Finite Group Databasebeta

← #25116945

Subgroups — #25116945

Order 11008.

1174 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583042C211yesmaximal, characteristic
2C2×#14583009C211yesmaximal, characteristic, complemented
3C2×#14582893C211yesmaximal, characteristic, complemented
4#19137426C211yesmaximal, characteristic, complemented
5#19135475C211yesmaximal, characteristic, complemented
6#19135284C211yesmaximal, characteristic, complemented
7#19135229C211yesmaximal, characteristic, complemented
8#19135024C211yesmaximal, characteristic, complemented
9#19134946C211yesmaximal, characteristic, complemented
10#19134929C211yesmaximal, characteristic, complemented
11#19134841C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134423C211yesmaximal, characteristic, complemented
14#19134373C211yesmaximal, characteristic, complemented
15C43×#2363C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22#14583042C418yescomplemented
23#14583009—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26#14582893—24no—
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37C2×#13063236C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582805C2211yescharacteristic
40#14582775—21no—
41#14582775—21no—
42#14582761—21no—
43#14582759C2211yescharacteristic
44#95×D43—21no—
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51C2×#121×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C43×#390—21no—
55C43×#390C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#388—21no—
58C43×#386—21no—
59C4×C4⋊C4×C43C2211yescharacteristic
60C4×C22⋊C4×C43—21no—
61C4×C22⋊C4×C43C2211yescharacteristic
62C2×#10621898—22no—
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C2×#10621898C2×C414yescomplemented
68C22×Dic86C2311yescharacteristic
69C22×D172C2311yescharacteristic
70C22×C22⋊D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C2×#10621883—41no—
75C2×#10621883—41no—
76C2×#10621883C2×C414yescomplemented
77C2×#10621882—22no—
78C2×#10621882—22no—
79C2×#10621882C2×C414yes—
80C22×C43⋊C8—22no—
81C22×C43⋊C8—22no—
82C22×C43⋊C8—41no—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C4×D172—22no—
88C4×D172—22no—
89C4×D172—41no—
90C4×D172—41no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C22⋊Dic43—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96#13063258—41no—
97#13063256—22no—
98#13063248—22no—
99#13063248—22no—
100#13063248C2×C414yescomplemented
101#13063246—22no—
102#13063246—41no—
103#13063245—22no—
104#13063245C2×C414yescomplemented
105#13063245D414yescomplemented
106C22⋊(C43⋊C8)C2×C414yescomplemented
107#13063236—22no—
108#13063236—41no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C22×D4×C43—21no—
115C22×D4×C43C2311yescharacteristic
116C23×C4×C43—21no—
117C23×C4×C43C2311yescharacteristic
118#121×C43—22no—
119#121×C43C2×C414yescomplemented
120C4×D4×C43—22no—
121C4×D4×C43—41no—
122#117×C43—22no—
123#117×C43—41no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43D411yescharacteristic
134C2×C22⋊C4×C43D411yescharacteristic
135C2×C42×C43—21no—
136C2×C42×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C2×C42×C43C2311yescharacteristic
139#95×C43—21no—
140#95×C43—21no—
141#95×C43D411yescharacteristic
142#95×C43D411yescharacteristic
143C24×C43—21no—
144C24×C43C2×D411yescharacteristic
145C23×D43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—24no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—81no—
