Finite Group Databasebeta

← C2×#24911789 #35573334

Subgroups — C2×#24911789 #35573334

Order 21248.

3114 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581775C211yesmaximal, characteristic
2C22×#14581771C211yesmaximal, characteristic, complemented
3#24911789C2116yesmaximal, direct product factor
4C2×#19127643C211yesmaximal, characteristic, complemented
5C2×#19127642C211yesmaximal, characteristic, complemented
6C2×#19127630C211yesmaximal, characteristic, complemented
7C2×#19127614C211yesmaximal, characteristic, complemented
8C2×#19127605C211yesmaximal, characteristic, complemented
9C2×#19127593C211yesmaximal, characteristic, complemented
10C2×#19127590C211yesmaximal, characteristic, complemented
11C2×#19127580C211yesmaximal, characteristic
12C2×#19127580C211yesmaximal, characteristic
13C2×#19127565C211yesmaximal, characteristic, complemented
14C2×#19127564C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic83C211yesmaximal, characteristic, complemented
16C22×#95×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×C22⋊D83C2211yescharacteristic
19C2×#14581775—28no—
20C2×#14581775C2218yes—
21C2×#14581771—28no—
22C2×#14581771C2218yescomplemented
23C22×C4⋊Dic83C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×C22⋊Dic83C2211yescharacteristic
29C22×C22⋊Dic83C2211yescharacteristic
30C22×C22⋊Dic83C2211yescharacteristic
31C22×(C2×D83)⋊C4C2211yescharacteristic
32C22×(C2×D83)⋊C4C2211yescharacteristic
33C22×(C2×D83)⋊C4C2211yescharacteristic
34C22×(C2×D83)⋊C4C2211yescharacteristic
35C22×(C2×D83)⋊C4C2211yescharacteristic
36C22×(C2×D83)⋊C4C2211yescharacteristic
37C22×C4×Dic83C2211yescharacteristic
38C22×C4×Dic83C2211yescharacteristic
39#19127643C2218yescomplemented
40#19127642C2218yescomplemented
41#19127630C2218yescomplemented
42#19127614C2218yescomplemented
43#19127605C2218yescomplemented
44#19127593C2218yescomplemented
45#19127590C2218yescomplemented
46#19127580C2218yes—
47#19127580C2218yes—
48#19127565C2218yescomplemented
49#19127564C2218yescomplemented
50C4×C22⋊Dic83C2218yescomplemented
51C2×C83⋊#95C2211yescharacteristic
52C2×C83⋊#95C2211yescharacteristic
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C24×C4×C83C2211yescharacteristic
62C24×C4×C83C2211yescharacteristic
63C24×C4×C83C2211yescharacteristic
64C2×#95×C83C2211yescharacteristic
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2218yescomplemented
69C24×D83C2311yescharacteristic
70C22×Dic166—24no—
71C22×Dic166—24no—
72C22×Dic166—42no—
73C22×Dic166C2314yes—
74C22×C22⋊D83—24no—
75C22×C22⋊D83—24no—
76C22×C22⋊D83—24no—
77C22×C22⋊D83C2314yes—
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85#14581775—232no—
86#14581771—232no—
87C2×C4⋊Dic83—24no—
88C2×C4⋊Dic83C2314yes—
89C2×Dic83⋊C4—24no—
90C2×Dic83⋊C4—24no—
91C2×Dic83⋊C4—24no—
92C2×Dic83⋊C4—24no—
93C2×Dic83⋊C4C2314yes—
94C2×Dic83⋊C4C2314yes—
95C2×Dic83⋊C4C2314yes—
96C2×Dic83⋊C4C2314yes—
97C2×C22⋊Dic83—24no—
