Finite Group Databasebeta

← C2×#19147638 #25977578

Subgroups — C2×#19147638 #25977578

Order 11008.

2314 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583632C211yesmaximal, characteristic, complemented
2C2×#14583570C211yesmaximal, characteristic, complemented
3#19147638C2116yesmaximal, direct product factor
4C2×#14583288C211yesmaximal, characteristic, complemented
5C2×#14583287C211yesmaximal, characteristic, complemented
6C2×#14583274C211yesmaximal, characteristic, complemented
7C2×#14583098C211yesmaximal, characteristic, complemented
8C2×#14583114C211yesmaximal, characteristic, complemented
9C2×#14583113C211yesmaximal, characteristic, complemented
10C2×#14583094C211yesmaximal, characteristic, complemented
11C2×#14583093C211yesmaximal, characteristic, complemented
12C2×#14583093C211yesmaximal, characteristic, complemented
13C2×#14583027C211yesmaximal, characteristic, complemented
14C2×#14583010C211yesmaximal, characteristic, complemented
15C2×#14582986C211yesmaximal, characteristic, complemented
16C2×C43×#442C211yesmaximal, characteristic, complemented
17C22×#10621898—21no—
18C22×#10621873C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×D344C2211yescharacteristic
22C22×D344C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621882C2211yescharacteristic
25C22×#10621882C2211yescharacteristic
26#14583632—24no—
27#14583632C2218yescomplemented
28#14583570—24no—
29#14583570C2218yescomplemented
30C2×#13063322C2211yescharacteristic
31C2×#13063321C2211yescharacteristic
32C2×#13063321C2211yescharacteristic
33C2×#13063321C2211yescharacteristic
34C2×#13063313C2211yescharacteristic
35C2×#13063312C2211yescharacteristic
36C2×#13063311—21no—
37C2×#13063308—21no—
38C2×#13063307—21no—
39C2×#13063299—21no—
40C2×#13063298—21no—
41C2×#13063298—21no—
42C2×C4×Dic86C2211yescharacteristic
43C2×#13063290C2211yescharacteristic
44C2×#13063287C2211yescharacteristic
45C2×#13063287C2211yescharacteristic
46C2×#13063287C2211yescharacteristic
47C2×C4×C22⋊D43—21no—
48#14583288C2218yescomplemented
49#14583287C2218yescomplemented
50#14583274C2218yescomplemented
51#14583114C2218yescomplemented
52#14583113C2218yescomplemented
53#14583098C2218yescomplemented
54#14583094C2218yescomplemented
55#14583093C2218yescomplemented
56#14583093C2218yescomplemented
57#14583027C2218yescomplemented
58#14583010C2218yescomplemented
59#14582986C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×D8×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C43×#442C2218yescomplemented
73C2×#106×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C2×#10621898—28no—
78C2×#10621898—48no—
79C22×Dic86D411yescharacteristic
80C22×Dic86C2311yescharacteristic
81C22×D172—21no—
82C22×D172—21no—
83C22×D172C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×D172C2311yescharacteristic
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C2×#10621873—24no—
96C2×#10621873—42no—
97C2×#10621873C2314yes—
98C2×#10621873C2314yes—
99C2×#10621883—42no—
100C2×#10621883C2314yes—
