Finite Group Databasebeta

← C2×#24915656 #35610652

Subgroups — C2×#24915656 #35610652

Order 21248.

1850 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24915656C2116yesmaximal, direct product factor
2C2×#19127643C211yesmaximal, characteristic, complemented
3C2×#19127642C211yesmaximal, characteristic, complemented
4C2×#19127637C211yesmaximal, characteristic
5C2×#19127635C211yesmaximal, characteristic, complemented
6C2×#19127633C211yesmaximal, characteristic, complemented
7C2×#19127632C211yesmaximal, characteristic, complemented
8C2×#19127631C211yesmaximal, characteristic, complemented
9C2×#19127629C211yesmaximal, characteristic
10C2×#19127629C211yesmaximal, characteristic
11C2×#19127626C211yesmaximal, characteristic
12C2×#19127624C211yesmaximal, characteristic
13C2×#19127624C211yesmaximal, characteristic
14C2×#19127599C211yesmaximal, characteristic, complemented
15C2×#19127585C211yesmaximal, characteristic, complemented
16C2×#388×C83C211yesmaximal, characteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×C4⋊Dic83C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×Dic83⋊C4C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2211yescharacteristic
29C22×C22⋊Dic83C2211yescharacteristic
30C22×C22⋊Dic83C2211yescharacteristic
31C22×C22⋊Dic83C2211yescharacteristic
32C22×C22⋊Dic83C2211yescharacteristic
33#19127643C2218yescomplemented
34#19127642C2218yescomplemented
35#19127637C2218yes—
36#19127635C2218yescomplemented
37#19127633C2218yescomplemented
38#19127632C2218yescomplemented
39#19127631C2218yescomplemented
40#19127629C2218yes—
41#19127629C2218yes—
42#19127626C2218yes—
43#19127624C2218yes—
44#19127624C2218yes—
45#19127599C2218yescomplemented
46#19127585C2218yescomplemented
47C2×C83⋊#95C2211yescharacteristic
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
59C22×C4⋊C4×C83C2211yescharacteristic
60C22×C22⋊C4×C83C2211yescharacteristic
61C22×C22⋊C4×C83C2211yescharacteristic
62C22×C22⋊C4×C83C2211yescharacteristic
63C22×C42×C83C2211yescharacteristic
64#388×C83C2218yes—
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C23×Dic83C2311yescharacteristic
68C23×Dic83C2311yescharacteristic
69C23×Dic83C2311yescharacteristic
70C23×Dic83C2311yescharacteristic
71C23×Dic83C2311yescharacteristic
72C23×Dic83C2311yescharacteristic
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C2×C4⋊Dic83—24no—
76C2×C4⋊Dic83—42no—
77C2×C4⋊Dic83—42no—
78C2×C4⋊Dic83—42no—
79C2×C4⋊Dic83C2314yes—
80C2×C4⋊Dic83C2314yes—
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⋊C4—42no—
90C2×Dic83⋊C4—42no—
91C2×Dic83⋊C4C2314yes—
92C2×Dic83⋊C4C2314yes—
93C2×Dic83⋊C4C2314yes—
94C2×Dic83⋊C4C2314yes—
95C2×Dic83⋊C4C2314yes—
96C2×Dic83⋊C4C2314yes—
97C2×Dic83⋊C4C2314yes—
98C2×Dic83⋊C4C2314yes—
99C2×C22⋊Dic83—42no—
100C2×C22⋊Dic83—42no—
101C2×C22⋊Dic83—42no—
102C2×C22⋊Dic83—42no—
103C2×C22⋊Dic83C2314yes—
104C2×C22⋊Dic83C2314yes—
105C2×C22⋊Dic83C2314yes—
106C2×C22⋊Dic83C2314yes—
107C83⋊#95C2314yes—
108C83⋊#95C2314yes—
