Finite Group Databasebeta

← #35327539

Subgroups — #35327539

Order 21248.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581768C211yesmaximal, characteristic
2C2×#19127608C211yesmaximal, characteristic, complemented
3C2×#19127597C211yesmaximal, characteristic, complemented
4C2×#19127558C211yesmaximal, characteristic
5C2×C4×C4⋊Dic83C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic
7#24905729C212yesmaximal, complemented
8#24905707C212yesmaximal
9#24905699C212yesmaximal
10Dic83⋊#95C212yesmaximal, complemented
11C2×#391×C83C211yesmaximal, characteristic, complemented
12C23×C4×D83C2211yescharacteristic
13C2×#14581768—24no—
14C2×#14581768—24no—
15C2×#14581768C418yescomplemented
16C22×C4⋊Dic83C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×Dic83⋊C4C2212yes—
19C22×Dic83⋊C4C2212yes—
20C22×(C2×D83)⋊C4C2211yescharacteristic
21C22×(C2×D83)⋊C4C2212yes—
22C22×(C2×D83)⋊C4C2212yes—
23C22×(C2×D83)⋊C4C2211yescharacteristic
24C22×C4×Dic83C2211yescharacteristic
25C22×C4×Dic83C2212yes—
26#19127608—24no—
27#19127597—24no—
28#19127558—24no—
29C4×C4⋊Dic83—24no—
30C4×(C2×D83)⋊C4—24no—
31C2×C83⋊#95C2211yescharacteristic
32C2×C83⋊#95C2212yes—
33C2×C83⋊#95C2212yes—
34C2×C83⋊#95C2212yes—
35C2×C83⋊#95C2212yes—
36C2×C83⋊#95C2212yes—
37C2×C83⋊#95C2211yescharacteristic
38C23×Q8×C83C2211yescharacteristic
39C22×C4⋊C4×C83C2211yescharacteristic
40C22×C42×C83C2211yescharacteristic
41#391×C83—24no—
42C2×#95×C83C2212yes—
43C2×#95×C83C2212yes—
44C24×D83C2311yescharacteristic
45C23×Dic83C2311yescharacteristic
46C23×Dic83C2312yes—
47C23×Dic83C2311yescharacteristic
48C23×Dic83C2311yescharacteristic
49C23×Dic83C2312yes—
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×D83C2×C414yes—
57#14581768—232no—
58C2×C4⋊Dic83—22no—
59C2×C4⋊Dic83—22no—
60C2×C4⋊Dic83C2×C414yes—
61C2×C4⋊Dic83D414yes—
62C2×C4⋊Dic83D414yes—
63C2×C4⋊Dic83D414yes—
64C2×Dic83⋊C4—24no—
65C2×Dic83⋊C4—24no—
66C2×Dic83⋊C4—24no—
67C2×Dic83⋊C4—24no—
68C2×Dic83⋊C4—42no—
69C2×Dic83⋊C4C2×C418yes—
70C2×(C2×D83)⋊C4—22no—
71C2×(C2×D83)⋊C4—24no—
72C2×(C2×D83)⋊C4—24no—
73C2×(C2×D83)⋊C4—22no—
74C2×(C2×D83)⋊C4—24no—
75C2×(C2×D83)⋊C4—24no—
76C2×(C2×D83)⋊C4—22no—
77C2×(C2×D83)⋊C4—22no—
78C2×(C2×D83)⋊C4—22no—
79C2×(C2×D83)⋊C4—42no—
80C2×(C2×D83)⋊C4C2×C418yes—
81C2×(C2×D83)⋊C4Q814yescomplemented
82C2×C4×Dic83—24no—
83C2×C4×Dic83—22no—
84C2×C4×Dic83—22no—
85C2×C4×Dic83—22no—
86C2×C4×Dic83—24no—
87C2×C4×Dic83—42no—
88C83⋊#95—24no—
89C83⋊#95—24no—
90C83⋊#95—24no—
91C83⋊#95—24no—
92C83⋊#95—24no—
93C83⋊#95—22no—
94C83⋊#95—22no—
95C22×Q8×C83—22no—
96C22×Q8×C83—22no—
97C22×Q8×C83—22no—
98C22×Q8×C83—22no—
99C22×Q8×C83—22no—
100C22×Q8×C83—22no—
101C22×Q8×C83C2×C414yes—
