Finite Group Databasebeta

← C2×#19146107 #25971580

Subgroups — C2×#19146107 #25971580

Order 11008.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063354C211yesmaximal, characteristic, complemented
2C22×SD16×D43C211yesmaximal, characteristic, complemented
3C2×Q8×D172C211yesmaximal, characteristic, complemented
4C2×#14583544C211yesmaximal, characteristic
5#19146107C2116yesmaximal, direct product factor
6C2×#14583293C211yesmaximal, characteristic, complemented
7C2×#14583146C211yesmaximal, characteristic, complemented
8C2×#14583141C211yesmaximal, characteristic, complemented
9C2×#14583121C211yesmaximal, characteristic, complemented
10C2×#14583104C211yesmaximal, characteristic, complemented
11C2×#14583062C211yesmaximal, characteristic, complemented
12C2×#14583056C211yesmaximal, characteristic, complemented
13C2×#14583039C211yesmaximal, characteristic, complemented
14C2×#14583051C211yesmaximal, characteristic, complemented
15C2×#14582972C211yesmaximal, characteristic, complemented
16C2×C43×#440C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×Q8×D43C2211yescharacteristic, complemented
20C22×D4×D43C2211yescharacteristic
21C2×#13063354—28no—
22C2×#13063354C2218yescomplemented
23C22×Dic172C2211yescharacteristic, complemented
24C22×Dic172C2211yescharacteristic, complemented
25C22×#10621885C2211yescharacteristic, complemented
26C22×#10621873C2211yescharacteristic
27C22×#10621873C2211yescharacteristic
28C22×#10621883C2211yescharacteristic
29C22×#10621883C2211yescharacteristic
30C22×#10621884C2211yescharacteristic
31C2×SD16×D43—28no—
32C2×SD16×D43C2218yescomplemented
33C22×#10621872C2211yescharacteristic, complemented
34C22×C8×D43C2211yescharacteristic
35Q8×D172—24no—
36Q8×D172C2218yescomplemented
37#14583544—24no—
38#14583544C2218yes—
39C2×#13063325—21no—
40C2×#13063325C2211yescharacteristic, complemented
41C2×#13063313C2211yescharacteristic
42C2×#13063309—21no—
43C2×#13063305—21no—
44C2×#13063305—21no—
45C2×#13063305C2211yescharacteristic
46C2×#13063305C2211yescharacteristic
47C2×#13063305C2211yescharacteristic, complemented
48C2×#13063300C2211yescharacteristic
49C2×#13063299—21no—
50C2×#13063295—21no—
51C2×C4×D172—21no—
52C2×C4×D172C2211yescharacteristic
53C22×(C2×D43)⋊C4—21no—
54#14583293C2218yescomplemented
55#14583146C2218yescomplemented
56#14583141C2218yescomplemented
57#14583121C2218yescomplemented
58#14583104C2218yescomplemented
59#14583062C2218yescomplemented
60#14583056C2218yescomplemented
61#14583051C2218yescomplemented
62#14583039C2218yescomplemented
63#14582972C2218yescomplemented
64C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
65C2×#13063248C2211yescharacteristic, complemented
66C2×#13063248C2211yescharacteristic, complemented
67C2×#13063248C2211yescharacteristic, complemented
68C2×#13063245C2211yescharacteristic
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×#10621900—24no—
81C2×#10621900—22no—
82C2×#10621900—42no—
