Finite Group Databasebeta

← C2×#19146636 #25973272

Subgroups — C2×#19146636 #25973272

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×#14583622C211yesmaximal, characteristic, complemented
2C2×#14583544C211yesmaximal, characteristic
3#19146636C2116yesmaximal, direct product factor
4C2×#14583259C211yesmaximal, characteristic, complemented
5C2×#14583242C211yesmaximal, characteristic, complemented
6C2×#14583226C211yesmaximal, characteristic, complemented
7C2×#14583189C211yesmaximal, characteristic, complemented
8C2×#14583156C211yesmaximal, characteristic, complemented
9C2×#14583131C211yesmaximal, characteristic, complemented
10C2×#14583121C211yesmaximal, characteristic, complemented
11C2×#14583058C211yesmaximal, characteristic, complemented
12C2×#14583048C211yesmaximal, characteristic, complemented
13C2×#14582972C211yesmaximal, characteristic, complemented
14C2×#14582902C211yesmaximal, characteristic, complemented
15C2×#14582892C211yesmaximal, characteristic, complemented
16C2×C43×#440C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C22×#10621885C2211yescharacteristic, complemented
20C22×#10621884C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic, complemented
23#14583622—24no—
24#14583622C2218yescomplemented
25#14583544—24no—
26#14583544C2218yes—
27C2×#13063325C2211yescharacteristic, complemented
28C2×#13063320—21no—
29C2×#13063320—21no—
30C2×#13063313—21no—
31C2×#13063313C2211yescharacteristic
32C2×#13063309—21no—
33C2×#13063305C2211yescharacteristic
34C2×#13063301C2211yescharacteristic
35C2×#13063301C2211yescharacteristic, complemented
36C2×#13063300C2211yescharacteristic
37C2×#13063299—21no—
38C2×#13063295—21no—
39C2×C4×Dic86—21no—
40C2×C4×D172C2211yescharacteristic
41C2×#13063283C2211yescharacteristic
42C2×#13063283C2211yescharacteristic, complemented
43C22×(C2×D43)⋊C4—21no—
44#14583259C2218yescomplemented
45#14583242C2218yescomplemented
46#14583226C2218yescomplemented
47#14583189C2218yescomplemented
48#14583156C2218yescomplemented
49#14583131C2218yescomplemented
50#14583121C2218yescomplemented
51#14583058C2218yescomplemented
52#14583048C2218yescomplemented
53#14582972C2218yescomplemented
54C2×#13063256C2211yescharacteristic, complemented
55C2×#13063256C2211yescharacteristic, complemented
56C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
57#14582902C2218yescomplemented
58#14582892C2218yescomplemented
59C2×#13063250C2211yescharacteristic, complemented
60C2×#13063250C2211yescharacteristic, complemented
61C2×#13063248C2211yescharacteristic, complemented
62C2×#13063247C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
69C22×SD16×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic, complemented
71C2×C4×D4×C43C2211yescharacteristic
72C43×#440C2218yescomplemented
73C2×#107×C43C2211yescharacteristic, complemented
74C2×#103×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621900—24no—
79C2×#10621900—22no—
80C2×#10621900—42no—
81C2×#10621900C2314yes—
82C22×Dic86—21no—
83C22×Dic86C2311yescharacteristic
84C22×D172—21no—
85C22×D172D411yescharacteristic
86C22×D172C2311yescharacteristic
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C2×D4×D43—24no—
90C2×D4×D43—22no—
91C2×D4×D43—42no—
92C2×D4×D43C2314yes—
93C23×Dic43—21no—
94C22×C4×D43C2311yescharacteristic
95C22×C4×D43C2311yescharacteristic
96C2×#10621885—42no—
97C2×#10621885C2314yescomplemented
98C2×#10621884—42no—
99C2×#10621884C2314yes—
100C2×#10621872—42no—
101C2×#10621872C2314yes—
102C22×C43⋊C8C2311yescharacteristic
103C22×C43⋊C8C2311yescharacteristic
