Finite Group Databasebeta

← C2×#24910769 #35570710

Subgroups — C2×#24910769 #35570710

Order 21248.

2078 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24910769C2116yesmaximal, direct product factor
2C2×#19127643C211yesmaximal, characteristic
3C2×#19127642C211yesmaximal, characteristic
4C2×#19127642C211yesmaximal, characteristic
5C2×#19127635C211yesmaximal, characteristic
6C2×#19127635C211yesmaximal, characteristic
7C2×#19127634C211yesmaximal, characteristic
8C2×#19127632C211yesmaximal, characteristic
9C2×C4⋊C4×Dic83C211yesmaximal, characteristic
10C2×C4⋊C4×Dic83C211yesmaximal, characteristic
11C2×#19127552C211yesmaximal, characteristic
12C2×#19127552C211yesmaximal, characteristic
13C2×#19127552C211yesmaximal, characteristic
14C2×#19127552C211yesmaximal, characteristic
15C2×#19127546C211yesmaximal, characteristic
16C2×#400×C83C211yesmaximal, characteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic
19C22×Dic83⋊C4C2211yescharacteristic
20C22×Dic83⋊C4C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×Dic83⋊C4C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×C4×Dic83C2211yescharacteristic
28C22×C4×Dic83C2211yescharacteristic
29C22×C4×Dic83C2211yescharacteristic
30C22×C4×Dic83C2211yescharacteristic
31C22×C4×Dic83C2211yescharacteristic
32C22×C4×Dic83C2211yescharacteristic
33C22×C4×Dic83C2211yescharacteristic
34#19127643C2218yes—
35#19127642C2218yes—
36#19127642C2218yes—
37#19127635C2218yes—
38#19127635C2218yes—
39#19127634C2218yes—
40#19127632C2218yes—
41C4⋊C4×Dic83C2218yes—
42C4⋊C4×Dic83C2218yes—
43#19127552C2218yes—
44#19127552C2218yes—
45#19127552C2218yes—
46#19127552C2218yes—
47#19127546C2218yes—
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
61#400×C83C2218yes—
62C2×#95×C83C2211yescharacteristic
63C2×#95×C83C2211yescharacteristic
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—24no—
77C2×C4⋊Dic83C2314yes—
78C2×C4⋊Dic83C2314yes—
79C2×Dic83⋊C4—24no—
80C2×Dic83⋊C4—24no—
81C2×Dic83⋊C4—24no—
82C2×Dic83⋊C4—24no—
83C2×Dic83⋊C4—24no—
84C2×Dic83⋊C4—24no—
85C2×Dic83⋊C4—24no—
86C2×Dic83⋊C4—24no—
87C2×Dic83⋊C4C2314yes—
88C2×Dic83⋊C4C2314yes—
89C2×Dic83⋊C4C2314yes—
90C2×Dic83⋊C4C2314yes—
91C2×Dic83⋊C4C2314yes—
92C2×Dic83⋊C4C2314yes—
93C2×Dic83⋊C4C2314yes—
94C2×Dic83⋊C4C2314yes—
95C2×C4×Dic83—24no—
96C2×C4×Dic83—24no—
97C2×C4×Dic83—24no—
98C2×C4×Dic83—24no—
99C2×C4×Dic83—24no—
100C2×C4×Dic83—24no—
101C2×C4×Dic83Q818yes—
102C2×C4×Dic83C2314yes—
103C2×C4×Dic83C2314yes—
104C2×C4×Dic83C2314yes—
105C2×C4×Dic83C2314yes—
106C2×C4×Dic83C2314yes—
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—
120C23×C4×C83C2311yescharacteristic
121C23×C4×C83C2311yescharacteristic
122C23×C4×C83C2311yescharacteristic
123C23×C4×C83C2311yescharacteristic
124C23×C4×C83C2311yescharacteristic
125C23×C4×C83C2311yescharacteristic
126C23×C4×C83C2311yescharacteristic
127C2×C4⋊C4×C83—24no—
128C2×C4⋊C4×C83—24no—
129C2×C4⋊C4×C83C2314yes—
130C2×C4⋊C4×C83C2314yes—
131#95×C83C2314yes—
132#95×C83C2314yes—
133#95×C83C2314yes—
134#95×C83C2314yes—
135#95×C83C2314yes—