83C2×#10621900C2314yes—
84C22×Dic86—21no—
85C22×Dic86—21no—
86C22×Dic86C2311yescharacteristic
87C22×Dic86C2311yescharacteristic
88C22×Dic86C2311yescharacteristic
89C2×Q8×D43—22no—
90C2×Q8×D43—22no—
91C2×Q8×D43—24no—
92C2×Q8×D43—24no—
93C2×Q8×D43—42no—
94C2×Q8×D43—42no—
95C2×Q8×D43C2314yes—
96C2×Q8×D43C2314yescomplemented
97C22×D172—21no—
98C22×D172D411yescharacteristic
99C22×D172C2311yescharacteristic
100C22×C22⋊D43—21no—
101C22×C22⋊D43—21no—
102C2×D4×D43—24no—
103C2×D4×D43—22no—
104C2×D4×D43—42no—
105C2×D4×D43C2314yes—
106C23×Dic43—21no—
107C22×C4×D43—21no—
108C22×C4×D43—21no—
109C22×C4×D43C2311yescharacteristic
110C22×C4×D43C2311yescharacteristic
111#13063354—232no—
112C2×Dic172—24no—
113C2×Dic172—42no—
114C2×Dic172C2314yescomplemented
115C2×Dic172C2314yescomplemented
116C2×#10621885—24no—
117C2×#10621885C2314yescomplemented
118C2×#10621873—24no—
119C2×#10621873—42no—
120C2×#10621873C2314yes—
121C2×#10621873C2314yes—
122C2×#10621883—24no—
123C2×#10621883—24no—
124C2×#10621883C2314yes—
125C2×#10621883C2314yes—
126C2×#10621884—24no—
127C2×#10621884C2314yes—
128SD16×D43—232no—
129C2×#10621872—24no—
130C2×#10621872C2314yescomplemented
131C22×C43⋊C8C2311yescharacteristic
132C22×C43⋊C8C2311yescharacteristic
133C2×C8×D43—24no—
134C2×C8×D43C2314yes—
135#13063325—22no—
136#13063325—28no—
137#13063325C2314yescomplemented
138#13063313—22no—
139#13063313C2314yes—
140#13063309—28no—
141#13063305—22no—
142#13063305—22no—
143#13063305—22no—
144#13063305—28no—
145#13063305—28no—
146#13063305C2314yes—
147#13063305C2314yes—
148#13063305C2314yescomplemented
149#13063300—22no—
150#13063300C2314yes—
151#13063299—28no—
152#13063295—28no—
153C4×D172—28no—
154C4×D172D414yes—
155C4×D172C2314yes—
156C2×C4⋊Dic43—21no—
157C2×C4⋊Dic43—21no—
158C2×C4⋊Dic43—21no—
159C2×C4⋊Dic43—21no—
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#13063248C2314yescomplemented
174#13063248C2314yescomplemented
175#13063245C2314yes—
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—24no—
202C23×D43—44no—
203C23×D43—44no—
204C23×D43—82no—
205C23×D43C2×D411yescharacteristic
206C23×D43C2×D411yescharacteristic
207C2×Q8×C43—21no—
208C2×Q8×C43—22no—
209C2×Q8×C43C2×D414yes—
210C2×Q8×C43C2412yes—
211C2×D4×C43—21no—
212C2×D4×C43—22no—
213C2×D4×C43C2×D414yes—
214C2×D4×C43C2412yes—
215C22×C4×C43—24no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—82no—
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2411yescharacteristic
223C2×C22⋊D43—24no—
224C2×C22⋊D43—24no—
225C2×C22⋊D43—44no—
226C2×C22⋊D43—44no—
227C22×Dic43—24no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—44no—
232C22×Dic43C2×D411yescharacteristic
233C22×Dic43C2×D411yescharacteristic
234Q8×D43—28no—
235Q8×D43—28no—
236Q8×D43—44no—
237Q8×D43—44no—
238Q8×D43—48no—
239Q8×D43—48no—
240#10621900—28no—
241#10621900—44no—
242#10621900—48no—
243D4×D43—28no—
244D4×D43—44no—
245D4×D43—48no—
246C2×D172—21no—
247C2×D172—24no—
248C2×D172—24no—
