Finite Group Databasebeta

← C2×#24915682 #35610641

Subgroups — C2×#24915682 #35610641

Order 21248.

2110 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24915682C2116yesmaximal, direct product factor
2C2×#19127639C211yesmaximal, characteristic, complemented
3C2×#19127636C211yesmaximal, characteristic, complemented
4C2×#19127636C211yesmaximal, characteristic, complemented
5C2×#19127634C211yesmaximal, characteristic, complemented
6C2×#19127631C211yesmaximal, characteristic, complemented
7C2×#19127629C211yesmaximal, characteristic, complemented
8C2×#19127628C211yesmaximal, characteristic, complemented
9C2×#19127624C211yesmaximal, characteristic, complemented
10C2×#19127617C211yesmaximal, characteristic
11C2×#19127616C211yesmaximal, characteristic
12C2×#19127616C211yesmaximal, characteristic
13C2×#19127598C211yesmaximal, characteristic, complemented
14C2×#19127591C211yesmaximal, characteristic, complemented
15C2×#19127589C211yesmaximal, characteristic, complemented
16C2×#396×C83C211yesmaximal, characteristic, complemented
17C23×C22⋊D83C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×Dic83⋊C4C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×Dic83⋊C4C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×C22⋊Dic83C2211yescharacteristic
27C22×C22⋊Dic83C2211yescharacteristic
28C22×C22⋊Dic83C2211yescharacteristic
29C22×(C2×D83)⋊C4C2211yescharacteristic
30C22×(C2×D83)⋊C4C2211yescharacteristic
31C22×(C2×D83)⋊C4C2211yescharacteristic
32C22×(C2×D83)⋊C4C2211yescharacteristic
33C22×(C2×D83)⋊C4C2211yescharacteristic
34C22×(C2×D83)⋊C4C2211yescharacteristic
35C22×C4×Dic83C2211yescharacteristic
36#19127639C2218yescomplemented
37#19127636C2218yescomplemented
38#19127636C2218yescomplemented
39#19127634C2218yescomplemented
40#19127631C2218yescomplemented
41#19127629C2218yescomplemented
42#19127628C2218yescomplemented
43#19127624C2218yescomplemented
44#19127617C2218yes—
45#19127616C2218yes—
46#19127616C2218yes—
47#19127598C2218yescomplemented
48#19127591C2218yescomplemented
49#19127589C2218yescomplemented
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
59C22×C4⋊C4×C83C2211yescharacteristic
60C22×C4⋊C4×C83C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C22⋊C4×C83C2211yescharacteristic
63C22×C22⋊C4×C83C2211yescharacteristic
64C22×C22⋊C4×C83C2211yescharacteristic
65#396×C83C2218yescomplemented
66C2×#95×C83C2211yescharacteristic
67C24×D83C2311yescharacteristic
68C22×C22⋊D83—42no—
69C22×C22⋊D83—42no—
70C22×C22⋊D83—42no—
71C22×C22⋊D83C2314yes—
72C23×Dic83C2311yescharacteristic
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C2×C4⋊Dic83—42no—
80C2×C4⋊Dic83—42no—
81C2×C4⋊Dic83C2314yes—
82C2×C4⋊Dic83C2314yes—
83C2×Dic83⋊C4—24no—
84C2×Dic83⋊C4—42no—
85C2×Dic83⋊C4—42no—
86C2×Dic83⋊C4—42no—
87C2×Dic83⋊C4—42no—
88C2×Dic83⋊C4—42no—
89C2×Dic83⋊C4C2314yes—
90C2×Dic83⋊C4C2314yes—
91C2×Dic83⋊C4C2314yes—
92C2×Dic83⋊C4C2314yes—
93C2×Dic83⋊C4C2314yes—
94C2×Dic83⋊C4C2314yes—
95C2×C22⋊Dic83—24no—
