Finite Group Databasebeta

← C2×#19146574 #25973238

Subgroups — C2×#19146574 #25973238

Order 11008.

2190 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583597C211yesmaximal, characteristic, complemented
2C2×#14583551C211yesmaximal, characteristic, complemented
3#19146574C2116yesmaximal, direct product factor
4C2×#14583266C211yesmaximal, characteristic, complemented
5C2×#14583243C211yesmaximal, characteristic, complemented
6C2×#14583198C211yesmaximal, characteristic, complemented
7C2×#14583147C211yesmaximal, characteristic, complemented
8C2×#14583129C211yesmaximal, characteristic, complemented
9C2×#14583103C211yesmaximal, characteristic, complemented
10C2×#14583047C211yesmaximal, characteristic, complemented
11C2×#14583046C211yesmaximal, characteristic, complemented
12C2×#14583010C211yesmaximal, characteristic, complemented
13C2×#14582973C211yesmaximal, characteristic, complemented
14C2×#14582898C211yesmaximal, characteristic, complemented
15C2×#14582894C211yesmaximal, characteristic, complemented
16C2×C43×#483C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621898C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×D344C2211yescharacteristic
22C22×#10621877C2211yescharacteristic
23C22×C8×D43C2211yescharacteristic
24#14583597—24no—
25#14583597C2218yescomplemented
26#14583551—24no—
27#14583551C2218yescomplemented
28C2×#13063323C2211yescharacteristic
29C2×#13063320—21no—
30C2×#13063316C2211yescharacteristic
31C2×#13063310—21no—
32C2×#13063310—21no—
33C2×#13063307—21no—
34C2×#13063305C2211yescharacteristic
35C2×#13063300C2211yescharacteristic
36C2×#13063299—21no—
37C2×#13063299C2211yescharacteristic
38C2×#13063298—21no—
39C2×#13063287C2211yescharacteristic
40C2×#13063287C2211yescharacteristic
41C2×C4×C22⋊D43—21no—
42C2×C4×C22⋊D43C2211yescharacteristic
43C2×#13063283C2211yescharacteristic
44C2×C4⋊C4×D43—21no—
45#14583266C2218yescomplemented
46#14583243C2218yescomplemented
47#14583198C2218yescomplemented
48#14583147C2218yescomplemented
49#14583129C2218yescomplemented
50#14583103C2218yescomplemented
51#14583047C2218yescomplemented
52#14583046C2218yescomplemented
53#14583010C2218yescomplemented
54#14582973C2218yescomplemented
55C2×#13063258C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57#14582898C2218yescomplemented
58#14582894C2218yescomplemented
59C2×#13063250C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C2×C22⋊Q8×C43C2211yescharacteristic
70C22×C4⋊C4×C43C2211yescharacteristic
71C43×#483C2218yescomplemented
72C2×#106×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—24no—
79C2×#10621902—42no—
80C2×#10621902C2314yes—
81C2×#10621898—22no—
82C2×#10621898—24no—
83C2×#10621898—42no—
84C2×#10621898C2314yes—
85C22×Dic86C2311yescharacteristic
86C22×D172—21no—
87C22×D172—21no—
88C22×D172C2311yescharacteristic
89C22×D172C2311yescharacteristic
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C22⋊D43D411yescharacteristic
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43C2311yescharacteristic
98C2×#10621873—42no—
99C2×#10621873C2314yes—
100C2×#10621884—42no—
101C2×#10621884C2314yes—
102C2×D344—24no—
103C2×D344C2314yes—
104C2×#10621877—42no—
105C2×#10621877C2314yes—
106C22×C43⋊C8C2311yescharacteristic
107C22×C43⋊C8C2311yescharacteristic
108C2×C8×D43—42no—
109C2×C8×D43C2314yes—
110#13063323—22no—
111#13063323C2314yes—
112#13063320—28no—
113#13063316—22no—
114#13063316C2314yes—
115#13063310—28no—
116#13063310—28no—
