Finite Group Databasebeta

← C2×#19145690 #25967953

Subgroups — C2×#19145690 #25967953

Order 11008.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583523C211yesmaximal, characteristic, complemented
2C2×#14583467C211yesmaximal, characteristic, complemented
3#19145690C2116yesmaximal, direct product factor
4C2×#14583288C211yesmaximal, characteristic, complemented
5C2×#14583281C211yesmaximal, characteristic, complemented
6C2×#14583247C211yesmaximal, characteristic, complemented
7C2×#14583124C211yesmaximal, characteristic, complemented
8C2×#14583098C211yesmaximal, characteristic, complemented
9C2×#14583117C211yesmaximal, characteristic, complemented
10C2×#14583093C211yesmaximal, characteristic, complemented
11C2×#14583064C211yesmaximal, characteristic, complemented
12C2×#14583047C211yesmaximal, characteristic, complemented
13C2×#14583051C211yesmaximal, characteristic, complemented
14C2×#14583034C211yesmaximal, characteristic, complemented
15C2×#14582961C211yesmaximal, characteristic, complemented
16C2×C43×#489C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C22×#10621885C2211yescharacteristic, complemented
20C22×#10621873C2211yescharacteristic
21C22×#10621873C2211yescharacteristic, complemented
22C22×#10621883C2211yescharacteristic
23C22×#10621884C2211yescharacteristic, complemented
24C22×D344C2211yescharacteristic
25C22×D344C2211yescharacteristic, complemented
26C22×#10621882C2211yescharacteristic
27#14583523—24no—
28#14583523C2218yescomplemented
29#14583467—24no—
30#14583467C2218yescomplemented
31C2×#13063322C2211yescharacteristic
32C2×#13063321C2211yescharacteristic
33C2×#13063320—21no—
34C2×#13063314—21no—
35C2×#13063314C2211yescharacteristic
36C2×#13063313C2211yescharacteristic, complemented
37C2×#13063310—21no—
38C2×#13063305C2211yescharacteristic
39C2×#13063301—21no—
40C2×#13063300C2211yescharacteristic
41C2×#13063298—21no—
42C2×#13063298—21no—
43C2×#13063295—21no—
44C2×#13063295—21no—
45C2×#13063290C2211yescharacteristic, complemented
46C2×#13063287C2211yescharacteristic, complemented
47C2×#13063282C2211yescharacteristic
48#14583288C2218yescomplemented
49#14583281C2218yescomplemented
50#14583247C2218yescomplemented
51#14583124C2218yescomplemented
52#14583117C2218yescomplemented
53#14583098C2218yescomplemented
54#14583093C2218yescomplemented
55#14583064C2218yescomplemented
56#14583051C2218yescomplemented
57#14583047C2218yescomplemented
58#14583034C2218yescomplemented
59#14582961C2218yescomplemented
60C2×Dic43⋊C8C2211yescharacteristic, complemented
61C2×Dic43⋊C8C2211yescharacteristic, complemented
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic, complemented
65C2×#13063245C2211yescharacteristic, complemented
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C4×C43⋊C8C2211yescharacteristic, complemented
69C2×C4⋊Q8×C43C2211yescharacteristic, complemented
70C2×#124×C43C2211yescharacteristic
71C43×#489C2218yescomplemented
