Finite Group Databasebeta

← C2×#19146918 #25973526

Subgroups — C2×#19146918 #25973526

Order 11008.

2426 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583568C211yesmaximal, characteristic, complemented
2C2×#14583550C211yesmaximal, characteristic, complemented
3#19146918C2116yesmaximal, direct product factor
4C2×#14583244C211yesmaximal, characteristic, complemented
5C2×#14583217C211yesmaximal, characteristic, complemented
6C2×#14583216C211yesmaximal, characteristic, complemented
7C2×#14583182C211yesmaximal, characteristic, complemented
8C2×#14583152C211yesmaximal, characteristic, complemented
9C2×#14583151C211yesmaximal, characteristic, complemented
10C2×#14583093C211yesmaximal, characteristic, complemented
11C2×#14583047C211yesmaximal, characteristic, complemented
12C2×#14583044C211yesmaximal, characteristic, complemented
13C2×#14582984C211yesmaximal, characteristic, complemented
14C2×#14582975C211yesmaximal, characteristic, complemented
15C2×#14582899C211yesmaximal, characteristic, complemented
16C2×C43×#417C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621898—21no—
19C22×#10621884C2211yescharacteristic
20C22×D344C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22C22×#10621872C2211yescharacteristic
23#14583568—24no—
24#14583568C2218yescomplemented
25#14583550—24no—
26#14583550C2218yescomplemented
27C2×#13063324C2211yescharacteristic
28C2×#13063321—21no—
29C2×#13063321C2211yescharacteristic
30C2×#13063310—21no—
31C2×#13063308—21no—
32C2×#13063303—21no—
33C2×#13063300C2211yescharacteristic
34C2×#13063299—21no—
35C2×#13063299C2211yescharacteristic
36C2×#13063299C2211yescharacteristic
37C2×#13063296—21no—
38C2×#13063296C2211yescharacteristic
39C2×Q8×Dic43C2211yescharacteristic
40C2×#13063287C2211yescharacteristic
41C2×C4×C22⋊D43—21no—
42C2×C4×C22⋊D43C2211yescharacteristic
43C2×C4⋊C4×D43C2211yescharacteristic
44#14583244C2218yescomplemented
45#14583217C2218yescomplemented
46#14583216C2218yescomplemented
47#14583182C2218yescomplemented
48#14583152C2218yescomplemented
49#14583151C2218yescomplemented
50#14583093C2218yescomplemented
51#14583047C2218yescomplemented
52#14583044C2218yescomplemented
53#14582984C2218yescomplemented
54#14582975C2218yescomplemented
55C2×#13063257C2211yescharacteristic
56C2×#13063256C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59#14582899C2218yescomplemented
60C2×#13063249C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×#41×C43C2211yescharacteristic
70C22×M16×C43C2211yescharacteristic
71C22×C4⋊C4×C43C2211yescharacteristic
72C43×#417C2218yescomplemented
73C2×#103×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—24no—
79C2×#10621902—42no—
80C2×#10621902C2314yes—
81C2×#10621898—28no—
82C2×#10621898—48no—
83C22×Dic86—21no—
84C22×D172—21no—
85C22×D172—21no—
86C22×D172C2311yescharacteristic
87C22×D172C2311yescharacteristic
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C22×C22⋊D43D411yescharacteristic
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43C2311yescharacteristic
98C2×#10621884—24no—
99C2×#10621884C2314yes—
100C2×D344—42no—
101C2×D344C2314yes—
102C2×#10621882—42no—
103C2×#10621882C2314yes—
