Finite Group Databasebeta

← C2×#19149209 #26003999

Subgroups — C2×#19149209 #26003999

Order 11008.

6598 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149209C2132yesmaximal, direct product factor
2C2×#14583650C212yesmaximal, complemented
3C2×#14583650C212yesmaximal, complemented
4C2×#14583620C212yesmaximal, complemented
5C2×#14583603C212yesmaximal, complemented
6C2×#14583591C212yesmaximal, complemented
7C2×#14583583C212yesmaximal, complemented
8C2×#14583575C212yesmaximal, complemented
9C2×#14583575C212yesmaximal, complemented
10C2×#14583528C211yesmaximal, characteristic, complemented
11C2×#14583519C212yesmaximal, complemented
12C2×#14583509C212yesmaximal, complemented
13C2×#14583509C212yesmaximal, complemented
14C2×#14583498C211yesmaximal, characteristic, complemented
15C2×#14583495C212yesmaximal, complemented
16C2×#14583487C211yesmaximal, characteristic
17C2×#14583451C211yesmaximal, characteristic, complemented
18C2×#14583435C211yesmaximal, characteristic, complemented
19C22×#13063318C211yesmaximal, characteristic, complemented
20C2×C43×#543C211yesmaximal, characteristic, complemented
21#14583650C22132yescomplemented
22#14583650C22132yescomplemented
23#14583620C22132yescomplemented
24#14583603C22132yescomplemented
25#14583591C22132yescomplemented
26#14583583C22132yescomplemented
27#14583575C22132yescomplemented
28#14583575C22132yescomplemented
29#14583528C22116yescomplemented
30#14583519C22132yescomplemented
31#14583509C22132yescomplemented
32#14583509C22132yescomplemented
33#14583498C22116yescomplemented
34#14583495C22132yescomplemented
35#14583487C22116yes—
36#14583451C22116yescomplemented
37C2×#13063324C2211yescharacteristic, complemented
38C2×#13063324C2212yescomplemented
39C2×#13063323C2212yescomplemented
40C2×#13063323C2211yescharacteristic, complemented
41C2×#13063323C2212yescomplemented
42#14583435C22116yescomplemented
43C2×#13063320C2212yescomplemented
44C2×#13063320C2212yescomplemented
45C2×#13063320C2212yescomplemented
46C2×#13063320C2212yescomplemented
47C2×#13063318C2212yes—
48C2×#13063318C2212yes—
49C2×#13063318C2212yes—
50C2×#13063318C2212yes—
51C2×#13063318C2212yes—
52C2×#13063318C2212yes—
53C2×#13063318C2212yes—
54C2×#13063318C2212yes—
55C2×#13063318C2212yes—
56C2×#13063318C22116yescomplemented
57C2×#13063316C2212yescomplemented
58C2×#13063316C2212yescomplemented
59C2×#13063316C2212yescomplemented
60C2×#13063316C2211yescharacteristic, complemented
61C2×#13063316C2212yescomplemented
62C2×#13063315C2212yescomplemented
63C2×#13063315C2212yescomplemented
64C2×#13063315C2212yescomplemented
65C2×#13063315C2212yescomplemented
66C2×#13063315C2212yescomplemented
67C2×#13063314C2211yescharacteristic, complemented
68C2×#13063311C2212yes—
69C2×#13063311C2212yes—
70C2×#13063311C2212yes—
71C2×#13063310C2212yescomplemented
72C2×#13063309C2212yes—
73C2×#13063309C2212yes—
74C2×#13063308C2212yes—
75C2×#13063308C2212yes—
76C2×#13063307C2212yes—
77C2×#13063307C2212yes—
78C2×#13063307C2212yes—
79C2×#13063304C2212yes—
80C2×#13063304C2212yes—
81C2×#13063304C2211yescharacteristic
82C2×#13063303C2212yescomplemented
83C2×#13063303C2212yescomplemented
84C2×#13063302C2212yes—
85C2×#13063302C2212yes—
86C2×#13063301C2212yescomplemented
87C2×#13063301C2212yescomplemented
88C2×#13063301C2212yescomplemented
89C2×#13063299C2211yescharacteristic
90C2×#13063298C2212yes—
91C2×#13063294C2212yes—
92C2×Q8×Dic43C2211yescharacteristic, complemented
93C2×Q8×Dic43C2212yescomplemented
94C2×Q8×Dic43C2211yescharacteristic, complemented
95C2×#13063290C2212yescomplemented
