Finite Group Databasebeta

← C2×#19146728 #25973322

Subgroups — C2×#19146728 #25973322

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×#14583590C211yesmaximal, characteristic, complemented
2C2×#14583569C211yesmaximal, characteristic
3#19146728C2116yesmaximal, direct product factor
4C2×#14583263C211yesmaximal, characteristic, complemented
5C2×#14583216C211yesmaximal, characteristic, complemented
6C2×#14583221C211yesmaximal, characteristic, complemented
7C2×#14583207C211yesmaximal, characteristic, complemented
8C2×#14583142C211yesmaximal, characteristic, complemented
9C2×#14583125C211yesmaximal, characteristic, complemented
10C2×#14583058C211yesmaximal, characteristic, complemented
11C2×#14583058C211yesmaximal, characteristic, complemented
12C2×#14583004C211yesmaximal, characteristic, complemented
13C2×#14582969C211yesmaximal, characteristic, complemented
14C2×#14582897C211yesmaximal, characteristic, complemented
15C2×#14582892C211yesmaximal, characteristic, complemented
16C2×C43×#460C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621872C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic
22#14583590—24no—
23#14583590C2218yescomplemented
24#14583569—24no—
25#14583569C2218yes—
26C2×#13063321—21no—
27C2×#13063319—21no—
28C2×#13063317C2211yescharacteristic
29C2×#13063315—21no—
30C2×#13063310—21no—
31C2×#13063301C2211yescharacteristic
32C2×#13063301C2211yescharacteristic
33C2×#13063297—21no—
34C2×#13063297—21no—
35C2×#13063296C2211yescharacteristic
36C2×#13063296C2211yescharacteristic
37C2×C4×Dic86C2211yescharacteristic
38C2×C4×D172C2211yescharacteristic
39C2×D4×Dic43—21no—
40C2×#13063283C2211yescharacteristic
41C2×#13063282—21no—
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583263C2218yescomplemented
44#14583221C2218yescomplemented
45#14583216C2218yescomplemented
46#14583207C2218yescomplemented
47#14583142C2218yescomplemented
48#14583125C2218yescomplemented
49#14583058C2218yescomplemented
50#14583058C2218yescomplemented
51#14583004C2218yescomplemented
52#14582969C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063257C2211yescharacteristic
55C2×#13063256C2211yescharacteristic
56#14582897C2218yescomplemented
57#14582892C2218yescomplemented
58C2×#13063250C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063246C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063236C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C2×#127×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C43×#460C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621900—22no—
78C2×#10621900—22no—
79C2×#10621900—24no—
80C2×#10621900—24no—
81C2×#10621900—42no—
82C2×#10621900—42no—
83C2×#10621900C2314yes—
84C2×#10621900C2314yes—
85C22×Dic86C2311yescharacteristic
86C22×D172D411yescharacteristic
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C23×Dic43—21no—
92C23×Dic43—21no—
93C22×C4×D43—21no—
94C22×C4×D43C2311yescharacteristic
95C22×C4×D43C2311yescharacteristic
96C2×#10621885—24no—
97C2×#10621885C2314yes—
98C2×#10621872—42no—
99C2×#10621872C2314yes—
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102C2×C8×D43—42no—
103C2×C8×D43C2314yes—
104#13063321—28no—
105#13063319—28no—
106#13063317—22no—
107#13063317C2314yes—
108#13063315—28no—
109#13063310—28no—
110#13063301—22no—
111#13063301—22no—
112#13063301C2314yes—
113#13063301C2314yes—
114#13063297—28no—
115#13063297—28no—
116#13063296—22no—
117#13063296—22no—
118#13063296C2314yes—
119#13063296C2314yes—
120C4×Dic86—22no—
121C4×Dic86C2314yes—
122C4×D172D414yes—
123C4×D172C2314yes—
124D4×Dic43—28no—
125#13063283—22no—
126#13063283C2314yes—
127#13063282—28no—
128C2×C4⋊Dic43D411yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C4⋊C4×D43—22no—
139C4⋊C4×D43C2314yes—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4D411yescharacteristic
146C2×(C2×D43)⋊C4D411yescharacteristic