72C2×#103×C43C2211yescharacteristic, complemented
73C2×#103×C43C2211yescharacteristic, complemented
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621902—22no—
79C2×#10621902—42no—
80C2×#10621902—42no—
81C2×#10621902C2314yes—
82C22×Dic86C2311yescharacteristic
83C22×D172—21no—
84C22×D172—21no—
85C22×D172—21no—
86C22×D172—21no—
87C22×D172C2311yescharacteristic
88C22×D172C2311yescharacteristic
89C22×D172C2311yescharacteristic
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C2×D4×D43—22no—
94C2×D4×D43—42no—
95C2×D4×D43—42no—
96C2×D4×D43C2314yes—
97C22×C4×D43—21no—
98C22×C4×D43—21no—
99C22×C4×D43C2311yescharacteristic
100C2×#10621885—42no—
101C2×#10621885C2314yescomplemented
102C2×#10621873—42no—
103C2×#10621873—42no—
104C2×#10621873C2314yes—
105C2×#10621873C2314yescomplemented
106C2×#10621883—42no—
107C2×#10621883C2314yes—
108C2×#10621884—42no—
109C2×#10621884C2314yescomplemented
110C2×D344—42no—
111C2×D344—42no—
112C2×D344C2314yes—
113C2×D344C2314yescomplemented
114C2×#10621882—42no—
115C2×#10621882C2314yes—
116C22×C43⋊C8C2311yescharacteristic
117C22×C43⋊C8C2311yescharacteristic
118#13063322—22no—
119#13063322C2314yes—
120#13063321—22no—
121#13063321C2314yes—
122#13063320—28no—
123#13063314—28no—
124#13063314—22no—
125#13063314C2314yes—
126#13063313—22no—
127#13063313C2314yescomplemented
128#13063310—28no—
129#13063305—22no—
130#13063305C2314yes—
131#13063301—28no—
132#13063300—22no—
133#13063300C2314yes—
134#13063298—28no—
135#13063298—28no—
136#13063295—28no—
137#13063295—28no—
138#13063290—22no—
139#13063290C2314yescomplemented
140#13063287—22no—
141#13063287C2314yescomplemented
142#13063282D414yes—
143#13063282C2314yes—
144C2×C4⋊Dic43—21no—
145C2×Dic43⋊C4—21no—
146C2×Dic43⋊C4D411yescharacteristic
147C2×Dic43⋊C4D411yescharacteristic
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×(C2×D43)⋊C4—21no—
154C2×(C2×D43)⋊C4—21no—
155C2×(C2×D43)⋊C4D411yescharacteristic
156C2×(C2×D43)⋊C4D411yescharacteristic
157C2×C4×Dic43—21no—
158C2×C4×Dic43C2311yescharacteristic
159Dic43⋊C8C2314yescomplemented
160Dic43⋊C8C2314yescomplemented
161#13063245C2314yes—
162#13063245C2314yes—
163#13063245C2314yescomplemented
164#13063245C2314yescomplemented
165(C2×D43)⋊C8C2314yes—
166(C2×D43)⋊C8C2314yes—
167C4×C43⋊C8C2314yescomplemented
168C22×Q8×C43—21no—
169C22×Q8×C43C2311yescharacteristic
170C22×D4×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173C4⋊Q8×C43—22no—
174C4⋊Q8×C43C2314yescomplemented
175#124×C43—22no—
176#124×C43C2314yes—
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×C43C2314yescomplemented
184#103×C43C2314yescomplemented
185#102×C43C2314yes—
186#102×C43C2314yes—
187#97×C43C2314yescomplemented
188C24×C43—21no—
189C23×D43—21no—
190C23×D43—21no—
191C23×D43—21no—
192C23×D43—24no—
193C23×D43—44no—
194C23×D43—82no—
195C23×D43—82no—
196C23×D43C2×D411yescharacteristic
197C2×Q8×C43—21no—
198C2×Q8×C43—24no—