98C2×C22⋊Dic83—24no—
99C2×C22⋊Dic83D418yes—
100C2×C22⋊Dic83C2314yes—
101C2×C22⋊Dic83C2314yes—
102C2×C22⋊Dic83C2314yes—
103C2×(C2×D83)⋊C4—24no—
104C2×(C2×D83)⋊C4—24no—
105C2×(C2×D83)⋊C4—24no—
106C2×(C2×D83)⋊C4—24no—
107C2×(C2×D83)⋊C4—42no—
108C2×(C2×D83)⋊C4—42no—
109C2×(C2×D83)⋊C4C2314yes—
110C2×(C2×D83)⋊C4C2314yes—
111C2×(C2×D83)⋊C4C2314yes—
112C2×(C2×D83)⋊C4C2314yes—
113C2×(C2×D83)⋊C4C2314yes—
114C2×(C2×D83)⋊C4C2314yes—
115C2×C4×Dic83—24no—
116C2×C4×Dic83—42no—
117C2×C4×Dic83C2314yes—
118C2×C4×Dic83C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2314yes—
129C25×C83C2311yescharacteristic
130C23×C4×C83—24no—
131C23×C4×C83—24no—
132C23×C4×C83—24no—
133C23×C4×C83—24no—
134C23×C4×C83—24no—
135C23×C4×C83—24no—
136C23×C4×C83—24no—
137C23×C4×C83—42no—
138C23×C4×C83—42no—
139C23×C4×C83C2314yes—
140C23×C4×C83C2311yescharacteristic
141C23×C4×C83C2311yescharacteristic
142C23×C4×C83C2311yescharacteristic
143C23×C4×C83C2311yescharacteristic
144C23×C4×C83C2314yes—
145C23×C4×C83C2314yes—
146C23×C4×C83C2311yescharacteristic
147C23×C4×C83C2311yescharacteristic
148#95×C83C2314yes—
149#95×C83C2314yes—
150#95×C83C2314yes—
151#95×C83C2314yes—
152C23×D83—22no—
153C23×D83—22no—
154C23×D83—22no—
155C23×D83—22no—
156C23×D83—22no—
157C23×D83—22no—
158C23×D83—22no—
159C23×D83C2412yes—
160C2×Dic166—28no—
161C2×Dic166—28no—
162C2×Dic166—44no—
163C2×Dic166—416no—
164C2×C22⋊D83—28no—
165C2×C22⋊D83—28no—
166C2×C22⋊D83—28no—
167C2×C22⋊D83—416no—
168C22×Dic83—22no—
169C22×Dic83—22no—
170C22×Dic83—22no—
171C22×Dic83—22no—
172C22×Dic83—22no—
173C22×Dic83—22no—
174C22×Dic83—22no—
175C22×Dic83—22no—
176C22×Dic83—22no—
177C22×Dic83—22no—
178C22×Dic83—22no—
179C22×Dic83—22no—
180C22×Dic83—22no—
181C22×Dic83—22no—
182C22×Dic83—22no—
183C22×Dic83—22no—
184C22×Dic83—22no—
185C22×Dic83—22no—
186C22×Dic83—22no—
187C22×Dic83C2×D414yes—
188C22×Dic83C2×D414yes—
189C22×Dic83C2412yes—
190C22×Dic83C2412yes—
191C22×Dic83C2412yes—
192C22×Dic83C2412yes—
193C22×Dic83C2412yes—
194C22×Dic83C2412yes—
195C22×Dic83C2412yes—
196C4⋊Dic83—28no—
197Dic83⋊C4—28no—
198Dic83⋊C4—28no—
199Dic83⋊C4—28no—
200Dic83⋊C4—28no—
201C22⋊Dic83—28no—
202C22⋊Dic83—28no—
203C22⋊Dic83C2×D4116yes—
204(C2×D83)⋊C4—28no—
205(C2×D83)⋊C4—28no—
206(C2×D83)⋊C4—28no—
207(C2×D83)⋊C4—28no—
208(C2×D83)⋊C4—44no—
209(C2×D83)⋊C4—44no—
210C4×Dic83—28no—
211C4×Dic83—44no—
212C24×C83—22no—
213C24×C83—22no—
214C24×C83—22no—
215C24×C83—22no—
216C24×C83C2×D414yes—
217C24×C83#4114yes—
218C24×C83#4114yes—
219C24×C83C2412yes—
220C24×C83C2411yescharacteristic
221C22×C4×C83—22no—
222C22×C4×C83—22no—
223C22×C4×C83—22no—
224C22×C4×C83—22no—
225C22×C4×C83—28no—
226C22×C4×C83—28no—
227C22×C4×C83—22no—
228C22×C4×C83—22no—
229C22×C4×C83—22no—
230C22×C4×C83—28no—
231C22×C4×C83—28no—
232C22×C4×C83—22no—
233C22×C4×C83—22no—
234C22×C4×C83—22no—
235C22×C4×C83—28no—
236C22×C4×C83—22no—
237C22×C4×C83—22no—
238C22×C4×C83—22no—
