2#2490859811yescharacteristic
858C2#2490860811yescharacteristic
859C2#2490869511yescharacteristic
860C2#2490870011yescharacteristic
861C2#2490883811yescharacteristic
862C2#2490885211yescharacteristic
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#11066
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×#19127597C2semidirect
5. C2×#19127463C2semidirect
6. C2×#19127455C2semidirect
7. C2×#340×C83C2semidirect
17. C2×#14581714C4semidirect
145. C2×D332C4⋊C4semidirect
177. C4⋊Dic83C22⋊C4semidirect
437. C2×#340D83semidirect
439. C83#11066semidirect

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×#191275972
C2×#191274632
C2×#191274552
C2×#340×C832
#1106683