117#13063307—28no—
118#13063305—22no—
119#13063305C2314yes—
120#13063300—22no—
121#13063300C2314yes—
122#13063299—22no—
123#13063299—28no—
124#13063299C2314yes—
125#13063298—28no—
126#13063287—22no—
127#13063287—22no—
128#13063287C2314yes—
129#13063287C2314yes—
130C4×C22⋊D43—28no—
131C4×C22⋊D43D414yes—
132C4×C22⋊D43C2314yes—
133#13063283—22no—
134#13063283C2314yes—
135C2×C4⋊Dic43—21no—
136C2×C4⋊Dic43—21no—
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4D411yescharacteristic
142C4⋊C4×D43—28no—
143C2×C22⋊Dic43D411yescharacteristic
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4D411yescharacteristic
151C2×C4×Dic43—21no—
152C2×C4×Dic43C2311yescharacteristic
153#13063258C2314yes—
154Dic43⋊C8C2314yes—
155#13063250C2314yes—
156#13063249C2314yes—
157#13063248C2314yes—
158#13063248C2314yes—
159#13063247C2314yes—
160#13063245C2314yes—
161#13063245C2314yes—
162#13063245C2314yes—
163(C2×D43)⋊C8C2314yes—
164#13063235C2314yes—
165C22×Q8×C43C2311yescharacteristic
166C23×C4×C43—21no—
167C23×C4×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170C22⋊Q8×C43—22no—
171C22⋊Q8×C43C2314yes—
172C2×C4⋊C4×C43—22no—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43—21no—
175C2×C4⋊C4×C43C2314yes—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C22⋊C4×C43—21no—
180#106×C43C2314yes—
181#106×C43C2314yes—
182#103×C43C2314yes—
183#103×C43C2314yes—
184C22⋊C8×C43C2314yes—
185C24×C43C2×D411yescharacteristic
186C23×D43—21no—
187C23×D43—21no—
188C23×D43C2×D411yescharacteristic
189C2×Q8×C43—21no—
190C2×Q8×C43—22no—
191C2×Q8×C43—22no—
192C2×Q8×C43C2412yes—
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—24no—
200C22×C4×C43—82no—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D412yes—
203C22×C4×C43C2412yes—
204C22×C4×C43C2411yescharacteristic
205C2×C22⋊D43—24no—
206C2×C22⋊D43—24no—
207C2×C22⋊D43—42no—
208C2×C22⋊D43—44no—
209C2×C22⋊D43—44no—
210C2×C22⋊D43C2×D414yes—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43C2×D411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216#10621902—28no—
217#10621902—44no—
218#10621902—48no—
219#10621898—28no—
220#10621898—44no—
221#10621898—48no—
222C2×D172—21no—
223C2×D172—22no—
224C2×D172—21no—
225C2×D172—24no—
226C2×D172—24no—
227C2×D172—22no—
228C2×D172—22no—
229C2×D172—44no—
230C2×D172—82no—
231C2×D172#4114yes—
232C2×D172C2412yes—
233C2×D172C2412yes—
234C2×C4×D43—22no—
235C2×C4×D43—22no—
236C2×C4×D43—24no—
237C2×C4×D43—24no—
238C2×C4×D43—24no—
239C2×C4×D43—24no—
240C2×C4×D43—44no—
241C2×C4×D43—44no—
242C2×C4×D43—44no—
243C2×C4×D43—82no—
244C2×C4×D43C2×D412yes—
245C2×C4×D43C2412yes—
246C2×Dic86—22no—
247C2×Dic86—22no—
248C2×Dic86—21no—
249C2×Dic86C2412yes—
250C2×C8×C43—22no—
251C2×C8×C43—22no—
252C2×C8×C43C2412yes—
253C2×C8×C43C2412yes—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—24no—
257C4⋊C4×C43—24no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43C2412yes—
260C4⋊C4×C43C2412yes—
261C4⋊C4×C43C2412yes—
262C22⋊C4×C43—24no—
263C22⋊Dic43C2×D414yes—
264#10621884—44no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4C2×D414yes—
272C4⋊Dic43—21no—
273C4⋊Dic43—24no—
274C4⋊Dic43—24no—
275C4⋊Dic43C2412yes—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4C2×D414yes—
280C4×Dic43—24no—
281C4×Dic43C2×D412yes—
282C4×Dic43C2412yes—
283#10621877—44no—
284C2×C43⋊C8—22no—
285C2×C43⋊C8—22no—
286C2×C43⋊C8C2412yes—
287C2×C43⋊C8C2412yes—
288D344—28no—
289#10621873—44no—
