Finite Group Databasebeta

← #35335643

Subgroups — #35335643

Order 21248.

2574 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D83C211yesmaximal, characteristic
2C2×#19127597C211yesmaximal, characteristic, complemented
3C2×#19127572C212yesmaximal
4C2×#19127558C211yesmaximal, characteristic
5C2×#19127558C211yesmaximal, characteristic
6#24905695C212yesmaximal, complemented
7#24905694C212yesmaximal, complemented
8#24905693C211yesmaximal, characteristic, complemented
9#24905692C211yesmaximal, characteristic, complemented
10(C2×D83)⋊#95C212yesmaximal
11C2×#389×C83C211yesmaximal, characteristic, complemented
12C23×C4×D83C2211yescharacteristic
13C23×C4×D83C2211yescharacteristic
14C23×C4×D83C2211yescharacteristic
15C22×C4⋊Dic83C2211yescharacteristic
16C22×C4⋊Dic83C2211yescharacteristic
17C22×Dic83⋊C4C2212yes—
18C22×(C2×D83)⋊C4C2212yes—
19C22×(C2×D83)⋊C4C2212yes—
20C22×C4×Dic83C2211yescharacteristic
21C22×C4×Dic83C2211yescharacteristic
22C22×C4×Dic83C2211yescharacteristic
23C2×C42×D83—24no—
24C2×C42×D83—24no—
25C2×C42×D83—24no—
26#19127597—24no—
27#19127572—28no—
28#19127558—24no—
29#19127558C418yescomplemented
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2212yes—
33C2×C83⋊#95C2212yes—
34C2×C83⋊#95C2212yes—
35C2×C83⋊#95C2212yes—
36C2×C83⋊#95C2212yes—
37C22×C4⋊C4×C83C2211yescharacteristic
38C22×C4⋊C4×C83C2212yes—
39C22×C4⋊C4×C83C2211yescharacteristic
40C22×C42×C83C2211yescharacteristic
41#389×C83—24no—
42C2×#95×C83C2212yes—
43C24×D83C2311yescharacteristic
44C23×Dic83C2312yes—
45C23×Dic83C2312yes—
46C23×Dic83C2311yescharacteristic
47C23×Dic83C2311yescharacteristic
48C23×Dic83C2311yescharacteristic
49C22×C4×D83—22no—
50C22×C4×D83—22no—
51C22×C4×D83—22no—
52C22×C4×D83—22no—
53C22×C4×D83—22no—
54C22×C4×D83—22no—
55C22×C4×D83—22no—
56C22×C4×D83—22no—
57C22×C4×D83—22no—
58C22×C4×D83—22no—
59C22×C4×D83—22no—
60C22×C4×D83—22no—
61C22×C4×D83—22no—
62C22×C4×D83—22no—
63C22×C4×D83—22no—
64C22×C4×D83—22no—
65C22×C4×D83C2×C414yes—
66C22×C4×D83D414yes—
67C22×C4×D83D414yes—
68C22×C4×D83Q814yes—
69C22×C4×D83Q814yes—
70C2×C4⋊Dic83—22no—
71C2×C4⋊Dic83—22no—
72C2×C4⋊Dic83—22no—
73C2×C4⋊Dic83—22no—
74C2×C4⋊Dic83—22no—
75C2×C4⋊Dic83C2×C414yescomplemented
76C2×Dic83⋊C4—24no—
77C2×Dic83⋊C4—24no—
78C2×Dic83⋊C4—24no—
79C2×(C2×D83)⋊C4—24no—
80C2×(C2×D83)⋊C4—24no—
81C2×(C2×D83)⋊C4—24no—
82C2×(C2×D83)⋊C4—24no—
83C2×(C2×D83)⋊C4—24no—
84C2×(C2×D83)⋊C4C2×C418yes—
85C2×C4×Dic83—22no—
86C2×C4×Dic83—22no—
87C2×C4×Dic83—22no—
88C2×C4×Dic83—22no—
89C2×C4×Dic83—22no—
90C2×C4×Dic83—22no—
91C2×C4×Dic83—22no—
92C2×C4×Dic83—22no—
93C2×C4×Dic83D414yes—
94C42×D83—232no—
95C83⋊#95—24no—
96C83⋊#95—24no—
97C83⋊#95—24no—
98C83⋊#95—24no—
99C83⋊#95—24no—
100C83⋊#95—24no—
101C83⋊#95C2×C418yescomplemented
102C23×C4×C83C2312yes—
103C23×C4×C83C2312yes—
