Finite Group Databasebeta

← C2×#24913459 #35570912

Subgroups — C2×#24913459 #35570912

Order 21248.

2330 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24913459C2116yesmaximal, direct product factor
2C2×#19127642C211yesmaximal, characteristic, complemented
3C2×#19127639C211yesmaximal, characteristic, complemented
4C2×#19127637C211yesmaximal, characteristic, complemented
5C2×#19127629C211yesmaximal, characteristic, complemented
6C2×#19127629C211yesmaximal, characteristic, complemented
7C2×#19127624C211yesmaximal, characteristic, complemented
8C2×#19127615C211yesmaximal, characteristic
9C2×#19127596C211yesmaximal, characteristic, complemented
10C2×#19127589C211yesmaximal, characteristic, complemented
11C2×#19127589C211yesmaximal, characteristic, complemented
12C2×#19127588C211yesmaximal, characteristic, complemented
13C2×#19127581C211yesmaximal, characteristic
14C2×#19127573C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic83C211yesmaximal, characteristic, complemented
16C2×#394×C83C211yesmaximal, characteristic
17C24×Dic83C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic
19C22×Dic83⋊C4C2211yescharacteristic
20C22×Dic83⋊C4C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×Dic83⋊C4C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×C22⋊Dic83C2211yescharacteristic
26C22×C22⋊Dic83C2211yescharacteristic
27C22×C22⋊Dic83C2211yescharacteristic
28C22×C22⋊Dic83C2211yescharacteristic
29C22×C22⋊Dic83C2211yescharacteristic
30C22×C22⋊Dic83C2211yescharacteristic
31C22×C22⋊Dic83C2211yescharacteristic
32C22×C4×Dic83C2211yescharacteristic
33C22×C4×Dic83C2211yescharacteristic
34#19127642C2218yescomplemented
35#19127639C2218yescomplemented
36#19127637C2218yescomplemented
37#19127629C2218yescomplemented
38#19127629C2218yescomplemented
39#19127624C2218yescomplemented
40#19127615C2218yes—
41#19127596C2218yescomplemented
42#19127589C2218yescomplemented
43#19127589C2218yescomplemented
44#19127588C2218yescomplemented
45#19127581C2218yes—
46#19127573C2218yescomplemented
47C22⋊C4×Dic83C2218yescomplemented
48C2×C83⋊#95C2211yescharacteristic
49C2×C83⋊#95C2211yescharacteristic
50C2×C83⋊#95C2211yescharacteristic
51C2×C83⋊#95C2211yescharacteristic
52C2×C83⋊#95C2211yescharacteristic
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C23×D4×C83C2211yescharacteristic
60C22×C4⋊C4×C83C2211yescharacteristic
61C22×C22⋊C4×C83C2211yescharacteristic
62C22×C22⋊C4×C83C2211yescharacteristic
63C22×C22⋊C4×C83C2211yescharacteristic
64C22×C22⋊C4×C83C2211yescharacteristic
65#394×C83C2218yes—
66C2×#95×C83C2211yescharacteristic
67C23×Dic83—24no—
68C23×Dic83—42no—
69C23×Dic83—42no—
70C23×Dic83C2311yescharacteristic
71C23×Dic83C2311yescharacteristic
72C23×Dic83C2311yescharacteristic
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2314yes—
79C2×C4⋊Dic83—42no—
80C2×C4⋊Dic83C2314yes—
81C2×Dic83⋊C4—24no—
82C2×Dic83⋊C4—24no—
83C2×Dic83⋊C4—42no—
84C2×Dic83⋊C4—42no—
85C2×Dic83⋊C4—42no—
86C2×Dic83⋊C4—42no—
87C2×Dic83⋊C4C2314yes—
88C2×Dic83⋊C4C2314yes—
89C2×Dic83⋊C4C2314yes—
90C2×Dic83⋊C4C2314yes—
91C2×Dic83⋊C4C2314yes—
92C2×Dic83⋊C4C2314yes—
93C2×C22⋊Dic83—24no—
94C2×C22⋊Dic83—24no—
95C2×C22⋊Dic83—24no—
96C2×C22⋊Dic83—24no—
