Finite Group Databasebeta

← C2×#19145654 #25967966

Subgroups — C2×#19145654 #25967966

Order 11008.

2150 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583502C211yesmaximal, characteristic, complemented
2C2×#14583470C211yesmaximal, characteristic, complemented
3#19145654C2116yesmaximal, direct product factor
4C2×#14583287C211yesmaximal, characteristic, complemented
5C2×#14583270C211yesmaximal, characteristic, complemented
6C2×#14583266C211yesmaximal, characteristic, complemented
7C2×#14583252C211yesmaximal, characteristic, complemented
8C2×#14583113C211yesmaximal, characteristic, complemented
9C2×#14583112C211yesmaximal, characteristic, complemented
10C2×#14583103C211yesmaximal, characteristic, complemented
11C2×#14583102C211yesmaximal, characteristic, complemented
12C2×#14583044C211yesmaximal, characteristic, complemented
13C2×#14583040C211yesmaximal, characteristic, complemented
14C2×#14583037C211yesmaximal, characteristic, complemented
15C2×#14582957C211yesmaximal, characteristic, complemented
16C2×C43×#449C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×#10621883C2211yescharacteristic
22C22×#10621884C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24#14583502—24no—
25#14583502C2218yescomplemented
26#14583470—24no—
27#14583470C2218yescomplemented
28C2×#13063323C2211yescharacteristic
29C2×#13063323C2211yescharacteristic
30C2×#13063321C2211yescharacteristic
31C2×#13063316C2211yescharacteristic
32C2×#13063312C2211yescharacteristic
33C2×#13063312C2211yescharacteristic
34C2×#13063309—21no—
35C2×#13063307—21no—
36C2×#13063306—21no—
37C2×#13063306—21no—
38C2×#13063304—21no—
39C2×#13063304—21no—
40C2×#13063299C2211yescharacteristic
41C2×#13063297—21no—
42C2×#13063296—21no—
43C2×D4×Dic43C2211yescharacteristic
44C2×#13063287C2211yescharacteristic
45C2×#13063284C2211yescharacteristic
46#14583287C2218yescomplemented
47#14583270C2218yescomplemented
48#14583266C2218yescomplemented
49#14583252C2218yescomplemented
50#14583113C2218yescomplemented
51#14583112C2218yescomplemented
52#14583103C2218yescomplemented
53#14583102C2218yescomplemented
54#14583044C2218yescomplemented
55#14583040C2218yescomplemented
56#14583037C2218yescomplemented
57#14582957C2218yescomplemented
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×#41×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C22×D8×C43C2211yescharacteristic
72C2×#121×C43C2211yescharacteristic
73C43×#449C2218yescomplemented
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86—22no—
79C22×Dic86—42no—
80C22×Dic86—42no—
81C22×Dic86C2311yescharacteristic
82C22×Dic86C2311yescharacteristic
83C22×Dic86C2314yes—
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C23×Dic43—21no—
89C23×Dic43—21no—
90C22×C4×D43—21no—
91C2×#10621873—42no—
92C2×#10621873—42no—
93C2×#10621873C2314yes—
94C2×#10621873C2314yes—
95C2×#10621883—42no—
96C2×#10621883—42no—
97C2×#10621883C2314yes—
98C2×#10621883C2314yes—
99C2×#10621884—42no—
100C2×#10621884C2314yes—