199C2×Q8×C43—22no—
200C2×Q8×C43—22no—
201C2×Q8×C43—82no—
202C2×Q8×C43C2412yes—
203C2×D4×C43—21no—
204C2×D4×C43—22no—
205C2×D4×C43—22no—
206C2×D4×C43C2412yes—
207C22×C4×C43—21no—
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—44no—
217C2×C22⋊D43—82no—
218C2×C22⋊D43—82no—
219C22×Dic43—21no—
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223#10621902—44no—
224#10621902—44no—
225#10621902—48no—
226D4×D43—44no—
227D4×D43—44no—
228D4×D43—48no—
229C2×D172—21no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—24no—
233C2×D172—24no—
234C2×D172—24no—
235C2×D172—24no—
236C2×D172—22no—
237C2×D172—22no—
238C2×D172—22no—
239C2×D172—22no—
240C2×D172—22no—
241C2×D172—22no—
242C2×D172—44no—
243C2×D172—82no—
244C2×D172—82no—
245C2×D172—82no—
246C2×D172C2412yes—
247C2×D172C2412yes—
248C2×D172C2412yes—
249C2×C4×D43—22no—
250C2×C4×D43—22no—
251C2×C4×D43—24no—
252C2×C4×D43—24no—
253C2×C4×D43—44no—
254C2×C4×D43—82no—
255C2×C4×D43C2×D412yes—
256C2×C4×D43C2412yes—
257C2×Dic86—22no—
258C2×Dic86—22no—
259C2×Dic86—21no—
260C2×Dic86C2412yes—
261C2×C8×C43—22no—
262C2×C8×C43—22no—
263C2×C8×C43C2412yes—
264C2×C8×C43C2412yes—
265C4⋊C4×C43—24no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43C2412yes—
269C4⋊C4×C43C2412yes—
270C22⋊C4×C43—24no—
271C22⋊C4×C43—24no—
272C42×C43C2×D412yes—
273C42×C43C2412yes—
274#10621885—44no—
275#10621884—44no—
276#10621883—44no—
277#10621882—44no—
278(C2×D43)⋊C4—24no—
279(C2×D43)⋊C4—24no—
280(C2×D43)⋊C4—24no—
281(C2×D43)⋊C4—24no—
282(C2×D43)⋊C4—24no—
283(C2×D43)⋊C4—24no—
284(C2×D43)⋊C4—24no—
285(C2×D43)⋊C4C2×D414yes—
286(C2×D43)⋊C4C2×D414yes—
287C4⋊Dic43—24no—
288Dic43⋊C4—24no—
289Dic43⋊C4C2×D414yes—
290Dic43⋊C4C2×D414yes—
291C4×Dic43—24no—
292C4×Dic43C2×D412yes—
293C4×Dic43C2412yes—
294C2×C43⋊C8—22no—
295C2×C43⋊C8—22no—
296C2×C43⋊C8C2412yes—
297C2×C43⋊C8C2412yes—
298D344—44no—
299D344—44no—
300#10621873—44no—
301#10621873—44no—
302C23×C43—22no—
303C23×C43—42no—
304C23×C43—42no—
305C23×C43—42no—
306C23×C43C22×D411yescharacteristic
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—48no—
314C22×D43—42no—
315C22×D43—42no—
316C22×D43—42no—
317C22×D43—42no—
318C22×D43—42no—
319C22×D43—42no—
320C22×D43—42no—
321C22×D43—42no—
322C22×D43—42no—
323C22×D43—84no—
324C22×D43—84no—
325C22×D43—816no—
326C22×D43C22×D412yes—
327Q8×C43—22no—
328Q8×C43—22no—
329Q8×C43—42no—
330Q8×C43—84no—
331D4×C43—22no—
332D4×C43—22no—
333D4×C43—42no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—42no—
340C2×C4×C43—42no—
341C2×C4×C43—42no—
342C2×C4×C43C22×D412yes—
343C2×C4×C43C22×D412yes—
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43H(5,𝔽2)12yes—
346C2×C4×C43H(5,𝔽2)12yes—
347C2×C4×C43C2511yescharacteristic
348C22⋊D43—48no—
349C22⋊D43—84no—
350C22⋊D43—84no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—42no—
356C2×Dic43C22×D412yes—
357C2×Dic43C22×D412yes—
358C2×Dic43C22×D412yes—
359D172—22no—
360D172—22no—
361D172—22no—
