Finite Group Databasebeta

← C2×#19145572 #25967818

Subgroups — C2×#19145572 #25967818

Order 11008.

2218 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×#14583448C211yesmaximal, characteristic, complemented
2C2×#14583434C211yesmaximal, characteristic, complemented
3#19145572C2116yesmaximal, direct product factor
4C2×#14583283C211yesmaximal, characteristic, complemented
5C2×#14583281C211yesmaximal, characteristic, complemented
6C2×#14583256C211yesmaximal, characteristic, complemented
7C2×#14583108C211yesmaximal, characteristic, complemented
8C2×#14583098C211yesmaximal, characteristic, complemented
9C2×#14583103C211yesmaximal, characteristic, complemented
10C2×#14583093C211yesmaximal, characteristic, complemented
11C2×#14583064C211yesmaximal, characteristic, complemented
12C2×#14583062C211yesmaximal, characteristic, complemented
13C2×#14583047C211yesmaximal, characteristic, complemented
14C2×#14583045C211yesmaximal, characteristic, complemented
15C2×#14582950C211yesmaximal, characteristic, complemented
16C2×C43×#488C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C22×Dic172C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C22×#10621873C2211yescharacteristic
22C22×#10621873C2211yescharacteristic
23C22×#10621883C2211yescharacteristic
24C22×#10621884C2211yescharacteristic
25C22×D344C2211yescharacteristic
26C22×#10621882C2211yescharacteristic
27#14583448—24no—
28#14583448C2218yescomplemented
29C2×#13063323C2211yescharacteristic
30C2×#13063321C2211yescharacteristic
31#14583434—24no—
32#14583434C2218yescomplemented
33C2×#13063320—21no—
34C2×#13063313C2211yescharacteristic
35C2×#13063313C2211yescharacteristic
36C2×#13063310—21no—
37C2×#13063305C2211yescharacteristic
38C2×#13063300C2211yescharacteristic
39C2×#13063298—21no—
40C2×#13063298—21no—
41C2×#13063290C2211yescharacteristic
42C2×#13063287—21no—
43C2×#13063287C2211yescharacteristic
44C2×(C22⋊D43)⋊C4—21no—
45C2×(C22⋊D43)⋊C4—21no—
46C2×#13063283—21no—
47C2×C42×D43C2211yescharacteristic
48#14583283C2218yescomplemented
49#14583281C2218yescomplemented
50#14583256C2218yescomplemented
51#14583108C2218yescomplemented
52#14583103C2218yescomplemented
53#14583098C2218yescomplemented
54#14583093C2218yescomplemented
55#14583064C2218yescomplemented
56#14583062C2218yescomplemented
57#14583047C2218yescomplemented
58#14583045C2218yescomplemented
59#14582950C2218yescomplemented
60C2×Dic43⋊C8C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C4×C43⋊C8C2211yescharacteristic
69C2×#125×C43C2211yescharacteristic
70C2×#124×C43C2211yescharacteristic
71C43×#488C2218yescomplemented
72C2×#103×C43C2211yescharacteristic
73C2×#103×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—42no—
79C2×#10621902—42no—
80C2×#10621902C2314yes—
81C2×#10621900—22no—
82C2×#10621900—42no—
83C2×#10621900—42no—
84C2×#10621900C2314yes—
85C22×Dic86C2311yescharacteristic
86C22×Dic86C2311yescharacteristic
87C22×D172—21no—
88C22×D172—21no—
89C22×D172C2311yescharacteristic
90C22×D172C2311yescharacteristic
