Finite Group Databasebeta

← #35576991

Subgroups — #35576991

Order 21248.

2866 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128327C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D83C211yesmaximal, characteristic
3#24915799C212yesmaximal, complemented
4#24915749C212yesmaximal, complemented
5#24913282C212yesmaximal, complemented
6#24913274C212yesmaximal, complemented
7#24911289C214yesmaximal, complemented
8#24911287C214yesmaximal, complemented
9#24911274C214yesmaximal, complemented
10#24911272C214yesmaximal, complemented
11#24910075C211yesmaximal, characteristic, complemented
12#24910038C211yesmaximal, characteristic
13#24910038C211yesmaximal, characteristic
14C2×#19127574C211yesmaximal, characteristic, complemented
15C2×#385×C83C211yesmaximal, characteristic, complemented
16C23×C22⋊D83C2211yescharacteristic
17C23×C4×D83C2211yescharacteristic
18#19128327—28no—
19C2×#14581771C2212yescomplemented
20C2×#14581771C2212yescomplemented
21C2×#14581770C2214yescomplemented
22C2×#14581769C2212yes—
23C2×#14581769C2212yes—
24C2×#14581769C2212yescomplemented
25C2×#14581769C2212yescomplemented
26C2×C4×C22⋊D83—28no—
27C2×C4×C22⋊D83C2214yes—
28C2×C4×C22⋊D83C2214yes—
29C22×Dic83⋊C4C2211yescharacteristic
30C22×Dic83⋊C4C2212yescomplemented
31C22×C22⋊Dic83C2211yescharacteristic
32C22×C22⋊Dic83C2211yescharacteristic
33C22×C22⋊Dic83C2211yescharacteristic
34C22×(C2×D83)⋊C4C2211yescharacteristic
35C22×C4×Dic83C2211yescharacteristic
36#19127642C2214yescomplemented
37#19127636C2214yescomplemented
38#19127635C2214yescomplemented
39#19127632C2214yescomplemented
40#19127625C2214yescomplemented
41#19127623C2214yescomplemented
42#19127621C2214yescomplemented
43#19127614C2214yescomplemented
44#19127605C2214yescomplemented
45#19127596C2214yescomplemented
46#19127587C2214yescomplemented
47#19127583C2214yescomplemented
48#19127580C2212yes—
49#19127580C2214yes—
50#19127580C2212yes—
51#19127578C2212yes—
52#19127578C2214yes—
53#19127578C2212yes—
54#19127575C2214yescomplemented
55#19127574C2212yes—
56#19127574C2212yes—
57#19127574C2214yescomplemented
58#19127574C2214yescomplemented
59#19127573C2214yescomplemented
60#19127572C2214yescomplemented
61#19127562C2212yes—
62#19127562C2212yes—
63#19127560C2214yescomplemented
64#19127559C2212yes—
65#19127559C2212yes—
66#19127556C2212yes—
67#19127556C2212yes—
68C2×C83⋊#95C2212yescomplemented
69C24×C4×C83C2211yescharacteristic
70C22×C4⋊C4×C83C2212yescomplemented
71C22×C22⋊C4×C83C2211yescharacteristic
72C22×C22⋊C4×C83C2211yescharacteristic