101C2×D344—24no—
102C2×D344—42no—
103C2×D344C2314yes—
104C2×D344C2314yes—
105C2×#10621882—42no—
106C2×#10621882—42no—
107C2×#10621882—42no—
108C2×#10621882C2314yes—
109C2×#10621882C2314yes—
110C2×#10621882C2314yes—
111C22×C43⋊C8C2311yescharacteristic
112C22×C43⋊C8C2311yescharacteristic
113#13063322—22no—
114#13063322C2314yes—
115#13063321—22no—
116#13063321—22no—
117#13063321—22no—
118#13063321C2314yes—
119#13063321C2314yes—
120#13063321C2314yes—
121#13063313—22no—
122#13063313C2314yes—
123#13063312—22no—
124#13063312C2314yes—
125#13063311—28no—
126#13063308—28no—
127#13063307—28no—
128#13063299—28no—
129#13063298—28no—
130#13063298—28no—
131C4×Dic86D414yes—
132C4×Dic86C2314yes—
133#13063290—22no—
134#13063290C2314yes—
135#13063287—22no—
136#13063287—22no—
137#13063287—22no—
138#13063287C2314yes—
139#13063287C2314yes—
140#13063287C2314yes—
141C4×C22⋊D43—28no—
142C2×C4⋊Dic43D411yescharacteristic
143C2×Dic43⋊C4—21no—
144C2×Dic43⋊C4D411yescharacteristic
145C2×Dic43⋊C4D411yescharacteristic
146C2×C22⋊Dic43—21no—
147C2×C22⋊Dic43—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4—21no—
152C2×(C2×D43)⋊C4—21no—
153C2×C4×Dic43—21no—
154C2×C4×Dic43C2311yescharacteristic
155C2×C4×Dic43C2311yescharacteristic
156C4⋊(C43⋊C8)C2314yes—
157Dic43⋊C8C2314yes—
158Dic43⋊C8C2314yes—
159#13063248C2314yes—
160#13063245C2314yes—
161#13063245C2314yes—
162#13063245C2314yes—
163#13063235C2314yes—
164C8×Dic43C2314yes—
165C22×D4×C43C2311yescharacteristic
166C22×D4×C43C2311yescharacteristic
167C23×C4×C43—21no—
168C23×C4×C43—21no—
169C2×D8×C43—24no—
170C2×D8×C43C2314yes—
171C22×C8×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173C4×D4×C43—22no—
174C4×D4×C43—22no—
175C4×D4×C43C2314yes—
176C4×D4×C43C2314yes—
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43—21no—
181C2×C42×C43C2311yescharacteristic
182#106×C43C2314yes—
183#102×C43C2314yes—
184#102×C43C2314yes—
185#97×C43C2314yes—
186C24×C43—21no—
187C24×C43—21no—
188C23×D43—21no—
189C23×D43—21no—
190C23×D43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—22no—
197C2×D4×C43C2412yes—
198C2×D4×C43C2412yes—
199C22×C4×C43—24no—
200C22×C4×C43—24no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—44no—
204C22×C4×C43—82no—
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2411yescharacteristic
208C2×C22⋊D43—24no—
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—24no—
214C2×C22⋊D43—44no—
215C2×C22⋊D43—44no—
216C2×C22⋊D43—44no—
217C2×C22⋊D43—82no—
218C2×C22⋊D43—82no—
219C2×C22⋊D43—82no—
220C22×Dic43—21no—
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224C22×Dic43C2×D411yescharacteristic
225#10621898—432no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172—21no—
229C2×D172—24no—
230C2×D172—24no—
231C2×D172—22no—
232C2×D172—22no—
233C2×D172—22no—
234C2×D172—22no—
235C2×D172—22no—
236C2×D172—22no—
237C2×D172—44no—
238C2×D172—82no—
239C2×D172C2412yes—
240C2×D172C2412yes—
241C2×D172C2412yes—
242C2×C4×D43—24no—
243C2×C4×D43—24no—
244C2×C4×D43—24no—
245C2×C4×D43—44no—
