Finite Group Databasebeta

← C2×#19147610 #25977548

Subgroups — C2×#19147610 #25977548

Order 11008.

2250 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×#14583621C211yesmaximal, characteristic, complemented
2C2×#14583569C211yesmaximal, characteristic, complemented
3#19147610C2116yesmaximal, direct product factor
4C2×#14583286C211yesmaximal, characteristic, complemented
5C2×#14583285C211yesmaximal, characteristic, complemented
6C2×#14583270C211yesmaximal, characteristic, complemented
7C2×#14583098C211yesmaximal, characteristic, complemented
8C2×#14583116C211yesmaximal, characteristic, complemented
9C2×#14583115C211yesmaximal, characteristic, complemented
10C2×#14583102C211yesmaximal, characteristic, complemented
11C2×#14583093C211yesmaximal, characteristic, complemented
12C2×#14583028C211yesmaximal, characteristic, complemented
13C2×#14582997C211yesmaximal, characteristic, complemented
14C2×#14582996C211yesmaximal, characteristic, complemented
15C2×#14582979C211yesmaximal, characteristic, complemented
16C2×C43×#460C211yesmaximal, characteristic, complemented
17C22×#10621900—21no—
18C22×#10621873C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22C22×D344C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621882C2211yescharacteristic
25#14583621—24no—
26#14583621C2218yescomplemented
27#14583569—24no—
28#14583569C2218yescomplemented
29C2×#13063323C2211yescharacteristic
30C2×#13063321C2211yescharacteristic
31C2×#13063321C2211yescharacteristic
32C2×#13063320—21no—
33C2×#13063319—21no—
34C2×#13063314C2211yescharacteristic
35C2×#13063313C2211yescharacteristic
36C2×#13063303—21no—
37C2×#13063297—21no—
38C2×#13063297—21no—
39C2×#13063296—21no—
40C2×C4×Dic86C2211yescharacteristic
41C2×#13063290C2211yescharacteristic
42C2×C4×D172C2211yescharacteristic
43C2×D4×Dic43C2211yescharacteristic
44C2×D4×Dic43C2211yescharacteristic
45C2×#13063287C2211yescharacteristic
46C2×#13063282—21no—
47#14583286C2218yescomplemented
48#14583285C2218yescomplemented
49#14583270C2218yescomplemented
50#14583116C2218yescomplemented
51#14583115C2218yescomplemented
52#14583102C2218yescomplemented
53#14583098C2218yescomplemented
54#14583093C2218yescomplemented
55#14583028C2218yescomplemented
56#14582997C2218yescomplemented
57#14582996C2218yescomplemented
58#14582979C2218yescomplemented
59C2×#13063258C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×#13063236C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C2×#127×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C43×#460C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621900—28no—
78C2×#10621900—48no—
79C22×Dic86D411yescharacteristic
80C22×Dic86C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×D172C2311yescharacteristic
83C22×C22⋊D43—21no—
84C22×C22⋊D43—21no—
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C23×Dic43—21no—
88C23×Dic43—21no—
89C22×C4×D43—21no—
90C22×C4×D43—21no—
91C2×#10621873—42no—
92C2×#10621873C2314yes—
93C2×#10621883—24no—
94C2×#10621883—42no—
95C2×#10621883C2314yes—
96C2×#10621883C2314yes—
97C2×#10621884—24no—
98C2×#10621884C2314yes—
99C2×D344—42no—
100C2×D344C2314yes—
101C2×#10621882—24no—
102C2×#10621882—42no—
103C2×#10621882C2314yes—
104C2×#10621882C2314yes—
105C22×C43⋊C8C2311yescharacteristic
106C22×C43⋊C8C2311yescharacteristic
107#13063323—22no—
108#13063323C2314yes—
109#13063321—22no—
110#13063321—22no—
111#13063321C2314yes—
112#13063321C2314yes—
113#13063320—28no—
114#13063319—28no—
115#13063314—22no—