104C23×C4×C83C2311yescharacteristic
105C23×C4×C83C2311yescharacteristic
106C23×C4×C83C2311yescharacteristic
107C2×C4⋊C4×C83—22no—
108C2×C4⋊C4×C83—22no—
109C2×C4⋊C4×C83—22no—
110C2×C4⋊C4×C83—24no—
111C2×C4⋊C4×C83—22no—
112C2×C4⋊C4×C83—22no—
113C2×C4⋊C4×C83—24no—
114C2×C4⋊C4×C83—24no—
115C2×C4⋊C4×C83C2×C414yescomplemented
116C2×C42×C83—22no—
117C2×C42×C83—22no—
118C2×C42×C83D414yes—
119#95×C83—24no—
120C23×D83—21no—
121C23×D83—21no—
122C23×D83—21no—
123C23×D83—21no—
124C23×D83—21no—
125C23×D83—21no—
126C23×D83—21no—
127C23×D83—21no—
128C23×D83C22×C412yes—
129C23×D83C2×D412yes—
130C23×D83C2×D412yes—
131C23×D83C2×Q812yes—
132C23×D83C2×Q812yes—
133C23×D83#4112yes—
134C23×D83#4112yes—
135C22×Dic83—21no—
136C22×Dic83—21no—
137C22×Dic83—21no—
138C22×Dic83—21no—
139C22×Dic83—21no—
140C22×Dic83—21no—
141C22×Dic83—21no—
142C22×Dic83—21no—
143C22×Dic83—21no—
144C22×Dic83—21no—
145C22×Dic83—21no—
146C22×Dic83—21no—
147C22×Dic83—22no—
148C22×Dic83—22no—
149C22×Dic83—22no—
150C22×Dic83—22no—
151C22×Dic83—22no—
152C22×Dic83—22no—
153C22×Dic83—22no—
154C22×Dic83—22no—
155C22×Dic83—22no—
156C22×Dic83—22no—
157C22×Dic83—22no—
158C22×Dic83—22no—
159C22×Dic83—22no—
160C22×Dic83C22×C414yes—
161C22×Dic83C22×C412yes—
162C22×Dic83C2×D412yes—
163C22×Dic83C2×D412yes—
164C22×Dic83C2×D412yes—
165C22×Dic83C2×D412yes—
166C22×Dic83C2×Q812yes—
167C22×Dic83C2×Q812yes—
168C22×Dic83#4112yes—
169C22×Dic83#4112yes—
170C2×C4×D83—28no—
171C2×C4×D83—28no—
172C2×C4×D83—28no—
173C2×C4×D83—28no—
174C2×C4×D83—28no—
175C2×C4×D83—28no—
176C2×C4×D83—28no—
177C2×C4×D83—28no—
178C2×C4×D83—28no—
179C2×C4×D83—28no—
180C2×C4×D83—28no—
181C2×C4×D83—28no—
182C2×C4×D83—28no—
183C2×C4×D83—28no—
184C2×C4×D83—28no—
185C2×C4×D83—28no—
186C2×C4×D83—28no—
187C2×C4×D83—28no—
188C2×C4×D83—28no—
189C2×C4×D83—28no—
190C2×C4×D83C4⋊C4116yescomplemented
191C4⋊Dic83—28no—
192C4⋊Dic83—44no—
193Dic83⋊C4—48no—
194(C2×D83)⋊C4—216no—
195(C2×D83)⋊C4—48no—
196C4×Dic83—28no—
197C4×Dic83—28no—
198C4×Dic83—28no—
199C24×C83C2411yescharacteristic
200C22×C4×C83—21no—
201C22×C4×C83—21no—
202C22×C4×C83—21no—
203C22×C4×C83—21no—
204C22×C4×C83—21no—
205C22×C4×C83—21no—
206C22×C4×C83—21no—
207C22×C4×C83—21no—
208C22×C4×C83—22no—
209C22×C4×C83—22no—
210C22×C4×C83—22no—
211C22×C4×C83—22no—
212C22×C4×C83—22no—
213C22×C4×C83—22no—
214C22×C4×C83—22no—
215C22×C4×C83—22no—
216C22×C4×C83—22no—
217C22×C4×C83—22no—
218C22×C4×C83—22no—
219C22×C4×C83—22no—
220C22×C4×C83—22no—
221C22×C4×C83C22×C414yes—
222C22×C4×C83C22×C412yes—
223C22×C4×C83C2×D412yes—
224C22×C4×C83C2×D412yes—
225C22×C4×C83C2×D412yes—
226C22×C4×C83C2×D412yes—
227C22×C4×C83C2×D412yes—
228C22×C4×C83C2×D412yes—
229C22×C4×C83C2×Q812yes—
230C22×C4×C83C2×Q812yes—
231C22×C4×C83#4112yes—
232C22×C4×C83#4112yes—
233C22×C4×C83#4112yes—
234C22×C4×C83#4112yes—
235C4⋊C4×C83—28no—
