Finite Group Databasebeta

← C2×#19148514 #26005101

Subgroups — C2×#19148514 #26005101

Order 11008.

7238 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148514C2132yesmaximal, direct product factor
2C2×#14583596C214yesmaximal, complemented
3C2×#14583594C214yesmaximal, complemented
4C2×#14583592C214yesmaximal, complemented
5C2×#14583586C214yesmaximal, complemented
6C2×#14583512C211yesmaximal, characteristic, complemented
7C2×#14583511C211yesmaximal, characteristic, complemented
8C2×#14583503C211yesmaximal, characteristic, complemented
9C2×#14583478C212yesmaximal, complemented
10C2×#14583447C211yesmaximal, characteristic, complemented
11C2×#14583431C212yesmaximal, complemented
12C2×#14583430C212yesmaximal, complemented
13C2×#125×D43C211yesmaximal, characteristic, complemented
14C2×#14583378C212yesmaximal, complemented
15C2×#14583367C211yesmaximal, characteristic, complemented
16C2×C43×#540C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621900C2212yes—
19#14583596C22164yescomplemented
20#14583594C22164yescomplemented
21#14583592C22164yescomplemented
22#14583586C22164yescomplemented
23#14583512C22116yescomplemented
24#14583511C22116yescomplemented
25#14583503C22116yescomplemented
26#14583478C22132yescomplemented
27#14583447C22116yescomplemented
28C2×#13063325C2211yescharacteristic
29#14583431C22132yescomplemented
30#14583430C22132yescomplemented
31C2×#13063320C2214yes—
32C2×#13063318C2214yes—
33C2×#13063318C2214yes—
34C2×#13063318C2214yes—
35C2×#13063317C2211yescharacteristic
36C2×#13063316C2212yes—
37C2×#13063316C2214yes—
38C2×#13063315C2214yes—
39C2×#13063315C2214yes—
40#125×D43C22116yescomplemented
41C2×#13063312C2212yes—
42C2×#13063307C2214yes—
43C2×#13063306C2214yes—
44C2×#13063306C2214yes—
45C2×#13063305C2212yes—
46C2×#13063304C2212yes—
47C2×#13063302C2214yes—
48C2×#13063298C2214yes—
49C2×#13063297C2214yes—
50C2×#13063297C2214yes—
51C2×#13063296C2214yes—
52C2×#13063296C2212yes—
53C2×#13063296C2214yes—
54#14583378C22132yescomplemented
55#14583367C22116yescomplemented
56C2×C4×Dic86C2212yes—
57C2×#13063290C2212yes—
58C2×#13063290C2212yes—
59C2×D4×Dic43C2212yes—
60C2×D4×Dic43C2214yes—
61C2×D4×Dic43C2214yes—
62C2×#13063287C2212yes—
63C2×C4×C22⋊D43C2214yes—
64C2×C4×C22⋊D43C2214yes—
65C2×(C22⋊D43)⋊C4C2214yes—
66C2×(C22⋊D43)⋊C4C2212yes—
67C2×(C22⋊D43)⋊C4C2212yes—
68C2×#13063284C2214yes—
69C2×#13063282C2211yescharacteristic
70C2×#13063282C2211yescharacteristic
71C2×#13063281C2214yes—
72C2×#13063281C2214yes—
73C22×Dic43⋊C4C2214yes—
74C2×C4⋊C4×D43C2212yes—
75C2×C4⋊C4×D43C2214yes—
76C22×C4×Dic43C2211yescharacteristic