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×C42×C83—22no—
111C2×C42×C83—22no—
112C2×C42×C83D414yes—
113#95×C83—24no—
114#95×C83—24no—
115C23×D83—21no—
116C23×D83—21no—
117C23×D83—21no—
118C23×D83—21no—
119C23×D83—21no—
120C23×D83—21no—
121C23×D83—21no—
122C23×D83—21no—
123C23×D83—21no—
124C23×D83—21no—
125C23×D83—21no—
126C23×D83—21no—
127C23×D83C22×C412yes—
128C23×D83C2×Q812yes—
129C23×D83#4112yes—
130C22×Dic83—22no—
131C22×Dic83—22no—
132C22×Dic83—22no—
133C22×Dic83—22no—
134C22×Dic83—21no—
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—22no—
144C22×Dic83—21no—
145C22×Dic83—21no—
146C22×Dic83—21no—
147C22×Dic83—22no—
148C22×Dic83—21no—
149C22×Dic83—22no—
150C22×Dic83—21no—
151C22×Dic83—22no—
152C22×Dic83—22no—
153C22×Dic83—21no—
154C22×Dic83—21no—
155C22×Dic83—22no—
156C22×Dic83—21no—
157C22×Dic83—21no—
158C22×Dic83C22×C412yes—
159C22×Dic83C22×C414yes—
160C22×Dic83C2×D414yes—
161C22×Dic83C2×D414yes—
162C22×Dic83C2×D414yes—
163C22×Dic83C2×Q812yes—
164C22×Dic83#4112yes—
165C2×C4×D83—28no—
166C2×C4×D83—28no—
167C2×C4×D83—28no—
168C2×C4×D83—44no—
169C2×C4×D83—44no—
170C2×C4×D83—44no—
171C2×C4×D83—44no—
172C4⋊Dic83—28no—
173C4⋊Dic83C22⋊C4116yescomplemented
174Dic83⋊C4—216no—
175Dic83⋊C4—48no—
176(C2×D83)⋊C4—28no—
177(C2×D83)⋊C4—28no—
178(C2×D83)⋊C4—216no—
179(C2×D83)⋊C4—48no—
180C4×Dic83—48no—
181C4×Dic83—44no—
182C24×C83C2411yescharacteristic
183C2×Q8×C83—28no—
184C2×Q8×C83—28no—
185C2×Q8×C83—28no—
186C2×Q8×C83—44no—
187C2×Q8×C83—44no—
188C2×Q8×C83—44no—
189C2×Q8×C83—44no—
190C22×C4×C83—21no—
191C22×C4×C83—21no—
192C22×C4×C83—21no—
193C22×C4×C83—21no—
194C22×C4×C83—22no—
195C22×C4×C83—21no—
196C22×C4×C83—22no—
197C22×C4×C83—22no—
198C22×C4×C83—22no—
199C22×C4×C83—21no—
200C22×C4×C83—22no—
201C22×C4×C83—22no—
202C22×C4×C83—21no—
203C22×C4×C83—21no—
204C22×C4×C83—21no—
205C22×C4×C83—21no—
206C22×C4×C83—22no—
207C22×C4×C83—22no—
208C22×C4×C83—22no—
209C22×C4×C83—22no—
210C22×C4×C83—22no—
211C22×C4×C83—22no—
212C22×C4×C83—22no—
213C22×C4×C83C22×C414yes—
214C22×C4×C83C22×C412yes—
215C22×C4×C83C2×D412yes—
216C22×C4×C83C2×D412yes—
217C22×C4×C83C2×D412yes—
218C22×C4×C83C2×D412yes—
219C22×C4×C83C2×D412yes—
220C22×C4×C83C2×D412yes—
221C22×C4×C83C2×Q812yes—
222C22×C4×C83#4112yes—
223C22×C4×C83#4112yes—
224C22×C4×C83#4112yes—
225C4⋊C4×C83—44no—
226C42×C83—28no—
227C23×C83C23×C411yescharacteristic
228C23×C83C22×D411yescharacteristic
229C23×C83C22×D411yescharacteristic
230C23×C83C22×D411yescharacteristic
231C23×C83C22×D411yescharacteristic
232C23×C83C22×Q811yescharacteristic
233C23×C83C2×#4111yescharacteristic
234C23×C83C2×#4111yescharacteristic
235C23×C83C2×#4111yescharacteristic
