Finite Group Databasebeta

← #25112734

Subgroups — #25112734

Order 11008.

1294 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583575C211yesmaximal, characteristic
2#19137440C212yesmaximal, complemented
3#19135578C212yesmaximal, complemented
4#19135052C212yesmaximal, complemented
5#19135048C212yesmaximal
6#19134671C211yesmaximal, characteristic, complemented
7#19134669C211yesmaximal, characteristic, complemented
8#19134582C211yesmaximal, characteristic, complemented
9#19134382C211yesmaximal, characteristic, complemented
10#19134326C211yesmaximal, characteristic, complemented
11C2×C43×#342C211yesmaximal, characteristic, complemented
12#14583575—22no—
13#14583575—22no—
14#14583575—22no—
15#14583575—22no—
16C2×#13063318C411yescharacteristic, complemented
17C2×#13063318C411yescharacteristic, complemented
18C2×#13063311C411yescharacteristic, complemented
19C2×#13063309C2211yescharacteristic
20C2×#13063308C411yescharacteristic, complemented
21C2×#13063307C411yescharacteristic, complemented
22C2×#13063304C411yescharacteristic, complemented
23C2×#13063302C2211yescharacteristic
24C2×#13063294C2211yescharacteristic
25C2×C4×C22⋊D43C411yescharacteristic, complemented
26C2×(C22⋊D43)⋊C4C2211yescharacteristic
27C2×#13063284C411yescharacteristic, complemented
28C2×#13063281C2212yes—
29C2×#13063281C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C2×#13063239C2212yes—
32C2×#13063239C2212yes—
33#14582793—22no—
34#14582787—22no—
35#14582772—22no—
36#14582760C2212yes—
37#14582757C2212yes—
38#14582755C2212yes—
39C22⋊C4×Dic43C2212yes—
40C4×C22⋊Dic43—22no—
41#14582666C2212yes—
42#14582666C2211yescharacteristic
43#14582666C2211yescharacteristic
44#14582665C2212yes—
45#14582665C2212yes—
46C22×C22⋊C4×C43C2211yescharacteristic
47C22×C22⋊C4×C43C2212yes—
48C43×#342C2212yes—
49C43×#342C2211yescharacteristic
50C43×#342C2211yescharacteristic
51C22×Dic86C2×C411yescharacteristic, complemented
52C22×C22⋊D43C2×C411yescharacteristic
53C22×C22⋊D43C2×C411yescharacteristic
54C22×C22⋊D43C2311yescharacteristic
55C23×Dic43C2311yescharacteristic
56C23×Dic43C2311yescharacteristic
57C22×C4×D43C2×C411yescharacteristic, complemented
58#13063318—22no—
59#13063318—22no—
60#13063318—22no—
61#13063318—22no—
62#13063311—22no—
63#13063311—22no—
64#13063309—22no—
65#13063309—22no—
66#13063308—22no—
67#13063308—22no—
68#13063307—22no—
69#13063307—22no—
70#13063304—22no—
71#13063304—22no—
72#13063302—22no—
73#13063302—22no—
74#13063294—22no—
75#13063294—22no—
76C4×C22⋊D43—21no—
77C4×C22⋊D43—21no—
78C4×C22⋊D43—21no—
79C4×C22⋊D43—21no—
80(C22⋊D43)⋊C4—22no—
81(C22⋊D43)⋊C4—22no—
82#13063284—21no—
83#13063284—21no—
84#13063284—21no—
85#13063284—21no—
86#13063281—22no—
87#13063281—22no—
88#13063281—24no—
89#13063281—42no—
90C2×C4⋊Dic43C2×C411yescharacteristic, complemented
91C2×C4⋊Dic43C2×C411yescharacteristic, complemented
92C2×C4⋊Dic43C2×C411yescharacteristic, complemented
93C2×Dic43⋊C4—22no—
94C2×Dic43⋊C4—22no—