249C2×D172—22no—
250C2×D172—22no—
251C2×D172—82no—
252C2×D172C2×D414yes—
253C2×D172C2412yes—
254C2×C4×D43—22no—
255C2×C4×D43—22no—
256C2×C4×D43—22no—
257C2×C4×D43—22no—
258C2×C4×D43—24no—
259C2×C4×D43—24no—
260C2×C4×D43—44no—
261C2×C4×D43—44no—
262C2×C4×D43C2×D412yes—
263C2×C4×D43C2×D412yes—
264C2×C4×D43C2412yes—
265C2×C4×D43C2412yes—
266C2×Dic86—22no—
267C2×Dic86—22no—
268C2×Dic86—22no—
269C2×Dic86—22no—
270C2×Dic86—22no—
271C2×Dic86—22no—
272C2×Dic86—21no—
273C2×Dic86—21no—
274C2×Dic86—21no—
275C2×Dic86—24no—
276C2×Dic86—24no—
277C2×Dic86—44no—
278C2×Dic86—44no—
279C2×Dic86C2412yes—
280C2×Dic86C2412yes—
281C2×Dic86C2412yes—
282SD16×C43C2×D4116yescomplemented
283C2×C8×C43—22no—
284C2×C8×C43C2×D414yes—
285C2×C8×C43C2412yes—
286C2×C8×C43C2412yes—
287C4⋊C4×C43—24no—
288C4⋊C4×C43—21no—
289C4⋊C4×C43—21no—
290C4⋊C4×C43C2412yes—
291C4⋊C4×C43C2412yes—
292C22⋊C4×C43—24no—
293C42×C43—24no—
294C42×C43C2×D412yes—
295C42×C43C2412yes—
296#10621885—28no—
297#10621884—28no—
298#10621883—28no—
299#10621883—28no—
300(C2×D43)⋊C4—24no—
301(C2×D43)⋊C4—24no—
302(C2×D43)⋊C4—24no—
303(C2×D43)⋊C4—24no—
304(C2×D43)⋊C4—24no—
305(C2×D43)⋊C4—24no—
306(C2×D43)⋊C4C2×D414yes—
307(C2×D43)⋊C4C2×D414yes—
308C4⋊Dic43—24no—
309C4⋊Dic43—24no—
310C4⋊Dic43—24no—
311C4⋊Dic43—24no—
312C4⋊Dic43—24no—
313C4⋊Dic43C2×D414yes—
314C2×C43⋊C8—22no—
315C2×C43⋊C8—22no—
316C2×C43⋊C8C2412yes—
317C2×C43⋊C8C2412yes—
318Dic172—28no—
319Dic172—44no—
320#10621873—28no—
321#10621873—44no—
322#10621872—28no—
323C8×D43—28no—
324C23×C43—24no—
325C23×C43—22no—
326C23×C43—42no—
327C23×C43—42no—
328C23×C43C22×D411yescharacteristic
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—22no—
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—48no—
336C22×D43—42no—
337C22×D43—42no—
338C22×D43—42no—
339C22×D43—48no—
340C22×D43—84no—
341C22×D43—816no—
342C22×D43#13714yescomplemented
343C22×D43C22×D412yes—
344C22×D43C22×D412yes—
345Q8×C43—24no—
346Q8×C43—22no—
347Q8×C43C22×D414yes—
348D4×C43—24no—
349D4×C43—22no—
350D4×C43C22×D414yes—
351C2×C4×C43—24no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—42no—
358C2×C4×C43—42no—
359C2×C4×C43—84no—
360C2×C4×C43C22×D412yes—
361C2×C4×C43C22×D412yes—
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C22×D412yes—
364C2×C4×C43H(5,𝔽2)12yes—
365C2×C4×C43C2511yescharacteristic
366C22⋊D43—48no—
367C22⋊D43—48no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—22no—
372C2×Dic43—22no—
373C2×Dic43—48no—
374C2×Dic43—42no—
375C2×Dic43—42no—
376C2×Dic43—42no—
377C2×Dic43C22×D412yes—
378C2×Dic43C22×D412yes—
379D172—28no—
380D172—22no—
381D172—22no—
382D172—42no—
383D172—84no—
384C4×D43—24no—
385C4×D43—24no—
386C4×D43—22no—
387C4×D43—22no—
388C4×D43—22no—
389C4×D43—22no—
390C4×D43—48no—
391C4×D43—48no—
392Dic86—22no—
393Dic86—22no—
394Dic86—22no—
395Dic86—22no—
396Dic86—22no—
397Dic86—22no—
398Dic86—48no—
399Dic86—48no—
400Dic86—42no—
401Dic86—42no—
402Dic86—42no—
403C8×C43—22no—