147C2×C4×Dic43—21no—
148C2×C4×Dic43—21no—
149#13063259C2314yes—
150#13063257C2314yes—
151#13063256C2314yes—
152#13063250C2314yes—
153#13063250C2314yes—
154#13063249C2314yes—
155#13063248C2314yes—
156#13063246C2314yes—
157#13063246C2314yes—
158#13063246C2314yes—
159#13063246C2314yes—
160(C2×D43)⋊C8C2314yes—
161(C2×D43)⋊C8C2314yes—
162#13063236C2314yes—
163C22×Q8×C43C2311yescharacteristic
164C22×D4×C43—21no—
165C22×D4×C43—21no—
166C22×D4×C43C2311yescharacteristic
167C22×D4×C43C2311yescharacteristic
168C2×SD16×C43—42no—
169C2×SD16×C43—42no—
170C2×SD16×C43C2314yes—
171C2×SD16×C43C2314yes—
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174#127×C43—22no—
175#127×C43C2314yes—
176C4×Q8×C43—22no—
177C4×Q8×C43C2314yes—
178C2×C4⋊C4×C43—21no—
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C42×C43—21no—
181C2×C42×C43C2311yescharacteristic
182C4⋊C8×C43C2314yes—
183#102×C43C2314yes—
184#102×C43C2314yes—
185C24×C43—21no—
186C24×C43—21no—
187C23×D43C2×D411yescharacteristic
188C23×D43C2×D411yescharacteristic
189C2×Q8×C43—21no—
190C2×Q8×C43—22no—
191C2×Q8×C43—22no—
192C2×Q8×C43C2412yes—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—24no—
196C2×D4×C43—24no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43—22no—
200C2×D4×C43—22no—
201C2×D4×C43—44no—
202C2×D4×C43—82no—
203C2×D4×C43C2412yes—
204C2×D4×C43C2412yes—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2411yescharacteristic
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—24no—
214C2×C22⋊D43—44no—
215C2×C22⋊D43—44no—
216C2×C22⋊D43—82no—
217C2×C22⋊D43—82no—
218C22×Dic43—24no—
219C22×Dic43—24no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—44no—
225C22×Dic43—44no—
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228#10621900—28no—
229#10621900—28no—
230#10621900—44no—
231#10621900—44no—
232#10621900—48no—
233#10621900—48no—
234C2×D172—42no—
235C2×D172C2×D414yes—
236C2×C4×D43—22no—
237C2×C4×D43—22no—
238C2×C4×D43—22no—
239C2×C4×D43—22no—
240C2×C4×D43—24no—
241C2×C4×D43—44no—
242C2×C4×D43C2×D412yes—
243C2×C4×D43C2×D412yes—
244C2×C4×D43C2412yes—
245C2×C4×D43C2412yes—
246C2×Dic86—21no—
247C2×Dic86—22no—
248C2×Dic86#4114yes—
249C2×Dic86C2412yes—
250SD16×C43—44no—
251SD16×C43—44no—
252C2×C8×C43—22no—
253C2×C8×C43—22no—
254C2×C8×C43C2412yes—
255C2×C8×C43C2412yes—
256C4⋊C4×C43—24no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43C2412yes—
259C42×C43—24no—
260C42×C43C2×D412yes—
261C42×C43C2412yes—
262C22⋊Dic43—24no—
263C22⋊Dic43—24no—
264#10621885—28no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4C2×D414yes—
269(C2×D43)⋊C4C2×D414yes—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43C2×D414yes—
274C4⋊Dic43C2412yes—
275C4⋊Dic43C2412yes—
276C4⋊Dic43C2412yes—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281Dic43⋊C4—24no—
282Dic43⋊C4—24no—
283C4×Dic43—24no—
284C4×Dic43—24no—
285C2×C43⋊C8—22no—
286C2×C43⋊C8—22no—
287C2×C43⋊C8C2412yes—
288C2×C43⋊C8C2412yes—
289#10621872—44no—
290C8×D43—44no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—42no—
294C23×C43—42no—
295C23×C43—42no—
296C23×C43—42no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43C22×D411yescharacteristic
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43C22×D412yes—
307C22×D43C22×D412yes—
308Q8×C43—22no—
309Q8×C43—22no—
310Q8×C43—42no—
311D4×C43—22no—
312D4×C43—22no—
313D4×C43—22no—
314D4×C43—22no—
315D4×C43—48no—
316D4×C43—42no—
317D4×C43—42no—
318D4×C43—84no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—42no—
324C2×C4×C43—42no—
325C2×C4×C43C22×D412yes—
326C2×C4×C43C22×D412yes—
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C2×#4112yes—
329C2×C4×C43H(5,𝔽2)12yes—
330C2×C4×C43C2511yescharacteristic
331C22⋊D43—48no—
332C22⋊D43—48no—
333C22⋊D43—84no—
334C22⋊D43—84no—
335C2×Dic43—24no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—48no—
