Finite Group Databasebeta

← C2×#19148992 #26004388

Subgroups — C2×#19148992 #26004388

Order 11008.

7810 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148992C2132yesmaximal, direct product factor
2C2×#14583646C214yesmaximal, complemented
3C2×#14583607C212yesmaximal, complemented
4C2×#14583604C212yesmaximal, complemented
5C2×#14583568C212yesmaximal, complemented
6C2×#14583567C212yesmaximal, complemented
7C2×#14583554C211yesmaximal, characteristic, complemented
8C2×#14583553C211yesmaximal, characteristic, complemented
9C2×#14583552C211yesmaximal, characteristic, complemented
10C2×#14583501C214yesmaximal, complemented
11C2×#14583480C212yesmaximal, complemented
12C2×#14583479C212yesmaximal, complemented
13C2×#14583478C212yesmaximal, complemented
14C2×#14583477C212yesmaximal, complemented
15C2×#14583454C211yesmaximal, characteristic, complemented
16C2×#14583446C211yesmaximal, characteristic, complemented
17C2×#14583446C211yesmaximal, characteristic, complemented
18C2×C43×#547C211yesmaximal, characteristic, complemented
19C22×#10621902C2212yes—
20C22×#10621898C2212yes—
21C22×#10621898C2212yes—
22C22×#10621898C2212yes—
23C22×#10621900C2212yes—
24#14583646C22164yescomplemented
25#14583607C22132yescomplemented
26#14583604C22132yescomplemented
27#14583568C22132yescomplemented
28#14583567C22132yescomplemented
29#14583554C22116yescomplemented
30#14583553C22116yescomplemented
31#14583552C22116yescomplemented
32#14583501C22164yescomplemented
33#14583480C22132yescomplemented
34#14583479C22132yescomplemented
35#14583478C22132yescomplemented
36#14583477C22132yescomplemented
37#14583454C22116yescomplemented
38#14583446C22116yescomplemented
39#14583446C22116yescomplemented
40C2×#13063325C2211yescharacteristic
41C2×#13063324C2211yescharacteristic
42C2×#13063324C2211yescharacteristic
43C2×#13063321C2211yescharacteristic
44C2×#13063321C2214yes—
45C2×#13063321C2211yescharacteristic
46C2×#13063316C2212yes—
47C2×#13063315C2214yes—
48C2×#13063311C2212yes—
49C2×#13063311C2212yes—
50C2×#13063310C2214yes—
51C2×#13063309C2214yes—
52C2×#13063307C2214yes—
53C2×#13063305C2212yes—
54C2×#13063305C2214yes—
55C2×#13063305C2212yes—
56C2×#13063304C2212yes—
57C2×#13063304C2214yes—
58C2×#13063303C2214yes—
59C2×#13063302C2214yes—
60C2×#13063301C2212yes—
61C2×#13063301C2212yes—
62C2×#13063300C2212yes—
63C2×#13063300C2211yescharacteristic
64C2×#13063300C2211yescharacteristic
65C2×#13063300C2214yes—
66C2×#13063299C2212yes—
67C2×#13063299C2214yes—
68C2×#13063299C2214yes—
69C2×#13063298C2214yes—
70C2×#13063298C2212yes—
71C2×#13063298C2212yes—
72C2×#13063298C2214yes—
73C2×#13063297C2214yes—
74C2×#13063297C2214yes—
75C2×#13063296C2212yes—
76C2×#13063296C2214yes—
77C2×#13063296C2211yescharacteristic
78C2×#13063296C2211yescharacteristic