77C2×C42×D43C2211yescharacteristic
78C2×C42×D43C2211yescharacteristic
79C43×#540C22116yescomplemented
80C2×#127×C43C2211yescharacteristic
81C2×#125×C43C2211yescharacteristic
82C2×#123×C43C2214yes—
83C2×#121×C43C2214yes—
84C2×#121×C43C2212yes—
85C2×C4×D4×C43C2212yes—
86C2×#117×C43C2211yescharacteristic
87C2×#10621898—28no—
88C2×#10621898C2318yes—
89C2×#10621900—216no—
90C2×#10621900C23116yes—
91C22×Dic86C2311yescharacteristic
92C22×Dic86C2312yes—
93C22×D172C2311yescharacteristic
94C22×C22⋊D43C2311yescharacteristic
95C22×C22⋊D43C2311yescharacteristic
96C22×C22⋊D43C2314yes—
97C22×C22⋊D43C2314yes—
98C23×Dic43C2314yes—
99C23×Dic43C2312yes—
100C23×Dic43C2314yes—
101C22×C4×D43C2311yescharacteristic
102C22×C4×D43C2312yes—
103C22×C4×D43C2312yes—
104C22×C4×D43C2314yes—
105C22×C4×D43C2311yescharacteristic
106#13063325C2318yes—
107#13063320C23132yes—
108#13063318C23132yes—
109#13063318C23132yes—
110#13063318C23132yes—
111#13063317C2318yes—
112#13063316C23132yes—
113#13063316C23116yes—
114#13063315C23132yes—
115#13063315C23132yes—
116#13063312C23116yes—
117#13063307C23132yes—
118#13063306C23132yes—
119#13063306C23132yes—
120#13063305C23116yes—
121#13063304C23116yes—
122#13063302C23132yes—
123#13063298C23132yes—
124#13063297C23132yes—
125#13063297C23132yes—
126#13063296C23132yes—
127#13063296C23132yes—
128#13063296C23116yes—
129C4×Dic86C23116yes—
130#13063290C23116yes—
131#13063290C23116yes—
132D4×Dic43C23132yes—
133D4×Dic43C23132yes—
134D4×Dic43C23116yes—
135#13063287C23116yes—
136C4×C22⋊D43C23132yes—
137C4×C22⋊D43C23132yes—
138(C22⋊D43)⋊C4C23116yes—
139(C22⋊D43)⋊C4C23132yes—
140(C22⋊D43)⋊C4C23116yes—
141#13063284C23132yes—
142#13063282C2318yes—
143#13063282C2318yes—
144#13063281C23132yes—
145#13063281C23132yes—
146C2×C4⋊Dic43C2314yes—
147C2×C4⋊Dic43C2312yes—
148C2×C4⋊Dic43C2314yes—
149C2×C4⋊Dic43C2314yes—
150C2×Dic43⋊C4C23132yes—
151C2×Dic43⋊C4C2314yes—
152C2×Dic43⋊C4C2314yes—
153C2×Dic43⋊C4C2314yes—
154C2×Dic43⋊C4C2312yes—
155C2×Dic43⋊C4C2314yes—
156C2×Dic43⋊C4C2314yes—
157C2×Dic43⋊C4C2314yes—
158C2×Dic43⋊C4C2312yes—
159C4⋊C4×D43C23132yes—
160C4⋊C4×D43C23116yes—
161C2×C22⋊Dic43C2314yes—
162C2×C22⋊Dic43C2314yes—
163C2×C22⋊Dic43C2314yes—
164C2×C22⋊Dic43C2314yes—
165C2×C22⋊Dic43C2314yes—
166C2×(C2×D43)⋊C4C2312yes—
167C2×(C2×D43)⋊C4C2312yes—
168C2×(C2×D43)⋊C4C2314yes—
169C2×C4×Dic43C2311yescharacteristic
170C2×C4×Dic43C2312yes—
171C2×C4×Dic43C2312yes—
172C2×C4×Dic43C2312yes—
173C2×C4×Dic43C2311yescharacteristic
174C2×C4×Dic43C2318yes—
175C2×C4×Dic43C2314yes—
176C2×C4×Dic43C2314yes—
177C42×D43C2318yes—
178C42×D43C2318yes—
