Finite Group Databasebeta

← C2×#24913343 #35571333

Subgroups — C2×#24913343 #35571333

Order 21248.

2286 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581782C211yesmaximal, characteristic
2C22×C4×Dic166C211yesmaximal, characteristic
3#24913343C2116yesmaximal, direct product factor
4C2×#19127643C211yesmaximal, characteristic
5C2×#19127643C211yesmaximal, characteristic
6C2×#19127642C211yesmaximal, characteristic
7C2×#19127642C211yesmaximal, characteristic
8C2×#19127635C211yesmaximal, characteristic
9C2×#19127634C211yesmaximal, characteristic
10C2×#19127622C211yesmaximal, characteristic
11C2×#19127621C211yesmaximal, characteristic
12C2×#19127586C211yesmaximal, characteristic
13C2×#19127585C211yesmaximal, characteristic
14C2×#19127582C211yesmaximal, characteristic
15C2×#19127568C211yesmaximal, characteristic
16C2×#387×C83C211yesmaximal, characteristic
17C23×Dic166C2211yescharacteristic
18C2×#14581782—28no—
19C2×#14581782C2218yes—
20C2×C4×Dic166—28no—
21C2×C4×Dic166C2218yes—
22C22×C4⋊Dic83C2211yescharacteristic
23C22×C4⋊Dic83C2211yescharacteristic
24C22×C4⋊Dic83C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2211yescharacteristic
29C22×Dic83⋊C4C2211yescharacteristic
30C22×Dic83⋊C4C2211yescharacteristic
31C22×Dic83⋊C4C2211yescharacteristic
32C22×Dic83⋊C4C2211yescharacteristic
33C22×C4×Dic83C2211yescharacteristic
34C22×C4×Dic83C2211yescharacteristic
35#19127643C2218yes—
36#19127643C2218yes—
37#19127642C2218yes—
38#19127642C2218yes—
39#19127635C2218yes—
40#19127634C2218yes—
41#19127622C2218yes—
42#19127621C2218yes—
43#19127586C2218yes—
44#19127585C2218yes—
45#19127582C2218yes—
46#19127568C2218yes—
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
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63C22×C42×C83C2211yescharacteristic
64#387×C83C2218yes—
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2211yescharacteristic
69C22×Dic166—24no—
70C22×Dic166—24no—
71C22×Dic166—24no—
72C22×Dic166C2314yes—
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81#14581782—232no—
82C4×Dic166—232no—
83C2×C4⋊Dic83—24no—
84C2×C4⋊Dic83—24no—
85C2×C4⋊Dic83—24no—
86C2×C4⋊Dic83C2314yes—
87C2×C4⋊Dic83C2314yes—
88C2×C4⋊Dic83C2314yes—
89C2×Dic83⋊C4—24no—
90C2×Dic83⋊C4—24no—
91C2×Dic83⋊C4—24no—
92C2×Dic83⋊C4—24no—
93C2×Dic83⋊C4—24no—
94C2×Dic83⋊C4—24no—
95C2×Dic83⋊C4—24no—
96C2×Dic83⋊C4—24no—
97C2×Dic83⋊C4C2314yes—
98C2×Dic83⋊C4C2314yes—
99C2×Dic83⋊C4C2314yes—
100C2×Dic83⋊C4C2314yes—
101C2×Dic83⋊C4C2314yes—
102C2×Dic83⋊C4C2314yes—
103C2×Dic83⋊C4C2314yes—
104C2×Dic83⋊C4C2314yes—
105C2×C4×Dic83—24no—
106C2×C4×Dic83D418yes—
107C2×C4×Dic83C2314yes—
108C2×C4×Dic83C2314yes—
109C83⋊#95C2314yes—
110C83⋊#95C2314yes—
111C83⋊#95C2314yes—
112C83⋊#95C2314yes—
113C83⋊#95C2314yes—
114C83⋊#95C2314yes—
115C83⋊#95C2314yes—
116C83⋊#95C2314yes—
117C83⋊#95C2314yes—
118C83⋊#95C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C23×C4×C83C2311yescharacteristic
124C23×C4×C83C2311yescharacteristic
125C23×C4×C83C2311yescharacteristic
126C23×C4×C83C2311yescharacteristic
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C2×C4⋊C4×C83—24no—
131C2×C4⋊C4×C83—24no—
132C2×C4⋊C4×C83C2314yes—
133C2×C4⋊C4×C83C2314yes—