104C2×#10621872—42no—
105C2×#10621872C2314yes—
106C22×C43⋊C8C2311yescharacteristic
107C22×C43⋊C8C2311yescharacteristic
108#13063324—22no—
109#13063324C2314yes—
110#13063321—28no—
111#13063321—22no—
112#13063321C2314yes—
113#13063310—28no—
114#13063308—28no—
115#13063303—28no—
116#13063300—22no—
117#13063300C2314yes—
118#13063299—22no—
119#13063299—22no—
120#13063299—28no—
121#13063299C2314yes—
122#13063299C2314yes—
123#13063296—22no—
124#13063296—28no—
125#13063296C2314yes—
126Q8×Dic43—22no—
127Q8×Dic43C2314yes—
128#13063287—22no—
129#13063287C2314yes—
130C4×C22⋊D43—28no—
131C4×C22⋊D43D414yes—
132C4×C22⋊D43C2314yes—
133C2×C4⋊Dic43—21no—
134C2×C4⋊Dic43C2311yescharacteristic
135C2×C4⋊Dic43C2311yescharacteristic
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4D411yescharacteristic
139C4⋊C4×D43—22no—
140C4⋊C4×D43C2314yes—
141C2×C22⋊Dic43—21no—
142C2×C22⋊Dic43D411yescharacteristic
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4D411yescharacteristic
148C2×C4×Dic43—21no—
149C2×C4×Dic43C2311yescharacteristic
150#13063257C2314yes—
151#13063256C2314yes—
152#13063256C2314yes—
153Dic43⋊C8C2314yes—
154#13063249C2314yes—
155#13063247C2314yes—
156#13063247C2314yes—
157#13063246C2314yes—
158#13063245C2314yes—
159#13063245C2314yes—
160C22⋊(C43⋊C8)C2314yes—
161(C2×D43)⋊C8C2314yes—
162C8×Dic43C2314yes—
163C2×#41×C43—22no—
164C2×#41×C43—24no—
165C2×#41×C43—42no—
166C2×#41×C43C2314yes—
167C22×Q8×C43C2311yescharacteristic
168C22×D4×C43—21no—
169C22×D4×C43C2311yescharacteristic
170C23×C4×C43—21no—
171C23×C4×C43—21no—
172C23×C4×C43C2311yescharacteristic
173C2×M16×C43—42no—
174C2×M16×C43C2314yes—
175C22×C8×C43C2311yescharacteristic
176C22×C8×C43C2311yescharacteristic
177C2×C4⋊C4×C43—21no—
178C2×C4⋊C4×C43—22no—
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C4⋊C4×C43C2314yes—
182#103×C43C2314yes—
183#103×C43C2314yes—
184#102×C43C2314yes—
185#102×C43C2314yes—
186C24×C43—21no—
187C24×C43C2×D411yescharacteristic
188C23×D43—21no—
189C23×D43—21no—
190C23×D43C2×D411yescharacteristic
191#41×C43—28no—
192#41×C43—44no—
193#41×C43—48no—
194C2×Q8×C43—21no—
195C2×Q8×C43—22no—
196C2×Q8×C43#4114yescomplemented
197C2×Q8×C43C2412yes—
198C2×D4×C43—21no—
199C2×D4×C43—24no—
200C2×D4×C43—22no—
201C2×D4×C43—22no—
202C2×D4×C43—44no—
203C2×D4×C43C2412yes—
204C22×C4×C43—22no—
205C22×C4×C43—22no—
206C22×C4×C43—24no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—24no—
211C22×C4×C43—44no—
212C22×C4×C43—44no—
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D412yes—
215C22×C4×C43C2412yes—
216C22×C4×C43C2411yescharacteristic
217C2×C22⋊D43—24no—
218C2×C22⋊D43—24no—
219C2×C22⋊D43—24no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—24no—
222C2×C22⋊D43—24no—
223C2×C22⋊D43—44no—
224C2×C22⋊D43—44no—
225C2×C22⋊D43—82no—
226C2×C22⋊D43—82no—
227C2×C22⋊D43—82no—
228C2×C22⋊D43C2×D414yes—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43C2×D411yescharacteristic
232C22×Dic43C2×D411yescharacteristic
233C22×Dic43C2×D411yescharacteristic
234#10621902—28no—
235#10621902—44no—
236#10621902—48no—
237#10621898—432no—
238C2×D172—21no—
239C2×D172—21no—
240C2×D172—24no—
241C2×D172—24no—