96C2×C22⋊Dic83—42no—
97C2×C22⋊Dic83—42no—
98C2×C22⋊Dic83C2314yes—
99C2×C22⋊Dic83C2314yes—
100C2×C22⋊Dic83C2314yes—
101C2×(C2×D83)⋊C4—24no—
102C2×(C2×D83)⋊C4—42no—
103C2×(C2×D83)⋊C4—42no—
104C2×(C2×D83)⋊C4—42no—
105C2×(C2×D83)⋊C4—42no—
106C2×(C2×D83)⋊C4—42no—
107C2×(C2×D83)⋊C4C2314yes—
108C2×(C2×D83)⋊C4C2314yes—
109C2×(C2×D83)⋊C4C2314yes—
110C2×(C2×D83)⋊C4C2314yes—
111C2×(C2×D83)⋊C4C2314yes—
112C2×(C2×D83)⋊C4C2314yes—
113C2×C4×Dic83—42no—
114C2×C4×Dic83C2314yes—
115C83⋊#95C2314yes—
116C83⋊#95C2314yes—
117C83⋊#95C2314yes—
118C83⋊#95C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2314yes—
124C25×C83C2311yescharacteristic
125C23×C4×C83C2311yescharacteristic
126C23×C4×C83C2311yescharacteristic
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C23×C4×C83C2311yescharacteristic
131C2×C4⋊C4×C83—42no—
132C2×C4⋊C4×C83—42no—
133C2×C4⋊C4×C83—42no—
134C2×C4⋊C4×C83C2314yes—
135C2×C4⋊C4×C83C2314yes—
136C2×C4⋊C4×C83C2314yes—
137C2×C22⋊C4×C83—42no—
138C2×C22⋊C4×C83—42no—
139C2×C22⋊C4×C83—42no—
140C2×C22⋊C4×C83C2314yes—
141C2×C22⋊C4×C83C2314yes—
142C2×C22⋊C4×C83C2314yes—
143#95×C83C2314yes—
144C23×D83—22no—
145C23×D83—22no—
146C23×D83—22no—
147C23×D83—22no—
148C23×D83—22no—
149C23×D83—22no—
150C23×D83—22no—
151C23×D83C2412yes—
152C2×C22⋊D83—44no—
153C2×C22⋊D83—44no—
154C2×C22⋊D83—44no—
155C2×C22⋊D83—416no—
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—22no—
167C22×Dic83—22no—
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#4114yes—
177C22×Dic83C2412yes—
178C22×Dic83C2412yes—
179C22×Dic83C2412yes—
180C22×Dic83C2412yes—
181C22×Dic83C2412yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C4⋊Dic83—44no—
185C4⋊Dic83—44no—
186Dic83⋊C4—28no—
187Dic83⋊C4—44no—
188Dic83⋊C4—44no—
189Dic83⋊C4—44no—
190Dic83⋊C4—44no—
191Dic83⋊C4—44no—
192C22⋊Dic83—28no—
193C22⋊Dic83—44no—
194C22⋊Dic83—44no—
195(C2×D83)⋊C4—28no—
196(C2×D83)⋊C4—44no—
197(C2×D83)⋊C4—44no—
198(C2×D83)⋊C4—44no—
199(C2×D83)⋊C4—44no—
200(C2×D83)⋊C4—44no—
201C4×Dic83—44no—
202C24×C83—22no—
203C24×C83—22no—
204C24×C83—22no—
205C24×C83—22no—
206C24×C83—22no—
207C24×C83—22no—
208C24×C83—22no—
209C24×C83C2412yes—
210C24×C83C2411yescharacteristic
211C22×C4×C83—22no—
212C22×C4×C83—22no—
213C22×C4×C83—22no—
214C22×C4×C83—22no—
215C22×C4×C83—22no—
216C22×C4×C83—22no—
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×C83C2412yes—
230C22×C4×C83C2412yes—
231C22×C4×C83C2412yes—
232C22×C4×C83C2412yes—
233C22×C4×C83C2412yes—
234C22×C4×C83C2412yes—
235C4⋊C4×C83—44no—
236C4⋊C4×C83—44no—
237C4⋊C4×C83—44no—
238C22⋊C4×C83—44no—
239C22⋊C4×C83—44no—
240C22⋊C4×C83—44no—
241C23×C83—22no—
242C23×C83—22no—
243C23×C83—22no—
244C23×C83—22no—
245C23×C83—22no—
246C23×C83—22no—
247C23×C83—22no—
248C23×C83—44no—
249C23×C83—44no—
250C23×C83—44no—
251C23×C83—44no—
252C23×C83—44no—
253C23×C83—44no—
254C23×C83—44no—
255C23×C83C2×#4112yes—
256C23×C83H(5,𝔽2)12yes—
257C23×C83H(5,𝔽2)12yes—
258C23×C83H(5,𝔽2)12yes—
259C23×C83H(5,𝔽2)12yes—
260C23×C832−1+412yes—