73#385×C83C2212yes—
74#385×C83C2212yes—
75#385×C83C2214yescomplemented
76C2×#95×C83C2212yescomplemented
77C24×D83C2311yescharacteristic
78C22×Dic166C2312yes—
79C22×Dic166C2312yes—
80C22×C22⋊D83—24no—
81C22×C22⋊D83—24no—
82C22×C22⋊D83Q818yescomplemented
83C22×C22⋊D83C2312yes—
84C22×C22⋊D83C2312yes—
85C23×Dic83C2311yescharacteristic
86C23×Dic83C2312yes—
87C23×Dic83C2311yescharacteristic
88C23×Dic83C2311yescharacteristic
89C23×Dic83C2311yescharacteristic
90C23×Dic83C2311yescharacteristic
91C22×C4×D83—24no—
92C22×C4×D83—44no—
93C22×C4×D83C2314yes—
94#14581771—28no—
95#14581771—28no—
96#14581770—48no—
97#14581769—28no—
98#14581769—28no—
99#14581769—28no—
100#14581769—28no—
101C4×C22⋊D83—216no—
102C4×C22⋊D83—216no—
103C2×C4⋊Dic83C2312yes—
104C2×C4⋊Dic83C2312yes—
105C2×Dic83⋊C4—24no—
106C2×Dic83⋊C4—44no—
107C2×Dic83⋊C4C2312yes—
108C2×Dic83⋊C4C2312yes—
109C2×Dic83⋊C4C2314yes—
110C2×Dic83⋊C4C2312yes—
111C2×Dic83⋊C4C2312yes—
112C2×Dic83⋊C4C2314yes—
113C2×Dic83⋊C4C2314yes—
114C2×Dic83⋊C4C2314yes—
115C2×Dic83⋊C4C2314yes—
116C2×C22⋊Dic83—24no—
117C2×C22⋊Dic83—24no—
118C2×C22⋊Dic83D418yes—
119C2×C22⋊Dic83C2312yes—
120C2×C22⋊Dic83C2312yes—
121C2×C22⋊Dic83C2312yes—
122C2×C22⋊Dic83C2312yes—
123C2×C22⋊Dic83C2312yes—
124C2×C22⋊Dic83C2312yes—
125C2×(C2×D83)⋊C4—24no—
126C2×(C2×D83)⋊C4C2314yes—
127C2×(C2×D83)⋊C4C2314yes—
128C2×(C2×D83)⋊C4C2314yes—
129C2×(C2×D83)⋊C4C2314yes—
130C2×(C2×D83)⋊C4C2314yes—
131C2×C4×Dic83—24no—
132C2×C4×Dic83C2314yes—
133C83⋊#95C2314yes—
134C83⋊#95C2314yes—
135C83⋊#95C2314yes—
136C83⋊#95C2314yes—
137C83⋊#95C2314yes—
138C83⋊#95C2314yes—
139C83⋊#95C2314yes—
140C83⋊#95C2314yes—
141C25×C83C2311yescharacteristic
142C23×C4×C83—24no—
143C23×C4×C83—44no—
144C23×C4×C83C2311yescharacteristic
145C23×C4×C83C2312yes—
146C23×C4×C83C2312yes—
147C23×C4×C83C2311yescharacteristic
148C23×C4×C83C2312yes—
149C23×C4×C83C2311yescharacteristic
150C23×C4×C83C2311yescharacteristic
151C2×C4⋊C4×C83—44no—
152C2×C4⋊C4×C83C2314yes—
153C2×C4⋊C4×C83C2314yes—
154C2×C22⋊C4×C83—24no—
155C2×C22⋊C4×C83—24no—
156C2×C22⋊C4×C83C2312yes—
157C2×C22⋊C4×C83C2312yes—
158C2×C22⋊C4×C83C2312yes—
159C2×C22⋊C4×C83C2312yes—
160#95×C83C2314yes—
161#95×C83C2314yes—
162C23×D83—22no—
163C23×D83—22no—
164C23×D83—42no—
165C23×D83—42no—
166C23×D83C2×Q814yes—
167C23×D83C2412yes—
168C2×Dic166—24no—
169C2×Dic166—24no—
170C2×Dic166—44no—
171C2×Dic166—44no—
172C2×C22⋊D83—232no—
173C2×C22⋊D83—24no—
174C2×C22⋊D83—24no—
175C2×C22⋊D83—24no—
176C2×C22⋊D83—24no—
177C2×C22⋊D83C2×Q818yes—
