Finite Group Databasebeta

← C2×#19144946 #25965830

Subgroups — C2×#19144946 #25965830

Order 11008.

2262 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583526C211yesmaximal, characteristic, complemented
2C2×#14583467C211yesmaximal, characteristic
3#19144946C2116yesmaximal, direct product factor
4C2×#14583264C211yesmaximal, characteristic, complemented
5C2×#14583262C211yesmaximal, characteristic, complemented
6C2×#14583260C211yesmaximal, characteristic, complemented
7C2×#14583255C211yesmaximal, characteristic, complemented
8C2×#14583253C211yesmaximal, characteristic, complemented
9C2×#14583247C211yesmaximal, characteristic, complemented
10C2×#14583244C211yesmaximal, characteristic, complemented
11C2×#14582899C211yesmaximal, characteristic, complemented
12C2×#14582902C211yesmaximal, characteristic, complemented
13C2×#14582894C211yesmaximal, characteristic, complemented
14C2×#102×D43C211yesmaximal, characteristic, complemented
15C2×#14582856C211yesmaximal, characteristic, complemented
16C2×C43×#489C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583526—24no—
22#14583526C2218yescomplemented
23#14583467—24no—
24#14583467C2218yes—
25C2×#13063324C2211yescharacteristic, complemented
26C2×#13063323—21no—
27C2×#13063322C2211yescharacteristic
28C2×#13063321C2211yescharacteristic
29C2×#13063317C2211yescharacteristic, complemented
30C2×#13063316C2211yescharacteristic, complemented
31C2×#13063315—21no—
32C2×#13063314C2211yescharacteristic
33C2×#13063303—21no—
34C2×#13063301—21no—
35C2×#13063298—21no—
36C2×#13063298—21no—
37C2×#13063295—21no—
38C2×#13063295—21no—
39C2×#13063283C2211yescharacteristic
40C2×#13063282C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42#14583264C2218yescomplemented
43#14583262C2218yescomplemented
44#14583260C2218yescomplemented
45#14583255C2218yescomplemented
46#14583253C2218yescomplemented
47#14583247C2218yescomplemented
48#14583244C2218yescomplemented
49#14582902C2218yescomplemented
50#14582899C2218yescomplemented
51#14582894C2218yescomplemented
52C2×#13063249C2211yescharacteristic, complemented
53C2×#13063249C2211yescharacteristic, complemented
54C2×#13063247C2211yescharacteristic
55C2×#13063247C2211yescharacteristic
56C2×#13063247C2211yescharacteristic, complemented
57C2×#13063247C2211yescharacteristic, complemented
58C2×#13063246C2211yescharacteristic
59C2×#13063246C2211yescharacteristic
60C2×#13063245C2211yescharacteristic
61C2×#13063245C2211yescharacteristic
62C2×#13063245C2211yescharacteristic, complemented
63C2×#13063245C2211yescharacteristic, complemented
64#102×D43C2218yescomplemented
65#14582856C2218yescomplemented
66C2×#13063235C2211yescharacteristic, complemented
67C2×C4×C43⋊C8C2211yescharacteristic, complemented
68C2×C8×Dic43C2211yescharacteristic, 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—24no—
80C2×#10621902—24no—
81C2×#10621902C2314yes—
82C22×Dic86—21no—
83C22×D172—21no—
84C22×D172—21no—
85C22×D172—21no—
86C22×D172C2311yescharacteristic
87C22×D172C2311yescharacteristic
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C2×D4×D43—22no—
92C2×D4×D43—24no—