362D172—22no—
363D172—22no—
364D172—22no—
365D172—48no—
366D172—42no—
367D172—42no—
368D172—42no—
369D172—84no—
370D172—84no—
371D172—84no—
372C4×D43—24no—
373C4×D43—22no—
374C4×D43—22no—
375C4×D43—48no—
376C4×D43—84no—
377Dic86—22no—
378Dic86—22no—
379Dic86—42no—
380C8×C43—22no—
381C8×C43—22no—
382C43⋊C8—22no—
383C43⋊C8—22no—
384C2×#3224—431nomaximal, Sylow
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—42no—
388C22×C43—84no—
389C22×C43#53512yes—
390C22×C43#57612yes—
391C22×C43#57712yes—
392C22×C43C23×D411yescharacteristic
393C2×D43—22no—
394C2×D43—22no—
395C2×D43—22no—
396C2×D43—44no—
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—42no—
401C2×D43—42no—
402C2×D43—42no—
403C2×D43—42no—
404C2×D43—42no—
405C2×D43—42no—
406C2×D43—816no—
407C2×D43—84no—
408C2×D43—84no—
409C2×D43—84no—
410C4×C43—22no—
411C4×C43—22no—
412C4×C43—42no—
413C4×C43—42no—
414C4×C43—42no—
415C4×C43#53512yes—
416C4×C43C2×H(5,𝔽2)11yescharacteristic
417C4×C43C2×H(5,𝔽2)11yescharacteristic
418Dic43—22no—
419Dic43—22no—
420Dic43—22no—
421Dic43—42no—
422C2×#542—431no—
423C2×#535—431no—
424#3224—4316no—
425C2×#496—431no—
426C2×#495—431no—
427C2×#489D4311yescharacteristic, complemented
428C2×#486—431no—
429C2×#464—431no—
430C2×#460—431no—
431C2×#463—431no—
432C2×#459—431no—
433C2×#452—431no—
434C2×#449—431no—
435C2×#450—431no—
436C2×#447—431no—
437C2×#433—431no—
438C2×C43—82no—
439C2×C43#322414yescomplemented
440C2×C43C2×#53511yescharacteristic
441C2×C43C2×#57611yescharacteristic
442C2×C43C2×#57711yescharacteristic
443D43—42no—
444D43—82no—
445D43—82no—
446D43—82no—
447C22×#41—431no—
448C23×D4—431no—
449C22×Q16—431no—
450C22×SD16—431no—
451C22×SD16—431no—
452C22×SD16—431no—
453C22×SD16—431no—
454C22×D8—431no—
455C22×D8—431no—
456C22×D8—431no—
457#542—438no—
458#542—864no—
459#535—438no—
460#535—864no—
461C2×C4⋊Q8C2×D4311yescharacteristic, complemented
462C2×#127—431no—
463C2×#127—431no—
464C2×#126—861no—
465C2×#124—431no—
466C2×#124—431no—
467C2×#124—861no—
468C2×#124C2×D4311yescharacteristic
469C2×#123—861no—
470C2×C22⋊Q8—431no—
471C2×C22⋊Q8—861no—
472C2×#121—431no—
473C2×#121—861no—
474C2×#121—861no—
475C2×#120—861no—
476C2×#120—861no—
477C2×C4×Q8—431no—
478C2×C4×D4—431no—
479C2×#117—431no—
480#496—438no—
481#495—438no—
482#489C2×D4318yescomplemented
483#486—438no—
484#464—438no—
485#463—438no—
486#460—438no—
487#459—438no—
488#452—438no—
489#450—438no—
490#449—438no—
491#447—438no—
492#433—438no—
493C2×C4⋊C8—431no—
494C2×C4⋊C8—431no—
495C2×#103C2×D4311yescharacteristic, complemented
496C2×#103C2×D4311yescharacteristic, complemented
497C2×#102—431no—
498C2×#102—431no—
499C2×#102—431no—
500C2×#102—431no—
501C2×#102C2×D4311yescharacteristic
502C2×#102C2×D4311yescharacteristic
503C2×C22⋊C8—431no—
504C2×C22⋊C8—431no—
505C2×#97C2×D4311yescharacteristic, complemented
506C2×C4×C8—431no—
507C43C2×#322411yescharacteristic, complemented, Sylow
508C25—861no—
509C2×#41—434no—
