Finite Group Databasebeta

← C2×#19146137 #25971612

Subgroups — C2×#19146137 #25971612

Order 11008.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063352C211yesmaximal, characteristic, complemented
2C22×#13063346C211yesmaximal, characteristic, complemented
3C2×#14583571C211yesmaximal, characteristic, complemented
4C2×#14583544C211yesmaximal, characteristic, complemented
5#19146137C2116yesmaximal, direct product factor
6C2×#14583288C211yesmaximal, characteristic, complemented
7C2×#14583146C211yesmaximal, characteristic, complemented
8C2×#14583136C211yesmaximal, characteristic, complemented
9C2×#14583121C211yesmaximal, characteristic, complemented
10C2×#14583094C211yesmaximal, characteristic, complemented
11C2×#14583064C211yesmaximal, characteristic, complemented
12C2×#14583047C211yesmaximal, characteristic, complemented
13C2×#14583045C211yesmaximal, characteristic, complemented
14C2×#14583034C211yesmaximal, characteristic, complemented
15C2×#14582972C211yesmaximal, characteristic, complemented
16C2×C43×#440C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621902C2211yescharacteristic, complemented
19C22×#10621900C2211yescharacteristic
20C22×D4×D43C2211yescharacteristic
21C2×#13063352—28no—
22C2×#13063352C2218yescomplemented
23C2×#13063346—28no—
24C2×#13063346C2218yescomplemented
25C22×#10621885C2211yescharacteristic, complemented
26C22×#10621873C2211yescharacteristic, complemented
27C22×#10621873C2211yescharacteristic, complemented
28C22×#10621884C2211yescharacteristic
29C22×D344C2211yescharacteristic
30C22×D344C2211yescharacteristic
31C22×#10621882C2211yescharacteristic
32C22×#10621882C2211yescharacteristic
33C22×#10621872C2211yescharacteristic
34C22×C8×D43C2211yescharacteristic, complemented
35#14583571—24no—
36#14583571C2218yescomplemented
37#14583544—24no—
38#14583544C2218yescomplemented
39C2×#13063322—21no—
40C2×#13063322C2211yescharacteristic, complemented
41C2×#13063313C2211yescharacteristic
42C2×#13063309—21no—
43C2×#13063305C2211yescharacteristic
44C2×#13063300—21no—
45C2×#13063300—21no—
46C2×#13063300C2211yescharacteristic
47C2×#13063300C2211yescharacteristic
48C2×#13063300C2211yescharacteristic, complemented
49C2×#13063299—21no—
50C2×#13063295—21no—
51C2×C4×D172—21no—
52C2×C4×D172C2211yescharacteristic
53C22×(C2×D43)⋊C4—21no—
54#14583288C2218yescomplemented
55#14583146C2218yescomplemented
56#14583136C2218yescomplemented
57#14583121C2218yescomplemented
58#14583094C2218yescomplemented
59#14583064C2218yescomplemented
60#14583047C2218yescomplemented
61#14583045C2218yescomplemented
62#14583034C2218yescomplemented
63#14582972C2218yescomplemented
64C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
65C2×#13063248C2211yescharacteristic, complemented
66C2×#13063245C2211yescharacteristic
67C2×#13063245C2211yescharacteristic, complemented
