Finite Group Databasebeta

← C2×#24915713 #35610690

Subgroups — C2×#24915713 #35610690

Order 21248.

1654 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24915713C2116yesmaximal, direct product factor
2C2×#19127643C211yesmaximal, characteristic
3C2×#19127643C211yesmaximal, characteristic
4C2×#19127641C211yesmaximal, characteristic
5C2×#19127640C211yesmaximal, characteristic
6C2×#19127640C211yesmaximal, characteristic
7C2×#19127639C211yesmaximal, characteristic
8C2×#19127639C211yesmaximal, characteristic
9C2×#19127634C211yesmaximal, characteristic
10C2×#19127634C211yesmaximal, characteristic
11C2×#19127633C211yesmaximal, characteristic
12C2×#19127631C211yesmaximal, characteristic
13C2×#19127597C211yesmaximal, characteristic
14C2×#19127583C211yesmaximal, characteristic
15C2×#19127583C211yesmaximal, characteristic
16C2×#398×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×C4×Dic83C2211yescharacteristic
28#19127643C2218yes—
29#19127643C2218yes—
30#19127641C2218yes—
31#19127640C2218yes—
32#19127640C2218yes—
33#19127639C2218yes—
34#19127639C2218yes—
35#19127634C2218yes—
36#19127634C2218yes—
37#19127633C2218yes—
38#19127631C2218yes—
39#19127597C2218yes—
40#19127583C2218yes—
41#19127583C2218yes—
42C2×C83⋊#95C2211yescharacteristic
43C2×C83⋊#95C2211yescharacteristic
44C2×C83⋊#95C2211yescharacteristic
45C2×C83⋊#95C2211yescharacteristic
46C2×C83⋊#95C2211yescharacteristic
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×C4⋊C4×C83C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63#398×C83C2218yes—
64C2×#95×C83C2211yescharacteristic
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—24no—
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×C4×Dic83—42no—
96C2×C4×Dic83C2314yes—
97C83⋊#95C2314yes—
98C83⋊#95C2314yes—
99C83⋊#95C2314yes—
100C83⋊#95C2314yes—
101C83⋊#95C2314yes—
102C83⋊#95C2314yes—
103C83⋊#95C2314yes—
104C83⋊#95C2314yes—
105C83⋊#95C2314yes—
106C83⋊#95C2314yes—
107C83⋊#95C2314yes—
108C83⋊#95C2314yes—
109C83⋊#95C2314yes—
110C83⋊#95C2314yes—
111C83⋊#95C2314yes—
112C83⋊#95C2314yes—
113C83⋊#95C2314yes—
114C23×C4×C83C2311yescharacteristic
115C23×C4×C83C2311yescharacteristic
116C23×C4×C83C2311yescharacteristic
117C23×C4×C83C2311yescharacteristic
118C23×C4×C83C2311yescharacteristic
119C23×C4×C83C2311yescharacteristic
120C23×C4×C83C2311yescharacteristic
121C2×C4⋊C4×C83—42no—
122C2×C4⋊C4×C83—42no—
123C2×C4⋊C4×C83—42no—
124C2×C4⋊C4×C83—42no—
125C2×C4⋊C4×C83C2314yes—
126C2×C4⋊C4×C83C2314yes—
127C2×C4⋊C4×C83C2314yes—
128C2×C4⋊C4×C83C2314yes—
129#95×C83C2314yes—
130#95×C83C2314yes—
131#95×C83C2314yes—
132C22×Dic83—22no—
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×Dic83—22no—
153C22×Dic83—22no—
154C22×Dic83—22no—
155C22×Dic83—22no—
156C22×Dic83C2412yes—
157C22×Dic83C2412yes—
158C22×Dic83C2412yes—
159C22×Dic83C2412yes—
160C22×Dic83C2412yes—
161C22×Dic83C2412yes—
162C22×Dic83C2412yes—
163C22×Dic83C2412yes—
164C4⋊Dic83—28no—
165C4⋊Dic83—44no—
166C4⋊Dic83—44no—
167C4⋊Dic83—44no—
168Dic83⋊C4—28no—
169Dic83⋊C4—28no—
170Dic83⋊C4—44no—
171Dic83⋊C4—44no—