93C2×D4×D43—24no—
94C2×D4×D43C2314yes—
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43C2311yescharacteristic
98C2×#10621872—24no—
99C2×#10621872C2314yes—
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102C2×C8×D43—24no—
103C2×C8×D43C2314yes—
104#13063324—22no—
105#13063324C2314yescomplemented
106#13063323—28no—
107#13063322—22no—
108#13063322C2314yes—
109#13063321—22no—
110#13063321C2314yes—
111#13063317—22no—
112#13063317C2314yescomplemented
113#13063316—22no—
114#13063316C2314yescomplemented
115#13063315—28no—
116#13063314—22no—
117#13063314C2314yes—
118#13063303—28no—
119#13063301—28no—
120#13063298—28no—
121#13063298—28no—
122#13063295—28no—
123#13063295—28no—
124#13063283—22no—
125#13063283C2314yes—
126#13063282D414yes—
127#13063282C2314yes—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4D411yescharacteristic
137C2×Dic43⋊C4D411yescharacteristic
138C4⋊C4×D43—22no—
139C4⋊C4×D43C2314yes—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4D411yescharacteristic
144C2×(C2×D43)⋊C4D411yescharacteristic
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063249C2314yescomplemented
148#13063249C2314yescomplemented
149#13063247C2314yes—
150#13063247C2314yes—
151#13063247C2314yescomplemented
152#13063247C2314yescomplemented
153#13063246C2314yes—
154#13063246C2314yes—
155#13063245C2314yes—
156#13063245C2314yes—
157#13063245C2314yescomplemented
158#13063245C2314yescomplemented
159#13063235C2314yescomplemented
160C4×C43⋊C8C2314yescomplemented
161C8×Dic43C2314yescomplemented
162C22×Q8×C43—21no—
163C22×Q8×C43C2311yescharacteristic
164C22×D4×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C4⋊Q8×C43—22no—
168C4⋊Q8×C43C2314yescomplemented
169#124×C43—22no—
170#124×C43C2314yes—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176C2×C42×C43C2311yescharacteristic
177#103×C43C2314yescomplemented
178#103×C43C2314yescomplemented
179#102×C43C2314yes—
180#102×C43C2314yes—
181#97×C43C2314yescomplemented
182C24×C43—21no—
183C23×D43—21no—
184C23×D43—21no—
185C23×D43—24no—
186C23×D43—44no—
187C23×D43—82no—
188C23×D43—82no—
189C23×D43C2×D411yescharacteristic
190C2×Q8×C43—21no—
191C2×Q8×C43—24no—
192C2×Q8×C43—22no—
193C2×Q8×C43—22no—
194C2×Q8×C43—82no—
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—82no—
211C2×C22⋊D43—82no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217#10621902—28no—
218#10621902—28no—
219#10621902—48no—
220D4×D43—28no—
221D4×D43—28no—
222D4×D43—48no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172—24no—
226C2×D172—24no—
227C2×D172—24no—
228C2×D172—22no—
229C2×D172—22no—
230C2×D172—22no—
231C2×D172—22no—
232C2×D172—44no—
233C2×D172—82no—
234C2×D172—82no—
235C2×D172C2412yes—
236C2×D172C2412yes—
237C2×C4×D43—24no—
238C2×C4×D43—24no—
239C2×C4×D43—44no—
240C2×C4×D43—82no—
241C2×C4×D43C2×D412yes—
242C2×C4×D43#4114yes—
243C2×C4×D43#4114yes—
244C2×C4×D43C2412yes—
245C2×Dic86—24no—
246C2×Dic86—82no—
247C2×C8×C43—22no—
248C2×C8×C43—22no—
249C2×C8×C43C2412yes—
250C2×C8×C43C2412yes—
251C4⋊C4×C43—24no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43C2412yes—