153C2×D4×C43—81no—
154C2×D4×C43C22×C412yes—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—42no—
163C22×C4×C43—42no—
164C22×C4×C43—81no—
165C22×C4×C43C22×C412yes—
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43#4112yes—
172C22×C4×C43C2411yescharacteristic
173C2×C22⋊D43—24no—
174C2×C22⋊D43—42no—
175C2×C22⋊D43—42no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179#10621898—28no—
180#10621898—44no—
181#10621898—44no—
182#10621898—44no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172C22×C412yes—
187C2×D172C2×D412yes—
188C2×D172#4112yes—
189C2×C4×D43—24no—
190C2×C4×D43—42no—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43—42no—
194C2×C4×D43—42no—
195C2×C4×D43—42no—
196C2×C4×D43—81no—
197C2×C4×D43—81no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86C22×C412yes—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—81no—
209C4⋊C4×C43C22×C412yes—
210C4⋊C4×C43C2×D412yes—
211C22⋊C4×C43—24no—
212C22⋊C4×C43—41no—
213C22⋊C4×C43—41no—
214C22⋊C4×C43—42no—
215C22⋊C4×C43—42no—
216C22⋊C4×C43—42no—
217C22⋊C4×C43—81no—
218C42×C43—21no—
219C42×C43—21no—
220C42×C43—21no—
221C42×C43—21no—
222C42×C43—42no—
223C42×C43—81no—
224C22⋊Dic43—81no—
225#10621883—44no—
226#10621882—28no—
227(C2×D43)⋊C4—42no—
228(C2×D43)⋊C4—42no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—44no—
243C2×C43⋊C8C22×C412yes—
244C2×C43⋊C8C22×C412yes—
245C2×C43⋊C8C2×D412yes—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—22no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43C4×D412yes—
260C23×C43C22×D411yescharacteristic
261C22×D43—22no—
262C22×D43—22no—
263C22×D43—22no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—41no—
271D4×C43—41no—
272D4×C43—84no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—22no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—84no—
301C2×C4×C43C4×D412yes—
302C2×C4×C43C23×C411yescharacteristic
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×C4×C43H(5,𝔽2)11yescharacteristic
308C22⋊D43—48no—
309C2×Dic43—22no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318D172—22no—
319D172—22no—
320D172—22no—
321D172C4×D414yes—
322C4×D43—48no—
323C4×D43—84no—
324C4×D43—84no—
325Dic86—22no—
326Dic86—22no—
327Dic86—41no—
328Dic86—41no—
329C43⋊C8—22no—
330C43⋊C8—22no—
331C43⋊C8—22no—
332C43⋊C8—41no—
333#22860—431nomaximal, Sylow
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43C2×C4×D411yescharacteristic
349C22×C43D4211yescharacteristic
350C22×C43#54611yescharacteristic
351C22×C43#57511yescharacteristic
352C22×C43#57511yescharacteristic
353C22×C43#57611yescharacteristic
354C22×C43#57711yescharacteristic
355C2×D43—24no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—42no—
362C4×C43—22no—
363C4×C43—42no—
364C4×C43—41no—
365C4×C43—42no—
366C4×C43—41no—
367C4×C43—41no—
368C4×C43—41no—
369C4×C43—81no—
370C4×C43C2×C4×D411yescharacteristic
371C4×C43#51811yescharacteristic
372C4×C43#54611yescharacteristic
373C4×C43#55111yescharacteristic
374Dic43—42no—
375Dic43—81no—
376Dic43—81no—
377C2×#449—431no—
378C2×#442—431no—
379C2×#416—431no—
380#2363D4311yescharacteristic, complemented
381#2339—431no—
382#1973—431no—
383#1935—431no—
384#1927—431no—
385#1893—431no—
386#1879—431no—
387#1877—431no—
388#1862—431no—
389#1854—431no—
390#1762—431no—
391#1752—431no—
392C2×C43—42no—
393C2×C43—82no—
394C2×C43#235811yescharacteristic
