Finite Group Databasebeta

← C2×#19145566 #25967812

Subgroups — C2×#19145566 #25967812

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×#14583428C211yesmaximal, characteristic, complemented
3#19145566C2116yesmaximal, direct product factor
4C2×#14583281C211yesmaximal, characteristic, complemented
5C2×#14583254C211yesmaximal, characteristic, complemented
6C2×#14583253C211yesmaximal, characteristic, complemented
7C2×#14583107C211yesmaximal, characteristic, complemented
8C2×#14583097C211yesmaximal, characteristic, complemented
9C2×#14583102C211yesmaximal, characteristic, complemented
10C2×#14583092C211yesmaximal, characteristic, complemented
11C2×#14583060C211yesmaximal, characteristic, complemented
12C2×#14583058C211yesmaximal, characteristic, complemented
13C2×#14583043C211yesmaximal, characteristic, complemented
14C2×#14583041C211yesmaximal, characteristic, complemented
15C2×#14582950C211yesmaximal, characteristic, complemented
16C2×C43×#495C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23#14583448—24no—
24#14583448C2218yescomplemented
25C2×#13063323C2211yescharacteristic
26C2×#13063321C2211yescharacteristic
27#14583428—24no—
28#14583428C2218yescomplemented
29C2×#13063318—21no—
30C2×#13063317C2211yescharacteristic
31C2×#13063313C2211yescharacteristic
32C2×#13063307—21no—
33C2×#13063301C2211yescharacteristic
34C2×#13063298—21no—
35C2×#13063298—21no—
36C2×#13063296C2211yescharacteristic
37C2×Q8×Dic43C2211yescharacteristic
38C2×D4×Dic43C2211yescharacteristic
39C2×(C22⋊D43)⋊C4—21no—
40C2×(C22⋊D43)⋊C4—21no—
41C2×(C22⋊D43)⋊C4—21no—
42C2×#13063281—21no—
43C2×C42×D43C2211yescharacteristic
44#14583281C2218yescomplemented
45#14583254C2218yescomplemented
46#14583253C2218yescomplemented
47#14583107C2218yescomplemented
48#14583102C2218yescomplemented
49#14583097C2218yescomplemented
50#14583092C2218yescomplemented
51#14583060C2218yescomplemented
52#14583058C2218yescomplemented
53#14583043C2218yescomplemented
54#14583041C2218yescomplemented
55#14582950C2218yescomplemented
56C2×Dic43⋊C8C2211yescharacteristic
57C2×Dic43⋊C8C2211yescharacteristic
58C2×#13063250C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C4×C43⋊C8C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C22×SD16×C43C2211yescharacteristic
72C22×D8×C43C2211yescharacteristic
73C2×#124×C43C2211yescharacteristic
74C2×#124×C43C2211yescharacteristic
75C43×#495C2218yescomplemented
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×D172—21no—
87C22×D172C2311yescharacteristic
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C23×Dic43—21no—
93C23×Dic43—21no—
94C22×C4×D43—21no—
95C22×C4×D43D411yescharacteristic
96C22×C4×D43D411yescharacteristic
97C22×C4×D43C2311yescharacteristic
98C2×#10621885—42no—
99C2×#10621885C2314yes—
100C2×#10621883—42no—
101C2×#10621883C2314yes—
102C2×#10621884—42no—
103C2×#10621884C2314yes—
104C2×#10621882—42no—
105C2×#10621882C2314yes—
106C22×C43⋊C8C2311yescharacteristic
107C22×C43⋊C8C2311yescharacteristic
108#13063323—22no—
109#13063323C2314yes—
110#13063321—22no—
111#13063321C2314yes—
112#13063318—28no—
113#13063317—22no—