134C2×C42×C83—24no—
135C2×C42×C83C2314yes—
136#95×C83C2314yes—
137#95×C83C2314yes—
138#95×C83C2314yes—
139#95×C83C2314yes—
140C2×Dic166—232no—
141C2×Dic166—28no—
142C2×Dic166—28no—
143C2×Dic166—28no—
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×Dic83C2×D414yes—
166C22×Dic83C2×D414yes—
167C22×Dic83#4114yes—
168C22×Dic83C2412yes—
169C22×Dic83C2412yes—
170C22×Dic83C2412yes—
171C22×Dic83C2412yes—
172C22×Dic83C2412yes—
173C22×Dic83C2412yes—
174C22×Dic83C2412yes—
175C22×Dic83C2412yes—
176C4⋊Dic83—28no—
177C4⋊Dic83—28no—
178C4⋊Dic83—28no—
179Dic83⋊C4—28no—
180Dic83⋊C4—28no—
181Dic83⋊C4—28no—
182Dic83⋊C4—28no—
183Dic83⋊C4—28no—
184Dic83⋊C4—28no—
185Dic83⋊C4—28no—
186Dic83⋊C4—28no—
187C4×Dic83—28no—
188C4×Dic83C2×D4116yes—
189C24×C83C2411yescharacteristic
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—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×C83C2×D414yes—
210C22×C4×C83#4114yes—
211C22×C4×C83C2412yes—
212C22×C4×C83C2412yes—
213C22×C4×C83C2412yes—
214C22×C4×C83C2412yes—
215C22×C4×C83C2412yes—
216C22×C4×C83C2412yes—
217C22×C4×C83C2412yes—
218C4⋊C4×C83—28no—
219C4⋊C4×C83—28no—
220C42×C83—28no—
221C23×C83C22×D412yes—
222C23×C83C2×#4112yes—
223C23×C83C2×#4112yes—
224C23×C832−1+412yes—
225C23×C832−1+412yes—
226C23×C832−1+412yes—
227C23×C832−1+412yes—
228C23×C83C2511yescharacteristic
229C2×C4×C83—28no—
230C2×C4×C83—28no—
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—22no—
238C2×C4×C83—22no—
239C2×C4×C83—22no—
240C2×C4×C83—22no—
241C2×C4×C83—22no—
242C2×C4×C83—22no—
243C2×C4×C83—22no—
244C2×C4×C83—22no—
245C2×C4×C83—22no—
246C2×C4×C83—22no—
247C2×C4×C83—22no—
248C2×C4×C83—22no—
249C2×C4×C83—22no—
250C2×C4×C83—44no—
251C2×C4×C83—44no—
252C2×C4×C83—44no—
253C2×C4×C83—44no—
254C2×C4×C83—44no—
255C2×C4×C83C22×D414yes—
256C2×C4×C83C2×#4114yes—
257C2×Dic83—28no—
258C2×Dic83—28no—
259C2×Dic83—28no—
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—22no—
269C2×Dic83—22no—
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—44no—
282C2×Dic83—44no—
283C2×Dic83—44no—
284C2×Dic83—44no—
285C2×Dic83—44no—
286C2×Dic83C22×D414yes—
287C2×Dic83C22×D414yes—
288C2×Dic83C2×#4114yes—
289Dic166—232no—
290C22×C83#52514yes—
291C22×C83#53614yes—
292C22×C83#53614yes—
293C22×C83#54114yes—
294C22×C83#54114yes—
295C22×C83#54114yes—
296C22×C83#54114yes—
297C22×C83C23×D411yescharacteristic
298C22×C83C22×#4111yescharacteristic
299C22×C83C22×#4111yescharacteristic
300C22×C83C2×2−1+411yescharacteristic
301C22×C83C2×2−1+411yescharacteristic
302C22×C83C2×2−1+411yescharacteristic
303C22×C83C2×2−1+411yescharacteristic
304C4×C83—24no—
305C4×C83—24no—
306C4×C83—42no—
307C4×C83—42no—
308C4×C83—42no—
309C4×C83—42no—
310C4×C83—42no—
311Dic83—24no—
312Dic83—24no—
313Dic83—24no—
314Dic83—42no—
315Dic83—42no—
316Dic83—42no—
317Dic83—42no—
318Dic83—42no—
319C2×#2634—831nomaximal, Sylow
320C2×C83#263418yescomplemented
321C2×C83C2×#52511yescharacteristic
322C2×C83C2×#53611yescharacteristic
323C2×C83C2×#53611yescharacteristic
324C2×C83C2×#54111yescharacteristic
325C2×C83C2×#54111yescharacteristic
326C2×C83C2×#54111yescharacteristic
327C2×C83C2×#54111yescharacteristic
328C22×#125—831no—
329C22×C4×Q8—831no—