109C83⋊#95C2314yes—
110C83⋊#95C2314yes—
111C83⋊#95C2314yes—
112C83⋊#95C2314yes—
113C83⋊#95C2314yes—
114C83⋊#95C2314yes—
115C83⋊#95C2314yes—
116C83⋊#95C2314yes—
117C83⋊#95C2314yes—
118C83⋊#95C2314yes—
119C25×C83C2311yescharacteristic
120C23×C4×C83C2311yescharacteristic
121C23×C4×C83C2311yescharacteristic
122C23×C4×C83C2311yescharacteristic
123C23×C4×C83C2311yescharacteristic
124C23×C4×C83C2311yescharacteristic
125C23×C4×C83C2311yescharacteristic
126C2×C4⋊C4×C83—42no—
127C2×C4⋊C4×C83C2314yes—
128C2×C22⋊C4×C83—24no—
129C2×C22⋊C4×C83—42no—
130C2×C22⋊C4×C83—42no—
131C2×C22⋊C4×C83C2314yes—
132C2×C22⋊C4×C83C2314yes—
133C2×C22⋊C4×C83C2314yes—
134C2×C42×C83—42no—
135C2×C42×C83C2314yes—
136#95×C83C2314yes—
137#95×C83C2314yes—
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×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×Dic83C2412yes—
163C22×Dic83C2412yes—
164C22×Dic83C2412yes—
165C22×Dic83C2412yes—
166C22×Dic83C2412yes—
167C22×Dic83C2412yes—
168C22×Dic83C2412yes—
169C22×Dic83C2412yes—
170C4⋊Dic83—28no—
171C4⋊Dic83—44no—
172C4⋊Dic83—44no—
173C4⋊Dic83—44no—
174Dic83⋊C4—28no—
175Dic83⋊C4—44no—
176Dic83⋊C4—44no—
177Dic83⋊C4—44no—
178Dic83⋊C4—44no—
179Dic83⋊C4—44no—
180Dic83⋊C4—44no—
181Dic83⋊C4—44no—
182C22⋊Dic83—44no—
183C22⋊Dic83—44no—
184C22⋊Dic83—44no—
185C22⋊Dic83—44no—
186C24×C83—22no—
187C24×C83—22no—
188C24×C83—22no—
189C24×C83—22no—
190C24×C83—22no—
191C24×C83—22no—
192C24×C83—22no—
193C24×C83C2412yes—
194C24×C83C2411yescharacteristic
195C22×C4×C83—22no—
196C22×C4×C83—22no—
197C22×C4×C83—22no—
198C22×C4×C83—22no—
199C22×C4×C83—22no—
200C22×C4×C83—22no—
201C22×C4×C83—22no—
202C22×C4×C83—22no—
203C22×C4×C83—22no—
204C22×C4×C83—22no—
205C22×C4×C83—22no—
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#4114yes—
213C22×C4×C83C2412yes—
214C22×C4×C83C2412yes—
215C22×C4×C83C2412yes—
216C22×C4×C83C2412yes—
217C22×C4×C83C2412yes—
218C22×C4×C83C2412yes—
219C4⋊C4×C83—44no—
220C22⋊C4×C83—28no—
221C22⋊C4×C83—44no—
222C22⋊C4×C83—44no—
223C42×C83—44no—
224C23×C83—22no—
225C23×C83—22no—
226C23×C83—22no—
227C23×C83—22no—
228C23×C83—22no—
229C23×C83—22no—
230C23×C83—22no—
231C23×C83—44no—
232C23×C83—44no—
233C23×C83—44no—
234C23×C83—44no—
235C23×C83—44no—
236C23×C83—44no—
237C23×C83—44no—
238C23×C83C2×#4112yes—
239C23×C83H(5,𝔽2)12yes—
240C23×C83H(5,𝔽2)12yes—
241C23×C83H(5,𝔽2)12yes—
242C23×C832−1+412yes—
243C23×C832−1+412yes—
244C23×C832−1+412yes—
245C23×C83C2511yescharacteristic
246C2×C4×C83—28no—
247C2×C4×C83—22no—
248C2×C4×C83—22no—
249C2×C4×C83—22no—
250C2×C4×C83—22no—
251C2×C4×C83—22no—
252C2×C4×C83—22no—
253C2×C4×C83—22no—
254C2×C4×C83—22no—
255C2×C4×C83—22no—
256C2×C4×C83—22no—
257C2×C4×C83—22no—
258C2×C4×C83—22no—
259C2×C4×C83—22no—
260C2×C4×C83—22no—
261C2×C4×C83—22no—
262C2×C4×C83—22no—
263C2×C4×C83—22no—
264C2×C4×C83—44no—
265C2×C4×C83—44no—
266C2×C4×C83—44no—
267C2×C4×C83—44no—
268C2×C4×C83—44no—
269C2×C4×C83C2×#4114yes—
270C2×Dic83—22no—
271C2×Dic83—22no—
272C2×Dic83—22no—