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C22×C22⋊D43—21no—
94C23×Dic43—21no—
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43D411yescharacteristic
98C22×C4×D43D411yescharacteristic
99C22×C4×D43C2311yescharacteristic
100C2×Dic172—42no—
101C2×Dic172C2314yes—
102C2×#10621885—42no—
103C2×#10621885C2314yes—
104C2×#10621873—42no—
105C2×#10621873—42no—
106C2×#10621873C2314yes—
107C2×#10621873C2314yes—
108C2×#10621883—42no—
109C2×#10621883C2314yes—
110C2×#10621884—42no—
111C2×#10621884C2314yes—
112C2×D344—42no—
113C2×D344C2314yes—
114C2×#10621882—42no—
115C2×#10621882C2314yes—
116C22×C43⋊C8C2311yescharacteristic
117C22×C43⋊C8C2311yescharacteristic
118#13063323—22no—
119#13063323C2314yes—
120#13063321—22no—
121#13063321C2314yes—
122#13063320—28no—
123#13063313—22no—
124#13063313—22no—
125#13063313C2314yes—
126#13063313C2314yes—
127#13063310—28no—
128#13063305—22no—
129#13063305C2314yes—
130#13063300—22no—
131#13063300C2314yes—
132#13063298—28no—
133#13063298—28no—
134#13063290—22no—
135#13063290C2314yes—
136#13063287—28no—
137#13063287—22no—
138#13063287C2314yes—
139(C22⋊D43)⋊C4—28no—
140(C22⋊D43)⋊C4—28no—
141#13063283—28no—
142C2×C4⋊Dic43—21no—
143C2×Dic43⋊C4—21no—
144C2×Dic43⋊C4—21no—
145C2×Dic43⋊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×(C2×D43)⋊C4—21no—
152C2×(C2×D43)⋊C4—21no—
153C2×C4×Dic43—21no—
154C2×C4×Dic43D411yescharacteristic
155C2×C4×Dic43D411yescharacteristic
156C2×C4×Dic43C2311yescharacteristic
157C42×D43D414yes—
158C42×D43C2314yes—
159Dic43⋊C8C2314yes—
160Dic43⋊C8C2314yes—
161#13063248C2314yes—
162#13063248C2314yes—
163#13063245C2314yes—
164#13063245C2314yes—
165(C2×D43)⋊C8C2314yes—
166(C2×D43)⋊C8C2314yes—
167C4×C43⋊C8C2314yes—
168C22×Q8×C43C2311yescharacteristic
169C22×D4×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172#125×C43—22no—
173#125×C43C2314yes—
174#124×C43—22no—
175#124×C43C2314yes—
176C2×C4⋊C4×C43—21no—
177C2×C4⋊C4×C43—21no—
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43—21no—
182C2×C42×C43C2311yescharacteristic
183#103×C43C2314yes—
184#103×C43C2314yes—
185#102×C43C2314yes—
186#102×C43C2314yes—
187C4×C8×C43C2314yes—
188C24×C43—21no—
189C23×D43—21no—
190C23×D43—21no—
191C23×D43C2×D411yescharacteristic
192C2×Q8×C43—21no—
193C2×Q8×C43—22no—
194C2×Q8×C43—22no—
195C2×Q8×C43C2412yes—
196C2×D4×C43—21no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43C2412yes—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—24no—
207C2×C22⋊D43—24no—
208C2×C22⋊D43—24no—
209C2×C22⋊D43—44no—
210C2×C22⋊D43—44no—
211C2×C22⋊D43—44no—
212C22×Dic43—24no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—44no—
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218C22×Dic43C2×D411yescharacteristic
219#10621902—44no—
220#10621902—44no—
221#10621902—48no—
222#10621900—44no—
223#10621900—44no—
224#10621900—48no—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172—24no—
228C2×D172—24no—
229C2×D172—22no—
230C2×D172—22no—
231C2×D172—22no—
232C2×D172—22no—
233C2×D172—44no—
234C2×D172—44no—