101C2×#10621882—42no—
102C2×#10621882C2314yes—
103C22×C43⋊C8C2311yescharacteristic
104C22×C43⋊C8C2311yescharacteristic
105#13063323—22no—
106#13063323—22no—
107#13063323C2314yes—
108#13063323C2314yes—
109#13063321—22no—
110#13063321C2314yes—
111#13063316—22no—
112#13063316C2314yes—
113#13063312—22no—
114#13063312—22no—
115#13063312C2314yes—
116#13063312C2314yes—
117#13063309—28no—
118#13063307—28no—
119#13063306—28no—
120#13063306—28no—
121#13063304—28no—
122#13063304—28no—
123#13063299—22no—
124#13063299C2314yes—
125#13063297—28no—
126#13063296—28no—
127D4×Dic43—22no—
128D4×Dic43C2314yes—
129#13063287—22no—
130#13063287C2314yes—
131#13063284D414yes—
132#13063284C2314yes—
133C2×C4⋊Dic43—21no—
134C2×C4⋊Dic43D411yescharacteristic
135C2×C4⋊Dic43D411yescharacteristic
136C2×C4⋊Dic43C2311yescharacteristic
137C2×Dic43⋊C4—21no—
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×C22⋊Dic43—21no—
146C2×C22⋊Dic43—21no—
147C2×C22⋊Dic43D411yescharacteristic
148C2×C22⋊Dic43D411yescharacteristic
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×C4×Dic43C2311yescharacteristic
152C2×C4×Dic43C2311yescharacteristic
153Dic43⋊C8C2314yes—
154Dic43⋊C8C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063249C2314yes—
158#13063248C2314yes—
159#13063248C2314yes—
160#13063246C2314yes—
161C22⋊(C43⋊C8)C2314yes—
162#13063235C2314yes—
163C8×Dic43C2314yes—
164C2×#41×C43—22no—
165C2×#41×C43—42no—
166C2×#41×C43—42no—
167C2×#41×C43C2314yes—
168C22×Q8×C43C2311yescharacteristic
169C22×D4×C43—21no—
170C22×D4×C43—21no—
171C22×D4×C43C2311yescharacteristic
172C22×D4×C43C2311yescharacteristic
173C23×C4×C43—21no—
174C23×C4×C43C2311yescharacteristic
175C2×SD16×C43—42no—
176C2×SD16×C43C2314yes—
177C2×D8×C43—42no—
178C2×D8×C43C2314yes—
179C22×C8×C43C2311yescharacteristic
180C22×C8×C43C2311yescharacteristic
181#121×C43—22no—
182#121×C43C2314yes—
183C2×C4⋊C4×C43C2311yescharacteristic
184C2×C22⋊C4×C43—21no—
185#103×C43C2314yes—
186#102×C43C2314yes—
187C22⋊C8×C43C2314yes—
188C24×C43—21no—
189C24×C43—21no—
190C24×C43C2×D411yescharacteristic
191C23×D43—21no—
192#41×C43—44no—
193#41×C43—44no—
194#41×C43—48no—
195C2×Q8×C43—21no—
196C2×Q8×C43—22no—
197C2×Q8×C43—22no—
198C2×Q8×C43C2412yes—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—24no—
202C2×D4×C43—24no—
203C2×D4×C43—22no—
204C2×D4×C43—22no—
205C2×D4×C43—22no—
206C2×D4×C43—22no—
207C2×D4×C43—44no—
208C2×D4×C43—82no—
209C2×D4×C43C2412yes—
210C2×D4×C43C2412yes—
211C22×C4×C43—22no—
212C22×C4×C43—22no—
213C22×C4×C43—24no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—44no—
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D412yes—
219C22×C4×C43C2412yes—
220C22×C4×C43C2411yescharacteristic
221C2×C22⋊D43—24no—
222C2×C22⋊D43—24no—
223C2×C22⋊D43—24no—
224C2×C22⋊D43—82no—
225C2×C22⋊D43—82no—
226C2×C22⋊D43—82no—
227C22×Dic43—24no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—24no—
232C22×Dic43—44no—
233C22×Dic43—82no—
234C22×Dic43C2×D411yescharacteristic