179C22×D4×C43C2312yes—
180C22×D4×C43C2314yes—
181C22×D4×C43C2314yes—
182C23×C4×C43C2311yescharacteristic
183C23×C4×C43C2314yes—
184#127×C43C2318yes—
185#125×C43C2318yes—
186#123×C43C23132yes—
187#121×C43C23132yes—
188#121×C43C23116yes—
189C4×D4×C43C23116yes—
190#117×C43C2318yes—
191C2×C4⋊C4×C43C2312yes—
192C2×C4⋊C4×C43C2312yes—
193C2×C4⋊C4×C43C2314yes—
194C2×C22⋊C4×C43C2312yes—
195C2×C22⋊C4×C43C2314yes—
196C2×C22⋊C4×C43C2314yes—
197C2×C42×C43C2311yescharacteristic
198C2×C42×C43C2311yescharacteristic
199C24×C43C2414yes—
200C24×C43C2411yescharacteristic
201C23×D43C2411yescharacteristic
202C23×D43C2411yescharacteristic
203C2×D4×C43—28no—
204C2×D4×C43—48no—
205C2×D4×C43—48no—
206C2×D4×C43C2418yes—
207C2×D4×C43C24116yes—
208C2×D4×C43C24116yes—
209C22×C4×C43—24no—
210C22×C4×C43—48no—
211C22×C4×C43C2412yes—
212C22×C4×C43C2412yes—
213C22×C4×C43C2411yescharacteristic
214C22×C4×C43C2414yes—
215C22×C4×C43C2414yes—
216C22×C4×C43C24116yes—
217C22×C4×C43C2411yescharacteristic
218C2×C22⋊D43—24no—
219C2×C22⋊D43—216no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—48no—
222C2×C22⋊D43C2414yes—
223C2×C22⋊D43C2414yes—
224C2×C22⋊D43C24116yes—
225C2×C22⋊D43C24116yes—
226C22×Dic43—216no—
227C22×Dic43—48no—
228C22×Dic43—44no—
229C22×Dic43C2412yes—
230C22×Dic43C2412yes—
231C22×Dic43C2414yes—
232C22×Dic43C2411yescharacteristic
233C22×Dic43C2414yes—
234C22×Dic43C24116yes—
235C22×Dic43C2418yes—
236C22×Dic43C24116yes—
237C22×Dic43C2411yescharacteristic
238#10621900—264no—
239#10621898—232no—
240C2×D172—24no—
241C2×D172C2414yes—
242C2×C4×D43—24no—
243C2×C4×D43—44no—
244C2×C4×D43—48no—
245C2×C4×D43—44no—
246C2×C4×D43#4118yes—
247C2×C4×D43C2414yes—
248C2×C4×D43C2418yes—
249C2×C4×D43C2418yes—
250C2×C4×D43C24116yes—
251C2×C4×D43C2414yes—
252C2×Dic86—28no—
253C2×Dic86—24no—
254C2×Dic86C2414yes—
255C2×Dic86C2418yes—
256C4⋊C4×C43C2418yes—
257C4⋊C4×C43C2418yes—
258C4⋊C4×C43C24116yes—
259C22⋊C4×C43C2418yes—
260C22⋊C4×C43C24116yes—
261C22⋊C4×C43C24116yes—
262C42×C43C2414yes—
263C42×C43C2414yes—
264C22⋊Dic43C24116yes—
265C22⋊Dic43C24116yes—
266C22⋊Dic43C24116yes—
267C22⋊Dic43C24116yes—
268C22⋊Dic43C24116yes—
269(C2×D43)⋊C4C2418yes—
270(C2×D43)⋊C4C2418yes—
271(C2×D43)⋊C4C24116yes—
272C4⋊Dic43C24116yes—
273C4⋊Dic43C2418yes—
274C4⋊Dic43C24116yes—
275C4⋊Dic43C24116yes—
276Dic43⋊C4C24116yes—
277Dic43⋊C4C24116yes—
278Dic43⋊C4C24116yes—
279Dic43⋊C4C2418yes—
280Dic43⋊C4C24116yes—
281Dic43⋊C4C24116yes—
282Dic43⋊C4C24116yes—
283Dic43⋊C4C2418yes—
284C4×Dic43C2414yes—
285C4×Dic43C2418yes—
286C4×Dic43C2418yes—
287C4×Dic43C2418yes—
288C4×Dic43C2414yes—
