Finite Group Databasebeta

← C2×#19146678 #25973125

Subgroups — C2×#19146678 #25973125

Order 11008.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583606C211yesmaximal, characteristic, complemented
2C2×#14583545C211yesmaximal, characteristic
3#19146678C2116yesmaximal, direct product factor
4C2×#14583259C211yesmaximal, characteristic, complemented
5C2×#14583235C211yesmaximal, characteristic, complemented
6C2×#14583213C211yesmaximal, characteristic, complemented
7C2×#14583180C211yesmaximal, characteristic, complemented
8C2×#14583145C211yesmaximal, characteristic, complemented
9C2×#14583140C211yesmaximal, characteristic, complemented
10C2×#14583122C211yesmaximal, characteristic, complemented
11C2×#14583063C211yesmaximal, characteristic, complemented
12C2×#14583052C211yesmaximal, characteristic, complemented
13C2×#14583001C211yesmaximal, characteristic, complemented
14C2×#14582901C211yesmaximal, characteristic, complemented
15C22×#13063247C211yesmaximal, characteristic, complemented
16C2×C43×#435C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×D172C2211yescharacteristic
19C22×Dic172C2211yescharacteristic, complemented
20C22×#10621873C2211yescharacteristic
21C22×#10621873C2211yescharacteristic
22#14583606—24no—
23#14583606C2218yescomplemented
24#14583545—24no—
25#14583545C2218yes—
26C2×#13063325C2211yescharacteristic, complemented
27C2×#13063316—21no—
28C2×#13063313C2211yescharacteristic
29C2×#13063310—21no—
30C2×#13063304C2211yescharacteristic
31C2×#13063304C2211yescharacteristic
32C2×#13063304C2211yescharacteristic, complemented
33C2×#13063302—21no—
34C2×#13063302—21no—
35C2×#13063299C2211yescharacteristic
36C2×#13063298—21no—
37C2×#13063293—21no—
38C2×C4×Dic86C2211yescharacteristic, complemented
39C2×C4×D172C2211yescharacteristic
40C2×D4×Dic43—21no—
41C22×C4⋊Dic43C2211yescharacteristic
42C22×C4⋊Dic43C2211yescharacteristic, complemented
43C2×C22⋊C4×D43—21no—
44#14583259C2218yescomplemented
45#14583235C2218yescomplemented
46#14583213C2218yescomplemented
47#14583180C2218yescomplemented
48#14583145C2218yescomplemented
49#14583140C2218yescomplemented
50#14583122C2218yescomplemented
51#14583063C2218yescomplemented
52#14583052C2218yescomplemented
53#14583001C2218yescomplemented
54C2×#13063259C2211yescharacteristic, complemented
55C2×#13063259C2211yescharacteristic, complemented
56C2×#13063259C2211yescharacteristic, complemented
57#14582901C2218yescomplemented
58C2×#13063250C2211yescharacteristic, complemented
59C2×#13063250C2211yescharacteristic, complemented
60C2×#13063250C2211yescharacteristic, complemented
61C2×#13063250C2211yescharacteristic, complemented
62C2×#13063247C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063247C2218yescomplemented
69C22×M16×C43C2211yescharacteristic, complemented
70C23×C8×C43C2211yescharacteristic
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—
94C23×Dic43—21no—
95C23×Dic43—21no—
96C22×C4×D43—21no—
97C22×C4×D43—21no—