104C2×C8×D43—42no—
105C2×C8×D43C2314yescomplemented
106#13063325—22no—
107#13063325C2314yescomplemented
108#13063320—28no—
109#13063320—28no—
110#13063313—28no—
111#13063313—22no—
112#13063313C2314yes—
113#13063309—28no—
114#13063305—22no—
115#13063305C2314yes—
116#13063301—22no—
117#13063301—22no—
118#13063301C2314yes—
119#13063301C2314yescomplemented
120#13063300—22no—
121#13063300C2314yes—
122#13063299—28no—
123#13063295—28no—
124C4×Dic86—28no—
125C4×D172D414yes—
126C4×D172C2314yes—
127#13063283—22no—
128#13063283—22no—
129#13063283C2314yes—
130#13063283C2314yescomplemented
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43—21no—
133C2×C4⋊Dic43D411yescharacteristic
134C2×C4⋊Dic43C2311yescharacteristic
135C2×C4⋊Dic43C2311yescharacteristic
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—28no—
147C2×(C2×D43)⋊C4D411yescharacteristic
148C2×(C2×D43)⋊C4D411yescharacteristic
149C2×C4×Dic43—21no—
150C2×C4×Dic43—21no—
151#13063256C2314yescomplemented
152#13063256C2314yescomplemented
153C4⋊(C43⋊C8)C2314yescomplemented
154#13063250C2314yescomplemented
155#13063250C2314yescomplemented
156#13063248C2314yescomplemented
157#13063247C2314yes—
158#13063247C2314yes—
159#13063246C2314yes—
160#13063246C2314yes—
161#13063245C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yescomplemented
164C22×Q8×C43C2311yescharacteristic
165C22×D4×C43C2311yescharacteristic
166C23×C4×C43—21no—
167C2×SD16×C43—24no—
168C2×SD16×C43C2314yes—
169C22×C8×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171C4×Q8×C43—22no—
172C4×Q8×C43C2314yescomplemented
173C4×D4×C43—22no—
174C4×D4×C43C2314yes—
175C2×C4⋊C4×C43—21no—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C22⋊C4×C43—21no—
179C2×C42×C43—21no—
180C2×C42×C43C2311yescharacteristic
181#107×C43C2314yescomplemented
182#103×C43C2314yescomplemented
183#102×C43C2314yes—
184#97×C43C2314yescomplemented
185C24×C43—21no—
186C23×D43—21no—
187C23×D43—24no—
188C23×D43—44no—
189C23×D43—44no—
190C23×D43—82no—
191C23×D43C2×D411yescharacteristic
192C23×D43C2×D411yescharacteristic
193C2×Q8×C43—21no—
194C2×Q8×C43—22no—
195C2×Q8×C43—22no—
196C2×Q8×C43C2412yes—
197C2×D4×C43—21no—
198C2×D4×C43—22no—
199C2×D4×C43#4114yes—
200C2×D4×C43C2412yes—
201C22×C4×C43—24no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—82no—
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2411yescharacteristic
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—44no—
212C2×C22⋊D43—44no—
213C22×Dic43—24no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—44no—
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220#10621900—28no—
221#10621900—44no—
222#10621900—48no—
223D4×D43—28no—
224D4×D43—44no—
225D4×D43—48no—
226C2×D172—21no—
227C2×D172—24no—
228C2×D172—22no—
229C2×D172—22no—
230C2×D172—42no—
231C2×D172—82no—
232C2×D172C2×D414yes—
233C2×D172C2412yes—
234C2×C4×D43—22no—
235C2×C4×D43—22no—
236C2×C4×D43—22no—
237C2×C4×D43—22no—
238C2×C4×D43C2×D412yes—
239C2×C4×D43C2×D412yes—
240C2×C4×D43C2412yes—
241C2×C4×D43C2412yes—
242C2×Dic86—22no—
243C2×Dic86—22no—
244C2×Dic86—24no—
245C2×Dic86—21no—
246C2×Dic86—44no—
247C2×Dic86C2412yes—
248SD16×C43—28no—
249C2×C8×C43—22no—
250C2×C8×C43—22no—
251C2×C8×C43C2412yes—
252C2×C8×C43C2412yes—
253C4⋊C4×C43—24no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43C2412yes—
257C4⋊C4×C43C2412yes—
258C22⋊C4×C43—24no—
259C42×C43—24no—
260C42×C43C2×D412yes—
261C42×C43C2412yes—
262#10621885—44no—
263#10621884—44no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
