Finite Group Databasebeta

← C2×#19146718 #25973312

Subgroups — C2×#19146718 #25973312

Order 11008.

2178 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×#14583587C211yesmaximal, characteristic, complemented
2C2×#14583571C211yesmaximal, characteristic
3#19146718C2116yesmaximal, direct product factor
4C2×#14583265C211yesmaximal, characteristic, complemented
5C2×#14583219C211yesmaximal, characteristic, complemented
6C2×#14583226C211yesmaximal, characteristic, complemented
7C2×#14583146C211yesmaximal, characteristic, complemented
8C2×#14583129C211yesmaximal, characteristic, complemented
9C2×#14583100C211yesmaximal, characteristic, complemented
10C2×#14583064C211yesmaximal, characteristic, complemented
11C2×#14583064C211yesmaximal, characteristic, complemented
12C2×#14583004C211yesmaximal, characteristic, complemented
13C2×#14582969C211yesmaximal, characteristic, complemented
14C2×#14582899C211yesmaximal, characteristic, complemented
15C2×#14582894C211yesmaximal, characteristic, complemented
16C2×C43×#479C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621902C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621873C2211yescharacteristic
22C22×#10621872C2211yescharacteristic
23C22×C8×D43C2211yescharacteristic
24#14583587—24no—
25#14583587C2218yescomplemented
26#14583571—24no—
27#14583571C2218yes—
28C2×#13063322—21no—
29C2×#13063322C2211yescharacteristic
30C2×#13063320—21no—
31C2×#13063316—21no—
32C2×#13063310—21no—
33C2×#13063305C2211yescharacteristic
34C2×#13063305C2211yescharacteristic
35C2×#13063300—21no—
36C2×#13063300—21no—
37C2×#13063300C2211yescharacteristic
38C2×#13063300C2211yescharacteristic
39C2×C4×Dic86C2211yescharacteristic
40C2×C4×D172—21no—
41C2×C4×D172C2211yescharacteristic
42C2×#13063283—21no—
43C2×#13063283C2211yescharacteristic
44C2×C4⋊C4×D43C2211yescharacteristic
45#14583265C2218yescomplemented
46#14583226C2218yescomplemented
47#14583219C2218yescomplemented
48#14583146C2218yescomplemented
49#14583129C2218yescomplemented
50#14583100C2218yescomplemented
51#14583064C2218yescomplemented
52#14583064C2218yescomplemented
53#14583004C2218yescomplemented
54#14582969C2218yescomplemented
55C2×#13063256C2211yescharacteristic
56#14582899C2218yescomplemented
57#14582894C2218yescomplemented
58C2×#13063249C2211yescharacteristic
59C2×#13063248C2211yescharacteristic
60C2×#13063247C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063236C2211yescharacteristic
69C2×#125×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C43×#479C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—22no—
79C2×#10621902—24no—
80C2×#10621902—24no—
81C2×#10621902—42no—
82C2×#10621902—42no—
83C2×#10621902C2314yes—
84C2×#10621902C2314yes—
85C22×Dic86C2311yescharacteristic
86C22×D172—21no—
87C22×D172—21no—
88C22×D172—21no—
89C22×D172—21no—
90C22×D172—21no—
91C22×D172—21no—
92C22×D172D411yescharacteristic
93C22×D172C2311yescharacteristic
94C22×D172C2311yescharacteristic
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43—21no—
98C22×C4×D43C2311yescharacteristic
99C22×C4×D43C2311yescharacteristic
100C2×#10621885—24no—
101C2×#10621885C2314yes—
102C2×#10621873—42no—
103C2×#10621873—42no—
104C2×#10621873C2314yes—
105C2×#10621873C2314yes—
106C2×#10621872—42no—
107C2×#10621872C2314yes—
108C22×C43⋊C8C2311yescharacteristic