289C4×Dic43C24116yes—
290C4×Dic43C24116yes—
291C23×C43—28no—
292C23×C43—22no—
293C23×C43—28no—
294C23×C43—24no—
295C23×C43—28no—
296C23×C43C2518yes—
297C23×C43C2512yes—
298C23×C43C2511yescharacteristic
299C22×D43—24no—
300C22×D43—22no—
301C22×D43—24no—
302C22×D43C2×#4114yes—
303C22×D43C2512yes—
304C22×D43C2512yes—
305D4×C43—216no—
306D4×C43—416no—
307D4×C43—416no—
308C2×C4×C43—22no—
309C2×C4×C43—24no—
310C2×C4×C43—28no—
311C2×C4×C43—24no—
312C2×C4×C43—28no—
313C2×C4×C43—416no—
314C2×C4×C43C2×#4114yes—
315C2×C4×C43C2514yes—
316C2×C4×C43C2512yes—
317C2×C4×C43C2514yes—
318C2×C4×C43C2518yes—
319C2×C4×C43C2512yes—
320C22⋊D43—28no—
321C22⋊D43—232no—
322C22⋊D43—28no—
323C22⋊D43—416no—
324C2×Dic43—22no—
325C2×Dic43—28no—
326C2×Dic43—24no—
327C2×Dic43—28no—
328C2×Dic43—24no—
329C2×Dic43—232no—
330C2×Dic43—48no—
331C2×Dic43—416no—
332C2×Dic43C2×#4114yes—
333C2×Dic43C2514yes—
334C2×Dic43C2514yes—
335C2×Dic43C2518yes—
336C2×Dic43C2512yes—
337C2×Dic43C2518yes—
338C2×Dic43C2512yes—
339D172—28no—
340C4×D43—28no—
341C4×D43—48no—
342C4×D43—48no—
343C4×D43—416no—
344C4×D43C2×#41116yes—
345Dic86—216no—
346Dic86—28no—
347C2×#3512—431nomaximal, Sylow
348C22×C43—28no—
349C22×C43—22no—
350C22×C43—28no—
351C22×C43—24no—
352C22×C43—28no—
353C22×C43—416no—
354C22×C43—44no—
355C22×C43C22×#4112yes—
356C22×C43#58514yes—
357C22×C43C2611yescharacteristic
358C2×D43—24no—
359C2×D43—28no—
360C2×D43—22no—
361C2×D43—24no—
362C2×D43—44no—
363C2×D43C22×#4114yes—
364C4×C43—22no—
365C4×C43—24no—
366C4×C43—28no—
367C4×C43—24no—
368C4×C43C22×#4114yes—
369Dic43—22no—
370Dic43—28no—
371Dic43—24no—
372Dic43—28no—
373Dic43—24no—
374Dic43C22×#4114yes—
375#3512—4332no—
376C2×#553—434no—
377C2×#553—434no—
378C2×#553—434no—
379C2×#552—434no—
380C2×#541—431no—
381C2×#541—431no—
382C2×#540—431no—
383C2×#540D4311yescharacteristic, complemented
384C2×#537—432no—
385C2×#532—431no—
386C2×#529—432no—
387C2×#529—432no—
388C22×#125—431no—
389C2×#520—432no—
390C2×C4×#41—431no—
391C2×C43—48no—
392C2×C43—42no—
393C2×C43#351214yescomplemented
394C2×C43C23×#4111yescharacteristic
395C2×C43C2×#58512yes—
396D43—24no—
397D43—42no—
398C22×#41—432no—
399C22×#41—431no—
400#553—4364no—
401#553—4364no—
402#553—4364no—
403#552—4364no—
404#541—4316no—
405#541—4316no—
406#540—4316no—
407#540C2×D43116yescomplemented
408#537—4332no—
409#532—4316no—
410C2×C4⋊Q8—431no—
411C2×#127C2×D4311yescharacteristic
412#529—4332no—
413#529—4332no—
414C2×#126—434no—
415C2×#126—434no—
416C2×#126—434no—
417C2×#126—434no—
418C2×#125—4316no—
419C2×#125—432no—
420C2×#125—434no—
421C2×#125—434no—