116#13063314C2314yes—
117#13063313—22no—
118#13063313C2314yes—
119#13063303—28no—
120#13063297—28no—
121#13063297—28no—
122#13063296—28no—
123C4×Dic86D414yes—
124C4×Dic86C2314yes—
125#13063290—22no—
126#13063290C2314yes—
127C4×D172—22no—
128C4×D172C2314yes—
129D4×Dic43—22no—
130D4×Dic43—22no—
131D4×Dic43C2314yes—
132D4×Dic43C2314yes—
133#13063287—22no—
134#13063287C2314yes—
135#13063282—28no—
136C2×C4⋊Dic43D411yescharacteristic
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4D411yescharacteristic
142C2×Dic43⋊C4D411yescharacteristic
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—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×C4×Dic43—21no—
152C2×C4×Dic43C2311yescharacteristic
153C2×C4×Dic43C2311yescharacteristic
154#13063258C2314yes—
155Dic43⋊C8C2314yes—
156Dic43⋊C8C2314yes—
157#13063250C2314yes—
158#13063249C2314yes—
159#13063247C2314yes—
160#13063245C2314yes—
161#13063236C2314yes—
162#13063235C2314yes—
163C8×Dic43C2314yes—
164C22×Q8×C43C2311yescharacteristic
165C22×D4×C43—21no—
166C22×D4×C43—21no—
167C22×D4×C43C2311yescharacteristic
168C22×D4×C43C2311yescharacteristic
169C2×SD16×C43—42no—
170C2×SD16×C43—42no—
171C2×SD16×C43C2314yes—
172C2×SD16×C43C2314yes—
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2311yescharacteristic
175#127×C43—22no—
176#127×C43C2314yes—
177C4×Q8×C43—22no—
178C4×Q8×C43C2314yes—
179C2×C4⋊C4×C43—21no—
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C42×C43—21no—
182C2×C42×C43C2311yescharacteristic
183C4⋊C8×C43C2314yes—
184#102×C43C2314yes—
185#102×C43C2314yes—
186C24×C43—21no—
187C24×C43—21no—
188C23×D43—21no—
189C23×D43—21no—
190C2×Q8×C43—21no—
191C2×Q8×C43—22no—
192C2×Q8×C43—22no—
193C2×Q8×C43C2412yes—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—24no—
197C2×D4×C43—24no—
198C2×D4×C43—22no—
199C2×D4×C43—22no—
200C2×D4×C43—22no—
201C2×D4×C43—22no—
202C2×D4×C43—44no—
203C2×D4×C43—82no—
204C2×D4×C43C2412yes—
205C2×D4×C43C2412yes—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2411yescharacteristic
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—24no—
214C2×C22⋊D43—24no—
215C2×C22⋊D43—44no—
216C2×C22⋊D43—44no—
217C2×C22⋊D43—82no—
218C2×C22⋊D43—82no—
219C22×Dic43—24no—
220C22×Dic43—24no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—44no—
224C22×Dic43—44no—
225C22×Dic43C2×D411yescharacteristic
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229#10621900—432no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—22no—
233C2×D172—22no—
234C2×D172—22no—
235C2×D172—22no—
236C2×D172C2412yes—
237C2×D172C2412yes—
238C2×C4×D43—24no—
239C2×C4×D43—24no—
240C2×C4×D43—44no—
241C2×C4×D43—44no—
242C2×Dic86—24no—
243C2×Dic86—22no—
244C2×Dic86—22no—
245C2×Dic86—21no—
246C2×Dic86C2×D414yes—
247C2×Dic86C2412yes—
248SD16×C43—44no—
249SD16×C43—44no—
250C2×C8×C43—22no—
251C2×C8×C43—22no—
252C2×C8×C43C2412yes—
253C2×C8×C43C2412yes—
254C4⋊C4×C43—24no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43C2412yes—
257C42×C43—24no—
258C42×C43C2×D412yes—
259C42×C43C2412yes—
260C22⋊Dic43—24no—
261C22⋊Dic43—24no—
262#10621884—28no—
263#10621883—28no—
264#10621883—44no—
265#10621882—28no—
266#10621882—44no—
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)⋊C4—24no—
273C4⋊Dic43—21no—
274C4⋊Dic43C2×D414yes—
275C4⋊Dic43C2412yes—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4C2×D414yes—
280Dic43⋊C4C2×D414yes—
281C4×Dic43—24no—
282C4×Dic43C2×D412yes—
283C4×Dic43C2×D412yes—
284C4×Dic43C2412yes—
285C4×Dic43C2412yes—
286C2×C43⋊C8—22no—