235C22×Dic43C2×D411yescharacteristic
236C22×Dic43C2×D411yescharacteristic
237C22×Dic43C2×D411yescharacteristic
238C2×D172—21no—
239C2×D172—22no—
240C2×D172—22no—
241C2×D172C2412yes—
242C2×C4×D43—24no—
243C2×C4×D43—82no—
244C2×Dic86—22no—
245C2×Dic86—22no—
246C2×Dic86—22no—
247C2×Dic86—22no—
248C2×Dic86—24no—
249C2×Dic86—21no—
250C2×Dic86—21no—
251C2×Dic86—44no—
252C2×Dic86—44no—
253C2×Dic86—44no—
254C2×Dic86—48no—
255C2×Dic86C2412yes—
256C2×Dic86C2412yes—
257SD16×C43—44no—
258D8×C43—44no—
259C2×C8×C43—22no—
260C2×C8×C43—22no—
261C2×C8×C43C2412yes—
262C2×C8×C43C2412yes—
263C4⋊C4×C43—21no—
264C4⋊C4×C43C2412yes—
265C22⋊C4×C43—24no—
266C22⋊Dic43—24no—
267C22⋊Dic43—24no—
268C22⋊Dic43—24no—
269C22⋊Dic43—24no—
270C22⋊Dic43—24no—
271C22⋊Dic43C2×D414yes—
272C22⋊Dic43C2×D414yes—
273#10621884—44no—
274#10621883—44no—
275#10621883—44no—
276#10621882—44no—
277(C2×D43)⋊C4—24no—
278(C2×D43)⋊C4—24no—
279C4⋊Dic43—21no—
280C4⋊Dic43—24no—
281C4⋊Dic43C2×D414yes—
282C4⋊Dic43C2×D414yes—
283C4⋊Dic43C2412yes—
284Dic43⋊C4—24no—
285Dic43⋊C4—24no—
286Dic43⋊C4—24no—
287Dic43⋊C4—24no—
288Dic43⋊C4—24no—
289C4×Dic43C2×D412yes—
290C4×Dic43C2×D412yes—
291C4×Dic43C2412yes—
292C4×Dic43C2412yes—
293C2×C43⋊C8—22no—
294C2×C43⋊C8—22no—
295C2×C43⋊C8C2412yes—
296C2×C43⋊C8C2412yes—
297#10621873—44no—
298#10621873—44no—
299C23×C43—22no—
300C23×C43—22no—
301C23×C43—22no—
302C23×C43—22no—
303C23×C43—22no—
304C23×C43—42no—
305C23×C43—42no—
306C23×C43—42no—
307C23×C43—42no—
308C23×C43—42no—
309C23×C43—42no—
310C23×C43C22×D412yes—
311C23×C43C22×D411yescharacteristic
312C22×D43—22no—
313C22×D43—42no—
314C22×D43—42no—
315C22×D43—42no—
316Q8×C43—22no—
317Q8×C43—22no—
318Q8×C43—42no—
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—22no—
322D4×C43—22no—
323D4×C43—48no—
324D4×C43—42no—
325D4×C43—42no—
326D4×C43—84no—
327C2×C4×C43—22no—
328C2×C4×C43—24no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—48no—
334C2×C4×C43—42no—
335C2×C4×C43—42no—
336C2×C4×C43C22×D412yes—
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43H(5,𝔽2)12yes—
339C2×C4×C43H(5,𝔽2)12yes—
340C2×C4×C43C2511yescharacteristic
341C22⋊D43—84no—
342C22⋊D43—84no—
343C22⋊D43—84no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—48no—
352C2×Dic43—42no—
353C2×Dic43—42no—
354C2×Dic43—42no—
355C2×Dic43—84no—
356C2×Dic43C22×D412yes—
357C2×Dic43C22×D412yes—
358C2×Dic43C22×D412yes—
359C2×Dic43C22×D412yes—
360D172—22no—
361D172—22no—
362D172—42no—
363C4×D43—84no—
364Dic86—22no—
365Dic86—22no—
366Dic86—22no—
367Dic86—22no—
368Dic86—48no—
369Dic86—42no—
370Dic86—42no—
371C8×C43—22no—
372C8×C43—22no—
373C43⋊C8—22no—
374C43⋊C8—22no—
375C2×#3221—431nomaximal, Sylow
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—44no—
380C22×C43—42no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—84no—
387C22×C43—84no—
388C22×C43#53512yes—
389C22×C43#57712yes—
390C22×C43#57712yes—
391C22×C43C23×D411yescharacteristic
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—84no—
396C4×C43—22no—