290C8×D43—44no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43C22×D412yes—
295C23×C43C22×D411yescharacteristic
296C22×D43—22no—
297C22×D43—24no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—42no—
303C22×D43—42no—
304C22×D43—42no—
305C22×D43—42no—
306C22×D43—42no—
307C22×D43C22×D412yes—
308Q8×C43—22no—
309Q8×C43—22no—
310Q8×C43—42no—
311C2×C4×C43—22no—
312C2×C4×C43—24no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—42no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43—42no—
323C2×C4×C43—84no—
324C2×C4×C43C22×D412yes—
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C2×#4112yes—
327C2×C4×C43H(5,𝔽2)12yes—
328C2×C4×C43C2511yescharacteristic
329C22⋊D43—44no—
330C22⋊D43—48no—
331C22⋊D43—48no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—42no—
338C2×Dic43—42no—
339C2×Dic43C22×D412yes—
340C2×Dic43C22×D412yes—
341C2×Dic43C22×D412yes—
342D172—24no—
343D172—22no—
344D172—22no—
345D172—22no—
346D172—48no—
347D172—42no—
348D172—84no—
349D172C2×#4114yes—
350C4×D43—24no—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—48no—
354C4×D43—48no—
355C4×D43—48no—
356C4×D43—84no—
357Dic86—22no—
358Dic86—22no—
359Dic86—42no—
360C8×C43—22no—
361C8×C43—22no—
362C43⋊C8—22no—
363C43⋊C8—22no—
364C2×#3307—431nomaximal, Sylow
365C22×C43—22no—
366C22×C43—22no—
367C22×C43—22no—
368C22×C43—44no—
369C22×C43#54612yes—
370C22×C43#57512yes—
371C22×C43#57712yes—
372C22×C43C23×D411yescharacteristic
373C2×D43—24no—
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—44no—
378C2×D43—48no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—84no—
385C4×C43—22no—
386C4×C43—42no—
387C4×C43—42no—
388C4×C43—42no—
389C4×C43—42no—
390C4×C43#54612yes—
391C4×C43C22×#4111yescharacteristic
392C4×C43C2×H(5,𝔽2)11yescharacteristic
393Dic43—22no—
394Dic43—22no—
395Dic43—22no—
396Dic43—42no—
397Dic43—42no—
398C2×#553—431no—
399C2×#547—431no—
400#3307—4316no—
401C2×#491—431no—
402C2×#485—431no—
403C2×#483D4311yescharacteristic, complemented
404C2×#478—431no—
405C2×#468—431no—
406C2×#465—431no—
407C2×#461—431no—
408C2×#449—431no—
409C2×#449—431no—
410C2×#442—431no—
411C2×#435—431no—
412C2×#417—431no—
413C2×#416—431no—
414C2×C43—42no—
415C2×C43#330714yescomplemented
416C2×C43C2×#54611yescharacteristic
417C2×C43C2×#57511yescharacteristic
418C2×C43C2×#57711yescharacteristic
419D43—42no—
420D43—44no—
421D43—82no—
422C22×#41—431no—
423C22×#41—431no—
424C22×SD16—431no—
425C22×SD16—431no—
426C22×D8—431no—
427C22×M16—431no—
428C23×C8—431no—
429#553—438no—
430#553—864no—
431#547—438no—
432#547—864no—
433C2×C4⋊Q8—431no—
434C2×#126—861no—
435C2×#125—431no—
436C2×#123—861no—
437C2×#123—861no—
438C2×#123—861no—
439C2×C22⋊Q8—431no—
440C2×C22⋊Q8C2×D4311yescharacteristic
441C2×#121—431no—
442C2×#121—431no—
443C2×#121—861no—
444C2×#121—861no—
445C2×C4×D4—431no—
446C2×C4×D4—431no—
447C2×C4×D4—431no—
448C2×C4×D4—861no—
449C2×#117—431no—
450C22×C4⋊C4—861no—
451C22×C4⋊C4C2×D4311yescharacteristic
452#491—438no—
453#485—438no—
454#483C2×D4318yescomplemented
455#478—438no—
456#468—438no—
457#465—438no—
458#461—438no—
459#449—438no—
460#449—438no—
461#442—438no—
462#435—438no—
463C2×#107—431no—
464C2×#106C2×D4311yescharacteristic
465C2×#106C2×D4311yescharacteristic
466C2×C4⋊C8—431no—
467#417—438no—
468#416—438no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103C2×D4311yescharacteristic
474C2×#103C2×D4311yescharacteristic
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×C22⋊C8—431no—
480C2×C22⋊C8C2×D4311yescharacteristic