68C2×#13063245C2211yescharacteristic, complemented
69C2×(C2×D43)⋊C8C2211yescharacteristic
70C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
71C22×SD16×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic, complemented
73C2×C4×D4×C43C2211yescharacteristic
74C43×#440C2218yescomplemented
75C2×#107×C43C2211yescharacteristic, complemented
76C2×#103×C43C2211yescharacteristic, complemented
77C2×#102×C43C2211yescharacteristic
78C2×#97×C43C2211yescharacteristic, complemented
79C24×D43—21no—
80C2×#10621902—22no—
81C2×#10621902—22no—
82C2×#10621902—24no—
83C2×#10621902—24no—
84C2×#10621902—42no—
85C2×#10621902—42no—
86C2×#10621902C2314yes—
87C2×#10621902C2314yescomplemented
88C2×#10621900—24no—
89C2×#10621900—22no—
90C2×#10621900—42no—
91C2×#10621900C2314yes—
92C22×Dic86C2311yescharacteristic
93C22×D172—21no—
94C22×D172—21no—
95C22×D172—21no—
96C22×D172—21no—
97C22×D172—21no—
98C22×D172—21no—
99C22×D172—21no—
100C22×D172D411yescharacteristic
101C22×D172C2311yescharacteristic
102C22×D172C2311yescharacteristic
103C22×D172C2311yescharacteristic
104C22×C22⋊D43—21no—
105C22×C22⋊D43—21no—
106C2×D4×D43—24no—
107C2×D4×D43—22no—
108C2×D4×D43—42no—
109C2×D4×D43C2314yes—
110C23×Dic43—21no—
111C22×C4×D43—21no—
112C22×C4×D43—21no—
113C22×C4×D43C2311yescharacteristic
114C22×C4×D43C2311yescharacteristic
115#13063352—232no—
116#13063346—232no—
117C2×#10621885—24no—
118C2×#10621885C2314yescomplemented
119C2×#10621873—24no—
120C2×#10621873—42no—
121C2×#10621873C2314yescomplemented
122C2×#10621873C2314yescomplemented
123C2×#10621884—24no—
124C2×#10621884C2314yes—
125C2×D344—24no—
126C2×D344—42no—
127C2×D344C2314yes—
128C2×D344C2314yes—
129C2×#10621882—24no—
130C2×#10621882—24no—
131C2×#10621882C2314yes—
132C2×#10621882C2314yes—
133C2×#10621872—24no—
134C2×#10621872C2314yes—
135C22×C43⋊C8C2311yescharacteristic
136C22×C43⋊C8C2311yescharacteristic
137C2×C8×D43—24no—
138C2×C8×D43C2314yescomplemented
139#13063322—28no—
140#13063322—22no—
141#13063322C2314yescomplemented
142#13063313—22no—
143#13063313C2314yes—
144#13063309—28no—
145#13063305—22no—
146#13063305C2314yes—
147#13063300—22no—
148#13063300—22no—
149#13063300—22no—
150#13063300—28no—
151#13063300—28no—
152#13063300C2314yes—
153#13063300C2314yes—
154#13063300C2314yescomplemented
155#13063299—28no—
156#13063295—28no—
157C4×D172—28no—
158C4×D172D414yes—
159C4×D172C2314yes—
160C2×C4⋊Dic43—21no—
161C2×C4⋊Dic43D411yescharacteristic
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4—21no—
168C2×(C2×D43)⋊C4—28no—
169C2×(C2×D43)⋊C4D411yescharacteristic
170C2×(C2×D43)⋊C4D411yescharacteristic
171C4⋊(C43⋊C8)C2314yescomplemented
172#13063248C2314yescomplemented
173#13063245C2314yes—
174#13063245C2314yescomplemented
175#13063245C2314yescomplemented
176(C2×D43)⋊C8C2314yes—
177(C2×D43)⋊C8C2314yescomplemented