287C2×C43⋊C8#4114yescomplemented
288C2×C43⋊C8C2412yes—
289C2×C43⋊C8C2412yes—
290D344—44no—
291#10621873—44no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—42no—
295C23×C43—42no—
296C23×C43—42no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43C22×D411yescharacteristic
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—42no—
304C22×D43—42no—
305C22×D43—42no—
306C22×D43—42no—
307C22×D43—42no—
308C22×D43—42no—
309Q8×C43—22no—
310Q8×C43—22no—
311Q8×C43—42no—
312D4×C43—22no—
313D4×C43—22no—
314D4×C43—22no—
315D4×C43—22no—
316D4×C43—48no—
317D4×C43—42no—
318D4×C43—42no—
319D4×C43—84no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—42no—
325C2×C4×C43—42no—
326C2×C4×C43C22×D412yes—
327C2×C4×C43C22×D412yes—
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C2×#4112yes—
330C2×C4×C43H(5,𝔽2)12yes—
331C2×C4×C43C2511yescharacteristic
332C22⋊D43—48no—
333C22⋊D43—48no—
334C22⋊D43—84no—
335C22⋊D43—84no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—48no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—48no—
345C2×Dic43AGL(1,ℤ/8)14yes—
346C2×Dic43C22×D412yes—
347C2×Dic43C22×D412yes—
348C2×Dic43C22×D412yes—
349C2×Dic43C22×D412yes—
350D172—22no—
351D172—22no—
352D172—22no—
353D172—22no—
354D172—42no—
355D172—42no—
356C4×D43—48no—
357C4×D43—48no—
358Dic86—28no—
359Dic86—22no—
360Dic86—22no—
361Dic86—42no—
362C8×C43—22no—
363C8×C43—22no—
364C43⋊C8—22no—
365C43⋊C8C2×#4114yescomplemented
366C2×#3397—431nomaximal, Sylow
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—84no—
374C22×C43—84no—
375C22×C43#55012yes—
376C22×C43C2×AGL(1,ℤ/8)12yes—
377C22×C43#57712yes—
378C22×C43C23×D411yescharacteristic
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—84no—
386C2×D43—84no—
387C4×C43—22no—
388C4×C43—22no—
389C4×C43—42no—
390C4×C43—42no—
391C4×C43#55012yes—
392C4×C43C22×#4111yescharacteristic
393C4×C43C2×H(5,𝔽2)11yescharacteristic
394Dic43—22no—
395Dic43—22no—
396Dic43—22no—
397Dic43—42no—
398Dic43—42no—
399Dic43C2×AGL(1,ℤ/8)14yes—
400C2×#556—431no—
401C2×#550—431no—
402#3397—4316no—
403C2×#496—431no—
404C2×#496—431no—
405C2×#492—431no—
406C2×#460—431no—
407C2×#460D4311yescharacteristic, complemented
408C2×#463—431no—
409C2×#463—431no—
410C2×#461—431no—
411C2×#459—431no—
412C2×#446—431no—
413C2×#440—431no—
414C2×#440—431no—
415C2×C4×D8—431no—
416C2×C43—82no—
417C2×C43—82no—
418C2×C43#339714yescomplemented
419C2×C43C2×#55011yescharacteristic
420C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
421C2×C43C2×#57711yescharacteristic
422D43—82no—
423D43—82no—
424C22×#41—861no—
425C22×SD16—431no—
426C22×SD16—431no—
427C22×SD16—431no—
428C22×SD16—431no—
429C22×SD16C2×D4311yescharacteristic
430C22×SD16C2×D4311yescharacteristic
431C22×D8—431no—
432C22×D8—431no—
433C22×D8—431no—
434#556—438no—
435#556—864no—
436#550—438no—
437#550—864no—
438C2×C4⋊Q8—431no—
439C2×#127—431no—
440C2×#127—431no—
441C2×#127C2×D4311yescharacteristic
442C2×#126—861no—
443C2×#126—861no—
444C2×#124—431no—
445C2×#124—431no—
446C2×C22⋊Q8—861no—
447C2×#121—861no—
448C2×#121—861no—
449C2×#121—861no—
450C2×C4×Q8—431no—
451C2×C4×Q8—431no—
452C2×C4×Q8C2×D4311yescharacteristic
453C2×C4×D4—431no—
454C2×C4×D4—431no—
455C2×C4×D4—431no—
456C2×C4×D4—431no—
457C2×#117—861no—
458#496—438no—
459#496—438no—
460#492—438no—
461#463—438no—
462#463—438no—
463#461—438no—
464#460—438no—
465#460C2×D4318yescomplemented
466#459—438no—
467#446—438no—
468#440—438no—
469#440—438no—
470C4×D8—438no—
471C2×#107—431no—
472C2×C4⋊C8—431no—
473C2×C4⋊C8—431no—