97C2×C22⋊Dic83—42no—
98C2×C22⋊Dic83—42no—
99C2×C22⋊Dic83—42no—
100C2×C22⋊Dic83C2314yes—
101C2×C22⋊Dic83C2314yes—
102C2×C22⋊Dic83C2314yes—
103C2×C22⋊Dic83C2314yes—
104C2×C22⋊Dic83C2314yes—
105C2×C22⋊Dic83C2314yes—
106C2×C22⋊Dic83C2314yes—
107C2×C4×Dic83—42no—
108C2×C4×Dic83—42no—
109C2×C4×Dic83C2314yes—
110C2×C4×Dic83C2314yes—
111C83⋊#95C2314yes—
112C83⋊#95C2314yes—
113C83⋊#95C2314yes—
114C83⋊#95C2314yes—
115C83⋊#95C2314yes—
116C83⋊#95C2314yes—
117C83⋊#95C2314yes—
118C83⋊#95C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C25×C83C2311yescharacteristic
123C25×C83C2311yescharacteristic
124C22×D4×C83—24no—
125C22×D4×C83—42no—
126C22×D4×C83—42no—
127C22×D4×C83C2314yes—
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C2×C4⋊C4×C83—42no—
134C2×C4⋊C4×C83C2314yes—
135C2×C22⋊C4×C83—24no—
136C2×C22⋊C4×C83—42no—
137C2×C22⋊C4×C83—42no—
138C2×C22⋊C4×C83—42no—
139C2×C22⋊C4×C83C2314yes—
140C2×C22⋊C4×C83C2314yes—
141C2×C22⋊C4×C83C2314yes—
142C2×C22⋊C4×C83C2314yes—
143#95×C83C2314yes—
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×Dic83—22no—
153C22×Dic83—22no—
154C22×Dic83—22no—
155C22×Dic83—22no—
156C22×Dic83—22no—
157C22×Dic83—22no—
158C22×Dic83—22no—
159C22×Dic83—22no—
160C22×Dic83—22no—
161C22×Dic83—22no—
162C22×Dic83—22no—
163C22×Dic83—22no—
164C22×Dic83—22no—
165C22×Dic83—22no—
166C22×Dic83—28no—
167C22×Dic83—44no—
168C22×Dic83—44no—
169C22×Dic83—416no—
170C22×Dic83#4114yes—
171C22×Dic83#4114yes—
172C22×Dic83C2412yes—
173C22×Dic83C2412yes—
174C22×Dic83C2412yes—
175C22×Dic83C2412yes—
176C22×Dic83C2412yes—
177C22×Dic83C2412yes—
178C22×Dic83C2412yes—
179C22×Dic83C2412yes—
180C4⋊Dic83—44no—
181Dic83⋊C4—28no—
182Dic83⋊C4—28no—
183Dic83⋊C4—44no—
184Dic83⋊C4—44no—
185Dic83⋊C4—44no—
186Dic83⋊C4—44no—
187C22⋊Dic83—28no—
188C22⋊Dic83—28no—
189C22⋊Dic83—28no—
190C22⋊Dic83—28no—
191C22⋊Dic83—44no—
192C22⋊Dic83—44no—
193C22⋊Dic83—44no—
194C4×Dic83—44no—
195C4×Dic83—44no—
196C24×C83—22no—
197C24×C83—22no—
198C24×C83—22no—
199C24×C83—22no—
200C24×C83—22no—
201C24×C83—22no—
202C24×C83—22no—
203C24×C83—22no—
204C24×C83—22no—
205C24×C83—22no—
206C24×C83—22no—
207C24×C83—22no—
208C24×C83—22no—
209C24×C83#4114yes—
210C24×C83C2412yes—
211C24×C83C2412yes—
212C24×C83C2411yescharacteristic
213C2×D4×C83—28no—
214C2×D4×C83—44no—
215C2×D4×C83—44no—
216C2×D4×C83—416no—
217C22×C4×C83—22no—
218C22×C4×C83—22no—
219C22×C4×C83—22no—
220C22×C4×C83—22no—
221C22×C4×C83—22no—
222C22×C4×C83—22no—
223C22×C4×C83—22no—
224C22×C4×C83—22no—
225C22×C4×C83—22no—
226C22×C4×C83—22no—
227C22×C4×C83—22no—
228C22×C4×C83—22no—
229C22×C4×C83—22no—
230C22×C4×C83—22no—
231C22×C4×C83—22no—
232C22×C4×C83C2412yes—
233C22×C4×C83C2412yes—
234C22×C4×C83C2412yes—
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C4⋊C4×C83—44no—
238C22⋊C4×C83—28no—
239C22⋊C4×C83—44no—
240C22⋊C4×C83—44no—
241C22⋊C4×C83—44no—
242C23×C83—28no—
243C23×C83—28no—
244C23×C83—28no—
245C23×C83—22no—
246C23×C83—22no—
247C23×C83—22no—
248C23×C83—22no—
249C23×C83—22no—
250C23×C83—22no—
251C23×C83—22no—
252C23×C83—22no—
253C23×C83—22no—
254C23×C83—22no—
255C23×C83—22no—
256C23×C83—22no—
257C23×C83—22no—
258C23×C83—44no—
259C23×C83—44no—
260C23×C83—44no—