114#13063317C2314yes—
115#13063313—22no—
116#13063313C2314yes—
117#13063307—28no—
118#13063301—22no—
119#13063301C2314yes—
120#13063298—28no—
121#13063298—28no—
122#13063296—22no—
123#13063296C2314yes—
124Q8×Dic43—22no—
125Q8×Dic43C2314yes—
126D4×Dic43—22no—
127D4×Dic43C2314yes—
128(C22⋊D43)⋊C4—28no—
129(C22⋊D43)⋊C4—28no—
130(C22⋊D43)⋊C4—28no—
131#13063281—28no—
132C2×C4⋊Dic43—21no—
133C2×C4⋊Dic43C2311yescharacteristic
134C2×C4⋊Dic43C2311yescharacteristic
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43D411yescharacteristic
147C2×C4×Dic43D411yescharacteristic
148C2×C4×Dic43C2311yescharacteristic
149C42×D43D414yes—
150C42×D43C2314yes—
151Dic43⋊C8C2314yes—
152Dic43⋊C8C2314yes—
153#13063250C2314yes—
154#13063250C2314yes—
155#13063249C2314yes—
156#13063249C2314yes—
157#13063247C2314yes—
158#13063247C2314yes—
159#13063246C2314yes—
160#13063246C2314yes—
161(C2×D43)⋊C8C2314yes—
162(C2×D43)⋊C8C2314yes—
163C4×C43⋊C8C2314yes—
164C22×Q8×C43C2311yescharacteristic
165C22×Q8×C43C2311yescharacteristic
166C22×D4×C43C2311yescharacteristic
167C22×D4×C43C2311yescharacteristic
168C2×Q16×C43—42no—
169C2×Q16×C43C2314yes—
170C2×SD16×C43—42no—
171C2×SD16×C43—42no—
172C2×SD16×C43C2314yes—
173C2×SD16×C43C2314yes—
174C2×D8×C43—42no—
175C2×D8×C43C2314yes—
176C22×C8×C43C2311yescharacteristic
177C22×C8×C43C2311yescharacteristic
178#124×C43—22no—
179#124×C43—22no—
180#124×C43C2314yes—
181#124×C43C2314yes—
182C2×C22⋊C4×C43—21no—
183C2×C22⋊C4×C43—21no—
184C2×C22⋊C4×C43—21no—
185C2×C22⋊C4×C43—21no—
186C2×C42×C43C2311yescharacteristic
187C4×C8×C43C2314yes—
188C24×C43—21no—
189C24×C43—21no—
190C23×D43—21no—
191C23×D43C2×D411yescharacteristic
192C2×Q8×C43—21no—
193C2×Q8×C43—21no—
194C2×Q8×C43—22no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43—22no—
198C2×Q8×C43C2412yes—
199C2×Q8×C43C2412yes—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—22no—
203C2×D4×C43—22no—
204C2×D4×C43—22no—
205C2×D4×C43—22no—
206C2×D4×C43C2412yes—
207C2×D4×C43C2412yes—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2411yescharacteristic
213C2×C22⋊D43—24no—
214C2×C22⋊D43—24no—
215C2×C22⋊D43—24no—
216C2×C22⋊D43—24no—
217C2×C22⋊D43—44no—
218C2×C22⋊D43—44no—
219C2×C22⋊D43—44no—
220C2×C22⋊D43—44no—
221C22×Dic43—24no—
222C22×Dic43—24no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—44no—
227C22×Dic43—44no—
228C22×Dic43C2×D411yescharacteristic
229C22×Dic43C2×D411yescharacteristic
230C22×Dic43C2×D411yescharacteristic
231#10621902—44no—
232#10621902—44no—
233#10621902—48no—
234#10621900—44no—
235#10621900—44no—
236#10621900—48no—
237C2×D172—21no—
238C2×D172—24no—
239C2×D172—22no—
240C2×D172—22no—
241C2×D172—44no—
242C2×D172C2412yes—
243C2×C4×D43—22no—
244C2×C4×D43—22no—
245C2×C4×D43—24no—
246C2×C4×D43—24no—
247C2×C4×D43—42no—
248C2×C4×D43—44no—
249C2×C4×D43C2×D412yes—
250C2×C4×D43C2×D414yes—
251C2×C4×D43C2×D414yes—
252C2×C4×D43C2412yes—
253C2×Dic86—22no—
254C2×Dic86—22no—
255C2×Dic86—21no—
256C2×Dic86C2412yes—
257Q16×C43—44no—
258SD16×C43—44no—
259SD16×C43—44no—
260D8×C43—44no—
261C2×C8×C43—22no—
262C2×C8×C43—22no—
263C2×C8×C43C2412yes—
264C2×C8×C43C2412yes—