235C2×D172C2412yes—
236C2×D172C2412yes—
237C2×C4×D43—22no—
238C2×C4×D43—22no—
239C2×C4×D43—24no—
240C2×C4×D43—24no—
241C2×C4×D43—24no—
242C2×C4×D43—42no—
243C2×C4×D43—44no—
244C2×C4×D43—44no—
245C2×C4×D43C2×D412yes—
246C2×C4×D43C2×D414yes—
247C2×C4×D43C2×D414yes—
248C2×C4×D43C2412yes—
249C2×Dic86—22no—
250C2×Dic86—22no—
251C2×Dic86—22no—
252C2×Dic86—22no—
253C2×Dic86—21no—
254C2×Dic86—21no—
255C2×Dic86C2412yes—
256C2×Dic86C2412yes—
257C2×C8×C43—22no—
258C2×C8×C43—22no—
259C2×C8×C43C2412yes—
260C2×C8×C43C2412yes—
261C4⋊C4×C43—24no—
262C4⋊C4×C43—24no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43C2412yes—
266C4⋊C4×C43C2412yes—
267C22⋊C4×C43—24no—
268C22⋊C4×C43—24no—
269C42×C43C2×D412yes—
270C42×C43C2412yes—
271#10621885—44no—
272#10621884—44no—
273#10621883—44no—
274#10621882—44no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4—24no—
278(C2×D43)⋊C4—24no—
279(C2×D43)⋊C4—24no—
280(C2×D43)⋊C4—24no—
281(C2×D43)⋊C4—24no—
282C4⋊Dic43—24no—
283Dic43⋊C4—24no—
284Dic43⋊C4—24no—
285Dic43⋊C4—24no—
286C4×Dic43—24no—
287C4×Dic43C2×D412yes—
288C4×Dic43C2×D414yes—
289C4×Dic43C2×D414yes—
290C4×Dic43C2412yes—
291C2×C43⋊C8—22no—
292C2×C43⋊C8—22no—
293C2×C43⋊C8C2412yes—
294C2×C43⋊C8C2412yes—
295Dic172—44no—
296D344—44no—
297#10621873—44no—
298#10621873—44no—
299C23×C43—22no—
300C23×C43—42no—
301C23×C43—42no—
302C23×C43—42no—
303C23×C43C22×D411yescharacteristic
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—42no—
310C22×D43—42no—
311C22×D43—42no—
312C22×D43—42no—
313C22×D43—42no—
314C22×D43—42no—
315C22×D43C22×D412yes—
316Q8×C43—22no—
317Q8×C43—22no—
318Q8×C43—42no—
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—42no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43—42no—
330C2×C4×C43C22×D412yes—
331C2×C4×C43C22×D412yes—
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43H(5,𝔽2)12yes—
334C2×C4×C43H(5,𝔽2)12yes—
335C2×C4×C43C2511yescharacteristic
336C22⋊D43—48no—
337C22⋊D43—48no—
338C22⋊D43—48no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—48no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43#13514yes—
347C2×Dic43C22×D412yes—
348C2×Dic43C22×D412yes—
349C2×Dic43C22×D412yes—
350D172—22no—
351D172—22no—
352D172—22no—
353D172—22no—
354D172—48no—
355D172—48no—
356D172—42no—
357D172—42no—
358C4×D43—24no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—28no—
362C4×D43—44no—
363C4×D43—48no—
364C4×D43—48no—
365Dic86—22no—
366Dic86—22no—
367Dic86—22no—
368Dic86—22no—
369Dic86—42no—
370Dic86—42no—
371C8×C43—22no—
372C8×C43—22no—
373C43⋊C8—22no—
374C43⋊C8—22no—
375C2×#3212—431nomaximal, Sylow
376C22×C43—42no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—84no—
380C22×C43#53512yes—
381C22×C43C2×#13512yes—
382C22×C43#57512yes—
383C22×C43C23×D411yescharacteristic
384C2×D43—22no—
385C2×D43—22no—
386C2×D43—22no—
387C2×D43—44no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—84no—
395C2×D43—84no—
396C4×C43—22no—
397C4×C43—22no—
398C4×C43—42no—
399C4×C43—42no—
400C4×C43—42no—
401C4×C43#53512yes—