242C2×D172—22no—
243C2×D172—22no—
244C2×D172—22no—
245C2×D172—22no—
246C2×D172—44no—
247C2×D172—44no—
248C2×D172C2412yes—
249C2×D172C2412yes—
250C2×C4×D43—22no—
251C2×C4×D43—22no—
252C2×C4×D43—24no—
253C2×C4×D43—24no—
254C2×C4×D43—24no—
255C2×C4×D43—44no—
256C2×C4×D43—44no—
257C2×C4×D43—44no—
258C2×C4×D43C2×D412yes—
259C2×C4×D43C2412yes—
260C2×Dic86—24no—
261C2×Dic86—44no—
262M16×C43—44no—
263C2×C8×C43—22no—
264C2×C8×C43—22no—
265C2×C8×C43C2412yes—
266C2×C8×C43C2412yes—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—24no—
270C4⋊C4×C43C2412yes—
271C4⋊C4×C43C2412yes—
272C22⋊Dic43—24no—
273C22⋊Dic43C2×D414yes—
274#10621884—28no—
275#10621882—44no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4—24no—
278(C2×D43)⋊C4—24no—
279(C2×D43)⋊C4—24no—
280(C2×D43)⋊C4C2×D414yes—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43—24no—
284C4⋊Dic43C2412yes—
285C4⋊Dic43C2412yes—
286Dic43⋊C4—24no—
287Dic43⋊C4—24no—
288Dic43⋊C4C2×D414yes—
289C4×Dic43—24no—
290C4×Dic43C2×D412yes—
291C4×Dic43C2412yes—
292C2×C43⋊C8—22no—
293C2×C43⋊C8—22no—
294C2×C43⋊C8C2412yes—
295C2×C43⋊C8C2412yes—
296D344—44no—
297#10621872—44no—
298C23×C43—22no—
299C23×C43—22no—
300C23×C43—22no—
301C23×C43—22no—
302C23×C43—42no—
303C23×C43—42no—
304C23×C43—42no—
305C23×C43C22×D412yes—
306C23×C43C22×D411yescharacteristic
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—42no—
313C22×D43—42no—
314C22×D43—42no—
315C22×D43—42no—
316C22×D43—42no—
317C22×D43—42no—
318C22×D43C22×D412yes—
319Q8×C43—24no—
320Q8×C43—22no—
321Q8×C43C2×#4114yescomplemented
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—48no—
325D4×C43—42no—
326C2×C4×C43—24no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—24no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—48no—
335C2×C4×C43—48no—
336C2×C4×C43—42no—
337C2×C4×C43—42no—
338C2×C4×C43C22×D412yes—
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C2×#4112yes—
341C2×C4×C43H(5,𝔽2)12yes—
342C2×C4×C43C2511yescharacteristic
343C22⋊D43—28no—
344C22⋊D43—48no—
345C22⋊D43—48no—
346C22⋊D43—84no—
347C22⋊D43—84no—
348C22⋊D43—84no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—42no—
354C2×Dic43—42no—
355C2×Dic43AGL(1,ℤ/8)14yes—
356C2×Dic43C22×D412yes—
357C2×Dic43C22×D412yes—
358C2×Dic43C22×D412yes—
359D172—22no—
360D172—22no—
361D172—22no—
362D172—22no—
363D172—48no—
364D172—48no—
365D172—42no—
366D172—42no—
367C4×D43—24no—
368C4×D43—22no—
369C4×D43—22no—
370C4×D43—48no—
371C4×D43—48no—
372C4×D43—48no—
373Dic86—48no—
374C8×C43—22no—
375C8×C43—22no—
376C43⋊C8—22no—
377C43⋊C8—22no—
378C2×#3332—431nomaximal, Sylow
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—44no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—84no—
387C22×C43#54612yes—
388C22×C43C2×AGL(1,ℤ/8)12yes—
389C22×C43#57712yes—
390C22×C43C23×D411yescharacteristic
391C2×D43—22no—
392C2×D43—22no—
393C2×D43—22no—
394C2×D43—44no—
395C2×D43—42no—
396C2×D43—42no—
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—42no—
401C2×D43—84no—
402C2×D43—84no—
403C4×C43—24no—
404C4×C43—22no—
405C4×C43—42no—
406C4×C43—42no—
407C4×C43#54612yes—
408C4×C43C22×#4111yescharacteristic