236C4⋊C4×C83—44no—
237C4⋊C4×C83—48no—
238C42×C83—28no—
239C23×C83C23×C411yescharacteristic
240C23×C83C22×D411yescharacteristic
241C23×C83C22×D411yescharacteristic
242C23×C83C22×D411yescharacteristic
243C23×C83C22×D411yescharacteristic
244C23×C83C22×Q811yescharacteristic
245C23×C83C22×Q811yescharacteristic
246C23×C83C2×#4111yescharacteristic
247C23×C83C2×#4111yescharacteristic
248C23×C83C2×#4111yescharacteristic
249C23×C83C2×#4111yescharacteristic
250C23×C83C2×#4111yescharacteristic
251C23×C83C2×#4111yescharacteristic
252C23×C83C2×#4111yescharacteristic
253C23×C83C2×#4111yescharacteristic
254C22×D83—22no—
255C22×D83—22no—
256C22×D83—22no—
257C22×D83—22no—
258C22×D83—22no—
259C22×D83—22no—
260C22×D83—22no—
261C22×D83—22no—
262C22×D83—22no—
263C22×D83—22no—
264C22×D83—22no—
265C22×D83—22no—
266C22×D83—22no—
267C22×D83—22no—
268C22×D83—22no—
269C22×D83—22no—
270C22×D83—22no—
271C22×D83—22no—
272C22×D83—22no—
273C22×D83—22no—
274C22×D83—22no—
275C22×D83—22no—
276C22×D83—22no—
277C22×D83—22no—
278C22×D83—22no—
279C22×D83—22no—
280C22×D83—22no—
281C22×D83—22no—
282C22×D83C2×C4⋊C414yes—
283C22×D83C4×D414yes—
284C22×D83C4×Q814yes—
285C22×D83#12114yes—
286C22×D83C22⋊Q814yes—
287C22×D83#12514yes—
288C22×D83C4⋊Q814yes—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
294C2×C4×C83—22no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—24no—
302C2×C4×C83—24no—
303C2×C4×C83—24no—
304C2×C4×C83—42no—
305C2×C4×C83—42no—
306C2×C4×C83—42no—
307C2×C4×C83—42no—
308C2×C4×C83—42no—
309C2×C4×C83—42no—
310C2×C4×C83—42no—
311C2×C4×C83—42no—
312C2×C4×C83—42no—
313C2×C4×C83—42no—
314C2×C4×C83—42no—
315C2×C4×C83C2×C4⋊C414yes—
316C2×C4×C83C4×D414yes—
317C2×C4×C83C4×D414yes—
318C2×C4×C83#12014yes—
319C2×C4×C83#12114yes—
320C2×C4×C83C22⋊Q814yes—
321C2×C4×C83C22⋊Q814yes—
322C2×C4×C83C22⋊Q814yes—
323C2×C4×C83#12314yes—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—22no—
327C2×Dic83—22no—
328C2×Dic83—22no—
329C2×Dic83—22no—
330C2×Dic83—22no—
331C2×Dic83—22no—
332C2×Dic83—22no—
333C2×Dic83—22no—
334C2×Dic83—22no—
335C2×Dic83—22no—
336C2×Dic83—22no—
337C2×Dic83—22no—
338C2×Dic83—22no—
339C2×Dic83—22no—
340C2×Dic83—22no—
341C2×Dic83—22no—
342C2×Dic83—24no—
343C2×Dic83—24no—
344C2×Dic83—24no—
345C2×Dic83—42no—
346C2×Dic83—42no—
347C2×Dic83—42no—
348C2×Dic83—42no—
349C2×Dic83—42no—
350C2×Dic83—42no—
351C2×Dic83—42no—
352C2×Dic83—42no—
353C2×Dic83—42no—
354C2×Dic83—42no—
355C2×Dic83—42no—
356C2×Dic83C2×C4⋊C414yes—
357C2×Dic83#12114yes—
358C2×Dic83C22⋊Q814yes—
359C4×D83—232no—
360C4×D83—232no—
361C4×D83—232no—
362C22×C83C22×C4⋊C411yescharacteristic
363C22×C83C2×C4×D411yescharacteristic
364C22×C83C2×C4×D411yescharacteristic
365C22×C83C2×C4×D411yescharacteristic
366C22×C83C2×C4×Q811yescharacteristic
367C22×C83C4×#4111yescharacteristic
368C22×C83C4×#4111yescharacteristic