98C2×Dic172—42no—
99C2×Dic172C2314yescomplemented
100C2×#10621873—24no—
101C2×#10621873—42no—
102C2×#10621873C2314yes—
103C2×#10621873C2314yes—
104#13063325—22no—
105#13063325C2314yescomplemented
106#13063316—28no—
107#13063313—22no—
108#13063313C2314yes—
109#13063310—28no—
110#13063304—22no—
111#13063304—22no—
112#13063304—22no—
113#13063304C2314yes—
114#13063304C2314yes—
115#13063304C2314yescomplemented
116#13063302—28no—
117#13063302—28no—
118#13063299—22no—
119#13063299C2314yes—
120#13063298—28no—
121#13063293—28no—
122C4×Dic86—22no—
123C4×Dic86C2314yescomplemented
124C4×D172—22no—
125C4×D172C2314yes—
126D4×Dic43—28no—
127C2×C4⋊Dic43—22no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43—22no—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43C2311yescharacteristic
133C2×C4⋊Dic43C2314yes—
134C2×C4⋊Dic43C2311yescharacteristic
135C2×C4⋊Dic43C2311yescharacteristic
136C2×C4⋊Dic43C2311yescharacteristic
137C2×C4⋊Dic43C2314yescomplemented
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4—21no—
142C2×C22⋊Dic43—21no—
143C2×C22⋊Dic43—21no—
144C2×C22⋊Dic43—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C22⋊C4×D43—28no—
150C2×C4×Dic43—21no—
151#13063259C2314yescomplemented
152#13063259C2314yescomplemented
153#13063259C2314yescomplemented
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×C43C2314yescomplemented
169C22×C8×C43—42no—
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2314yes—
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—24no—
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—
218C22×Dic43—24no—
219C22×Dic43—24no—
220C22×Dic43—82no—
221C22×Dic43—82no—
222#10621898—28no—
223#10621898—44no—
224#10621898—48no—
225C2×D172—21no—
226C2×D172—22no—
227C2×D172—24no—
228C2×D172—21no—
229C2×D172—22no—
230C2×D172—22no—
231C2×D172—28no—
232C2×D172—44no—
233C2×D172—44no—
234C2×D172—48no—
235C2×D172#4114yes—
236C2×D172C2412yes—
237C2×D172C2412yes—
238C2×C4×D43—24no—
239C2×C4×D43—24no—
240C2×C4×D43—44no—
241C2×C4×D43—82no—
242C2×Dic86—22no—
243C2×Dic86—22no—
244C2×Dic86—22no—
245C2×Dic86—22no—
246C2×Dic86—21no—
247C2×Dic86—21no—
248C2×Dic86—24no—
249C2×Dic86—82no—
250C2×Dic86C2412yes—
251C2×Dic86C2412yes—
252M16×C43—44no—
253C2×C8×C43—22no—
254C2×C8×C43—22no—
255C2×C8×C43—22no—
256C2×C8×C43—22no—
257C2×C8×C43—44no—
258C2×C8×C43C2412yes—
259C2×C8×C43C2412yes—
260C2×C8×C43C2412yes—
261C2×C8×C43C2412yes—
262C4⋊C4×C43C2×D414yes—
263C22⋊C4×C43C2×D414yes—
264C22⋊C4×C43C2×D414yes—
265C42×C43C2×D412yes—
266C42×C43C2412yes—
267C22⋊Dic43—24no—
268C22⋊Dic43—24no—
269C22⋊Dic43—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274C4⋊Dic43—21no—
275C4⋊Dic43—24no—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—24no—
279C4⋊Dic43—24no—
280C4⋊Dic43—21no—
281C4⋊Dic43C2412yes—
282C4⋊Dic43C2412yes—
283C4⋊Dic43C2412yes—
284C4⋊Dic43C2412yes—
285Dic43⋊C4—24no—
286Dic43⋊C4—24no—
287Dic43⋊C4—24no—
288Dic43⋊C4—24no—
289C4×Dic43—24no—
290Dic172—44no—
291#10621873—28no—