402C4×C43C2×H(5,𝔽2)11yescharacteristic
403C4×C43C2×H(5,𝔽2)11yescharacteristic
404Dic43—22no—
405Dic43—22no—
406Dic43—42no—
407Dic43—42no—
408Dic43C2×#13514yes—
409C2×#532—431no—
410C2×#529—431no—
411#3212—4316no—
412C2×#495—431no—
413C2×#495—431no—
414C2×#488—431no—
415C2×#488D4311yescharacteristic, complemented
416C2×#462—431no—
417C2×#460—431no—
418C2×#461—431no—
419C2×#459—431no—
420C2×#452—431no—
421C2×#452—431no—
422C2×#449—431no—
423C2×#449—431no—
424C2×#431—431no—
425C2×C43—82no—
426C2×C43#321214yescomplemented
427C2×C43C2×#53511yescharacteristic
428C2×C43C22×#13511yescharacteristic
429C2×C43C2×#57511yescharacteristic
430D43—42no—
431D43—82no—
432D43—82no—
433C22×#41—431no—
434C22×#41—431no—
435C22×Q16—431no—
436C22×Q16—431no—
437C22×SD16—431no—
438C22×SD16—431no—
439C22×SD16—431no—
440C22×SD16—431no—
441C22×D8—431no—
442C22×D8—431no—
443#532—438no—
444#532—864no—
445C2×C4⋊Q8—431no—
446C2×#127—431no—
447#529—438no—
448#529—864no—
449C2×#126—861no—
450C2×#125C2×D4311yescharacteristic
451C2×#124—431no—
452C2×#124—431no—
453C2×#124C2×D4311yescharacteristic
454C2×#123—861no—
455C2×C22⋊Q8—431no—
456C2×#121—431no—
457C2×#121—861no—
458C2×#121—861no—
459C2×C4×Q8—431no—
460C2×C4×D4—431no—
461C2×C4×D4—861no—
462C2×C4×D4—861no—
463C2×C4×D4—861no—
464C2×#117—861no—
465C22×C42—431no—
466#495—438no—
467#495—438no—
468#488—438no—
469#488C2×D4318yescomplemented
470#462—438no—
471#461—438no—
472#460—438no—
473#459—438no—
474#452—438no—
475#452—438no—
476#449—438no—
477#449—438no—
478#431—438no—
479C2×C4⋊C8—431no—
480C2×C4⋊C8—431no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103C2×D4311yescharacteristic
484C2×#103C2×D4311yescharacteristic
485C2×#102—431no—
486C2×#102—431no—
487C2×#102C2×D4311yescharacteristic
488C2×#102C2×D4311yescharacteristic
489C2×C22⋊C8—431no—
490C2×C22⋊C8—431no—
491C2×C4×C8—431no—
492C2×C4×C8C2×D4311yescharacteristic
493C43C2×#321211yescharacteristic, complemented, Sylow
494C2×#41—434no—
495C2×#41—434no—
496C2×#41—862no—
497C2×#41—862no—
498C2×#41—1722no—
499C2×#41—1722no—
500C2×#41—1722no—
501C2×#41—1722no—
502C22×Q8—431no—
503C22×Q8—431no—
504C22×Q8C22×D4311yescharacteristic
505C22×D4—431no—
506C22×D4—431no—
507C22×D4—861no—
508C22×D4—861no—
509C22×D4—861no—
510C22×D4—861no—
511C22×D4—861no—
512C22×D4C22×D4311yescharacteristic
513C23×C4—431no—
514C23×C4—431no—
515C23×C4—431no—
516C23×C4—861no—
517C23×C4—861no—
518C23×C4—861no—
519C2×Q16—434no—
520C2×Q16—434no—
521C2×Q16—1722no—
522C2×Q16—1722no—
523C2×SD16—434no—
524C2×SD16—434no—
525C2×SD16—434no—
526C2×SD16—434no—
527C2×SD16—1722no—
528C2×SD16—1722no—
529C2×SD16—1722no—
530C2×SD16—1722no—
531C2×D8—434no—
532C2×D8—434no—
533C2×D8—1722no—
534C2×D8—1722no—
535C22×C8—431no—
536C22×C8—431no—
537C22×C8C22×D4311yescharacteristic
538C22×C8C22×D4311yescharacteristic
539C4⋊Q8—434no—
540C4⋊Q8—862no—
541#127—434no—
542#127—862no—
543#126—868no—
544#125—22no—
545#125C22×D4314yes—
546#124—22no—
547#124—434no—
548#124—434no—
549#124—862no—
550#124—862no—