395C2×C43#294311yescharacteristic
396C2×C43#294611yescharacteristic
397C2×C43#326711yescharacteristic
398C2×C43#326811yescharacteristic
399C2×C43#330711yescharacteristic
400C2×C43#331911yescharacteristic
401D43—44no—
402C22×#41—431no—
403C22×SD16—431no—
404C22×D8—431no—
405C23×C8—431no—
406C2×#121C2×D4311yescharacteristic
407C2×C4×D4—431no—
408C2×C4×D4—431no—
409C2×C4×D4C2×D4311yescharacteristic
410C2×#117C2×D4311yescharacteristic
411#449—438no—
412#442—864no—
413C2×#107—431no—
414C2×#106—431no—
415#416—864no—
416C2×#103—431no—
417C2×#103—431no—
418C2×#103—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×#102—431no—
424C2×C22⋊C8—431no—
425C2×#97—431no—
426C2×#97—431no—
427#391—431no—
428#391—431no—
429#390—21no—
430#390C2×D4311yescharacteristic
431#389C2×D4311yescharacteristic
432#388—21no—
433#386—21no—
434#386—861no—
435#386—861no—
436#381—861no—
437#380—431no—
438C4×C4⋊C4C2×D4311yescharacteristic
439C4×C22⋊C4—21no—
440C4×C22⋊C4C2×D4311yescharacteristic
441C2×#95—861no—
442#340—431no—
443#340—431no—
444#340—431no—
445#340—431no—
446#336—431no—
447#336—431no—
448C43#2286011yescharacteristic, complemented, Sylow
449C2×#41—434no—
450C2×#41—862no—
451C2×#41—862no—
452C2×#41—862no—
453C2×#41—1721no—
454C2×#41—1721no—
455C22×Q8—431no—
456C22×D4—21no—
457C22×D4—431no—
458C22×D4—861no—
459C22×D4C22×D4311yescharacteristic
460C23×C4—21no—
461C23×C4—861no—
462C23×C4—861no—
463C23×C4—861no—
464C23×C4C22×D4311yescharacteristic
465C2×SD16—434no—
466C2×SD16—1721no—
467C2×SD16—1721no—
468C2×D8—434no—
469C2×D8—862no—
470C2×D8—862no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8—431no—
474C22×C8—431no—
475C22×C8—862no—
476C22×C8—862no—
477C22×C8—1721no—
478#121—22no—
479#121C4×D4314yescomplemented
480C4×D4—22no—
481C4×D4—41no—
482C4×D4—862no—
483C4×D4—862no—
484C4×D4—1721no—
485C4×D4—1721no—
486#117—22no—
487#117—41no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4C22×D4311yescharacteristic
492C2×C4⋊C4C22×D4311yescharacteristic
493C2×C4⋊C4C22×D4311yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4C22⋊D4311yescharacteristic
503C2×C22⋊C4C22⋊D4311yescharacteristic
504C2×C42—21no—
505C2×C42—21no—
506C2×C42C22×D4311yescharacteristic
507C2×C42C22×D4311yescharacteristic
508#107—1721no—
509#106—862no—
510#103—434no—
511#103—862no—
512#103—862no—
513#102—434no—
514#102—434no—
515#102—862no—
516#102—862no—
517#102—1721no—
518C22⋊C8—434no—
519#97—862no—
520#97—1721no—
521#95—21no—
522#95—21no—
523#95—861no—
524#95—861no—
525#95—861no—
526#95—861no—
527#95—861no—
528#95C22⋊D4311yescharacteristic
529#95C22⋊D4311yescharacteristic
530C24—21no—
531C24—861no—
532C24C2×C22⋊D4311yescharacteristic
533#41—868no—
534#41—1724no—
535#41—1724no—
536#41—1724no—
537C2×Q8—432no—
538C2×Q8—861no—
539C2×Q8—861no—
540C2×Q8—861no—
541C2×Q8—861no—
542C2×Q8—861no—
543C2×D4—24no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—81no—
550C2×D4—81no—
551C2×D4—432no—
552C2×D4—432no—
553C2×D4—432no—
554C2×D4—864no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—1722no—
559C2×D4—1722no—
560C2×D4C2×C4×D4312yes—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—81no—
571C22×C4—861no—
572C22×C4—864no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—3441no—
576C22×C4—3441no—
577C22×C4—1722no—
578C22×C4—1722no—
579C22×C4—1722no—
580C22×C4—1722no—
581C22×C4—1722no—
582C22×C4—1722no—