292#10621873—44no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43#13714yes—
299C23×C43C22×D412yes—
300C23×C43C22×D412yes—
301C23×C43C22×D411yescharacteristic
302C22×D43—24no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—48no—
306C22×D43—42no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—48no—
310C22×D43—42no—
311C22×D43—42no—
312C22×D43—84no—
313C22×D43—816no—
314D4×C43—28no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—24no—
320C2×C4×C43—24no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43C22×D412yes—
326C2×C4×C43C22×D412yes—
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—84no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43—84no—
348C2×Dic43—84no—
349D172—24no—
350D172—22no—
351D172—22no—
352D172—22no—
353D172—48no—
354D172—42no—
355D172C2×#4114yes—
356C4×D43—48no—
357C4×D43—84no—
358Dic86—22no—
359Dic86—22no—
360Dic86—22no—
361Dic86—22no—
362Dic86—42no—
363Dic86—42no—
364Dic86—84no—
365C8×C43—22no—
366C8×C43—22no—
367C8×C43—22no—
368C8×C43—22no—
369C2×#3314—431nomaximal, Sylow
370C22×C43—22no—
371C22×C43—28no—
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—22no—
376C22×C43—44no—
377C22×C43#54612yes—
378C22×C43C2×#13714yes—
379C22×C43C2×#13712yes—
380C22×C43#57612yes—
381C22×C43C23×D411yescharacteristic
382C2×D43—24no—
383C2×D43—48no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—816no—
390C2×D43—84no—
391C4×C43—22no—
392C4×C43—22no—
393C4×C43—22no—
394C4×C43—22no—
395C4×C43#54612yes—
396C4×C43C22×#4111yescharacteristic
397C4×C43C2×H(5,𝔽2)11yescharacteristic
398Dic43—42no—
399Dic43—42no—
400Dic43—42no—
401Dic43—42no—
402Dic43—42no—
403Dic43—42no—
404C2×#554—431no—
405C2×#546—431no—
406#3314—4316no—
407C2×#489—431no—
408C2×#484—431no—
409C2×#480—431no—
410C2×#474—431no—
411C2×#468—431no—
412C2×#467—431no—
413C2×#464—431no—
414C2×#452—431no—
415C2×#450—431no—
416C2×#440—431no—
417C2×#435D4311yescharacteristic, complemented
418C2×#417—431no—
419C22×#102—431no—
420C2×C43—24no—
421C2×C43—42no—
422C2×C43#331414yescomplemented
423C2×C43C2×#54611yescharacteristic
424C2×C43C22×#13711yescharacteristic
425C2×C43C2×#57611yescharacteristic
426D43—44no—
427D43—82no—
428C22×#41—431no—
429C23×D4—431no—
430C22×Q16—431no—
431C22×SD16—431no—
432C22×SD16—431no—
433C22×M16C2×D4311yescharacteristic, complemented
434C23×C8C2×D4311yescharacteristic
435#554—438no—
436#554—864no—
437#546—438no—
438#546—864no—
439C2×C4⋊Q8—431no—
440C2×#125—861no—
441C2×#124—431no—
442C2×#123—861no—
443C2×C22⋊Q8—431no—
444C2×C22⋊Q8—431no—
445C2×C22⋊Q8—431no—
446C2×C22⋊Q8—861no—
447C2×C22⋊Q8—861no—
448C2×#121—431no—
449C2×#121—861no—
450C2×#120—861no—
451C2×C4×Q8—431no—
452C2×C4×D4—431no—
453C2×C4×D4—861no—
454C2×C4×D4C2×D4311yescharacteristic
455C22×C4⋊C4—431no—
456C22×C4⋊C4—431no—
457C22×C22⋊C4—861no—
458#489—438no—
459#484—438no—
460#480—438no—
461#474—438no—
462#468—438no—
463#467—438no—
464#464—438no—
465#452—438no—
466#450—438no—
467#440—438no—