79C2×Q8×Dic43C2212yes—
80C2×#13063290C2212yes—
81C2×C4×D172C2211yescharacteristic
82C2×C4×D172C2211yescharacteristic
83C2×C4×C22⋊D43C2212yes—
84C2×C4×C22⋊D43C2214yes—
85C2×C4×C22⋊D43C2212yes—
86C2×(C22⋊D43)⋊C4C2214yes—
87C2×#13063283C2212yes—
88C22×C4⋊Dic43C2212yes—
89C2×C4⋊C4×D43C2212yes—
90C2×C4⋊C4×D43C2212yes—
91C2×C42×D43C2211yescharacteristic
92C22×#41×C43C2212yes—
93C43×#547C22116yescomplemented
94C2×C4⋊Q8×C43C2211yescharacteristic
95C2×#123×C43C2214yes—
96C2×C22⋊Q8×C43C2212yes—
97C2×#121×C43C2212yes—
98C2×C4×D4×C43C2211yescharacteristic
99C2×C4×D4×C43C2211yescharacteristic
100C22×C4⋊C4×C43C2212yes—
101C2×#10621902—48no—
102C2×#10621902C23116yes—
103C2×#10621898—48no—
104C2×#10621898—48no—
105C2×#10621898—48no—
106C2×#10621898C23116yes—
107C2×#10621898C23116yes—
108C2×#10621898C23116yes—
109C2×#10621900—48no—
110C2×#10621900C23116yes—
111C22×Dic86C2312yes—
112C22×Dic86C2312yes—
113C22×Dic86C2312yes—
114C22×D172C2311yescharacteristic
115C22×D172C2311yescharacteristic
116C22×D172C2312yes—
117C22×D172C2312yes—
118C22×D172C2314yes—
119C22×C22⋊D43C2312yes—
120C22×C22⋊D43C2312yes—
121C22×C22⋊D43C2312yes—
122C22×C22⋊D43C2312yes—
123C22×C22⋊D43C2312yes—
124C22×C22⋊D43C2314yes—
125C22×C22⋊D43C2314yes—
126C22×C22⋊D43C2312yes—
127C23×Dic43C2314yes—
128C22×C4×D43C2311yescharacteristic
129C22×C4×D43C2311yescharacteristic
130C22×C4×D43C2311yescharacteristic
131C22×C4×D43C2312yes—
132C22×C4×D43C2312yes—
133C22×C4×D43C2314yes—
134C22×C4×D43C2314yes—
135#13063325C2318yes—
136#13063324C2318yes—
137#13063324C2318yes—
138#13063321C2318yes—
139#13063321C23132yes—
140#13063321C2318yes—
141#13063316C23116yes—
142#13063315C23132yes—
143#13063311C23116yes—
144#13063311C23116yes—
145#13063310C23132yes—
146#13063309C23132yes—
147#13063307C23132yes—
148#13063305C23116yes—
149#13063305C23132yes—
150#13063305C23116yes—
151#13063304C23116yes—
152#13063304C23132yes—
153#13063303C23132yes—
154#13063302C23132yes—
155#13063301C23116yes—
156#13063301C23116yes—
157#13063300C23116yes—
158#13063300C2318yes—
159#13063300C2318yes—
160#13063300C23132yes—
161#13063299C23116yes—
162#13063299C23132yes—
163#13063299C23132yes—
164#13063298C23132yes—
165#13063298C23116yes—
166#13063298C23116yes—
167#13063298C23132yes—
168#13063297C23132yes—
169#13063297C23132yes—
170#13063296C23116yes—
171#13063296C23132yes—
172#13063296C2318yes—
173#13063296C2318yes—
174Q8×Dic43C23116yes—
175#13063290C23116yes—
176C4×D172C2318yes—
177C4×D172C2318yes—
178C4×C22⋊D43C23116yes—
179C4×C22⋊D43C23132yes—
180C4×C22⋊D43C23116yes—
181(C22⋊D43)⋊C4C23132yes—
182#13063283C23116yes—
183C2×C4⋊Dic43C23116yes—
184C2×C4⋊Dic43C2311yescharacteristic
185C2×C4⋊Dic43C2312yes—
186C2×C4⋊Dic43C2311yescharacteristic
187C2×C4⋊Dic43C2314yes—
188C2×C4⋊Dic43C2312yes—
