Finite Group Databasebeta

← #35327845

Subgroups — #35327845

Order 21248.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127603C211yesmaximal, characteristic
2C2×#19127603C211yesmaximal, characteristic
3C2×#19127603C211yesmaximal, characteristic
4C2×#19127591C212yesmaximal, complemented
5C2×C4×C4⋊Dic83C211yesmaximal, characteristic, complemented
6#24905711C212yesmaximal, complemented
7#24905705C212yesmaximal, complemented
8#24905699C212yesmaximal, complemented
9#24905693C211yesmaximal, characteristic, complemented
10#24905693C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊C4×C83C211yesmaximal, characteristic, complemented
12C23×D332C2211yescharacteristic
13C22×C4⋊Dic83C2211yescharacteristic
14C22×C4⋊Dic83C2211yescharacteristic
15C22×C4⋊Dic83C2211yescharacteristic
16C22×(C2×D83)⋊C4C2212yes—
17C22×(C2×D83)⋊C4C2212yes—
18C22×(C2×D83)⋊C4C2212yes—
19C22×(C2×D83)⋊C4C2212yes—
20C22×(C2×D83)⋊C4C2212yes—
21C22×(C2×D83)⋊C4C2212yes—
22C22×C4×Dic83C2212yes—
23#19127603—24no—
24#19127603—24no—
25#19127603C418yescomplemented
26#19127591—28no—
27C4×C4⋊Dic83—24no—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2212yes—
33C22×C4⋊C4×C83C2211yescharacteristic
34C22×C4⋊C4×C83C2211yescharacteristic
35C22×C42×C83C2211yescharacteristic
36C22×C42×C83C2211yescharacteristic
37C22×C42×C83C2211yescharacteristic
38C4×C4⋊C4×C83—24no—
39C2×#95×C83C2211yescharacteristic
40C2×#95×C83C2211yescharacteristic
41C24×D83C2312yes—
42C22×D332—22no—
43C22×D332—22no—
44C22×D332—22no—
45C22×D332—22no—
46C22×D332—22no—
47C22×D332—22no—
48C22×D332C2×C414yes—
49C23×Dic83C2312yes—
50C23×Dic83C2312yes—
51C23×Dic83C2312yes—
52C2×C4⋊Dic83—22no—
53C2×C4⋊Dic83—22no—
54C2×C4⋊Dic83—22no—
55C2×C4⋊Dic83—22no—
56C2×C4⋊Dic83—22no—
57C2×C4⋊Dic83—22no—
58C2×C4⋊Dic83—22no—
59C2×C4⋊Dic83C2×C414yes—
60C2×C4⋊Dic83D414yes—
61C2×(C2×D83)⋊C4—24no—
62C2×(C2×D83)⋊C4—24no—
63C2×(C2×D83)⋊C4—24no—
64C2×(C2×D83)⋊C4—24no—
65C2×(C2×D83)⋊C4—24no—
66C2×(C2×D83)⋊C4—24no—
67C2×(C2×D83)⋊C4—24no—
68C2×(C2×D83)⋊C4—24no—
69C2×(C2×D83)⋊C4—24no—
70C2×(C2×D83)⋊C4—24no—
71C2×(C2×D83)⋊C4—42no—
72C2×(C2×D83)⋊C4—42no—
73C2×(C2×D83)⋊C4—42no—
74C2×(C2×D83)⋊C4—42no—
75C2×(C2×D83)⋊C4—42no—
76C2×(C2×D83)⋊C4—42no—
77C2×(C2×D83)⋊C4C2×C418yes—
78C2×(C2×D83)⋊C4C2×C418yes—
79C2×C4×Dic83—24no—
80C2×C4×Dic83—24no—
81C2×C4×Dic83—42no—
82C83⋊#95—24no—
83C83⋊#95—24no—
84C83⋊#95—24no—
85C83⋊#95—42no—
86C83⋊#95—42no—
87C23×C4×C83C2311yescharacteristic
88C23×C4×C83C2311yescharacteristic
89C23×C4×C83C2311yescharacteristic
90C23×C4×C83C2311yescharacteristic
91C23×C4×C83C2311yescharacteristic
92C23×C4×C83C2311yescharacteristic
93C23×C4×C83C2311yescharacteristic
94C2×C4⋊C4×C83—22no—
95C2×C4⋊C4×C83—22no—
96C2×C4⋊C4×C83—22no—
97C2×C4⋊C4×C83—22no—
98C2×C4⋊C4×C83—22no—
99C2×C4⋊C4×C83D414yescomplemented
100C2×C42×C83—22no—
101C2×C42×C83—22no—
102C2×C42×C83—22no—
103C2×C42×C83—22no—
104C2×C42×C83—22no—
105C2×C42×C83—22no—
106C2×C42×C83—22no—
107C2×C42×C83C2×C414yes—
108C2×C42×C83D414yes—
109#95×C83—22no—
110#95×C83—22no—
