Finite Group Databasebeta

← C2×#19146633 #25973269

Subgroups — C2×#19146633 #25973269

Order 11008.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583619C211yesmaximal, characteristic, complemented
2C2×#14583545C211yesmaximal, characteristic
3#19146633C2116yesmaximal, direct product factor
4C2×#14583259C211yesmaximal, characteristic, complemented
5C2×#14583241C211yesmaximal, characteristic, complemented
6C2×#14583224C211yesmaximal, characteristic, complemented
7C2×#14583190C211yesmaximal, characteristic, complemented
8C2×#14583157C211yesmaximal, characteristic, complemented
9C2×#14583128C211yesmaximal, characteristic, complemented
10C2×#14583122C211yesmaximal, characteristic, complemented
11C2×#14583063C211yesmaximal, characteristic, complemented
12C2×#14583052C211yesmaximal, characteristic, complemented
13C2×#14583001C211yesmaximal, characteristic, complemented
14C2×#14582905C211yesmaximal, characteristic, complemented
15C2×#14582896C211yesmaximal, characteristic, complemented
16C2×C43×#435C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×D172C2211yescharacteristic
19C22×Dic172C2211yescharacteristic, complemented
20C22×#10621873C2211yescharacteristic
21C22×#10621873C2211yescharacteristic
22#14583619—24no—
23#14583619C2218yescomplemented
24#14583545—24no—
25#14583545C2218yes—
26C2×#13063325C2211yescharacteristic, complemented
27C2×#13063318—21no—
28C2×#13063318—21no—
29C2×#13063313C2211yescharacteristic
30C2×#13063312—21no—
31C2×#13063310—21no—
32C2×#13063304C2211yescharacteristic
33C2×#13063304C2211yescharacteristic
34C2×#13063304C2211yescharacteristic, complemented
35C2×#13063299C2211yescharacteristic
36C2×#13063298—21no—
37C2×#13063293—21no—
38C2×C4×Dic86C2211yescharacteristic, complemented
39C2×#13063290—21no—
40C2×C4×D172C2211yescharacteristic
41C2×#13063284C2211yescharacteristic
42C2×#13063284C2211yescharacteristic, complemented
43C2×C22⋊C4×D43—21no—
44#14583259C2218yescomplemented
45#14583241C2218yescomplemented
46#14583224C2218yescomplemented
47#14583190C2218yescomplemented
48#14583157C2218yescomplemented
49#14583128C2218yescomplemented
50#14583122C2218yescomplemented
51#14583063C2218yescomplemented
52#14583052C2218yescomplemented
53#14583001C2218yescomplemented
54C2×#13063259C2211yescharacteristic, complemented
55C2×#13063257C2211yescharacteristic, complemented
56C2×#13063257C2211yescharacteristic, complemented
57#14582905C2218yescomplemented
58#14582896C2218yescomplemented
59C2×#13063250C2211yescharacteristic, complemented
60C2×#13063250C2211yescharacteristic, complemented
61C2×#13063250C2211yescharacteristic, complemented
62C2×#13063250C2211yescharacteristic, complemented
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C22×M16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic, complemented
71C2×C4×D4×C43C2211yescharacteristic
72C43×#435C2218yescomplemented
73C2×C4⋊C8×C43C2211yescharacteristic, complemented
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×C22⋊C8×C43C2211yescharacteristic, complemented
76C2×#97×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621898—22no—
79C2×#10621898—24no—