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×Dic83C2×Q814yes—
154C22×Dic83C2×Q814yes—
155C22×Dic83#4114yes—
156C22×Dic83#4114yes—
157C22×Dic83#4114yes—
158C22×Dic83#4114yes—
159C22×Dic83#4114yes—
160C22×Dic83C2412yes—
161C22×Dic83C2412yes—
162C22×Dic83C2412yes—
163C22×Dic83C2412yes—
164C22×Dic83C2412yes—
165C22×Dic83C2412yes—
166C22×Dic83C2412yes—
167C22×Dic83C2412yes—
168C4⋊Dic83—28no—
169C4⋊Dic83—28no—
170Dic83⋊C4—28no—
171Dic83⋊C4—28no—
172Dic83⋊C4—28no—
173Dic83⋊C4—28no—
174Dic83⋊C4—28no—
175Dic83⋊C4—28no—
176Dic83⋊C4—28no—
177Dic83⋊C4—28no—
178C4×Dic83—28no—
179C4×Dic83—28no—
180C4×Dic83—28no—
181C4×Dic83—28no—
182C4×Dic83—28no—
183C4×Dic83—28no—
184C4×Dic83C2×Q8116yes—
185C24×C83C2411yescharacteristic
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—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×C83C2×Q814yes—
206C22×C4×C83#4114yes—
207C22×C4×C83C2412yes—
208C22×C4×C83C2412yes—
209C22×C4×C83C2412yes—
210C22×C4×C83C2412yes—
211C22×C4×C83C2412yes—
212C22×C4×C83C2412yes—
213C22×C4×C83C2412yes—
214C4⋊C4×C83—28no—
215C4⋊C4×C83—28no—
216C23×C83C22×Q812yes—
217C23×C83C2×#4112yes—
218C23×C83C2×#4112yes—
219C23×C83C2×#4112yes—
220C23×C83C2×#4112yes—
221C23×C83C2×#4112yes—
222C23×C83C2×#4112yes—
223C23×C83C2511yescharacteristic
224C2×C4×C83—28no—
225C2×C4×C83—28no—
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—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—44no—
246C2×C4×C83—44no—
247C2×C4×C83—44no—
248C2×C4×C83—44no—
249C2×C4×C83—44no—
250C2×C4×C83C22×Q814yes—
251C2×C4×C83C2×#4114yes—
252C2×Dic83—28no—
253C2×Dic83—28no—
254C2×Dic83—28no—
255C2×Dic83—28no—
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—22no—
269C2×Dic83—22no—
270C2×Dic83—22no—
271C2×Dic83—22no—
272C2×Dic83—22no—
273C2×Dic83—44no—
274C2×Dic83—44no—
275C2×Dic83—44no—
276C2×Dic83#125116yes—
277C2×Dic83C22×Q814yes—
278C2×Dic83C22×Q814yes—
279C2×Dic83C2×#4114yes—
280C2×Dic83C2×#4114yes—
281C2×Dic83C2×#4114yes—
282C2×Dic83C2×#4114yes—
283C2×Dic83C2×#4114yes—
284C22×C83C2×#12514yes—
285C22×C83#52914yes—
286C22×C83#52914yes—
287C22×C83#52914yes—
288C22×C83#52914yes—
289C22×C83#53314yes—
290C22×C83#53314yes—
291C22×C83C23×Q811yescharacteristic
292C22×C83C22×#4111yescharacteristic
293C22×C83C22×#4111yescharacteristic
294C22×C83C22×#4111yescharacteristic
295C22×C83C22×#4111yescharacteristic
296C22×C83C22×#4111yescharacteristic
297C22×C83C22×#4111yescharacteristic
298C4×C83—24no—
299C4×C83—24no—
300C4×C83—42no—
301C4×C83—42no—
302C4×C83—42no—
303C4×C83—42no—
304C4×C83—42no—
305Dic83—24no—
306Dic83—24no—
307Dic83—24no—
308Dic83—24no—
309Dic83—42no—
310Dic83—42no—
311Dic83—42no—
312Dic83C2×#12518yes—
313C2×#2402—831nomaximal, Sylow
314C2×C83#240218yescomplemented
315C2×C83C22×#12511yescharacteristic
316C2×C83C2×#52911yescharacteristic
317C2×C83C2×#52911yescharacteristic
318C2×C83C2×#52911yescharacteristic
319C2×C83C2×#52911yescharacteristic
320C2×C83C2×#53311yescharacteristic
321C2×C83C2×#53311yescharacteristic
322#2402—8316no—
323C2×#400—831no—
324C2×#400—831no—