109C22×C43⋊C8C2311yescharacteristic
110C2×C8×D43—42no—
111C2×C8×D43C2314yes—
112#13063322—28no—
113#13063322—22no—
114#13063322C2314yes—
115#13063320—28no—
116#13063316—28no—
117#13063310—28no—
118#13063305—22no—
119#13063305—22no—
120#13063305C2314yes—
121#13063305C2314yes—
122#13063300—22no—
123#13063300—22no—
124#13063300—28no—
125#13063300—28no—
126#13063300C2314yes—
127#13063300C2314yes—
128C4×Dic86—22no—
129C4×Dic86C2314yes—
130C4×D172—28no—
131C4×D172D414yes—
132C4×D172C2314yes—
133#13063283—22no—
134#13063283—28no—
135#13063283C2314yes—
136C2×C4⋊Dic43—21no—
137C2×C4⋊Dic43—21no—
138C2×C4⋊Dic43D411yescharacteristic
139C2×C4⋊Dic43C2311yescharacteristic
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4—21no—
142C4⋊C4×D43—22no—
143C4⋊C4×D43C2314yes—
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)⋊C4D411yescharacteristic
150C2×(C2×D43)⋊C4D411yescharacteristic
151C2×C4×Dic43—21no—
152C2×C4×Dic43—21no—
153#13063256C2314yes—
154#13063249C2314yes—
155#13063248C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158#13063245C2314yes—
159#13063245C2314yes—
160#13063245C2314yes—
161#13063245C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164#13063236C2314yes—
165C22×Q8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168#125×C43—22no—
169#125×C43C2314yes—
170C4×Q8×C43—22no—
171C4×Q8×C43C2314yes—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43—21no—
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C42×C43—21no—
179C2×C42×C43C2311yescharacteristic
180#107×C43C2314yes—
181#106×C43C2314yes—
182C4⋊C8×C43C2314yes—
183#103×C43C2314yes—
184#103×C43C2314yes—
185C23×D43—21no—
186C23×D43—21no—
187C23×D43C2×D411yescharacteristic
188C23×D43C2×D411yescharacteristic
189C2×Q8×C43—21no—
190C2×Q8×C43—22no—
191C2×Q8×C43#4114yes—
192C2×Q8×C43C2412yes—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2411yescharacteristic
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204#10621902—28no—
205#10621902—28no—
206#10621902—44no—
207#10621902—44no—
208#10621902—48no—
209#10621902—48no—
210C2×D172—24no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—24no—
214C2×D172—24no—
215C2×D172—24no—
216C2×D172—24no—
217C2×D172—24no—
218C2×D172—22no—
219C2×D172—22no—
220C2×D172—22no—
221C2×D172—22no—
222C2×D172—42no—
223C2×D172—44no—
224C2×D172—44no—
225C2×D172—44no—
226C2×D172—82no—
227C2×D172—82no—
228C2×D172—82no—
229C2×D172C2×D414yes—
230C2×D172C2412yes—
231C2×D172C2412yes—
232C2×C4×D43—22no—
233C2×C4×D43—22no—
234C2×C4×D43—22no—
235C2×C4×D43—22no—
236C2×C4×D43—24no—
237C2×C4×D43—24no—
238C2×C4×D43—24no—
239C2×C4×D43—44no—
240C2×C4×D43—44no—
241C2×C4×D43—44no—
242C2×C4×D43C2×D412yes—
243C2×C4×D43C2×D412yes—
244C2×C4×D43C2412yes—
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—24no—
255C4⋊C4×C43—24no—
256C4⋊C4×C43—24no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43C2412yes—
261C4⋊C4×C43C2412yes—
262C4⋊C4×C43C2412yes—
263C42×C43—24no—
264C42×C43C2×D412yes—
265C42×C43C2412yes—
266#10621885—28no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4C2×D414yes—
273(C2×D43)⋊C4C2×D414yes—
274C4⋊Dic43—21no—
275C4⋊Dic43—24no—
276C4⋊Dic43—24no—
277C4⋊Dic43C2×D414yes—
278C4⋊Dic43C2412yes—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281C4×Dic43—24no—
282C4×Dic43—24no—
283C2×C43⋊C8—22no—
284C2×C43⋊C8—22no—
285C2×C43⋊C8C2412yes—