178C22×Q8×C43C2311yescharacteristic
179C22×D4×C43C2311yescharacteristic
180C23×C4×C43—21no—
181C2×SD16×C43D418yescomplemented
182C2×SD16×C43C2314yes—
183C22×C8×C43C2311yescharacteristic
184C22×C8×C43C2311yescharacteristic
185C4×Q8×C43—22no—
186C4×Q8×C43C2314yescomplemented
187C4×D4×C43—22no—
188C4×D4×C43C2314yes—
189C2×C4⋊C4×C43—21no—
190C2×C4⋊C4×C43C2311yescharacteristic
191C2×C4⋊C4×C43C2311yescharacteristic
192C2×C22⋊C4×C43—21no—
193C2×C42×C43—21no—
194C2×C42×C43C2311yescharacteristic
195#107×C43C2314yescomplemented
196#103×C43C2314yescomplemented
197#102×C43C2314yes—
198#97×C43C2314yescomplemented
199C24×C43—21no—
200C23×D43—21no—
201C23×D43—21no—
202C23×D43—21no—
203C23×D43—24no—
204C23×D43—44no—
205C23×D43—44no—
206C23×D43—82no—
207C23×D43C2×D411yescharacteristic
208C23×D43C2×D411yescharacteristic
209C2×Q8×C43—21no—
210C2×Q8×C43—22no—
211C2×Q8×C43C2×D414yes—
212C2×Q8×C43C2412yes—
213C2×D4×C43—21no—
214C2×D4×C43—22no—
215C2×D4×C43C2×D414yes—
216C2×D4×C43C2412yes—
217C22×C4×C43—24no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—82no—
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2411yescharacteristic
225C2×C22⋊D43—24no—
226C2×C22⋊D43—24no—
227C2×C22⋊D43—44no—
228C2×C22⋊D43—44no—
229C22×Dic43—24no—
230C22×Dic43—21no—
231C22×Dic43—44no—
232C22×Dic43C2×D411yescharacteristic
233C22×Dic43C2×D411yescharacteristic
234#10621902—28no—
235#10621902—28no—
236#10621902—44no—
237#10621902—44no—
238#10621902—48no—
239#10621902—48no—
240#10621900—28no—
241#10621900—44no—
242#10621900—48no—
243D4×D43—28no—
244D4×D43—44no—
245D4×D43—48no—
246C2×D172—24no—
247C2×D172—21no—
248C2×D172—21no—
249C2×D172—21no—
250C2×D172—24no—
251C2×D172—24no—
252C2×D172—24no—
253C2×D172—24no—
254C2×D172—24no—
255C2×D172—24no—
256C2×D172—22no—
257C2×D172—22no—
258C2×D172—22no—
259C2×D172—22no—
260C2×D172—22no—
261C2×D172—22no—
262C2×D172—42no—
263C2×D172—44no—
264C2×D172—44no—
265C2×D172—44no—
266C2×D172—82no—
267C2×D172—82no—
268C2×D172—82no—
269C2×D172—82no—
270C2×D172C2×D414yes—
271C2×D172C2412yes—
272C2×D172C2412yes—
273C2×D172C2412yes—
274C2×C4×D43—22no—
275C2×C4×D43—22no—
276C2×C4×D43—22no—
277C2×C4×D43—22no—
278C2×C4×D43—24no—
279C2×C4×D43—24no—
280C2×C4×D43—44no—
281C2×C4×D43—44no—
282C2×C4×D43C2×D412yes—
283C2×C4×D43C2×D412yes—
284C2×C4×D43C2412yes—
285C2×C4×D43C2412yes—
286C2×Dic86—22no—
287C2×Dic86—22no—
288C2×Dic86—21no—
289C2×Dic86C2412yes—
290SD16×C43C2×D4116yescomplemented
291C2×C8×C43—22no—
292C2×C8×C43C2×D414yes—
293C2×C8×C43C2412yes—
294C2×C8×C43C2412yes—
295C4⋊C4×C43—24no—
296C4⋊C4×C43—21no—
297C4⋊C4×C43—21no—
298C4⋊C4×C43C2412yes—
299C4⋊C4×C43C2412yes—
300C22⋊C4×C43—24no—
301C42×C43—24no—
302C42×C43C2×D412yes—
303C42×C43C2412yes—
304#10621885—28no—
305#10621884—28no—
306#10621882—28no—
307#10621882—28no—
308(C2×D43)⋊C4—24no—
309(C2×D43)⋊C4—24no—
310(C2×D43)⋊C4—24no—