325C2×#400—831no—
326C2×#400D8311yescharacteristic
327C2×#398—831no—
328C2×#398—831no—
329C2×#398—831no—
330C2×#398—831no—
331C2×C4×C4⋊C4—831no—
332C2×C4×C4⋊C4—831no—
333C2×C4×C4⋊C4—831no—
334C2×C4×C4⋊C4—831no—
335C2×C4×C4⋊C4—831no—
336C2×C4×C4⋊C4—831no—
337C2×#376—831no—
338C83C2×#240211yescharacteristic, complemented, Sylow
339C22×C4⋊C4—831no—
340C22×C4⋊C4—831no—
341C22×C4⋊C4—831no—
342C22×C4⋊C4—831no—
343C22×C4⋊C4—831no—
344C22×C4⋊C4—831no—
345C22×C4⋊C4—831no—
346C22×C4⋊C4—831no—
347C22×C4⋊C4—831no—
348C22×C4⋊C4—831no—
349C22×C4⋊C4C2×D8311yescharacteristic
350C22×C4⋊C4C2×D8311yescharacteristic
351C22×C42—831no—
352C22×C42—831no—
353C22×C42—831no—
354C22×C42—831no—
355C22×C42—831no—
356C22×C42—831no—
357C22×C42—831no—
358#400—838no—
359#400—838no—
360#400—838no—
361#400C2×D8318yes—
362#398—838no—
363#398—838no—
364#398—838no—
365#398—838no—
366C4×C4⋊C4—838no—
367C4×C4⋊C4—838no—
368C4×C4⋊C4—838no—
369C4×C4⋊C4—838no—
370C4×C4⋊C4—838no—
371C4×C4⋊C4—838no—
372#376—838no—
373C2×#95—831no—
374C2×#95—831no—
375C2×#95—831no—
376C2×#95—831no—
377C2×#95—831no—
378C2×#95—831no—
379C2×#95—831no—
380C2×#95—831no—
381C2×#95—831no—
382C2×#95—831no—
383C2×#95—831no—
384C2×#95C2×D8311yescharacteristic
385C2×#95C2×D8311yescharacteristic
386C2×#95C2×D8311yescharacteristic
387C2×#95C2×D8311yescharacteristic
388C2×#95C2×D8311yescharacteristic
389C23×C4—831no—
390C23×C4—831no—
391C23×C4—831no—
392C23×C4—831no—
393C23×C4—831no—
394C23×C4—831no—
395C23×C4—831no—
396C23×C4—831no—
397C23×C4C22×D8311yescharacteristic
398C23×C4C22×D8311yescharacteristic
399C23×C4C22×D8311yescharacteristic
400C23×C4C22×D8311yescharacteristic
401C23×C4C22×D8311yescharacteristic
402C23×C4C22×D8311yescharacteristic
403C23×C4C22×D8311yescharacteristic
404C2×C4⋊C4—24no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—834no—
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—1664no—
417C2×C4⋊C4—1664no—
418C2×C4⋊C4—1664no—
419C2×C4⋊C4—1664no—
420C2×C4⋊C4—1664no—
421C2×C4⋊C4—1664no—
422C2×C4⋊C4—1664no—
423C2×C4⋊C4—1664no—
424C2×C4⋊C4—1664no—
425C2×C4⋊C4—1664no—
426C2×C4⋊C4C22×D8314yes—
427C2×C4⋊C4C22×D8314yes—
428C2×C42—838no—
429C2×C42—834no—
430C2×C42—834no—
431C2×C42—834no—
432C2×C42—834no—
433C2×C42—834no—
434C2×C42—834no—
435C2×C42—834no—
436C2×C42—1664no—
437C2×C42—1664no—
438C2×C42—1664no—
439C2×C42—1664no—
440C2×C42—1664no—
441C2×C42—1664no—
442#95—834no—
443#95—834no—
444#95—834no—
445#95—834no—
446#95—834no—
447#95—834no—
448#95—834no—
449#95—834no—
450#95—834no—
451#95—834no—
452#95—834no—
453#95C22×D8314yes—
454#95C22×D8314yes—
455#95C22×D8314yes—
456#95C22×D8314yes—
457#95C22×D8314yes—
458C24C23×D8311yescharacteristic
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—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—834no—
479C22×C4—834no—
480C22×C4—834no—
481C22×C4—832no—
482C22×C4—834no—
483C22×C4—834no—
484C22×C4—834no—
485C22×C4—834no—
486C22×C4—832no—
487C22×C4—832no—
488C22×C4—832no—
489C22×C4—832no—
490C22×C4—832no—
491C22×C4—832no—
492C22×C4—832no—