474C2×C4⋊C8C2×D4311yescharacteristic
475C2×#103—431no—
476C2×#103—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×#102C2×D4311yescharacteristic
480C2×#102C2×D4311yescharacteristic
481C2×#97—431no—
482C2×#97—431no—
483C2×C4×C8—431no—
484C43C2×#339711yescharacteristic, complemented, Sylow
485C2×#41—868no—
486C2×#41—1728no—
487C22×Q8—431no—
488C22×Q8—431no—
489C22×Q8C22×D4311yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—431no—
493C22×D4—431no—
494C22×D4—861no—
495C22×D4—861no—
496C22×D4—861no—
497C22×D4—861no—
498C22×D4C22×D4311yescharacteristic
499C22×D4C22×D4311yescharacteristic
500C23×C4—861no—
501C23×C4—861no—
502C23×C4—861no—
503C23×C4—861no—
504C2×SD16—42no—
505C2×SD16—42no—
506C2×SD16—434no—
507C2×SD16—434no—
508C2×SD16—434no—
509C2×SD16—434no—
510C2×SD16—864no—
511C2×SD16—864no—
512C2×SD16—1722no—
513C2×SD16—1722no—
514C2×SD16C22×D4314yes—
515C2×SD16C22×D4314yes—
516C2×D8—434no—
517C2×D8—434no—
518C2×D8—434no—
519C2×D8—864no—
520C2×D8—1722no—
521C2×D8—1722no—
522C22×C8—431no—
523C22×C8—431no—
524C22×C8C22×D4311yescharacteristic
525C22×C8C22×D4311yescharacteristic
526C4⋊Q8—434no—
527C4⋊Q8—862no—
528#127—22no—
529#127—434no—
530#127—434no—
531#127—862no—
532#127—862no—
533#127C22×D4314yes—
534#126—868no—
535#126—868no—
536#124—434no—
537#124—434no—
538#124—862no—
539#124—862no—
540C22⋊Q8—868no—
541#121—868no—
542#121—868no—
543#121—868no—
544C4×Q8—22no—
545C4×Q8—434no—
546C4×Q8—434no—
547C4×Q8—434no—
548C4×Q8—862no—
549C4×Q8C22×D4314yes—
550C4×D4—434no—
551C4×D4—434no—
552C4×D4—434no—
553C4×D4—434no—
554C4×D4—862no—
555C4×D4—862no—
556C4×D4—862no—
557C4×D4—862no—
558#117—868no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4C22×D4311yescharacteristic
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—861no—
576C2×C42—21no—
577C2×C42—431no—
578C2×C42—431no—
579C2×C42—861no—
580C2×C42C22×D4311yescharacteristic
581#107—434no—
582C4⋊C8—434no—
583C4⋊C8—434no—
584C4⋊C8C22×D4314yes—
585#103—434no—
586#103—434no—
587#102—434no—
588#102—434no—
589#102C22×D4314yes—
590#102C22×D4314yes—
591#97—434no—
592#97—434no—
593C4×C8—434no—
594C24—21no—
595C24—21no—
596C24—861no—
597C24—861no—
598#41—17232no—
599C2×Q8—21no—
600C2×Q8—22no—
601C2×Q8—22no—
602C2×Q8—434no—
603C2×Q8—432no—
604C2×Q8—864no—
605C2×Q8—861no—
606C2×Q8—862no—
607C2×Q8—862no—
608C2×Q8C23×D4312yes—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—82no—
619C2×D4—432no—
620C2×D4—432no—
621C2×D4—864no—
622C2×D4—864no—
623C2×D4—864no—
624C2×D4—864no—
625C2×D4—861no—
626C2×D4—861no—
627C2×D4—862no—
628C2×D4—862no—
629C2×D4—862no—
630C2×D4—862no—
631C2×D4—3442no—
632C2×D4—3442no—
633C2×D4—1724no—
634C2×D4—1724no—
635C2×D4C23×D4312yes—
636C2×D4C23×D4312yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—431no—
642C22×C4—431no—
643C22×C4—864no—
644C22×C4—864no—
645C22×C4—864no—
646C22×C4—861no—
647C22×C4—861no—
648C22×C4—864no—
649C22×C4—1724no—
650C22×C4—1724no—
651C22×C4—1724no—
652C22×C4—1724no—
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4C23×D4311yescharacteristic
656SD16—44no—
657SD16—44no—
658SD16—868no—
659SD16—868no—
660SD16—1724no—
661SD16—1724no—
662D8—868no—
663D8—1724no—
664D8—1724no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—434no—
668C2×C8—432no—
669C2×C8—432no—
670C2×C8—862no—
671C2×C8C23×D4312yes—
672C2×C8C23×D4312yes—
673C4⋊C4—24no—
674C4⋊C4—21no—
675C4⋊C4—434no—
676C4⋊C4—434no—
677C4⋊C4—434no—
678C4⋊C4—432no—
679C4⋊C4—864no—
680C4⋊C4—864no—
681C4⋊C4—864no—
682C4⋊C4—861no—