189C2×C4⋊Dic43C2314yes—
190C2×Dic43⋊C4C2314yes—
191C2×Dic43⋊C4C2314yes—
192C2×Dic43⋊C4C2312yes—
193C2×Dic43⋊C4C2312yes—
194C2×Dic43⋊C4C2314yes—
195C4⋊C4×D43C23116yes—
196C4⋊C4×D43C23116yes—
197C2×C22⋊Dic43C2312yes—
198C2×C22⋊Dic43C2314yes—
199C2×C22⋊Dic43C2312yes—
200C2×(C2×D43)⋊C4C2314yes—
201C2×(C2×D43)⋊C4C2314yes—
202C2×(C2×D43)⋊C4C2312yes—
203C2×(C2×D43)⋊C4C2314yes—
204C2×(C2×D43)⋊C4C2312yes—
205C2×(C2×D43)⋊C4C2312yes—
206C2×(C2×D43)⋊C4C2312yes—
207C2×C4×Dic43C2311yescharacteristic
208C2×C4×Dic43C2311yescharacteristic
209C2×C4×Dic43C2311yescharacteristic
210C2×C4×Dic43C2314yes—
211C42×D43C2318yes—
212C2×#41×C43—48no—
213C2×#41×C43C23116yes—
214C22×Q8×C43C2312yes—
215C22×D4×C43C2311yescharacteristic
216C22×D4×C43C2311yescharacteristic
217C22×D4×C43C2314yes—
218C23×C4×C43C2312yes—
219C23×C4×C43C2312yes—
220C23×C4×C43C2314yes—
221C4⋊Q8×C43C2318yes—
222#123×C43C23132yes—
223C22⋊Q8×C43C23116yes—
224#121×C43C23116yes—
225C4×D4×C43C2318yes—
226C4×D4×C43C2318yes—
227C2×C4⋊C4×C43C2311yescharacteristic
228C2×C4⋊C4×C43C2312yes—
229C2×C4⋊C4×C43C2314yes—
230C2×C4⋊C4×C43C23116yes—
231C2×C4⋊C4×C43C2311yescharacteristic
232C2×C4⋊C4×C43C2312yes—
233C2×C22⋊C4×C43C2312yes—
234C2×C22⋊C4×C43C2312yes—
235C2×C22⋊C4×C43C2314yes—
236C2×C42×C43C2311yescharacteristic
237C24×C43C2412yes—
238C24×C43C2412yes—
239C23×D43C2412yes—
240C23×D43C2411yescharacteristic
241C23×D43C2412yes—
242#41×C43—432no—
243C2×Q8×C43—28no—
244C2×Q8×C43C2418yes—
245C2×D4×C43—24no—
246C2×D4×C43—24no—
247C2×D4×C43—48no—
248C2×D4×C43C2414yes—
249C2×D4×C43C2414yes—
250C2×D4×C43C24116yes—
251C22×C4×C43—28no—
252C22×C4×C43—28no—
253C22×C4×C43—48no—
254C22×C4×C43C2411yescharacteristic
255C22×C4×C43C2412yes—
256C22×C4×C43C2412yes—
257C22×C4×C43C2414yes—
258C22×C4×C43C2418yes—
259C22×C4×C43C2418yes—
260C22×C4×C43C24116yes—
261C22×C4×C43C2411yescharacteristic
262C22×C4×C43C2411yescharacteristic
263C2×C22⋊D43—28no—
264C2×C22⋊D43—28no—
265C2×C22⋊D43—48no—
266C2×C22⋊D43—44no—
267C2×C22⋊D43—44no—
268C2×C22⋊D43—44no—
269C2×C22⋊D43—44no—
270C2×C22⋊D43—48no—
271C2×C22⋊D43C2418yes—
272C2×C22⋊D43C2418yes—
273C2×C22⋊D43C2418yes—
274C2×C22⋊D43C2418yes—
275C2×C22⋊D43C2418yes—
276C2×C22⋊D43C24116yes—
277C2×C22⋊D43C24116yes—
278C2×C22⋊D43C2418yes—
279C22×Dic43—48no—
280C22×Dic43C2411yescharacteristic
281C22×Dic43C2411yescharacteristic
282C22×Dic43C2414yes—
283C22×Dic43C2412yes—
284C22×Dic43C2412yes—
285C22×Dic43C24116yes—
286C22×Dic43C2411yescharacteristic
287#10621902—432no—
288#10621900—432no—
289#10621898—432no—
290#10621898—432no—
291#10621898—432no—
292C2×D172—24no—
293C2×D172—24no—
294C2×D172—44no—
295C2×D172—44no—
296C2×D172—48no—
297C2×D172C2414yes—
298C2×D172C2414yes—
299C2×D172C2418yes—
300C2×D172C2418yes—
301C2×D172C24116yes—
302C2×C4×D43—28no—
303C2×C4×D43—24no—