330#2634—8316no—
331C2×#400—831no—
332C2×#400—831no—
333C2×#400—831no—
334C2×#400—831no—
335C2×#398—831no—
336C2×#398—831no—
337C2×#395—831no—
338C2×#395—831no—
339C2×#387—831no—
340C2×#387—831no—
341C2×#387—831no—
342C2×#387D8311yescharacteristic
343C2×#383—831no—
344C83C2×#263411yescharacteristic, complemented, Sylow
345C23×Q8—831no—
346C2×#125—838no—
347C2×#125—1668no—
348C2×C4×Q8—838no—
349C2×C4×Q8—1668no—
350C22×C4⋊C4—831no—
351C22×C4⋊C4—831no—
352C22×C4⋊C4—831no—
353C22×C4⋊C4—831no—
354C22×C4⋊C4—831no—
355C22×C4⋊C4—831no—
356C22×C4⋊C4—831no—
357C22×C4⋊C4—831no—
358C22×C4⋊C4—831no—
359C22×C4⋊C4—831no—
360C22×C4⋊C4—831no—
361C22×C4⋊C4C2×D8311yescharacteristic
362C22×C4⋊C4C2×D8311yescharacteristic
363C22×C42—831no—
364C22×C42—831no—
365C22×C42C2×D8311yescharacteristic
366#400—838no—
367#400—838no—
368#400—838no—
369#400—838no—
370#398—838no—
371#398—838no—
372#395—838no—
373#395—838no—
374#387—838no—
375#387—838no—
376#387—838no—
377#387C2×D8318yes—
378#383—838no—
379C2×#95—831no—
380C2×#95—831no—
381C2×#95—831no—
382C2×#95—831no—
383C2×#95—831no—
384C2×#95—831no—
385C2×#95—831no—
386C2×#95—831no—
387C2×#95—831no—
388C2×#95—831no—
389C2×#95—831no—
390C2×#95—831no—
391C2×#95—831no—
392C2×#95—831no—
393C2×#95C2×D8311yescharacteristic
394C2×#95C2×D8311yescharacteristic
395C2×#95C2×D8311yescharacteristic
396C2×#95C2×D8311yescharacteristic
397C22×Q8—834no—
398C22×Q8—1664no—
399C22×Q8—1664no—
400C22×Q8—1664no—
401C23×C4—831no—
402C23×C4—831no—
403C23×C4—831no—
404C23×C4—831no—
405C23×C4—831no—
406C23×C4—831no—
407C23×C4—831no—
408C23×C4—831no—
409C23×C4C22×D8311yescharacteristic
410C23×C4C22×D8311yescharacteristic
411C23×C4C22×D8311yescharacteristic
412C23×C4C22×D8311yescharacteristic
413C23×C4C22×D8311yescharacteristic
414C23×C4C22×D8311yescharacteristic
415C23×C4C22×D8311yescharacteristic
416#125—16632no—
417C4×Q8—16632no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—834no—
421C2×C4⋊C4—834no—
422C2×C4⋊C4—834no—
423C2×C4⋊C4—834no—
424C2×C4⋊C4—834no—
425C2×C4⋊C4—834no—
426C2×C4⋊C4—834no—
427C2×C4⋊C4—834no—
428C2×C4⋊C4—834no—
429C2×C4⋊C4—834no—
430C2×C4⋊C4—834no—
431C2×C4⋊C4—1664no—
432C2×C4⋊C4—1664no—
433C2×C4⋊C4—1664no—
434C2×C4⋊C4—1664no—
435C2×C4⋊C4—1664no—
436C2×C4⋊C4—1664no—
437C2×C4⋊C4—1664no—
438C2×C4⋊C4—1664no—
439C2×C4⋊C4—1664no—
440C2×C4⋊C4—1664no—
441C2×C4⋊C4—1664no—
442C2×C4⋊C4C22×D8314yes—
443C2×C4⋊C4C22×D8314yes—
444C2×C42—24no—
445C2×C42—838no—
446C2×C42—834no—
447C2×C42—834no—
448C2×C42—1664no—
449C2×C42C22×D8314yes—
450#95—834no—
451#95—834no—
452#95—834no—
453#95—834no—
454#95—834no—
455#95—834no—
456#95—834no—
457#95—834no—
458#95—834no—
459#95—834no—
460#95—834no—
461#95—834no—
462#95—834no—
463#95—834no—
464#95C22×D8314yes—
465#95C22×D8314yes—
466#95C22×D8314yes—
467#95C22×D8314yes—
468C24C23×D8311yescharacteristic
469C2×Q8—1668no—
470C2×Q8—1668no—
471C2×Q8—16632no—
472C2×Q8—1668no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—834no—
493C22×C4—834no—
494C22×C4—834no—
495C22×C4—832no—
496C22×C4—832no—
497C22×C4—832no—
498C22×C4—832no—
499C22×C4—832no—
500C22×C4—832no—
501C22×C4—832no—
502C22×C4—832no—
503C22×C4—1662no—
504C22×C4—1662no—
505C22×C4—1662no—