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—24no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—24no—
278C4⋊Dic43C2×D414yes—
279C4⋊Dic43C2412yes—
280C4⋊Dic43C2412yes—
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—24no—
292C23×C43—22no—
293C23×C43—42no—
294C23×C43—42no—
295C23×C43C22×D411yescharacteristic
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—48no—
304C22×D43—48no—
305C22×D43—42no—
306C22×D43—42no—
307C22×D43—42no—
308C22×D43—84no—
309C22×D43—816no—
310C22×D43C22×D412yes—
311C22×D43C22×D412yes—
312Q8×C43—22no—
313Q8×C43—22no—
314Q8×C43—42no—
315D4×C43—24no—
316D4×C43—22no—
317D4×C43C2×#4114yes—
318C2×C4×C43—22no—
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×C43—42no—
326C2×C4×C43—84no—
327C2×C4×C43C22×D412yes—
328C2×C4×C43C22×D412yes—
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C2×#4112yes—
331C2×C4×C43H(5,𝔽2)12yes—
332C2×C4×C43C2511yescharacteristic
333C22⋊D43—48no—
334C22⋊D43—48no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—48no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43C22×D412yes—
345C2×Dic43C22×D412yes—
346D172—22no—
347D172—22no—
348D172—44no—
349D172—42no—
350D172—84no—
351C4×D43—24no—
352C4×D43—24no—
353C4×D43—22no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—22no—
357Dic86—22no—
358Dic86—22no—
359Dic86—48no—
360Dic86—42no—
361C8×C43—22no—
362C8×C43—22no—
363C43⋊C8—22no—
364C43⋊C8—22no—
365C2×#3311—431nomaximal, Sylow
366C22×C43—24no—
367C22×C43—48no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43#54612yes—
371C22×C43#57512yes—
372C22×C43#57712yes—
373C22×C43C23×D411yescharacteristic
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—22no—
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—44no—
381C2×D43—44no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—816no—
386C2×D43—84no—
387C4×C43—22no—
388C4×C43—22no—
389C4×C43—42no—
390C4×C43—42no—
391C4×C43—42no—
392C4×C43#54612yes—
393C4×C43C22×#4111yescharacteristic
394C4×C43C2×H(5,𝔽2)11yescharacteristic
395Dic43—22no—
396Dic43—22no—
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×#440D4311yescharacteristic, complemented
413C2×#435—431no—
414C2×#418—431no—
415C2×#416—431no—
416C2×C43—44no—
417C2×C43#331114yescomplemented
418C2×C43C2×#54611yescharacteristic
419C2×C43C2×#57511yescharacteristic
420C2×C43C2×#57711yescharacteristic
421D43—42no—
422D43—42no—
423D43—82no—
424C22×#41—431no—
425C23×D4—431no—
426C22×Q16—431no—
427C22×SD16—431no—
428C22×SD16C2×D4311yescharacteristic
429C22×M16—431no—
430C23×C8—431no—
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—861no—
448C2×C4×Q8C2×D4311yescharacteristic, complemented
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#440C2×D4318yescomplemented
464#435—438no—
465C2×#107C2×D4311yescharacteristic, complemented
466C2×#106—431no—
467C2×#106—431no—
468C2×C4⋊C8—431no—
469#418—438no—
470#416—438no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103—431no—
474C2×#103C2×D4311yescharacteristic, complemented
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×#102—431no—
480C2×#102C2×D4311yescharacteristic
481C2×C22⋊C8—431no—
482C2×C22⋊C8—431no—
483C2×#97C2×D4311yescharacteristic, complemented
484C43C2×#331111yescharacteristic, complemented, Sylow
485C25—861no—
486C2×#41—434no—
487C2×#41—862no—
488C2×#41—864no—
489C2×#41—1722no—
490C22×Q8—431no—
491C22×Q8—861no—
492C22×Q8C22×D4311yescharacteristic
493C22×D4—434no—
494C22×D4—431no—
495C22×D4—431no—
496C22×D4—861no—
497C22×D4—862no—
498C22×D4—861no—
499C22×D4—864no—
500C22×D4—861no—