369C22×C83C2×#12011yescharacteristic
370C22×C83C2×#12111yescharacteristic
371C22×C83C2×#12111yescharacteristic
372C22×C83C2×#12111yescharacteristic
373C22×C83C2×C22⋊Q811yescharacteristic
374C22×C83C2×C22⋊Q811yescharacteristic
375C22×C83C2×C22⋊Q811yescharacteristic
376C22×C83C2×C22⋊Q811yescharacteristic
377C22×C83C2×C22⋊Q811yescharacteristic
378C22×C83C2×#12311yescharacteristic
379C22×C83#52511yescharacteristic
380C22×C83#52511yescharacteristic
381C22×C83#52511yescharacteristic
382C22×C83#52511yescharacteristic
383C22×C83#52511yescharacteristic
384C22×C83#52511yescharacteristic
385C22×C83C2×#12511yescharacteristic
386C22×C83#52911yescharacteristic
387C22×C83#52911yescharacteristic
388C22×C83#52911yescharacteristic
389C22×C83#52911yescharacteristic
390C22×C83C2×C4⋊Q811yescharacteristic
391C22×C83#53211yescharacteristic
392C22×C83#53211yescharacteristic
393C22×C83#53311yescharacteristic
394C22×C83#53311yescharacteristic
395C22×C83#53311yescharacteristic
396C22×C83#53311yescharacteristic
397C2×D83—24no—
398C2×D83—24no—
399C2×D83—24no—
400C2×D83—24no—
401C2×D83—24no—
402C2×D83—24no—
403C2×D83—24no—
404C2×D83—24no—
405C2×D83—24no—
406C2×D83—24no—
407C2×D83—24no—
408C2×D83—24no—
409C2×D83—24no—
410C2×D83—24no—
411C2×D83#38918yescomplemented
412C4×C83—24no—
413C4×C83—24no—
414C4×C83—44no—
415C4×C83—82no—
416C4×C83#38518yescomplemented
417Dic83—24no—
418Dic83—24no—
419Dic83—24no—
420Dic83—44no—
421Dic83—82no—
422#14697—831nomaximal, Sylow
423C2×C83C2×#38511yescharacteristic
424C2×C83C2×#38911yescharacteristic
425C2×C83#229611yescharacteristic
426C2×C83C4×#12111yescharacteristic
427C2×C83C4×#12111yescharacteristic
428C2×C83C4×C22⋊Q811yescharacteristic
429C2×C83C4×C22⋊Q811yescharacteristic
430C2×C83#284711yescharacteristic
431C2×C83#284811yescharacteristic
432C2×C83#285111yescharacteristic
433C2×C83#285111yescharacteristic
434C2×C83#285411yescharacteristic
435C2×C83#285511yescharacteristic
436C2×C83#285711yescharacteristic
437C2×C83#285711yescharacteristic
438D83—28no—
439C23×C42—831no—
440C2×#389—831no—
441C2×#389D8311yescharacteristic, complemented
442C2×#385—832no—
443C2×#380—831no—
444C2×#380—831no—
445#1436—832no—
446#1436—832no—
447C4⋊#95—831no—
448C4⋊#95—831no—
449C22⋊#95—832no—
450C83#1469711yescharacteristic, complemented, Sylow
451C24×C4—831no—
452C24×C4—831no—
453C24×C4—831no—
454C22×C4⋊C4—831no—
455C22×C4⋊C4—832no—
456C22×C4⋊C4—831no—
457C22×C4⋊C4C2×D8312yes—
458C22×C4⋊C4C2×D8311yescharacteristic
459C22×C4⋊C4C2×D8311yescharacteristic
460C22×C22⋊C4—832no—
461C22×C22⋊C4—832no—
462C22×C42—831no—
463C22×C42—831no—
464C22×C42—831no—
465C22×C42—1664no—
466C22×C42—1664no—
467C22×C42—1664no—
468C22×C42C2×D8311yescharacteristic
469#389—24no—
470#389—1664no—
471#385—1668no—
472#380—838no—
473#380—1664no—
474C2×#95—832no—