493C22×C4—1662no—
494C22×C4—1662no—
495C22×C4—1662no—
496C22×C4—1662no—
497C22×C4—1662no—
498C22×C4—1662no—
499C22×C4—1662no—
500C22×C4—1662no—
501C22×C4—1662no—
502C22×C4—1662no—
503C22×C4—1662no—
504C22×C4—1662no—
505C22×C4—1662no—
506C22×C4—1662no—
507C22×C4—1662no—
508C22×C4—1662no—
509C22×C4—1662no—
510C22×C4Q8×D8314yes—
511C22×C4#1305058914yes—
512C22×C4C23×D8312yes—
513C22×C4C23×D8312yes—
514C22×C4C23×D8312yes—
515C22×C4C23×D8312yes—
516C22×C4C23×D8312yes—
517C22×C4C23×D8312yes—
518C22×C4C23×D8312yes—
519C4⋊C4—28no—
520C4⋊C4—28no—
521C4⋊C4—1668no—
522C4⋊C4—1668no—
523C4⋊C4—1668no—
524C4⋊C4—1668no—
525C4⋊C4—1668no—
526C4⋊C4—1668no—
527C4⋊C4—1668no—
528C4⋊C4—1668no—
529C4⋊C4—1668no—
530C4⋊C4—1668no—
531C42—8316no—
532C42—1668no—
533C42—1668no—
534C42—1668no—
535C42—1668no—
536C42—1668no—
537C42—1668no—
538C23C2×Q8×D8312yes—
539C23#41×D8312yes—
540C23#41×D8312yes—
541C23#41×D8312yes—
542C23#41×D8312yes—
543C23#41×D8312yes—
544C23C2×#1305058912yes—
545C23C24×D8311yescharacteristic
546C2×C4—28no—
547C2×C4—28no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—44no—
572C2×C4—3324no—
573C2×C4—3324no—
574C2×C4—3324no—
575C2×C4—8316no—
576C2×C4—834no—
577C2×C4—834no—
578C2×C4—834no—
579C2×C4—834no—
580C2×C4—834no—
581C2×C4—834no—
582C2×C4—834no—
583C2×C4—1662no—
584C2×C4—1662no—
585C2×C4—1662no—
586C2×C4—1662no—
587C2×C4—1662no—
588C2×C4—1662no—
589C2×C4—1662no—
590C2×C4—1662no—
591C2×C4—1662no—
592C2×C4—1668no—
593C2×C4—1668no—
594C2×C4—1668no—
595C2×C4—1668no—
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×C4C2×Q8×D8314yes—
605C2×C4C2×#1305058914yes—
606C22#125×D8314yes—
607C22#1912822814yes—
608C22#1912823014yes—
609C22#1912823414yes—
610C22#1912823414yes—
611C22#1912825314yes—
612C22#1912825714yes—
613C22C22×Q8×D8311yescharacteristic
614C22C2×#41×D8311yescharacteristic
615C22C2×#41×D8311yescharacteristic
616C22C2×#41×D8311yescharacteristic
617C22C2×#41×D8311yescharacteristic
618C22C2×#41×D8311yescharacteristic
619C22C22×#1305058911yescharacteristic
620C4—24no—
621C4—24no—
622C4—42no—
623C4—42no—
624C4—42no—
625C4—42no—
626C4—42no—
627C4—3322no—
628C4—3322no—
629C4—3322no—
630C4—838no—
631C4—1664no—
632C4—1664no—
633C4—1664no—
634C4—1664no—
635C2#2491076918yesdirect product factor
636C2C2×#125×D8311yescharacteristic
637C2C2×#1912822811yescharacteristic
638C2C2×#1912823011yescharacteristic
639C2C2×#1912823411yescharacteristic
640C2C2×#1912823411yescharacteristic
641C2C2×#1912825311yescharacteristic
642C2C2×#1912825711yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#400×C83C2
socle, prime radicalC24×C83C24
hypercenterC2×#400D83
hypocenterC83C2×#2402
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #24910769C2direct (N × H)
314. C2×C83#2402semidirect
338. C83C2×#2402semidirect
635. C2#24910769direct (N × H)

Maximal subgroups

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

subgroupindex
#249107692
C2×#191276432
C2×#191276422
C2×#191276352
C2×#191276342
C2×#191276322
C2×C4⋊C4×Dic832
C2×#191275522
C2×#191275462
C2×#400×C832
C2×#240283