111C23×D83—22no—
112C23×D83—22no—
113C23×D83—22no—
114C23×D83—22no—
115C23×D83—22no—
116C23×D83—22no—
117C23×D83—22no—
118C23×D83—22no—
119C23×D83—22no—
120C23×D83—22no—
121C23×D83—22no—
122C23×D83—22no—
123C23×D83—22no—
124C23×D83—22no—
125C23×D83C22×C414yes—
126C2×D332—28no—
127C2×D332—28no—
128C2×D332—28no—
129C2×D332—44no—
130C2×D332—44no—
131C2×D332—44no—
132C2×D332—44no—
133C22×Dic83—22no—
134C22×Dic83—22no—
135C22×Dic83—22no—
136C22×Dic83—22no—
137C22×Dic83—22no—
138C22×Dic83—22no—
139C22×Dic83—22no—
140C22×Dic83—22no—
141C22×Dic83—22no—
142C22×Dic83—22no—
143C22×Dic83—22no—
144C22×Dic83—22no—
145C22×Dic83—22no—
146C22×Dic83—22no—
147C22×Dic83—22no—
148C22×Dic83—22no—
149C22×Dic83—22no—
150C22×Dic83—22no—
151C22×Dic83—22no—
152C22×Dic83C22×C414yes—
153C22×Dic83C2×D414yes—
154C4⋊Dic83—28no—
155C4⋊Dic83—28no—
156C4⋊Dic83—44no—
157(C2×D83)⋊C4—216no—
158(C2×D83)⋊C4—48no—
159(C2×D83)⋊C4—48no—
160(C2×D83)⋊C4—48no—
161(C2×D83)⋊C4—48no—
162(C2×D83)⋊C4—48no—
163C4×Dic83—48no—
164C24×C83C2411yescharacteristic
165C22×C4×C83—21no—
166C22×C4×C83—21no—
167C22×C4×C83—21no—
168C22×C4×C83—21no—
169C22×C4×C83—21no—
170C22×C4×C83—21no—
171C22×C4×C83—21no—
172C22×C4×C83—21no—
173C22×C4×C83—21no—
174C22×C4×C83—21no—
175C22×C4×C83—21no—
176C22×C4×C83—21no—
177C22×C4×C83—21no—
178C22×C4×C83—21no—
179C22×C4×C83—21no—
180C22×C4×C83—21no—
181C22×C4×C83—21no—
182C22×C4×C83—21no—
183C22×C4×C83—21no—
184C22×C4×C83—21no—
185C22×C4×C83—21no—
186C22×C4×C83—21no—
187C22×C4×C83—21no—
188C22×C4×C83—21no—
189C22×C4×C83—21no—
190C22×C4×C83—21no—
191C22×C4×C83—21no—
192C22×C4×C83—21no—
193C22×C4×C83—21no—
194C22×C4×C83—21no—
195C22×C4×C83—21no—
196C22×C4×C83—21no—
197C22×C4×C83C22×C412yes—
198C22×C4×C83C22×C412yes—
199C22×C4×C83C22×C412yes—
200C22×C4×C83C2×D412yes—
201C22×C4×C83C2×D412yes—
202C22×C4×C83C2×D412yes—
203C22×C4×C83C2×D412yes—
204C22×C4×C83C2×D412yes—
205C22×C4×C83C2×D412yes—
206C22×C4×C83C2×D412yes—
207C22×C4×C83#4112yes—
208C22×C4×C83#4112yes—
209C22×C4×C83#4112yes—
210C22×C4×C83#4112yes—
211C22×C4×C83#4112yes—
212C22×C4×C83#4112yes—
213C22×C4×C83#4112yes—
214C4⋊C4×C83—28no—
215C4⋊C4×C83—28no—
216C42×C83—28no—
217C42×C83—28no—
218C42×C83—44no—
219C23×C83C23×C411yescharacteristic
220C23×C83C22×D411yescharacteristic
221C23×C83C22×D411yescharacteristic
222C23×C83C22×D411yescharacteristic
223C23×C83C2×#4111yescharacteristic
224C23×C83C2×#4111yescharacteristic
225C23×C83C2×#4111yescharacteristic
226C23×C83C2×#4111yescharacteristic
227C23×C83C2×#4111yescharacteristic
228C23×C83C2×#4111yescharacteristic
229C23×C83C2×#4111yescharacteristic
230C23×C83H(5,𝔽2)11yescharacteristic
231C23×C83H(5,𝔽2)11yescharacteristic
232C23×C83H(5,𝔽2)11yescharacteristic
233C23×C832−1+411yescharacteristic
234C22×D83—24no—
235C22×D83—24no—
236C22×D83—24no—
237C22×D83—24no—
238C22×D83—24no—
239C22×D83—24no—
240C22×D83—24no—
241C22×D83—42no—
242C22×D83—42no—
243C22×D83—42no—
244C22×D83—42no—
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—42no—
264C22×D83—42no—