172Dic83⋊C4—44no—
173Dic83⋊C4—44no—
174C4×Dic83—44no—
175C24×C83C2411yescharacteristic
176C22×C4×C83—22no—
177C22×C4×C83—22no—
178C22×C4×C83—22no—
179C22×C4×C83—22no—
180C22×C4×C83—22no—
181C22×C4×C83—22no—
182C22×C4×C83—22no—
183C22×C4×C83—22no—
184C22×C4×C83—22no—
185C22×C4×C83—22no—
186C22×C4×C83—22no—
187C22×C4×C83—22no—
188C22×C4×C83—22no—
189C22×C4×C83—22no—
190C22×C4×C83—22no—
191C22×C4×C83—22no—
192C22×C4×C83—22no—
193C22×C4×C83—22no—
194C22×C4×C83—22no—
195C22×C4×C83—22no—
196C22×C4×C83#4114yes—
197C22×C4×C83C2412yes—
198C22×C4×C83C2412yes—
199C22×C4×C83C2412yes—
200C22×C4×C83C2412yes—
201C22×C4×C83C2412yes—
202C22×C4×C83C2412yes—
203C22×C4×C83C2412yes—
204C4⋊C4×C83—44no—
205C4⋊C4×C83—44no—
206C4⋊C4×C83—44no—
207C4⋊C4×C83—44no—
208C23×C83C2×#4112yes—
209C23×C83H(5,𝔽2)12yes—
210C23×C83H(5,𝔽2)12yes—
211C23×C832−1+412yes—
212C23×C832−1+412yes—
213C23×C832−1+412yes—
214C23×C832−1+412yes—
215C23×C83C2511yescharacteristic
216C2×C4×C83—28no—
217C2×C4×C83—22no—
218C2×C4×C83—22no—
219C2×C4×C83—22no—
220C2×C4×C83—22no—
221C2×C4×C83—22no—
222C2×C4×C83—22no—
223C2×C4×C83—22no—
224C2×C4×C83—22no—
225C2×C4×C83—22no—
226C2×C4×C83—22no—
227C2×C4×C83—22no—
228C2×C4×C83—22no—
229C2×C4×C83—22no—
230C2×C4×C83—22no—
231C2×C4×C83—22no—
232C2×C4×C83—22no—
233C2×C4×C83—22no—
234C2×C4×C83—22no—
235C2×C4×C83—22no—
236C2×C4×C83—22no—
237C2×C4×C83—44no—
238C2×C4×C83—44no—
239C2×C4×C83—44no—
240C2×C4×C83—44no—
241C2×C4×C83—44no—
242C2×C4×C83—44no—
243C2×C4×C83C2×#4114yes—
244C2×Dic83—22no—
245C2×Dic83—22no—
246C2×Dic83—22no—
247C2×Dic83—22no—
248C2×Dic83—22no—
249C2×Dic83—22no—
250C2×Dic83—22no—
251C2×Dic83—22no—
252C2×Dic83—22no—
253C2×Dic83—22no—
254C2×Dic83—22no—
255C2×Dic83—22no—
256C2×Dic83—22no—
257C2×Dic83—22no—
258C2×Dic83—22no—
259C2×Dic83—22no—
260C2×Dic83—22no—
261C2×Dic83—22no—
262C2×Dic83—22no—
263C2×Dic83—22no—
264C2×Dic83—22no—
265C2×Dic83—22no—
266C2×Dic83—22no—
267C2×Dic83—22no—
268C2×Dic83—44no—
269C2×Dic83—44no—
270C2×Dic83—44no—
271C2×Dic83—44no—
272C2×Dic83—44no—
273C2×Dic83—44no—
274C2×Dic83—44no—
275C2×Dic83—44no—
276C22×C83#53914yes—
277C22×C83#54114yes—
278C22×C83#54214yes—
279C22×C83#56214yes—
280C22×C83#56314yes—
281C22×C83#56314yes—
282C22×C83#56414yes—
283C22×C83C22×#4111yescharacteristic
284C22×C83C2×H(5,𝔽2)11yescharacteristic
285C22×C83C2×H(5,𝔽2)11yescharacteristic
286C22×C83C2×2−1+411yescharacteristic
287C22×C83C2×2−1+411yescharacteristic
288C22×C83C2×2−1+411yescharacteristic
289C22×C83C2×2−1+411yescharacteristic
290C4×C83—24no—
291C4×C83—42no—
292C4×C83—42no—
293C4×C83—42no—
294C4×C83—42no—
295C4×C83—42no—
296C4×C83—42no—
297Dic83—42no—
298Dic83—42no—
299Dic83—42no—
300Dic83—42no—
301Dic83—42no—
302Dic83—42no—
303Dic83—42no—
304Dic83—42no—
305C2×#2839—831nomaximal, Sylow
306C2×C83#283918yescomplemented
307C2×C83C2×#53911yescharacteristic
308C2×C83C2×#54111yescharacteristic
309C2×C83C2×#54211yescharacteristic
310C2×C83C2×#56211yescharacteristic
311C2×C83C2×#56311yescharacteristic
312C2×C83C2×#56311yescharacteristic
313C2×C83C2×#56411yescharacteristic