255C4⋊C4×C43C2412yes—
256C22⋊C4×C43—24no—
257C22⋊C4×C43—24no—
258C42×C43C2×D412yes—
259C42×C43C2412yes—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4C2×D414yes—
264(C2×D43)⋊C4C2×D414yes—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—24no—
268C4⋊Dic43C2412yes—
269C4⋊Dic43C2412yes—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272Dic43⋊C4—24no—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4C2×D414yes—
276Dic43⋊C4C2×D414yes—
277C4×Dic43—24no—
278C4×Dic43C2×D412yes—
279C4×Dic43C2412yes—
280C2×C43⋊C8—22no—
281C2×C43⋊C8—22no—
282C2×C43⋊C8C2412yes—
283C2×C43⋊C8C2412yes—
284#10621872—28no—
285C8×D43—28no—
286C23×C43—22no—
287C23×C43—42no—
288C23×C43—42no—
289C23×C43—42no—
290C23×C43C22×D411yescharacteristic
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—42no—
296C22×D43—42no—
297C22×D43—42no—
298C22×D43—42no—
299C22×D43—42no—
300C22×D43—42no—
301C22×D43—48no—
302C22×D43—84no—
303C22×D43—84no—
304C22×D43—816no—
305C22×D43#12414yes—
306C22×D43C22×D412yes—
307Q8×C43—22no—
308Q8×C43—22no—
309Q8×C43—42no—
310Q8×C43—84no—
311D4×C43—22no—
312D4×C43—22no—
313D4×C43—42no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—42no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43C22×D412yes—
323C2×C4×C43C22×D412yes—
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C2×#4112yes—
326C2×C4×C43C2×#4112yes—
327C2×C4×C43C2511yescharacteristic
328C22⋊D43—48no—
329C22⋊D43—84no—
330C22⋊D43—84no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43#12414yes—
338C2×Dic43C22×D412yes—
339C2×Dic43C22×D412yes—
340C2×Dic43C22×D412yes—
341D172—22no—
342D172—22no—
343D172—22no—
344D172—22no—
345D172—48no—
346D172—42no—
347D172—42no—
348D172—84no—
349D172—84no—
350C4×D43—48no—
351C4×D43—84no—
352C4×D43#12418yes—
353C4×D43C2×#4114yes—
354C4×D43C2×#4114yes—
355Dic86—84no—
356C8×C43—22no—
357C8×C43—22no—
358C43⋊C8—22no—
359C43⋊C8—22no—
360C2×#3136—431nomaximal, Sylow
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—84no—
365C22×C43C2×#12412yes—
366C22×C43#57612yes—
367C22×C43#57712yes—
368C22×C43C23×D411yescharacteristic
369C2×D43—28no—
370C2×D43—22no—
371C2×D43—22no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—816no—
379C2×D43—84no—
380C2×D43—84no—
381C2×D43C2×#12414yes—
382C4×C43—22no—
383C4×C43—22no—
384C4×C43—42no—
385C4×C43—42no—
386C4×C43—42no—
387C4×C43C2×#12412yes—
388C4×C43C22×#4111yescharacteristic
389C4×C43C22×#4111yescharacteristic
390Dic43—22no—
391Dic43—22no—
392Dic43—42no—
393Dic43—42no—
394Dic43C2×#12414yes—
395C2×#544—431no—
396C2×#535—431no—
397#3136—4316no—
398C2×#490—431no—
399C2×#490—431no—
400C2×#489—431no—
401C2×#489D4311yescharacteristic, complemented
402C2×#488—431no—
403C2×#488—431no—
404C2×#486—431no—
405C2×#486—431no—
406C2×#417—431no—
407C2×#418—431no—
408C2×#416—431no—
409C22×#102—431no—
410C2×#405—431no—
411C2×C43—82no—
412C2×C43#313614yescomplemented
413C2×C43C22×#12411yescharacteristic
414C2×C43C2×#57611yescharacteristic
415C2×C43C2×#57711yescharacteristic
416D43—24no—
417D43—82no—
418D43—82no—
419C22×#41—431no—
420C23×D4—431no—
421C22×M16—431no—
422C23×C8—431no—
423#544—438no—