683C4⋊C4C23×D4312yes—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—864no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C42—24no—
693C42—432no—
694C42—432no—
695C42—432no—
696C42—432no—
697C42—864no—
698C42D4×D4312yes—
699C42C23×D4312yes—
700C23—22no—
701C23—22no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—862no—
709C23—862no—
710C23—1722no—
711C23—1722no—
712C23—1722no—
713C23—1722no—
714C23—1722no—
715C23—1722no—
716C23C2×D4×D4311yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—42no—
720Q8—868no—
721Q8—862no—
722Q8—862no—
723Q8—1722no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—48no—
729D4—42no—
730D4—42no—
731D4—84no—
732D4—862no—
733D4—862no—
734D4—862no—
735D4—862no—
736D4—3444no—
737D4—3444no—
738D4—1728no—
739D4—1728no—
740D4—1722no—
741D4—1722no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—434no—
749C2×C4—432no—
750C2×C4—432no—
751C2×C4—432no—
752C2×C4—432no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—1728no—
759C2×C4—1728no—
760C2×C4—1728no—
761C2×C4—1728no—
762C2×C4—1722no—
763C2×C4—1722no—
764C2×C4C2×D4×D4312yes—
765C2×C4C2×D4×D4312yes—
766C2×C4C2×D4×D4311yescharacteristic
767C2×C4#41×D4312yes—
768C2×C4#1306337012yes—
769C2×C4C24×D4311yescharacteristic
770C8—22no—
771C8—22no—
772C8—434no—
773C8—862no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—84no—
782C22—3444no—
783C22—3444no—
784C22—1722no—
785C22—1722no—
786C22—1722no—
787C22—1722no—
788C22—1722no—
789C22—1722no—
790C22#1458356712yes—
791C22AGL(1,ℤ/8)×D4312yes—
792C22#1458370512yes—
793C22C22×D4×D4311yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—434no—
799C4—862no—
800C4—862no—
801C4—862no—
802C4—1722no—
803C4—1722no—
804C4#1458356712yes—
805C4C2×#41×D4311yescharacteristic
806C4C2×#1306337011yescharacteristic
807C2—82no—
808C2—82no—
809C2—3442no—
810C2—3442no—
811C2#1914761014yesdirect product factor
812C2C2×#1458356711yescharacteristic
813C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
814C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#460C2
socleC23×C43C22×D4
hypercenterC2×#460D43
hypocenterC43C2×#3397
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#14583621C2semidirect
2. C2×#14583569C2semidirect
3. #19147610C2direct (N × H)
4. C2×#14583286C2semidirect
5. C2×#14583285C2semidirect
6. C2×#14583270C2semidirect
7. C2×#14583098C2semidirect
8. C2×#14583116C2semidirect
9. C2×#14583115C2semidirect
10. C2×#14583102C2semidirect
11. C2×#14583093C2semidirect
12. C2×#14583028C2semidirect
13. C2×#14582997C2semidirect
14. C2×#14582996C2semidirect
15. C2×#14582979C2semidirect
16. C2×C43×#460C2semidirect
26. #14583621C22semidirect
28. #14583569C22semidirect
47. #14583286C22semidirect
48. #14583285C22semidirect
49. #14583270C22semidirect
50. #14583116C22semidirect
51. #14583115C22semidirect
52. #14583102C22semidirect
53. #14583098C22semidirect
54. #14583093C22semidirect
55. #14583028C22semidirect
56. #14582997C22semidirect
57. #14582996C22semidirect
58. #14582979C22semidirect
73. C43×#460C22semidirect
287. C2×C43⋊C8#41semidirect
365. C43⋊C8C2×#41semidirect
407. C2×#460D43semidirect
418. C2×C43#3397semidirect
465. #460C2×D43semidirect
484. C43C2×#3397semidirect
811. C2#19147610direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836212
C2×#145835692
#191476102
C2×#145832862
C2×#145832852
C2×#145832702
C2×#145830982
C2×#145831162
C2×#145831152
C2×#145831022
C2×#145830932
C2×#145830282
C2×#145829972
C2×#145829962
C2×#145829792
C2×C43×#4602
C2×#339743