236C23×C83C2×#4111yescharacteristic
237C23×C83C2×#4111yescharacteristic
238C23×C83H(5,𝔽2)11yescharacteristic
239C23×C832−1+411yescharacteristic
240C23×C832−1+411yescharacteristic
241C23×C832−1+411yescharacteristic
242C22×D83—22no—
243C22×D83—22no—
244C22×D83—22no—
245C22×D83—22no—
246C22×D83—22no—
247C22×D83—22no—
248C22×D83—22no—
249C22×D83—22no—
250C22×D83—22no—
251C22×D83—22no—
252C22×D83—22no—
253C22×D83—22no—
254C22×D83—22no—
255C22×D83—22no—
256C22×D83—22no—
257C22×D83—22no—
258C22×D83—22no—
259C22×D83—22no—
260C22×D83—41no—
261C22×D83—41no—
262C22×D83—41no—
263C22×D83—41no—
264C22×D83—41no—
265C22×D83—41no—
266C22×D83—41no—
267C22×D83—41no—
268C22×D83—41no—
269C22×D83—41no—
270C22×D83—41no—
271C22×D83—41no—
272C22×D83—41no—
273C22×D83—41no—
274C22×D83—41no—
275C22×D83—41no—
276C22×D83C4×Q814yes—
277Q8×C83—416no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—24no—
285C2×C4×C83—24no—
286C2×C4×C83—24no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—42no—
291C2×C4×C83—42no—
292C2×C4×C83—42no—
293C2×C4×C83—42no—
294C2×C4×C83—41no—
295C2×C4×C83—41no—
296C2×C4×C83—41no—
297C2×C4×C83—41no—
298C2×C4×C83—42no—
299C2×C4×C83—42no—
300C2×C4×C83—42no—
301C2×C4×C83—42no—
302C2×C4×C83—42no—
303C2×C4×C83—42no—
304C2×C4×C83—42no—
305C2×C4×C83C2×C22⋊C414yes—
306C2×C4×C83C4×D414yes—
307C2×C4×C83C4×D414yes—
308C2×C4×C83#12114yes—
309C2×C4×C83#12114yes—
310C2×C4×C83C22⋊Q814yescomplemented
311C2×C4×C83#12414yes—
312C2×C4×C83#12714yes—
313C2×Dic83—24no—
314C2×Dic83—24no—
315C2×Dic83—24no—
316C2×Dic83—24no—
317C2×Dic83—24no—
318C2×Dic83—24no—
319C2×Dic83—22no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—24no—
323C2×Dic83—22no—
324C2×Dic83—22no—
325C2×Dic83—24no—
326C2×Dic83—22no—
327C2×Dic83—24no—
328C2×Dic83—22no—
329C2×Dic83—22no—
330C2×Dic83—22no—
331C2×Dic83—41no—
332C2×Dic83—41no—
333C2×Dic83—41no—
334C2×Dic83—42no—
335C2×Dic83—41no—
336C2×Dic83—41no—
337C2×Dic83—41no—
338C2×Dic83—41no—
339C2×Dic83—41no—
340C2×Dic83—42no—
341C2×Dic83—42no—
342C2×Dic83—41no—
343C2×Dic83—41no—
344C2×Dic83—41no—
345C2×Dic83—41no—
346C2×Dic83—42no—
347C2×Dic83C2×C22⋊C418yes—
348C4×D83—416no—
349C22×C83C22×C22⋊C411yescharacteristic
350C22×C83C2×C4×D411yescharacteristic
351C22×C83C2×C4×D411yescharacteristic
352C22×C83C2×C4×Q811yescharacteristic
353C22×C83C4×#4111yescharacteristic
354C22×C83#51911yescharacteristic
355C22×C83#52011yescharacteristic
356C22×C83C2×#12111yescharacteristic
357C22×C83C2×#12111yescharacteristic
358C22×C83C2×C22⋊Q811yescharacteristic
359C22×C83#52511yescharacteristic
360C22×C83C2×#12411yescharacteristic
361C22×C83#52911yescharacteristic
362C22×C83C2×#12711yescharacteristic