178C2×C22⋊D83C2×Q818yes—
179C22×Dic83—22no—
180C22×Dic83—22no—
181C22×Dic83—24no—
182C22×Dic83—22no—
183C22×Dic83—22no—
184C22×Dic83—42no—
185C22×Dic83—42no—
186C22×Dic83—42no—
187C22×Dic83—42no—
188C22×Dic83—42no—
189C22×Dic83—42no—
190C22×Dic83C2×D414yes—
191C22×Dic83C2×D414yes—
192C22×Dic83C2×Q814yes—
193C22×Dic83C2412yes—
194C22×Dic83C2412yes—
195C22×Dic83C2414yes—
196C22×Dic83C2412yes—
197C22×Dic83C2412yes—
198C22×Dic83C2412yes—
199C2×C4×D83—28no—
200C2×C4×D83—28no—
201C2×C4×D83—44no—
202C2×C4×D83—416no—
203C4⋊Dic83—24no—
204C4⋊Dic83—24no—
205Dic83⋊C4—28no—
206Dic83⋊C4—24no—
207Dic83⋊C4—24no—
208Dic83⋊C4—24no—
209Dic83⋊C4—24no—
210Dic83⋊C4—28no—
211Dic83⋊C4—44no—
212Dic83⋊C4—44no—
213Dic83⋊C4—44no—
214C22⋊Dic83—24no—
215C22⋊Dic83—24no—
216C22⋊Dic83—24no—
217C22⋊Dic83—24no—
218C22⋊Dic83C2×D418yes—
219C22⋊Dic83C2×D418yes—
220(C2×D83)⋊C4—28no—
221(C2×D83)⋊C4—44no—
222(C2×D83)⋊C4—44no—
223(C2×D83)⋊C4—44no—
224(C2×D83)⋊C4—44no—
225C4×Dic83—28no—
226C24×C83—42no—
227C24×C83—42no—
228C24×C83C2×D414yes—
229C24×C83C2×Q814yes—
230C24×C83#4114yes—
231C24×C83C2411yescharacteristic
232C24×C83C2411yescharacteristic
233C24×C83C2411yescharacteristic
234C22×C4×C83—22no—
235C22×C4×C83—24no—
236C22×C4×C83—22no—
237C22×C4×C83—24no—
238C22×C4×C83—24no—
239C22×C4×C83—24no—
240C22×C4×C83—22no—
241C22×C4×C83—22no—
242C22×C4×C83—24no—
243C22×C4×C83—24no—
244C22×C4×C83—42no—
245C22×C4×C83—42no—
246C22×C4×C83—42no—
247C22×C4×C83—42no—
248C22×C4×C83—42no—
249C22×C4×C83—42no—
250C22×C4×C83—42no—
251C22×C4×C83—416no—
252C22×C4×C83C2412yes—
253C22×C4×C83C2412yes—
254C22×C4×C83C2414yes—
255C22×C4×C83C2412yes—
256C22×C4×C83C2412yes—
257C4⋊C4×C83—28no—
258C4⋊C4×C83—44no—
259C22⋊C4×C83—24no—
260C22⋊C4×C83—24no—
261C22⋊C4×C83—24no—
262C22⋊C4×C83—24no—
263C23×C83—22no—
264C23×C83—22no—
265C23×C83—22no—
266C23×C83—22no—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83—44no—
270C23×C83—44no—
271C23×C83—48no—
272C23×C83—48no—
273C23×C83C22⋊Q8116yescomplemented
274C23×C83C22×D412yes—
275C23×C83C22×D412yes—
276C23×C83C22×D412yes—
277C23×C83C22×Q812yes—
278C23×C83C22×Q812yes—
279C23×C83C22×Q812yes—
280C23×C83C2×#4112yes—
281C23×C83C2×#4112yes—
282C23×C83C2×#4112yes—
283C23×C83C2511yescharacteristic
284C22×D83—28no—
285C22×D83—22no—
286C22×D83—22no—
287C22×D83—24no—
288C22×D83—24no—
289C22×D83—48no—
290C22×D83—44no—
291C22×D83—48no—
292C22×D83—44no—
293C22×D83C22×Q814yes—
294C2×C4×C83—28no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—24no—
301C2×C4×C83—24no—
302C2×C4×C83—24no—