424#544—864no—
425#535—438no—
426#535—864no—
427C2×C4⋊Q8—431no—
428C2×C4⋊Q8—861no—
429C2×C4⋊Q8C2×D4311yescharacteristic, complemented
430C2×#127—431no—
431C2×#127—431no—
432C2×#125—431no—
433C2×#125—431no—
434C2×#125—861no—
435C2×#124—431no—
436C2×#124C2×D4311yescharacteristic
437C2×C22⋊Q8—861no—
438C2×C22⋊Q8—861no—
439C2×#121—861no—
440C2×#121—861no—
441C2×#120—861no—
442C2×#120—861no—
443C2×#117—431no—
444C2×#117—431no—
445C22×C4⋊C4—431no—
446#490—438no—
447#490—438no—
448#489—438no—
449#489C2×D4318yescomplemented
450#488—438no—
451#488—438no—
452#486—438no—
453#486—438no—
454#418—438no—
455#417—438no—
456#416—438no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103C2×D4311yescharacteristic, complemented
460C2×#103C2×D4311yescharacteristic, complemented
461C2×#102—431no—
462C2×#102—431no—
463C2×#102—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×#102—431no—
469C2×#102—431no—
470C2×#102—431no—
471C2×#102—438no—
472C2×#102C2×D4311yescharacteristic
473C2×#102C2×D4311yescharacteristic
474#405—438no—
475C2×#97—431no—
476C2×#97C2×D4311yescharacteristic, complemented
477C2×C4×C8—431no—
478C2×C4×C8—431no—
479C43C2×#313611yescharacteristic, complemented, Sylow
480C25—861no—
481C2×#41—434no—
482C2×#41—862no—
483C2×#41—864no—
484C2×#41—864no—
485C22×Q8—21no—
486C22×Q8—861no—
487C22×Q8C22×D4311yescharacteristic
488C22×D4—434no—
489C22×D4—431no—
490C22×D4—431no—
491C22×D4—861no—
492C22×D4—864no—
493C22×D4—864no—
494C22×D4—862no—
495C22×D4—861no—
496C22×D4—861no—
497C22×D4—861no—
498C22×D4—861no—
499C22×D4—861no—
500C22×D4C22×D4311yescharacteristic
501C23×C4—431no—
502C23×C4—861no—
503C23×C4—861no—
504C2×M16—434no—
505C2×M16—864no—
506C22×C8—431no—
507C22×C8—431no—
508C22×C8—434no—
509C22×C8—864no—
510C22×C8C22×D4311yescharacteristic
511C22×C8C22×D4311yescharacteristic
512C4⋊Q8—22no—
513C4⋊Q8—434no—
514C4⋊Q8—862no—
515C4⋊Q8—868no—
516C4⋊Q8C22×D4314yescomplemented
517#127—434no—
518#127—434no—
519#127—862no—
520#127—862no—
521#125—434no—
522#125—434no—
523#125—862no—
524#125—868no—
525#125—862no—
526#124—22no—
527#124—434no—
528#124—862no—
529#124C22×D4314yes—
530C22⋊Q8—868no—
531C22⋊Q8—868no—
532#121—868no—
533#121—868no—
534#120—868no—
535#120—868no—
536#117—434no—
537#117—434no—
538#117—434no—
539#117—862no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—431no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—434no—
546C2×C4⋊C4—862no—
547C2×C4⋊C4—861no—
548C2×C4⋊C4—861no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4C22×D4311yescharacteristic
554C2×C4⋊C4C22×D4311yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—431no—
558C2×C22⋊C4—431no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C42—431no—
563C2×C42—861no—
564C2×C42C22×D4311yescharacteristic
565#103—434no—
566#103—434no—
567#103C22×D4314yescomplemented
568#103C22×D4314yescomplemented
569#102—434no—
570#102—434no—
571#102—434no—
572#102—434no—
573#102—434no—
574#102—434no—
575#102—434no—
576#102—434no—
577#102—434no—
578#102—434no—
579#102C22×D4314yes—
580#102C22×D4314yes—
581#97—434no—
582#97C22×D4314yescomplemented
583C4×C8—434no—