404C8×C43C22×D414yes—
405C43⋊C8—22no—
406C43⋊C8—22no—
407C2×#3266—431nomaximal, Sylow
408C22×C43—24no—
409C22×C43—48no—
410C22×C43—42no—
411C22×C43—42no—
412C22×C43D4212yes—
413C22×C43C2×#13712yes—
414C22×C43#57712yes—
415C22×C43C23×D411yescharacteristic
416C2×D43—22no—
417C2×D43—28no—
418C2×D43—22no—
419C2×D43—22no—
420C2×D43—22no—
421C2×D43—22no—
422C2×D43—44no—
423C2×D43—42no—
424C2×D43—42no—
425C2×D43—42no—
426C2×D43—816no—
427C2×D43—84no—
428C2×D43C2×#13714yescomplemented
429C4×C43—24no—
430C4×C43—22no—
431C4×C43—22no—
432C4×C43—42no—
433C4×C43—42no—
434C4×C43D4212yes—
435C4×C43C23×D411yescharacteristic
436C4×C43C2×H(5,𝔽2)11yescharacteristic
437Dic43—22no—
438Dic43—22no—
439Dic43—42no—
440Dic43—42no—
441Dic43—42no—
442C22×#137—431no—
443C23×SD16—431no—
444C2×D4×Q8—431no—
445C2×#546—431no—
446#3266—4316no—
447C2×#497—431no—
448C2×#468—431no—
449C2×#467—431no—
450C2×#464—431no—
451C2×#461—431no—
452C2×#452—431no—
453C2×#451—431no—
454C2×#448—431no—
455C2×#450—431no—
456C2×#440D4311yescharacteristic, complemented
457C2×#435—431no—
458C2×C43—44no—
459C2×C43#326614yescomplemented
460C2×C43C2×D4211yescharacteristic
461C2×C43C22×#13711yescharacteristic
462C2×C43C2×#57711yescharacteristic
463D43—24no—
464D43—42no—
465D43—82no—
466C22×#41—431no—
467C23×Q8—431no—
468C23×Q8—431no—
469C23×D4—431no—
470C2×#137—438no—
471C2×#137—868no—
472C22×Q16—431no—
473C22×Q16—431no—
474C22×Q16—431no—
475C22×SD16—431no—
476C22×SD16—431no—
477C22×SD16—431no—
478C22×SD16—438no—
479C22×SD16—431no—
480C22×SD16—431no—
481C22×SD16—868no—
482C22×SD16C2×D4311yescharacteristic
483C22×M16—431no—
484C23×C8—431no—
485D4×Q8—438no—
486D4×Q8—864no—
487#546—438no—
488#546—864no—
489C2×C4⋊Q8—431no—
490C2×C4⋊Q8—861no—
491C2×#124—431no—
492C2×#123—861no—
493C2×C22⋊Q8—431no—
494C2×C22⋊Q8—431no—
495C2×C22⋊Q8—431no—
496C2×C22⋊Q8—861no—
497C2×C22⋊Q8—861no—
498C2×#121—431no—
499C2×#121—861no—
500C2×#120—861no—
501C2×C4×Q8C2×D4311yescharacteristic, complemented
502C2×C4×D4—431no—
503C2×C4×D4—861no—
504C2×C4×D4C2×D4311yescharacteristic
505C22×C22⋊C4—861no—
506#497—438no—
507#468—438no—
508#467—438no—
509#464—438no—
510#461—438no—
511#452—438no—
512#451—438no—
513#450—438no—
514#448—438no—
515#440C2×D4318yescomplemented
516#435—438no—
517C2×#107C2×D4311yescharacteristic, complemented
518C2×C4⋊C8—431no—
519C2×#103—431no—
520C2×#103—431no—
521C2×#103—431no—
522C2×#103C2×D4311yescharacteristic, complemented
523C2×#102—431no—
524C2×#102C2×D4311yescharacteristic
525C2×C22⋊C8—431no—
526C2×C22⋊C8—431no—
527C2×#97C2×D4311yescharacteristic, complemented
528C43C2×#326611yescharacteristic, complemented, Sylow
529C25—861no—
530C2×#41—434no—
531C2×#41—862no—
532C2×#41—864no—
533C2×#41—1722no—
534C22×Q8—434no—
535C22×Q8—434no—
536C22×Q8—431no—
537C22×Q8—431no—
538C22×Q8—431no—
539C22×Q8—861no—
540C22×Q8—861no—
541C22×Q8—862no—
542C22×Q8—862no—
543C22×Q8—864no—
544C22×Q8—864no—
545C22×Q8—1722no—
546C22×Q8—1722no—