96C2×#13063290C2211yescharacteristic, complemented
97C2×#13063290C2212yescomplemented
98C2×#13063287C2211yescharacteristic, complemented
99C2×C4×C22⋊D43C2212yes—
100C2×C4×C22⋊D43C2212yes—
101C2×C4×C22⋊D43C2212yes—
102C2×(C22⋊D43)⋊C4C2212yes—
103C2×(C22⋊D43)⋊C4C2212yes—
104C2×#13063284C2212yes—
105C2×#13063284C2212yes—
106C2×#13063283C2212yescomplemented
107C2×#13063283C2212yescomplemented
108C2×#13063281C2212yes—
109C2×#13063281C2212yes—
110C22×C4⋊Dic43C2211yescharacteristic
111C22×Dic43⋊C4C2211yescharacteristic
112C22×Dic43⋊C4C2211yescharacteristic
113C2×C4⋊C4×D43C2212yescomplemented
114C22×C22⋊Dic43C2211yescharacteristic
115C22×C22⋊Dic43C2211yescharacteristic
116C22×C4×Dic43C2211yescharacteristic
117C43×#543C22116yescomplemented
118C2×C22⋊Q8×C43C2212yes—
119C2×C22⋊Q8×C43C2212yes—
120C2×C22⋊Q8×C43C2211yescharacteristic
121C2×C22⋊Q8×C43C2211yescharacteristic
122C2×C22⋊Q8×C43C2212yes—
123C2×C22⋊Q8×C43C2212yes—
124C2×C22⋊Q8×C43C2212yes—
125C22×C22⋊C4×C43C2212yes—
126C22×C22⋊C4×C43C2211yescharacteristic
127C22×Dic86C2312yes—
128C22×Dic86C2312yes—
129C22×Dic86C2311yescharacteristic
130C22×D172C2311yescharacteristic
131C22×C22⋊D43C2312yes—
132C22×C22⋊D43C2312yes—
133C22×C22⋊D43C2312yes—
134C23×Dic43C2311yescharacteristic
135C23×Dic43C2311yescharacteristic
136C23×Dic43C2311yescharacteristic
137C23×Dic43C2311yescharacteristic
138C22×C4×D43C2312yes—
139C22×C4×D43C2312yes—
140C22×C4×D43C2312yes—
141#13063324C23116yescomplemented
142#13063324C2318yescomplemented
143#13063323C23116yescomplemented
144#13063323C2318yescomplemented
145#13063323C23116yescomplemented
146#13063320C23116yescomplemented
147#13063320C23116yescomplemented
148#13063320C23116yescomplemented
149#13063320C23116yescomplemented
150#13063318C23116yes—
151#13063318C23116yes—
152#13063318C23116yes—
153#13063318C23116yes—
154#13063318C23116yes—
155#13063318C23116yes—
156#13063318C23116yes—
157#13063318C23116yes—
158#13063318C23116yes—
159#13063316C23116yescomplemented
160#13063316C23116yescomplemented
161#13063316C23116yescomplemented
162#13063316C2318yescomplemented
163#13063316C23116yescomplemented
164#13063315C23116yescomplemented
165#13063315C23116yescomplemented
166#13063315C23116yescomplemented
167#13063315C23116yescomplemented
168#13063315C23116yescomplemented
169#13063314C2318yescomplemented
170#13063311C23116yes—
171#13063311C23116yes—
172#13063311C23116yes—
173#13063310C23116yescomplemented
174#13063309C23116yes—
175#13063309C23116yes—
176#13063308C23116yes—
177#13063308C23116yes—
178#13063307C23116yes—
179#13063307C23116yes—
180#13063307C23116yes—
181#13063304C23116yes—
182#13063304C23116yes—
183#13063304C2318yes—
184#13063303C23116yescomplemented
185#13063303C23116yescomplemented
186#13063302C23116yes—
187#13063302C23116yes—
188#13063301C23116yescomplemented
189#13063301C23116yescomplemented
190#13063301C23116yescomplemented
191#13063299C2318yes—
192#13063298C23116yes—
193#13063294C23116yes—
194Q8×Dic43C2318yescomplemented
195Q8×Dic43C23116yescomplemented
196Q8×Dic43C2318yescomplemented
197#13063290C23116yescomplemented
198#13063290C2318yescomplemented
199#13063290C23116yescomplemented
200#13063287C2318yescomplemented
201C4×C22⋊D43C23116yes—
202C4×C22⋊D43C23116yes—
203C4×C22⋊D43C23116yes—
204(C22⋊D43)⋊C4C23116yes—
205(C22⋊D43)⋊C4C23116yes—
206#13063284C23116yes—
207#13063284C23116yes—
208#13063283C23116yescomplemented
209#13063283C23116yescomplemented
210#13063281C23116yes—
211#13063281C23116yes—
212C2×C4⋊Dic43C2318yes—
213C2×C4⋊Dic43C2312yes—
214C2×C4⋊Dic43C2312yes—