397C4×C43—42no—
398C4×C43—42no—
399C4×C43#53512yes—
400C4×C43C2×H(5,𝔽2)11yescharacteristic
401C4×C43C2×H(5,𝔽2)11yescharacteristic
402Dic43—22no—
403Dic43—22no—
404Dic43—22no—
405Dic43—22no—
406Dic43—42no—
407Dic43—42no—
408Dic43—42no—
409C2×#540—431no—
410C2×#536—431no—
411#3221—4316no—
412C2×#496—431no—
413C2×#492—431no—
414C2×#491—431no—
415C2×#488—431no—
416C2×#463—431no—
417C2×#463—431no—
418C2×#461—431no—
419C2×#461—431no—
420C2×#449—431no—
421C2×#449D4311yescharacteristic, complemented
422C2×#448—431no—
423C2×#448—431no—
424C2×#433—431no—
425C2×C43—42no—
426C2×C43—82no—
427C2×C43—82no—
428C2×C43#322114yescomplemented
429C2×C43C2×#53511yescharacteristic
430C2×C43C2×#57711yescharacteristic
431C2×C43C2×#57711yescharacteristic
432D43—82no—
433C22×#41C2×D4311yescharacteristic
434C23×Q8—431no—
435C22×SD16—431no—
436C22×SD16—431no—
437C22×SD16—431no—
438C22×SD16—431no—
439C22×SD16—431no—
440C22×SD16C2×D4311yescharacteristic
441C22×D8—431no—
442C22×D8C2×D4311yescharacteristic
443#540—438no—
444#540—864no—
445#536—438no—
446#536—864no—
447C2×C4⋊Q8—431no—
448C2×C4⋊Q8—431no—
449C2×#127—431no—
450C2×#125—431no—
451C2×#124—431no—
452C2×#124—431no—
453C2×#123—861no—
454C2×#123—861no—
455C2×#123—861no—
456C2×#123—861no—
457C2×C22⋊Q8—861no—
458C2×C22⋊Q8—861no—
459C2×#121—431no—
460C2×#121—861no—
461C2×#121—861no—
462C2×#121C2×D4311yescharacteristic
463C2×C4×D4—431no—
464C2×C4×D4—431no—
465C2×#117—431no—
466#496—438no—
467#492—438no—
468#491—438no—
469#488—438no—
470#463—438no—
471#463—438no—
472#461—438no—
473#461—438no—
474#449—438no—
475#449C2×D4318yescomplemented
476#448—438no—
477#448—438no—
478#433—438no—
479C2×C4⋊C8—431no—
480C2×C4⋊C8—431no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103—431no—
485C2×#103—431no—
486C2×#103C2×D4311yescharacteristic
487C2×#102—431no—
488C2×#102C2×D4311yescharacteristic
489C2×C22⋊C8—431no—
490C2×C22⋊C8C2×D4311yescharacteristic
491C2×#97—431no—
492C2×C4×C8—431no—
493C43C2×#322111yescharacteristic, complemented, Sylow
494C2×#41—22no—
495C2×#41—42no—
496C2×#41—42no—
497C2×#41C22×D4314yes—
498C22×Q8—431no—
499C22×Q8—431no—
500C22×Q8—434no—
501C22×Q8—861no—
502C22×Q8—862no—
503C22×Q8—1722no—
504C22×Q8—1722no—
505C22×Q8C22×D4311yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—431no—
509C22×D4—861no—
510C22×D4—861no—
511C22×D4—861no—
512C22×D4C22×D4311yescharacteristic
513C22×D4C22×D4311yescharacteristic
514C23×C4—21no—
515C23×C4—861no—
516C23×C4—861no—
517C23×C4—861no—
518C23×C4C22×D4311yescharacteristic
519C2×SD16—42no—
520C2×SD16—434no—
521C2×SD16—434no—
522C2×SD16—434no—
523C2×SD16—434no—
524C2×SD16—434no—
525C2×SD16—1722no—
526C2×SD16—1722no—
527C2×SD16—1722no—
528C2×SD16—1722no—
529C2×SD16—1722no—
530C2×SD16C22×D4314yes—
531C2×D8—42no—
532C2×D8—434no—
533C2×D8—1722no—
534C2×D8C22×D4314yes—
535C22×C8—431no—
536C22×C8—431no—
537C22×C8C22×D4311yescharacteristic
538C22×C8C22×D4311yescharacteristic
539C4⋊Q8—434no—
540C4⋊Q8—434no—
541C4⋊Q8—862no—