246C2×C4×D43—44no—
247C2×C4×D43—82no—
248C2×Dic86—24no—
249C2×Dic86—22no—
250C2×Dic86—22no—
251C2×Dic86—21no—
252C2×Dic86C2×D414yes—
253C2×Dic86C2412yes—
254D8×C43—28no—
255C2×C8×C43—22no—
256C2×C8×C43#4114yescomplemented
257C2×C8×C43C2412yes—
258C2×C8×C43C2412yes—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43C2412yes—
262C4⋊C4×C43C2412yes—
263C22⋊C4×C43—24no—
264C22⋊C4×C43—24no—
265C42×C43C2×D412yes—
266C42×C43C2412yes—
267C22⋊Dic43—24no—
268C22⋊Dic43—24no—
269#10621883—44no—
270#10621882—44no—
271#10621882—44no—
272#10621882—44no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4—24no—
278C4⋊Dic43C2×D414yes—
279Dic43⋊C4—24no—
280Dic43⋊C4C2×D414yes—
281Dic43⋊C4C2×D414yes—
282C4×Dic43—24no—
283C4×Dic43C2×D412yes—
284C4×Dic43C2×D412yes—
285C4×Dic43C2412yes—
286C4×Dic43C2412yes—
287C2×C43⋊C8—22no—
288C2×C43⋊C8—22no—
289C2×C43⋊C8C2412yes—
290C2×C43⋊C8C2412yes—
291D344—28no—
292D344—44no—
293#10621873—28no—
294#10621873—44no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43—42no—
301C23×C43—42no—
302C23×C43—42no—
303C23×C43C22×D411yescharacteristic
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—42no—
310C22×D43—42no—
311C22×D43—42no—
312C22×D43—42no—
313C22×D43—42no—
314C22×D43—42no—
315C22×D43—42no—
316D4×C43—22no—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43—42no—
321D4×C43—42no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—48no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43—84no—
330C2×C4×C43C22×D412yes—
331C2×C4×C43C22×D412yes—
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C2×#4112yes—
334C2×C4×C43H(5,𝔽2)12yes—
335C2×C4×C43C2511yescharacteristic
336C22⋊D43—48no—
337C22⋊D43—48no—
338C22⋊D43—48no—
339C22⋊D43—84no—
340C22⋊D43—84no—
341C22⋊D43—84no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—42no—
347C2×Dic43AGL(1,ℤ/8)14yes—
348C2×Dic43C22×D412yes—
349C2×Dic43C22×D412yes—
350C2×Dic43C22×D412yes—
351C2×Dic43C22×D412yes—
352D172—22no—
353D172—22no—
354D172—22no—
355D172—22no—
356D172—22no—
357D172—22no—
358D172—48no—
359D172—42no—
360D172—42no—
361D172—42no—
362D172—84no—
363C4×D43—48no—
364C4×D43—48no—
365C4×D43—84no—
366Dic86—28no—
367Dic86—22no—
368Dic86—22no—
369Dic86—42no—
370C8×C43—22no—
371C8×C43C2×#4114yescomplemented
372C43⋊C8—22no—
373C43⋊C8—22no—
374C2×#3399—431nomaximal, Sylow
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—42no—
380C22×C43—42no—
381C22×C43—84no—
382C22×C43—84no—
383C22×C43#55012yes—
384C22×C43C2×AGL(1,ℤ/8)12yes—
385C22×C43#57612yes—
386C22×C43C23×D411yescharacteristic
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—84no—
397C2×D43—84no—
398C2×D43—84no—
399C4×C43—22no—
400C4×C43—22no—
401C4×C43—42no—
402C4×C43—42no—
403C4×C43#55012yes—
404C4×C43C22×#4111yescharacteristic
405C4×C43C2×H(5,𝔽2)11yescharacteristic
406Dic43—22no—
407Dic43—22no—
408Dic43—22no—
409Dic43—42no—
410Dic43C2×AGL(1,ℤ/8)14yes—
411C2×#559—431no—
412C2×#550—431no—
413#3399—4316no—
414C2×#496—431no—
415C2×#496—431no—
416C2×#493—431no—