510C2×#41—862no—
511C2×#41—1722no—
512C2×#41—1722no—
513C22×Q8—21no—
514C22×Q8—431no—
515C22×Q8C22×D4311yescharacteristic
516C22×D4—434no—
517C22×D4—431no—
518C22×D4—431no—
519C22×D4—431no—
520C22×D4—861no—
521C22×D4—861no—
522C22×D4—862no—
523C22×D4—861no—
524C22×D4—861no—
525C22×D4—861no—
526C22×D4—861no—
527C22×D4—861no—
528C22×D4—1722no—
529C22×D4—1722no—
530C22×D4C22×D4311yescharacteristic
531C23×C4—431no—
532C23×C4—861no—
533C23×C4—861no—
534C2×Q16—434no—
535C2×Q16—1722no—
536C2×SD16—434no—
537C2×SD16—434no—
538C2×SD16—434no—
539C2×SD16—434no—
540C2×SD16—1722no—
541C2×SD16—1722no—
542C2×SD16—1722no—
543C2×SD16—1722no—
544C2×D8—434no—
545C2×D8—434no—
546C2×D8—434no—
547C2×D8—1722no—
548C2×D8—1722no—
549C2×D8—1722no—
550C22×C8—431no—
551C22×C8—431no—
552C22×C8C22×D4311yescharacteristic
553C22×C8C22×D4311yescharacteristic
554C4⋊Q8—22no—
555C4⋊Q8C22×D4314yescomplemented
556#127—434no—
557#127—434no—
558#127—862no—
559#127—862no—
560#126—868no—
561#124—22no—
562#124—434no—
563#124—434no—
564#124—862no—
565#124—868no—
566#124—862no—
567#124C22×D4314yes—
568#123—868no—
569C22⋊Q8—434no—
570C22⋊Q8—862no—
571C22⋊Q8—868no—
572#121—434no—
573#121—868no—
574#121—868no—
575#121—862no—
576#120—868no—
577#120—868no—
578C4×Q8—434no—
579C4×Q8—862no—
580C4×D4—434no—
581C4×D4—862no—
582#117—434no—
583#117—434no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—431no—
586C2×C4⋊C4—431no—
587C2×C4⋊C4—861no—
588C2×C4⋊C4—861no—
589C2×C4⋊C4C22×D4311yescharacteristic
590C2×C4⋊C4C22×D4311yescharacteristic
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—431no—
594C2×C22⋊C4—431no—
595C2×C22⋊C4—861no—
596C2×C22⋊C4—861no—
597C2×C22⋊C4—861no—
598C2×C22⋊C4—861no—
599C2×C22⋊C4—861no—
600C2×C22⋊C4—861no—
601C2×C22⋊C4—861no—
602C2×C42—431no—
603C2×C42—861no—
604C2×C42C22×D4311yescharacteristic
605C4⋊C8—434no—
606C4⋊C8—434no—
607#103C22×D4314yescomplemented
608#103C22×D4314yescomplemented
609#102—434no—
610#102—434no—
611#102—434no—
612#102—434no—
613#102C22×D4314yes—
614#102C22×D4314yes—
615C22⋊C8—434no—
616C22⋊C8—434no—
617#97C22×D4314yescomplemented
618C4×C8—434no—
619C24—21no—
620C24—431no—
621C24—864no—
622C24—861no—
623C24—861no—
624C24—861no—
625C24—3442no—
626C24—3442no—
627C24—1724no—
628#41—1724no—
629#41—1724no—
630#41—1728no—
631C2×Q8—21no—
632C2×Q8—24no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—82no—
636C2×Q8—432no—
637C2×Q8—861no—
638C2×Q8—862no—
639C2×Q8—862no—
640C2×Q8C23×D4312yes—
641C2×D4—21no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—432no—
645C2×D4—432no—
646C2×D4—432no—
647C2×D4—864no—
648C2×D4—864no—
649C2×D4—864no—
650C2×D4—864no—
651C2×D4—864no—
652C2×D4—864no—
653C2×D4—864no—
654C2×D4—861no—
655C2×D4—861no—
656C2×D4—861no—
657C2×D4—862no—
658C2×D4—862no—
659C2×D4—862no—
660C2×D4—862no—
661C2×D4—862no—
662C2×D4—862no—
663C2×D4—3442no—
664C2×D4—3442no—
665C2×D4—3442no—
666C2×D4—3442no—
667C2×D4—3442no—