542C4⋊Q8—862no—
543#127—434no—
544#127—862no—
545#125—434no—
546#125—862no—
547#124—434no—
548#124—434no—
549#124—862no—
550#124—862no—
551#123—868no—
552#123—868no—
553#123—868no—
554#123—868no—
555C22⋊Q8—868no—
556C22⋊Q8—868no—
557#121—22no—
558#121—434no—
559#121—868no—
560#121—868no—
561#121—862no—
562#121C22×D4314yes—
563C4×D4—434no—
564C4×D4—434no—
565C4×D4—862no—
566C4×D4—862no—
567#117—434no—
568#117—434no—
569C2×C4⋊C4—431no—
570C2×C4⋊C4—431no—
571C2×C4⋊C4—431no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4—861no—
574C2×C4⋊C4—861no—
575C2×C4⋊C4—861no—
576C2×C4⋊C4—861no—
577C2×C4⋊C4—861no—
578C2×C4⋊C4C22×D4311yescharacteristic
579C2×C22⋊C4—21no—
580C2×C22⋊C4—431no—
581C2×C22⋊C4—431no—
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—
591C4⋊C8—434no—
592C4⋊C8—434no—
593#103—434no—
594#103—434no—
595#103—434no—
596#103—434no—
597#103—434no—
598#103C22×D4314yes—
599#102—434no—
600#102C22×D4314yes—
601C22⋊C8—434no—
602C22⋊C8C22×D4314yes—
603#97—434no—
604C4×C8—434no—
605C24—21no—
606C24—21no—
607C24—861no—
608C24D4×D4311yescharacteristic
609#41—44no—
610#41—44no—
611#41—48no—
612C2×Q8—21no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—432no—
616C2×Q8—432no—
617C2×Q8—864no—
618C2×Q8—861no—
619C2×Q8—861no—
620C2×Q8—862no—
621C2×Q8—862no—
622C2×Q8—862no—
623C2×Q8—862no—
624C2×Q8—1724no—
625C2×Q8—1724no—
626C2×Q8—1724no—
627C2×Q8—1728no—
628C2×Q8C23×D4312yes—
629C2×D4—24no—
630C2×D4—24no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—44no—
638C2×D4—82no—
639C2×D4—432no—
640C2×D4—864no—
641C2×D4—864no—
642C2×D4—864no—
643C2×D4—861no—
644C2×D4—862no—
645C2×D4—862no—
646C2×D4—3442no—
647C2×D4—3442no—
648C2×D4—3442no—
649C2×D4C23×D4312yes—
650C2×D4C23×D4312yes—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—44no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—864no—
662C22×C4—864no—
663C22×C4—864no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—3442no—
668C22×C4—3442no—
669C22×C4—1724no—
670C22×C4D4×D4312yes—
671C22×C4D4×D4311yescharacteristic
672C22×C4C23×D4312yes—
673C22×C4C23×D4311yescharacteristic
674SD16—44no—
675SD16—1724no—
676SD16—1724no—
677SD16—1724no—
678SD16—1724no—
679SD16—1724no—
680D8—44no—
681D8—1724no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—432no—
685C2×C8—432no—
686C2×C8—862no—
687C2×C8—862no—
688C2×C8C23×D4312yes—
689C2×C8C23×D4312yes—
690C4⋊C4—21no—
691C4⋊C4—434no—
692C4⋊C4—434no—
693C4⋊C4—432no—
694C4⋊C4—864no—
695C4⋊C4—864no—
696C4⋊C4—864no—
697C4⋊C4—864no—
698C4⋊C4—864no—
699C4⋊C4—864no—
700C4⋊C4—861no—
701C4⋊C4C23×D4312yes—
702C22⋊C4—24no—
703C22⋊C4—434no—
704C22⋊C4—434no—
705C22⋊C4—864no—
706C22⋊C4—864no—
707C22⋊C4—864no—
708C22⋊C4—864no—
709C22⋊C4—864no—
710C22⋊C4—864no—
711C22⋊C4—864no—
712C42—432no—
713C42—432no—
714C42—432no—
715C42—432no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—862no—
728C23—1722no—
729C23—1722no—
730C23—1722no—
731C23C2×D4×D4312yes—
732C23C2×D4×D4311yescharacteristic
733Q8—22no—