80C2×#10621898—42no—
81C2×#10621898C2314yes—
82C22×Dic86—21no—
83C22×Dic86C2311yescharacteristic
84C22×Dic86C2311yescharacteristic
85C22×D172—24no—
86C22×D172—21no—
87C22×D172—22no—
88C22×D172—42no—
89C22×D172C2311yescharacteristic
90C22×D172C2314yes—
91C22×D172C2311yescharacteristic
92C22×C22⋊D43—21no—
93C22×C22⋊D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C2×Dic172—42no—
97C2×Dic172C2314yescomplemented
98C2×#10621873—24no—
99C2×#10621873—42no—
100C2×#10621873C2314yes—
101C2×#10621873C2314yes—
102#13063325—22no—
103#13063325C2314yescomplemented
104#13063318—28no—
105#13063318—28no—
106#13063313—22no—
107#13063313C2314yes—
108#13063312—28no—
109#13063310—28no—
110#13063304—22no—
111#13063304—22no—
112#13063304—22no—
113#13063304C2314yes—
114#13063304C2314yes—
115#13063304C2314yescomplemented
116#13063299—22no—
117#13063299C2314yes—
118#13063298—28no—
119#13063293—28no—
120C4×Dic86—22no—
121C4×Dic86C2314yescomplemented
122#13063290—28no—
123C4×D172—22no—
124C4×D172C2314yes—
125#13063284—22no—
126#13063284—22no—
127#13063284C2314yes—
128#13063284C2314yescomplemented
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43C2311yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×C4⋊Dic43C2311yescharacteristic
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×C22⋊Dic43—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C22⋊C4×D43—28no—
148C2×C4×Dic43—21no—
149C2×C4×Dic43—21no—
150C2×C4×Dic43—21no—
151#13063259C2314yescomplemented
152#13063257C2314yescomplemented
153#13063257C2314yescomplemented
154#13063250C2314yescomplemented
155#13063250C2314yescomplemented
156#13063250C2314yescomplemented
157#13063250C2314yescomplemented
158#13063247C2314yes—
159#13063247C2314yes—
160#13063247C2314yes—
161#13063247C2314yes—
162#13063247C2314yes—
163#13063247C2314yes—
164C22×D4×C43D411yescharacteristic
165C23×C4×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167C2×M16×C43—42no—
168C2×M16×C43C2314yes—
169C22×C8×C43—42no—
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2314yescomplemented
175C4×D4×C43D414yes—
176C4×D4×C43C2314yes—
177C2×C4⋊C4×C43D411yescharacteristic
178C2×C22⋊C4×C43D411yescharacteristic
179C2×C22⋊C4×C43D411yescharacteristic
180C2×C42×C43C2311yescharacteristic
181C4⋊C8×C43C2314yescomplemented
182C22⋊C8×C43C2314yes—
183C22⋊C8×C43C2314yescomplemented
184#97×C43C2314yescomplemented
185C24×C43C2×D411yescharacteristic
186C24×C43C2×D411yescharacteristic
187C23×D43—21no—
188C23×D43—21no—
189C23×D43—24no—
190C23×D43—44no—
191C23×D43—44no—
192C23×D43—82no—
193C2×D4×C43—42no—
194C2×D4×C43C2×D414yes—
195C22×C4×C43—22no—
196C22×C4×C43—22no—
197C22×C4×C43—22no—
198C22×C4×C43—22no—
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D412yes—
204C22×C4×C43C2×D412yes—
205C22×C4×C43C2412yes—
206C22×C4×C43C2412yes—
207C22×C4×C43C2411yescharacteristic
208C2×C22⋊D43—24no—
209C2×C22⋊D43—24no—
210C2×C22⋊D43—44no—
211C2×C22⋊D43—82no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218#10621898—28no—
219#10621898—44no—
220#10621898—48no—
221C2×D172—21no—
222C2×D172—22no—
223C2×D172—24no—
224C2×D172—21no—
225C2×D172—22no—