551#124C22×D4314yes—
552#123—868no—
553C22⋊Q8—434no—
554C22⋊Q8—862no—
555#121—434no—
556#121—868no—
557#121—868no—
558#121—862no—
559C4×Q8—434no—
560C4×Q8—862no—
561C4×D4—434no—
562C4×D4—868no—
563C4×D4—868no—
564C4×D4—862no—
565C4×D4—868no—
566#117—868no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—861no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4C22×D4311yescharacteristic
574C2×C4⋊C4C22×D4311yescharacteristic
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C22⋊C4—861no—
582C2×C22⋊C4—861no—
583C2×C22⋊C4—861no—
584C2×C42—431no—
585C2×C42—431no—
586C2×C42—431no—
587C2×C42—434no—
588C2×C42—434no—
589C2×C42—861no—
590C2×C42C22×D4311yescharacteristic
591C4⋊C8—434no—
592C4⋊C8—434no—
593#103—434no—
594#103—434no—
595#103C22×D4314yes—
596#103C22×D4314yes—
597#102—434no—
598#102—434no—
599#102C22×D4314yes—
600#102C22×D4314yes—
601C22⋊C8—434no—
602C22⋊C8—434no—
603C4×C8—434no—
604C4×C8C22×D4314yes—
605C24—21no—
606C24—431no—
607C24—861no—
608C24—861no—
609#41—1724no—
610#41—1724no—
611#41—1728no—
612#41—1724no—
613#41—1724no—
614#41—1728no—
615C2×Q8—21no—
616C2×Q8—22no—
617C2×Q8—22no—
618C2×Q8—432no—
619C2×Q8—432no—
620C2×Q8—861no—
621C2×Q8—861no—
622C2×Q8—862no—
623C2×Q8—862no—
624C2×Q8—862no—
625C2×Q8—862no—
626C2×Q8C23×D4312yes—
627C2×D4—21no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—432no—
631C2×D4—432no—
632C2×D4—864no—
633C2×D4—864no—
634C2×D4—864no—
635C2×D4—864no—
636C2×D4—864no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—862no—
640C2×D4—862no—
641C2×D4—862no—
642C2×D4—862no—
643C2×D4—1724no—
644C2×D4—1724no—
645C2×D4—1724no—
646C2×D4—1724no—
647C2×D4—1724no—
648C2×D4C23×D4312yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—431no—
653C22×C4—431no—
654C22×C4—431no—
655C22×C4—434no—
656C22×C4—432no—
657C22×C4—432no—
658C22×C4—434no—
659C22×C4—864no—
660C22×C4—864no—
661C22×C4—864no—
662C22×C4—864no—
663C22×C4—862no—
664C22×C4—862no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—1722no—
668C22×C4—1724no—
669C22×C4—1724no—
670C22×C4—1724no—
671C22×C4D4×D4311yescharacteristic
672C22×C4D4×D4311yescharacteristic
673C22×C4C23×D4311yescharacteristic
674Q16—1724no—
675Q16—1724no—
676SD16—1724no—
677SD16—1724no—
678SD16—1724no—
679SD16—1724no—
680D8—1724no—
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—24no—
691C4⋊C4—24no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—864no—
695C4⋊C4—864no—
696C4⋊C4—864no—
697C4⋊C4—864no—
698C4⋊C4C23×D4312yes—
699C4⋊C4C23×D4312yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—864no—
707C22⋊C4—864no—
708C22⋊C4—864no—
709C42—434no—
710C42—434no—
711C42—432no—
712C42—432no—
713C42—864no—
714C42D4×D4312yes—
715C42C23×D4312yes—
716C23—22no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—432no—
721C23—862no—
722C23—862no—
723C23—862no—
724C23—862no—
725C23—862no—
726C23—1722no—
727C23—1722no—
728C23—1722no—
729C23—1722no—
730C23—1722no—
731C23—1722no—
732C23C2×D4×D4311yescharacteristic
733Q8—22no—
734Q8—22no—
735Q8—42no—
736Q8—862no—
737Q8—862no—