417C2×#460—431no—
418C2×#463—431no—
419C2×#463—431no—
420C2×#459—431no—
421C2×#459—431no—
422C2×#459—431no—
423C2×#446—431no—
424C2×#442—431no—
425C2×#442D4311yescharacteristic, complemented
426C2×C4×SD16—431no—
427C2×C43—82no—
428C2×C43—82no—
429C2×C43#339914yescomplemented
430C2×C43C2×#55011yescharacteristic
431C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
432C2×C43C2×#57611yescharacteristic
433D43—82no—
434D43—82no—
435D43—82no—
436C22×#41—861no—
437C22×SD16—431no—
438C22×SD16—431no—
439C22×SD16—431no—
440C22×D8—431no—
441C22×D8—431no—
442C22×D8—431no—
443C22×D8—431no—
444C22×D8—431no—
445C22×D8C2×D4311yescharacteristic
446#559—438no—
447#559—864no—
448#550—438no—
449#550—864no—
450C2×#127—431no—
451C2×#127—431no—
452C2×#127—431no—
453C2×#127—431no—
454C2×#124—431no—
455C2×#124—431no—
456C2×#124—861no—
457C2×#123—861no—
458C2×#123—861no—
459C2×#121—861no—
460C2×#121—861no—
461C2×#121—861no—
462C2×C4×Q8—431no—
463C2×C4×Q8—431no—
464C2×C4×D4—431no—
465C2×C4×D4—431no—
466C2×C4×D4—431no—
467C2×C4×D4—861no—
468C2×C4×D4C2×D4311yescharacteristic
469C2×C4×D4C2×D4311yescharacteristic
470#496—438no—
471#496—438no—
472#493—438no—
473#463—438no—
474#463—438no—
475#460—438no—
476#459—438no—
477#459—438no—
478#459—438no—
479#446—438no—
480#442—438no—
481#442C2×D4318yescomplemented
482C4×SD16—438no—
483C2×#106C2×D4311yescharacteristic
484C2×C4⋊C8—431no—
485C2×C4⋊C8—431no—
486C2×C4⋊C8—431no—
487C2×#103—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102C2×D4311yescharacteristic
492C2×#102C2×D4311yescharacteristic
493C2×#97—431no—
494C2×#97C2×D4311yescharacteristic
495C2×C4×C8—431no—
496C43C2×#339911yescharacteristic, complemented, Sylow
497C2×#41—868no—
498C2×#41—1728no—
499C22×Q8—431no—
500C22×Q8—431no—
501C22×D4—431no—
502C22×D4—431no—
503C22×D4—431no—
504C22×D4—861no—
505C22×D4—861no—
506C22×D4—861no—
507C22×D4—861no—
508C22×D4—861no—
509C22×D4—861no—
510C22×D4—861no—
511C22×D4—861no—
512C22×D4C22×D4311yescharacteristic
513C22×D4C22×D4311yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—861no—
517C23×C4—861no—
518C23×C4—861no—
519C2×SD16—434no—
520C2×SD16—434no—
521C2×SD16—434no—
522C2×SD16—864no—
523C2×SD16—1722no—
524C2×SD16—1722no—
525C2×D8—24no—
526C2×D8—434no—
527C2×D8—434no—
528C2×D8—434no—
529C2×D8—434no—
530C2×D8—434no—
531C2×D8—864no—
532C2×D8—1722no—
533C2×D8—1722no—
534C2×D8—1722no—
535C2×D8—1722no—
536C2×D8C22×D4314yes—
537C22×C8—431no—
538C22×C8—431no—
539C22×C8C22×D4311yescharacteristic
540C22×C8C22×D4311yescharacteristic
541#127—434no—
542#127—434no—
543#127—434no—
544#127—434no—
545#127—862no—
546#127—862no—
547#127—862no—
548#127—862no—
549#124—434no—
550#124—434no—
551#124—862no—
552#124—868no—
553#124—862no—
554#123—868no—
555#123—868no—
556#121—868no—
557#121—868no—
558#121—868no—
559C4×Q8—434no—
560C4×Q8—434no—
561C4×Q8—434no—
562C4×Q8—862no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—434no—
566C4×D4—434no—
567C4×D4—434no—
568C4×D4—862no—
569C4×D4—862no—
570C4×D4—862no—