304C2×C4×D43—24no—
305C2×C4×D43—28no—
306C2×C4×D43—24no—
307C2×C4×D43—48no—
308C2×C4×D43—48no—
309C2×C4×D43C2414yes—
310C2×C4×D43C2414yes—
311C2×C4×D43C2414yes—
312C2×C4×D43C2418yes—
313C2×C4×D43C2418yes—
314C2×C4×D43C24116yes—
315C2×C4×D43C24116yes—
316C2×Dic86—28no—
317C2×Dic86—44no—
318C2×Dic86—44no—
319C2×Dic86C2418yes—
320C2×Dic86C2418yes—
321C2×Dic86C2418yes—
322C4⋊C4×C43C2414yes—
323C4⋊C4×C43C2418yes—
324C4⋊C4×C43C24116yes—
325C4⋊C4×C43C2414yes—
326C4⋊C4×C43C2418yes—
327C22⋊C4×C43C2418yes—
328C22⋊C4×C43C2418yes—
329C22⋊C4×C43C24116yes—
330C42×C43C2414yes—
331C22⋊Dic43C2418yes—
332C22⋊Dic43C24116yes—
333C22⋊Dic43C2418yes—
334(C2×D43)⋊C4C24116yes—
335(C2×D43)⋊C4C24116yes—
336(C2×D43)⋊C4C2418yes—
337(C2×D43)⋊C4C24116yes—
338(C2×D43)⋊C4C2418yes—
339(C2×D43)⋊C4C2418yes—
340(C2×D43)⋊C4C2418yes—
341C4⋊Dic43C2414yes—
342C4⋊Dic43C2418yes—
343C4⋊Dic43C2414yes—
344C4⋊Dic43C24116yes—
345C4⋊Dic43C2418yes—
346C4⋊Dic43C24116yes—
347Dic43⋊C4C24116yes—
348Dic43⋊C4C24116yes—
349Dic43⋊C4C2418yes—
350Dic43⋊C4C2418yes—
351Dic43⋊C4C24116yes—
352C4×Dic43C2414yes—
353C4×Dic43C2414yes—
354C4×Dic43C2414yes—
355C4×Dic43C24116yes—
356C23×C43—24no—
357C23×C43—24no—
358C23×C43—24no—
359C23×C43—24no—
360C23×C43—24no—
361C23×C43—24no—
362C23×C43C2514yes—
363C23×C43C2514yes—
364C23×C43C2511yescharacteristic
365C22×D43—24no—
366C22×D43—22no—
367C22×D43—22no—
368C22×D43—24no—
369C22×D43—24no—
370C22×D43—24no—
371C22×D43—22no—
372C22×D43—24no—
373C22×D43—24no—
374C22×D43C2514yes—
375C22×D43C2512yes—
376C22×D43C2514yes—
377Q8×C43—216no—
378D4×C43—28no—
379D4×C43—28no—
380D4×C43—416no—
381C2×C4×C43—24no—
382C2×C4×C43—24no—
383C2×C4×C43—28no—
384C2×C4×C43—22no—
385C2×C4×C43—216no—
386C2×C4×C43—216no—
387C2×C4×C43—416no—
388C2×C4×C43H(5,𝔽2)14yes—
389C2×C4×C43H(5,𝔽2)14yes—
390C2×C4×C43C2518yes—
391C2×C4×C43C2512yes—
392C2×C4×C43C2514yes—
393C2×C4×C43C2514yes—
394C2×C4×C43C2512yes—
395C2×C4×C43C2512yes—
396C22⋊D43—216no—
397C22⋊D43—216no—
398C22⋊D43—416no—
399C22⋊D43—48no—
400C22⋊D43—48no—
401C22⋊D43—48no—
402C22⋊D43—48no—
403C22⋊D43—416no—
404C2×Dic43—28no—
405C2×Dic43—22no—
406C2×Dic43—22no—
407C2×Dic43—24no—
408C2×Dic43—24no—
409C2×Dic43—416no—
410C2×Dic432−1+414yes—
411C2×Dic43C2512yes—
412C2×Dic43C2512yes—
413C2×Dic43C2518yes—
414C2×Dic43C2514yes—
415C2×Dic43C2514yes—
416C2×Dic43C2512yes—
417D172—28no—
418D172—28no—
419D172—48no—
420D172—48no—
421D172—416no—
422C4×D43—28no—
423C4×D43—28no—
424C4×D43—216no—
425C4×D43—216no—
426C4×D43—28no—
427C4×D43—416no—
428C4×D43—416no—
429Dic86—216no—
430Dic86—48no—
431Dic86—48no—
432C2×#3548—431nomaximal, Sylow
433C22×C43—24no—
434C22×C43—24no—
435C22×C43—24no—
436C22×C43—24no—
437C22×C43—24no—
438C22×C43—24no—
439C22×C43—48no—
440C22×C43—48no—
441C22×C43C2×H(5,𝔽2)12yes—