468#435C2×D4318yescomplemented
469C2×#107—431no—
470C2×#107—431no—
471C2×#107—431no—
472C2×C4⋊C8C2×D4311yescharacteristic, complemented
473#417—438no—
474C2×#103—431no—
475C2×#103—431no—
476C2×#103—431no—
477C2×#103—431no—
478C2×#102—431no—
479C2×#102—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—438no—
484C2×#102—431no—
485C2×C22⋊C8C2×D4311yescharacteristic
486C2×C22⋊C8C2×D4311yescharacteristic, complemented
487C2×#97C2×D4311yescharacteristic, complemented
488C43C2×#331411yescharacteristic, complemented, Sylow
489C25—861no—
490C2×#41—434no—
491C2×#41—864no—
492C2×#41—862no—
493C2×#41—1722no—
494C22×Q8—431no—
495C22×Q8—431no—
496C22×Q8—861no—
497C22×D4—431no—
498C22×D4—431no—
499C22×D4—434no—
500C22×D4—864no—
501C22×D4—861no—
502C22×D4—861no—
503C22×D4—861no—
504C22×D4—862no—
505C22×D4—1722no—
506C22×D4D17211yescharacteristic
507C23×C4—861no—
508C23×C4—861no—
509C23×C4—861no—
510C23×C4—861no—
511C23×C4C22×D4311yescharacteristic
512C23×C4C22×D4311yescharacteristic
513C2×Q16—434no—
514C2×Q16—1722no—
515C2×SD16—434no—
516C2×SD16—434no—
517C2×SD16—864no—
518C2×SD16—1722no—
519C2×M16—42no—
520C2×M16C22×D4314yescomplemented
521C22×C8—42no—
522C22×C8C22×D4311yescharacteristic
523C22×C8C22×D4311yescharacteristic
524C22×C8C22×D4311yescharacteristic
525C22×C8C22×D4311yescharacteristic
526C22×C8C22×D4314yes—
527C4⋊Q8—434no—
528C4⋊Q8—862no—
529#125—868no—
530#124—434no—
531#124—862no—
532#123—868no—
533C22⋊Q8—434no—
534C22⋊Q8—434no—
535C22⋊Q8—434no—
536C22⋊Q8—862no—
537C22⋊Q8—862no—
538C22⋊Q8—862no—
539C22⋊Q8—868no—
540C22⋊Q8—868no—
541#121—434no—
542#121—862no—
543#121—868no—
544#120—868no—
545C4×Q8—434no—
546C4×Q8—862no—
547C4×D4—434no—
548C4×D4—868no—
549C4×D4—862no—
550C4×D4D17214yes—
551C4×D4C22×D4314yes—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—431no—
555C2×C4⋊C4—434no—
556C2×C4⋊C4—434no—
557C2×C4⋊C4—431no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4—862no—
561C2×C4⋊C4—862no—
562C2×C4⋊C4—861no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4D17211yescharacteristic
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—868no—
576C2×C22⋊C4D17211yescharacteristic
577C2×C22⋊C4D17211yescharacteristic
578C2×C42—861no—
579C2×C42C22×D4311yescharacteristic
580#107—434no—
581#107—434no—
582#107—434no—
583C4⋊C8C22×D4314yescomplemented
584#103—434no—
585#103—434no—
586#103—434no—
587#103—434no—
588#102—434no—
589#102—434no—
590#102—434no—
591#102—434no—
592#102—434no—
593#102—434no—
594C22⋊C8C22×D4314yes—
595C22⋊C8C22×D4314yescomplemented
596#97C22×D4314yescomplemented
597C24—861no—
598C24—864no—
599C24—861no—
600C24—3442no—
601C24—1724no—
602C24—1724no—
603C24C2×D17211yescharacteristic
604C24C2×D17211yescharacteristic
605#41—868no—
606#41—1724no—
607#41—1728no—
608C2×Q8—432no—
609C2×Q8—432no—
610C2×Q8—864no—
611C2×Q8—861no—
612C2×Q8—861no—
613C2×Q8—862no—
614C2×Q8—862no—
615C2×Q8—862no—
616C2×Q8—862no—
617C2×Q8—3442no—
618C2×D4—24no—
619C2×D4—434no—
620C2×D4—432no—