571C4×D4—868no—
572C4×D4C22×D4314yes—
573C4×D4C22×D4314yes—
574C2×C4⋊C4—431no—
575C2×C4⋊C4—431no—
576C2×C4⋊C4—431no—
577C2×C4⋊C4—861no—
578C2×C4⋊C4C22×D4311yescharacteristic
579C2×C4⋊C4C22×D4311yescharacteristic
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—861no—
583C2×C22⋊C4—861no—
584C2×C22⋊C4—861no—
585C2×C22⋊C4—861no—
586C2×C22⋊C4—861no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C42—431no—
590C2×C42—431no—
591C2×C42—861no—
592C2×C42C22×D4311yescharacteristic
593#106C22×D4314yes—
594C4⋊C8—434no—
595C4⋊C8—434no—
596C4⋊C8—434no—
597#103—434no—
598#102—434no—
599#102—434no—
600#102—434no—
601#102C22×D4314yes—
602#102C22×D4314yes—
603#97—434no—
604#97C22×D4314yes—
605C4×C8—434no—
606C24—21no—
607C24—21no—
608C24—861no—
609C24—861no—
610C24—861no—
611#41—17232no—
612C2×Q8—434no—
613C2×Q8—432no—
614C2×Q8—864no—
615C2×Q8—861no—
616C2×Q8—862no—
617C2×Q8—862no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—432no—
625C2×D4—432no—
626C2×D4—432no—
627C2×D4—864no—
628C2×D4—864no—
629C2×D4—864no—
630C2×D4—864no—
631C2×D4—864no—
632C2×D4—864no—
633C2×D4—864no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—864no—
638C2×D4—862no—
639C2×D4—862no—
640C2×D4—862no—
641C2×D4—862no—
642C2×D4—862no—
643C2×D4—862no—
644C2×D4—3442no—
645C2×D4—3442no—
646C2×D4—3442no—
647C2×D4—3442no—
648C2×D4—1724no—
649C2×D4—1724no—
650C2×D4—1724no—
651C2×D4—1724no—
652C2×D4C23×D4312yes—
653C2×D4C23×D4312yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—44no—
659C22×C4—82no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—864no—
665C22×C4—864no—
666C22×C4—864no—
667C22×C4—861no—
668C22×C4—3442no—
669C22×C4—1724no—
670C22×C4—1724no—
671C22×C4D4×D4311yescharacteristic
672C22×C4D4×D4311yescharacteristic
673C22×C4C23×D4311yescharacteristic
674SD16—868no—
675SD16—1724no—
676SD16—1724no—
677D8—28no—
678D8—868no—
679D8—1724no—
680D8—1724no—
681D8—1724no—
682D8—1724no—
683C2×C8—22no—
684C2×C8—432no—
685C2×C8—432no—
686C2×C8—862no—
687C2×C8—862no—
688C2×C8#1062189814yescomplemented
689C2×C8C23×D4312yes—
690C2×C8C23×D4312yes—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—434no—
694C4⋊C4—434no—
695C4⋊C4—434no—
696C4⋊C4—864no—
697C4⋊C4C23×D4312yes—
698C4⋊C4C23×D4312yes—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—864no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—864no—
707C22⋊C4—864no—
708C42—432no—
709C42—432no—
710C42—432no—
711C42—432no—
712C42—864no—
713C42D4×D4312yes—
714C42C23×D4312yes—
715C23—22no—
716C23—22no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—862no—
724C23—862no—
725C23—862no—
726C23—1722no—
727C23—1722no—
728C23—1722no—
729C23—1722no—
730C23—1722no—
731C23—1722no—
732C23—1722no—
733C23—1722no—
734C23—1722no—
735C23C2×D4×D4311yescharacteristic
736Q8—868no—
737Q8—862no—
738Q8—862no—
739Q8—1722no—
740D4—22no—
741D4—22no—
742D4—22no—
743D4—22no—
744D4—42no—
745D4—42no—
746D4—862no—
747D4—862no—
748D4—862no—
749D4—862no—
750D4—862no—
751D4—862no—
752D4—3444no—
753D4—3444no—
754D4—3444no—