226C2×D172—22no—
227C2×D172—28no—
228C2×D172—44no—
229C2×D172—44no—
230C2×D172—48no—
231C2×D172#4114yes—
232C2×D172C2412yes—
233C2×D172C2412yes—
234C2×C4×D43—24no—
235C2×C4×D43—24no—
236C2×C4×D43—44no—
237C2×C4×D43—82no—
238C2×Dic86—22no—
239C2×Dic86—22no—
240C2×Dic86—22no—
241C2×Dic86—22no—
242C2×Dic86—24no—
243C2×Dic86—21no—
244C2×Dic86—21no—
245C2×Dic86—44no—
246C2×Dic86C2412yes—
247C2×Dic86C2412yes—
248M16×C43—44no—
249C2×C8×C43—22no—
250C2×C8×C43—22no—
251C2×C8×C43—22no—
252C2×C8×C43—22no—
253C2×C8×C43—44no—
254C2×C8×C43C2412yes—
255C2×C8×C43C2412yes—
256C2×C8×C43C2412yes—
257C2×C8×C43C2412yes—
258C4⋊C4×C43C2×D414yes—
259C22⋊C4×C43C2×D414yes—
260C22⋊C4×C43C2×D414yes—
261C42×C43C2×D412yes—
262C42×C43C2412yes—
263C22⋊Dic43—24no—
264C22⋊Dic43—24no—
265C22⋊Dic43—24no—
266C22⋊Dic43—24no—
267C22⋊Dic43—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272C4⋊Dic43—24no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43C2412yes—
278C4⋊Dic43C2412yes—
279C4⋊Dic43C2412yes—
280C4⋊Dic43C2412yes—
281Dic43⋊C4—24no—
282Dic43⋊C4—24no—
283Dic43⋊C4—24no—
284Dic43⋊C4—24no—
285C4×Dic43—24no—
286C4×Dic43—24no—
287C4×Dic43—24no—
288Dic172—44no—
289#10621873—28no—
290#10621873—44no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43C22×D412yes—
298C23×C43C22×D412yes—
299C23×C43C22×D411yescharacteristic
300C22×D43—24no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—48no—
304C22×D43—42no—
305C22×D43—42no—
306C22×D43—48no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—42no—
310C22×D43—84no—
311C22×D43—816no—
312D4×C43—44no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—24no—
318C2×C4×C43—24no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43C22×D412yes—
324C2×C4×C43C22×D412yes—
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—84no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—42no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345D172—24no—
346D172—22no—
347D172—22no—
348D172—22no—
349D172—48no—
350D172—42no—
351D172C2×#4114yes—
352C4×D43—48no—
353C4×D43—84no—
354Dic86—22no—
355Dic86—22no—
356Dic86—22no—
357Dic86—22no—
358Dic86—48no—
359Dic86—42no—
360Dic86—42no—
361C8×C43—22no—
362C8×C43—22no—
363C8×C43—22no—
364C8×C43—22no—
365C2×#3311—431nomaximal, Sylow
366C22×C43—22no—
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—44no—
373C22×C43—44no—
374C22×C43#54612yes—
375C22×C43#57512yes—
376C22×C43#57712yes—
377C22×C43C23×D411yescharacteristic
378C2×D43—24no—
379C2×D43—48no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—816no—
386C2×D43—84no—
387C4×C43—22no—
388C4×C43—22no—
389C4×C43—22no—
390C4×C43—22no—
391C4×C43#54612yes—
392C4×C43C22×#4111yescharacteristic
393C4×C43C2×H(5,𝔽2)11yescharacteristic
394Dic43—42no—
395Dic43—42no—
396Dic43—42no—
397Dic43—42no—
398Dic43—42no—
399Dic43—42no—
400C2×#556—431no—
401C2×#546—431no—
402#3311—4316no—
403C2×#489—431no—
404C2×#485—431no—
405C2×#482—431no—
406C2×#476—431no—
407C2×#470—431no—
408C2×#465—431no—
409C2×#464—431no—
410C2×#452—431no—
411C2×#450—431no—
412C2×#440—431no—
413C2×#435D4311yescharacteristic, complemented
414C2×#418—431no—
415C2×#416—431no—