547C22×Q8C22×D4311yescharacteristic
548C22×D4—434no—
549C22×D4—431no—
550C22×D4—431no—
551C22×D4—861no—
552C22×D4—862no—
553C22×D4—861no—
554C22×D4—864no—
555C22×D4—861no—
556C22×D4—1722no—
557C22×D4C22×D4311yescharacteristic
558C23×C4—21no—
559C23×C4—431no—
560C23×C4—431no—
561C23×C4—861no—
562C23×C4—861no—
563C23×C4—861no—
564#137—8632no—
565C2×Q16—434no—
566C2×Q16—434no—
567C2×Q16—434no—
568C2×Q16—864no—
569C2×Q16—864no—
570C2×Q16—1722no—
571C2×SD16—434no—
572C2×SD16—434no—
573C2×SD16—434no—
574C2×SD16—434no—
575C2×SD16—434no—
576C2×SD16—864no—
577C2×SD16—864no—
578C2×SD16—864no—
579C2×SD16—8632no—
580C2×SD16—864no—
581C2×SD16—1722no—
582C2×SD16D17218yescomplemented
583C2×SD16C22×D4314yes—
584C2×M16—434no—
585C2×M16—864no—
586C22×C8—431no—
587C22×C8—431no—
588C22×C8—434no—
589C22×C8—864no—
590C22×C8C22×D4311yescharacteristic
591C22×C8C22×D4311yescharacteristic
592C4⋊Q8—434no—
593C4⋊Q8—868no—
594C4⋊Q8—862no—
595#124—434no—
596#124—862no—
597#123—868no—
598C22⋊Q8—434no—
599C22⋊Q8—434no—
600C22⋊Q8—434no—
601C22⋊Q8—868no—
602C22⋊Q8—868no—
603C22⋊Q8—862no—
604C22⋊Q8—862no—
605C22⋊Q8—862no—
606#121—434no—
607#121—868no—
608#121—862no—
609#120—868no—
610C4×Q8—22no—
611C4×Q8C22×D4314yescomplemented
612C4×D4—22no—
613C4×D4—434no—
614C4×D4—434no—
615C4×D4—868no—
616C4×D4C22×D4314yes—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—431no—
619C2×C4⋊C4—861no—
620C2×C4⋊C4—861no—
621C2×C4⋊C4—861no—
622C2×C4⋊C4—861no—
623C2×C4⋊C4—861no—
624C2×C4⋊C4C22×D4311yescharacteristic
625C2×C4⋊C4C22×D4311yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—431no—
628C2×C22⋊C4—431no—
629C2×C22⋊C4—868no—
630C2×C22⋊C4—861no—
631C2×C22⋊C4—861no—
632C2×C22⋊C4—861no—
633C2×C22⋊C4—861no—
634C2×C22⋊C4—861no—
635C2×C22⋊C4—861no—
636C2×C42—21no—
637C2×C42C22×D4311yescharacteristic
638#107C22×D4314yescomplemented
639C4⋊C8—434no—
640#103—434no—
641#103—434no—
642#103—434no—
643#103C22×D4314yescomplemented
644#102—434no—
645#102C22×D4314yes—
646C22⋊C8—434no—
647C22⋊C8—434no—
648#97C22×D4314yescomplemented
649C24—21no—
650C24—431no—
651C24—431no—
652C24—864no—
653C24—861no—
654C24—3442no—
655C24—1724no—
656C24—1724no—
657#41—868no—
658#41—1724no—
659#41—1728no—
660C2×Q8—21no—
661C2×Q8—22no—
662C2×Q8—432no—
663C2×Q8—432no—
664C2×Q8—432no—
665C2×Q8—864no—
666C2×Q8—864no—
667C2×Q8—861no—
668C2×Q8—861no—
669C2×Q8—861no—
670C2×Q8—868no—
671C2×Q8—868no—
672C2×Q8—862no—
673C2×Q8—862no—
674C2×Q8—862no—
675C2×Q8—862no—
676C2×Q8—862no—
677C2×Q8—862no—
678C2×Q8—1724no—
679C2×Q8—1724no—
680C2×Q8—1724no—
681C2×Q8—1724no—
682C2×Q8—1728no—
683C2×Q8—1728no—
684C2×Q8C2×D17214yes—
685C2×Q8C23×D4312yes—
686C2×D4—21no—
687C2×D4—22no—
688C2×D4—434no—
689C2×D4—432no—
690C2×D4—864no—
691C2×D4—864no—
692C2×D4—864no—
693C2×D4—868no—
694C2×D4—864no—
695C2×D4—861no—
696C2×D4—862no—
697C2×D4—862no—
698C2×D4—3442no—
699C2×D4—1724no—
700C2×D4—1728no—
701C2×D4—1724no—
702C2×D4—1724no—
703C2×D4C2×D17214yes—