215C2×C4⋊Dic43C2312yes—
216C2×C4⋊Dic43C2312yes—
217C2×C4⋊Dic43C2312yes—
218C2×C4⋊Dic43C2312yes—
219C2×C4⋊Dic43C2311yescharacteristic
220C2×C4⋊Dic43C2311yescharacteristic
221C2×C4⋊Dic43C2312yes—
222C2×C4⋊Dic43C2312yes—
223C2×Dic43⋊C4C2318yes—
224C2×Dic43⋊C4C2312yes—
225C2×Dic43⋊C4C2312yes—
226C2×Dic43⋊C4C2312yes—
227C2×Dic43⋊C4C2312yes—
228C2×Dic43⋊C4C2312yes—
229C2×Dic43⋊C4C2318yes—
230C2×Dic43⋊C4C2312yes—
231C2×Dic43⋊C4C2312yes—
232C2×Dic43⋊C4C2312yes—
233C2×Dic43⋊C4C2312yes—
234C2×Dic43⋊C4C2312yes—
235C2×Dic43⋊C4C2312yes—
236C2×Dic43⋊C4C2312yes—
237C2×Dic43⋊C4C2312yes—
238C2×Dic43⋊C4C2312yes—
239C2×Dic43⋊C4C2312yes—
240C2×Dic43⋊C4C2312yes—
241C4⋊C4×D43C23116yescomplemented
242C2×C22⋊Dic43C2318yes—
243C2×C22⋊Dic43C2318yes—
244C2×C22⋊Dic43C2312yes—
245C2×C22⋊Dic43C2312yes—
246C2×C22⋊Dic43C2312yes—
247C2×C22⋊Dic43C2312yes—
248C2×C22⋊Dic43C2312yes—
249C2×C22⋊Dic43C2312yes—
250C2×C22⋊Dic43C2312yes—
251C2×(C2×D43)⋊C4C2312yes—
252C2×(C2×D43)⋊C4C2312yes—
253C2×(C2×D43)⋊C4C2312yes—
254C2×(C2×D43)⋊C4C2312yes—
255C2×(C2×D43)⋊C4C2312yes—
256C2×(C2×D43)⋊C4C2312yes—
257C2×(C2×D43)⋊C4C2312yes—
258C2×(C2×D43)⋊C4C2312yes—
259C2×C4×Dic43C2311yescharacteristic
260C2×C4×Dic43C2311yescharacteristic
261C2×C4×Dic43C2311yescharacteristic
262C2×C4×Dic43C2311yescharacteristic
263C2×C4×Dic43C2318yes—
264C2×C4×Dic43C2312yes—
265C2×C4×Dic43C2312yes—
266C2×C4×Dic43C2312yes—
267C2×C4×Dic43C2312yes—
268C2×C4×Dic43C2312yes—
269C2×C4×Dic43C2312yes—
270C2×C4×Dic43C2312yes—
271C25×C43C2311yescharacteristic
272C22×Q8×C43C2311yescharacteristic
273C22×Q8×C43C2312yes—
274C22×Q8×C43C2311yescharacteristic
275C23×C4×C43C2311yescharacteristic
276C23×C4×C43C2311yescharacteristic
277C23×C4×C43C2312yes—
278C23×C4×C43C2312yes—
279C22⋊Q8×C43C23116yes—
280C22⋊Q8×C43C23116yes—
281C22⋊Q8×C43C23116yes—
282C22⋊Q8×C43C2318yes—
283C22⋊Q8×C43C2318yes—
284C22⋊Q8×C43C23116yes—
285C22⋊Q8×C43C23116yes—
286C2×C4⋊C4×C43C2312yes—
287C2×C4⋊C4×C43C2312yes—
288C2×C4⋊C4×C43C2312yes—
289C2×C4⋊C4×C43C2311yescharacteristic
290C2×C4⋊C4×C43C2312yes—
291C2×C4⋊C4×C43C2312yes—
292C2×C4⋊C4×C43C2311yescharacteristic
293C2×C22⋊C4×C43C23116yes—
294C2×C22⋊C4×C43C2312yes—
295C2×C22⋊C4×C43C2312yes—
296C2×C22⋊C4×C43C2312yes—
297C2×C22⋊C4×C43C2312yes—
298C2×C22⋊C4×C43C2312yes—
299C2×C22⋊C4×C43C2312yes—
300C2×C22⋊C4×C43C2318yes—
301C24×C43—24no—
302C24×C43—42no—
303C24×C43—42no—
304C24×C43C2412yes—
305C24×C43C2411yescharacteristic
306C24×C43C2414yes—
307C23×D43C2412yes—
308C2×Q8×C43—42no—
309C2×Q8×C43—42no—
310C2×Q8×C43—44no—
311C2×Q8×C43C2414yes—
312C2×Q8×C43C2418yes—
313C2×Q8×C43C2414yes—
314C22×C4×C43—42no—
315C22×C4×C43—42no—
316C22×C4×C43—44no—
317C22×C4×C43—44no—
318C22×C4×C43C2412yes—
319C22×C4×C43C2412yes—
320C22×C4×C43C2411yescharacteristic
321C22×C4×C43C2411yescharacteristic
322C22×C4×C43C2412yes—
323C22×C4×C43C2412yes—
324C22×C4×C43C2412yes—
325C22×C4×C43C2414yes—
326C22×C4×C43C2414yes—
327C22×C4×C43C2418yes—
328C22×C4×C43C2418yes—
329C2×C22⋊D43—28no—
330C2×C22⋊D43—44no—
331C2×C22⋊D43—44no—
332C2×C22⋊D43C2418yes—
333C2×C22⋊D43C2418yes—
334C2×C22⋊D43C2418yes—
335C22×Dic43—24no—
336C22×Dic43—24no—
337C22×Dic43—42no—
338C22×Dic43—42no—
339C22×Dic43C2411yescharacteristic
340C22×Dic43C2411yescharacteristic
341C22×Dic43C2412yes—
342C22×Dic43C2412yes—
343C22×Dic43C2411yescharacteristic
344C22×Dic43C2411yescharacteristic
345C22×Dic43C2412yes—
346C22×Dic43C2412yes—
347C22×Dic43C2414yes—
348C22×Dic43C2412yes—
349C22×Dic43C2414yes—
350C22×Dic43C2414yes—
351C22×Dic43C2414yes—
352C2×D172—42no—
353C2×D172C2414yes—