265C22×D83—42no—
266C22×D83—42no—
267C22×D83—42no—
268C22×D83—42no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—22no—
274C2×C4×C83—22no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
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—22no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—41no—
294C2×C4×C83—41no—
295C2×C4×C83—41no—
296C2×C4×C83—41no—
297C2×C4×C83—41no—
298C2×C4×C83—41no—
299C2×C4×C83—41no—
300C2×C4×C83—41no—
301C2×C4×C83—41no—
302C2×C4×C83—41no—
303C2×C4×C83—41no—
304C2×C4×C83—41no—
305C2×C4×C83—41no—
306C2×C4×C83—41no—
307C2×C4×C83—41no—
308C2×C4×C83—41no—
309C2×C4×C83#11714yes—
310C2×C4×C83C4×D414yes—
311C2×C4×C83C4×D414yes—
312C2×C4×C83C4×D414yes—
313C2×C4×C83#12114yes—
314C2×C4×C83#12114yes—
315C2×C4×C83#12314yes—
316C2×C4×C83#12414yes—
317C2×C4×C83#12614yes—
318C2×Dic83—24no—
319C2×Dic83—24no—
320C2×Dic83—24no—
321C2×Dic83—24no—
322C2×Dic83—24no—
323C2×Dic83—24no—
324C2×Dic83—42no—
325C2×Dic83—42no—
326C2×Dic83—42no—
327C2×Dic83—42no—
328C2×Dic83—42no—
329C2×Dic83—42no—
330C2×Dic83—42no—
331C2×Dic83—42no—
332C2×Dic83—42no—
333C2×Dic83—42no—
334C2×Dic83—42no—
335C2×Dic83—42no—
336C2×Dic83—42no—
337C2×Dic83—42no—
338C2×Dic83—42no—
339D332—416no—
340C22×C83C2×#11711yescharacteristic
341C22×C83C2×C4×D411yescharacteristic
342C22×C83C2×C4×D411yescharacteristic
343C22×C83C2×C4×D411yescharacteristic
344C22×C83C4×#4111yescharacteristic
345C22×C83#51811yescharacteristic
346C22×C83#52011yescharacteristic
347C22×C83C2×#12111yescharacteristic
348C22×C83C2×#12111yescharacteristic
349C22×C83C2×#12311yescharacteristic
350C22×C83#52511yescharacteristic
351C22×C83C2×#12411yescharacteristic
352C22×C83C2×#12611yescharacteristic
353C22×C83#52911yescharacteristic
354C22×C83#53211yescharacteristic
355C22×C83#53511yescharacteristic
356C22×C83#53711yescharacteristic
357C22×C83#54011yescharacteristic
358C22×C83#54211yescharacteristic
359C22×C83D4211yescharacteristic
360C22×C83#54611yescharacteristic
361C22×C83#54711yescharacteristic
362C22×C83#54811yescharacteristic
363C22×C83#55011yescharacteristic
364C22×C83#55011yescharacteristic
365C22×C83#55011yescharacteristic
366C22×C83#55311yescharacteristic
367C22×C83#55311yescharacteristic
368C22×C83#55511yescharacteristic
369C22×C83#55611yescharacteristic
370C22×C83#55611yescharacteristic
371C22×C83#55911yescharacteristic
372C22×C83#55911yescharacteristic
373C22×C83#55911yescharacteristic
374C22×C83#55911yescharacteristic
375C2×D83—44no—
376C2×D83—44no—
377C2×D83—44no—
378C2×D83—44no—
379C2×D83—44no—
380C2×D83—44no—
381C2×D83—44no—
382C2×D83—82no—
383C2×D83—82no—
384C2×D83—82no—
385C2×D83—82no—
386C2×D83—82no—
387C2×D83—82no—
388C2×D83—82no—
389C2×D83—82no—
390C4×C83—24no—
391C4×C83—24no—
392C4×C83—42no—
393C4×C83—42no—
394C4×C83—42no—
395C4×C83—42no—
396C4×C83#38818yescomplemented
397Dic83—44no—
398Dic83—44no—
399Dic83—82no—
400#14022—831nomaximal, Sylow
401C2×C83C2×#38811yescharacteristic
402C2×C83C4×#12111yescharacteristic
403C2×C83#232411yescharacteristic