409C4×C43C2×H(5,𝔽2)11yescharacteristic
410Dic43—22no—
411Dic43—22no—
412Dic43—42no—
413Dic43—42no—
414Dic43C2×AGL(1,ℤ/8)14yes—
415C2×#550—431no—
416C2×#547—431no—
417#3332—4316no—
418C2×#486—431no—
419C2×#481—431no—
420C2×#481—431no—
421C2×#475—431no—
422C2×#469—431no—
423C2×#469—431no—
424C2×#459—431no—
425C2×#449—431no—
426C2×#449—431no—
427C2×C4×SD16—431no—
428C2×#436—431no—
429C2×#417—431no—
430C2×#417D4311yescharacteristic, complemented
431C2×C43—42no—
432C2×C43—82no—
433C2×C43#333214yescomplemented
434C2×C43C2×#54611yescharacteristic
435C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
436C2×C43C2×#57711yescharacteristic
437D43—42no—
438D43—82no—
439D43—82no—
440C22×#41—431no—
441C22×#41—861no—
442C22×#41C2×D4311yescharacteristic
443C22×SD16—431no—
444C22×D8—431no—
445C22×D8—431no—
446C22×M16—431no—
447C22×M16C2×D4311yescharacteristic
448#550—438no—
449#550—864no—
450#547—438no—
451#547—864no—
452C2×C4⋊Q8—431no—
453C2×#127—431no—
454C2×#127—861no—
455C2×#123—861no—
456C2×#123—861no—
457C2×C22⋊Q8—861no—
458C2×#121—431no—
459C2×#121—431no—
460C2×#121—431no—
461C2×#121—431no—
462C2×#121—861no—
463C2×#121—861no—
464C2×C4×Q8—431no—
465C2×C4×D4—431no—
466C2×C4×D4—431no—
467C2×C4×D4—861no—
468C22×C4⋊C4—431no—
469C22×C4⋊C4C2×D4311yescharacteristic
470#486—438no—
471#481—438no—
472#481—438no—
473#475—438no—
474#469—438no—
475#469—438no—
476#459—438no—
477#449—438no—
478#449—438no—
479C4×SD16—438no—
480#436—438no—
481C2×#106—431no—
482C2×#106—431no—
483C2×#106—431no—
484C2×C4⋊C8—431no—
485#417—438no—
486#417C2×D4318yescomplemented
487C2×#103—431no—
488C2×#103C2×D4311yescharacteristic
489C2×#103C2×D4311yescharacteristic
490C2×#102—431no—
491C2×#102—431no—
492C2×#102—431no—
493C2×#102—431no—
494C2×#102—431no—
495C2×#102C2×D4311yescharacteristic
496C2×#102C2×D4311yescharacteristic
497C2×C22⋊C8—431no—
498C2×C22⋊C8—431no—
499C2×C4×C8—431no—
500C43C2×#333211yescharacteristic, complemented, Sylow
501C2×#41—22no—
502C2×#41—24no—
503C2×#41—42no—
504C2×#41—434no—
505C2×#41—868no—
506C2×#41—862no—
507C2×#41—864no—
508C2×#41—1728no—
509C2×#41—1722no—
510C2×#41C22×D4314yes—
511C22×Q8—861no—
512C22×Q8C22×D4311yescharacteristic
513C22×D4—21no—
514C22×D4—431no—
515C22×D4—431no—
516C22×D4—431no—
517C22×D4—861no—
518C22×D4—861no—
519C22×D4—861no—
520C22×D4—861no—
521C22×D4—861no—
522C22×D4—861no—
523C22×D4—861no—
524C22×D4C22×D4311yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—431no—
528C23×C4—861no—
529C23×C4—861no—
530C23×C4—861no—
531C23×C4C22×D4311yescharacteristic
532C2×SD16—434no—
533C2×SD16—864no—
534C2×D8—434no—
535C2×D8—434no—
536C2×D8—1722no—
537C2×D8—1722no—
538C2×M16—42no—
539C2×M16—434no—
540C2×M16—1722no—
541C2×M16C22×D4314yes—
542C22×C8—431no—
543C22×C8—431no—
544C22×C8C22×D4311yescharacteristic
545C22×C8C22×D4311yescharacteristic
546C4⋊Q8—434no—
547C4⋊Q8—862no—
548#127—434no—
549#127—862no—
550#127—868no—
551#123—868no—
552#123—868no—
553C22⋊Q8—868no—
554#121—434no—
555#121—434no—
556#121—434no—
557#121—434no—
558#121—868no—
559#121—868no—
560#121—862no—
561#121—862no—
562#121—862no—
563#121—862no—
564C4×Q8—434no—
565C4×Q8—862no—
566C4×D4—434no—
567C4×D4—434no—