475C2×#95—832no—
476C2×#95—832no—
477C2×#95—832no—
478C2×#95—832no—
479C2×#95—832no—
480C2×#95—832no—
481C2×#95C2×D8312yes—
482C25—831no—
483C23×C4—831no—
484C23×C4—831no—
485C23×C4—831no—
486C23×C4—834no—
487C23×C4—834no—
488C23×C4—834no—
489C23×C4—832no—
490C23×C4—834no—
491C23×C4—834no—
492C23×C4—832no—
493C23×C4—1662no—
494C23×C4—1662no—
495C23×C4—1662no—
496C23×C4—1662no—
497C23×C4—1662no—
498C23×C4—1662no—
499C23×C4—1662no—
500C23×C4—1662no—
501C23×C4—1662no—
502C23×C4—1662no—
503C23×C4—1662no—
504C23×C4—1662no—
505C23×C4—1662no—
506C23×C4—1662no—
507C23×C4—1662no—
508C23×C4—1662no—
509C23×C4C22×D8312yes—
510C23×C4C22×D8312yes—
511C23×C4C22×D8311yescharacteristic
512C23×C4C22×D8311yescharacteristic
513C23×C4C22×D8311yescharacteristic
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—24no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—834no—
523C2×C4⋊C4—1664no—
524C2×C4⋊C4—1664no—
525C2×C4⋊C4—1664no—
526C2×C4⋊C4—1662no—
527C2×C4⋊C4—1662no—
528C2×C4⋊C4—1662no—
529C2×C4⋊C4—1662no—
530C2×C4⋊C4—1662no—
531C2×C4⋊C4C4×D8314yescomplemented
532C2×C22⋊C4—838no—
533C2×C22⋊C4—1664no—
534C2×C22⋊C4—1664no—
535C2×C22⋊C4—1664no—
536C2×C22⋊C4—1664no—
537C2×C22⋊C4—1664no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—834no—
541C2×C42—16632no—
542C2×C42—1662no—
543C2×C42—1662no—
544C2×C42—1662no—
545C2×C42—1662no—
546C2×C42—1662no—
547C2×C42—1662no—
548C2×C42—1662no—
549C2×C42—1662no—
550C2×C42C22⋊D8314yes—
551#95—24no—
552#95—838no—
553#95—1664no—
554#95—1664no—
555#95—1664no—
556#95—1664no—
557#95—1664no—
558#95—1664no—
559C24—832no—
560C24—832no—
561C24—832no—
562C24—832no—
563C24—832no—
564C24—832no—
565C24—832no—
566C24—1661no—
567C24—1661no—
568C24—1661no—
569C24—1661no—
570C24—1661no—
571C24—1661no—
572C24—1661no—
573C24—1661no—
574C24C23×D8311yescharacteristic
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—832no—
597C22×C4—832no—
598C22×C4—832no—
599C22×C4—832no—
600C22×C4—832no—
601C22×C4—832no—
602C22×C4—832no—
603C22×C4—832no—
604C22×C4—832no—
605C22×C4—8316no—
606C22×C4—834no—
607C22×C4—1668no—
608C22×C4—1668no—
609C22×C4—1668no—
610C22×C4—1668no—
611C22×C4—1668no—
612C22×C4—1668no—
613C22×C4—1668no—
614C22×C4—1668no—
615C22×C4—1668no—
616C22×C4—1668no—
617C22×C4—1668no—
618C22×C4—1668no—
619C22×C4—1662no—
620C22×C4—1662no—
621C22×C4—1662no—
622C22×C4—1662no—
623C22×C4—1662no—
624C22×C4—1662no—
625C22×C4—1662no—
626C22×C4—1662no—
627C22×C4—1662no—
628C22×C4—1662no—
629C22×C4—1662no—
630C22×C4—1662no—
631C22×C4—1662no—
632C22×C4—1661no—
633C22×C4—1661no—
634C22×C4—1661no—
635C22×C4—1661no—
636C22×C4—1661no—
637C22×C4—1661no—
638C22×C4—1661no—
639C22×C4—1661no—
640C22×C4—1661no—
641C22×C4—1661no—
642C22×C4—1661no—
643C22×C4—1661no—
644C22×C4—1668no—
645C22×C4—1668no—
646C22×C4—1668no—
647C22×C4—1668no—