265C22⋊C4×C43—24no—
266C22⋊C4×C43—24no—
267C22⋊C4×C43—24no—
268C22⋊C4×C43—24no—
269C42×C43C2×D412yes—
270C42×C43C2412yes—
271C22⋊Dic43—24no—
272C22⋊Dic43—24no—
273#10621885—44no—
274#10621884—44no—
275#10621883—44no—
276#10621882—44no—
277(C2×D43)⋊C4—24no—
278(C2×D43)⋊C4—24no—
279(C2×D43)⋊C4—24no—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43—24no—
283C4⋊Dic43C2412yes—
284C4⋊Dic43C2412yes—
285Dic43⋊C4—24no—
286Dic43⋊C4—24no—
287Dic43⋊C4—24no—
288Dic43⋊C4—24no—
289Dic43⋊C4—24no—
290C4×Dic43—24no—
291C4×Dic43C2×D412yes—
292C4×Dic43C2×D414yes—
293C4×Dic43C2×D414yes—
294C4×Dic43C2412yes—
295C2×C43⋊C8—22no—
296C2×C43⋊C8—22no—
297C2×C43⋊C8C2412yes—
298C2×C43⋊C8C2412yes—
299C23×C43—22no—
300C23×C43—22no—
301C23×C43—42no—
302C23×C43—42no—
303C23×C43—42no—
304C23×C43—42no—
305C23×C43—42no—
306C23×C43—42no—
307C23×C43C22×D411yescharacteristic
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—42no—
313C22×D43—42no—
314C22×D43—42no—
315C22×D43C22×D412yes—
316Q8×C43—22no—
317Q8×C43—22no—
318Q8×C43—22no—
319Q8×C43—22no—
320Q8×C43—42no—
321Q8×C43—42no—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—22no—
325D4×C43—22no—
326D4×C43—42no—
327D4×C43—42no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—42no—
333C2×C4×C43—42no—
334C2×C4×C43C22×D412yes—
335C2×C4×C43C22×D412yes—
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43H(5,𝔽2)12yes—
338C2×C4×C43H(5,𝔽2)12yes—
339C2×C4×C43C2511yescharacteristic
340C22⋊D43—48no—
341C22⋊D43—48no—
342C22⋊D43—48no—
343C22⋊D43—48no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—48no—
350C2×Dic43—42no—
351C2×Dic43—42no—
352C2×Dic43—42no—
353C2×Dic43—48no—
354C2×Dic43#13514yes—
355C2×Dic43C22×D412yes—
356C2×Dic43C22×D412yes—
357C2×Dic43C22×D412yes—
358D172—22no—
359D172—22no—
360D172—48no—
361D172—42no—
362C4×D43—24no—
363C4×D43—22no—
364C4×D43—22no—
365C4×D43—28no—
366C4×D43—44no—
367C4×D43—48no—
368Dic86—22no—
369Dic86—22no—
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—42no—
380C22×C43—42no—
381C22×C43—42no—
382C22×C43—84no—
383C22×C43—84no—
384C22×C43#53512yes—
385C22×C43C2×#13512yes—
386C22×C43#57512yes—
387C22×C43C23×D411yescharacteristic
388C2×D43—22no—
389C2×D43—22no—
390C2×D43—22no—
391C2×D43—44no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—84no—
396C4×C43—22no—
397C4×C43—22no—
398C4×C43—42no—
399C4×C43—42no—
400C4×C43#53512yes—
401C4×C43C2×H(5,𝔽2)11yescharacteristic
402C4×C43C2×H(5,𝔽2)11yescharacteristic
403Dic43—22no—
404Dic43—22no—
405Dic43—42no—
406Dic43—42no—
407Dic43—42no—
408Dic43C2×#13514yes—
409C2×#532—431no—
410C2×#529—431no—
411#3212—4316no—
412C2×#495—431no—
413C2×#495D4311yescharacteristic, complemented
414C2×#488—431no—
415C2×#488—431no—
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—82no—
427C2×C43#321214yescomplemented
428C2×C43C2×#53511yescharacteristic
429C2×C43C22×#13511yescharacteristic
430C2×C43C2×#57511yescharacteristic
431D43—42no—
432D43—82no—
433C22×#41—431no—
434C22×#41—431no—
435C22×Q16—431no—
436C22×Q16C2×D4311yescharacteristic
437C22×SD16—431no—
438C22×SD16—431no—
439C22×SD16C2×D4311yescharacteristic