755D4—3444no—
756D4—1728no—
757D4—1728no—
758D4—1728no—
759D4—1728no—
760D4—1722no—
761D4—1722no—
762D4—1722no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—48no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—84no—
771C2×C4—434no—
772C2×C4—432no—
773C2×C4—432no—
774C2×C4—432no—
775C2×C4—432no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—3444no—
781C2×C4—1728no—
782C2×C4—1728no—
783C2×C4—1722no—
784C2×C4C2×D4×D4312yes—
785C2×C4C2×D4×D4312yes—
786C2×C4C2×D4×D4311yescharacteristic
787C2×C4C2×#1062189812yes—
788C2×C4#1306337112yes—
789C2×C4C24×D4311yescharacteristic
790C8—22no—
791C8—862no—
792C8—862no—
793C8C2×#1062189814yescomplemented
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—84no—
802C22—3444no—
803C22—3444no—
804C22—3444no—
805C22—1722no—
806C22—1722no—
807C22—1722no—
808C22—1722no—
809C22—1722no—
810C22—1722no—
811C22—1722no—
812C22—1722no—
813C22—1722no—
814C22#1458357012yes—
815C22AGL(1,ℤ/8)×D4312yes—
816C22#1458370312yes—
817C22C22×D4×D4311yescharacteristic
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—434no—
823C4—862no—
824C4—862no—
825C4—862no—
826C4—1722no—
827C4#1458357012yes—
828C4C22×#1062189811yescharacteristic
829C4C2×#1306337111yescharacteristic
830C2—82no—
831C2—82no—
832C2—3442no—
833C2—3442no—
834C2—3442no—
835C2#1914763814yesdirect product factor
836C2C2×#1458357011yescharacteristic
837C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
838C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#442C2
socleC23×C43C22×D4
hypercenterC2×#442D43
hypocenterC43C2×#3399
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#14583632C2semidirect
2. C2×#14583570C2semidirect
3. #19147638C2direct (N × H)
4. C2×#14583288C2semidirect
5. C2×#14583287C2semidirect
6. C2×#14583274C2semidirect
7. C2×#14583098C2semidirect
8. C2×#14583114C2semidirect
9. C2×#14583113C2semidirect
10. C2×#14583094C2semidirect
11. C2×#14583093C2semidirect
12. C2×#14583093C2semidirect
13. C2×#14583027C2semidirect
14. C2×#14583010C2semidirect
15. C2×#14582986C2semidirect
16. C2×C43×#442C2semidirect
27. #14583632C22semidirect
29. #14583570C22semidirect
48. #14583288C22semidirect
49. #14583287C22semidirect
50. #14583274C22semidirect
51. #14583114C22semidirect
52. #14583113C22semidirect
53. #14583098C22semidirect
54. #14583094C22semidirect
55. #14583093C22semidirect
56. #14583093C22semidirect
57. #14583027C22semidirect
58. #14583010C22semidirect
59. #14582986C22semidirect
72. C43×#442C22semidirect
256. C2×C8×C43#41semidirect
371. C8×C43C2×#41semidirect
425. C2×#442D43semidirect
429. C2×C43#3399semidirect
481. #442C2×D43semidirect
496. C43C2×#3399semidirect
688. C2×C8#10621898semidirect
793. C8C2×#10621898semidirect
835. C2#19147638direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836322
C2×#145835702
#191476382
C2×#145832882
C2×#145832872
C2×#145832742
C2×#145830982
C2×#145831142
C2×#145831132
C2×#145830942
C2×#145830932
C2×#145830272
C2×#145830102
C2×#145829862
C2×C43×#4422
C2×#339943