261C23×C832−1+412yes—
262C23×C83C2511yescharacteristic
263C22×D83—22no—
264C22×D83—22no—
265C22×D83—22no—
266C22×D83—22no—
267C22×D83—22no—
268C22×D83—22no—
269C22×D83—22no—
270C22×D83—44no—
271C22×D83—44no—
272C22×D83—44no—
273C22×D83—44no—
274C22×D83—44no—
275C22×D83—44no—
276C22×D83—44no—
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—22no—
294C2×C4×C83—22no—
295C2×C4×C83—44no—
296C2×C4×C83—44no—
297C2×C4×C83—44no—
298C2×C4×C83—44no—
299C2×C4×C83—44no—
300C2×C4×C83—44no—
301C22⋊D83—416no—
302C2×Dic83—28no—
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—44no—
324C2×Dic83—44no—
325C2×Dic83—44no—
326C2×Dic83—44no—
327C2×Dic83—44no—
328C2×Dic83—44no—
329C2×Dic83C2×#4114yes—
330C22×C83—42no—
331C22×C83—42no—
332C22×C83—42no—
333C22×C83—42no—
334C22×C83—42no—
335C22×C83—42no—
336C22×C83—42no—
337C22×C83—88no—
338C22×C83#53914yes—
339C22×C83#54014yes—
340C22×C83#54214yes—
341C22×C83#56014yes—
342C22×C83#56214yes—
343C22×C83#56214yes—
344C22×C83#56314yes—
345C22×C83C22×#4111yescharacteristic
346C22×C83C2×H(5,𝔽2)11yescharacteristic
347C22×C83C2×H(5,𝔽2)11yescharacteristic
348C22×C83C2×H(5,𝔽2)11yescharacteristic
349C22×C83C2×H(5,𝔽2)11yescharacteristic
350C22×C83C2×2−1+411yescharacteristic
351C22×C83C2×2−1+411yescharacteristic
352C2×D83—42no—
353C2×D83—42no—
354C2×D83—42no—
355C2×D83—42no—
356C2×D83—42no—
357C2×D83—42no—
358C2×D83—42no—
359C2×D83—88no—
360C4×C83—42no—
361C4×C83—42no—
362C4×C83—42no—
363C4×C83—42no—
364C4×C83—42no—
365C4×C83—42no—
366Dic83—24no—
367Dic83—42no—
368Dic83—42no—
369Dic83—42no—
370Dic83—42no—
371Dic83—42no—
372Dic83—42no—
373C2×#2837—831nomaximal, Sylow
374C2×C83—82no—
375C2×C83#283718yescomplemented
376C2×C83C2×#53911yescharacteristic
377C2×C83C2×#54011yescharacteristic
378C2×C83C2×#54211yescharacteristic
379C2×C83C2×#56011yescharacteristic
380C2×C83C2×#56211yescharacteristic
381C2×C83C2×#56211yescharacteristic
382C2×C83C2×#56311yescharacteristic
383D83—82no—
384#2837—8316no—
385C2×#400—831no—
386C2×#399—831no—
387C2×#399—831no—
388C2×#398—831no—
389C2×#398—831no—
390C2×#397—831no—
391C2×#397—831no—
392C2×#396—831no—
393C2×#396D8311yescharacteristic, complemented
394C2×#394—831no—
395C2×#394—831no—
396C2×#394—831no—
397C2×#389—831no—
398C2×#388—831no—
399C2×#388—831no—
400C83C2×#283711yescharacteristic, complemented, Sylow
401C23×D4—831no—
402C22×C4⋊C4—831no—
403C22×C4⋊C4—831no—
404C22×C4⋊C4—831no—
405C22×C4⋊C4—831no—
406C22×C4⋊C4—831no—
407C22×C4⋊C4—831no—
408C22×C4⋊C4—831no—
409C22×C4⋊C4—831no—
410C22×C4⋊C4C2×D8311yescharacteristic
411C22×C4⋊C4C2×D8311yescharacteristic
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⋊C4—831no—
421C22×C22⋊C4—831no—
422C22×C22⋊C4C2×D8311yescharacteristic
423C22×C22⋊C4C2×D8311yescharacteristic
424C22×C22⋊C4C2×D8311yescharacteristic
425C22×C42—831no—
426#400—838no—
427#399—838no—
428#399—838no—
429#398—838no—
430#398—838no—
431#397—838no—
432#397—838no—
433#396—838no—
434#396C2×D8318yescomplemented
435#394—838no—