239C22×C4×C83—22no—
240C22×C4×C83—22no—
241C22×C4×C83—22no—
242C22×C4×C83—28no—
243C22×C4×C83—28no—
244C22×C4×C83—44no—
245C22×C4×C83—44no—
246C22×C4×C83—416no—
247C22×C4×C83—416no—
248C22×C4×C83—416no—
249C22×C4×C83#4114yes—
250C22×C4×C83#4114yes—
251C22×C4×C83C2412yes—
252C22×C4×C83C2412yes—
253C22×C4×C83C2412yes—
254C22×C4×C83C2412yes—
255C22×C4×C83C2412yes—
256C22×C4×C83C2412yes—
257C23×C83—28no—
258C23×C83—28no—
259C23×C83—28no—
260C23×C83—28no—
261C23×C83—28no—
262C23×C83—28no—
263C23×C83—22no—
264C23×C83—22no—
265C23×C83—22no—
266C23×C83—22no—
267C23×C83#124116yes—
268C23×C83C22×D414yes—
269C23×C83C22×D412yes—
270C23×C83C2×#4114yes—
271C23×C83C2×#4112yes—
272C23×C83C2×#4114yes—
273C23×C83C2×#4112yes—
274C23×C83C2×#4112yes—
275C23×C83C2×#4112yes—
276C23×C83H(5,𝔽2)12yes—
277C23×C832−1+412yes—
278C23×C83C2511yescharacteristic
279C22×D83—22no—
280C22×D83—22no—
281C22×D83—22no—
282C22×D83—22no—
283C22×D83—22no—
284C22×D83—22no—
285C22×D83—22no—
286C22×D83—44no—
287C22×D83—44no—
288C22×D83—44no—
289C22×D83—44no—
290C22×D83—44no—
291C22×D83—44no—
292C22×D83—44no—
293C2×C4×C83—28no—
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—22no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—22no—
304C2×C4×C83—22no—
305C2×C4×C83—22no—
306C2×C4×C83—22no—
307C2×C4×C83—22no—
308C2×C4×C83—22no—
309C2×C4×C83—22no—
310C2×C4×C83—22no—
311C2×C4×C83—416no—
312C2×C4×C83—416no—
313C2×C4×C83—416no—
314C2×C4×C83—44no—
315C2×C4×C83—44no—
316C2×C4×C83—44no—
317C2×C4×C83—44no—
318C2×C4×C83C2×#4114yes—
319C2×C4×C83C2×#4114yes—
320C22⋊D83—416no—
321C2×Dic83—28no—
322C2×Dic83—28no—
323C2×Dic83—22no—
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—44no—
343C2×Dic83—44no—
344C2×Dic83—44no—
345C2×Dic83—44no—
346C2×Dic83—44no—
347C2×Dic83C22×D414yes—
348C2×Dic83C22×D414yes—
349Dic166—416no—
350C22×C83—24no—
351C22×C83—24no—
352C22×C83—24no—
353C22×C83—24no—
354C22×C83—24no—
355C22×C83—24no—
356C22×C83—232no—
357C22×C83C2×#12418yes—
358C22×C83C2×#12414yes—
359C22×C83#52914yes—
360C22×C83#53914yes—
361C22×C83#54614yes—
362C22×C83#54714yes—
363C22×C83#55114yes—
364C22×C83#55214yes—
365C22×C83C23×D411yescharacteristic
366C22×C83C22×#4111yescharacteristic
367C22×C83C22×#4111yescharacteristic
368C22×C83C22×#4111yescharacteristic
369C22×C83C22×#4111yescharacteristic
370C22×C83C2×H(5,𝔽2)11yescharacteristic
371C22×C83C2×2−1+411yescharacteristic
372C2×D83—42no—
373C2×D83—42no—
374C2×D83—42no—
375C2×D83—42no—
376C2×D83—42no—
377C2×D83—42no—
378C2×D83—42no—
379C2×D83—88no—
380C4×C83—24no—
381C4×C83—24no—
382C4×C83—42no—
383C4×C83—42no—
384C4×C83—42no—
385C4×C83—42no—
386Dic83—24no—
387Dic83—24no—
388Dic83—42no—
389Dic83—42no—
390Dic83—42no—
391Dic83—42no—
392Dic83—42no—
393C2×#2488—831nomaximal, Sylow
394C2×C83—28no—
395C2×C83#248818yescomplemented
396C2×C83C22×#12411yescharacteristic
397C2×C83C2×#52911yescharacteristic
398C2×C83C2×#53911yescharacteristic