584C4×C8—434no—
585C24—21no—
586C24—431no—
587C24—864no—
588C24—861no—
589C24—861no—
590C24—3442no—
591C24—3442no—
592C24—1724no—
593#41—868no—
594#41—868no—
595#41—1728no—
596C2×Q8—21no—
597C2×Q8—24no—
598C2×Q8—22no—
599C2×Q8—22no—
600C2×Q8—82no—
601C2×Q8—864no—
602C2×Q8—3442no—
603C2×Q8C23×D4312yes—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—432no—
608C2×D4—432no—
609C2×D4—864no—
610C2×D4—868no—
611C2×D4—868no—
612C2×D4—864no—
613C2×D4—864no—
614C2×D4—864no—
615C2×D4—864no—
616C2×D4—864no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—862no—
620C2×D4—862no—
621C2×D4—862no—
622C2×D4—862no—
623C2×D4—3442no—
624C2×D4—3442no—
625C2×D4—3442no—
626C2×D4—3442no—
627C2×D4—1724no—
628C2×D4—1728no—
629C2×D4—1724no—
630C2×D4C23×D4312yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—431no—
635C22×C4—432no—
636C22×C4—434no—
637C22×C4—434no—
638C22×C4—432no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—864no—
642C22×C4—864no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—3442no—
646C22×C4—1724no—
647C22×C4D4×D4311yescharacteristic
648C22×C4D4×D4311yescharacteristic
649C22×C4C23×D4311yescharacteristic
650M16—868no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—432no—
654C2×C8—432no—
655C2×C8—868no—
656C2×C8—862no—
657C2×C8—862no—
658C2×C8C23×D4312yes—
659C2×C8C23×D4312yes—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—434no—
664C4⋊C4—434no—
665C4⋊C4—432no—
666C4⋊C4—432no—
667C4⋊C4—864no—
668C4⋊C4—864no—
669C4⋊C4—864no—
670C4⋊C4—864no—
671C4⋊C4—861no—
672C4⋊C4—861no—
673C4⋊C4—864no—
674C4⋊C4—864no—
675C4⋊C4C23×D4312yes—
676C4⋊C4C23×D4312yes—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—434no—
680C22⋊C4—434no—
681C22⋊C4—864no—
682C22⋊C4—864no—
683C22⋊C4—864no—
684C42—432no—
685C42—432no—
686C42—864no—
687C42D4×D4312yes—
688C42C23×D4312yes—
689C23—22no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—434no—
694C23—432no—
695C23—862no—
696C23—862no—
697C23—862no—
698C23—862no—
699C23—3444no—
700C23—3444no—
701C23—34416no—
702C23—1728no—
703C23—1722no—
704C23—1722no—
705C23—1722no—
706C23—1722no—
707C23—1722no—
708C23—1722no—
709C23C2×D4×D4311yescharacteristic
710Q8—22no—
711Q8—22no—
712Q8—42no—
713Q8—84no—
714Q8—3444no—
715D4—22no—
716D4—22no—
717D4—42no—
718D4—862no—
719D4—862no—
720D4—862no—
721D4—862no—
722D4—3444no—
723D4—3444no—
724D4—3444no—
725D4—3444no—
726D4—1728no—
727D4—1728no—
728D4—1722no—
729D4—1722no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—434no—
739C2×C4—432no—
740C2×C4—438no—
741C2×C4—434no—
742C2×C4—434no—
743C2×C4—432no—
744C2×C4—432no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—3444no—
750C2×C4—1728no—
751C2×C4—1722no—
752C2×C4—1722no—
753C2×C4C2×D4×D4312yes—
754C2×C4C2×D4×D4312yes—
755C2×C4C2×D4×D4311yescharacteristic
756C2×C4#41×D4312yes—
757C2×C4#41×D4312yes—
758C2×C4C24×D4311yescharacteristic
759C8—22no—
760C8—22no—
761C8—862no—
762C8—862no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22—434no—
768C22—862no—
769C22—862no—
770C22—868no—
771C22—34416no—
772C22—3444no—
773C22—3444no—
774C22—1722no—
775C22—1722no—