354C2×C4×D43—44no—
355C2×C4×D43—44no—
356C2×C4×D43—44no—
357C2×C4×D43C2418yes—
358C2×C4×D43C2418yes—
359C2×C4×D43C2418yes—
360C2×Dic86—44no—
361C2×Dic86—42no—
362C2×Dic86—44no—
363C2×Dic86C2418yes—
364C2×Dic86C2418yes—
365C2×Dic86C2414yes—
366C4⋊C4×C43C2418yes—
367C4⋊C4×C43C2418yes—
368C4⋊C4×C43C2418yes—
369C4⋊C4×C43C2414yes—
370C4⋊C4×C43C2418yes—
371C4⋊C4×C43C2418yes—
372C4⋊C4×C43C2414yes—
373C22⋊C4×C43C2418yes—
374C22⋊C4×C43C2418yes—
375C22⋊C4×C43C2418yes—
376C22⋊C4×C43C2418yes—
377C22⋊C4×C43C2418yes—
378C22⋊C4×C43C2418yes—
379C22⋊Dic43C2418yes—
380C22⋊Dic43C2418yes—
381C22⋊Dic43C2418yes—
382C22⋊Dic43C2418yes—
383C22⋊Dic43C2418yes—
384C22⋊Dic43C2418yes—
385C22⋊Dic43C2418yes—
386(C2×D43)⋊C4C2418yes—
387(C2×D43)⋊C4C2418yes—
388(C2×D43)⋊C4C2418yes—
389(C2×D43)⋊C4C2418yes—
390(C2×D43)⋊C4C2418yes—
391(C2×D43)⋊C4C2418yes—
392(C2×D43)⋊C4C2418yes—
393(C2×D43)⋊C4C2418yes—
394C4⋊Dic43C2418yes—
395C4⋊Dic43C2418yes—
396C4⋊Dic43C2418yes—
397C4⋊Dic43C2418yes—
398C4⋊Dic43C2418yes—
399C4⋊Dic43C2418yes—
400C4⋊Dic43C2414yes—
401C4⋊Dic43C2414yes—
402C4⋊Dic43C2418yes—
403C4⋊Dic43C2418yes—
404Dic43⋊C4C2418yes—
405Dic43⋊C4C2418yes—
406Dic43⋊C4C2418yes—
407Dic43⋊C4C2418yes—
408Dic43⋊C4C2418yes—
409Dic43⋊C4C2418yes—
410Dic43⋊C4C2418yes—
411Dic43⋊C4C2418yes—
412Dic43⋊C4C2418yes—
413Dic43⋊C4C2418yes—
414Dic43⋊C4C2418yes—
415Dic43⋊C4C2418yes—
416Dic43⋊C4C2418yes—
417Dic43⋊C4C2418yes—
418Dic43⋊C4C2418yes—
419Dic43⋊C4C2418yes—
420C4×Dic43C2414yes—
421C4×Dic43C2414yes—
422C4×Dic43C2414yes—
423C4×Dic43C2414yes—
424C4×Dic43C2418yes—
425C4×Dic43C2418yes—
426C4×Dic43C2418yes—
427C4×Dic43C2418yes—
428C4×Dic43C2418yes—
429C4×Dic43C2418yes—
430C4×Dic43C2418yes—
431C23×C43—22no—
432C23×C43—22no—
433C23×C43—24no—
434C23×C43—24no—
435C23×C43—24no—
436C23×C43—28no—
437C23×C43—44no—
438C23×C43—44no—
439C23×C43—88no—
440C23×C432−1+414yes—
441C23×C43C2514yes—
442C23×C43C2512yes—
443C23×C43C2511yescharacteristic
444C22×D43—24no—
445C22×D43—24no—
446C22×D43—24no—
447C22×D43C2514yes—
448Q8×C43—44no—
449Q8×C43—44no—
450Q8×C43—48no—
451C2×C4×C43—24no—
452C2×C4×C43—22no—
453C2×C4×C43—24no—
454C2×C4×C43—24no—
455C2×C4×C43—24no—
456C2×C4×C43—24no—
457C2×C4×C43—22no—
458C2×C4×C43—48no—
459C2×C4×C43—48no—
460C2×C4×C43—44no—
461C2×C4×C43—44no—
462C2×C4×C43C2512yes—
463C2×C4×C43C2512yes—
464C2×C4×C43C2514yes—
465C2×C4×C43C2514yes—
466C2×C4×C43C2514yes—
467C2×C4×C43C2514yes—
468C2×C4×C43C2514yes—
469C22⋊D43—216no—
470C22⋊D43—48no—
471C22⋊D43—48no—
472C2×Dic43—28no—
473C2×Dic43—28no—
474C2×Dic43—22no—
475C2×Dic43—22no—
476C2×Dic43—24no—
477C2×Dic43—24no—
478C2×Dic43—22no—
479C2×Dic43—24no—
480C2×Dic43—24no—
481C2×Dic43—24no—
482C2×Dic43—22no—
483C2×Dic43—44no—
484C2×Dic43—44no—
485C2×Dic43C2512yes—
486C2×Dic43C2512yes—
487C2×Dic43C2514yes—
488C2×Dic43C2514yes—
489C2×Dic43C2514yes—
490C2×Dic43C2512yes—
491C2×Dic43C2512yes—
492C2×Dic43C2514yes—
493C2×Dic43C2514yes—
494D172—44no—
495C4×D43—48no—
496C4×D43—48no—
497C4×D43—48no—
498Dic86—48no—
499Dic86—44no—
500Dic86—48no—
501C2×#3564—431nomaximal, Sylow
502C22×C43—22no—
503C22×C43—22no—
504C22×C43—28no—
505C22×C43—24no—
506C22×C43—24no—
507C22×C43—24no—
508C22×C43—48no—
509C22×C43—88no—
510C22×C43C2×2−1+414yes—
511C22×C43C2×2−1+412yes—
512C22×C43#58512yes—
513C22×C43#58512yes—
514C22×C43C2611yescharacteristic
515C2×D43—24no—
516C2×D43—24no—
517C2×D43—24no—
518C2×D43—48no—
519C4×C43—24no—
520C4×C43—22no—
521C4×C43—24no—
522C4×C43—24no—
523C4×C43—24no—
524C4×C43—24no—
525C4×C43—22no—
526Dic43—22no—
527Dic43—22no—
528Dic43—24no—
529Dic43—24no—
530Dic43—22no—