363C22×C83#53311yescharacteristic
364C22×C83#53611yescharacteristic
365C22×C83#53711yescharacteristic
366C22×C83#54111yescharacteristic
367C22×C83#54211yescharacteristic
368C22×C83#54611yescharacteristic
369C22×C83#54611yescharacteristic
370C22×C83#54611yescharacteristic
371C22×C83#54711yescharacteristic
372C22×C83#54711yescharacteristic
373C22×C83#54711yescharacteristic
374C22×C83#54811yescharacteristic
375C22×C83#54811yescharacteristic
376C22×C83#54811yescharacteristic
377C22×C83D4×Q811yescharacteristic
378C22×C83D4×Q811yescharacteristic
379C22×C83D4×Q811yescharacteristic
380C22×C83#55211yescharacteristic
381C22×C83#55211yescharacteristic
382C22×C83#55411yescharacteristic
383C22×C83#55611yescharacteristic
384C2×D83—24no—
385C2×D83—24no—
386C2×D83—24no—
387C2×D83—42no—
388C2×D83—42no—
389C2×D83—42no—
390C2×D83—42no—
391C2×D83—42no—
392C2×D83—42no—
393C2×D83—42no—
394C2×D83—42no—
395C2×D83—42no—
396C2×D83—42no—
397C2×D83—42no—
398C2×D83—42no—
399C4×C83—24no—
400C4×C83—42no—
401C4×C83—44no—
402C4×C83—82no—
403C4×C83#39018yes—
404Dic83—28no—
405Dic83—44no—
406Dic83—42no—
407Dic83—42no—
408Dic83—42no—
409#13997—831nomaximal, Sylow
410C2×C83C2×#39011yescharacteristic
411C2×C83C4×C22⋊Q811yescharacteristic
412C2×C83#232311yescharacteristic
413C2×C83#233911yescharacteristic
414C2×C83Q8×C22⋊C411yescharacteristic
415C2×C83#236011yescharacteristic
416C2×C83#236211yescharacteristic
417C2×C83#241511yescharacteristic
418C2×C83#241711yescharacteristic
419C2×C83#242711yescharacteristic
420C2×C83#242911yescharacteristic
421C2×C83#248911yescharacteristic
422C2×C83#249211yescharacteristic
423C2×C83#254011yescharacteristic
424C2×C83#254211yescharacteristic
425D83—44no—
426C22×C22⋊Q8—831no—
427C2×#391—831no—
428C2×#391D8311yescharacteristic, complemented
429C2×#389—831no—
430C2×#380—831no—
431C2×C4×C4⋊C4—831no—
432C2×C4×C22⋊C4—831no—
433#1445—832no—
434#1439—832no—
435#1437—832no—
436C4⋊#95—832no—
437C83#1399711yescharacteristic, complemented, Sylow
438C23×Q8C2×D8311yescharacteristic
439C24×C4—831no—
440C2×C22⋊Q8—838no—
441C2×C22⋊Q8—1664no—
442C2×C22⋊Q8—1664no—
443C22×C4⋊C4—832no—
444C22×C4⋊C4—831no—
445C22×C4⋊C4—832no—
446C22×C4⋊C4—831no—
447C22×C4⋊C4C2×D8311yescharacteristic
448C22×C22⋊C4—832no—
449C22×C22⋊C4—832no—
450C22×C22⋊C4—831no—
451C22×C22⋊C4—831no—
452C22×C42—832no—
453C22×C42—831no—
454C22×C42C2×D8311yescharacteristic
455#391—24no—
456#391—1664no—
457#389—1664no—
458#380—1664no—
459C4×C4⋊C4—1664no—
460C4×C22⋊C4—1664no—
461C2×#95—831no—
462C2×#95—832no—
463C2×#95—832no—
464C2×#95—832no—
465C2×#95—832no—
466C2×#95—832no—
467C2×#95—831no—
468C2×#95C2×D8312yes—
469C2×#95C2×D8312yes—