95C2×Dic43⋊C4C2×C411yescharacteristic, complemented
96C2×Dic43⋊C4C2×C411yescharacteristic, complemented
97C2×Dic43⋊C4C2×C411yescharacteristic, complemented
98C2×Dic43⋊C4C2×C411yescharacteristic, complemented
99C2×Dic43⋊C4C2×C411yescharacteristic, complemented
100C2×C22⋊Dic43—22no—
101C2×C22⋊Dic43—22no—
102C2×C22⋊Dic43C2×C411yescharacteristic
103C2×C22⋊Dic43C2×C411yescharacteristic
104C2×C22⋊Dic43C2×C411yescharacteristic
105C2×C22⋊Dic43C2×C411yescharacteristic
106C2×C22⋊Dic43C2×C411yescharacteristic
107C2×C22⋊Dic43C2×C411yescharacteristic
108C2×C22⋊Dic43D412yes—
109C2×C22⋊Dic43D412yes—
110C2×C22⋊Dic43D412yes—
111C2×C22⋊Dic43D412yes—
112C2×C22⋊Dic43C2312yes—
113C2×C22⋊Dic43C2312yes—
114C2×C22⋊Dic43C2311yescharacteristic
115C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
116C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
117C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
118C2×C4×Dic43—22no—
119C2×C4×Dic43—22no—
120C2×C4×Dic43C2×C411yescharacteristic, complemented
121C2×C4×Dic43C2×C411yescharacteristic, complemented
122C2×C4×Dic43C2×C411yescharacteristic, complemented
123#13063239—24no—
124#13063239—42no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C25×C43C2311yescharacteristic
130C23×C4×C43—22no—
131C23×C4×C43C2×C411yescharacteristic
132C23×C4×C43C2×C411yescharacteristic
133C2×C22⋊C4×C43—22no—
134C2×C22⋊C4×C43—22no—
135C2×C22⋊C4×C43—24no—
136C2×C22⋊C4×C43—22no—
137C2×C22⋊C4×C43—42no—
138C2×C22⋊C4×C43C2×C411yescharacteristic
139C2×C22⋊C4×C43C2×C411yescharacteristic
140C2×C22⋊C4×C43C2312yes—
141C2×C22⋊C4×C43C2311yescharacteristic
142C2×C22⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43C2312yes—
144C24×C43—22no—
145C24×C43—21no—
146C24×C43—21no—
147C24×C43—42no—
148C24×C43—81no—
149C24×C43C22×C411yescharacteristic
150C24×C43C22×C411yescharacteristic
151C24×C43C2×D412yes—
152C24×C43C2×D412yes—
153C24×C43C2411yescharacteristic
154C23×D43C22×C411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—44no—
162C22×C4×C43—42no—
163C22×C4×C43—44no—
164C22×C4×C43—81no—
165C22×C4×C43—82no—
166C22×C4×C43C22×C411yescharacteristic
167C22×C4×C43C22×C411yescharacteristic
168C22×C4×C43C22×C411yescharacteristic
169C22×C4×C43C22×C411yescharacteristic
170C2×C22⋊D43—21no—
171C2×C22⋊D43—21no—
172C2×C22⋊D43—22no—
173C2×C22⋊D43—22no—
174C2×C22⋊D43—22no—
175C2×C22⋊D43—21no—
176C2×C22⋊D43—21no—
177C2×C22⋊D43—42no—
178C2×C22⋊D43—81no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—81no—
185C22×Dic43C22×C411yescharacteristic
186C22×Dic43C22×C411yescharacteristic
187C22×Dic43C22×C411yescharacteristic
188C22×Dic43C22×C411yescharacteristic
189C22×Dic43C22×C411yescharacteristic
190C22×Dic43C22×C411yescharacteristic
191C22×Dic43C22×C411yescharacteristic
192C22×Dic43C2×D412yes—
193C22×Dic43C2×D412yes—
194C22×Dic43C2×D412yes—
195C22×Dic43C2×D412yes—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—81no—
199C2×Dic86—22no—
200C2×Dic86—81no—
201C22⋊C4×C43—22no—
202C22⋊C4×C43—22no—
203C22⋊C4×C43—22no—