621C2×D4—432no—
622C2×D4—868no—
623C2×D4—864no—
624C2×D4—864no—
625C2×D4—861no—
626C2×D4—864no—
627C2×D4—861no—
628C2×D4—862no—
629C2×D4—862no—
630C2×D4—862no—
631C2×D4—3442no—
632C2×D4—1724no—
633C2×D4—1728no—
634C2×D4—1724no—
635C2×D4—1724no—
636C2×D4C2×D17214yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—864no—
642C22×C4—864no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—861no—
646C22×C4—861no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—864no—
650C22×C4—864no—
651C22×C4—3442no—
652C22×C4—3442no—
653C22×C4—3442no—
654C22×C4—1724no—
655C22×C4C2×D17212yes—
656C22×C4C2×D17212yes—
657C22×C4C2×D17211yescharacteristic
658C22×C4C2×D17211yescharacteristic
659C22×C4C2×D17211yescharacteristic
660C22×C4C2×D17211yescharacteristic
661C22×C4C23×D4312yes—
662C22×C4C23×D4312yes—
663C22×C4C23×D4311yescharacteristic
664Q16—1724no—
665SD16—868no—
666SD16—1724no—
667M16—44no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—44no—
673C2×C8C23×D4312yes—
674C2×C8C23×D4312yes—
675C2×C8C23×D4312yes—
676C2×C8C23×D4312yes—
677C4⋊C4—432no—
678C4⋊C4—432no—
679C4⋊C4—432no—
680C4⋊C4—432no—
681C4⋊C4—861no—
682C4⋊C4—864no—
683C4⋊C4—864no—
684C4⋊C4—861no—
685C4⋊C4—861no—
686C4⋊C4—861no—
687C4⋊C4—864no—
688C4⋊C4—864no—
689C4⋊C4—864no—
690C4⋊C4—864no—
691C4⋊C4—864no—
692C4⋊C4C2×D17214yes—
693C22⋊C4—864no—
694C22⋊C4—864no—
695C22⋊C4—864no—
696C22⋊C4—864no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C22⋊C4—864no—
700C22⋊C4C2×D17214yes—
701C22⋊C4C2×D17214yes—
702C42—864no—
703C42C2×D17212yes—
704C42C23×D4312yes—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—862no—
711C23—864no—
712C23—862no—
713C23—34416no—
714C23—3444no—
715C23—1728no—
716C23—1728no—
717C23—1722no—
718C23—1722no—
719C23—1722no—
720C23—1722no—
721C23—1722no—
722C23#1306335814yes—
723C23C22×D17212yes—
724C23C22×D17212yes—
725C23C22×D17211yescharacteristic
726Q8—862no—
727Q8—862no—
728Q8—862no—
729Q8—862no—
730Q8—3444no—
731Q8—1722no—
732Q8—1722no—
733D4—28no—
734D4—434no—
735D4—862no—
736D4—862no—
737D4—862no—
738D4—864no—
739D4—3444no—
740D4—1728no—
741D4—1728no—
742D4—1722no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—3444no—
760C2×C4—3444no—
761C2×C4—3444no—
762C2×C4—1728no—
763C2×C4—1722no—
764C2×C4—1722no—
765C2×C4—1722no—
766C2×C4—1722no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4C22×D17212yes—
770C2×C4C22×D17212yes—
771C2×C4C22×D17212yes—
772C2×C4C22×D17212yes—
773C2×C4C22×D17211yescharacteristic
774C2×C4#41×D4312yes—
775C2×C4#1306337012yes—
776C2×C4C24×D4311yescharacteristic
777C8—22no—
778C8—22no—
779C8—22no—
780C8—22no—
781C22—22no—
782C22—22no—
783C22—28no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—44no—
788C22—864no—
789C22—34416no—
790C22—3444no—
791C22—1722no—
792C22—1722no—
793C22—1722no—
794C22—1722no—
795C22—1722no—
796C22—1728no—
797C22#1458354412yes—
798C22C2×#1306335814yes—
799C22C2×#1306335812yes—
800C22#1458370412yes—
801C22C23×D17211yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—1722no—