343C2×Dic43—48no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43C22×D412yes—
348C2×Dic43C22×D412yes—
349D172—44no—
350C4×D43—24no—
351C4×D43—24no—
352C4×D43—22no—
353C4×D43—22no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—48no—
357Dic86—24no—
358Dic86—22no—
359Dic86C2×#4114yes—
360C8×C43—22no—
361C8×C43—22no—
362C43⋊C8—22no—
363C43⋊C8—22no—
364C2×#3317—431nomaximal, Sylow
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—84no—
372C22×C43—84no—
373C22×C43#54612yes—
374C22×C43#57512yes—
375C22×C43#57712yes—
376C22×C43C23×D411yescharacteristic
377C2×D43—22no—
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—44no—
384C2×D43—44no—
385C4×C43—22no—
386C4×C43—22no—
387C4×C43—42no—
388C4×C43—42no—
389C4×C43#54612yes—
390C4×C43C22×#4111yescharacteristic
391C4×C43C2×H(5,𝔽2)11yescharacteristic
392Dic43—24no—
393Dic43—22no—
394Dic43—22no—
395Dic43—42no—
396Dic43—42no—
397Dic43—42no—
398C2×#552—431no—
399C2×#550—431no—
400#3317—4316no—
401C2×#490—431no—
402C2×#481—431no—
403C2×#482—431no—
404C2×#479—431no—
405C2×#468—431no—
406C2×#465—431no—
407C2×#460D4311yescharacteristic, complemented
408C2×#452—431no—
409C2×#452—431no—
410C2×#441—431no—
411C2×#435—431no—
412C2×#417—431no—
413C2×#416—431no—
414C2×C43—82no—
415C2×C43—82no—
416C2×C43#331714yescomplemented
417C2×C43C2×#54611yescharacteristic
418C2×C43C2×#57511yescharacteristic
419C2×C43C2×#57711yescharacteristic
420D43—42no—
421D43—42no—
422C22×#41—431no—
423C22×#41—431no—
424C22×Q16—431no—
425C22×SD16C2×D4311yescharacteristic
426C22×SD16C2×D4311yescharacteristic
427C22×M16—431no—
428C23×C8—431no—
429#552—438no—
430#552—864no—
431#550—438no—
432#550—864no—
433C2×#127—861no—
434C2×#127C2×D4311yescharacteristic
435C2×#126—861no—
436C2×#125—431no—
437C2×#125—861no—
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#479—438no—
456#468—438no—
457#465—438no—
458#460C2×D4318yescomplemented
459#452—438no—
460#452—438no—
461#441—438no—
462#435—438no—
463C2×#107—431no—
464C2×#106—431no—
465C2×#106—431no—
466C2×C4⋊C8C2×D4311yescharacteristic
467#417—438no—
468#416—438no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#102—431no—
474C2×#102—431no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102C2×D4311yescharacteristic
478C2×#102C2×D4311yescharacteristic
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—21no—
494C22×D4—21no—
495C22×D4—431no—
496C22×D4—861no—
497C22×D4—861no—
498C22×D4—861no—
499C22×D4—861no—
500C22×D4C22×D4311yescharacteristic
501C22×D4C22×D4311yescharacteristic
502C23×C4—431no—
503C23×C4—431no—
504C23×C4—861no—
505C23×C4—861no—
506C23×C4—861no—
507C2×Q16—434no—
508C2×Q16—864no—
509C2×SD16—42no—
510C2×SD16—42no—
511C2×SD16C22×D4314yes—
512C2×SD16C22×D4314yes—
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—22no—
522#127—868no—
523#127C22×D4314yes—
524#126—868no—
525#125—434no—
526#125—868no—
527#125—862no—
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—431no—
551C2×C4⋊C4—431no—
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⋊C4—861no—
561C2×C4⋊C4—861no—
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#107—434no—
575#106—434no—
576#106—434no—
577C4⋊C8C22×D4314yes—
578#103—434no—
579#103—434no—
580#103—434no—
581#103—434no—
582#102—434no—
583#102—434no—
584#102—434no—
585#102—434no—
586#102C22×D4314yes—
587#102C22×D4314yes—
588C22⋊C8—434no—
589C22⋊C8—434no—
590#97—434no—
591C24—21no—
592C24—21no—
593C24—431no—
594C24—431no—
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—22no—
604C2×Q8—434no—
605C2×Q8—432no—
606C2×Q8—861no—
607C2×Q8—862no—
608C2×Q8C23×D4312yes—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—82no—
619C2×D4—434no—
620C2×D4—864no—
621C2×D4—864no—
622C2×D4—864no—
623C2×D4—864no—
624C2×D4—3442no—
625C2×D4—3442no—
626C2×D4—1722no—
627C2×D4—1724no—
628C2×D4—1724no—
629C2×D4C23×D4312yes—