204C22⋊C4×C43—22no—
205C22⋊C4×C43—22no—
206C22⋊C4×C43—22no—
207C22⋊C4×C43—22no—
208C22⋊C4×C43—44no—
209C22⋊C4×C43#4114yes—
210C22⋊Dic43—21no—
211C22⋊Dic43—21no—
212C22⋊Dic43—22no—
213C22⋊Dic43—22no—
214C22⋊Dic43—22no—
215C22⋊Dic43—22no—
216C22⋊Dic43—22no—
217C22⋊Dic43—22no—
218C22⋊Dic43—44no—
219C22⋊Dic43—82no—
220C22⋊Dic43C22⋊C411yescharacteristic
221C22⋊Dic43C22⋊C411yescharacteristic
222C22⋊Dic43C22⋊C411yescharacteristic
223C22⋊Dic43C22⋊C411yescharacteristic
224C22⋊Dic43C22⋊C412yes—
225C22⋊Dic43C22⋊C412yes—
226C22⋊Dic43C22⋊C412yes—
227C22⋊Dic43C22⋊C412yes—
228C22⋊Dic43C22⋊C412yes—
229C22⋊Dic43C22⋊C412yes—
230(C2×D43)⋊C4—22no—
231(C2×D43)⋊C4—21no—
232(C2×D43)⋊C4—21no—
233(C2×D43)⋊C4—22no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—22no—
239Dic43⋊C4—22no—
240Dic43⋊C4—22no—
241Dic43⋊C4—22no—
242Dic43⋊C4—21no—
243Dic43⋊C4—21no—
244Dic43⋊C4—22no—
245Dic43⋊C4—44no—
246Dic43⋊C4—82no—
247C4×Dic43—21no—
248C4×Dic43—21no—
249C4×Dic43—21no—
250C4×Dic43—21no—
251C4×Dic43—21no—
252C4×Dic43—21no—
253C4×Dic43—44no—
254C4×Dic43—82no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—22no—
258C23×C43—22no—
259C23×C43—24no—
260C23×C43—22no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—22no—
264C23×C43—22no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—42no—
268C23×C43—41no—
269C23×C43—42no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—42no—
273C23×C43—84no—
274C23×C43—82no—
275C23×C43—82no—
276C23×C43C2×C22⋊C412yes—
277C23×C43C2×C22⋊C411yescharacteristic
278C23×C43C2×C22⋊C411yescharacteristic
279C23×C43C23×C411yescharacteristic
280C23×C43C22×D412yes—
281C23×C43C2×#4112yes—
282C23×C43H(5,𝔽2)11yescharacteristic
283C23×C432−1+411yescharacteristic
284C22×D43—21no—
285C22×D43—21no—
286C22×D43—21no—
287C22×D43—41no—
288C22×D43—41no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—24no—
294C2×C4×C43—42no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43—81no—
306C2×C4×C43—81no—
307C2×C4×C43—88no—
308C22⋊D43—42no—
309C22⋊D43—42no—
310C22⋊D43—42no—
311C22⋊D43—42no—
312C22⋊D43—82no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43C2×C22⋊C411yescharacteristic
339C2×Dic43C2×C22⋊C411yescharacteristic
340C2×Dic43C2×C22⋊C411yescharacteristic
341C2×Dic43C2×C22⋊C411yescharacteristic
342C2×Dic43C2×C22⋊C412yes—
343C2×Dic43C2×C22⋊C412yes—
344C4×D43—81no—
345C4×D43—81no—
346Dic86—82no—
347#22477—431nomaximal, Sylow
348C22×C43—21no—
349C22×C43—21no—
350C22×C43—22no—
351C22×C43—21no—
352C22×C43—21no—
353C22×C43—22no—
354C22×C43—21no—
355C22×C43—22no—
356C22×C43—22no—
357C22×C43—21no—
358C22×C43—22no—
359C22×C43—21no—
360C22×C43—42no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—44no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—44no—
367C22×C43—82no—
368C22×C43—82no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43#41012yes—
372C22×C43C22×C22⋊C411yescharacteristic
373C22×C43C4×#4111yescharacteristic
374C22×C43#52011yescharacteristic
375C22×C43#54612yes—