568C4×D4—434no—
569C4×D4—862no—
570C4×D4—868no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—431no—
574C2×C4⋊C4—431no—
575C2×C4⋊C4—431no—
576C2×C4⋊C4—434no—
577C2×C4⋊C4—862no—
578C2×C4⋊C4—861no—
579C2×C4⋊C4—861no—
580C2×C4⋊C4—861no—
581C2×C4⋊C4C22×D4311yescharacteristic
582C2×C4⋊C4C22×D4311yescharacteristic
583C2×C4⋊C4C22×D4314yes—
584C2×C22⋊C4—431no—
585C2×C22⋊C4—431no—
586C2×C22⋊C4—861no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4—861no—
590C2×C22⋊C4—861no—
591C2×C42—431no—
592C2×C42—861no—
593#106—434no—
594#106—434no—
595#106—434no—
596C4⋊C8—434no—
597#103—434no—
598#103C22×D4314yes—
599#103C22×D4314yes—
600#102—434no—
601#102—434no—
602#102—434no—
603#102—434no—
604#102—434no—
605#102C22×D4314yes—
606#102C22×D4314yes—
607C22⋊C8—434no—
608C22⋊C8—434no—
609C4×C8—434no—
610C24—21no—
611C24—431no—
612C24—861no—
613C24—861no—
614C24D4×D4311yescharacteristic
615#41—28no—
616#41—44no—
617#41—48no—
618#41—868no—
619#41—17232no—
620#41—1724no—
621#41—1728no—
622C2×Q8—21no—
623C2×Q8—22no—
624C2×Q8—864no—
625C2×Q8—1724no—
626C2×Q8#1062189814yescomplemented
627C2×Q8C23×D4312yes—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—44no—
633C2×D4—434no—
634C2×D4—432no—
635C2×D4—432no—
636C2×D4—864no—
637C2×D4—864no—
638C2×D4—864no—
639C2×D4—864no—
640C2×D4—864no—
641C2×D4—864no—
642C2×D4—864no—
643C2×D4—864no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4—862no—
647C2×D4—862no—
648C2×D4—862no—
649C2×D4—862no—
650C2×D4—3442no—
651C2×D4—3442no—
652C2×D4—3442no—
653C2×D4—1724no—
654C2×D4—1724no—
655C2×D4—1724no—
656C2×D4—1724no—
657C2×D4C23×D4312yes—
658C22×C4—21no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—24no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—431no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—432no—
671C22×C4—432no—
672C22×C4—864no—
673C22×C4—864no—
674C22×C4—864no—
675C22×C4—862no—
676C22×C4—862no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—1724no—
680C22×C4—1724no—
681C22×C4—1724no—
682C22×C4D4×D4312yes—
683C22×C4D4×D4311yescharacteristic
684C22×C4C23×D4312yes—
685C22×C4C23×D4311yescharacteristic
686SD16—868no—
687D8—1724no—
688D8—1724no—
689M16—44no—
690M16—1724no—
691C2×C8—22no—
692C2×C8—22no—
693C2×C8—432no—
694C2×C8—432no—
695C2×C8—862no—
696C2×C8—862no—
697C2×C8C23×D4312yes—
698C2×C8C23×D4312yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—24no—
702C4⋊C4—434no—
703C4⋊C4—432no—
704C4⋊C4—432no—
705C4⋊C4—864no—
706C4⋊C4—864no—
707C4⋊C4—864no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4C23×D4312yes—
711C4⋊C4C23×D4312yes—
712C22⋊C4—434no—
713C22⋊C4—434no—
714C22⋊C4—864no—
715C22⋊C4—864no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—864no—
719C42—432no—
720C42—432no—
721C42—864no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—432no—
730C23—862no—
731C23—862no—
732C23—862no—
733C23—862no—
734C23—862no—
735C23—1722no—
736C23—1722no—
737C23—1722no—
738C23—1722no—
739C23—1722no—
740C23—1722no—
741C23C2×D4×D4312yes—
742C23C2×D4×D4311yescharacteristic
743Q8—22no—
744Q8—24no—
745Q8—1728no—
746Q8C2×#1062189814yescomplemented
747D4—22no—
748D4—22no—
749D4—48no—
750D4—42no—