399C2×C83C2×#54611yescharacteristic
400C2×C83C2×#54711yescharacteristic
401C2×C83C2×#55111yescharacteristic
402C2×C83C2×#55211yescharacteristic
403D83—82no—
404C22×#123—831no—
405C22×C22⋊Q8—831no—
406#2488—8316no—
407C2×#400—831no—
408C2×#400—831no—
409C2×#397—831no—
410C2×#393—831no—
411C2×#391—831no—
412C2×#388—831no—
413C2×#388—831no—
414C2×#386—831no—
415C2×#386—831no—
416C2×#382—831no—
417C2×#381—831no—
418C2×C4×C22⋊C4—831no—
419C22×#95D8311yescharacteristic, complemented
420C83C2×#248811yescharacteristic, complemented, Sylow
421C23×Q8—831no—
422C23×D4—831no—
423C24×C4C2×D8311yescharacteristic
424C24×C4C2×D8311yescharacteristic
425C24×C4C2×D8311yescharacteristic
426C2×#123—838no—
427C2×#123—1668no—
428C2×C22⋊Q8—838no—
429C2×C22⋊Q8—1668no—
430C22×C4⋊C4—831no—
431C22×C4⋊C4—831no—
432C22×C4⋊C4—831no—
433C22×C4⋊C4—831no—
434C22×C4⋊C4—831no—
435C22×C22⋊C4—831no—
436C22×C22⋊C4—831no—
437C22×C22⋊C4—831no—
438C22×C22⋊C4—831no—
439C22×C22⋊C4—831no—
440C22×C22⋊C4—831no—
441C22×C22⋊C4—831no—
442C22×C22⋊C4—831no—
443C22×C22⋊C4—831no—
444C22×C42—831no—
445C22×C42—831no—
446#400—838no—
447#400—838no—
448#397—838no—
449#393—838no—
450#391—838no—
451#388—838no—
452#388—838no—
453#386—838no—
454#386—838no—
455#382—838no—
456#381—838no—
457C4×C22⋊C4—838no—
458C2×#95—831no—
459C2×#95—831no—
460C2×#95—831no—
461C2×#95—831no—
462C2×#95—831no—
463C2×#95—831no—
464C2×#95—831no—
465C2×#95—831no—
466C2×#95—831no—
467C2×#95—831no—
468C2×#95C2×D8311yescharacteristic
469C2×#95C2×D8311yescharacteristic
470C2×#95C2×D8311yescharacteristic
471C2×#95C2×D8311yescharacteristic
472C2×#95C2×D8318yescomplemented
473C25—831no—
474C25C22×D8311yescharacteristic
475C22×Q8—3322no—
476C22×Q8—834no—
477C22×Q8—1664no—
478C22×Q8—1664no—
479C22×D4—834no—
480C22×D4—1664no—
481C22×D4—1664no—
482C22×D4—1664no—
483C23×C4—24no—
484C23×C4—24no—
485C23×C4—24no—
486C23×C4—24no—
487C23×C4—24no—
488C23×C4—24no—
489C23×C4—24no—
490C23×C4—42no—
491C23×C4—42no—
492C23×C4—831no—
493C23×C4—831no—
494C23×C4—831no—
495C23×C4—831no—
496C23×C4—831no—
497C23×C4—831no—
498C23×C4—831no—
499C23×C4C22×D8314yes—
500C23×C4C22×D8311yescharacteristic
501C23×C4C22×D8311yescharacteristic
502C23×C4C22×D8311yescharacteristic
503C23×C4C22×D8311yescharacteristic
504C23×C4C22×D8314yes—
505C23×C4C22×D8314yes—
506C23×C4C22×D8311yescharacteristic
507C23×C4C22×D8311yescharacteristic
508#123—16632no—
509C22⋊Q8—16632no—
510C2×C4⋊C4—834no—
511C2×C4⋊C4—834no—
512C2×C4⋊C4—834no—
513C2×C4⋊C4—834no—
514C2×C4⋊C4—834no—
515C2×C4⋊C4—1664no—
516C2×C4⋊C4—1664no—
517C2×C4⋊C4—1664no—
518C2×C4⋊C4—1664no—
519C2×C4⋊C4—1664no—
520C2×C22⋊C4—3322no—
521C2×C22⋊C4—3322no—
522C2×C22⋊C4—834no—
523C2×C22⋊C4—834no—
524C2×C22⋊C4—838no—
525C2×C22⋊C4—834no—
526C2×C22⋊C4—834no—
527C2×C22⋊C4—834no—
528C2×C22⋊C4—834no—
529C2×C22⋊C4—834no—
530C2×C22⋊C4—834no—
531C2×C22⋊C4—834no—
532C2×C22⋊C4—1664no—
533C2×C22⋊C4—1664no—
534C2×C22⋊C4—1664no—