303C2×C4×C83—22no—
304C2×C4×C83—22no—
305C2×C4×C83—24no—
306C2×C4×C83—24no—
307C2×C4×C83—48no—
308C2×C4×C83—48no—
309C2×C4×C83—48no—
310C2×C4×C83—44no—
311C2×C4×C83—82no—
312C2×C4×C83—82no—
313C2×C4×C83H(5,𝔽2)14yes—
314C22⋊D83—216no—
315C22⋊D83—216no—
316C2×Dic83—28no—
317C2×Dic83—22no—
318C2×Dic83—22no—
319C2×Dic83—24no—
320C2×Dic83—24no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—24no—
324C2×Dic83—24no—
325C2×Dic83—24no—
326C2×Dic83—24no—
327C2×Dic83—24no—
328C2×Dic83—44no—
329C2×Dic83—44no—
330C2×Dic83—48no—
331C2×Dic83—82no—
332C2×Dic83—82no—
333C2×Dic83C22×D414yes—
334C2×Dic83C22×D414yes—
335C2×Dic83C22×Q814yes—
336C4×D83—416no—
337Dic166—84no—
338Dic166—84no—
339C22×C83—24no—
340C22×C83—24no—
341C22×C83—24no—
342C22×C83—22no—
343C22×C83—22no—
344C22×C83—22no—
345C22×C83—22no—
346C22×C83—22no—
347C22×C83—22no—
348C22×C83—24no—
349C22×C83—24no—
350C22×C83—24no—
351C22×C83—416no—
352C22×C83C2×C22⋊Q814yes—
353C22×C83C2×C22⋊Q814yes—
354C22×C83C2×C22⋊Q814yes—
355C22×C83C23×D411yescharacteristic
356C22×C83C23×Q811yescharacteristic
357C22×C83C22×#4111yescharacteristic
358C22×C83C2×H(5,𝔽2)12yes—
359C22×C83#58512yes—
360C2×D83—24no—
361C2×D83—28no—
362C2×D83—416no—
363C2×D83—44no—
364C2×D83—42no—
365C2×D83—42no—
366C4×C83—24no—
367C4×C83—44no—
368C4×C83—42no—
369C4×C83—42no—
370C4×C83—42no—
371Dic83—24no—
372Dic83—24no—
373Dic83—24no—
374Dic83—44no—
375Dic83—42no—
376Dic83—42no—
377#34985—831nomaximal, Sylow
378C2×C83—24no—
379C2×C83—24no—
380C2×C83—24no—
381C2×C83C22×C22⋊Q811yescharacteristic
382C2×C83#345912yes—
383C2×C83#348411yescharacteristic
384C2×C83#348511yescharacteristic
385C2×C83#350112yes—
386D83—44no—
387C2×#543—831no—
388C22×C4×D4—831no—
389#2855—832no—
390#2848—832no—
391#2627—832no—
392#2626—832no—
393#2450—834no—
394#2450—834no—
395#2449—834no—
396#2449—834no—
397#2315—831no—
398#2308—831no—
399#2308—831no—
400C2×#385—831no—
401C2×#385D8311yescharacteristic, complemented
402C83#3498511yescharacteristic, complemented, Sylow
403C23×D4—831no—
404C24×C4—831no—
405C24×C4C2×D8311yescharacteristic
406#543—1668no—
407C2×C22⋊Q8—832no—
408C2×C22⋊Q8—832no—
409C2×C22⋊Q8—834no—
410C2×C22⋊Q8—832no—
411C2×C22⋊Q8—832no—
412C2×C22⋊Q8—832no—
413C2×C22⋊Q8—832no—
414C2×C4×D4—834no—
415C2×C4×D4—834no—
416C2×C4×D4—1668no—
417C22×C4⋊C4—832no—
418C22×C4⋊C4—831no—
419C22×C4⋊C4C2×D8312yescomplemented
420C22×C22⋊C4—831no—
421C22×C22⋊C4—831no—
422C22×C22⋊C4—831no—
423C22×C22⋊C4—831no—
424C22×C22⋊C4C2×D8311yescharacteristic
425C22×C22⋊C4C2×D8311yescharacteristic