648C22×C4—1668no—
649C22×C4—1668no—
650C22×C4—1668no—
651C22×C4—1668no—
652C22×C4C2×C4×D8314yes—
653C22×C4C2×C4×D8312yes—
654C22×C4D4×D8312yes—
655C22×C4D4×D8312yes—
656C22×C4D4×D8312yes—
657C22×C4C2×C22⋊D8312yes—
658C22×C4C2×C22⋊D8312yes—
659C22×C4C2×C22⋊D8312yes—
660C22×C4Q8×D8312yes—
661C22×C4Q8×D8312yes—
662C22×C4#1305058912yes—
663C22×C4#1305059012yes—
664C22×C4#1305059112yes—
665C22×C4#1305059112yes—
666C4⋊C4—28no—
667C4⋊C4—44no—
668C4⋊C4—48no—
669C4⋊C4—3328no—
670C4⋊C4—3324no—
671C4⋊C4—1668no—
672C22⋊C4—3328no—
673C22⋊C4—16616no—
674C42—28no—
675C42—1668no—
676C42—1668no—
677C42—1668no—
678C23—834no—
679C23—834no—
680C23—834no—
681C23—834no—
682C23—834no—
683C23—834no—
684C23—834no—
685C23—1662no—
686C23—1662no—
687C23—1662no—
688C23—1662no—
689C23—1662no—
690C23—1662no—
691C23—1662no—
692C23—1662no—
693C23—1662no—
694C23—1662no—
695C23—1662no—
696C23—1662no—
697C23—1662no—
698C23—1662no—
699C23—1662no—
700C23—1662no—
701C23—1662no—
702C23—1662no—
703C23—1662no—
704C23—1662no—
705C23—1662no—
706C23—1662no—
707C23—1662no—
708C23—1662no—
709C23—1662no—
710C23—1662no—
711C23—1662no—
712C23—1662no—
713C23C22×C4×D8311yescharacteristic
714C23C2×D4×D8311yescharacteristic
715C23C2×D4×D8311yescharacteristic
716C23C2×D4×D8311yescharacteristic
717C23C22×C22⋊D8311yescharacteristic
718C23C2×Q8×D8311yescharacteristic
719C23C2×Q8×D8311yescharacteristic
720C23#41×D8311yescharacteristic
721C23#41×D8311yescharacteristic
722C23#41×D8311yescharacteristic
723C23#41×D8311yescharacteristic
724C23C2×#1305058911yescharacteristic
725C23C2×#1305059011yescharacteristic
726C23C2×#1305059111yescharacteristic
727C23C2×#1305059111yescharacteristic
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—3322no—
755C2×C4—3322no—
756C2×C4—3322no—
757C2×C4—3322no—
758C2×C4—3322no—
759C2×C4—3322no—
760C2×C4—3322no—
761C2×C4—3322no—
762C2×C4—3322no—
763C2×C4—3322no—
764C2×C4—3322no—
765C2×C4—834no—
766C2×C4—834no—
767C2×C4—834no—
768C2×C4—16632no—
769C2×C4—16632no—
770C2×C4—1664no—
771C2×C4—1664no—
772C2×C4—1664no—
773C2×C4—1662no—
774C2×C4—1662no—
775C2×C4—1662no—
776C2×C4—1662no—
777C2×C4—1662no—
778C2×C4—1662no—
779C2×C4—1662no—
780C2×C4—1662no—
781C2×C4—1662no—
782C2×C4—1662no—
783C2×C4—1662no—
784C2×C4—1662no—
785C2×C4—1662no—
786C2×C4—1662no—
787C2×C4—1662no—
788C2×C4—1662no—
789C2×C4—1662no—
790C2×C4—1662no—
791C2×C4—16632no—
792C2×C4C4⋊C4×D8314yes—
793C2×C4C4×C22⋊D8314yes—
794C2×C4#1458175414yes—
795C2×C4#1458176014yes—
796C2×C4#1458176314yes—
797C2×C4#1458176814yes—
798C2×C4#1458176814yes—
799C2×C4#1458177014yes—
800C2×C4#1458177714yes—
801C22—838no—
802C22—1664no—
803C22—1664no—
804C22—1664no—
805C22—1664no—
806C22—1664no—
807C22—1664no—
808C22—1664no—
809C22—1664no—
810C22—1664no—
811C22—1664no—
812C22—1664no—
813C22—1664no—
814C22—1664no—