481C2×#97—431no—
482C43C2×#330711yescharacteristic, complemented, Sylow
483C2×#41—434no—
484C2×#41—434no—
485C2×#41—864no—
486C2×#41—862no—
487C2×#41—862no—
488C2×#41—864no—
489C2×#41—1722no—
490C2×#41—1722no—
491C22×Q8—431no—
492C22×Q8C22×D4311yescharacteristic
493C22×D4—431no—
494C22×D4—431no—
495C22×D4—431no—
496C22×D4—861no—
497C22×D4—861no—
498C22×D4—861no—
499C22×D4—861no—
500C23×C4—21no—
501C23×C4—431no—
502C23×C4—861no—
503C23×C4—861no—
504C23×C4—861no—
505C23×C4—861no—
506C23×C4C22×D4311yescharacteristic
507C2×SD16—434no—
508C2×SD16—434no—
509C2×SD16—1722no—
510C2×SD16—1722no—
511C2×D8—434no—
512C2×D8—864no—
513C2×M16—434no—
514C2×M16—1722no—
515C22×C8—431no—
516C22×C8—431no—
517C22×C8—434no—
518C22×C8—1722no—
519C22×C8C22×D4311yescharacteristic
520C22×C8C22×D4311yescharacteristic
521C4⋊Q8—434no—
522C4⋊Q8—862no—
523#126—868no—
524#125—434no—
525#125—862no—
526#123—868no—
527#123—868no—
528#123—868no—
529C22⋊Q8—22no—
530C22⋊Q8—434no—
531C22⋊Q8—862no—
532C22⋊Q8C22×D4314yes—
533#121—434no—
534#121—434no—
535#121—868no—
536#121—862no—
537#121—868no—
538#121—862no—
539C4×D4—434no—
540C4×D4—434no—
541C4×D4—434no—
542C4×D4—434no—
543C4×D4—862no—
544C4×D4—862no—
545C4×D4—868no—
546#117—434no—
547#117—862no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—868no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4C22×D4311yescharacteristic
560C2×C4⋊C4C22×D4311yescharacteristic
561C2×C4⋊C4C22×D4314yes—
562C2×C4⋊C4C22×D4311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—431no—
565C2×C22⋊C4—431no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C42—431no—
573C2×C42—861no—
574#107—434no—
575#106C22×D4314yes—
576#106C22×D4314yes—
577C4⋊C8—434no—
578#103—434no—
579#103—434no—
580#103—434no—
581#103—434no—
582#103C22×D4314yes—
583#103C22×D4314yes—
584#102—434no—
585#102—434no—
586#102—434no—
587#102—434no—
588C22⋊C8—434no—
589C22⋊C8C22×D4314yes—
590#97—434no—
591C24—431no—
592C24—861no—
593C24—861no—
594C24D4×D4311yescharacteristic
595#41—868no—
596#41—868no—
597#41—1724no—
598#41—1728no—
599#41—1724no—
600#41—1728no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—432no—
605C2×Q8—861no—
606C2×Q8—862no—
607C2×Q8—862no—
608C2×Q8C23×D4312yes—
609C2×D4—434no—
610C2×D4—434no—
611C2×D4—432no—
612C2×D4—432no—
613C2×D4—864no—
614C2×D4—864no—
615C2×D4—864no—
616C2×D4—864no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—862no—
620C2×D4—862no—
621C2×D4—862no—
622C2×D4—3442no—
623C2×D4—1724no—
624C2×D4—1722no—
625C2×D4—1724no—
626C2×D4—1724no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—24no—
634C22×C4—82no—
635C22×C4—431no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—432no—
639C22×C4—432no—
640C22×C4—864no—
641C22×C4—864no—
642C22×C4—864no—
643C22×C4—862no—
644C22×C4—862no—
645C22×C4—861no—
646C22×C4—861no—
647C22×C4—864no—
648C22×C4—3442no—
649C22×C4—1724no—
650C22×C4—1724no—
651C22×C4—1724no—
652C22×C4D4×D4312yes—
653C22×C4D4×D4311yescharacteristic
654C22×C4C23×D4312yes—
655C22×C4C23×D4311yescharacteristic
656SD16—1724no—
657SD16—1724no—
658D8—868no—
659M16—1724no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—432no—
663C2×C8—432no—
664C2×C8—862no—
665C2×C8—862no—
666C2×C8—1724no—
667C2×C8C23×D4312yes—
668C2×C8C23×D4312yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—21no—
674C4⋊C4—434no—
675C4⋊C4—432no—
676C4⋊C4—864no—
677C4⋊C4—864no—
678C4⋊C4—864no—
679C4⋊C4—864no—
680C4⋊C4—864no—
681C4⋊C4—861no—