470C25—831no—
471C22×Q8—22no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—22no—
475C22×Q8—22no—
476C22×Q8—22no—
477C22×Q8C4×D8314yes—
478C23×C4—832no—
479C23×C4—831no—
480C23×C4—832no—
481C23×C4—831no—
482C23×C4—831no—
483C23×C4—834no—
484C23×C4—1662no—
485C23×C4—1662no—
486C23×C4—1662no—
487C23×C4—1662no—
488C23×C4—1662no—
489C23×C4—1662no—
490C23×C4C22×D8312yes—
491C23×C4C22×D8312yes—
492C23×C4C22×D8311yescharacteristic
493C23×C4C22×D8311yescharacteristic
494C23×C4C22×D8311yescharacteristic
495C22⋊Q8—16632no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—3322no—
500C2×C4⋊C4—834no—
501C2×C4⋊C4—834no—
502C2×C4⋊C4—834no—
503C2×C4⋊C4—838no—
504C2×C4⋊C4—834no—
505C2×C4⋊C4—1664no—
506C2×C4⋊C4—1664no—
507C2×C4⋊C4—1664no—
508C2×C4⋊C4—1664no—
509C2×C4⋊C4—1662no—
510C2×C4⋊C4—1662no—
511C2×C22⋊C4—3322no—
512C2×C22⋊C4—838no—
513C2×C22⋊C4—834no—
514C2×C22⋊C4—1664no—
515C2×C22⋊C4—1664no—
516C2×C22⋊C4—1664no—
517C2×C22⋊C4—1664no—
518C2×C22⋊C4—1662no—
519C2×C22⋊C4—1662no—
520C2×C22⋊C4—1662no—
521C2×C22⋊C4—1662no—
522C2×C22⋊C4—1662no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—3322no—
526C2×C42—1664no—
527C2×C42—1662no—
528C2×C42—1662no—
529C2×C42—1662no—
530C2×C42—1664no—
531C2×C42C22⋊D8314yes—
532#95—24no—
533#95—24no—
534#95—1664no—
535#95—1664no—
536#95—1664no—
537#95—1664no—
538#95—1664no—
539#95—1662no—
540#95—1662no—
541C24—832no—
542C24—832no—
543C24—832no—
544C24—1661no—
545C24—1661no—
546C24—1661no—
547C24—1661no—
548C24—1661no—
549C24—1661no—
550C24—1661no—
551C24—1661no—
552C24—1661no—
553C24—1661no—
554C24—1661no—
555C24—1661no—
556C24C23×D8311yescharacteristic
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—44no—
561C2×Q8—44no—
562C2×Q8—44no—
563C2×Q8—44no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—3324no—
588C22×C4—3324no—
589C22×C4—3324no—
590C22×C4—3324no—
591C22×C4—834no—
592C22×C4—834no—
593C22×C4—834no—
594C22×C4—832no—
595C22×C4—834no—
596C22×C4—832no—
597C22×C4—832no—
598C22×C4—1661no—
599C22×C4—1661no—
600C22×C4—1661no—
601C22×C4—1661no—
602C22×C4—1662no—
603C22×C4—1661no—
604C22×C4—1661no—
605C22×C4—1661no—
606C22×C4—1661no—
607C22×C4—1661no—
608C22×C4—1661no—
609C22×C4—1661no—
610C22×C4—1662no—
611C22×C4—1661no—
612C22×C4—1662no—
613C22×C4—1661no—
614C22×C4—1662no—
615C22×C4—1661no—
616C22×C4—1662no—
617C22×C4—1661no—
618C22×C4—1661no—
619C22×C4—1662no—
620C22×C4—1661no—
621C22×C4—1661no—
622C22×C4—1668no—
623C22×C4—1668no—
624C22×C4—1668no—
625C22×C4—1662no—
626C22×C4—1662no—
627C22×C4—1662no—
628C22×C4—1662no—
629C22×C4C2×C4×D8314yes—
630C22×C4C2×C4×D8312yes—
631C22×C4D4×D8312yes—
632C22×C4D4×D8312yes—
633C22×C4D4×D8312yes—