734Q8—22no—
735Q8—42no—
736Q8—862no—
737Q8—862no—
738Q8—862no—
739Q8—862no—
740Q8—1728no—
741Q8—1722no—
742Q8—1722no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—22no—
747D4—48no—
748D4—42no—
749D4—42no—
750D4—84no—
751D4—862no—
752D4—862no—
753D4—3444no—
754D4—3444no—
755D4—3444no—
756D4—1722no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—48no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—432no—
767C2×C4—432no—
768C2×C4—432no—
769C2×C4—432no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—3444no—
778C2×C4—3444no—
779C2×C4—1728no—
780C2×C4—1722no—
781C2×C4—1722no—
782C2×C4—1722no—
783C2×C4C2×D4×D4312yes—
784C2×C4C2×D4×D4311yescharacteristic
785C2×C4#1306337012yes—
786C2×C4#1306337012yes—
787C2×C4C24×D4311yescharacteristic
788C8—22no—
789C8—22no—
790C8—862no—
791C8—862no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—44no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—84no—
803C22—84no—
804C22—3444no—
805C22—1722no—
806C22—1722no—
807C22—1722no—
808C22#1458346412yes—
809C22#1458370612yes—
810C22#1458370912yes—
811C22C22×D4×D4311yescharacteristic
812C4—22no—
813C4—42no—
814C4—42no—
815C4—862no—
816C4—862no—
817C4—862no—
818C4—862no—
819C4—1722no—
820C4—1722no—
821C4—1722no—
822C4#1458346412yes—
823C4C2×#1306337011yescharacteristic
824C4C2×#1306337011yescharacteristic
825C2—42no—
826C2—82no—
827C2—82no—
828C2—3442no—
829C2#1914565414yesdirect product factor
830C2C2×#1458346411yescharacteristic
831C2C2×#1458370611yescharacteristic
832C2C2×#1458370911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#449C2
socleC23×C43C22×D4
hypercenterC2×#449D43
hypocenterC43C2×#3221
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#14583502C2semidirect
2. C2×#14583470C2semidirect
3. #19145654C2direct (N × H)
4. C2×#14583287C2semidirect
5. C2×#14583270C2semidirect
6. C2×#14583266C2semidirect
7. C2×#14583252C2semidirect
8. C2×#14583113C2semidirect
9. C2×#14583112C2semidirect
10. C2×#14583103C2semidirect
11. C2×#14583102C2semidirect
12. C2×#14583044C2semidirect
13. C2×#14583040C2semidirect
14. C2×#14583037C2semidirect
15. C2×#14582957C2semidirect
16. C2×C43×#449C2semidirect
25. #14583502C22semidirect
27. #14583470C22semidirect
46. #14583287C22semidirect
47. #14583270C22semidirect
48. #14583266C22semidirect
49. #14583252C22semidirect
50. #14583113C22semidirect
51. #14583112C22semidirect
52. #14583103C22semidirect
53. #14583102C22semidirect
54. #14583044C22semidirect
55. #14583040C22semidirect
56. #14583037C22semidirect
57. #14582957C22semidirect
73. C43×#449C22semidirect
421. C2×#449D43semidirect
428. C2×C43#3221semidirect
475. #449C2×D43semidirect
493. C43C2×#3221semidirect
829. C2#19145654direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835022
C2×#145834702
#191456542
C2×#145832872
C2×#145832702
C2×#145832662
C2×#145832522
C2×#145831132
C2×#145831122
C2×#145831032
C2×#145831022
C2×#145830442
C2×#145830402
C2×#145830372
C2×#145829572
C2×C43×#4492
C2×#322143