751D4—868no—
752D4—862no—
753D4—862no—
754D4—862no—
755D4—862no—
756D4—3444no—
757D4—3444no—
758D4—3444no—
759D4—1728no—
760D4—1728no—
761D4—1728no—
762D4—1728no—
763D4—1722no—
764D4—1722no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—48no—
774C2×C4—48no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—434no—
778C2×C4—432no—
779C2×C4—432no—
780C2×C4—432no—
781C2×C4—862no—
782C2×C4—862no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—864no—
786C2×C4—862no—
787C2×C4—862no—
788C2×C4—1728no—
789C2×C4—1728no—
790C2×C4—1728no—
791C2×C4—1722no—
792C2×C4—1722no—
793C2×C4C2×D4×D4312yes—
794C2×C4C2×D4×D4311yescharacteristic
795C2×C4C2×#1062189812yes—
796C2×C4#1306337012yes—
797C2×C4C24×D4311yescharacteristic
798C8—22no—
799C8—22no—
800C8—862no—
801C8—862no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—44no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—84no—
810C22—862no—
811C22—862no—
812C22—862no—
813C22—3444no—
814C22—3444no—
815C22—1722no—
816C22—1722no—
817C22—1722no—
818C22—1722no—
819C22—1722no—
820C22—1722no—
821C22—1724no—
822C22#1458353912yes—
823C22AGL(1,ℤ/8)×D4312yes—
824C22#1458370812yes—
825C22C22×D4×D4311yescharacteristic
826C4—22no—
827C4—24no—
828C4—42no—
829C4—42no—
830C4—434no—
831C4—862no—
832C4—862no—
833C4—1722no—
834C4—1722no—
835C4#1458353912yes—
836C4C22×#1062189811yescharacteristic
837C4C2×#1306337011yescharacteristic
838C2—42no—
839C2—82no—
840C2—3442no—
841C2—3442no—
842C2—1722no—
843C2#1914691814yesdirect product factor
844C2C2×#1458353911yescharacteristic
845C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
846C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
hypercenterC2×#417D43
hypocenterC43C2×#3332
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#14583568C2semidirect
2. C2×#14583550C2semidirect
3. #19146918C2direct (N × H)
4. C2×#14583244C2semidirect
5. C2×#14583217C2semidirect
6. C2×#14583216C2semidirect
7. C2×#14583182C2semidirect
8. C2×#14583152C2semidirect
9. C2×#14583151C2semidirect
10. C2×#14583093C2semidirect
11. C2×#14583047C2semidirect
12. C2×#14583044C2semidirect
13. C2×#14582984C2semidirect
14. C2×#14582975C2semidirect
15. C2×#14582899C2semidirect
16. C2×C43×#417C2semidirect
24. #14583568C22semidirect
26. #14583550C22semidirect
44. #14583244C22semidirect
45. #14583217C22semidirect
46. #14583216C22semidirect
47. #14583182C22semidirect
48. #14583152C22semidirect
49. #14583151C22semidirect
50. #14583093C22semidirect
51. #14583047C22semidirect
52. #14583044C22semidirect
53. #14582984C22semidirect
54. #14582975C22semidirect
59. #14582899C22semidirect
72. C43×#417C22semidirect
196. C2×Q8×C43#41semidirect
321. Q8×C43C2×#41semidirect
430. C2×#417D43semidirect
433. C2×C43#3332semidirect
486. #417C2×D43semidirect
500. C43C2×#3332semidirect
626. C2×Q8#10621898semidirect
746. Q8C2×#10621898semidirect
843. C2#19146918direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835682
C2×#145835502
#191469182
C2×#145832442
C2×#145832172
C2×#145832162
C2×#145831822
C2×#145831522
C2×#145831512
C2×#145830932
C2×#145830472
C2×#145830442
C2×#145829842
C2×#145829752
C2×#145828992
C2×C43×#4172
C2×#333243