261C23×C83—44no—
262C23×C83—44no—
263C23×C83—44no—
264C23×C83—44no—
265C23×C83—44no—
266C23×C83—44no—
267C23×C83—44no—
268C23×C83—44no—
269C23×C83C2×#4112yes—
270C23×C83C2×#4112yes—
271C23×C83C2×#4114yes—
272C23×C83C2×#4112yes—
273C23×C83H(5,𝔽2)12yes—
274C23×C83H(5,𝔽2)12yes—
275C23×C83H(5,𝔽2)12yes—
276C23×C832−1+412yes—
277C23×C83C2511yescharacteristic
278D4×C83—416no—
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—22no—
294C2×C4×C83—44no—
295C2×C4×C83—44no—
296C2×C4×C83—44no—
297C2×C4×C83—44no—
298C2×C4×C83—44no—
299C2×Dic83—28no—
300C2×Dic83—28no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—22no—
314C2×Dic83—22no—
315C2×Dic83—22no—
316C2×Dic83—22no—
317C2×Dic83—22no—
318C2×Dic83—22no—
319C2×Dic83—22no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—416no—
324C2×Dic83—44no—
325C2×Dic83—44no—
326C2×Dic83—44no—
327C2×Dic83—44no—
328C2×Dic83—44no—
329C2×Dic83—44no—
330C2×Dic83C2×#4114yes—
331C2×Dic83C2×#4114yes—
332C22×C83—24no—
333C22×C83—24no—
334C22×C83—24no—
335C22×C83—416no—
336C22×C83—42no—
337C22×C83—42no—
338C22×C83—42no—
339C22×C83—42no—
340C22×C83—42no—
341C22×C83—42no—
342C22×C83—42no—
343C22×C83—42no—
344C22×C83—42no—
345C22×C83—42no—
346C22×C83—42no—
347C22×C83—88no—
348C22×C83#52914yes—
349C22×C83#53814yes—
350C22×C83#53814yes—
351C22×C83#53914yes—
352C22×C83#53914yes—
353C22×C83#54014yes—
354C22×C83#54214yes—
355C22×C83C22×#4111yescharacteristic
356C22×C83C22×#4111yescharacteristic
357C22×C83C22×#4111yescharacteristic
358C22×C83C2×H(5,𝔽2)11yescharacteristic
359C22×C83C2×H(5,𝔽2)11yescharacteristic
360C22×C83C2×H(5,𝔽2)11yescharacteristic
361C22×C83C2×2−1+411yescharacteristic
362C4×C83—42no—
363C4×C83—42no—
364C4×C83—42no—
365C4×C83—42no—
366C4×C83—42no—
367Dic83—24no—
368Dic83—24no—
369Dic83—42no—
370Dic83—42no—
371Dic83—42no—
372Dic83—42no—
373Dic83—42no—
374Dic83—42no—
375C2×#2649—831nomaximal, Sylow
376C2×C83—44no—
377C2×C83—82no—
378C2×C83#264918yescomplemented
379C2×C83C2×#52911yescharacteristic
380C2×C83C2×#53811yescharacteristic
381C2×C83C2×#53811yescharacteristic
382C2×C83C2×#53911yescharacteristic
383C2×C83C2×#53911yescharacteristic
384C2×C83C2×#54011yescharacteristic
385C2×C83C2×#54211yescharacteristic
386#2649—8316no—
387C2×#400—831no—
388C2×#400—831no—
389C2×#399—831no—
390C2×#397—831no—
391C2×#397—831no—
392C2×#396—831no—
393C2×#394—831no—
394C2×#394D8311yescharacteristic
395C2×#389—831no—
396C2×#388—831no—
397C2×#388—831no—
398C2×#387—831no—
399C2×#386—831no—
400C2×#385—831no—
401C2×C4×C22⋊C4—831no—
402C83C2×#264911yescharacteristic, complemented, Sylow
403C23×D4C2×D8311yescharacteristic
404C24×C4—831no—
405C22×C4⋊C4—831no—
406C22×C4⋊C4—831no—
407C22×C4⋊C4—831no—
408C22×C4⋊C4—831no—
409C22×C4⋊C4—831no—
410C22×C4⋊C4—831no—
411C22×C4⋊C4—831no—
412C22×C4⋊C4C2×D8311yescharacteristic
413C22×C22⋊C4—831no—
414C22×C22⋊C4—831no—
415C22×C22⋊C4—831no—
416C22×C22⋊C4—831no—
417C22×C22⋊C4—831no—
418C22×C22⋊C4—831no—
419C22×C22⋊C4—831no—
420C22×C22⋊C4C2×D8311yescharacteristic
421C22×C22⋊C4C2×D8311yescharacteristic
422C22×C22⋊C4C2×D8311yescharacteristic
423C22×C22⋊C4C2×D8311yescharacteristic
424C22×C42—831no—
425C22×C42—831no—
426#400—838no—
427#400—838no—