442C22×C43C2×H(5,𝔽2)12yes—
443C22×C43C2×2−1+412yes—
444C22×C43C2611yescharacteristic
445C2×D43—24no—
446C2×D43—22no—
447C2×D43—22no—
448C2×D43—24no—
449C2×D43—24no—
450C2×D43—24no—
451C2×D43—22no—
452C2×D43—24no—
453C2×D43—24no—
454C2×D43—48no—
455C2×D43—44no—
456C2×D43—48no—
457C4×C43—24no—
458C4×C43—24no—
459C4×C43—28no—
460C4×C43—22no—
461C4×C43C2×H(5,𝔽2)14yes—
462C4×C43C2×H(5,𝔽2)14yes—
463Dic43—28no—
464Dic43—22no—
465Dic43—22no—
466Dic43—24no—
467Dic43—24no—
468Dic43C2×2−1+414yes—
469#3548—4332no—
470C2×#562—434no—
471C2×#554—432no—
472C2×#554—432no—
473C2×#550—432no—
474C2×#550—432no—
475C2×#547—431no—
476C2×#547—431no—
477C2×#547—431no—
478C2×#547D4311yescharacteristic, complemented
479C2×#540—434no—
480C2×#537—432no—
481C2×#537—432no—
482C2×#537—432no—
483C2×#537—432no—
484C2×#533—431no—
485C2×#532—431no—
486C2×#532—431no—
487C2×C43—44no—
488C2×C43—44no—
489C2×C43#354814yescomplemented
490C2×C43C22×H(5,𝔽2)11yescharacteristic
491C2×C43C22×H(5,𝔽2)11yescharacteristic
492C2×C43C22×2−1+411yescharacteristic
493D43—44no—
494D43—42no—
495D43—44no—
496C22×#41—432no—
497C22×#41—432no—
498C22×#41—432no—
499C22×#41—432no—
500C22×#41—432no—
501C22×#41C2×D4312yes—
502#562—4364no—
503#554—4332no—
504#554—4332no—
505#550—4332no—
506#550—4332no—
507#547—4316no—
508#547—4316no—
509#547—4316no—
510#547C2×D43116yescomplemented
511#540—4364no—
512#537—4332no—
513#537—4332no—
514#537—4332no—
515#537—4332no—
516#533—4316no—
517#532—4316no—
518#532—4316no—
519C2×C4⋊Q8—431no—
520C2×C4⋊Q8—431no—
521C2×C4⋊Q8—431no—
522C2×C4⋊Q8C2×D4311yescharacteristic
523C2×#127—431no—
524C2×#127—431no—
525C2×#127—434no—
526C2×#125—432no—
527C2×#125—434no—
528C2×#124—432no—
529C2×#124—432no—
530C2×#123—434no—
531C2×#123—434no—
532C2×#123—434no—
533C2×#123C2×D4314yes—
534C2×C22⋊Q8—432no—
535C2×C22⋊Q8—432no—
536C2×C22⋊Q8—432no—
537C2×C22⋊Q8—434no—
538C2×C22⋊Q8—434no—
539C2×C22⋊Q8—432no—
540C2×C22⋊Q8—432no—
541C2×C22⋊Q8—434no—
542C2×C22⋊Q8—434no—
543C2×C22⋊Q8C2×D4312yes—
544C2×#121—431no—
545C2×#121—431no—
546C2×#121—432no—
547C2×#121—434no—
548C2×#121—434no—
549C2×#121—434no—
550C2×#121—434no—
551C2×#121—432no—
552C2×#121—434no—
553C2×#121—431no—
554C2×#121—431no—
555C2×#121—434no—
556C2×#121—432no—
557C2×#121—432no—
558C2×#121—432no—
559C2×#121—434no—
560C2×#121—434no—
561C2×#121C2×D4312yes—
562C2×C4×Q8—432no—
563C2×C4×Q8—432no—
564C2×C4×D4—432no—
565C2×C4×D4—432no—
566C2×C4×D4—434no—
567C2×C4×D4—434no—
568C2×C4×D4—431no—
569C2×C4×D4—431no—
570C2×C4×D4C2×D4311yescharacteristic
571C2×C4×D4C2×D4311yescharacteristic
572C2×#117—432no—
573C22×C4⋊C4—432no—
574C22×C4⋊C4—432no—
575C22×C4⋊C4—432no—
576C22×C4⋊C4C2×D4312yes—
577C22×C42—431no—
578C43C2×#354811yescharacteristic, complemented, Sylow
579C2×#41—48no—
580C2×#41—4316no—
581C2×#41—4316no—