704C2×D4C23×D4312yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—24no—
709C22×C4—82no—
710C22×C4—431no—
711C22×C4—431no—
712C22×C4—432no—
713C22×C4—432no—
714C22×C4—432no—
715C22×C4—432no—
716C22×C4—864no—
717C22×C4—864no—
718C22×C4—864no—
719C22×C4—862no—
720C22×C4—862no—
721C22×C4—862no—
722C22×C4—862no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—1724no—
727C22×C4—1724no—
728C22×C4—1724no—
729C22×C4D4×D4311yescharacteristic
730C22×C4D4×D4311yescharacteristic
731C22×C4C23×D4311yescharacteristic
732Q16—868no—
733Q16—868no—
734Q16—1724no—
735SD16—868no—
736SD16—868no—
737SD16—868no—
738SD16—868no—
739SD16—1724no—
740SD16C2×D172116yescomplemented
741M16—868no—
742C2×C8—22no—
743C2×C8—432no—
744C2×C8—432no—
745C2×C8—862no—
746C2×C8—862no—
747C2×C8—868no—
748C2×C8C2×D17214yes—
749C2×C8C23×D4312yes—
750C2×C8C23×D4312yes—
751C4⋊C4—24no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—434no—
755C4⋊C4—864no—
756C4⋊C4—864no—
757C4⋊C4—864no—
758C4⋊C4—864no—
759C4⋊C4—864no—
760C4⋊C4C23×D4312yes—
761C4⋊C4C23×D4312yes—
762C22⋊C4—24no—
763C22⋊C4—434no—
764C22⋊C4—434no—
765C22⋊C4—864no—
766C22⋊C4—864no—
767C22⋊C4—864no—
768C22⋊C4—864no—
769C22⋊C4—864no—
770C22⋊C4—864no—
771C42—24no—
772C42D4×D4312yes—
773C42C23×D4312yes—
774C23—22no—
775C23—24no—
776C23—42no—
777C23—42no—
778C23—434no—
779C23—432no—
780C23—432no—
781C23—862no—
782C23—862no—
783C23—862no—
784C23—862no—
785C23—862no—
786C23—862no—
787C23—34416no—
788C23—3444no—
789C23—1728no—
790C23—1728no—
791C23—1722no—
792C23—1722no—
793C23—1722no—
794C23C2×D4×D4311yescharacteristic
795Q8—22no—
796Q8—24no—
797Q8—862no—
798Q8—862no—
799Q8—862no—
800Q8—862no—
801Q8—862no—
802Q8—862no—
803Q8—1728no—
804Q8—1728no—
805Q8—1722no—
806Q8—1722no—
807Q8—1722no—
808Q8C22×D17214yes—
809D4—22no—
810D4—24no—
811D4—868no—
812D4—862no—
813D4—862no—
814D4—3444no—
815D4—1728no—
816D4—1728no—
817D4—1722no—
818D4C22×D17214yes—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—84no—
828C2×C4—432no—
829C2×C4—432no—
830C2×C4—862no—
831C2×C4—862no—
832C2×C4—862no—
833C2×C4—862no—
834C2×C4—862no—
835C2×C4—862no—
836C2×C4—864no—
837C2×C4—864no—
838C2×C4—862no—
839C2×C4—862no—
840C2×C4—862no—
841C2×C4—1728no—
842C2×C4—1728no—
843C2×C4—1728no—
844C2×C4—1722no—
845C2×C4—1722no—
846C2×C4—1722no—
847C2×C4C2×D4×D4312yes—
848C2×C4C2×D4×D4312yes—
849C2×C4C2×D4×D4311yescharacteristic
850C2×C4C22×D17212yes—
851C2×C4#1306337112yes—
852C2×C4C24×D4311yescharacteristic
853C8—22no—
854C8—862no—
855C8—862no—
856C8C22×D17214yes—
857C22—24no—
858C22—42no—
859C22—42no—
860C22—48no—
861C22—434no—
862C22—862no—
863C22—862no—
864C22—868no—
865C22—862no—
866C22—862no—
867C22—862no—
868C22—34416no—
869C22—3444no—
870C22—1722no—
871C22—1722no—
872C22—1722no—
873C22—1724no—
874C22D4×D17212yes—
875C22#137×D4312yes—
876C22#1458370912yes—
877C22C22×D4×D4311yescharacteristic
878C4—24no—
879C4—22no—
880C4—22no—
881C4—42no—
882C4—42no—
883C4—862no—