311(C2×D43)⋊C4—24no—
312(C2×D43)⋊C4—24no—
313(C2×D43)⋊C4—24no—
314(C2×D43)⋊C4C2×D414yes—
315(C2×D43)⋊C4C2×D414yes—
316C4⋊Dic43—24no—
317C4⋊Dic43C2×D414yes—
318C2×C43⋊C8—22no—
319C2×C43⋊C8—22no—
320C2×C43⋊C8C2412yes—
321C2×C43⋊C8C2412yes—
322D344—28no—
323D344—44no—
324#10621873—28no—
325#10621873—44no—
326#10621872—28no—
327C8×D43—28no—
328C23×C43—24no—
329C23×C43—22no—
330C23×C43—42no—
331C23×C43—42no—
332C23×C43C22×D411yescharacteristic
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
339C22×D43—22no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—48no—
343C22×D43—48no—
344C22×D43—42no—
345C22×D43—42no—
346C22×D43—42no—
347C22×D43—42no—
348C22×D43—42no—
349C22×D43—42no—
350C22×D43—42no—
351C22×D43—42no—
352C22×D43—42no—
353C22×D43—84no—
354C22×D43—816no—
355C22×D43C22×D412yes—
356C22×D43C22×D412yes—
357Q8×C43—24no—
358Q8×C43—22no—
359Q8×C43C22×D414yes—
360D4×C43—24no—
361D4×C43—22no—
362D4×C43C22×D414yes—
363C2×C4×C43—24no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—22no—
367C2×C4×C43—22no—
368C2×C4×C43—22no—
369C2×C4×C43—42no—
370C2×C4×C43—42no—
371C2×C4×C43—84no—
372C2×C4×C43C22×D412yes—
373C2×C4×C43C22×D412yes—
374C2×C4×C43C22×D411yescharacteristic
375C2×C4×C43C22×D412yes—
376C2×C4×C43H(5,𝔽2)12yes—
377C2×C4×C43C2511yescharacteristic
378C22⋊D43—48no—
379C22⋊D43—48no—
380C2×Dic43—22no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—48no—
384C2×Dic43—42no—
385C2×Dic43C22×D412yes—
386C2×Dic43C22×D412yes—
387D172—22no—
388D172—22no—
389D172—22no—
390D172—22no—
391D172—22no—
392D172—22no—
393D172—44no—
394D172—48no—
395D172—48no—
396D172—48no—
397D172—42no—
398D172—42no—
399D172—42no—
400D172—84no—
401D172—84no—
402D172—84no—
403D172—84no—
404C4×D43—24no—
405C4×D43—24no—
406C4×D43—22no—
407C4×D43—22no—
408C4×D43—22no—
409C4×D43—22no—
410C4×D43—48no—
411C4×D43—48no—
412Dic86—22no—
413Dic86—22no—
414Dic86—42no—
415C8×C43—22no—
416C8×C43C22×D414yes—
417C43⋊C8—22no—
418C43⋊C8—22no—
419C2×#3268—431nomaximal, Sylow
420C22×C43—24no—
421C22×C43—48no—
422C22×C43—42no—
423C22×C43—42no—
424C22×C43D4212yes—
425C22×C43#57512yes—
426C22×C43#57612yes—
427C22×C43C23×D411yescharacteristic
428C2×D43—22no—
429C2×D43—22no—
430C2×D43—22no—
431C2×D43—22no—
432C2×D43—22no—
433C2×D43—22no—
434C2×D43—44no—
435C2×D43—44no—
436C2×D43—42no—
437C2×D43—42no—
438C2×D43—42no—
439C2×D43—42no—
440C2×D43—42no—
441C2×D43—42no—
442C2×D43—42no—
443C2×D43—42no—
444C2×D43—42no—
445C2×D43—816no—
446C2×D43—84no—
447C2×D43—84no—
448C2×D43—84no—
449C4×C43—24no—
450C4×C43—22no—
451C4×C43—22no—
452C4×C43—42no—
453C4×C43—42no—
454C4×C43D4212yes—
455C4×C43C23×D411yescharacteristic
456C4×C43C2×H(5,𝔽2)11yescharacteristic
457Dic43—22no—
458Dic43—22no—
459Dic43—42no—
460C22×AGL(1,ℤ/8)—431no—
461C22×#135—431no—
462C2×#550—431no—
463C2×#546—431no—
464#3268—4316no—
465C2×#496—431no—