582C2×#41—4316no—
583C2×#41—4316no—
584C2×#41—4316no—
585C2×#41—1728no—
586C2×#41—1728no—
587C2×#41—1728no—
588C2×#41—1728no—
589C2×#41—1728no—
590C2×#41C22×D43116yes—
591C22×Q8—432no—
592C22×Q8—432no—
593C22×Q8—432no—
594C22×Q8C22×D4312yes—
595C22×D4—432no—
596C22×D4—432no—
597C22×D4—432no—
598C22×D4—432no—
599C22×D4—434no—
600C22×D4—434no—
601C22×D4—432no—
602C22×D4—432no—
603C22×D4—431no—
604C22×D4—431no—
605C22×D4—432no—
606C22×D4—432no—
607C22×D4—434no—
608C22×D4C22×D4311yescharacteristic
609C22×D4C22×D4311yescharacteristic
610C22×D4C22×D4314yes—
611C23×C4—434no—
612C23×C4—432no—
613C23×C4—432no—
614C23×C4—431no—
615C23×C4—431no—
616C23×C4—431no—
617C23×C4—434no—
618C23×C4—434no—
619C23×C4C22×D4312yes—
620C23×C4C22×D4312yes—
621C23×C4C22×D4314yes—
622C4⋊Q8—438no—
623C4⋊Q8—438no—
624C4⋊Q8—438no—
625C4⋊Q8C22×D4318yes—
626#127—438no—
627#127—438no—
628#127—4332no—
629#125—4316no—
630#125—4332no—
631#124—4316no—
632#124—4316no—
633#123—4332no—
634#123—4332no—
635#123—4332no—
636#123C22×D43132yes—
637C22⋊Q8—4316no—
638C22⋊Q8—4316no—
639C22⋊Q8—4316no—
640C22⋊Q8—4332no—
641C22⋊Q8—4316no—
642C22⋊Q8—4316no—
643C22⋊Q8—4332no—
644C22⋊Q8—4332no—
645C22⋊Q8—4332no—
646C22⋊Q8C22×D43116yes—
647#121—438no—
648#121—438no—
649#121—4332no—
650#121—4316no—
651#121—4332no—
652#121—4332no—
653#121—4332no—
654#121—4316no—
655#121—4332no—
656#121—438no—
657#121—438no—
658#121—4332no—
659#121—4316no—
660#121—4316no—
661#121—4316no—
662#121—4332no—
663#121—4332no—
664#121C22×D43116yes—
665C4×Q8—4316no—
666C4×Q8—4316no—
667C4×D4—4316no—
668C4×D4—4316no—
669C4×D4—4332no—
670C4×D4—4332no—
671C4×D4—438no—
672C4×D4—438no—
673C4×D4C22×D4318yes—
674C4×D4C22×D4318yes—
675#117—4316no—
676C2×C4⋊C4—431no—
677C2×C4⋊C4—431no—
678C2×C4⋊C4—432no—
679C2×C4⋊C4—434no—
680C2×C4⋊C4—434no—
681C2×C4⋊C4—434no—
682C2×C4⋊C4—4316no—
683C2×C4⋊C4—432no—
684C2×C4⋊C4—432no—
685C2×C4⋊C4—432no—
686C2×C4⋊C4—434no—
687C2×C4⋊C4—434no—
688C2×C4⋊C4—4316no—
689C2×C4⋊C4—4316no—
690C2×C4⋊C4C22×D4311yescharacteristic
691C2×C4⋊C4C22×D4312yes—
692C2×C4⋊C4C22×D4311yescharacteristic
693C2×C4⋊C4C22×D4314yes—
694C2×C4⋊C4C22×D43116yes—
695C2×C4⋊C4C22×D4312yes—
696C2×C22⋊C4—434no—
697C2×C22⋊C4—432no—
698C2×C22⋊C4—432no—
699C2×C22⋊C4—434no—
700C2×C22⋊C4—434no—
701C2×C22⋊C4—434no—
702C2×C22⋊C4—432no—
703C2×C22⋊C4—432no—
704C2×C22⋊C4—432no—
705C2×C22⋊C4—432no—
706C2×C22⋊C4C22×D4314yes—
707C2×C22⋊C4C22×D4312yes—
708C2×C22⋊C4C22×D4312yes—
709C2×C42—434no—
710C2×C42—431no—
711C2×C42—431no—
712C2×C42—431no—
713C2×C42—438no—
714C2×C42C22×D4311yescharacteristic
715C24—431no—
716C24—432no—
717C24—432no—
718C24C23×D4312yes—
719C24C23×D4312yes—
720#41—432no—
721#41—17232no—
722#41—17232no—
723#41—17232no—
724#41—17232no—
725#41—17232no—
726C2×Q8—28no—
727C2×Q8—438no—