314#2839—8316no—
315C2×#400—831no—
316C2×#400—831no—
317C2×#400—831no—
318C2×#400—831no—
319C2×#400—831no—
320C2×#400—831no—
321C2×#400—831no—
322C2×#398—831no—
323C2×#398—831no—
324C2×#398—831no—
325C2×#398—831no—
326C2×#398D8311yescharacteristic
327C2×#389—831no—
328C2×#387—831no—
329C2×#387—831no—
330C83C2×#283911yescharacteristic, complemented, Sylow
331C22×C4⋊C4—831no—
332C22×C4⋊C4—831no—
333C22×C4⋊C4—831no—
334C22×C4⋊C4—831no—
335C22×C4⋊C4—831no—
336C22×C4⋊C4—831no—
337C22×C4⋊C4—831no—
338C22×C4⋊C4—831no—
339C22×C4⋊C4—831no—
340C22×C4⋊C4—831no—
341C22×C4⋊C4C2×D8311yescharacteristic
342C22×C4⋊C4C2×D8311yescharacteristic
343C22×C4⋊C4C2×D8311yescharacteristic
344C22×C4⋊C4C2×D8311yescharacteristic
345C22×C42—831no—
346#400—838no—
347#400—838no—
348#400—838no—
349#400—838no—
350#400—838no—
351#400—838no—
352#400—838no—
353#398—838no—
354#398—838no—
355#398—838no—
356#398—838no—
357#398C2×D8318yes—
358#389—838no—
359#387—838no—
360#387—838no—
361C2×#95—831no—
362C2×#95—831no—
363C2×#95—831no—
364C2×#95—831no—
365C2×#95—831no—
366C2×#95—831no—
367C2×#95—831no—
368C2×#95—831no—
369C2×#95—831no—
370C2×#95—831no—
371C2×#95—831no—
372C2×#95—831no—
373C2×#95—831no—
374C2×#95—831no—
375C2×#95—831no—
376C2×#95—831no—
377C2×#95—831no—
378C2×#95C2×D8311yescharacteristic
379C2×#95C2×D8311yescharacteristic
380C2×#95C2×D8311yescharacteristic
381C23×C4—831no—
382C23×C4—831no—
383C23×C4—831no—
384C23×C4—831no—
385C23×C4—831no—
386C23×C4—831no—
387C23×C4—831no—
388C23×C4—831no—
389C23×C4C22×D8311yescharacteristic
390C23×C4C22×D8311yescharacteristic
391C23×C4C22×D8311yescharacteristic
392C23×C4C22×D8311yescharacteristic
393C23×C4C22×D8311yescharacteristic
394C23×C4C22×D8311yescharacteristic
395C23×C4C22×D8311yescharacteristic
396C2×C4⋊C4—42no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—42no—
400C2×C4⋊C4—3322no—
401C2×C4⋊C4—3322no—
402C2×C4⋊C4—3322no—
403C2×C4⋊C4—3322no—
404C2×C4⋊C4—3322no—
405C2×C4⋊C4—3322no—
406C2×C4⋊C4—3322no—
407C2×C4⋊C4—834no—
408C2×C4⋊C4—834no—
409C2×C4⋊C4—834no—
410C2×C4⋊C4—834no—
411C2×C4⋊C4—834no—
412C2×C4⋊C4—834no—
413C2×C4⋊C4—834no—
414C2×C4⋊C4—834no—
415C2×C4⋊C4—834no—
416C2×C4⋊C4—834no—
417C2×C4⋊C4—1664no—
418C2×C4⋊C4—1664no—
419C2×C4⋊C4—1664no—
420C2×C4⋊C4C22×D8314yes—
421C2×C4⋊C4C22×D8314yes—
422C2×C4⋊C4C22×D8314yes—
423C2×C4⋊C4C22×D8314yes—
424C2×C42—3322no—
425C2×C42—834no—
426#95—834no—
427#95—834no—
428#95—834no—
429#95—834no—
430#95—834no—
431#95—834no—
432#95—834no—
433#95—834no—
434#95—834no—
435#95—834no—
436#95—834no—
437#95—834no—
438#95—834no—
439#95—834no—
440#95—834no—
441#95—834no—
442#95—834no—
443#95C22×D8314yes—
444#95C22×D8314yes—
445#95C22×D8314yes—
446C24C23×D8311yescharacteristic
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—832no—
468C22×C4—832no—
469C22×C4—832no—
470C22×C4—832no—
471C22×C4—832no—
472C22×C4—832no—
473C22×C4—832no—
474C22×C4—832no—
475C22×C4—1662no—
476C22×C4—1662no—
477C22×C4—1662no—
478C22×C4—1662no—
479C22×C4—1662no—
480C22×C4—1662no—
481C22×C4—1662no—
482C22×C4—1662no—
483C22×C4—1662no—