286C2×C43⋊C8C2412yes—
287#10621873—44no—
288#10621873—44no—
289#10621872—44no—
290C8×D43—44no—
291C23×C43C22×D411yescharacteristic
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—42no—
301C22×D43—42no—
302C22×D43—42no—
303C22×D43—42no—
304C22×D43—42no—
305C22×D43—42no—
306C22×D43C22×D412yes—
307C22×D43C22×D412yes—
308Q8×C43—24no—
309Q8×C43—22no—
310Q8×C43C2×#4114yes—
311C2×C4×C43—24no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43—42no—
321C2×C4×C43C22×D412yes—
322C2×C4×C43C22×D412yes—
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C2×#4112yes—
325C2×C4×C43H(5,𝔽2)12yes—
326C2×C4×C43C2511yescharacteristic
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333C2×Dic43C22×D412yes—
334C2×Dic43C22×D412yes—
335D172—22no—
336D172—22no—
337D172—22no—
338D172—22no—
339D172—44no—
340D172—48no—
341D172—48no—
342D172—48no—
343D172—42no—
344D172—42no—
345D172—84no—
346D172—84no—
347D172—84no—
348C4×D43—24no—
349C4×D43—24no—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—22no—
354C4×D43—48no—
355C4×D43—48no—
356C4×D43—48no—
357Dic86—22no—
358Dic86—22no—
359Dic86—42no—
360C8×C43—22no—
361C8×C43—22no—
362C43⋊C8—22no—
363C43⋊C8—22no—
364C2×#3317—431nomaximal, Sylow
365C22×C43#54612yes—
366C22×C43#57512yes—
367C22×C43#57712yes—
368C22×C43C23×D411yescharacteristic
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—22no—
372C2×D43—22no—
373C2×D43—22no—
374C2×D43—22no—
375C2×D43—44no—
376C2×D43—44no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—84no—
384C2×D43—84no—
385C4×C43—24no—
386C4×C43—22no—
387C4×C43—22no—
388C4×C43—42no—
389C4×C43—42no—
390C4×C43—42no—
391C4×C43#54612yes—
392C4×C43C22×#4111yescharacteristic
393C4×C43C2×H(5,𝔽2)11yescharacteristic
394Dic43—22no—
395Dic43—22no—
396Dic43—42no—
397Dic43—42no—
398C2×#552—431no—
399C2×#550—431no—
400#3317—4316no—
401C2×#490—431no—
402C2×#481—431no—
403C2×#482—431no—
404C2×#479D4311yescharacteristic, complemented
405C2×#468—431no—
406C2×#465—431no—
407C2×#460—431no—
408C2×#452—431no—
409C2×#452—431no—
410C2×#441—431no—
411C2×#435—431no—
412C2×#417—431no—
413C2×#416—431no—
414C2×C43#331714yescomplemented
415C2×C43C2×#54611yescharacteristic
416C2×C43C2×#57511yescharacteristic
417C2×C43C2×#57711yescharacteristic
418D43—42no—
419D43—42no—
420D43—82no—
421D43—82no—
422C22×#41—431no—
423C22×#41—431no—
424C22×Q16—431no—
425C22×SD16—431no—
426C22×SD16—431no—
427C22×M16—431no—
428C23×C8—431no—
429#552—438no—
430#552—864no—
431#550—438no—
432#550—864no—
433C2×#127—431no—
434C2×#127—861no—
435C2×#126—861no—
436C2×#125—861no—
437C2×#125C2×D4311yescharacteristic
438C2×#123—861no—
439C2×C22⋊Q8—431no—
440C2×C22⋊Q8—431no—
441C2×#121—431no—
442C2×#121—431no—
443C2×#121—861no—
444C2×#121—861no—
445C2×C4×Q8—431no—
446C2×C4×Q8C2×D4311yescharacteristic
447C2×C4×D4—431no—
448C2×C4×D4—861no—
449C2×#117—431no—
450C2×#117—861no—
451C22×C4⋊C4—431no—
452#490—438no—
453#482—438no—
454#481—438no—
455#479C2×D4318yescomplemented
456#468—438no—
457#465—438no—
458#460—438no—
459#452—438no—
460#452—438no—
461#441—438no—
462#435—438no—
463C2×#107C2×D4311yescharacteristic
464C2×#106—431no—
465C2×#106C2×D4311yescharacteristic
466C2×C4⋊C8C2×D4311yescharacteristic
467#417—438no—
468#416—438no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103C2×D4311yescharacteristic
472C2×#103C2×D4311yescharacteristic