728C2×Q8—438no—
729C2×Q8—438no—
730C2×Q8—868no—
731C2×Q8—1724no—
732C2×Q8—1724no—
733C2×Q8C23×D4318yes—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—48no—
737C2×D4—438no—
738C2×D4—438no—
739C2×D4—438no—
740C2×D4—438no—
741C2×D4—4316no—
742C2×D4—4316no—
743C2×D4—438no—
744C2×D4—438no—
745C2×D4—434no—
746C2×D4—434no—
747C2×D4—438no—
748C2×D4—438no—
749C2×D4—4316no—
750C2×D4—868no—
751C2×D4—868no—
752C2×D4—864no—
753C2×D4—864no—
754C2×D4—1724no—
755C2×D4—1728no—
756C2×D4—1724no—
757C2×D4—1724no—
758C2×D4—1724no—
759C2×D4—1724no—
760C2×D4—1724no—
761C2×D4—1728no—
762C2×D4—1728no—
763C2×D4C23×D4314yes—
764C2×D4C23×D4314yes—
765C2×D4C23×D43116yes—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—48no—
769C22×C4—431no—
770C22×C4—431no—
771C22×C4—431no—
772C22×C4—434no—
773C22×C4—432no—
774C22×C4—432no—
775C22×C4—4316no—
776C22×C4—434no—
777C22×C4—434no—
778C22×C4—434no—
779C22×C4—438no—
780C22×C4—438no—
781C22×C4—4316no—
782C22×C4—4316no—
783C22×C4—864no—
784C22×C4—868no—
785C22×C4—864no—
786C22×C4—868no—
787C22×C4—864no—
788C22×C4—1728no—
789C22×C4—1728no—
790C22×C4—1728no—
791C22×C4C23×D4318yes—
792C22×C4C23×D4318yes—
793C22×C4C23×D4311yescharacteristic
794C22×C4C23×D4314yes—
795C22×C4C23×D4312yes—
796C22×C4C23×D4312yes—
797C22×C4C23×D43116yes—
798C22×C4C23×D4311yescharacteristic
799C22×C4C23×D4311yescharacteristic
800C4⋊C4—434no—
801C4⋊C4—434no—
802C4⋊C4—438no—
803C4⋊C4—4316no—
804C4⋊C4—4316no—
805C4⋊C4—4316no—
806C4⋊C4—438no—
807C4⋊C4—438no—
808C4⋊C4—438no—
809C4⋊C4—4316no—
810C4⋊C4—4316no—
811C4⋊C4C23×D4314yes—
812C4⋊C4C23×D4318yes—
813C4⋊C4C23×D4314yes—
814C4⋊C4C23×D43116yes—
815C4⋊C4C23×D4318yes—
816C22⋊C4—4316no—
817C22⋊C4—438no—
818C22⋊C4—438no—
819C22⋊C4—4316no—
820C22⋊C4—4316no—
821C22⋊C4—4316no—
822C22⋊C4—438no—
823C22⋊C4—438no—
824C22⋊C4—438no—
825C22⋊C4—438no—
826C22⋊C4C23×D43116yes—
827C22⋊C4C23×D4318yes—
828C22⋊C4C23×D4318yes—
829C42—434no—
830C42—434no—
831C42—434no—
832C42—4316no—
833C42C23×D4314yes—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—24no—
840C23—432no—
841C23—434no—
842C23—434no—
843C23—864no—
844C23—862no—
845C23—864no—
846C23—862no—
847C23—864no—
848C23—864no—
849C23—862no—
850C23—864no—
851C23—864no—
852C23C24×D4314yes—
853C23C24×D4314yes—
854C23C24×D4311yescharacteristic
855Q8—216no—
856Q8—8616no—
857Q8—1728no—
858Q8—1728no—
859D4—28no—
860D4—28no—
861D4—416no—
862D4—8616no—
863D4—8616no—
864D4—868no—
865D4—868no—
866D4—1728no—
867D4—17216no—
868D4—1728no—
869D4—1728no—
870D4—1728no—
871D4—1728no—
872D4—1728no—
873D4—17216no—
874D4—17216no—
875C2×C4—24no—
876C2×C4—28no—
877C2×C4—24no—
878C2×C4—22no—
879C2×C4—216no—
880C2×C4—216no—
881C2×C4—416no—
882C2×C4—434no—
883C2×C4—432no—
884C2×C4—432no—
885C2×C4—432no—
886C2×C4—438no—
887C2×C4—434no—