416C2×C43—42no—
417C2×C43—42no—
418C2×C43#331114yescomplemented
419C2×C43C2×#54611yescharacteristic
420C2×C43C2×#57511yescharacteristic
421C2×C43C2×#57711yescharacteristic
422D43—44no—
423D43—82no—
424C22×#41—431no—
425C23×D4—431no—
426C22×Q16—431no—
427C22×SD16—431no—
428C22×SD16—431no—
429C22×M16C2×D4311yescharacteristic
430C23×C8C2×D4311yescharacteristic, complemented
431#556—438no—
432#556—864no—
433#546—438no—
434#546—864no—
435C2×C4⋊Q8—431no—
436C2×#126—861no—
437C2×#126—861no—
438C2×#124—431no—
439C2×#124—861no—
440C2×#123—861no—
441C2×C22⋊Q8—431no—
442C2×C22⋊Q8—431no—
443C2×C22⋊Q8—431no—
444C2×#121—431no—
445C2×#121—861no—
446C2×#120—861no—
447C2×C4×Q8—431no—
448C2×C4×Q8—861no—
449C2×C4×D4—431no—
450C2×C4×D4C2×D4311yescharacteristic
451C2×#117—431no—
452C2×#117—431no—
453C22×C22⋊C4—861no—
454#489—438no—
455#485—438no—
456#482—438no—
457#476—438no—
458#470—438no—
459#465—438no—
460#464—438no—
461#452—438no—
462#450—438no—
463#440—438no—
464#435C2×D4318yescomplemented
465C2×#107—431no—
466C2×#106—431no—
467C2×#106—431no—
468C2×C4⋊C8C2×D4311yescharacteristic, complemented
469#418—438no—
470#416—438no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103—431no—
474C2×#103—431no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×#102—431no—
480C2×#102—431no—
481C2×C22⋊C8C2×D4311yescharacteristic
482C2×C22⋊C8C2×D4311yescharacteristic, complemented
483C2×#97C2×D4311yescharacteristic, complemented
484C43C2×#331111yescharacteristic, complemented, Sylow
485C25—861no—
486C2×#41—434no—
487C2×#41—864no—
488C2×#41—862no—
489C2×#41—1722no—
490C22×Q8—431no—
491C22×Q8—431no—
492C22×Q8—861no—
493C22×D4—431no—
494C22×D4—431no—
495C22×D4—434no—
496C22×D4—864no—
497C22×D4—861no—
498C22×D4—861no—
499C22×D4—861no—
500C22×D4—862no—
501C22×D4—1722no—
502C22×D4D17211yescharacteristic
503C23×C4—861no—
504C23×C4—861no—
505C23×C4C22×D4311yescharacteristic
506C23×C4C22×D4311yescharacteristic
507C2×Q16—434no—
508C2×Q16—1722no—
509C2×SD16—434no—
510C2×SD16—434no—
511C2×SD16—864no—
512C2×SD16—1722no—
513C2×M16—42no—
514C2×M16C22×D4314yes—
515C22×C8—42no—
516C22×C8C22×D4311yescharacteristic
517C22×C8C22×D4311yescharacteristic
518C22×C8C22×D4311yescharacteristic
519C22×C8C22×D4311yescharacteristic
520C22×C8C22×D4314yescomplemented
521C4⋊Q8—434no—
522C4⋊Q8—862no—
523#126—868no—
524#126—868no—
525#124—434no—
526#124—868no—
527#124—862no—
528#123—868no—
529C22⋊Q8—434no—
530C22⋊Q8—434no—
531C22⋊Q8—434no—
532C22⋊Q8—862no—
533C22⋊Q8—862no—
534C22⋊Q8—862no—
535#121—434no—
536#121—862no—
537#121—868no—
538#120—868no—
539C4×Q8—434no—
540C4×Q8—868no—
541C4×Q8—862no—
542C4×D4—434no—
543C4×D4—862no—
544C4×D4D17214yes—
545C4×D4C22×D4314yes—
546#117—434no—
547#117—434no—
548#117—862no—
549#117—862no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4D17211yescharacteristic
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—868no—
570C2×C22⋊C4D17211yescharacteristic
571C2×C22⋊C4D17211yescharacteristic
572C2×C42—861no—
573C2×C42—861no—
574C2×C42—861no—
575C2×C42C22×D4311yescharacteristic
576#107—434no—
577#106—434no—
578#106—434no—
579C4⋊C8C22×D4314yescomplemented