376C22×C43#54712yes—
377C2×D43—41no—
378C2×D43—41no—
379C2×D43—41no—
380C2×D43—81no—
381C2×D43—81no—
382C4×C43—44no—
383C4×C43—41no—
384C4×C43—41no—
385C4×C43—41no—
386C4×C43—41no—
387C4×C43—82no—
388Dic43—21no—
389Dic43—22no—
390Dic43—21no—
391Dic43—22no—
392Dic43—21no—
393Dic43—21no—
394Dic43—41no—
395Dic43—41no—
396Dic43—41no—
397Dic43—82no—
398Dic43—82no—
399C2×#551—431no—
400#2342—432no—
401#1996—432no—
402#1899—432no—
403#1898—432no—
404#1820—431no—
405#1819—431no—
406#1799—431no—
407C4×#99—431no—
408#1740—431no—
409C2×#342D4311yescharacteristic, complemented
410C2×C43—22no—
411C2×C43—22no—
412C2×C43—21no—
413C2×C43—21no—
414C2×C43—22no—
415C2×C43—42no—
416C2×C43—41no—
417C2×C43#233911yescharacteristic
418C2×C43C2×#41011yescharacteristic
419C2×C43#288311yescharacteristic
420D43—81no—
421#551—862no—
422#551—862no—
423#551—862no—
424#551—862no—
425C2×#126—431no—
426C2×#126—431no—
427C2×#124—431no—
428C2×#123—431no—
429C2×#123—431no—
430C2×#123—431no—
431C2×C22⋊Q8—431no—
432C2×C22⋊Q8—431no—
433C2×#120—431no—
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×#117—431no—
437C2×#117—431no—
438C2×#117—432no—
439C22×C22⋊C4—431no—
440C22×C22⋊C4C2×D4311yescharacteristic
441C22×C22⋊C4C2×D4312yes—
442C2×#99—432no—
443C2×#99—432no—
444#388—862no—
445#388—862no—
446#385—862no—
447#381—432no—
448#380—432no—
449#379—432no—
450C4×C22⋊C4—432no—
451C4×C22⋊C4—862no—
452#342—431no—
453#342—431no—
454#342—432no—
455#342—432no—
456#342—432no—
457#342C2×D4311yescharacteristic
458#342C2×D4312yes—
459#342C2×D4311yescharacteristic
460C43#2247711yescharacteristic, complemented, Sylow
461C25C22×D4311yescharacteristic
462C22×Q8—431no—
463C22×D4—431no—
464C22×D4—431no—
465C22×D4—431no—
466C23×C4—22no—
467C23×C4—431no—
468C23×C4—431no—
469C23×C4—431no—
470C23×C4C4×D4311yescharacteristic
471C23×C4C4×D4311yescharacteristic
472#126—862no—
473#126—862no—
474#126—862no—
475#126—862no—
476#124—862no—
477#124—862no—
478#123—862no—
479#123—862no—
480#123—862no—
481#123—862no—
482#123—862no—
483#123—862no—
484C22⋊Q8—862no—
485C22⋊Q8—862no—
486C22⋊Q8—862no—
487C22⋊Q8—862no—
488#120—862no—
489#120—862no—
490C4×D4—862no—
491C4×D4—862no—
492C4×D4—861no—
493C4×D4—861no—
494C4×D4—861no—
495C4×D4—861no—
496#117—862no—
497#117—862no—
498#117—861no—
499#117—861no—
500#117—861no—
501#117—861no—
502#117—864no—
503#117—1722no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—862no—
513C2×C4⋊C4—862no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—431no—
520C2×C22⋊C4—431no—
521C2×C22⋊C4—431no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—432no—
524C2×C22⋊C4—432no—
525C2×C22⋊C4—432no—
526C2×C22⋊C4—432no—
527C2×C22⋊C4—431no—
528C2×C22⋊C4—431no—
529C2×C22⋊C4—431no—
530C2×C22⋊C4—431no—
531C2×C22⋊C4—431no—
532C2×C22⋊C4—431no—
533C2×C22⋊C4—432no—
534C2×C22⋊C4—432no—
535C2×C22⋊C4—862no—
536C2×C22⋊C4—862no—
537C2×C22⋊C4C4×D4311yescharacteristic
538C2×C22⋊C4C4×D4311yescharacteristic
539C2×C22⋊C4C22×D4312yes—
540C2×C22⋊C4C22×D4311yescharacteristic