273C2×Dic83—22no—
274C2×Dic83—22no—
275C2×Dic83—22no—
276C2×Dic83—22no—
277C2×Dic83—22no—
278C2×Dic83—22no—
279C2×Dic83—22no—
280C2×Dic83—22no—
281C2×Dic83—22no—
282C2×Dic83—22no—
283C2×Dic83—22no—
284C2×Dic83—22no—
285C2×Dic83—22no—
286C2×Dic83—22no—
287C2×Dic83—22no—
288C2×Dic83—22no—
289C2×Dic83—22no—
290C2×Dic83—22no—
291C2×Dic83—22no—
292C2×Dic83—22no—
293C2×Dic83—22no—
294C2×Dic83—44no—
295C2×Dic83—44no—
296C2×Dic83—44no—
297C2×Dic83—44no—
298C2×Dic83—44no—
299C2×Dic83—44no—
300C2×Dic83—44no—
301C2×Dic83—44no—
302C22×C83—42no—
303C22×C83—42no—
304C22×C83—42no—
305C22×C83—42no—
306C22×C83—42no—
307C22×C83—42no—
308C22×C83—42no—
309C22×C83—88no—
310C22×C83#53914yes—
311C22×C83#54014yes—
312C22×C83#54114yes—
313C22×C83#56214yes—
314C22×C83#56214yes—
315C22×C83#56314yes—
316C22×C83#56314yes—
317C22×C83C22×#4111yescharacteristic
318C22×C83C2×H(5,𝔽2)11yescharacteristic
319C22×C83C2×H(5,𝔽2)11yescharacteristic
320C22×C83C2×H(5,𝔽2)11yescharacteristic
321C22×C83C2×2−1+411yescharacteristic
322C22×C83C2×2−1+411yescharacteristic
323C22×C83C2×2−1+411yescharacteristic
324C4×C83—24no—
325C4×C83—42no—
326C4×C83—42no—
327C4×C83—42no—
328C4×C83—42no—
329C4×C83—42no—
330Dic83—42no—
331Dic83—42no—
332Dic83—42no—
333Dic83—42no—
334Dic83—42no—
335Dic83—42no—
336Dic83—42no—
337Dic83—42no—
338C2×#2836—831nomaximal, Sylow
339C2×C83—82no—
340C2×C83#283618yescomplemented
341C2×C83C2×#53911yescharacteristic
342C2×C83C2×#54011yescharacteristic
343C2×C83C2×#54111yescharacteristic
344C2×C83C2×#56211yescharacteristic
345C2×C83C2×#56211yescharacteristic
346C2×C83C2×#56311yescharacteristic
347C2×C83C2×#56311yescharacteristic
348#2836—8316no—
349C2×#400—831no—
350C2×#400—831no—
351C2×#399—831no—
352C2×#398—831no—
353C2×#398—831no—
354C2×#398—831no—
355C2×#398—831no—
356C2×#397—831no—
357C2×#397—831no—
358C2×#397—831no—
359C2×#396—831no—
360C2×#396—831no—
361C2×#389—831no—
362C2×#388D8311yescharacteristic
363C2×#387—831no—
364C83C2×#283611yescharacteristic, complemented, Sylow
365C22×C4⋊C4—831no—
366C22×C4⋊C4—831no—
367C22×C4⋊C4—831no—
368C22×C4⋊C4—831no—
369C22×C4⋊C4—831no—
370C22×C4⋊C4—831no—
371C22×C4⋊C4—831no—
372C22×C4⋊C4—831no—
373C22×C4⋊C4—831no—
374C22×C4⋊C4—831no—
375C22×C4⋊C4—831no—
376C22×C4⋊C4—831no—
377C22×C4⋊C4C2×D8311yescharacteristic
378C22×C22⋊C4—831no—
379C22×C22⋊C4—831no—
380C22×C22⋊C4—831no—
381C22×C22⋊C4—831no—
382C22×C22⋊C4C2×D8311yescharacteristic
383C22×C22⋊C4C2×D8311yescharacteristic
384C22×C22⋊C4C2×D8311yescharacteristic
385C22×C42C2×D8311yescharacteristic
386#400—838no—
387#400—838no—
388#399—838no—
389#398—838no—
390#398—838no—
391#398—838no—
392#398—838no—
393#397—838no—
394#397—838no—
395#397—838no—
396#396—838no—
397#396—838no—
398#389—838no—
399#388C2×D8318yes—
400#387—838no—
401C2×#95—831no—
402C2×#95—831no—
403C2×#95—831no—
404C2×#95—831no—
405C2×#95—831no—
406C2×#95—831no—
407C2×#95—831no—
408C2×#95—831no—
409C2×#95—831no—
410C2×#95—831no—
411C2×#95—831no—
412C2×#95—831no—