580#103—434no—
581#103—434no—
582#103—434no—
583#103—434no—
584#102—434no—
585#102—434no—
586#102—434no—
587#102—434no—
588#102—434no—
589#102—434no—
590C22⋊C8C22×D4314yes—
591C22⋊C8C22×D4314yescomplemented
592#97C22×D4314yescomplemented
593C24—861no—
594C24—864no—
595C24—861no—
596C24—3442no—
597C24—1724no—
598C24—1724no—
599C24C2×D17211yescharacteristic
600C24C2×D17211yescharacteristic
601#41—868no—
602#41—1724no—
603#41—1728no—
604C2×Q8—432no—
605C2×Q8—432no—
606C2×Q8—861no—
607C2×Q8—864no—
608C2×Q8—861no—
609C2×Q8—862no—
610C2×Q8—862no—
611C2×Q8—862no—
612C2×Q8—862no—
613C2×Q8—1724no—
614C2×D4—42no—
615C2×D4—434no—
616C2×D4—432no—
617C2×D4—432no—
618C2×D4—868no—
619C2×D4—864no—
620C2×D4—864no—
621C2×D4—861no—
622C2×D4—864no—
623C2×D4—861no—
624C2×D4—862no—
625C2×D4—862no—
626C2×D4—862no—
627C2×D4—3442no—
628C2×D4—1724no—
629C2×D4—1728no—
630C2×D4—1724no—
631C2×D4—1724no—
632C2×D4C2×D17214yes—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—861no—
640C22×C4—861no—
641C22×C4—861no—
642C22×C4—861no—
643C22×C4—864no—
644C22×C4—864no—
645C22×C4—3442no—
646C22×C4—1724no—
647C22×C4C2×D17212yes—
648C22×C4C2×D17212yes—
649C22×C4C2×D17211yescharacteristic
650C22×C4C2×D17211yescharacteristic
651C22×C4C2×D17211yescharacteristic
652C22×C4C2×D17211yescharacteristic
653C22×C4C23×D4312yes—
654C22×C4C23×D4312yes—
655C22×C4C23×D4311yescharacteristic
656Q16—1724no—
657SD16—868no—
658SD16—1724no—
659M16—44no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—44no—
665C2×C8C23×D4312yes—
666C2×C8C23×D4312yes—
667C2×C8C23×D4312yes—
668C2×C8C23×D4312yes—
669C4⋊C4—432no—
670C4⋊C4—432no—
671C4⋊C4—432no—
672C4⋊C4—432no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—864no—
678C4⋊C4—864no—
679C4⋊C4—864no—
680C4⋊C4—864no—
681C4⋊C4—864no—
682C4⋊C4C2×D17214yes—
683C22⋊C4—864no—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—864no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C22⋊C4C2×D17214yes—
693C22⋊C4C2×D17214yes—
694C42—864no—
695C42—864no—
696C42—864no—
697C42C2×D17212yes—
698C42C23×D4312yes—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—862no—
706C23—864no—
707C23—862no—
708C23—3444no—
709C23—34416no—
710C23—1728no—
711C23—1728no—
712C23—1722no—
713C23—1722no—
714C23—1722no—
715C23—1722no—
716C23—1722no—
717C23C22×D17212yes—
718C23C22×D17212yes—
719C23C22×D17211yescharacteristic
720Q8—862no—
721Q8—862no—
722Q8—862no—
723Q8—862no—
724Q8—1728no—
725Q8—1722no—
726Q8—1722no—
727D4—44no—
728D4—434no—
729D4—862no—
730D4—862no—
731D4—862no—
732D4—864no—
733D4—3444no—
734D4—1728no—
735D4—1728no—
736D4—1722no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—3444no—
754C2×C4—1728no—
755C2×C4—1722no—
756C2×C4—1722no—
757C2×C4—1722no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4C22×D17212yes—
762C2×C4C22×D17212yes—
763C2×C4C22×D17212yes—
764C2×C4C22×D17212yes—
765C2×C4C22×D17211yescharacteristic
766C2×C4#41×D4312yes—
767C2×C4#1306337012yes—
768C2×C4C24×D4311yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—44no—
780C22—44no—
781C22—864no—
782C22—34416no—
783C22—3444no—
784C22—1722no—
785C22—1722no—