630C2×D4C23×D4312yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—432no—
636C22×C4—432no—
637C22×C4—432no—
638C22×C4—432no—
639C22×C4—864no—
640C22×C4—864no—
641C22×C4—864no—
642C22×C4—861no—
643C22×C4—862no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—861no—
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—44no—
658SD16—44no—
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—21no—
671C4⋊C4—434no—
672C4⋊C4—432no—
673C4⋊C4—432no—
674C4⋊C4—432no—
675C4⋊C4—864no—
676C4⋊C4—864no—
677C4⋊C4—864no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—861no—
681C4⋊C4—864no—
682C4⋊C4—864no—
683C4⋊C4—864no—
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—22no—
698C23—22no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—432no—
706C23—432no—
707C23—862no—
708C23—862no—
709C23—862no—
710C23—862no—
711C23—862no—
712C23—862no—
713C23C2×D4×D4311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—434no—
718Q8—862no—
719Q8—864no—
720D4—22no—
721D4—22no—
722D4—22no—
723D4—22no—
724D4—48no—
725D4—42no—
726D4—42no—
727D4—84no—
728D4—3444no—
729D4—3444no—
730D4—1724no—
731D4—1728no—
732D4—1728no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—432no—
740C2×C4—432no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—864no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—864no—
750C2×C4—864no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—1728no—
755C2×C4—1728no—
756C2×C4—1728no—
757C2×C4—1722no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4C2×D4×D4312yes—
761C2×C4C2×D4×D4312yes—
762C2×C4C2×D4×D4311yescharacteristic
763C2×C4#41×D4312yes—
764C2×C4#1306337012yes—
765C2×C4C24×D4311yescharacteristic
766C8—22no—
767C8—22no—
768C8—862no—
769C8—862no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—84no—
777C22—84no—
778C22—862no—
779C22—862no—
780C22—862no—
781C22—862no—
782C22—862no—
783C22—862no—
784C22—1724no—
785C22—1724no—
786C22#1458354612yes—
787C22#1458369512yes—
788C22#1458370512yes—
789C22C22×D4×D4311yescharacteristic
790C4—22no—
791C4—22no—
792C4—42no—
793C4—42no—
794C4—862no—
795C4—862no—
796C4—864no—
797C4—1722no—
798C4—1722no—
799C4—1722no—
800C4#1458354612yes—
801C4C2×#41×D4311yescharacteristic
802C4C2×#1306337011yescharacteristic
803C2—82no—
804C2—82no—
805C2—1722no—
806C2—1722no—
807C2#1914672814yesdirect product factor
808C2C2×#1458354611yescharacteristic
809C2C2×#1458369511yescharacteristic
810C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#460C2
socleC23×C43C22×D4
prime radicalC2×#14583569C2
hypercenterC2×#460D43
hypocenterC43C2×#3317
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#14583590C2semidirect
3. #19146728C2direct (N × H)
4. C2×#14583263C2semidirect
5. C2×#14583216C2semidirect
6. C2×#14583221C2semidirect
7. C2×#14583207C2semidirect
8. C2×#14583142C2semidirect
9. C2×#14583125C2semidirect
10. C2×#14583058C2semidirect
11. C2×#14583058C2semidirect
12. C2×#14583004C2semidirect
13. C2×#14582969C2semidirect
14. C2×#14582897C2semidirect
15. C2×#14582892C2semidirect
16. C2×C43×#460C2semidirect
23. #14583590C22semidirect
43. #14583263C22semidirect
44. #14583221C22semidirect
45. #14583216C22semidirect
46. #14583207C22semidirect
47. #14583142C22semidirect
48. #14583125C22semidirect
49. #14583058C22semidirect
50. #14583058C22semidirect
51. #14583004C22semidirect
52. #14582969C22semidirect
56. #14582897C22semidirect
57. #14582892C22semidirect
73. C43×#460C22semidirect
407. C2×#460D43semidirect
416. C2×C43#3317semidirect
458. #460C2×D43semidirect
482. C43C2×#3317semidirect
807. C2#19146728direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835902
C2×#145835692
#191467282
C2×#145832632
C2×#145832162
C2×#145832212
C2×#145832072
C2×#145831422
C2×#145831252
C2×#145830582
C2×#145830042
C2×#145829692
C2×#145828972
C2×#145828922
C2×C43×#4602
C2×#331743