436#394—838no—
437#394—838no—
438#389—838no—
439#388—838no—
440#388—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×#95C2×D8311yescharacteristic
451C25—831no—
452C25C22×D8311yescharacteristic
453C22×D4—3322no—
454C22×D4—3322no—
455C22×D4—3322no—
456C22×D4—834no—
457C23×C4—831no—
458C23×C4—831no—
459C23×C4—831no—
460C23×C4—831no—
461C23×C4—831no—
462C23×C4—831no—
463C23×C4—831no—
464C23×C4C22×D8311yescharacteristic
465C23×C4C22×D8311yescharacteristic
466C23×C4C22×D8311yescharacteristic
467C23×C4C22×D8311yescharacteristic
468C23×C4C22×D8311yescharacteristic
469C23×C4C22×D8311yescharacteristic
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—3322no—
474C2×C4⋊C4—3322no—
475C2×C4⋊C4—3322no—
476C2×C4⋊C4—3322no—
477C2×C4⋊C4—3322no—
478C2×C4⋊C4—3322no—
479C2×C4⋊C4—3322no—
480C2×C4⋊C4—834no—
481C2×C4⋊C4—834no—
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—1664no—
489C2×C4⋊C4C22×D8314yes—
490C2×C4⋊C4C22×D8314yes—
491C2×C4⋊C4C22×D8314yes—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—3322no—
496C2×C22⋊C4—3322no—
497C2×C22⋊C4—3322no—
498C2×C22⋊C4—3322no—
499C2×C22⋊C4—3322no—
500C2×C22⋊C4—3322no—
501C2×C22⋊C4—3322no—
502C2×C22⋊C4—834no—
503C2×C22⋊C4—834no—
504C2×C22⋊C4—834no—
505C2×C22⋊C4—834no—
506C2×C22⋊C4—834no—
507C2×C22⋊C4—834no—
508C2×C22⋊C4—834no—
509C2×C22⋊C4—834no—
510C2×C22⋊C4—834no—
511C2×C22⋊C4—1664no—
512C2×C22⋊C4—1664no—
513C2×C22⋊C4C22×D8314yes—
514C2×C22⋊C4C22×D8314yes—
515C2×C22⋊C4C22×D8314yes—
516C2×C42—3322no—
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#95C22×D8314yes—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—832no—
536C24—1662no—
537C24—1662no—
538C24—1662no—
539C24—1662no—
540C24—1662no—
541C24—1662no—
542C24—1662no—
543C24C23×D8312yes—
544C24C23×D8311yescharacteristic
545C2×D4—33216no—
546C2×D4—3324no—
547C2×D4—3324no—
548C2×D4—3324no—
549C22×C4—22no—
550C22×C4—22no—
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—22no—
567C22×C4—834no—
568C22×C4—832no—
569C22×C4—832no—
570C22×C4—832no—
571C22×C4—832no—
572C22×C4—832no—
573C22×C4—832no—
574C22×C4—832no—
575C22×C4—1662no—
576C22×C4—1662no—
577C22×C4—1662no—
578C22×C4—1662no—
579C22×C4—1662no—
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×C4C23×D8312yes—
596C22×C4C23×D8312yes—
597C22×C4C23×D8312yes—
598C22×C4C23×D8312yes—
599C22×C4C23×D8312yes—
600C22×C4C23×D8312yes—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—3324no—
605C4⋊C4—3324no—
606C4⋊C4—3324no—
607C4⋊C4—3324no—
608C4⋊C4—3324no—
609C4⋊C4—3324no—
610C4⋊C4—3324no—
611C4⋊C4—1668no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—3324no—
616C22⋊C4—3324no—
617C22⋊C4—3324no—
618C22⋊C4—3324no—
619C22⋊C4—3324no—
620C22⋊C4—3324no—
621C22⋊C4—3324no—
622C22⋊C4—1668no—
623C22⋊C4—1668no—
624C42—3324no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—3324no—
640C23—3324no—
641C23—3324no—
642C23—3324no—
643C23—3324no—
644C23—3324no—
645C23—3324no—
646C23—1662no—
647C23—1662no—
648C23—1662no—
649C23—1662no—