426C22×C42—831no—
427#400—834no—
428#399—834no—
429#398—834no—
430#398—834no—
431#396—834no—
432#396—834no—
433#395—834no—
434#393—834no—
435#391—834no—
436#389—834no—
437#387—834no—
438#387—834no—
439#386—832no—
440#386—834no—
441#386—832no—
442#386—832no—
443#386—834no—
444#386—832no—
445#385—834no—
446#385—832no—
447#385—832no—
448#385—834no—
449#385—834no—
450#385—834no—
451#385—834no—
452#385C2×D8312yes—
453#385C2×D8312yes—
454#385C2×D8314yescomplemented
455#381—832no—
456#381—832no—
457#380—832no—
458#380—832no—
459#380—834no—
460#379—832no—
461#379—832no—
462C2×#95—832no—
463C2×#95C2×D8312yescomplemented
464C25—831no—
465C25C22×D8311yescharacteristic
466C22×Q8—832no—
467C22×Q8—832no—
468C22×D4—838no—
469C22×D4—832no—
470C22×D4—832no—
471C22×D4—1664no—
472C22×D4—1664no—
473C23×C4—24no—
474C23×C4—44no—
475C23×C4—3324no—
476C23×C4—831no—
477C23×C4—831no—
478C23×C4—831no—
479C23×C4—832no—
480C23×C4—831no—
481C23×C4—834no—
482C23×C4—831no—
483C23×C4—1664no—
484C23×C4C22×D8311yescharacteristic
485C23×C4C22×D8312yes—
486C23×C4C22×D8312yes—
487C23×C4C22×D8311yescharacteristic
488C23×C4C22×D8311yescharacteristic
489C23×C4C22×D8312yes—
490C23×C4C22×D8311yescharacteristic
491C22⋊Q8—3328no—
492C22⋊Q8—1668no—
493C22⋊Q8—1668no—
494C22⋊Q8—1668no—
495C22⋊Q8—1668no—
496C22⋊Q8—1668no—
497C22⋊Q8—1668no—
498C4×D4—16616no—
499C4×D4—16616no—
500C2×C4⋊C4—44no—
501C2×C4⋊C4—3324no—
502C2×C4⋊C4—834no—
503C2×C4⋊C4—834no—
504C2×C4⋊C4—834no—
505C2×C4⋊C4—834no—
506C2×C4⋊C4—834no—
507C2×C4⋊C4—832no—
508C2×C4⋊C4—832no—
509C2×C4⋊C4—832no—
510C2×C4⋊C4—832no—
511C2×C4⋊C4—832no—
512C2×C4⋊C4—832no—
513C2×C4⋊C4—1664no—
514C2×C4⋊C4C22×D8314yes—
515C2×C4⋊C4C22×D8314yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—834no—
519C2×C22⋊C4—834no—
520C2×C22⋊C4—834no—
521C2×C22⋊C4—834no—
522C2×C22⋊C4—838no—
523C2×C22⋊C4—832no—
524C2×C22⋊C4—832no—
525C2×C22⋊C4—832no—
526C2×C22⋊C4—832no—
527C2×C22⋊C4—832no—
528C2×C22⋊C4—832no—
529C2×C22⋊C4—834no—
530C2×C22⋊C4—1664no—
531C2×C22⋊C4—1664no—
532C2×C22⋊C4—1664no—
533C2×C22⋊C4C22×D8312yes—
534C2×C22⋊C4C22×D8312yes—
535C2×C22⋊C4C22×D8312yes—
536C2×C22⋊C4C22×D8312yes—
537C2×C42—834no—
538C2×C42—1664no—
539#95—834no—
540#95—834no—
541#95—834no—
542#95—834no—
543#95—834no—
544#95—834no—
545#95—834no—
546#95—834no—
547#95C22×D8314yes—
548#95C22×D8314yes—
549C24—42no—
550C24—42no—
551C24—3322no—
552C24—3322no—
553C24—834no—
554C24—832no—
555C24—1662no—
556C24—1662no—
557C24D4×D8314yes—
558C24Q8×D8314yes—
559C24#1305059014yes—