473C2×#102—431no—
474C2×#102—431no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×C22⋊C8—431no—
480C2×C22⋊C8—431no—
481C2×#97—431no—
482C43C2×#331711yescharacteristic, complemented, Sylow
483C2×#41—434no—
484C2×#41—434no—
485C2×#41—862no—
486C2×#41—862no—
487C2×#41—864no—
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—
500C22×D4—861no—
501C22×D4—861no—
502C23×C4—431no—
503C23×C4—431no—
504C23×C4—861no—
505C23×C4—861no—
506C23×C4—861no—
507C2×Q16—434no—
508C2×Q16—864no—
509C2×SD16—434no—
510C2×SD16—434no—
511C2×SD16—1722no—
512C2×SD16—1722no—
513C2×M16—434no—
514C2×M16—1722no—
515C22×C8—431no—
516C22×C8—431no—
517C22×C8—434no—
518C22×C8—1722no—
519C22×C8C22×D4311yescharacteristic
520C22×C8C22×D4311yescharacteristic
521#127—434no—
522#127—868no—
523#127—862no—
524#126—868no—
525#125—22no—
526#125—868no—
527#125C22×D4314yes—
528#123—868no—
529C22⋊Q8—434no—
530C22⋊Q8—434no—
531C22⋊Q8—862no—
532C22⋊Q8—862no—
533#121—434no—
534#121—434no—
535#121—868no—
536#121—868no—
537#121—862no—
538#121—862no—
539C4×Q8—22no—
540C4×Q8—434no—
541C4×Q8—862no—
542C4×Q8C22×D4314yes—
543C4×D4—434no—
544C4×D4—434no—
545C4×D4—868no—
546#117—434no—
547#117—868no—
548#117—862no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—434no—
555C2×C4⋊C4—862no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4C22×D4311yescharacteristic
561C2×C4⋊C4C22×D4311yescharacteristic
562C2×C4⋊C4C22×D4311yescharacteristic
563C2×C22⋊C4—431no—
564C2×C22⋊C4—431no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C42—21no—
571C2×C42—861no—
572C2×C42—861no—
573C2×C42C22×D4311yescharacteristic
574#107C22×D4314yes—
575#106—434no—
576#106C22×D4314yes—
577C4⋊C8C22×D4314yes—
578#103—434no—
579#103—434no—
580#103C22×D4314yes—
581#103C22×D4314yes—
582#102—434no—
583#102—434no—
584#102—434no—
585#102—434no—
586#102—434no—
587#102—434no—
588C22⋊C8—434no—
589C22⋊C8—434no—
590#97—434no—
591C24—431no—
592C24—431no—
593C24—861no—
594C24—861no—
595#41—868no—
596#41—868no—
597#41—1724no—
598#41—1724no—
599#41—1728no—
600#41—1728no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—432no—
604C2×Q8—861no—
605C2×Q8—862no—
606C2×Q8—862no—
607C2×Q8#1062190214yes—
608C2×Q8C23×D4312yes—
609C2×D4—434no—
610C2×D4—432no—
611C2×D4—432no—
612C2×D4—864no—
613C2×D4—864no—
614C2×D4—864no—
615C2×D4—864no—
616C2×D4—864no—
617C2×D4—864no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4—862no—
621C2×D4—862no—
622C2×D4—862no—
623C2×D4—862no—
624C2×D4—3442no—
625C2×D4—3442no—
626C2×D4—3442no—
627C2×D4—1722no—
628C2×D4—1724no—
629C2×D4—1724no—
630C2×D4—1724no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—431no—
636C22×C4—431no—
637C22×C4—432no—
638C22×C4—432no—
639C22×C4—432no—
640C22×C4—432no—
641C22×C4—864no—
642C22×C4—864no—
643C22×C4—864no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—1724no—
651C22×C4—1724no—
652C22×C4—1724no—
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4C23×D4311yescharacteristic
656Q16—868no—
657SD16—1724no—
658SD16—1724no—
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—24no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—434no—
676C4⋊C4—432no—
677C4⋊C4—864no—
678C4⋊C4—864no—
679C4⋊C4—864no—
680C4⋊C4—861no—
681C4⋊C4—864no—
682C4⋊C4C23×D4312yes—
683C4⋊C4C23×D4312yes—
684C4⋊C4C23×D4312yes—
685C22⋊C4—434no—