501C22×D4—1722no—
502C22×D4C22×D4311yescharacteristic
503C23×C4—21no—
504C23×C4—431no—
505C23×C4—431no—
506C23×C4—861no—
507C2×Q16—434no—
508C2×Q16—1722no—
509C2×SD16—24no—
510C2×SD16—434no—
511C2×SD16—1722no—
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
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—868no—
537#121—862no—
538#120—868no—
539C4×Q8—22no—
540C4×Q8—868no—
541C4×Q8C22×D4314yescomplemented
542C4×D4—22no—
543C4×D4—434no—
544C4×D4—434no—
545C4×D4C22×D4314yes—
546#117—434no—
547#117—434no—
548#117—862no—
549#117—862no—
550C2×C4⋊C4—21no—
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⋊C4C22×D4311yescharacteristic
559C2×C4⋊C4C22×D4311yescharacteristic
560C2×C22⋊C4—21no—
561C2×C22⋊C4—431no—
562C2×C22⋊C4—431no—
563C2×C22⋊C4—868no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C42—21no—
573C2×C42—861no—
574C2×C42—861no—
575C2×C42C22×D4311yescharacteristic
576#107C22×D4314yescomplemented
577#106—434no—
578#106—434no—
579C4⋊C8—434no—
580#103—434no—
581#103—434no—
582#103—434no—
583#103C22×D4314yescomplemented
584#102—434no—
585#102—434no—
586#102—434no—
587#102—434no—
588#102—434no—
589#102C22×D4314yes—
590C22⋊C8—434no—
591C22⋊C8—434no—
592#97C22×D4314yescomplemented
593C24—21no—
594C24—431no—
595C24—431no—
596C24—864no—
597C24—861no—
598C24—3442no—
599C24—1724no—
600C24—1724no—
601#41—868no—
602#41—1724no—
603#41—1728no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—432no—
608C2×Q8—864no—
609C2×Q8—861no—
610C2×Q8—862no—
611C2×Q8—862no—
612C2×Q8—1724no—
613C2×Q8C23×D4312yes—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—434no—
617C2×D4—432no—
618C2×D4—864no—
619C2×D4—864no—
620C2×D4—868no—
621C2×D4—864no—
622C2×D4—861no—
623C2×D4—862no—
624C2×D4—862no—
625C2×D4—3442no—
626C2×D4—1722no—
627C2×D4—1724no—
628C2×D4—1728no—
629C2×D4—1724no—
630C2×D4—1724no—
631C2×D4#1062189814yes—
632C2×D4C23×D4312yes—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—82no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—432no—
641C22×C4—432no—
642C22×C4—432no—
643C22×C4—432no—
644C22×C4—864no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—861no—
652C22×C4—1724no—
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4C23×D4311yescharacteristic
656Q16—1724no—
657SD16—28no—
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—21no—
671C4⋊C4—21no—
672C4⋊C4—434no—
673C4⋊C4—432no—
674C4⋊C4—432no—
675C4⋊C4—864no—
676C4⋊C4—864no—
677C4⋊C4—864no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—864no—
681C4⋊C4C23×D4312yes—
682C4⋊C4C23×D4312yes—
683C22⋊C4—24no—
684C22⋊C4—434no—
685C22⋊C4—434no—
686C22⋊C4—864no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C22⋊C4—864no—
693C22⋊C4—864no—
694C42—24no—
695C42—864no—
696C42—864no—
697C42D4×D4312yes—
698C42C23×D4312yes—
699C23—22no—
700C23—24no—
701C23—42no—
702C23—42no—
703C23—432no—
704C23—432no—
705C23—862no—
706C23—862no—
707C23—862no—
708C23—862no—
709C23—862no—
710C23—862no—
711C23—862no—
712C23—3444no—
713C23—34416no—
714C23—1728no—
715C23—1728no—
716C23—1722no—
717C23—1722no—
718C23—1722no—
719C23C2×D4×D4311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—862no—
724Q8—862no—
725Q8—1728no—
726Q8—1722no—
727D4—22no—
728D4—24no—
729D4—862no—
730D4—862no—
731D4—3444no—
732D4—1724no—
733D4—1728no—
734D4—1728no—
735D4—1722no—
736D4C2×#1062189814yes—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—84no—
746C2×C4—432no—
747C2×C4—432no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—864no—
755C2×C4—864no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—1728no—