404C2×C83#235411yescharacteristic
405C2×C83#235711yescharacteristic
406C2×C83#236611yescharacteristic
407C2×C83#236711yescharacteristic
408C2×C83#241411yescharacteristic
409C2×C83#241611yescharacteristic
410C2×C83#244511yescharacteristic
411C2×C83#244811yescharacteristic
412C2×C83#251211yescharacteristic
413C2×C83#251311yescharacteristic
414C2×C83#254811yescharacteristic
415C2×C83#259211yescharacteristic
416D83—84no—
417C2×#390—831no—
418C2×#390—831no—
419C2×#390—831no—
420C2×#388—832no—
421C2×C4×C4⋊C4—831no—
422C2×C4×C4⋊C4D8311yescharacteristic, complemented
423#1440—832no—
424#1439—832no—
425#1437—832no—
426C4⋊#95—831no—
427C4⋊#95—831no—
428C83#1402211yescharacteristic, complemented, Sylow
429C23×D4—831no—
430C22×C4⋊C4—831no—
431C22×C4⋊C4—831no—
432C22×C4⋊C4—831no—
433C22×C4⋊C4C2×D8311yescharacteristic
434C22×C4⋊C4C2×D8311yescharacteristic
435C22×C22⋊C4—832no—
436C22×C22⋊C4—832no—
437C22×C22⋊C4—832no—
438C22×C22⋊C4—832no—
439C22×C22⋊C4—832no—
440C22×C22⋊C4—832no—
441C22×C42—832no—
442C22×C42C2×D8311yescharacteristic
443C22×C42C2×D8311yescharacteristic
444C22×C42C2×D8311yescharacteristic
445#390—838no—
446#390—1664no—
447#390—1664no—
448#388—1668no—
449C4×C4⋊C4—24no—
450C4×C4⋊C4—1664no—
451C2×#95—832no—
452C2×#95—832no—
453C2×#95—832no—
454C2×#95—832no—
455C2×#95—832no—
456C2×#95C2×D8311yescharacteristic
457C2×#95C2×D8311yescharacteristic
458C25—832no—
459C22×D4—834no—
460C22×D4—1662no—
461C22×D4—1662no—
462C22×D4—1662no—
463C22×D4—1662no—
464C22×D4—1662no—
465C22×D4—1662no—
466C23×C4—832no—
467C23×C4—832no—
468C23×C4—832no—
469C23×C4C22×D8311yescharacteristic
470C23×C4C22×D8311yescharacteristic
471C23×C4C22×D8311yescharacteristic
472C23×C4C22×D8311yescharacteristic
473C23×C4C22×D8311yescharacteristic
474C23×C4C22×D8311yescharacteristic
475C23×C4C22×D8311yescharacteristic
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—834no—
482C2×C4⋊C4—834no—
483C2×C4⋊C4—1662no—
484C2×C4⋊C4—1662no—
485C2×C4⋊C4—1662no—
486C2×C4⋊C4—1662no—
487C2×C4⋊C4—1662no—
488C2×C4⋊C4—1662no—
489C2×C4⋊C4—1662no—
490C2×C4⋊C4D33214yescomplemented
491C2×C22⋊C4—3322no—
492C2×C22⋊C4—3322no—
493C2×C22⋊C4—3322no—
494C2×C22⋊C4—3322no—
495C2×C22⋊C4—3322no—
496C2×C22⋊C4—3322no—
497C2×C22⋊C4—838no—
498C2×C22⋊C4—838no—
499C2×C22⋊C4—1664no—
500C2×C22⋊C4—1664no—
501C2×C22⋊C4—1664no—
502C2×C22⋊C4—1664no—
503C2×C22⋊C4—1664no—
504C2×C22⋊C4—1664no—
505C2×C22⋊C4—1664no—
506C2×C22⋊C4—1664no—
507C2×C22⋊C4—1664no—
508C2×C22⋊C4—1664no—
509C2×C42—22no—
510C2×C42—22no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—22no—
515C2×C42—22no—
516C2×C42—3322no—
517C2×C42—1664no—
518C2×C42—1664no—
519C2×C42C4×D8314yes—
520C2×C42C22⋊D8314yes—
521#95—22no—
522#95—22no—
523#95—3322no—
524#95—3322no—
525#95—1664no—
526#95—1664no—
527#95—1664no—
528C24—834no—
529C24—1662no—
530C24—1662no—
531C24—1662no—
532C24—1662no—
533C24—1662no—
534C24—1662no—
535C24—1662no—
536C24—1662no—
537C24—1662no—
538C24—1662no—
539C24—1662no—
540C24—1662no—
541C24—1662no—
542C24—1662no—