888C2×C4—434no—
889C2×C4—868no—
890C2×C4—864no—
891C2×C4—862no—
892C2×C4—864no—
893C2×C4—862no—
894C2×C4—868no—
895C2×C4—8616no—
896C2×C4—868no—
897C2×C4—8616no—
898C2×C4—868no—
899C2×C4—17216no—
900C2×C4—17216no—
901C2×C4—17216no—
902C2×C4#1306337014yes—
903C2×C4#1306337114yes—
904C2×C4C24×D4312yes—
905C2×C4C24×D4318yes—
906C2×C4C24×D4314yes—
907C2×C4C24×D4314yes—
908C2×C4C24×D4312yes—
909C2×C4C24×D4312yes—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—48no—
917C22—48no—
918C22—864no—
919C22—862no—
920C22—864no—
921C22—862no—
922C22—864no—
923C22—864no—
924C22—862no—
925C22—864no—
926C22—864no—
927C22—1724no—
928C22—1728no—
929C22—1728no—
930C22C2×#1306337012yes—
931C22C2×#1306337112yes—
932C222−1+4×D4312yes—
933C22C25×D4311yescharacteristic
934C4—24no—
935C4—28no—
936C4—24no—
937C4—22no—
938C4—434no—
939C4—864no—
940C4—862no—
941C4—864no—
942C4—862no—
943C4—868no—
944C4C2×#1306337014yes—
945C4C2×#1306337114yes—
946C2—44no—
947C2—44no—
948C2—1722no—
949C2—1724no—
950C2—1724no—
951C2#1914899214yesdirect product factor
952C2C22×#1306337011yescharacteristic
953C2C22×#1306337111yescharacteristic
954C2C2×2−1+4×D4311yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#547C2
socleC23×C43C25
hypercenterC2×#547D43
hypocenterC43C2×#3548
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #19148992C2direct (N × H)
2. C2×#14583646C2semidirect
3. C2×#14583607C2semidirect
4. C2×#14583604C2semidirect
5. C2×#14583568C2semidirect
6. C2×#14583567C2semidirect
7. C2×#14583554C2semidirect
8. C2×#14583553C2semidirect
9. C2×#14583552C2semidirect
10. C2×#14583501C2semidirect
11. C2×#14583480C2semidirect
12. C2×#14583479C2semidirect
13. C2×#14583478C2semidirect
14. C2×#14583477C2semidirect
15. C2×#14583454C2semidirect
16. C2×#14583446C2semidirect
17. C2×#14583446C2semidirect
18. C2×C43×#547C2semidirect
24. #14583646C22semidirect
25. #14583607C22semidirect
26. #14583604C22semidirect
27. #14583568C22semidirect
28. #14583567C22semidirect
29. #14583554C22semidirect
30. #14583553C22semidirect
31. #14583552C22semidirect
32. #14583501C22semidirect
33. #14583480C22semidirect
34. #14583479C22semidirect
35. #14583478C22semidirect
36. #14583477C22semidirect
37. #14583454C22semidirect
38. #14583446C22semidirect
39. #14583446C22semidirect
93. C43×#547C22semidirect
478. C2×#547D43semidirect
489. C2×C43#3548semidirect
510. #547C2×D43semidirect
578. C43C2×#3548semidirect
951. C2#19148992direct (N × H)

Maximal subgroups

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

subgroupindex
#191489922
C2×#145836462
C2×#145836072
C2×#145836042
C2×#145835682
C2×#145835672
C2×#145835542
C2×#145835532
C2×#145835522
C2×#145835012
C2×#145834802
C2×#145834792
C2×#145834782
C2×#145834772
C2×#145834542
C2×#145834462
C2×C43×#5472
C2×#354843