531Dic43—24no—
532Dic43—24no—
533Dic43—24no—
534Dic43—22no—
535#3564—4332no—
536C2×#563—432no—
537C2×#563—432no—
538C2×#556—432no—
539C2×#554—432no—
540C2×#552—432no—
541C2×#552—432no—
542C2×#551—432no—
543C2×#551—432no—
544C2×#544—431no—
545C2×#543D4311yescharacteristic, complemented
546C2×#542—432no—
547C2×#541—432no—
548C2×#541—432no—
549C2×#539—432no—
550C2×#539—431no—
551C2×#538—431no—
552C2×#533—431no—
553C2×#529—431no—
554C22×#126—431no—
555C2×C43—24no—
556C2×C43—44no—
557C2×C43#356414yescomplemented
558C2×C43C22×2−1+411yescharacteristic
559C2×C43C2×#58511yescharacteristic
560C2×C43C2×#58511yescharacteristic
561D43—44no—
562#563—4332no—
563#563—4332no—
564#556—4332no—
565#554—4332no—
566#552—4332no—
567#552—4332no—
568#551—4332no—
569#551—4332no—
570#544—4316no—
571#543C2×D43116yescomplemented
572#542—4332no—
573#541—4332no—
574#541—4332no—
575#539—4332no—
576#539—4316no—
577#538—4316no—
578#533—4316no—
579C2×C4⋊Q8—431no—
580C2×C4⋊Q8—432no—
581C2×C4⋊Q8—432no—
582C2×C4⋊Q8—431no—
583C2×C4⋊Q8—432no—
584#529—4316no—
585C2×#126—432no—
586C2×#126—432no—
587C2×#126—432no—
588C2×#126—432no—
589C2×#126—432no—
590C2×#126—432no—
591C2×#126—432no—
592C2×#126—432no—
593C2×#126—4316no—
594C2×#126—432no—
595C2×#126—432no—
596C2×#126—432no—
597C2×#126—432no—
598C2×#126—432no—
599C2×#125—431no—
600C2×#125—432no—
601C2×#125—432no—
602C2×#125—432no—
603C2×#125—432no—
604C2×#125—432no—
605C2×#125—432no—
606C2×#125—432no—
607C2×#125—432no—
608C2×#125—432no—
609C2×#124—431no—
610C2×#124—432no—
611C2×#124—432no—
612C2×#124—432no—
613C2×#123—432no—
614C2×#123—432no—
615C2×#123—432no—
616C2×#123—432no—
617C2×#123—432no—
618C2×#123—432no—
619C2×#123—432no—
620C2×#123—432no—
621C2×C22⋊Q8—432no—
622C2×C22⋊Q8—432no—
623C2×C22⋊Q8—432no—
624C2×C22⋊Q8—431no—
625C2×C22⋊Q8—432no—
626C2×C22⋊Q8—432no—
627C2×C22⋊Q8—432no—
628C2×C22⋊Q8—432no—
629C2×C22⋊Q8—432no—
630C2×C22⋊Q8—432no—
631C2×C22⋊Q8C2×D4311yescharacteristic
632C2×C22⋊Q8C2×D4311yescharacteristic
633C2×C22⋊Q8C2×D4312yes—
634C2×C22⋊Q8C2×D4312yes—
635C2×C22⋊Q8C2×D4312yes—
636C2×C22⋊Q8C2×D4312yes—
637C2×C22⋊Q8C2×D4312yes—
638C2×#121—431no—
639C2×#121—432no—
640C2×#120—432no—
641C2×C4×Q8—431no—
642C2×C4×Q8—431no—
643C2×C4×Q8—432no—
644C2×C4×Q8—432no—
645C2×C4×Q8—431no—
646C2×C4×Q8—432no—
647C2×C4×D4—432no—
648C2×C4×D4—432no—
649C2×C4×D4—432no—
650C2×C4×D4—431no—
651C2×C4×D4—432no—
652C2×C4×D4—432no—
653C2×#117—432no—
654C2×#117—432no—
655C2×#117—432no—
656C2×#117—432no—
657C2×#117—432no—
658C2×#117—432no—
659C22×C4⋊C4—431no—
660C22×C4⋊C4—431no—
661C22×C4⋊C4—431no—
662C22×C4⋊C4—432no—
663C22×C22⋊C4—431no—
664C22×C22⋊C4—431no—
665C22×C22⋊C4C2×D4311yescharacteristic
666C22×C22⋊C4C2×D4312yes—
667C22×C42—431no—
668C43C2×#356411yescharacteristic, complemented, Sylow
669C25C22×D4311yescharacteristic
670C22×Q8—432no—
671C22×Q8—432no—
672C22×Q8—431no—
673C22×Q8C22×D4311yescharacteristic
674C22×Q8C22×D4312yes—
675C22×Q8C22×D4311yescharacteristic
676C22×D4—432no—
677C22×D4—432no—
678C22×D4—432no—
679C22×D4—431no—
680C23×C4—431no—
681C23×C4—431no—
682C23×C4—431no—
683C23×C4—431no—
684C23×C4—432no—
685C23×C4—432no—
686C23×C4—432no—
687C23×C4C22×D4311yescharacteristic
688C23×C4C22×D4311yescharacteristic
689C23×C4C22×D4312yes—
690C23×C4C22×D4312yes—
691C4⋊Q8—438no—
692C4⋊Q8—4316no—
693C4⋊Q8—4316no—
694C4⋊Q8—438no—
695C4⋊Q8—4316no—
696#126—4316no—
697#126—4316no—
698#126—4316no—
699#126—4316no—
700#126—4316no—
701#126—4316no—
702#126—4316no—
703#126—4316no—
704#126—4316no—
705#126—4316no—
706#126—4316no—
707#126—4316no—