543C24C23×D8311yescharacteristic
544C2×D4—3324no—
545C2×D4—3324no—
546C2×D4—3324no—
547C2×D4—3324no—
548C2×D4—1668no—
549C2×D4—1668no—
550C2×D4—1668no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
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—834no—
584C22×C4—834no—
585C22×C4—1662no—
586C22×C4—1662no—
587C22×C4—1662no—
588C22×C4—1662no—
589C22×C4—1662no—
590C22×C4—1662no—
591C22×C4—1662no—
592C22×C4—1662no—
593C22×C4—1662no—
594C22×C4—1662no—
595C22×C4—1662no—
596C22×C4—1662no—
597C22×C4—1662no—
598C22×C4—1662no—
599C22×C4—1662no—
600C22×C4—1662no—
601C22×C4—1662no—
602C22×C4—1662no—
603C22×C4—1662no—
604C22×C4C2×C4×D8312yes—
605C22×C4C2×C4×D8312yes—
606C22×C4C2×C4×D8312yes—
607C22×C4D4×D8312yes—
608C22×C4C2×C22⋊D8312yes—
609C22×C4C2×C22⋊D8312yes—
610C22×C4C2×C22⋊D8312yes—
611C22×C4C2×D33212yes—
612C22×C4C2×D33212yes—
613C22×C4C2×D33212yes—
614C22×C4#1305058912yes—
615C22×C4#1305059012yes—
616C22×C4#1305059012yes—
617C22×C4#1305059012yes—
618C22×C4#1305059012yes—
619C22×C4#1305059112yes—
620C22×C4#1305059112yes—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—3324no—
624C4⋊C4—1668no—
625C4⋊C4—1668no—
626C22⋊C4—3328no—
627C22⋊C4—3328no—
628C22⋊C4—3328no—
629C22⋊C4—3328no—
630C22⋊C4—3328no—
631C22⋊C4—16616no—
632C42—28no—
633C42—28no—
634C42—44no—
635C42—3328no—
636C23—3322no—
637C23—3322no—
638C23—3322no—
639C23—3322no—
640C23—3322no—
641C23—3322no—
642C23—3322no—
643C23—3322no—
644C23—3322no—
645C23—3322no—
646C23—3322no—
647C23—3322no—
648C23—3322no—
649C23—3322no—
650C23—3322no—
651C23—3322no—
652C23—3322no—
653C23—3322no—
654C23—3322no—
655C23—3322no—
656C23—3322no—
657C23—3322no—
658C23—3322no—
659C23—3322no—
660C23—3322no—
661C23—3322no—
662C23—3322no—
663C23—3322no—
664C23—1664no—
665C23—1664no—
666C23—1664no—
667C23—1664no—
668C23—1664no—
669C23—1664no—
670C23—1664no—
671C23C22×C4×D8311yescharacteristic
672C23C2×D4×D8311yescharacteristic
673C23C22×C22⋊D8311yescharacteristic
674C23C22×D33211yescharacteristic
675C23C2×#1305058911yescharacteristic
676C23C2×#1305059011yescharacteristic
677C23C2×#1305059011yescharacteristic
678C23C2×#1305059011yescharacteristic
679C23C2×#1305059011yescharacteristic
680C23C2×#1305059111yescharacteristic
681C23C2×#1305059111yescharacteristic
682C23#1458183811yescharacteristic
683C23#1458183811yescharacteristic
684C23#1458183811yescharacteristic
685C23#1458183911yescharacteristic
686D4—33216no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—3322no—
728C2×C4—3322no—
729C2×C4—3322no—
730C2×C4—3322no—
731C2×C4—3322no—
732C2×C4—3322no—
733C2×C4—3322no—
734C2×C4—3322no—
735C2×C4—3322no—
736C2×C4—3322no—
737C2×C4—3322no—
738C2×C4—3322no—
739C2×C4—3322no—
740C2×C4—3322no—
741C2×C4—3322no—
742C2×C4—1664no—
743C2×C4—1664no—
744C2×C4—1664no—
745C2×C4—1664no—
746C2×C4—1664no—
747C2×C4—1664no—
748C2×C4#1458175014yes—
749C2×C4C4×C22⋊D8314yes—
750C2×C4#1458175414yes—
751C2×C4C4×D33214yes—
752C2×C4#1458176414yes—
753C2×C4#1458176614yes—
754C2×C4#1458177714yes—
755C2×C4#1458178114yes—