541C2×C22⋊C4C22×D4311yescharacteristic
542C2×C22⋊C4C22×D4312yes—
543C2×C42—431no—
544C2×C42—431no—
545C2×C42—431no—
546C2×C42—862no—
547C2×C42—862no—
548#99—864no—
549#99—1722no—
550#95—862no—
551#95—862no—
552#95—862no—
553#95—862no—
554C24—22no—
555C24—21no—
556C24—21no—
557C24—42no—
558C24—81no—
559C24—431no—
560C24C2×C4×D4311yescharacteristic
561C24C2×C4×D4311yescharacteristic
562C24D4×D4312yes—
563C24D4×D4312yes—
564C24C23×D4311yescharacteristic
565C2×Q8—862no—
566C2×Q8—3441no—
567C2×D4—862no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4—862no—
571C2×D4—862no—
572C2×D4—861no—
573C2×D4—861no—
574C2×D4—3441no—
575C2×D4—1722no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—44no—
583C22×C4—42no—
584C22×C4—44no—
585C22×C4—82no—
586C22×C4—81no—
587C22×C4—431no—
588C22×C4—431no—
589C22×C4—432no—
590C22×C4—432no—
591C22×C4—431no—
592C22×C4—431no—
593C22×C4—432no—
594C22×C4—432no—
595C22×C4—431no—
596C22×C4—431no—
597C22×C4—431no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—862no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—862no—
604C22×C4—862no—
605C22×C4—3441no—
606C22×C4—3441no—
607C22×C4C2×C4×D4311yescharacteristic
608C22×C4C2×C4×D4311yescharacteristic
609C22×C4C2×C4×D4311yescharacteristic
610C22×C4C2×C4×D4311yescharacteristic
611C4⋊C4—862no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—862no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—862no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—862no—
621C4⋊C4—862no—
622C4⋊C4—3442no—
623C4⋊C4—1724no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—44no—
632C22⋊C4—431no—
633C22⋊C4—431no—
634C22⋊C4—431no—
635C22⋊C4—431no—
636C22⋊C4—432no—
637C22⋊C4—432no—
638C22⋊C4—432no—
639C22⋊C4—432no—
640C22⋊C4—432no—
641C22⋊C4—432no—
642C22⋊C4—862no—
643C22⋊C4—861no—
644C22⋊C4—861no—
645C22⋊C4—862no—
646C22⋊C4—861no—
647C22⋊C4—861no—
648C22⋊C4—862no—
649C22⋊C4—862no—
650C22⋊C4—862no—
651C22⋊C4—862no—
652C22⋊C4—862no—
653C22⋊C4—862no—
654C22⋊C4—3442no—
655C22⋊C4—1724no—
656C22⋊C4#1062189814yes—
657C42—861no—
658C42—861no—
659C42—861no—
660C42—861no—
661C42—861no—
662C42—861no—
663C42—3442no—
664C42—1724no—
665C23—21no—
666C23—21no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—22no—
674C23—22no—
675C23—41no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—41no—
681C23—41no—
682C23—42no—
683C23—84no—
684C23—82no—
685C23—82no—
686C23—861no—
687C23—861no—
688C23—861no—
689C23—1721no—
690C23—1721no—
691C23C22⋊C4×D4312yes—
692C23C22⋊C4×D4311yescharacteristic
693C23C22⋊C4×D4311yescharacteristic
694C23C22×C4×D4311yescharacteristic
695C23C2×D4×D4312yes—
696C23C2×#1062189812yes—
697C23#1306337011yescharacteristic
698C23#1306337311yescharacteristic
699Q8—3442no—
700D4—3442no—
701D4—1722no—
702D4—1722no—
703D4—1722no—
704D4—1722no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—24no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—88no—
724C2×C4—431no—
725C2×C4—431no—