786C22—1722no—
787C22—1722no—
788C22—1722no—
789C22—1728no—
790C22#1458354412yes—
791C22#1458369912yes—
792C22#1458371112yes—
793C22C23×D17211yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—1722no—
799C4—1722no—
800C4—1722no—
801C4—1722no—
802C4—1722no—
803C4—1722no—
804C4#1458354412yes—
805C4C2×#41×D4311yescharacteristic
806C4C2×#1306337011yescharacteristic
807C2—42no—
808C2—42no—
809C2—3442no—
810C2—1724no—
811C2#1914663314yesdirect product factor
812C2C2×#1458354411yescharacteristic
813C2C2×#1458369911yescharacteristic
814C2C2×#1458371111yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
prime radicalC2×#14583545C2
hypercenterC2×#435D43
hypocenterC43C2×#3311
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#14583619C2semidirect
3. #19146633C2direct (N × H)
4. C2×#14583259C2semidirect
5. C2×#14583241C2semidirect
6. C2×#14583224C2semidirect
7. C2×#14583190C2semidirect
8. C2×#14583157C2semidirect
9. C2×#14583128C2semidirect
10. C2×#14583122C2semidirect
11. C2×#14583063C2semidirect
12. C2×#14583052C2semidirect
13. C2×#14583001C2semidirect
14. C2×#14582905C2semidirect
15. C2×#14582896C2semidirect
16. C2×C43×#435C2semidirect
19. C22×Dic172C22semidirect
23. #14583619C22semidirect
26. C2×#13063325C22semidirect
34. C2×#13063304C22semidirect
38. C2×C4×Dic86C22semidirect
42. C2×#13063284C22semidirect
44. #14583259C22semidirect
45. #14583241C22semidirect
46. #14583224C22semidirect
47. #14583190C22semidirect
48. #14583157C22semidirect
49. #14583128C22semidirect
50. #14583122C22semidirect
51. #14583063C22semidirect
52. #14583052C22semidirect
53. #14583001C22semidirect
54. C2×#13063259C22semidirect
55. C2×#13063257C22semidirect
56. C2×#13063257C22semidirect
57. #14582905C22semidirect
58. #14582896C22semidirect
59. C2×#13063250C22semidirect
60. C2×#13063250C22semidirect
61. C2×#13063250C22semidirect
62. C2×#13063250C22semidirect
70. C23×C8×C43C22semidirect
72. C43×#435C22semidirect
73. C2×C4⋊C8×C43C22semidirect
75. C2×C22⋊C8×C43C22semidirect
76. C2×#97×C43C22semidirect
97. C2×Dic172C23semidirect
103. #13063325C23semidirect
115. #13063304C23semidirect
121. C4×Dic86C23semidirect
128. #13063284C23semidirect
151. #13063259C23semidirect
152. #13063257C23semidirect
153. #13063257C23semidirect
154. #13063250C23semidirect
155. #13063250C23semidirect
156. #13063250C23semidirect
157. #13063250C23semidirect
174. C22×C8×C43C23semidirect
181. C4⋊C8×C43C23semidirect
183. C22⋊C8×C43C23semidirect
184. #97×C43C23semidirect
413. C2×#435D43semidirect
418. C2×C43#3311semidirect
430. C23×C8C2×D43semidirect
464. #435C2×D43semidirect
468. C2×C4⋊C8C2×D43semidirect
482. C2×C22⋊C8C2×D43semidirect
483. C2×#97C2×D43semidirect
484. C43C2×#3311semidirect
520. C22×C8C22×D43semidirect
579. C4⋊C8C22×D43semidirect
591. C22⋊C8C22×D43semidirect
592. #97C22×D43semidirect
811. C2#19146633direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836192
C2×#145835452
#191466332
C2×#145832592
C2×#145832412
C2×#145832242
C2×#145831902
C2×#145831572
C2×#145831282
C2×#145831222
C2×#145830632
C2×#145830522
C2×#145830012
C2×#145829052
C2×#145828962
C2×C43×#4352
C2×#331143