535C2×C22⋊C4—1664no—
536C2×C22⋊C4—1664no—
537C2×C22⋊C4—1664no—
538C2×C42—3322no—
539C2×C42—834no—
540C2×C42—834no—
541C2×C42—1664no—
542#95—834no—
543#95—834no—
544#95—834no—
545#95—834no—
546#95—834no—
547#95—834no—
548#95—834no—
549#95—834no—
550#95—834no—
551#95—834no—
552#95C22×D8314yes—
553#95C22×D8314yes—
554#95C22×D8314yes—
555#95C22×D8314yes—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—832no—
561C24—1662no—
562C24—1662no—
563C24—1662no—
564C24—1662no—
565C24—1662no—
566C24—1662no—
567C24—1662no—
568C24D4×D8314yes—
569C24#1305058914yes—
570C24#1305059014yes—
571C24C23×D8312yes—
572C24C23×D8311yescharacteristic
573C2×Q8—33216no—
574C2×Q8—3324no—
575C2×Q8—1668no—
576C2×Q8—1668no—
577C2×D4—33216no—
578C2×D4—1668no—
579C2×D4—1668no—
580C2×D4—1668no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—28no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—22no—
592C22×C4—28no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—28no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—28no—
603C22×C4—28no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—416no—
607C22×C4—416no—
608C22×C4—416no—
609C22×C4—834no—
610C22×C4—834no—
611C22×C4—832no—
612C22×C4—832no—
613C22×C4—832no—
614C22×C4—832no—
615C22×C4—832no—
616C22×C4—832no—
617C22×C4—832no—
618C22×C4—1662no—
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—1662no—
633C22×C4—1662no—
634C22×C4—1662no—
635C22×C4—1662no—
636C22×C4—1662no—
637C22×C4#1305059014yes—
638C22×C4#1305059014yes—
639C22×C4C23×D8312yes—
640C22×C4C23×D8312yes—
641C22×C4C23×D8312yes—
642C22×C4C23×D8312yes—
643C22×C4C23×D8312yes—
644C22×C4C23×D8312yes—
645C4⋊C4—1668no—
646C4⋊C4—1668no—
647C4⋊C4—1668no—
648C4⋊C4—1668no—
649C4⋊C4—1668no—
650C22⋊C4—3324no—
651C22⋊C4—3324no—
652C22⋊C4—8316no—
653C22⋊C4—1668no—
654C22⋊C4—1668no—
655C22⋊C4—1668no—
656C22⋊C4—1668no—
657C22⋊C4—1668no—
658C22⋊C4—1668no—
659C42—3324no—
660C42—1668no—
661C23—28no—
662C23—28no—
663C23—28no—
664C23—28no—
665C23—28no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—28no—
671C23—3324no—
672C23—3324no—
673C23—3324no—
674C23—3324no—
675C23—3324no—
676C23—3324no—
677C23—3324no—
678C23—1662no—
679C23—1662no—
680C23—1662no—
681C23—1662no—
682C23—1662no—
683C23—1662no—
684C23—1662no—
685C23#14581778116yes—
686C23C2×D4×D8314yes—
687C23C2×D4×D8312yes—
688C23C2×#1305058914yes—
689C23C2×#1305058912yes—
690C23C2×#1305059014yes—
691C23C2×#1305059012yes—
692C23C2×#1305059012yes—
693C23C2×#1305059012yes—
694C23#1458183712yes—
695C23#1458184012yes—
696C23C24×D8311yescharacteristic
697Q8—33216no—
698D4—33216no—
699C2×C4—28no—
700C2×C4—28no—
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—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—416no—
718C2×C4—416no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—416no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—3324no—
725C2×C4—3324no—
726C2×C4—3324no—
727C2×C4—3324no—