428#399—838no—
429#397—838no—
430#397—838no—
431#396—838no—
432#394—838no—
433#394C2×D8318yes—
434#389—838no—
435#388—838no—
436#388—838no—
437#387—838no—
438#386—838no—
439#385—838no—
440C4×C22⋊C4—838no—
441C2×#95—831no—
442C2×#95—831no—
443C2×#95—831no—
444C2×#95—831no—
445C2×#95—831no—
446C2×#95—831no—
447C2×#95—831no—
448C2×#95—831no—
449C2×#95—831no—
450C2×#95—831no—
451C2×#95—831no—
452C2×#95C2×D8311yescharacteristic
453C25C22×D8311yescharacteristic
454C25C22×D8311yescharacteristic
455C22×D4—24no—
456C22×D4—42no—
457C22×D4—42no—
458C22×D4C22×D8314yes—
459C23×C4—3322no—
460C23×C4—3322no—
461C23×C4—834no—
462C23×C4—831no—
463C23×C4—831no—
464C23×C4—831no—
465C23×C4—831no—
466C23×C4—831no—
467C23×C4—831no—
468C23×C4—831no—
469C23×C4—831no—
470C23×C4—1664no—
471C23×C4C22×D8311yescharacteristic
472C23×C4C22×D8311yescharacteristic
473C23×C4C22×D8311yescharacteristic
474C23×C4C22×D8311yescharacteristic
475C23×C4C22×D8311yescharacteristic
476C2×C4⋊C4—42no—
477C2×C4⋊C4—3322no—
478C2×C4⋊C4—3322no—
479C2×C4⋊C4—3322no—
480C2×C4⋊C4—3322no—
481C2×C4⋊C4—3322no—
482C2×C4⋊C4—834no—
483C2×C4⋊C4—834no—
484C2×C4⋊C4—834no—
485C2×C4⋊C4—834no—
486C2×C4⋊C4—834no—
487C2×C4⋊C4—834no—
488C2×C4⋊C4—834no—
489C2×C4⋊C4—1664no—
490C2×C4⋊C4—1664no—
491C2×C4⋊C4C22×D8314yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—3322no—
497C2×C22⋊C4—3322no—
498C2×C22⋊C4—3322no—
499C2×C22⋊C4—834no—
500C2×C22⋊C4—834no—
501C2×C22⋊C4—834no—
502C2×C22⋊C4—834no—
503C2×C22⋊C4—834no—
504C2×C22⋊C4—834no—
505C2×C22⋊C4—834no—
506C2×C22⋊C4—1664no—
507C2×C22⋊C4—1664no—
508C2×C22⋊C4—1664no—
509C2×C22⋊C4—1664no—
510C2×C22⋊C4C22×D8314yes—
511C2×C22⋊C4C22×D8314yes—
512C2×C22⋊C4C22×D8314yes—
513C2×C22⋊C4C22×D8314yes—
514C2×C42—3322no—
515C2×C42—3322no—
516C2×C42—834no—
517C2×C42—834no—
518#95—834no—
519#95—834no—
520#95—834no—
521#95—834no—
522#95—834no—
523#95—834no—
524#95—834no—
525#95—834no—
526#95—834no—
527#95—834no—
528#95—834no—
529#95C22×D8314yes—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24#1305058914yes—
544C24C23×D8312yes—
545C24C23×D8312yes—
546C24C23×D8311yescharacteristic
547C2×D4—28no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—416no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—33216no—
567C22×C4—3324no—
568C22×C4—3324no—
569C22×C4—834no—
570C22×C4—834no—
571C22×C4—832no—
572C22×C4—832no—
573C22×C4—832no—
574C22×C4—832no—
575C22×C4—832no—
576C22×C4—832no—
577C22×C4—832no—
578C22×C4—832no—
579C22×C4—1668no—
580C22×C4—1662no—
581C22×C4—1662no—
582C22×C4—1662no—
583C22×C4—1662no—
584C22×C4—1662no—
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×C4C23×D8312yes—
603C22×C4C23×D8312yes—
604C22×C4C23×D8312yes—
605C22×C4C23×D8312yes—
606C22×C4C23×D8312yes—
607C4⋊C4—44no—
608C4⋊C4—3324no—
609C4⋊C4—3324no—
610C4⋊C4—3324no—
611C4⋊C4—3324no—
612C4⋊C4—3324no—
613C4⋊C4—1668no—
614C4⋊C4—1668no—
615C22⋊C4—28no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—3324no—
620C22⋊C4—3324no—
621C22⋊C4—3324no—
622C22⋊C4—1668no—
623C22⋊C4—1668no—
624C22⋊C4—1668no—
625C22⋊C4—1668no—
626C42—3324no—
627C42—3324no—
628C23—28no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—28no—