422C2×#125—434no—
423C2×#125—431no—
424C2×#125C2×D4311yescharacteristic
425C2×#124—432no—
426C2×#123—434no—
427C2×#123—434no—
428C2×#123—434no—
429C2×#123C2×D4314yes—
430C2×C22⋊Q8—432no—
431C2×C22⋊Q8—432no—
432C2×C22⋊Q8—434no—
433C2×#121—432no—
434C2×#121—434no—
435C2×#121—434no—
436C2×#121—434no—
437C2×#121—434no—
438C2×#121—434no—
439C2×#121C2×D4312yes—
440C2×#121C2×D4314yes—
441#520—4332no—
442C4×#41—4316no—
443C2×C4×Q8—432no—
444C2×C4×Q8—432no—
445C2×C4×Q8—432no—
446C2×C4×D4—432no—
447C2×C4×D4—434no—
448C2×C4×D4—434no—
449C2×C4×D4—434no—
450C2×C4×D4—434no—
451C2×C4×D4—432no—
452C2×C4×D4—432no—
453C2×C4×D4—432no—
454C2×C4×D4—434no—
455C2×C4×D4C2×D4312yes—
456C2×#117—434no—
457C2×#117—434no—
458C2×#117—434no—
459C2×#117—431no—
460C2×#117—431no—
461C2×#117C2×D4311yescharacteristic
462C22×C4⋊C4—434no—
463C22×C4⋊C4—432no—
464C22×C4⋊C4—434no—
465C22×C42—431no—
466C22×C42—431no—
467C22×C42—431no—
468C43C2×#351211yescharacteristic, complemented, Sylow
469C2×#41—4316no—
470C2×#41—438no—
471C2×#41—868no—
472C2×#41—8616no—
473C22×Q8—431no—
474C22×Q8—432no—
475C22×D4—431no—
476C22×D4—434no—
477C22×D4—431no—
478C22×D4—434no—
479C22×D4—431no—
480C22×D4C22×D4312yes—
481C22×D4C22×D4314yes—
482C22×D4C22×D4314yes—
483C23×C4—431no—
484C23×C4—434no—
485C23×C4—434no—
486C23×C4—432no—
487C23×C4—431no—
488C23×C4—434no—
489C23×C4—432no—
490C23×C4—432no—
491C23×C4C22×D4311yescharacteristic
492C23×C4C22×D4314yes—
493C4⋊Q8—438no—
494#127C22×D4318yes—
495#126—4332no—
496#126—4332no—
497#126—4332no—
498#126—4332no—
499#125—4316no—
500#125—4332no—
501#125—4332no—
502#125—4332no—
503#125—438no—
504#125C22×D4318yes—
505#124—4316no—
506#123—4332no—
507#123—4332no—
508#123—4332no—
509#123C22×D43132yes—
510C22⋊Q8—4316no—
511C22⋊Q8—4316no—
512C22⋊Q8—4332no—
513#121—4316no—
514#121—4332no—
515#121—4332no—
516#121—4332no—
517#121—4332no—
518#121—4332no—
519#121C22×D43116yes—
520#121C22×D43132yes—
521C4×Q8—4316no—
522C4×Q8—4316no—
523C4×Q8—4316no—
524C4×D4—4316no—
525C4×D4—4332no—
526C4×D4—4332no—
527C4×D4—4332no—
528C4×D4—4332no—
529C4×D4—4316no—
530C4×D4—4316no—
531C4×D4—4316no—
532C4×D4—4332no—
533C4×D4C22×D43116yes—
534#117—4332no—
535#117—4332no—
536#117—4332no—
537#117—438no—
538#117—438no—
539#117C22×D4318yes—
540C2×C4⋊C4—432no—
541C2×C4⋊C4—434no—
542C2×C4⋊C4—434no—
543C2×C4⋊C4—434no—
544C2×C4⋊C4—432no—
545C2×C4⋊C4—434no—
546C2×C4⋊C4—434no—
547C2×C4⋊C4—4332no—
548C2×C4⋊C4—434no—
549C2×C4⋊C4—432no—
550C2×C4⋊C4—434no—
551C2×C4⋊C4—434no—
552C2×C4⋊C4—434no—
553C2×C4⋊C4—4316no—
554C2×C4⋊C4—4332no—
555C2×C4⋊C4C22×D4312yes—
556C2×C4⋊C4C22×D4314yes—