560C24C23×D8311yescharacteristic
561C24C23×D8311yescharacteristic
562C24C23×D8311yescharacteristic
563C2×Q8—3324no—
564C2×Q8—3324no—
565C2×Q8—1664no—
566C2×Q8—1664no—
567C2×D4—838no—
568C2×D4—838no—
569C2×D4—16632no—
570C2×D4—1664no—
571C2×D4—1664no—
572C2×D4—1664no—
573C2×D4—1664no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—416no—
592C22×C4—33216no—
593C22×C4—3324no—
594C22×C4—3322no—
595C22×C4—3322no—
596C22×C4—3322no—
597C22×C4—3322no—
598C22×C4—3322no—
599C22×C4—3322no—
600C22×C4—834no—
601C22×C4—834no—
602C22×C4—834no—
603C22×C4—832no—
604C22×C4—832no—
605C22×C4—832no—
606C22×C4—834no—
607C22×C4—832no—
608C22×C4—832no—
609C22×C4—1668no—
610C22×C4—1664no—
611C22×C4—1668no—
612C22×C4—1662no—
613C22×C4—1662no—
614C22×C4—1662no—
615C22×C4—1662no—
616C22×C4C23×D8314yes—
617C22×C4C23×D8312yes—
618C22×C4C23×D8312yes—
619C22×C4C23×D8312yes—
620C22×C4C23×D8312yes—
621C4⋊C4—28no—
622C4⋊C4—44no—
623C4⋊C4—3324no—
624C4⋊C4—3324no—
625C4⋊C4—3324no—
626C4⋊C4—1668no—
627C4⋊C4—1664no—
628C4⋊C4—1664no—
629C4⋊C4—1664no—
630C4⋊C4—1664no—
631C4⋊C4—1664no—
632C4⋊C4—1664no—
633C4⋊C4—1668no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—3324no—
639C22⋊C4—3324no—
640C22⋊C4—3324no—
641C22⋊C4—3324no—
642C22⋊C4—838no—
643C22⋊C4—838no—
644C22⋊C4—1668no—
645C22⋊C4—1664no—
646C22⋊C4—1664no—
647C22⋊C4—1664no—
648C22⋊C4—1664no—
649C42—1668no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—44no—
657C23—44no—
658C23—48no—
659C23—48no—
660C23—3324no—
661C23—3324no—
662C23—3328no—
663C23—3328no—
664C23—834no—
665C23—1668no—
666C23—1662no—
667C23—1662no—
668C23—1664no—
669C23—1664no—
670C23#14581770116yescomplemented
671C23C2×D4×D8312yes—
672C23C2×D4×D8312yes—
673C23C2×D4×D8312yes—
674C23C2×Q8×D8312yes—
675C23C2×Q8×D8312yes—
676C23C2×Q8×D8312yes—
677C23C2×#1305059012yes—
678C23C2×#1305059012yes—
679C23C2×#1305059012yes—
680C23C24×D8311yescharacteristic
681Q8—6644no—
682Q8—6644no—
683D4—16616no—
684D4—16616no—
685C2×C4—28no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—48no—
699C2×C4—48no—
700C2×C4—44no—
701C2×C4—48no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—33216no—
705C2×C4—3328no—
706C2×C4—3324no—
707C2×C4—3324no—
708C2×C4—834no—
709C2×C4—834no—
710C2×C4—834no—
711C2×C4—6642no—
712C2×C4—6642no—
713C2×C4—1662no—
714C2×C4—1662no—
715C2×C4—1664no—
716C2×C4—1664no—
717C2×C4—1664no—
718C2×C4—1664no—
719C2×C4—1664no—
720C2×C4—1668no—
721C2×C4—1662no—
722C2×C4—1662no—
723C2×C4—1664no—
724C2×C4—1664no—