466C2×#468—431no—
467C2×#466—431no—
468C2×#464—431no—
469C2×#459—431no—
470C2×#452—431no—
471C2×#449—431no—
472C2×#449—431no—
473C2×#447—431no—
474C2×#440D4311yescharacteristic, complemented
475C2×#435—431no—
476C2×C43—44no—
477C2×C43#326814yescomplemented
478C2×C43C2×D4211yescharacteristic
479C2×C43C2×#57511yescharacteristic
480C2×C43C2×#57611yescharacteristic
481D43—42no—
482D43—42no—
483D43—82no—
484D43—82no—
485D43—82no—
486C22×#41—431no—
487C22×#41—431no—
488C22×#41—431no—
489C23×D4—431no—
490C2×AGL(1,ℤ/8)—438no—
491C2×AGL(1,ℤ/8)—868no—
492C2×#135—438no—
493C2×#135—868no—
494C22×Q16—431no—
495C22×SD16—431no—
496C22×SD16—431no—
497C22×SD16—431no—
498C22×SD16C2×D4311yescharacteristic
499C22×D8—431no—
500C22×D8—431no—
501C22×D8—431no—
502C22×D8—431no—
503C22×M16—431no—
504C23×C8—431no—
505#550—438no—
506#550—864no—
507#546—438no—
508#546—864no—
509C2×#127—431no—
510C2×#127—861no—
511C2×#124—431no—
512C2×#123—861no—
513C2×C22⋊Q8—431no—
514C2×#121—431no—
515C2×#121—431no—
516C2×#121—431no—
517C2×#121—861no—
518C2×#121—861no—
519C2×#121—861no—
520C2×#120—861no—
521C2×C4×Q8C2×D4311yescharacteristic, complemented
522C2×C4×D4—431no—
523C2×C4×D4—861no—
524C2×C4×D4C2×D4311yescharacteristic
525C22×C22⋊C4—861no—
526#496—438no—
527#468—438no—
528#466—438no—
529#464—438no—
530#459—438no—
531#452—438no—
532#449—438no—
533#449—438no—
534#447—438no—
535#440C2×D4318yescomplemented
536#435—438no—
537C2×#107C2×D4311yescharacteristic, complemented
538C2×C4⋊C8—431no—
539C2×#103—431no—
540C2×#103C2×D4311yescharacteristic, complemented
541C2×#102—431no—
542C2×#102—431no—
543C2×#102—431no—
544C2×#102C2×D4311yescharacteristic
545C2×C22⋊C8—431no—
546C2×C22⋊C8—431no—
547C2×#97C2×D4311yescharacteristic, complemented
548C43C2×#326811yescharacteristic, complemented, Sylow
549C25—861no—
550C2×#41—434no—
551C2×#41—434no—
552C2×#41—434no—
553C2×#41—862no—
554C2×#41—862no—
555C2×#41—862no—
556C2×#41—864no—
557C2×#41—864no—
558C2×#41—864no—
559C2×#41—1722no—
560C2×#41—1722no—
561C2×#41—1722no—
562C22×Q8—431no—
563C22×Q8C22×D4311yescharacteristic
564C22×D4—434no—
565C22×D4—431no—
566C22×D4—431no—
567C22×D4—431no—
568C22×D4—431no—
569C22×D4—861no—
570C22×D4—861no—
571C22×D4—861no—
572C22×D4—861no—
573C22×D4—861no—
574C22×D4—862no—
575C22×D4—861no—
576C22×D4—864no—
577C22×D4—861no—
578C22×D4—861no—
579C22×D4—861no—
580C22×D4—1722no—
581C22×D4C22×D4311yescharacteristic
582C23×C4—21no—
583C23×C4—431no—
584C23×C4—431no—
585C23×C4—861no—
586C23×C4—861no—
587C23×C4—861no—
588AGL(1,ℤ/8)—8632no—
589#135—8632no—
590C2×Q16—434no—
591C2×Q16—864no—
592C2×SD16—434no—
593C2×SD16—434no—
594C2×SD16—434no—
595C2×SD16—864no—
596C2×SD16—864no—
597C2×SD16—1722no—
598C2×SD16D17218yescomplemented
599C2×SD16C22×D4314yes—
600C2×D8—434no—
601C2×D8—434no—
602C2×D8—434no—
603C2×D8—434no—
604C2×D8—864no—
605C2×D8—864no—