776C22—1722no—
777C22—1722no—
778C22—1722no—
779C22—1722no—
780C22#124×D4312yes—
781C22#1458370312yes—
782C22#1458370812yes—
783C22C22×D4×D4311yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—434no—
790C4—862no—
791C4—862no—
792C4—1722no—
793C4—1722no—
794C4#124×D4312yes—
795C4C2×#41×D4311yescharacteristic
796C4C2×#41×D4311yescharacteristic
797C2—82no—
798C2—864no—
799C2—3442no—
800C2—3442no—
801C2#1914494614yesdirect product factor
802C2C2×#124×D4311yescharacteristic
803C2C2×#1458370311yescharacteristic
804C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#489C2
socleC23×C43C22×D4
prime radicalC2×#14583467C2
hypercenterC2×#489D43
hypocenterC43C2×#3136
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×#14583526C2semidirect
3. #19144946C2direct (N × H)
4. C2×#14583264C2semidirect
5. C2×#14583262C2semidirect
6. C2×#14583260C2semidirect
7. C2×#14583255C2semidirect
8. C2×#14583253C2semidirect
9. C2×#14583247C2semidirect
10. C2×#14583244C2semidirect
11. C2×#14582899C2semidirect
12. C2×#14582902C2semidirect
13. C2×#14582894C2semidirect
14. C2×#102×D43C2semidirect
15. C2×#14582856C2semidirect
16. C2×C43×#489C2semidirect
22. #14583526C22semidirect
25. C2×#13063324C22semidirect
29. C2×#13063317C22semidirect
30. C2×#13063316C22semidirect
42. #14583264C22semidirect
43. #14583262C22semidirect
44. #14583260C22semidirect
45. #14583255C22semidirect
46. #14583253C22semidirect
47. #14583247C22semidirect
48. #14583244C22semidirect
49. #14582902C22semidirect
50. #14582899C22semidirect
51. #14582894C22semidirect
52. C2×#13063249C22semidirect
53. C2×#13063249C22semidirect
56. C2×#13063247C22semidirect
57. C2×#13063247C22semidirect
62. C2×#13063245C22semidirect
63. C2×#13063245C22semidirect
64. #102×D43C22semidirect
65. #14582856C22semidirect
66. C2×#13063235C22semidirect
67. C2×C4×C43⋊C8C22semidirect
68. C2×C8×Dic43C22semidirect
69. C2×C4⋊Q8×C43C22semidirect
71. C43×#489C22semidirect
72. C2×#103×C43C22semidirect
73. C2×#103×C43C22semidirect
76. C2×#97×C43C22semidirect
105. #13063324C23semidirect
112. #13063317C23semidirect
114. #13063316C23semidirect
147. #13063249C23semidirect
148. #13063249C23semidirect
151. #13063247C23semidirect
152. #13063247C23semidirect
157. #13063245C23semidirect
158. #13063245C23semidirect
159. #13063235C23semidirect
160. C4×C43⋊C8C23semidirect
161. C8×Dic43C23semidirect
168. C4⋊Q8×C43C23semidirect
177. #103×C43C23semidirect
178. #103×C43C23semidirect
181. #97×C43C23semidirect
401. C2×#489D43semidirect
412. C2×C43#3136semidirect
429. C2×C4⋊Q8C2×D43semidirect
449. #489C2×D43semidirect
459. C2×#103C2×D43semidirect
460. C2×#103C2×D43semidirect
476. C2×#97C2×D43semidirect
479. C43C2×#3136semidirect
516. C4⋊Q8C22×D43semidirect
567. #103C22×D43semidirect
568. #103C22×D43semidirect
582. #97C22×D43semidirect
801. C2#19144946direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835262
C2×#145834672
#191449462
C2×#145832642
C2×#145832622
C2×#145832602
C2×#145832552
C2×#145832532
C2×#145832472
C2×#145832442
C2×#145828992
C2×#145829022
C2×#145828942
C2×#102×D432
C2×#145828562
C2×C43×#4892
C2×#313643