413C2×#95C2×D8311yescharacteristic
414C2×#95C2×D8311yescharacteristic
415C25C22×D8311yescharacteristic
416C23×C4—831no—
417C23×C4—831no—
418C23×C4—831no—
419C23×C4—831no—
420C23×C4—831no—
421C23×C4—831no—
422C23×C4—831no—
423C23×C4—831no—
424C23×C4C22×D8311yescharacteristic
425C23×C4C22×D8311yescharacteristic
426C23×C4C22×D8311yescharacteristic
427C23×C4C22×D8311yescharacteristic
428C23×C4C22×D8311yescharacteristic
429C23×C4C22×D8311yescharacteristic
430C2×C4⋊C4—42no—
431C2×C4⋊C4—3322no—
432C2×C4⋊C4—3322no—
433C2×C4⋊C4—3322no—
434C2×C4⋊C4—3322no—
435C2×C4⋊C4—3322no—
436C2×C4⋊C4—3322no—
437C2×C4⋊C4—3322no—
438C2×C4⋊C4—3322no—
439C2×C4⋊C4—3322no—
440C2×C4⋊C4—3322no—
441C2×C4⋊C4—834no—
442C2×C4⋊C4—834no—
443C2×C4⋊C4—834no—
444C2×C4⋊C4—834no—
445C2×C4⋊C4—834no—
446C2×C4⋊C4—834no—
447C2×C4⋊C4—834no—
448C2×C4⋊C4—834no—
449C2×C4⋊C4—834no—
450C2×C4⋊C4—834no—
451C2×C4⋊C4—834no—
452C2×C4⋊C4—834no—
453C2×C4⋊C4—1664no—
454C2×C4⋊C4—1664no—
455C2×C4⋊C4C22×D8314yes—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—42no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—3322no—
460C2×C22⋊C4—3322no—
461C2×C22⋊C4—3322no—
462C2×C22⋊C4—3322no—
463C2×C22⋊C4—834no—
464C2×C22⋊C4—834no—
465C2×C22⋊C4—834no—
466C2×C22⋊C4—834no—
467C2×C22⋊C4C22×D8314yes—
468C2×C22⋊C4C22×D8314yes—
469C2×C22⋊C4C22×D8314yes—
470C2×C42—42no—
471C2×C42C22×D8314yes—
472#95—834no—
473#95—834no—
474#95—834no—
475#95—834no—
476#95—834no—
477#95—834no—
478#95—834no—
479#95—834no—
480#95—834no—
481#95—834no—
482#95—834no—
483#95—834no—
484#95C22×D8314yes—
485#95C22×D8314yes—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24C23×D8312yes—
494C24C23×D8311yescharacteristic
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—832no—
513C22×C4—832no—
514C22×C4—832no—
515C22×C4—832no—
516C22×C4—832no—
517C22×C4—832no—
518C22×C4—832no—
519C22×C4—832no—
520C22×C4—1662no—
521C22×C4—1662no—
522C22×C4—1662no—
523C22×C4—1662no—
524C22×C4—1662no—
525C22×C4—1662no—
526C22×C4—1662no—
527C22×C4—1662no—
528C22×C4—1662no—
529C22×C4—1662no—
530C22×C4—1662no—
531C22×C4—1662no—
532C22×C4—1662no—
533C22×C4—1662no—
534C22×C4—1662no—
535C22×C4—1662no—
536C22×C4—1662no—
537C22×C4—1662no—
538C22×C4—1662no—
539C22×C4—1662no—
540C22×C4—1662no—
541C22×C4—1662no—
542C22×C4—1662no—
543C22×C4—1662no—
544C22×C4#1305059014yes—
545C22×C4C23×D8312yes—
546C22×C4C23×D8312yes—
547C22×C4C23×D8312yes—
548C22×C4C23×D8312yes—
549C22×C4C23×D8312yes—
550C22×C4C23×D8312yes—
551C4⋊C4—44no—
552C4⋊C4—3324no—
553C4⋊C4—3324no—
554C4⋊C4—3324no—
555C4⋊C4—3324no—
556C4⋊C4—3324no—
557C4⋊C4—3324no—
558C4⋊C4—3324no—
559C4⋊C4—3324no—
560C4⋊C4—3324no—
561C4⋊C4—3324no—
562C4⋊C4—1668no—
563C4⋊C4—1668no—
564C22⋊C4—28no—
565C22⋊C4—44no—
566C22⋊C4—44no—
567C22⋊C4—3324no—
568C22⋊C4—3324no—
569C22⋊C4—3324no—
570C22⋊C4—3324no—
571C42—44no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—44no—
580C23—44no—
581C23—44no—
582C23—44no—
583C23—44no—
584C23—44no—
585C23—44no—
586C23C2×#1305059012yes—