606C2×D8—864no—
607C2×D8—1722no—
608C2×M16—434no—
609C2×M16—864no—
610C22×C8—431no—
611C22×C8—431no—
612C22×C8—434no—
613C22×C8—864no—
614C22×C8C22×D4311yescharacteristic
615C22×C8C22×D4311yescharacteristic
616#127—434no—
617#127—868no—
618#127—862no—
619#124—434no—
620#124—862no—
621#123—868no—
622C22⋊Q8—434no—
623C22⋊Q8—862no—
624#121—434no—
625#121—434no—
626#121—434no—
627#121—868no—
628#121—868no—
629#121—868no—
630#121—862no—
631#121—862no—
632#121—862no—
633#120—868no—
634C4×Q8—22no—
635C4×Q8C22×D4314yescomplemented
636C4×D4—22no—
637C4×D4—434no—
638C4×D4—434no—
639C4×D4—868no—
640C4×D4C22×D4314yes—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—431no—
643C2×C4⋊C4—861no—
644C2×C4⋊C4C22×D4311yescharacteristic
645C2×C4⋊C4C22×D4311yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—431no—
648C2×C22⋊C4—431no—
649C2×C22⋊C4—868no—
650C2×C22⋊C4—861no—
651C2×C22⋊C4—861no—
652C2×C22⋊C4—861no—
653C2×C22⋊C4—861no—
654C2×C22⋊C4—861no—
655C2×C22⋊C4—861no—
656C2×C42—21no—
657C2×C42C22×D4311yescharacteristic
658#107C22×D4314yescomplemented
659C4⋊C8—434no—
660#103—434no—
661#103C22×D4314yescomplemented
662#102—434no—
663#102—434no—
664#102—434no—
665#102C22×D4314yes—
666C22⋊C8—434no—
667C22⋊C8—434no—
668#97C22×D4314yescomplemented
669C24—21no—
670C24—431no—
671C24—431no—
672C24—864no—
673C24—861no—
674C24—861no—
675C24—861no—
676C24—3442no—
677C24—1724no—
678C24—1724no—
679#41—868no—
680#41—868no—
681#41—868no—
682#41—1724no—
683#41—1728no—
684#41—1724no—
685#41—1724no—
686#41—1728no—
687#41—1728no—
688C2×Q8—21no—
689C2×Q8—22no—
690C2×Q8—432no—
691C2×Q8—861no—
692C2×Q8—862no—
693C2×Q8—862no—
694C2×Q8C2×D17214yes—
695C2×Q8C23×D4312yes—
696C2×D4—21no—
697C2×D4—22no—
698C2×D4—434no—
699C2×D4—432no—
700C2×D4—432no—
701C2×D4—432no—
702C2×D4—864no—
703C2×D4—864no—
704C2×D4—864no—
705C2×D4—864no—
706C2×D4—864no—
707C2×D4—864no—
708C2×D4—868no—
709C2×D4—864no—
710C2×D4—864no—
711C2×D4—864no—
712C2×D4—861no—
713C2×D4—861no—
714C2×D4—861no—
715C2×D4—862no—
716C2×D4—862no—
717C2×D4—862no—
718C2×D4—862no—
719C2×D4—862no—
720C2×D4—862no—
721C2×D4—3442no—
722C2×D4—3442no—
723C2×D4—3442no—
724C2×D4—3442no—
725C2×D4—1722no—
726C2×D4—1724no—
727C2×D4—1724no—
728C2×D4—1724no—
729C2×D4—1724no—
730C2×D4—1728no—
731C2×D4—1724no—
732C2×D4—1724no—
733C2×D4C2×D17214yes—
734C2×D4C23×D4312yes—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—24no—
739C22×C4—82no—
740C22×C4—431no—
741C22×C4—431no—
742C22×C4—432no—
743C22×C4—432no—
744C22×C4—432no—
745C22×C4—432no—
746C22×C4—864no—
747C22×C4—864no—
748C22×C4—864no—
749C22×C4—862no—
750C22×C4—862no—
751C22×C4—862no—
752C22×C4—862no—
753C22×C4—861no—
754C22×C4—1724no—
755C22×C4—1724no—
756C22×C4—1724no—
757C22×C4D4×D4311yescharacteristic
758C22×C4D4×D4311yescharacteristic
759C22×C4C23×D4311yescharacteristic
760Q16—868no—