815C22—1664no—
816C22C2×C4⋊C4×D8311yescharacteristic
817C22C4×D4×D8311yescharacteristic
818C22C2×C4×C22⋊D8311yescharacteristic
819C22C2×#1458175411yescharacteristic
820C22C4×Q8×D8311yescharacteristic
821C22C4×#1305058911yescharacteristic
822C22C4×#1305059111yescharacteristic
823C22C2×#1458176011yescharacteristic
824C22#121×D8311yescharacteristic
825C22#121×D8311yescharacteristic
826C22C2×#1458176311yescharacteristic
827C22C22⋊Q8×D8311yescharacteristic
828C22C22⋊Q8×D8311yescharacteristic
829C22C2×#1458176811yescharacteristic
830C22C2×#1458176811yescharacteristic
831C22C2×#1458177011yescharacteristic
832C22C2×#1458177711yescharacteristic
833C22#1912820811yescharacteristic
834C22#1912820811yescharacteristic
835C22#1912821111yescharacteristic
836C22#1912821111yescharacteristic
837C22#1912821411yescharacteristic
838C22#1912821411yescharacteristic
839C22#125×D8311yescharacteristic
840C22#1912823311yescharacteristic
841C22#1912823611yescharacteristic
842C22#1912823611yescharacteristic
843C22#1912823811yescharacteristic
844C22C4⋊Q8×D8311yescharacteristic
845C22#1912824811yescharacteristic
846C22#1912825211yescharacteristic
847C22#1912825511yescharacteristic
848C22#1912825611yescharacteristic
849C22#1912825611yescharacteristic
850C22#1912825711yescharacteristic
851C4—24no—
852C4—24no—
853C4—44no—
854C4—82no—
855C4—3324no—
856C4—6642no—
857C4—1664no—
858C4—1664no—
859C4—1664no—
860C4#1912757218yescomplemented
861C2—1668no—
862C2C2×#1912757211yescharacteristic
863C2#389×D8311yescharacteristic
864C2#2490994411yescharacteristic
865C2C4×#1458176311yescharacteristic
866C2#2490997111yescharacteristic
867C2C4×#1458176811yescharacteristic
868C2#2490999311yescharacteristic
869C2#2491574211yescharacteristic
870C2#2491574711yescharacteristic
871C2#2491576811yescharacteristic
872C2#2491577211yescharacteristic
873C2#2491579611yescharacteristic
874C2#2491580111yescharacteristic
875C2#2491581011yescharacteristic
876C2#2491581411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#389×C83C2
socle, cosocleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×#389D83
hypocenterC83#14697
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#19127597C2semidirect
6. #24905695C2semidirect
7. #24905694C2semidirect
8. #24905693C2semidirect
9. #24905692C2semidirect
11. C2×#389×C83C2semidirect
29. #19127558C4semidirect
75. C2×C4⋊Dic83C2×C4semidirect
101. C83⋊#95C2×C4semidirect
115. C2×C4⋊C4×C83C2×C4semidirect
190. C2×C4×D83C4⋊C4semidirect
411. C2×D83#389semidirect
416. C4×C83#385semidirect
441. C2×#389D83semidirect
450. C83#14697semidirect
531. C2×C4⋊C4C4×D83semidirect
860. C4#19127572semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D832
C2×#191275972
C2×#191275722
C2×#191275582
#249056952
#249056942
#249056932
#249056922
(C2×D83)⋊#952
C2×#389×C832
#1469783