807C4—1722no—
808C4—1722no—
809C4—1722no—
810C4—1722no—
811C4—1722no—
812C4#1458354412yes—
813C4C2×#41×D4311yescharacteristic
814C4C2×#1306337011yescharacteristic
815C2—24no—
816C2—42no—
817C2—3442no—
818C2—1724no—
819C2#1914667814yesdirect product factor
820C2C2×#1458354411yescharacteristic
821C2C22×#1306335811yescharacteristic
822C2C2×#1458370411yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
prime radicalC2×#14583545C2
hypercenterC2×#435D43
hypocenterC43C2×#3314
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×#14583606C2semidirect
3. #19146678C2direct (N × H)
4. C2×#14583259C2semidirect
5. C2×#14583235C2semidirect
6. C2×#14583213C2semidirect
7. C2×#14583180C2semidirect
8. C2×#14583145C2semidirect
9. C2×#14583140C2semidirect
10. C2×#14583122C2semidirect
11. C2×#14583063C2semidirect
12. C2×#14583052C2semidirect
13. C2×#14583001C2semidirect
14. C2×#14582901C2semidirect
15. C22×#13063247C2semidirect
16. C2×C43×#435C2semidirect
19. C22×Dic172C22semidirect
23. #14583606C22semidirect
26. C2×#13063325C22semidirect
32. C2×#13063304C22semidirect
38. C2×C4×Dic86C22semidirect
42. C22×C4⋊Dic43C22semidirect
44. #14583259C22semidirect
45. #14583235C22semidirect
46. #14583213C22semidirect
47. #14583180C22semidirect
48. #14583145C22semidirect
49. #14583140C22semidirect
50. #14583122C22semidirect
51. #14583063C22semidirect
52. #14583052C22semidirect
53. #14583001C22semidirect
54. C2×#13063259C22semidirect
55. C2×#13063259C22semidirect
56. C2×#13063259C22semidirect
57. #14582901C22semidirect
58. C2×#13063250C22semidirect
59. C2×#13063250C22semidirect
60. C2×#13063250C22semidirect
61. C2×#13063250C22semidirect
68. C2×#13063247C22semidirect
69. C22×M16×C43C22semidirect
72. C43×#435C22semidirect
73. C2×C4⋊C8×C43C22semidirect
75. C2×C22⋊C8×C43C22semidirect
76. C2×#97×C43C22semidirect
99. C2×Dic172C23semidirect
105. #13063325C23semidirect
115. #13063304C23semidirect
123. C4×Dic86C23semidirect
137. C2×C4⋊Dic43C23semidirect
151. #13063259C23semidirect
152. #13063259C23semidirect
153. #13063259C23semidirect
154. #13063250C23semidirect
155. #13063250C23semidirect
156. #13063250C23semidirect
157. #13063250C23semidirect
168. C2×M16×C43C23semidirect
181. C4⋊C8×C43C23semidirect
183. C22⋊C8×C43C23semidirect
184. #97×C43C23semidirect
417. C2×#435D43semidirect
422. C2×C43#3314semidirect
433. C22×M16C2×D43semidirect
468. #435C2×D43semidirect
472. C2×C4⋊C8C2×D43semidirect
486. C2×C22⋊C8C2×D43semidirect
487. C2×#97C2×D43semidirect
488. C43C2×#3314semidirect
520. C2×M16C22×D43semidirect
583. C4⋊C8C22×D43semidirect
595. C22⋊C8C22×D43semidirect
596. #97C22×D43semidirect
819. C2#19146678direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836062
C2×#145835452
#191466782
C2×#145832592
C2×#145832352
C2×#145832132
C2×#145831802
C2×#145831452
C2×#145831402
C2×#145831222
C2×#145830632
C2×#145830522
C2×#145830012
C2×#145829012
C22×#130632472
C2×C43×#4352
C2×#331443