650C23—1662no—
651C23—1662no—
652C23—1662no—
653C23#41×D8312yes—
654C23#1458183712yes—
655C23#1458183712yes—
656C23#1458183712yes—
657C23#1458183812yes—
658C23#1458183912yes—
659C23#1458184012yes—
660C23C24×D8311yescharacteristic
661D4—33216no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
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—44no—
686C2×C4—3324no—
687C2×C4—3324no—
688C2×C4—3324no—
689C2×C4—3324no—
690C2×C4—3324no—
691C2×C4—3324no—
692C2×C4—834no—
693C2×C4—1662no—
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—1668no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—88no—
722C22—3322no—
723C22—3322no—
724C22—3322no—
725C22—3322no—
726C22—3322no—
727C22—3322no—
728C22—3322no—
729C22—6648no—
730C22#1912829714yes—
731C22#1912830114yes—
732C22#1912831714yes—
733C22#1912843914yes—
734C22#1912844614yes—
735C22#1912844714yes—
736C22#1912845214yes—
737C22C2×#41×D8311yescharacteristic
738C22C2×#1458183711yescharacteristic
739C22C2×#1458183711yescharacteristic
740C22C2×#1458183711yescharacteristic
741C22C2×#1458183811yescharacteristic
742C22C2×#1458183911yescharacteristic
743C22C2×#1458184011yescharacteristic
744C4—42no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—3322no—
751C4—3322no—
752C4—3322no—
753C4—3322no—
754C4—3322no—
755C4—3322no—
756C4—1664no—
757C2—82no—
758C2—6642no—
759C2#2491568218yesdirect product factor
760C2C2×#1912829711yescharacteristic
761C2C2×#1912830111yescharacteristic
762C2C2×#1912831711yescharacteristic
763C2C2×#1912843911yescharacteristic
764C2C2×#1912844611yescharacteristic
765C2C2×#1912844711yescharacteristic
766C2C2×#1912845211yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#396×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC2×#396D83
hypocenterC83C2×#2837
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. #24915682C2direct (N × H)
2. C2×#19127639C2semidirect
3. C2×#19127636C2semidirect
4. C2×#19127636C2semidirect
5. C2×#19127634C2semidirect
6. C2×#19127631C2semidirect
7. C2×#19127629C2semidirect
8. C2×#19127628C2semidirect
9. C2×#19127624C2semidirect
13. C2×#19127598C2semidirect
14. C2×#19127591C2semidirect
15. C2×#19127589C2semidirect
16. C2×#396×C83C2semidirect
36. #19127639C22semidirect
37. #19127636C22semidirect
38. #19127636C22semidirect
39. #19127634C22semidirect
40. #19127631C22semidirect
41. #19127629C22semidirect
42. #19127628C22semidirect
43. #19127624C22semidirect
47. #19127598C22semidirect
48. #19127591C22semidirect
49. #19127589C22semidirect
65. #396×C83C22semidirect
375. C2×C83#2837semidirect
393. C2×#396D83semidirect
400. C83C2×#2837semidirect
434. #396C2×D83semidirect
759. C2#24915682direct (N × H)

Maximal subgroups

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

subgroupindex
#249156822
C2×#191276392
C2×#191276362
C2×#191276342
C2×#191276312
C2×#191276292
C2×#191276282
C2×#191276242
C2×#191276172
C2×#191276162
C2×#191275982
C2×#191275912
C2×#191275892
C2×#396×C832
C2×#283783