708#126—4316no—
709#125—438no—
710#125—4316no—
711#125—4316no—
712#125—4316no—
713#125—4316no—
714#125—4316no—
715#125—4316no—
716#125—4316no—
717#125—4316no—
718#125—4316no—
719#124—438no—
720#124—4316no—
721#124—4316no—
722#124—4316no—
723#123—4316no—
724#123—4316no—
725#123—4316no—
726#123—4316no—
727#123—4316no—
728#123—4316no—
729#123—4316no—
730#123—4316no—
731C22⋊Q8—4316no—
732C22⋊Q8—4316no—
733C22⋊Q8—4316no—
734C22⋊Q8—438no—
735C22⋊Q8—4316no—
736C22⋊Q8—4316no—
737C22⋊Q8—4316no—
738C22⋊Q8—4316no—
739C22⋊Q8—4316no—
740C22⋊Q8—4316no—
741C22⋊Q8C22×D4318yes—
742C22⋊Q8C22×D4318yes—
743C22⋊Q8C22×D43116yes—
744C22⋊Q8C22×D43116yes—
745C22⋊Q8C22×D43116yes—
746C22⋊Q8C22×D43116yes—
747C22⋊Q8C22×D43116yes—
748#121—438no—
749#121—4316no—
750#120—4316no—
751C4×Q8—438no—
752C4×Q8—438no—
753C4×Q8—4316no—
754C4×Q8—4316no—
755C4×Q8—438no—
756C4×Q8—4316no—
757C4×D4—4316no—
758C4×D4—4316no—
759C4×D4—4316no—
760C4×D4—438no—
761C4×D4—4316no—
762C4×D4—4316no—
763#117—4316no—
764#117—4316no—
765#117—4316no—
766#117—4316no—
767#117—4316no—
768#117—4316no—
769C2×C4⋊C4—432no—
770C2×C4⋊C4—432no—
771C2×C4⋊C4—432no—
772C2×C4⋊C4—432no—
773C2×C4⋊C4—432no—
774C2×C4⋊C4—432no—
775C2×C4⋊C4—432no—
776C2×C4⋊C4—432no—
777C2×C4⋊C4—438no—
778C2×C4⋊C4—438no—
779C2×C4⋊C4—438no—
780C2×C4⋊C4—432no—
781C2×C4⋊C4—432no—
782C2×C4⋊C4—432no—
783C2×C4⋊C4—432no—
784C2×C4⋊C4—432no—
785C2×C4⋊C4—432no—
786C2×C4⋊C4—432no—
787C2×C4⋊C4—432no—
788C2×C4⋊C4—432no—
789C2×C4⋊C4—432no—
790C2×C4⋊C4—432no—
791C2×C4⋊C4—432no—
792C2×C4⋊C4—432no—
793C2×C4⋊C4—431no—
794C2×C4⋊C4—432no—
795C2×C4⋊C4—431no—
796C2×C4⋊C4—432no—
797C2×C4⋊C4—432no—
798C2×C4⋊C4—4316no—
799C2×C4⋊C4C22×D4312yes—
800C2×C4⋊C4C22×D4312yes—
801C2×C4⋊C4C22×D4312yes—
802C2×C4⋊C4C22×D4311yescharacteristic
803C2×C4⋊C4C22×D4312yes—
804C2×C4⋊C4C22×D4312yes—
805C2×C4⋊C4C22×D4311yescharacteristic
806C2×C22⋊C4—432no—
807C2×C22⋊C4—432no—
808C2×C22⋊C4—432no—
809C2×C22⋊C4—432no—
810C2×C22⋊C4—438no—
811C2×C22⋊C4—438no—
812C2×C22⋊C4—432no—
813C2×C22⋊C4—432no—
814C2×C22⋊C4—432no—
815C2×C22⋊C4—432no—
816C2×C22⋊C4—432no—
817C2×C22⋊C4—432no—
818C2×C22⋊C4—432no—
819C2×C22⋊C4—432no—
820C2×C22⋊C4—432no—
821C2×C22⋊C4—432no—
822C2×C22⋊C4—432no—
823C2×C22⋊C4C22×D4312yes—
824C2×C22⋊C4C22×D4312yes—
825C2×C22⋊C4C22×D4312yes—
826C2×C22⋊C4C22×D4312yes—
827C2×C22⋊C4C22×D4312yes—
828C2×C22⋊C4C22×D4312yes—
829C2×C22⋊C4C22×D4318yes—
830C2×C22⋊C4C22×D43116yes—
831C2×C42—432no—
832C2×C42—432no—
833C2×C42—432no—
834C2×C42—432no—
835C2×C42—431no—
836C2×C42—432no—
837C2×C42—432no—
838C2×C42—432no—
839C2×C42—431no—
840C2×C42—431no—
841C2×C42—431no—
842C2×C42—438no—
843C24—24no—
844C24—42no—
845C24—42no—
846C24—432no—
847C24C23×D4312yes—
848C24C23×D4311yescharacteristic
849C24C23×D4314yes—
850C2×Q8—42no—
851C2×Q8—44no—
852C2×Q8—42no—
853C2×Q8—438no—
854C2×Q8—438no—
855C2×Q8—434no—
856C2×Q8—1724no—
857C2×Q8—1724no—
858C2×Q8—1722no—
859C2×Q8C23×D4314yes—
860C2×Q8C23×D4318yes—
861C2×Q8C23×D4314yes—
862C2×D4—438no—
863C2×D4—438no—
864C2×D4—438no—
865C2×D4—434no—
866C2×D4—868no—
867C2×D4—1722no—
868C2×D4—1724no—
869C2×D4—1724no—
870C22×C4—42no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—42no—
874C22×C4—434no—
875C22×C4—434no—
876C22×C4—431no—
877C22×C4—431no—
878C22×C4—432no—
879C22×C4—432no—
880C22×C4—432no—
881C22×C4—431no—
882C22×C4—431no—
883C22×C4—432no—
884C22×C4—432no—
885C22×C4—434no—
886C22×C4—434no—
887C22×C4—438no—
888C22×C4—438no—
889C22×C4—438no—
890C22×C4—864no—
891C22×C4—864no—
892C22×C4—1724no—
893C22×C4—1724no—
894C22×C4—1724no—
895C22×C4—1722no—
896C22×C4—1722no—