587C23#1458183712yes—
588C23#1458183712yes—
589C23#1458183812yes—
590C23#1458183912yes—
591C23#1458183912yes—
592C23#1458183912yes—
593C23C24×D8311yescharacteristic
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—28no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—44no—
613C2×C4—44no—
614C2×C4—44no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—3324no—
618C2×C4—3324no—
619C2×C4—3324no—
620C2×C4—3324no—
621C2×C4—3324no—
622C2×C4—3324no—
623C2×C4—3324no—
624C2×C4—3324no—
625C2×C4—1662no—
626C2×C4—1662no—
627C2×C4—1662no—
628C2×C4—1662no—
629C2×C4—1662no—
630C2×C4—1662no—
631C2×C4—1662no—
632C2×C4—1662no—
633C2×C4—1662no—
634C2×C4—1662no—
635C2×C4—1662no—
636C2×C4—1662no—
637C2×C4—1662no—
638C2×C4—1662no—
639C2×C4—1662no—
640C2×C4—1662no—
641C2×C4—1662no—
642C2×C4—1662no—
643C2×C4—1662no—
644C2×C4—1662no—
645C2×C4—1662no—
646C2×C4—1662no—
647C2×C4—1662no—
648C2×C4—1662no—
649C2×C4C2×#1305059014yes—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—88no—
658C22#1912829314yes—
659C22#1912830214yes—
660C22#1912831314yes—
661C22#1912844614yes—
662C22#1912844814yes—
663C22#1912845114yes—
664C22#1912845314yes—
665C22C22×#1305059011yescharacteristic
666C22C2×#1458183711yescharacteristic
667C22C2×#1458183711yescharacteristic
668C22C2×#1458183811yescharacteristic
669C22C2×#1458183911yescharacteristic
670C22C2×#1458183911yescharacteristic
671C22C2×#1458183911yescharacteristic
672C4—24no—
673C4—42no—
674C4—42no—
675C4—42no—
676C4—42no—
677C4—42no—
678C4—3322no—
679C4—3322no—
680C4—3322no—
681C4—3322no—
682C4—3322no—
683C4—3322no—
684C4—3322no—
685C4—3322no—
686C2—82no—
687C2#2491565618yesdirect product factor
688C2C2×#1912829311yescharacteristic
689C2C2×#1912830211yescharacteristic
690C2C2×#1912831311yescharacteristic
691C2C2×#1912844611yescharacteristic
692C2C2×#1912844811yescharacteristic
693C2C2×#1912845111yescharacteristic
694C2C2×#1912845311yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#388×C83C2
socleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#388D83
hypocenterC83C2×#2836
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. #24915656C2direct (N × H)
2. C2×#19127643C2semidirect
3. C2×#19127642C2semidirect
5. C2×#19127635C2semidirect
6. C2×#19127633C2semidirect
7. C2×#19127632C2semidirect
8. C2×#19127631C2semidirect
14. C2×#19127599C2semidirect
15. C2×#19127585C2semidirect
33. #19127643C22semidirect
34. #19127642C22semidirect
36. #19127635C22semidirect
37. #19127633C22semidirect
38. #19127632C22semidirect
39. #19127631C22semidirect
45. #19127599C22semidirect
46. #19127585C22semidirect
340. C2×C83#2836semidirect
364. C83C2×#2836semidirect
687. C2#24915656direct (N × H)

Maximal subgroups

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

subgroupindex
#249156562
C2×#191276432
C2×#191276422
C2×#191276372
C2×#191276352
C2×#191276332
C2×#191276322
C2×#191276312
C2×#191276292
C2×#191276262
C2×#191276242
C2×#191275992
C2×#191275852
C2×#388×C832
C2×#283683