884C4—862no—
885C4—1722no—
886C4—1722no—
887C4—1722no—
888C4D4×D17212yes—
889C4C23×D17211yescharacteristic
890C4C2×#1306337111yescharacteristic
891C2—44no—
892C2—864no—
893C2—3442no—
894C2—1722no—
895C2#1914610714yesdirect product factor
896C2C2×D4×D17211yescharacteristic
897C2C2×#137×D4311yescharacteristic
898C2C2×#1458370911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
prime radicalC2×#14583544C2
hypercenterC2×#440D43
hypocenterC43C2×#3266
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×#13063354C2semidirect
2. C22×SD16×D43C2semidirect
3. C2×Q8×D172C2semidirect
5. #19146107C2direct (N × H)
6. C2×#14583293C2semidirect
7. C2×#14583146C2semidirect
8. C2×#14583141C2semidirect
9. C2×#14583121C2semidirect
10. C2×#14583104C2semidirect
11. C2×#14583062C2semidirect
12. C2×#14583056C2semidirect
13. C2×#14583039C2semidirect
14. C2×#14583051C2semidirect
15. C2×#14582972C2semidirect
16. C2×C43×#440C2semidirect
19. C22×Q8×D43C22semidirect
22. C2×#13063354C22semidirect
23. C22×Dic172C22semidirect
24. C22×Dic172C22semidirect
25. C22×#10621885C22semidirect
32. C2×SD16×D43C22semidirect
33. C22×#10621872C22semidirect
36. Q8×D172C22semidirect
40. C2×#13063325C22semidirect
47. C2×#13063305C22semidirect
54. #14583293C22semidirect
55. #14583146C22semidirect
56. #14583141C22semidirect
57. #14583121C22semidirect
58. #14583104C22semidirect
59. #14583062C22semidirect
60. #14583056C22semidirect
61. #14583051C22semidirect
62. #14583039C22semidirect
63. #14582972C22semidirect
64. C2×C4⋊(C43⋊C8)C22semidirect
65. C2×#13063248C22semidirect
66. C2×#13063248C22semidirect
67. C2×#13063248C22semidirect
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
96. C2×Q8×D43C23semidirect
114. C2×Dic172C23semidirect
115. C2×Dic172C23semidirect
117. C2×#10621885C23semidirect
130. C2×#10621872C23semidirect
137. #13063325C23semidirect
148. #13063305C23semidirect
171. C4⋊(C43⋊C8)C23semidirect
172. #13063248C23semidirect
173. #13063248C23semidirect
174. #13063248C23semidirect
177. (C2×D43)⋊C8C23semidirect
181. C2×SD16×C43D4semidirect
186. C4×Q8×C43C23semidirect
195. #107×C43C23semidirect
196. #103×C43C23semidirect
198. #97×C43C23semidirect
282. SD16×C43C2×D4semidirect
342. C22×D43#137semidirect
428. C2×D43C2×#137semidirect
456. C2×#440D43semidirect
459. C2×C43#3266semidirect
501. C2×C4×Q8C2×D43semidirect
515. #440C2×D43semidirect
517. C2×#107C2×D43semidirect
522. C2×#103C2×D43semidirect
527. C2×#97C2×D43semidirect
528. C43C2×#3266semidirect
582. C2×SD16D172semidirect
611. C4×Q8C22×D43semidirect
638. #107C22×D43semidirect
643. #103C22×D43semidirect
648. #97C22×D43semidirect
740. SD16C2×D172semidirect
895. C2#19146107direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633542
C22×SD16×D432
C2×Q8×D1722
C2×#145835442
#191461072
C2×#145832932
C2×#145831462
C2×#145831412
C2×#145831212
C2×#145831042
C2×#145830622
C2×#145830562
C2×#145830392
C2×#145830512
C2×#145829722
C2×C43×#4402
C2×#326643