484C22×C4—1662no—
485C22×C4—1662no—
486C22×C4—1662no—
487C22×C4—1662no—
488C22×C4—1662no—
489C22×C4—1662no—
490C22×C4—1662no—
491C22×C4—1662no—
492C22×C4—1662no—
493C22×C4—1662no—
494C22×C4—1662no—
495C22×C4—1662no—
496C22×C4—1662no—
497C22×C4—1662no—
498C22×C4—1662no—
499C22×C4#1305059114yes—
500C22×C4C23×D8312yes—
501C22×C4C23×D8312yes—
502C22×C4C23×D8312yes—
503C22×C4C23×D8312yes—
504C22×C4C23×D8312yes—
505C22×C4C23×D8312yes—
506C22×C4C23×D8312yes—
507C4⋊C4—44no—
508C4⋊C4—44no—
509C4⋊C4—44no—
510C4⋊C4—44no—
511C4⋊C4—3324no—
512C4⋊C4—3324no—
513C4⋊C4—3324no—
514C4⋊C4—3324no—
515C4⋊C4—3324no—
516C4⋊C4—3324no—
517C4⋊C4—3324no—
518C4⋊C4—1668no—
519C4⋊C4—1668no—
520C4⋊C4—1668no—
521C42—3324no—
522C23C2×#1305059112yes—
523C23#1458183712yes—
524C23#1458183712yes—
525C23#1458183912yes—
526C23#1458183912yes—
527C23#1458183912yes—
528C23#1458184012yes—
529C23C24×D8311yescharacteristic
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—28no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—3324no—
558C2×C4—3324no—
559C2×C4—3324no—
560C2×C4—3324no—
561C2×C4—3324no—
562C2×C4—3324no—
563C2×C4—3324no—
564C2×C4—3324no—
565C2×C4—1662no—
566C2×C4—1662no—
567C2×C4—1662no—
568C2×C4—1662no—
569C2×C4—1662no—
570C2×C4—1662no—
571C2×C4—1662no—
572C2×C4—1662no—
573C2×C4—1662no—
574C2×C4—1662no—
575C2×C4—1662no—
576C2×C4—1662no—
577C2×C4—1662no—
578C2×C4—1662no—
579C2×C4—1662no—
580C2×C4—1662no—
581C2×C4—1662no—
582C2×C4—1662no—
583C2×C4—1662no—
584C2×C4—1662no—
585C2×C4—1662no—
586C2×C4—1662no—
587C2×C4—1662no—
588C2×C4—1662no—
589C2×C4C2×#1305059114yes—
590C22#1912830014yes—
591C22#1912831414yes—
592C22#1912832514yes—
593C22#1912844614yes—
594C22#1912845214yes—
595C22#1912845414yes—
596C22C83⋊#56414yes—
597C22C22×#1305059111yescharacteristic
598C22C2×#1458183711yescharacteristic
599C22C2×#1458183711yescharacteristic
600C22C2×#1458183911yescharacteristic
601C22C2×#1458183911yescharacteristic
602C22C2×#1458183911yescharacteristic
603C22C2×#1458184011yescharacteristic
604C4—24no—
605C4—42no—
606C4—42no—
607C4—42no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—3322no—
612C4—3322no—
613C4—3322no—
614C4—3322no—
615C4—3322no—
616C4—3322no—
617C4—3322no—
618C4—3322no—
619C2#2491571318yesdirect product factor
620C2C2×#1912830011yescharacteristic
621C2C2×#1912831411yescharacteristic
622C2C2×#1912832511yescharacteristic
623C2C2×#1912844611yescharacteristic
624C2C2×#1912845211yescharacteristic
625C2C2×#1912845411yescharacteristic
626C2C2×C83⋊#56411yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#398×C83C2
socle, prime radicalC24×C83C24
hypercenterC2×#398D83
hypocenterC83C2×#2839
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. #24915713C2direct (N × H)
306. C2×C83#2839semidirect
330. C83C2×#2839semidirect
619. C2#24915713direct (N × H)

Maximal subgroups

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

subgroupindex
#249157132
C2×#191276432
C2×#191276412
C2×#191276402
C2×#191276392
C2×#191276342
C2×#191276332
C2×#191276312
C2×#191275972
C2×#191275832
C2×#398×C832
C2×#283983