668C2×D4—1724no—
669C2×D4—1724no—
670C2×D4—1724no—
671C2×D4—1728no—
672C2×D4—1724no—
673C2×D4C23×D4312yes—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—431no—
678C22×C4—431no—
679C22×C4—431no—
680C22×C4—432no—
681C22×C4—432no—
682C22×C4—864no—
683C22×C4—864no—
684C22×C4—862no—
685C22×C4—862no—
686C22×C4—861no—
687C22×C4—3442no—
688C22×C4—1724no—
689C22×C4D4×D4311yescharacteristic
690C22×C4D4×D4311yescharacteristic
691C22×C4C23×D4311yescharacteristic
692Q16—1724no—
693SD16—1724no—
694SD16—1724no—
695SD16—1724no—
696SD16—1724no—
697D8—1724no—
698D8—1724no—
699D8—1724no—
700C2×C8—22no—
701C2×C8—22no—
702C2×C8—432no—
703C2×C8—432no—
704C2×C8—862no—
705C2×C8—862no—
706C2×C8C23×D4312yes—
707C2×C8C23×D4312yes—
708C4⋊C4—24no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—434no—
712C4⋊C4—434no—
713C4⋊C4—864no—
714C4⋊C4—864no—
715C4⋊C4C23×D4312yes—
716C4⋊C4C23×D4312yes—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—434no—
720C22⋊C4—434no—
721C22⋊C4—864no—
722C22⋊C4—864no—
723C22⋊C4—864no—
724C22⋊C4—864no—
725C22⋊C4—864no—
726C22⋊C4—864no—
727C22⋊C4—864no—
728C42—432no—
729C42—432no—
730C42—864no—
731C42D4×D4312yes—
732C42C23×D4312yes—
733C23—22no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—432no—
738C23—862no—
739C23—862no—
740C23—862no—
741C23—862no—
742C23—862no—
743C23—862no—
744C23—3444no—
745C23—3444no—
746C23—34416no—
747C23—1728no—
748C23—1722no—
749C23—1722no—
750C23—1722no—
751C23—1722no—
752C23—1722no—
753C23—1722no—
754C23—1722no—
755C23—1722no—
756C23—1722no—
757C23C2×D4×D4311yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—42no—
761Q8—84no—
762Q8—862no—
763Q8—862no—
764Q8—1722no—
765D4—22no—
766D4—22no—
767D4—42no—
768D4—862no—
769D4—862no—
770D4—862no—
771D4—862no—
772D4—862no—
773D4—862no—
774D4—3444no—
775D4—3444no—
776D4—3444no—
777D4—3444no—
778D4—3444no—
779D4—1728no—
780D4—1728no—
781D4—1722no—
782D4—1722no—
783D4—1722no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—432no—
793C2×C4—432no—
794C2×C4—432no—
795C2×C4—862no—
796C2×C4—862no—
797C2×C4—862no—
798C2×C4—864no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—3444no—
803C2×C4—1728no—
804C2×C4—1722no—
805C2×C4C2×D4×D4312yes—
806C2×C4C2×D4×D4312yes—
807C2×C4C2×D4×D4311yescharacteristic
808C2×C4#1306337112yes—
809C2×C4#1306337112yes—
810C2×C4C24×D4311yescharacteristic
811C8—22no—
812C8—22no—
813C8—862no—
814C8—862no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—84no—
819C22—862no—
820C22—862no—
821C22—862no—
822C22—34416no—
823C22—3444no—
824C22—3444no—
825C22—3444no—
826C22—1722no—
827C22—1722no—
828C22—1722no—
829C22—1722no—
830C22—1722no—
831C22—1722no—
832C22—1722no—
833C22—1722no—
834C22—1722no—
835C22—1724no—
836C22#1458346712yes—
837C22#1458370312yes—
838C22#1458370812yes—
839C22C22×D4×D4311yescharacteristic
840C4—22no—
841C4—22no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—862no—
846C4—862no—