761SD16—868no—
762SD16—868no—
763SD16—1724no—
764SD16C2×D172116yescomplemented
765D8—868no—
766D8—868no—
767D8—868no—
768D8—1724no—
769M16—868no—
770C2×C8—22no—
771C2×C8—432no—
772C2×C8—432no—
773C2×C8—862no—
774C2×C8—862no—
775C2×C8—868no—
776C2×C8C2×D17214yes—
777C2×C8C23×D4312yes—
778C2×C8C23×D4312yes—
779C4⋊C4—24no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—434no—
783C4⋊C4—864no—
784C4⋊C4C23×D4312yes—
785C4⋊C4C23×D4312yes—
786C22⋊C4—24no—
787C22⋊C4—434no—
788C22⋊C4—434no—
789C22⋊C4—864no—
790C22⋊C4—864no—
791C22⋊C4—864no—
792C22⋊C4—864no—
793C22⋊C4—864no—
794C22⋊C4—864no—
795C42—24no—
796C42D4×D4312yes—
797C42C23×D4312yes—
798C23—22no—
799C23—24no—
800C23—42no—
801C23—42no—
802C23—432no—
803C23—432no—
804C23—862no—
805C23—862no—
806C23—862no—
807C23—862no—
808C23—862no—
809C23—862no—
810C23—862no—
811C23—862no—
812C23—862no—
813C23—3444no—
814C23—34416no—
815C23—1728no—
816C23—1728no—
817C23—1722no—
818C23—1722no—
819C23—1722no—
820C23—1722no—
821C23—1722no—
822C23—1722no—
823C23—1722no—
824C23—1722no—
825C23—1722no—
826C23C2×D4×D4311yescharacteristic
827Q8—22no—
828Q8—24no—
829Q8—862no—
830Q8—862no—
831Q8—1722no—
832Q8C22×D17214yes—
833D4—22no—
834D4—24no—
835D4—862no—
836D4—862no—
837D4—862no—
838D4—862no—
839D4—862no—
840D4—862no—
841D4—3444no—
842D4—3444no—
843D4—3444no—
844D4—3444no—
845D4—1724no—
846D4—1728no—
847D4—1728no—
848D4—1728no—
849D4—1728no—
850D4—1728no—
851D4—1722no—
852D4—1722no—
853D4—1722no—
854D4C22×D17214yes—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—24no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—84no—
864C2×C4—432no—
865C2×C4—432no—
866C2×C4—862no—
867C2×C4—862no—
868C2×C4—862no—
869C2×C4—862no—
870C2×C4—862no—
871C2×C4—862no—
872C2×C4—864no—
873C2×C4—864no—
874C2×C4—862no—
875C2×C4—1728no—
876C2×C4—1728no—
877C2×C4—1728no—
878C2×C4—1722no—
879C2×C4C2×D4×D4312yes—
880C2×C4C2×D4×D4312yes—
881C2×C4C2×D4×D4311yescharacteristic
882C2×C4C22×D17212yes—
883C2×C4#1306337112yes—
884C2×C4C24×D4311yescharacteristic
885C8—22no—
886C8—862no—
887C8—862no—
888C8C22×D17214yes—
889C22—24no—
890C22—42no—
891C22—42no—
892C22—48no—
893C22—862no—
894C22—862no—
895C22—862no—
896C22—862no—
897C22—862no—
898C22—862no—
899C22—34416no—
900C22—3444no—
901C22—3444no—
902C22—3444no—
903C22—1722no—
904C22—1722no—
905C22—1722no—
906C22—1722no—
907C22—1722no—
908C22—1722no—
909C22—1722no—
910C22—1722no—
911C22—1722no—
912C22—1724no—
913C22—1724no—
914C22D4×D17212yes—
915C22#1458369812yes—
916C22#1458370312yes—
917C22C22×D4×D4311yescharacteristic
918C4—24no—
919C4—22no—
920C4—22no—
921C4—42no—
922C4—42no—
923C4—862no—
924C4—862no—
925C4—1722no—
926C4D4×D17212yes—
927C4C23×D17211yescharacteristic
928C4C2×#1306337111yescharacteristic
929C2—44no—
930C2—3442no—
931C2—3442no—
932C2—3442no—
933C2—1722no—
934C2—1722no—