440C22×SD16C2×D4311yescharacteristic
441C22×D8—431no—
442C22×D8C2×D4311yescharacteristic
443#532—438no—
444#532—864no—
445C2×C4⋊Q8—431no—
446C2×#127—431no—
447#529—438no—
448#529—864no—
449C2×#126—861no—
450C2×#125—431no—
451C2×#124—431no—
452C2×#124C2×D4311yescharacteristic
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#495C2×D4318yescomplemented
468#488—438no—
469#488—438no—
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×#103—431no—
484C2×#103—431no—
485C2×#102—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
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×Q8C22×D4311yescharacteristic
504C22×Q8C22×D4311yescharacteristic
505C22×D4—431no—
506C22×D4—861no—
507C22×D4—861no—
508C22×D4—861no—
509C22×D4—861no—
510C22×D4—861no—
511C22×D4C22×D4311yescharacteristic
512C22×D4C22×D4311yescharacteristic
513C23×C4—431no—
514C23×C4—431no—
515C23×C4—431no—
516C23×C4—861no—
517C23×C4—861no—
518C23×C4—861no—
519C2×Q16—42no—
520C2×Q16—434no—
521C2×Q16—1722no—
522C2×Q16C22×D4314yes—
523C2×SD16—42no—
524C2×SD16—42no—
525C2×SD16—434no—
526C2×SD16—434no—
527C2×SD16—1722no—
528C2×SD16—1722no—
529C2×SD16C22×D4314yes—
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—862no—
541#127—434no—
542#127—862no—
543#126—868no—
544#125—434no—
545#125—862no—
546#124—22no—
547#124—22no—
548#124—434no—
549#124—862no—
550#124C22×D4314yes—
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—431no—
568C2×C4⋊C4—431no—
569C2×C4⋊C4—861no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4—861no—
574C2×C4⋊C4—861no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
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#103—434no—
596#103—434no—
597#102—434no—
598#102—434no—
599#102—434no—
600#102—434no—
601C22⋊C8—434no—
602C22⋊C8—434no—
603C4×C8—434no—
604C4×C8C22×D4314yes—
605C24—21no—
606C24—21no—
607C24—431no—
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—21no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—22no—
621C2×Q8—432no—
622C2×Q8—861no—
623C2×Q8—862no—
624C2×Q8—862no—
625C2×Q8C23×D4312yes—
626C2×Q8C23×D4312yes—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—432no—
634C2×D4—864no—
635C2×D4—864no—
636C2×D4—864no—
637C2×D4—864no—
638C2×D4—864no—
639C2×D4—861no—
640C2×D4—862no—
641C2×D4—862no—
642C2×D4—1724no—
643C2×D4—1724no—
644C2×D4—1724no—
645C2×D4—1724no—
646C2×D4—1724no—
647C2×D4C23×D4312yes—
648C2×D4C23×D4312yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—431no—
652C22×C4—431no—
653C22×C4—431no—
654C22×C4—434no—
655C22×C4—432no—
656C22×C4—432no—
657C22×C4—434no—
658C22×C4—864no—
659C22×C4—864no—
660C22×C4—864no—
661C22×C4—864no—
662C22×C4—862no—
663C22×C4—862no—
664C22×C4—861no—
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—44no—
675Q16—1724no—
676SD16—44no—
677SD16—44no—
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—432no—
691C4⋊C4—432no—
692C4⋊C4—864no—
693C4⋊C4—864no—
694C4⋊C4—864no—
695C4⋊C4—864no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—864no—
699C4⋊C4—864no—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