897C22×C4C23×D4312yes—
898C22×C4C23×D4312yes—
899C22×C4C23×D4311yescharacteristic
900C22×C4C23×D4311yescharacteristic
901C22×C4C23×D4312yes—
902C22×C4C23×D4312yes—
903C22×C4C23×D4312yes—
904C22×C4C23×D4314yes—
905C22×C4C23×D4314yes—
906C22×C4C23×D4318yes—
907C22×C4C23×D4318yes—
908C4⋊C4—438no—
909C4⋊C4—438no—
910C4⋊C4—438no—
911C4⋊C4—438no—
912C4⋊C4—438no—
913C4⋊C4—438no—
914C4⋊C4—438no—
915C4⋊C4—438no—
916C4⋊C4—438no—
917C4⋊C4—438no—
918C4⋊C4—438no—
919C4⋊C4—438no—
920C4⋊C4—438no—
921C4⋊C4—438no—
922C4⋊C4—438no—
923C4⋊C4—438no—
924C4⋊C4—438no—
925C4⋊C4—438no—
926C4⋊C4—438no—
927C4⋊C4—438no—
928C4⋊C4—438no—
929C4⋊C4—434no—
930C4⋊C4—438no—
931C4⋊C4—434no—
932C4⋊C4—438no—
933C4⋊C4—438no—
934C4⋊C4C23×D4318yes—
935C4⋊C4C23×D4318yes—
936C4⋊C4C23×D4318yes—
937C4⋊C4C23×D4314yes—
938C4⋊C4C23×D4318yes—
939C4⋊C4C23×D4318yes—
940C4⋊C4C23×D4314yes—
941C22⋊C4—438no—
942C22⋊C4—438no—
943C22⋊C4—438no—
944C22⋊C4—438no—
945C22⋊C4—438no—
946C22⋊C4—438no—
947C22⋊C4—438no—
948C22⋊C4—438no—
949C22⋊C4—438no—
950C22⋊C4—438no—
951C22⋊C4—438no—
952C22⋊C4—438no—
953C22⋊C4—438no—
954C22⋊C4—438no—
955C22⋊C4—438no—
956C22⋊C4C23×D4318yes—
957C22⋊C4C23×D4318yes—
958C22⋊C4C23×D4318yes—
959C22⋊C4C23×D4318yes—
960C22⋊C4C23×D4318yes—
961C22⋊C4C23×D4318yes—
962C42—434no—
963C42—434no—
964C42—434no—
965C42—434no—
966C42—438no—
967C42—438no—
968C42—438no—
969C42—438no—
970C42—438no—
971C42—438no—
972C42—438no—
973C23—22no—
974C23—22no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—28no—
979C23—44no—
980C23—44no—
981C23—88no—
982C23—434no—
983C23—864no—
984C23—864no—
985C23—864no—
986C23#1306337314yes—
987C23C24×D4314yes—
988C23C24×D4312yes—
989C23C24×D4311yescharacteristic
990Q8—44no—
991Q8—48no—
992Q8—44no—
993Q8—1728no—
994Q8—1728no—
995Q8—1724no—
996D4—8616no—
997D4—1724no—
998D4—1728no—
999D4—1728no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—44no—
1008C2×C4—48no—
1009C2×C4—48no—
1010C2×C4—44no—
1011C2×C4—432no—
1012C2×C4—432no—
1013C2×C4—434no—
1014C2×C4—434no—
1015C2×C4—432no—
1016C2×C4—434no—
1017C2×C4—432no—
1018C2×C4—434no—
1019C2×C4—434no—
1020C2×C4—868no—
1021C2×C4—868no—
1022C2×C4—862no—
1023C2×C4—864no—
1024C2×C4—862no—
1025C2×C4—864no—
1026C2×C4—862no—
1027C2×C4—864no—
1028C2×C4—864no—
1029C2×C4—862no—
1030C2×C4—864no—
1031C2×C4—1728no—
1032C2×C4—1728no—
1033C2×C4—1728no—
1034C2×C4—1724no—
1035C2×C4—1724no—
1036C2×C4C24×D4312yes—
1037C2×C4C24×D4314yes—
1038C2×C4C24×D4314yes—
1039C2×C4C24×D4312yes—
1040C2×C4C24×D4314yes—
1041C2×C4C24×D4314yes—
1042C2×C4C24×D4314yes—
1043C22—22no—
1044C22—22no—
1045C22—28no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—48no—
1050C22—88no—
1051C22—864no—
1052C22—864no—
1053C22—864no—
1054C22—1728no—
1055C22C2×#1306337314yes—
1056C22C2×#1306337312yes—
1057C22#1458373412yes—
1058C22#1458373412yes—
1059C22C25×D4311yescharacteristic
1060C4—24no—
1061C4—24no—
1062C4—24no—
1063C4—22no—
1064C4—24no—
1065C4—24no—
1066C4—22no—
1067C4—862no—
1068C4—862no—
1069C4—864no—
1070C4—864no—
1071C4—862no—
1072C4—864no—
1073C4—864no—
1074C4—862no—
1075C4—864no—
1076C2—24no—
1077C2—44no—
1078C2—1724no—
1079C2#1914920914yesdirect product factor
1080C2C22×#1306337311yescharacteristic
1081C2C2×#1458373411yescharacteristic
1082C2C2×#1458373411yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#543C2
socleC23×C43C25
prime radicalC2×#14583487C2
hypercenterC2×#543D43
hypocenterC43C2×#3564
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
1. #19149209C2direct (N × H)
2. C2×#14583650C2semidirect
3. C2×#14583650C2semidirect