636C23—28no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23#41×D8312yes—
656C23#41×D8312yes—
657C23C2×#1305058914yes—
658C23C2×#1305058912yes—
659C23#1458183712yes—
660C23#1458183712yes—
661C23#1458183712yes—
662C23#1458183912yes—
663C23C24×D8311yescharacteristic
664D4—416no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—3324no—
686C2×C4—3324no—
687C2×C4—3324no—
688C2×C4—3324no—
689C2×C4—3324no—
690C2×C4—3324no—
691C2×C4—33216no—
692C2×C4—834no—
693C2×C4—834no—
694C2×C4—1662no—
695C2×C4—1662no—
696C2×C4—1662no—
697C2×C4—1662no—
698C2×C4—1662no—
699C2×C4—1662no—
700C2×C4—1662no—
701C2×C4—1662no—
702C2×C4—1662no—
703C2×C4—1662no—
704C2×C4—1662no—
705C2×C4—1662no—
706C2×C4—1662no—
707C2×C4—1662no—
708C2×C4—1662no—
709C2×C4—1662no—
710C2×C4—1662no—
711C2×C4—1662no—
712C2×C4—1662no—
713C2×C4—1662no—
714C2×C4—1662no—
715C2×C4—1662no—
716C2×C4—1668no—
717C2×C4—1668no—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—42no—
722C22—416no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—88no—
734C22#1912822814yes—
735C22#1912828314yes—
736C22#1912828614yes—
737C22#1912829414yes—
738C22#1912829614yes—
739C22#1912830114yes—
740C22#1912831514yes—
741C22C2×#41×D8311yescharacteristic
742C22C2×#41×D8311yescharacteristic
743C22C22×#1305058911yescharacteristic
744C22C2×#1458183711yescharacteristic
745C22C2×#1458183711yescharacteristic
746C22C2×#1458183711yescharacteristic
747C22C2×#1458183911yescharacteristic
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—3322no—
754C4—3322no—
755C4—3322no—
756C4—3322no—
757C4—3322no—
758C4—3322no—
759C4—1664no—
760C4—1664no—
761C2—44no—
762C2—82no—
763C2#2491345918yesdirect product factor
764C2C2×#1912822811yescharacteristic
765C2C2×#1912828311yescharacteristic
766C2C2×#1912828611yescharacteristic
767C2C2×#1912829411yescharacteristic
768C2C2×#1912829611yescharacteristic
769C2C2×#1912830111yescharacteristic
770C2C2×#1912831511yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#394×C83C2
socleC24×C83C24
prime radicalC23×D4×C83C22
hypercenterC2×#394D83
hypocenterC83C2×#2649
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #24913459C2direct (N × H)
2. C2×#19127642C2semidirect
3. C2×#19127639C2semidirect
4. C2×#19127637C2semidirect
5. C2×#19127629C2semidirect
6. C2×#19127629C2semidirect
7. C2×#19127624C2semidirect
9. C2×#19127596C2semidirect
10. C2×#19127589C2semidirect
11. C2×#19127589C2semidirect
12. C2×#19127588C2semidirect
14. C2×#19127573C2semidirect
15. C2×C22⋊C4×Dic83C2semidirect
34. #19127642C22semidirect
35. #19127639C22semidirect
36. #19127637C22semidirect
37. #19127629C22semidirect
38. #19127629C22semidirect
39. #19127624C22semidirect
41. #19127596C22semidirect
42. #19127589C22semidirect
43. #19127589C22semidirect
44. #19127588C22semidirect
46. #19127573C22semidirect
47. C22⋊C4×Dic83C22semidirect
378. C2×C83#2649semidirect
402. C83C2×#2649semidirect
763. C2#24913459direct (N × H)

Maximal subgroups

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

subgroupindex
#249134592
C2×#191276422
C2×#191276392
C2×#191276372
C2×#191276292
C2×#191276242
C2×#191276152
C2×#191275962
C2×#191275892
C2×#191275882
C2×#191275812
C2×#191275732
C2×C22⋊C4×Dic832
C2×#394×C832
C2×#264983