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—22no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—432no—
725C23—862no—
726C23—862no—
727C23—862no—
728C23—862no—
729C23—1722no—
730C23—1722no—
731C23—1722no—
732C23C2×D4×D4311yescharacteristic
733Q8—22no—
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8—42no—
738Q8—42no—
739Q8—862no—
740Q8—862no—
741Q8—1722no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—42no—
747D4—42no—
748D4—862no—
749D4—862no—
750D4—1728no—
751D4—1728no—
752D4—1728no—
753D4—1728no—
754D4—1728no—
755D4—1722no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—434no—
763C2×C4—432no—
764C2×C4—432no—
765C2×C4—432no—
766C2×C4—868no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—864no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—1724no—
776C2×C4—1728no—
777C2×C4—1728no—
778C2×C4—1728no—
779C2×C4—1722no—
780C2×C4—1722no—
781C2×C4—1722no—
782C2×C4C2×D4×D4312yes—
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—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—84no—
799C22—84no—
800C22—862no—
801C22—862no—
802C22—862no—
803C22—3444no—
804C22—1722no—
805C22—1722no—
806C22—1722no—
807C22—1724no—
808C22#1458346212yes—
809C22#135×D4312yes—
810C22#1458369612yes—
811C22C22×D4×D4311yescharacteristic
812C4—22no—
813C4—22no—
814C4—42no—
815C4—42no—
816C4—434no—
817C4—862no—
818C4—862no—
819C4—1722no—
820C4—1722no—
821C4—1722no—
822C4#1458346212yes—
823C4C2×#1306337011yescharacteristic
824C4C2×#1306337011yescharacteristic
825C2—82no—
826C2—82no—
827C2—3442no—
828C2—1722no—
829C2#1914556614yesdirect product factor
830C2C2×#1458346211yescharacteristic
831C2C2×#135×D4311yescharacteristic
832C2C2×#1458369611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#495C2
socleC23×C43C22×D4
hypercenterC2×#495D43
hypocenterC43C2×#3212
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C2×#14583448C2semidirect
2. C2×#14583428C2semidirect
3. #19145566C2direct (N × H)
4. C2×#14583281C2semidirect
5. C2×#14583254C2semidirect
6. C2×#14583253C2semidirect
7. C2×#14583107C2semidirect
8. C2×#14583097C2semidirect
9. C2×#14583102C2semidirect
10. C2×#14583092C2semidirect
11. C2×#14583060C2semidirect
12. C2×#14583058C2semidirect
13. C2×#14583043C2semidirect
14. C2×#14583041C2semidirect
15. C2×#14582950C2semidirect
16. C2×C43×#495C2semidirect
24. #14583448C22semidirect
28. #14583428C22semidirect
44. #14583281C22semidirect
45. #14583254C22semidirect
46. #14583253C22semidirect
47. #14583107C22semidirect
48. #14583102C22semidirect
49. #14583097C22semidirect
50. #14583092C22semidirect
51. #14583060C22semidirect
52. #14583058C22semidirect
53. #14583043C22semidirect
54. #14583041C22semidirect
55. #14582950C22semidirect
75. C43×#495C22semidirect
413. C2×#495D43semidirect
427. C2×C43#3212semidirect
467. #495C2×D43semidirect
493. C43C2×#3212semidirect
829. C2#19145566direct (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×#145834282
#191455662
C2×#145832812
C2×#145832542
C2×#145832532
C2×#145831072
C2×#145830972
C2×#145831022
C2×#145830922
C2×#145830602
C2×#145830582
C2×#145830432
C2×#145830412
C2×#145829502
C2×C43×#4952
C2×#321243