760C2×C4—1722no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4C2×D4×D4312yes—
764C2×C4C2×D4×D4312yes—
765C2×C4C2×D4×D4311yescharacteristic
766C2×C4C2×#1062189812yes—
767C2×C4#1306337112yes—
768C2×C4C24×D4311yescharacteristic
769C8—22no—
770C8—22no—
771C8—862no—
772C8—862no—
773C22—24no—
774C22—42no—
775C22—42no—
776C22—48no—
777C22—862no—
778C22—862no—
779C22—862no—
780C22—862no—
781C22—862no—
782C22—862no—
783C22—34416no—
784C22—3444no—
785C22—1722no—
786C22—1722no—
787C22—1722no—
788C22—1724no—
789C22—1724no—
790C22#1458354512yes—
791C22#1458369812yes—
792C22#1458370912yes—
793C22C22×D4×D4311yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—862no—
800C4—862no—
801C4—1722no—
802C4—1722no—
803C4—1722no—
804C4#1458354512yes—
805C4C22×#1062189811yescharacteristic
806C4C2×#1306337111yescharacteristic
807C2—44no—
808C2—3442no—
809C2—1722no—
810C2—1722no—
811C2#1914663614yesdirect product factor
812C2C2×#1458354511yescharacteristic
813C2C2×#1458369811yescharacteristic
814C2C2×#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×#3311
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. C2×#14583622C2semidirect
3. #19146636C2direct (N × H)
4. C2×#14583259C2semidirect
5. C2×#14583242C2semidirect
6. C2×#14583226C2semidirect
7. C2×#14583189C2semidirect
8. C2×#14583156C2semidirect
9. C2×#14583131C2semidirect
10. C2×#14583121C2semidirect
11. C2×#14583058C2semidirect
12. C2×#14583048C2semidirect
13. C2×#14582972C2semidirect
14. C2×#14582902C2semidirect
15. C2×#14582892C2semidirect
16. C2×C43×#440C2semidirect
19. C22×#10621885C22semidirect
22. C22×C8×D43C22semidirect
24. #14583622C22semidirect
27. C2×#13063325C22semidirect
35. C2×#13063301C22semidirect
42. C2×#13063283C22semidirect
44. #14583259C22semidirect
45. #14583242C22semidirect
46. #14583226C22semidirect
47. #14583189C22semidirect
48. #14583156C22semidirect
49. #14583131C22semidirect
50. #14583121C22semidirect
51. #14583058C22semidirect
52. #14583048C22semidirect
53. #14582972C22semidirect
54. C2×#13063256C22semidirect
55. C2×#13063256C22semidirect
56. C2×C4⋊(C43⋊C8)C22semidirect
57. #14582902C22semidirect
58. #14582892C22semidirect
59. C2×#13063250C22semidirect
60. C2×#13063250C22semidirect
61. C2×#13063248C22semidirect
68. C2×(C2×D43)⋊C8C22semidirect
70. C2×C4×Q8×C43C22semidirect
72. C43×#440C22semidirect
73. C2×#107×C43C22semidirect
74. C2×#103×C43C22semidirect
76. C2×#97×C43C22semidirect
97. C2×#10621885C23semidirect
105. C2×C8×D43C23semidirect
107. #13063325C23semidirect
119. #13063301C23semidirect
130. #13063283C23semidirect
151. #13063256C23semidirect
152. #13063256C23semidirect
153. C4⋊(C43⋊C8)C23semidirect
154. #13063250C23semidirect
155. #13063250C23semidirect
156. #13063248C23semidirect
163. (C2×D43)⋊C8C23semidirect
172. C4×Q8×C43C23semidirect
181. #107×C43C23semidirect
182. #103×C43C23semidirect
184. #97×C43C23semidirect
412. C2×#440D43semidirect
417. C2×C43#3311semidirect
448. C2×C4×Q8C2×D43semidirect
463. #440C2×D43semidirect
465. C2×#107C2×D43semidirect
474. C2×#103C2×D43semidirect
483. C2×#97C2×D43semidirect
484. C43C2×#3311semidirect
541. C4×Q8C22×D43semidirect
576. #107C22×D43semidirect
583. #103C22×D43semidirect
592. #97C22×D43semidirect
811. C2#19146636direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836222
C2×#145835442
#191466362
C2×#145832592
C2×#145832422
C2×#145832262
C2×#145831892
C2×#145831562
C2×#145831312
C2×#145831212
C2×#145830582
C2×#145830482
C2×#145829722
C2×#145829022
C2×#145828922
C2×C43×#4402
C2×#331143