634C22×C4C2×C22⋊D8312yes—
635C22×C4C2×C22⋊D8312yes—
636C22×C4C2×C22⋊D8312yes—
637C22×C4Q8×D8312yes—
638C22×C4#1305058912yes—
639C22×C4#1305059012yes—
640C22×C4#1305059112yes—
641C4⋊C4—44no—
642C4⋊C4—3328no—
643C4⋊C4—8316no—
644C4⋊C4—16616no—
645C4⋊C4—1668no—
646C22⋊C4—3328no—
647C22⋊C4—16616no—
648C22⋊C4—1668no—
649C22⋊C4—1668no—
650C42—28no—
651C42—3328no—
652C42—3324no—
653C23—3321no—
654C23—3321no—
655C23—3321no—
656C23—3321no—
657C23—3321no—
658C23—3321no—
659C23—3321no—
660C23—3321no—
661C23—3321no—
662C23—3321no—
663C23—3321no—
664C23—3321no—
665C23—3321no—
666C23—3321no—
667C23—3321no—
668C23—3321no—
669C23—834no—
670C23—1662no—
671C23—1662no—
672C23—1662no—
673C23—1662no—
674C23—1662no—
675C23—1662no—
676C23—1662no—
677C23—1662no—
678C23—1662no—
679C23—1662no—
680C23—1662no—
681C23—1662no—
682C23—1662no—
683C23—1662no—
684C23—1662no—
685C23—1662no—
686C23—1662no—
687C23—1662no—
688C23C22×C4×D8311yescharacteristic
689C23C2×D4×D8311yescharacteristic
690C23C2×D4×D8311yescharacteristic
691C23C2×D4×D8311yescharacteristic
692C23C22×C22⋊D8311yescharacteristic
693C23C2×Q8×D8311yescharacteristic
694C23#41×D8311yescharacteristic
695C23#41×D8311yescharacteristic
696C23C2×#1305058911yescharacteristic
697C23C2×#1305059011yescharacteristic
698C23C2×#1305059111yescharacteristic
699C23#1458183811yescharacteristic
700C23#1458183911yescharacteristic
701C23#1458184011yescharacteristic
702C23#1458184011yescharacteristic
703Q8—416no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—3322no—
732C2×C4—3322no—
733C2×C4—3321no—
734C2×C4—3321no—
735C2×C4—3321no—
736C2×C4—3321no—
737C2×C4—3322no—
738C2×C4—3321no—
739C2×C4—3321no—
740C2×C4—3321no—
741C2×C4—3322no—
742C2×C4—3321no—
743C2×C4—3321no—
744C2×C4—3321no—
745C2×C4—3321no—
746C2×C4—3321no—
747C2×C4—33216no—
748C2×C4—838no—
749C2×C4—1664no—
750C2×C4—1662no—
751C2×C4—1664no—
752C2×C4—1662no—
753C2×C4—1662no—
754C2×C4—1662no—
755C2×C4—1662no—
756C2×C4—1662no—
757C2×C4—1662no—
758C2×C4—1664no—
759C2×C4—1662no—
760C2×C4—1662no—
761C2×C4—1664no—
762C2×C4—1664no—
763C2×C4—1664no—
764C2×C4—1664no—
765C2×C4—1664no—
766C2×C4—1664no—
767C2×C4C22⋊C4×D8314yes—
768C2×C4(C22⋊D83)⋊C414yes—
769C2×C4C4×C22⋊D8314yes—
770C2×C4#1458176414yes—
771C2×C4#1458176514yes—
772C2×C4#1458176814yescomplemented
773C2×C4#1458177814yes—
774C2×C4#1458178814yes—
775C22—3322no—
776C22—3322no—
777C22—3322no—
778C22—3322no—
779C22—3322no—
780C22—3322no—
781C22—3322no—
782C22—3322no—
783C22—3322no—
784C22—3322no—
785C22—3322no—
786C22—3322no—
787C22—1664no—
788C22—1664no—
789C22—1664no—
790C22C2×C22⋊C4×D8311yescharacteristic
791C22C2×(C22⋊D83)⋊C411yescharacteristic
792C22C2×C4×C22⋊D8311yescharacteristic