4. C2×#14583620C2semidirect
5. C2×#14583603C2semidirect
6. C2×#14583591C2semidirect
7. C2×#14583583C2semidirect
8. C2×#14583575C2semidirect
9. C2×#14583575C2semidirect
10. C2×#14583528C2semidirect
11. C2×#14583519C2semidirect
12. C2×#14583509C2semidirect
13. C2×#14583509C2semidirect
14. C2×#14583498C2semidirect
15. C2×#14583495C2semidirect
17. C2×#14583451C2semidirect
18. C2×#14583435C2semidirect
19. C22×#13063318C2semidirect
20. C2×C43×#543C2semidirect
21. #14583650C22semidirect
22. #14583650C22semidirect
23. #14583620C22semidirect
24. #14583603C22semidirect
25. #14583591C22semidirect
26. #14583583C22semidirect
27. #14583575C22semidirect
28. #14583575C22semidirect
29. #14583528C22semidirect
30. #14583519C22semidirect
31. #14583509C22semidirect
32. #14583509C22semidirect
33. #14583498C22semidirect
34. #14583495C22semidirect
36. #14583451C22semidirect
37. C2×#13063324C22semidirect
38. C2×#13063324C22semidirect
39. C2×#13063323C22semidirect
40. C2×#13063323C22semidirect
41. C2×#13063323C22semidirect
42. #14583435C22semidirect
43. C2×#13063320C22semidirect
44. C2×#13063320C22semidirect
45. C2×#13063320C22semidirect
46. C2×#13063320C22semidirect
56. C2×#13063318C22semidirect
57. C2×#13063316C22semidirect
58. C2×#13063316C22semidirect
59. C2×#13063316C22semidirect
60. C2×#13063316C22semidirect
61. C2×#13063316C22semidirect
62. C2×#13063315C22semidirect
63. C2×#13063315C22semidirect
64. C2×#13063315C22semidirect
65. C2×#13063315C22semidirect
66. C2×#13063315C22semidirect
67. C2×#13063314C22semidirect
71. C2×#13063310C22semidirect
82. C2×#13063303C22semidirect
83. C2×#13063303C22semidirect
86. C2×#13063301C22semidirect
87. C2×#13063301C22semidirect
88. C2×#13063301C22semidirect
92. C2×Q8×Dic43C22semidirect
93. C2×Q8×Dic43C22semidirect
94. C2×Q8×Dic43C22semidirect
95. C2×#13063290C22semidirect
96. C2×#13063290C22semidirect
97. C2×#13063290C22semidirect
98. C2×#13063287C22semidirect
106. C2×#13063283C22semidirect
107. C2×#13063283C22semidirect
113. C2×C4⋊C4×D43C22semidirect
117. C43×#543C22semidirect
141. #13063324C23semidirect
142. #13063324C23semidirect
143. #13063323C23semidirect
144. #13063323C23semidirect
145. #13063323C23semidirect
146. #13063320C23semidirect
147. #13063320C23semidirect
148. #13063320C23semidirect
149. #13063320C23semidirect
159. #13063316C23semidirect
160. #13063316C23semidirect
161. #13063316C23semidirect
162. #13063316C23semidirect
163. #13063316C23semidirect
164. #13063315C23semidirect
165. #13063315C23semidirect
166. #13063315C23semidirect
167. #13063315C23semidirect
168. #13063315C23semidirect
169. #13063314C23semidirect
173. #13063310C23semidirect
184. #13063303C23semidirect
185. #13063303C23semidirect
188. #13063301C23semidirect
189. #13063301C23semidirect
190. #13063301C23semidirect
194. Q8×Dic43C23semidirect
195. Q8×Dic43C23semidirect
196. Q8×Dic43C23semidirect
197. #13063290C23semidirect
198. #13063290C23semidirect
199. #13063290C23semidirect
200. #13063287C23semidirect
208. #13063283C23semidirect
209. #13063283C23semidirect
241. C4⋊C4×D43C23semidirect
545. C2×#543D43semidirect
557. C2×C43#3564semidirect
571. #543C2×D43semidirect
668. C43C2×#3564semidirect
1079. C2#19149209direct (N × H)

Maximal subgroups

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

subgroupindex
#191492092
C2×#145836502
C2×#145836202
C2×#145836032
C2×#145835912
C2×#145835832
C2×#145835752
C2×#145835282
C2×#145835192
C2×#145835092
C2×#145834982
C2×#145834952
C2×#145834872
C2×#145834512
C2×#145834352
C22×#130633182
C2×C43×#5432
C2×#356443