847C4—862no—
848C4—1722no—
849C4#1458346712yes—
850C4C2×#1306337111yescharacteristic
851C4C2×#1306337111yescharacteristic
852C2—82no—
853C2—3442no—
854C2—3442no—
855C2—3442no—
856C2—1722no—
857C2#1914569014yesdirect product factor
858C2C2×#1458346711yescharacteristic
859C2C2×#1458370311yescharacteristic
860C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#489C2
socleC23×C43C22×D4
hypercenterC2×#489D43
hypocenterC43C2×#3224
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#14583523C2semidirect
2. C2×#14583467C2semidirect
3. #19145690C2direct (N × H)
4. C2×#14583288C2semidirect
5. C2×#14583281C2semidirect
6. C2×#14583247C2semidirect
7. C2×#14583124C2semidirect
8. C2×#14583098C2semidirect
9. C2×#14583117C2semidirect
10. C2×#14583093C2semidirect
11. C2×#14583064C2semidirect
12. C2×#14583047C2semidirect
13. C2×#14583051C2semidirect
14. C2×#14583034C2semidirect
15. C2×#14582961C2semidirect
16. C2×C43×#489C2semidirect
19. C22×#10621885C22semidirect
21. C22×#10621873C22semidirect
23. C22×#10621884C22semidirect
25. C22×D344C22semidirect
28. #14583523C22semidirect
30. #14583467C22semidirect
36. C2×#13063313C22semidirect
45. C2×#13063290C22semidirect
46. C2×#13063287C22semidirect
48. #14583288C22semidirect
49. #14583281C22semidirect
50. #14583247C22semidirect
51. #14583124C22semidirect
52. #14583117C22semidirect
53. #14583098C22semidirect
54. #14583093C22semidirect
55. #14583064C22semidirect
56. #14583051C22semidirect
57. #14583047C22semidirect
58. #14583034C22semidirect
59. #14582961C22semidirect
60. C2×Dic43⋊C8C22semidirect
61. C2×Dic43⋊C8C22semidirect
64. C2×#13063245C22semidirect
65. C2×#13063245C22semidirect
68. C2×C4×C43⋊C8C22semidirect
69. C2×C4⋊Q8×C43C22semidirect
71. C43×#489C22semidirect
72. C2×#103×C43C22semidirect
73. C2×#103×C43C22semidirect
76. C2×#97×C43C22semidirect
101. C2×#10621885C23semidirect
105. C2×#10621873C23semidirect
109. C2×#10621884C23semidirect
113. C2×D344C23semidirect
127. #13063313C23semidirect
139. #13063290C23semidirect
141. #13063287C23semidirect
159. Dic43⋊C8C23semidirect
160. Dic43⋊C8C23semidirect
163. #13063245C23semidirect
164. #13063245C23semidirect
167. C4×C43⋊C8C23semidirect
174. C4⋊Q8×C43C23semidirect
183. #103×C43C23semidirect
184. #103×C43C23semidirect
187. #97×C43C23semidirect
427. C2×#489D43semidirect
439. C2×C43#3224semidirect
461. C2×C4⋊Q8C2×D43semidirect
482. #489C2×D43semidirect
495. C2×#103C2×D43semidirect
496. C2×#103C2×D43semidirect
505. C2×#97C2×D43semidirect
507. C43C2×#3224semidirect
555. C4⋊Q8C22×D43semidirect
607. #103C22×D43semidirect
608. #103C22×D43semidirect
617. #97C22×D43semidirect
857. C2#19145690direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835232
C2×#145834672
#191456902
C2×#145832882
C2×#145832812
C2×#145832472
C2×#145831242
C2×#145830982
C2×#145831172
C2×#145830932
C2×#145830642
C2×#145830472
C2×#145830512
C2×#145830342
C2×#145829612
C2×C43×#4892
C2×#322443