935C2#1914613714yesdirect product factor
936C2C2×D4×D17211yescharacteristic
937C2C2×#1458369811yescharacteristic
938C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
hypercenterC2×#440D43
hypocenterC43C2×#3268
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C22×#13063352C2semidirect
2. C22×#13063346C2semidirect
3. C2×#14583571C2semidirect
4. C2×#14583544C2semidirect
5. #19146137C2direct (N × H)
6. C2×#14583288C2semidirect
7. C2×#14583146C2semidirect
8. C2×#14583136C2semidirect
9. C2×#14583121C2semidirect
10. C2×#14583094C2semidirect
11. C2×#14583064C2semidirect
12. C2×#14583047C2semidirect
13. C2×#14583045C2semidirect
14. C2×#14583034C2semidirect
15. C2×#14582972C2semidirect
16. C2×C43×#440C2semidirect
18. C22×#10621902C22semidirect
22. C2×#13063352C22semidirect
24. C2×#13063346C22semidirect
25. C22×#10621885C22semidirect
26. C22×#10621873C22semidirect
27. C22×#10621873C22semidirect
34. C22×C8×D43C22semidirect
36. #14583571C22semidirect
38. #14583544C22semidirect
40. C2×#13063322C22semidirect
48. C2×#13063300C22semidirect
54. #14583288C22semidirect
55. #14583146C22semidirect
56. #14583136C22semidirect
57. #14583121C22semidirect
58. #14583094C22semidirect
59. #14583064C22semidirect
60. #14583047C22semidirect
61. #14583045C22semidirect
62. #14583034C22semidirect
63. #14582972C22semidirect
64. C2×C4⋊(C43⋊C8)C22semidirect
65. C2×#13063248C22semidirect
67. C2×#13063245C22semidirect
68. C2×#13063245C22semidirect
70. C2×(C2×D43)⋊C8C22semidirect
72. C2×C4×Q8×C43C22semidirect
74. C43×#440C22semidirect
75. C2×#107×C43C22semidirect
76. C2×#103×C43C22semidirect
78. C2×#97×C43C22semidirect
87. C2×#10621902C23semidirect
118. C2×#10621885C23semidirect
121. C2×#10621873C23semidirect
122. C2×#10621873C23semidirect
138. C2×C8×D43C23semidirect
141. #13063322C23semidirect
154. #13063300C23semidirect
171. C4⋊(C43⋊C8)C23semidirect
172. #13063248C23semidirect
174. #13063245C23semidirect
175. #13063245C23semidirect
177. (C2×D43)⋊C8C23semidirect
181. C2×SD16×C43D4semidirect
186. C4×Q8×C43C23semidirect
195. #107×C43C23semidirect
196. #103×C43C23semidirect
198. #97×C43C23semidirect
290. SD16×C43C2×D4semidirect
474. C2×#440D43semidirect
477. C2×C43#3268semidirect
521. C2×C4×Q8C2×D43semidirect
535. #440C2×D43semidirect
537. C2×#107C2×D43semidirect
540. C2×#103C2×D43semidirect
547. C2×#97C2×D43semidirect
548. C43C2×#3268semidirect
598. C2×SD16D172semidirect
635. C4×Q8C22×D43semidirect
658. #107C22×D43semidirect
661. #103C22×D43semidirect
668. #97C22×D43semidirect
764. SD16C2×D172semidirect
935. C2#19146137direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633522
C22×#130633462
C2×#145835712
C2×#145835442
#191461372
C2×#145832882
C2×#145831462
C2×#145831362
C2×#145831212
C2×#145830942
C2×#145830642
C2×#145830472
C2×#145830452
C2×#145830342
C2×#145829722
C2×C43×#4402
C2×#326843