728C2×C4—3324no—
729C2×C4—834no—
730C2×C4—834no—
731C2×C4—1662no—
732C2×C4—1662no—
733C2×C4—1662no—
734C2×C4—1662no—
735C2×C4—1662no—
736C2×C4—1662no—
737C2×C4—1662no—
738C2×C4—1662no—
739C2×C4—1662no—
740C2×C4—1662no—
741C2×C4—1662no—
742C2×C4—1662no—
743C2×C4—1662no—
744C2×C4—1662no—
745C2×C4—1662no—
746C2×C4—1668no—
747C2×C4—1668no—
748C2×C4—1662no—
749C2×C4—1662no—
750C2×C4—1662no—
751C2×C4—1662no—
752C2×C4C2×#1305059014yes—
753C2×C4C2×#1305059014yes—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—232no—
760C22—24no—
761C22—3322no—
762C22—3322no—
763C22—3322no—
764C22—3322no—
765C22—3322no—
766C22—3322no—
767C22—3322no—
768C22—6648no—
769C22C2×#1458177818yes—
770C22C2×#1458177814yes—
771C22#1912823514yes—
772C22#1912829814yes—
773C22#1912834114yes—
774C22#1912835214yes—
775C22#1912837714yes—
776C22#1912838614yes—
777C22C22×D4×D8311yescharacteristic
778C22C22×#1305058911yescharacteristic
779C22C22×#1305059011yescharacteristic
780C22C22×#1305059011yescharacteristic
781C22C22×#1305059011yescharacteristic
782C22C2×#1458183711yescharacteristic
783C22C2×#1458184011yescharacteristic
784C4—24no—
785C4—24no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—3322no—
791C4—3322no—
792C4—3322no—
793C4—3322no—
794C4—3322no—
795C4—1664no—
796C4—1664no—
797C2—28no—
798C2—6642no—
799C2#2491178918yesdirect product factor
800C2C22×#1458177811yescharacteristic
801C2C2×#1912823511yescharacteristic
802C2C2×#1912829811yescharacteristic
803C2C2×#1912834111yescharacteristic
804C2C2×#1912835211yescharacteristic
805C2C2×#1912837711yescharacteristic
806C2C2×#1912838611yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC22×#95×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC22×#95D83
hypocenterC83C2×#2488
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
2. C22×#14581771C2semidirect
3. #24911789C2direct (N × H)
4. C2×#19127643C2semidirect
5. C2×#19127642C2semidirect
6. C2×#19127630C2semidirect
7. C2×#19127614C2semidirect
8. C2×#19127605C2semidirect
9. C2×#19127593C2semidirect
10. C2×#19127590C2semidirect
13. C2×#19127565C2semidirect
14. C2×#19127564C2semidirect
15. C2×C4×C22⋊Dic83C2semidirect
16. C22×#95×C83C2semidirect
22. C2×#14581771C22semidirect
39. #19127643C22semidirect
40. #19127642C22semidirect
41. #19127630C22semidirect
42. #19127614C22semidirect
43. #19127605C22semidirect
44. #19127593C22semidirect
45. #19127590C22semidirect
48. #19127565C22semidirect
49. #19127564C22semidirect
50. C4×C22⋊Dic83C22semidirect
68. C2×#95×C83C22semidirect
395. C2×C83#2488semidirect
419. C22×#95D83semidirect
420. C83C2×#2488semidirect
472. C2×#95C2×D83semidirect
799. C2#24911789direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817752
C22×#145817712
#249117892
C2×#191276432
C2×#191276422
C2×#191276302
C2×#191276142
C2×#191276052
C2×#191275932
C2×#191275902
C2×#191275802
C2×#191275652
C2×#191275642
C2×C4×C22⋊Dic832
C22×#95×C832
C2×#248883