726C2×C4—431no—
727C2×C4—431no—
728C2×C4—432no—
729C2×C4—432no—
730C2×C4—861no—
731C2×C4—861no—
732C2×C4—861no—
733C2×C4—861no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—861no—
739C2×C4—861no—
740C2×C4—861no—
741C2×C4—861no—
742C2×C4—861no—
743C2×C4—3441no—
744C2×C4—3441no—
745C2×C4—1722no—
746C2×C4—1722no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1722no—
750C2×C4—1722no—
751C2×C4—1722no—
752C2×C4—1722no—
753C2×C4—1722no—
754C2×C4—1722no—
755C2×C4—1721no—
756C2×C4—1721no—
757C22—22no—
758C22—21no—
759C22—22no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—22no—
765C22—21no—
766C22—22no—
767C22—21no—
768C22—22no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—44no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—82no—
777C22—82no—
778C22—81no—
779C22—81no—
780C22—3441no—
781C22—3441no—
782C22—1721no—
783C22—1721no—
784C22—1721no—
785C22#1458287112yes—
786C22C2×C22⋊C4×D4311yescharacteristic
787C22C4×#1062189811yescharacteristic
788C22#1458338011yescharacteristic
789C22#1458353912yes—
790C22#1458355012yes—
791C4—44no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—82no—
797C4—861no—
798C4—861no—
799C4—862no—
800C4—861no—
801C4—861no—
802C4—862no—
803C4—3442no—
804C4—3442no—
805C4—1721no—
806C4—1721no—
807C4—1721no—
808C2—22no—
809C2—22no—
810C2—22no—
811C2—21no—
812C2—21no—
813C2—41no—
814C2—42no—
815C2—3441no—
816C2#1913742211yescharacteristic
817C2C2×#1458287111yescharacteristic
818C2#1914305311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC2×C43×#342C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063294C22
cosocleC24×C43C24
hypercenterC2×#342D43
hypocenterC43#22477
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
2. #19137440C2semidirect
3. #19135578C2semidirect
4. #19135052C2semidirect
6. #19134671C2semidirect
7. #19134669C2semidirect
8. #19134582C2semidirect
9. #19134382C2semidirect
10. #19134326C2semidirect
11. C2×C43×#342C2semidirect
16. C2×#13063318C4semidirect
17. C2×#13063318C4semidirect
18. C2×#13063311C4semidirect
20. C2×#13063308C4semidirect
21. C2×#13063307C4semidirect
22. C2×#13063304C4semidirect
25. C2×C4×C22⋊D43C4semidirect
27. C2×#13063284C4semidirect
51. C22×Dic86C2×C4semidirect
57. C22×C4×D43C2×C4semidirect
90. C2×C4⋊Dic43C2×C4semidirect
91. C2×C4⋊Dic43C2×C4semidirect
92. C2×C4⋊Dic43C2×C4semidirect
95. C2×Dic43⋊C4C2×C4semidirect
96. C2×Dic43⋊C4C2×C4semidirect
97. C2×Dic43⋊C4C2×C4semidirect
98. C2×Dic43⋊C4C2×C4semidirect
99. C2×Dic43⋊C4C2×C4semidirect
115. C2×(C2×D43)⋊C4C2×C4semidirect
116. C2×(C2×D43)⋊C4C2×C4semidirect
117. C2×(C2×D43)⋊C4C2×C4semidirect
120. C2×C4×Dic43C2×C4semidirect
121. C2×C4×Dic43C2×C4semidirect
122. C2×C4×Dic43C2×C4semidirect
409. C2×#342D43semidirect
460. C43#22477semidirect

Maximal subgroups

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

subgroupindex
C2×#145835752
#191374402
#191355782
#191350522
#191350482
#191346712
#191346692
#191345822
#191343822
#191343262
C2×C43×#3422
#2247743