682C4⋊C4C23×D4312yes—
683C4⋊C4C23×D4312yes—
684C4⋊C4C23×D4312yes—
685C22⋊C4—24no—
686C22⋊C4—434no—
687C22⋊C4—434no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C22⋊C4—864no—
693C22⋊C4—864no—
694C42—432no—
695C42—432no—
696C42—864no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—432no—
701C23—862no—
702C23—862no—
703C23—862no—
704C23—862no—
705C23—864no—
706C23—862no—
707C23—1722no—
708C23—1722no—
709C23—1722no—
710C23—1722no—
711C23—1722no—
712C23C2×D4×D4312yes—
713C23C2×D4×D4311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—862no—
718Q8—862no—
719Q8—1722no—
720D4—434no—
721D4—862no—
722D4—862no—
723D4—862no—
724D4—864no—
725D4—3444no—
726D4—1728no—
727D4—1724no—
728D4—1728no—
729D4—1728no—
730D4—1722no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—84no—
744C2×C4—432no—
745C2×C4—432no—
746C2×C4—432no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—864no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—3444no—
756C2×C4—1728no—
757C2×C4—1728no—
758C2×C4—1728no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4C2×D4×D4312yes—
762C2×C4C2×D4×D4311yescharacteristic
763C2×C4#41×D4312yes—
764C2×C4#1306337112yes—
765C2×C4C24×D4311yescharacteristic
766C8—22no—
767C8—22no—
768C8—862no—
769C8—862no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—44no—
774C22—862no—
775C22—864no—
776C22—862no—
777C22—862no—
778C22—3444no—
779C22—1722no—
780C22—1722no—
781C22—1722no—
782C22—1722no—
783C22—1722no—
784C22—1724no—
785C22—1728no—
786C22#1458354112yes—
787C22#1458369812yes—
788C22#1458370512yes—
789C22C22×D4×D4311yescharacteristic
790C4—22no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—862no—
796C4—862no—
797C4—862no—
798C4—1722no—
799C4—1722no—
800C4#1458354112yes—
801C4C2×#41×D4311yescharacteristic
802C4C2×#1306337111yescharacteristic
803C2—42no—
804C2—3442no—
805C2—1722no—
806C2—1724no—
807C2#1914657414yesdirect product factor
808C2C2×#1458354111yescharacteristic
809C2C2×#1458369811yescharacteristic
810C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#483C2
socleC23×C43C22×D4
hypercenterC2×#483D43
hypocenterC43C2×#3307
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#14583597C2semidirect
2. C2×#14583551C2semidirect
3. #19146574C2direct (N × H)
4. C2×#14583266C2semidirect
5. C2×#14583243C2semidirect
6. C2×#14583198C2semidirect
7. C2×#14583147C2semidirect
8. C2×#14583129C2semidirect
9. C2×#14583103C2semidirect
10. C2×#14583047C2semidirect
11. C2×#14583046C2semidirect
12. C2×#14583010C2semidirect
13. C2×#14582973C2semidirect
14. C2×#14582898C2semidirect
15. C2×#14582894C2semidirect
16. C2×C43×#483C2semidirect
25. #14583597C22semidirect
27. #14583551C22semidirect
45. #14583266C22semidirect
46. #14583243C22semidirect
47. #14583198C22semidirect
48. #14583147C22semidirect
49. #14583129C22semidirect
50. #14583103C22semidirect
51. #14583047C22semidirect
52. #14583046C22semidirect
53. #14583010C22semidirect
54. #14582973C22semidirect
57. #14582898C22semidirect
58. #14582894C22semidirect
71. C43×#483C22semidirect
403. C2×#483D43semidirect
415. C2×C43#3307semidirect
454. #483C2×D43semidirect
482. C43C2×#3307semidirect
807. C2#19146574direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835972
C2×#145835512
#191465742
C2×#145832662
C2×#145832432
C2×#145831982
C2×#145831472
C2×#145831292
C2×#145831032
C2×#145830472
C2×#145830462
C2×#145830102
C2×#145829732
C2×#145828982
C2×#145828942
C2×C43×#4832
C2×#330743