738Q8—862no—
739Q8—862no—
740Q8—1722no—
741Q8—1722no—
742D4—22no—
743D4—22no—
744D4—42no—
745D4—862no—
746D4—862no—
747D4—862no—
748D4—862no—
749D4—1728no—
750D4—1728no—
751D4—1728no—
752D4—1728no—
753D4—1728no—
754D4—1722no—
755D4—1722no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—434no—
765C2×C4—432no—
766C2×C4—432no—
767C2×C4—432no—
768C2×C4—868no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—864no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—1724no—
777C2×C4—1728no—
778C2×C4—1728no—
779C2×C4—1728no—
780C2×C4—1722no—
781C2×C4—1722no—
782C2×C4C2×D4×D4312yes—
783C2×C4C2×D4×D4312yes—
784C2×C4C2×D4×D4311yescharacteristic
785C2×C4#1306337112yes—
786C2×C4#1306337112yes—
787C2×C4C24×D4311yescharacteristic
788C8—22no—
789C8—22no—
790C8—862no—
791C8—862no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—84no—
796C22—862no—
797C22—862no—
798C22—862no—
799C22—3444no—
800C22—3444no—
801C22—1722no—
802C22—1722no—
803C22—1722no—
804C22—1722no—
805C22—1722no—
806C22—1722no—
807C22—1724no—
808C22#1458346712yes—
809C22#135×D4312yes—
810C22#1458369612yes—
811C22C22×D4×D4311yescharacteristic
812C4—22no—
813C4—22no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—434no—
818C4—862no—
819C4—862no—
820C4—1722no—
821C4—1722no—
822C4#1458346712yes—
823C4C2×#1306337111yescharacteristic
824C4C2×#1306337111yescharacteristic
825C2—82no—
826C2—3442no—
827C2—3442no—
828C2—1722no—
829C2#1914557214yesdirect product factor
830C2C2×#1458346711yescharacteristic
831C2C2×#135×D4311yescharacteristic
832C2C2×#1458369611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#488C2
socleC23×C43C22×D4
hypercenterC2×#488D43
hypocenterC43C2×#3212
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#14583448C2semidirect
2. C2×#14583434C2semidirect
3. #19145572C2direct (N × H)
4. C2×#14583283C2semidirect
5. C2×#14583281C2semidirect
6. C2×#14583256C2semidirect
7. C2×#14583108C2semidirect
8. C2×#14583098C2semidirect
9. C2×#14583103C2semidirect
10. C2×#14583093C2semidirect
11. C2×#14583064C2semidirect
12. C2×#14583062C2semidirect
13. C2×#14583047C2semidirect
14. C2×#14583045C2semidirect
15. C2×#14582950C2semidirect
16. C2×C43×#488C2semidirect
28. #14583448C22semidirect
32. #14583434C22semidirect
48. #14583283C22semidirect
49. #14583281C22semidirect
50. #14583256C22semidirect
51. #14583108C22semidirect
52. #14583103C22semidirect
53. #14583098C22semidirect
54. #14583093C22semidirect
55. #14583064C22semidirect
56. #14583062C22semidirect
57. #14583047C22semidirect
58. #14583045C22semidirect
59. #14582950C22semidirect
71. C43×#488C22semidirect
415. C2×#488D43semidirect
426. C2×C43#3212semidirect
469. #488C2×D43semidirect
493. C43C2×#3212semidirect
829. C2#19145572direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834482
C2×#145834342
#191455722
C2×#145832832
C2×#145832812
C2×#145832562
C2×#145831082
C2×#145830982
C2×#145831032
C2×#145830932
C2×#145830642
C2×#145830622
C2×#145830472
C2×#145830452
C2×#145829502
C2×C43×#4882
C2×#321243