557C2×C4⋊C4C22×D4312yes—
558C2×C22⋊C4—434no—
559C2×C22⋊C4—434no—
560C2×C22⋊C4—434no—
561C2×C22⋊C4—434no—
562C2×C22⋊C4—434no—
563C2×C22⋊C4—432no—
564C2×C22⋊C4—432no—
565C2×C22⋊C4—434no—
566C2×C22⋊C4C22×D4314yes—
567C2×C22⋊C4C22×D4314yes—
568C2×C22⋊C4C22×D4312yes—
569C2×C42—431no—
570C2×C42—434no—
571C2×C42—434no—
572C2×C42—432no—
573C2×C42—432no—
574C2×C42—432no—
575C2×C42—438no—
576C2×C42—431no—
577C2×C42—438no—
578C2×C42—438no—
579C2×C42C22×D4311yescharacteristic
580C2×C42C22×D4311yescharacteristic
581C24—431no—
582C24—431no—
583C24C23×D4311yescharacteristic
584C24C23×D4314yes—
585#41—8632no—
586#41—8664no—
587C2×Q8—434no—
588C2×Q8—438no—
589C2×Q8—864no—
590C2×Q8—868no—
591C2×D4—28no—
592C2×D4—48no—
593C2×D4—48no—
594C2×D4—434no—
595C2×D4—4316no—
596C2×D4—434no—
597C2×D4—4316no—
598C2×D4—434no—
599C2×D4—864no—
600C2×D4—864no—
601C2×D4—864no—
602C2×D4—8616no—
603C2×D4—1728no—
604C2×D4C23×D4318yes—
605C2×D4C23×D43116yes—
606C2×D4C23×D43116yes—
607C22×C4—24no—
608C22×C4—48no—
609C22×C4—431no—
610C22×C4—438no—
611C22×C4—434no—
612C22×C4—4316no—
613C22×C4—432no—
614C22×C4—432no—
615C22×C4—434no—
616C22×C4—431no—
617C22×C4—434no—
618C22×C4—438no—
619C22×C4—4316no—
620C22×C4—434no—
621C22×C4—438no—
622C22×C4—438no—
623C22×C4—4316no—
624C22×C4—8616no—
625C22×C4—864no—
626C22×C4—1724no—
627C22×C4—1728no—
628C22×C4—1724no—
629C22×C4—1724no—
630C22×C4—1728no—
631C22×C4C23×D4314yes—
632C22×C4C23×D4312yes—
633C22×C4C23×D4311yescharacteristic
634C22×C4C23×D4312yes—
635C22×C4C23×D4314yes—
636C22×C4C23×D43116yes—
637C22×C4C23×D4311yescharacteristic
638C4⋊C4—438no—
639C4⋊C4—4316no—
640C4⋊C4—4316no—
641C4⋊C4—4316no—
642C4⋊C4—438no—
643C4⋊C4—4316no—
644C4⋊C4—4316no—
645C4⋊C4—4316no—
646C4⋊C4—438no—
647C4⋊C4—4316no—
648C4⋊C4—4316no—
649C4⋊C4—4316no—
650C4⋊C4C23×D4318yes—
651C4⋊C4C23×D43116yes—
652C4⋊C4C23×D4318yes—
653C22⋊C4—4316no—
654C22⋊C4—4316no—
655C22⋊C4—4316no—
656C22⋊C4—4316no—
657C22⋊C4—4316no—
658C22⋊C4—438no—
659C22⋊C4—438no—
660C22⋊C4—4316no—
661C22⋊C4C23×D43116yes—
662C22⋊C4C23×D43116yes—
663C22⋊C4C23×D4318yes—
664C42—434no—
665C42—434no—
666C42—438no—
667C42—438no—
668C42—438no—
669C42—4316no—
670C42—4316no—
671C42C23×D4314yes—
672C42C23×D4314yes—
673C23—22no—
674C23—28no—
675C23—28no—
676C23—24no—
677C23—28no—
678C23—434no—
679C23—432no—
680C23—432no—
681C23—864no—
682C23—862no—
683C23—864no—
684C23C24×D4312yes—
685C23C24×D4318yes—
686C23C24×D4311yescharacteristic
687Q8—868no—
688Q8—8616no—
689D4—216no—
690D4—416no—
691D4—416no—
692D4—868no—
693D4—868no—
694D4—868no—
695D4—8632no—