756C2×C4#1458178714yes—
757C22—3324no—
758C22—3324no—
759C22—3324no—
760C22—3324no—
761C22—3324no—
762C22—3324no—
763C22—3324no—
764C22—6642no—
765C22—6642no—
766C22—6642no—
767C22—6642no—
768C22—6642no—
769C22—6642no—
770C22—6642no—
771C22—6642no—
772C22C2×#1458175011yescharacteristic
773C22C2×C4×C22⋊D8311yescharacteristic
774C22C2×#1458175411yescharacteristic
775C22C2×C4×D33211yescharacteristic
776C22C4×#1305059011yescharacteristic
777C22#1912817511yescharacteristic
778C22#1912818111yescharacteristic
779C22C2×#1458176411yescharacteristic
780C22C2×#1458176611yescharacteristic
781C22C2×#1458177711yescharacteristic
782C22#1912821211yescharacteristic
783C22C2×#1458178111yescharacteristic
784C22C2×#1458178711yescharacteristic
785C22#1912823511yescharacteristic
786C22#1912825111yescharacteristic
787C22#1912826511yescharacteristic
788C22#1912827911yescharacteristic
789C22#1912830611yescharacteristic
790C22#1912832211yescharacteristic
791C22D4×D33211yescharacteristic
792C22#1912834711yescharacteristic
793C22#1912835511yescharacteristic
794C22#1912836011yescharacteristic
795C22#1912837211yescharacteristic
796C22#1912837311yescharacteristic
797C22#1912837311yescharacteristic
798C22#1912839711yescharacteristic
799C22#1912839711yescharacteristic
800C22#1912841611yescharacteristic
801C22#1912842411yescharacteristic
802C22#1912842411yescharacteristic
803C22#1912843611yescharacteristic
804C22#1912843611yescharacteristic
805C22#1912843611yescharacteristic
806C22#1912843611yescharacteristic
807C4—24no—
808C4—24no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—3324no—
814C4—3324no—
815C4—6642no—
816C4#1912759118yescomplemented
817C2—6644no—
818C2C2×#1912759111yescharacteristic
819C2C4×#1458176611yescharacteristic
820C2#2491015611yescharacteristic
821C2#2491041011yescharacteristic
822C2#2491043411yescharacteristic
823C2#2491052711yescharacteristic
824C2#2491053211yescharacteristic
825C2#2491088111yescharacteristic
826C2#2491090311yescharacteristic
827C2#2491122811yescharacteristic
828C2#2491126111yescharacteristic
829C2#2491204911yescharacteristic
830C2#2491206011yescharacteristic
831C2#2491246211yescharacteristic
832C2#2491295111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×C4×C4⋊C4×C83C2
socle, cosocleC24×C83C24
prime radicalC23×D332C22
hypercenterC2×C4×C4⋊C4D83
hypocenterC83#14022
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#19127591C2semidirect
5. C2×C4×C4⋊Dic83C2semidirect
6. #24905711C2semidirect
7. #24905705C2semidirect
8. #24905699C2semidirect
9. #24905693C2semidirect
10. #24905693C2semidirect
11. C2×C4×C4⋊C4×C83C2semidirect
25. #19127603C4semidirect
99. C2×C4⋊C4×C83D4semidirect
396. C4×C83#388semidirect
422. C2×C4×C4⋊C4D83semidirect
428. C83#14022semidirect
490. C2×C4⋊C4D332semidirect
816. C4#19127591semidirect

Maximal subgroups

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

subgroupindex
C2×#191276032
C2×#191275912
C2×C4×C4⋊Dic832
#249057112
#249057052
#249056992
#249056932
C2×C4×C4⋊C4×C832
#1402283