506C22×C4—1662no—
507C22×C4—1662no—
508C22×C4—1662no—
509C22×C4—1662no—
510C22×C4—1662no—
511C22×C4—1662no—
512C22×C4—1662no—
513C22×C4—1662no—
514C22×C4—1662no—
515C22×C4—1662no—
516C22×C4—1662no—
517C22×C4—1662no—
518C22×C4—1662no—
519C22×C4—1662no—
520C22×C4—1662no—
521C22×C4—1662no—
522C22×C4—1662no—
523C22×C4—1662no—
524C22×C4D4×D8314yes—
525C22×C4#1305059014yes—
526C22×C4C23×D8312yes—
527C22×C4C23×D8312yes—
528C22×C4C23×D8312yes—
529C22×C4C23×D8312yes—
530C22×C4C23×D8312yes—
531C22×C4C23×D8312yes—
532C22×C4C23×D8312yes—
533C4⋊C4—28no—
534C4⋊C4—28no—
535C4⋊C4—1668no—
536C4⋊C4—1668no—
537C4⋊C4—1668no—
538C4⋊C4—1668no—
539C4⋊C4—1668no—
540C4⋊C4—1668no—
541C4⋊C4—1668no—
542C4⋊C4—1668no—
543C4⋊C4—1668no—
544C4⋊C4—1668no—
545C4⋊C4—1668no—
546C42—28no—
547C42—8316no—
548C42—1668no—
549C23C2×D4×D8312yes—
550C23#41×D8312yes—
551C23C2×#1305059012yes—
552C23#1458183912yes—
553C23#1458183912yes—
554C23#1458183912yes—
555C23#1458184012yes—
556C23C24×D8311yescharacteristic
557Q8—16632no—
558C2×C4—28no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—28no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—3324no—
585C2×C4—3324no—
586C2×C4—3324no—
587C2×C4—3324no—
588C2×C4—3324no—
589C2×C4—834no—
590C2×C4—834no—
591C2×C4—834no—
592C2×C4—1662no—
593C2×C4—1662no—
594C2×C4—1662no—
595C2×C4—1662no—
596C2×C4—1662no—
597C2×C4—1662no—
598C2×C4—1662no—
599C2×C4—1662no—
600C2×C4—1662no—
601C2×C4—1662no—
602C2×C4—1662no—
603C2×C4—1662no—
604C2×C4—1662no—
605C2×C4—1662no—
606C2×C4—1662no—
607C2×C4—1668no—
608C2×C4—1668no—
609C2×C4—1662no—
610C2×C4—1662no—
611C2×C4—1662no—
612C2×C4—1662no—
613C2×C4—1668no—
614C2×C4—1662no—
615C2×C4—1662no—
616C2×C4C2×D4×D8314yes—
617C2×C4C2×#1305059014yes—
618C22#1912821014yes—
619C22#1912827314yes—
620C22#1912827414yes—
621C22#1912830814yes—
622C22#1912830914yes—
623C22#1912831014yes—
624C22#1912831314yes—
625C22C22×D4×D8311yescharacteristic
626C22C2×#41×D8311yescharacteristic
627C22C22×#1305059011yescharacteristic
628C22C2×#1458183911yescharacteristic
629C22C2×#1458183911yescharacteristic
630C22C2×#1458183911yescharacteristic
631C22C2×#1458184011yescharacteristic
632C4—24no—
633C4—24no—
634C4—42no—
635C4—42no—
636C4—42no—
637C4—42no—
638C4—42no—
639C4—3322no—
640C4—3322no—
641C4—3322no—
642C4—3322no—
643C4—3322no—
644C4—1664no—
645C4—1664no—
646C4—1664no—
647C2#2491334318yesdirect product factor
648C2C2×#1912821011yescharacteristic
649C2C2×#1912827311yescharacteristic
650C2C2×#1912827411yescharacteristic
651C2C2×#1912830811yescharacteristic
652C2C2×#1912830911yescharacteristic
653C2C2×#1912831011yescharacteristic
654C2C2×#1912831311yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#387×C83C2
socle, prime radicalC24×C83C24
hypercenterC2×#387D83
hypocenterC83C2×#2634
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. #24913343C2direct (N × H)
320. C2×C83#2634semidirect
344. C83C2×#2634semidirect
647. C2#24913343direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817822
C22×C4×Dic1662
#249133432
C2×#191276432
C2×#191276422
C2×#191276352
C2×#191276342
C2×#191276222
C2×#191276212
C2×#191275862
C2×#191275852
C2×#191275822
C2×#191275682
C2×#387×C832
C2×#263483