696D4—17216no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—28no—
702C2×C4—416no—
703C2×C4—434no—
704C2×C4—432no—
705C2×C4—4316no—
706C2×C4—434no—
707C2×C4—434no—
708C2×C4—432no—
709C2×C4—438no—
710C2×C4—438no—
711C2×C4—8632no—
712C2×C4—868no—
713C2×C4—862no—
714C2×C4—864no—
715C2×C4—864no—
716C2×C4—868no—
717C2×C4—868no—
718C2×C4—1728no—
719C2×C4—17216no—
720C2×C4—1728no—
721C2×C4—1728no—
722C2×C4—17216no—
723C2×C4#41×D4314yes—
724C2×C4C24×D4314yes—
725C2×C4C24×D4312yes—
726C2×C4C24×D4314yes—
727C2×C4C24×D4318yes—
728C2×C4C24×D4312yes—
729C22—22no—
730C22—28no—
731C22—28no—
732C22—24no—
733C22—28no—
734C22—44no—
735C22—416no—
736C22—434no—
737C22—864no—
738C22—868no—
739C22—862no—
740C22—864no—
741C22—1724no—
742C22C2×#41×D4312yes—
743C22#1458373414yes—
744C22C25×D4311yescharacteristic
745C4—22no—
746C4—24no—
747C4—28no—
748C4—24no—
749C4—434no—
750C4—868no—
751C4—862no—
752C4—864no—
753C4—864no—
754C4—868no—
755C4C2×#41×D4314yes—
756C2—42no—
757C2—48no—
758C2—864no—
759C2—1722no—
760C2#1914851414yesdirect product factor
761C2C22×#41×D4311yescharacteristic
762C2C2×#1458373412yes—
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#540C2
socleC23×C43C25
hypercenterC2×#540D43
hypocenterC43C2×#3512
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #19148514C2direct (N × H)
2. C2×#14583596C2semidirect
3. C2×#14583594C2semidirect
4. C2×#14583592C2semidirect
5. C2×#14583586C2semidirect
6. C2×#14583512C2semidirect
7. C2×#14583511C2semidirect
8. C2×#14583503C2semidirect
9. C2×#14583478C2semidirect
10. C2×#14583447C2semidirect
11. C2×#14583431C2semidirect
12. C2×#14583430C2semidirect
13. C2×#125×D43C2semidirect
14. C2×#14583378C2semidirect
15. C2×#14583367C2semidirect
16. C2×C43×#540C2semidirect
19. #14583596C22semidirect
20. #14583594C22semidirect
21. #14583592C22semidirect
22. #14583586C22semidirect
23. #14583512C22semidirect
24. #14583511C22semidirect
25. #14583503C22semidirect
26. #14583478C22semidirect
27. #14583447C22semidirect
29. #14583431C22semidirect
30. #14583430C22semidirect
40. #125×D43C22semidirect
54. #14583378C22semidirect
55. #14583367C22semidirect
79. C43×#540C22semidirect
383. C2×#540D43semidirect
393. C2×C43#3512semidirect
407. #540C2×D43semidirect
468. C43C2×#3512semidirect
760. C2#19148514direct (N × H)

Maximal subgroups

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

subgroupindex
#191485142
C2×#145835962
C2×#145835942
C2×#145835922
C2×#145835862
C2×#145835122
C2×#145835112
C2×#145835032
C2×#145834782
C2×#145834472
C2×#145834312
C2×#145834302
C2×#125×D432
C2×#145833782
C2×#145833672
C2×C43×#5402
C2×#351243