793C22C4×Q8×D8311yescharacteristic
794C22C4×#1305059111yescharacteristic
795C22#1912817711yescharacteristic
796C22#1912818311yescharacteristic
797C22C2×#1458176411yescharacteristic
798C22C2×#1458176511yescharacteristic
799C22C2×#1458176811yescharacteristic
800C22#1912820811yescharacteristic
801C22C2×#1458177811yescharacteristic
802C22#1912823811yescharacteristic
803C22C2×#1458178811yescharacteristic
804C22#1912825511yescharacteristic
805C22#1912827511yescharacteristic
806C22#1912827911yescharacteristic
807C22#1912830911yescharacteristic
808C22#1912832311yescharacteristic
809C22#1912834211yescharacteristic
810C22#1912834411yescharacteristic
811C22#1912834411yescharacteristic
812C22#1912835311yescharacteristic
813C22#1912835411yescharacteristic
814C22#1912835411yescharacteristic
815C22#1912835911yescharacteristic
816C22#1912835911yescharacteristic
817C22#1912836111yescharacteristic
818C22#1912836411yescharacteristic
819C22#1912836611yescharacteristic
820C22#1912836611yescharacteristic
821C22#1912838511yescharacteristic
822C22#1912839311yescharacteristic
823C22#1912840911yescharacteristic
824C22#1912842211yescharacteristic
825C4—24no—
826C4—42no—
827C4—44no—
828C4—82no—
829C4—3322no—
830C4—3322no—
831C4—3322no—
832C4—3324no—
833C4—1668no—
834C4#1912760118yes—
835C2—3324no—
836C2C2×#1912760111yescharacteristic
837C2C4×#1458176811yescharacteristic
838C2#2491013911yescharacteristic
839C2#2491029211yescharacteristic
840C2#2491029711yescharacteristic
841C2#2491047311yescharacteristic
842C2#2491049511yescharacteristic
843C2#2491089311yescharacteristic
844C2#2491091511yescharacteristic
845C2#2491104111yescharacteristic
846C2#2491106311yescharacteristic
847C2#2491180511yescharacteristic
848C2#2491183811yescharacteristic
849C2#2491240311yescharacteristic
850C2#2491241711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#391×C83C2
socle, cosocleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×#391D83
hypocenterC83#13997
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×#19127608C2semidirect
3. C2×#19127597C2semidirect
5. C2×C4×C4⋊Dic83C2semidirect
7. #24905729C2semidirect
10. Dic83⋊#95C2semidirect
11. C2×#391×C83C2semidirect
15. C2×#14581768C4semidirect
81. C2×(C2×D83)⋊C4Q8semidirect
173. C4⋊Dic83C22⋊C4semidirect
310. C2×C4×C83C22⋊Q8semidirect
428. C2×#391D83semidirect
437. C83#13997semidirect
772. C2×C4#14581768semidirect

Maximal subgroups

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

subgroupindex
C22×#145817682
C2×#191276082
C2×#191275972
C2×#191275582
C2×C4×C4⋊Dic832
C2×C4×(C2×D83)⋊C42
#249057292
#249057072
#249056992
Dic83⋊#952
C2×#391×C832
#1399783