725C2×C4#1458183714yes—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—416no—
739C22—33216no—
740C22—3322no—
741C22—3322no—
742C22—3324no—
743C22—1664no—
744C22—1668no—
745C22C2×#1458177014yes—
746C22C2×#1458177014yes—
747C22C2×#1458177014yes—
748C22C22×D4×D8311yescharacteristic
749C22C22×Q8×D8311yescharacteristic
750C22C22×#1305059011yescharacteristic
751C22C2×#1458183712yes—
752C22#1912853712yes—
753C4—24no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—44no—
758C4—3322no—
759C4—3322no—
760C4—3324no—
761C4—1664no—
762C4—1664no—
763C4—1664no—
764C2—24no—
765C2—24no—
766C2—24no—
767C2—3324no—
768C2C22×#1458177011yescharacteristic
769C2#2492087212yes—
770C2#2492109211yescharacteristic
771C2#2492110111yescharacteristic
772C2#2492125912yes—
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC2×#385×C83C2
prime radicalC23×C22⋊D83C22
hypercenterC2×#385D83
hypocenterC83#34985
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#19128327C2semidirect
3. #24915799C2semidirect
4. #24915749C2semidirect
5. #24913282C2semidirect
6. #24913274C2semidirect
7. #24911289C2semidirect
8. #24911287C2semidirect
9. #24911274C2semidirect
10. #24911272C2semidirect
11. #24910075C2semidirect
14. C2×#19127574C2semidirect
15. C2×#385×C83C2semidirect
19. C2×#14581771C22semidirect
20. C2×#14581771C22semidirect
21. C2×#14581770C22semidirect
24. C2×#14581769C22semidirect
25. C2×#14581769C22semidirect
30. C22×Dic83⋊C4C22semidirect
36. #19127642C22semidirect
37. #19127636C22semidirect
38. #19127635C22semidirect
39. #19127632C22semidirect
40. #19127625C22semidirect
41. #19127623C22semidirect
42. #19127621C22semidirect
43. #19127614C22semidirect
44. #19127605C22semidirect
45. #19127596C22semidirect
46. #19127587C22semidirect
47. #19127583C22semidirect
54. #19127575C22semidirect
57. #19127574C22semidirect
58. #19127574C22semidirect
59. #19127573C22semidirect
60. #19127572C22semidirect
63. #19127560C22semidirect
68. C2×C83⋊#95C22semidirect
70. C22×C4⋊C4×C83C22semidirect
75. #385×C83C22semidirect
76. C2×#95×C83C22semidirect
82. C22×C22⋊D83Q8semidirect
273. C23×C83C22⋊Q8semidirect
401. C2×#385D83semidirect
402. C83#34985semidirect
419. C22×C4⋊C4C2×D83semidirect
454. #385C2×D83semidirect
463. C2×#95C2×D83semidirect
670. C23#14581770semidirect

Maximal subgroups

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

subgroupindex
C2×#191283272
C22×C4×C22⋊D832
#249157992
#249157492
#249132822
#249132742
#249112892
#249112872
#249112742
#249112722
#249100752
#249100382
C2×#191275742
C2×#385×C832
#3498583