686C22⋊C4—434no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C42—24no—
693C42—864no—
694C42—864no—
695C42D4×D4312yes—
696C42C23×D4312yes—
697C23—432no—
698C23—432no—
699C23—862no—
700C23—862no—
701C23—862no—
702C23—862no—
703C23—862no—
704C23—862no—
705C23—862no—
706C23—862no—
707C23—1722no—
708C23—1722no—
709C23—1722no—
710C23—1722no—
711C23—1722no—
712C23—1722no—
713C23C2×D4×D4311yescharacteristic
714Q8—22no—
715Q8—24no—
716Q8—862no—
717Q8—862no—
718Q8—1722no—
719Q8C2×#1062190214yes—
720D4—862no—
721D4—862no—
722D4—862no—
723D4—862no—
724D4—3444no—
725D4—3444no—
726D4—3444no—
727D4—1724no—
728D4—1728no—
729D4—1728no—
730D4—1728no—
731D4—1722no—
732D4—1722no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—432no—
744C2×C4—432no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—864no—
752C2×C4—864no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—1728no—
756C2×C4—1728no—
757C2×C4—1728no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4C2×D4×D4312yes—
761C2×C4C2×D4×D4312yes—
762C2×C4C2×D4×D4311yescharacteristic
763C2×C4C2×#1062190212yes—
764C2×C4#1306337112yes—
765C2×C4C24×D4311yescharacteristic
766C8—22no—
767C8—22no—
768C8—862no—
769C8—862no—
770C22—862no—
771C22—862no—
772C22—862no—
773C22—862no—
774C22—862no—
775C22—862no—
776C22—3444no—
777C22—3444no—
778C22—1722no—
779C22—1722no—
780C22—1722no—
781C22—1722no—
782C22—1722no—
783C22—1722no—
784C22—1724no—
785C22—1724no—
786C22#1458354012yes—
787C22#1458369812yes—
788C22#1458370612yes—
789C22C22×D4×D4311yescharacteristic
790C4—24no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—862no—
797C4—862no—
798C4—1722no—
799C4—1722no—
800C4#1458354012yes—
801C4C22×#1062190211yescharacteristic
802C4C2×#1306337111yescharacteristic
803C2—3442no—
804C2—3442no—
805C2—1722no—
806C2—1722no—
807C2#1914671814yesdirect product factor
808C2C2×#1458354011yescharacteristic
809C2C2×#1458369811yescharacteristic
810C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#479C2
socleC23×C43C22×D4
prime radicalC2×#14583571C2
hypercenterC2×#479D43
hypocenterC43C2×#3317
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#14583587C2semidirect
3. #19146718C2direct (N × H)
4. C2×#14583265C2semidirect
5. C2×#14583219C2semidirect
6. C2×#14583226C2semidirect
7. C2×#14583146C2semidirect
8. C2×#14583129C2semidirect
9. C2×#14583100C2semidirect
10. C2×#14583064C2semidirect
11. C2×#14583064C2semidirect
12. C2×#14583004C2semidirect
13. C2×#14582969C2semidirect
14. C2×#14582899C2semidirect
15. C2×#14582894C2semidirect
16. C2×C43×#479C2semidirect
25. #14583587C22semidirect
45. #14583265C22semidirect
46. #14583226C22semidirect
47. #14583219C22semidirect
48. #14583146C22semidirect
49. #14583129C22semidirect
50. #14583100C22semidirect
51. #14583064C22semidirect
52. #14583064C22semidirect
53. #14583004C22semidirect
54. #14582969C22semidirect
56. #14582899C22semidirect
57. #14582894C22semidirect
71. C43×#479C22semidirect
404. C2×#479D43semidirect
414. C2×C43#3317semidirect
455. #479C2×D43semidirect
482. C43C2×#3317semidirect
807. C2#19146718direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835872
C2×#145835712
#191467182
C2×#145832652
C2×#145832192
C2×#145832262
C2×#145831462
C2×#145831292
C2×#145831002
C2×#145830642
C2×#145830042
C2×#145829692
C2×#145828992
C2×#145828942
C2×C43×#4792
C2×#331743