583C22×C4C2×C4×D4312yes—
584C22×C4#1062189812yes—
585C22×C4C2×C22⋊D4311yescharacteristic
586C22×C4C2×C22⋊D4311yescharacteristic
587C22×C4C2×C22⋊D4311yescharacteristic
588C22×C4C2×C22⋊D4311yescharacteristic
589C22×C4C2×C22⋊D4311yescharacteristic
590C22×C4C23×D4311yescharacteristic
591SD16—1724no—
592D8—868no—
593C2×C8—432no—
594C2×C8—432no—
595C2×C8—432no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—1724no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—81no—
611C4⋊C4—861no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4C2×C4×D4312yes—
616C4⋊C4D4×D4312yes—
617C22⋊C4—24no—
618C22⋊C4—41no—
619C22⋊C4—41no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—81no—
624C22⋊C4—3441no—
625C22⋊C4—1722no—
626C22⋊C4—1722no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—42no—
632C42—81no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—862no—
647C23—862no—
648C23—862no—
649C23—1721no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23C4×C22⋊D4312yes—
654C23C22×C22⋊D4311yescharacteristic
655Q8—862no—
656Q8—862no—
657Q8—1721no—
658Q8—1721no—
659D4—22no—
660D4—22no—
661D4—41no—
662D4—41no—
663D4—84no—
664D4—434no—
665D4—862no—
666D4—862no—
667D4—862no—
668D4—1728no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—84no—
697C2×C4—862no—
698C2×C4—3444no—
699C2×C4—3444no—
700C2×C4—1728no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4C4×C22⋊D4312yes—
710C2×C4C22×C4×D4311yescharacteristic
711C2×C4C2×D4×D4311yescharacteristic
712C2×C4#41×D4311yescharacteristic
713C2×C4C2×#1062189811yescharacteristic
714C2×C4#1306337011yescharacteristic
715C2×C4#1306337111yescharacteristic
716C8—862no—
717C8—862no—
718C8—862no—
719C8—1721no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—864no—
735C22—1722no—
736C22—1722no—
737C22—1722no—
738C22—1722no—
739C22—1722no—
740C22—1722no—
741C22C2×C4×C22⋊D4311yescharacteristic
742C22D4×C22⋊D4311yescharacteristic
743C22#1458353711yescharacteristic
744C22#1458369711yescharacteristic
745C22#1458369711yescharacteristic
746C22#1458370211yescharacteristic
747C22#1458371011yescharacteristic
748C4—22no—
749C4—42no—
750C4—41no—
751C4—41no—
752C4—42no—
753C4—41no—
754C4—41no—
755C4—81no—
756C4—3441no—
757C4—3441no—
758C4—1722no—
759C4C4×D4×D4311yescharacteristic
760C4#1458337111yescharacteristic
761C4#1458354511yescharacteristic
762C4#1458357811yescharacteristic
763C2—42no—
764C2—82no—
765C2—1724no—
766C2#1913757211yescharacteristic
767C2#1914339311yescharacteristic
768C2#1914342711yescharacteristic
769C2#1914611611yescharacteristic
770C2#1914613611yescharacteristic
771C2#1914656511yescharacteristic
772C2#1914674511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2363C2
socleC23×C43C22×D4
prime radicalC2×#14583042C2
cosocleC22×C4×C43C24
hypercenter#2363D43
hypocenterC43#22860
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. C2×#14583009C2semidirect
3. C2×#14582893C2semidirect
4. #19137426C2semidirect
5. #19135475C2semidirect
6. #19135284C2semidirect
7. #19135229C2semidirect
8. #19135024C2semidirect
9. #19134946C2semidirect
10. #19134929C2semidirect
11. #19134841C2semidirect
12. #19134794C2semidirect
13. #19134423C2semidirect
14. #19134373C2semidirect
15. C43×#2363C2semidirect
22. #14583042C4semidirect
67. C2×#10621898C2×C4semidirect
76. C2×#10621883C2×C4semidirect
100. #13063248C2×C4semidirect
104. #13063245C2×C4semidirect
105. #13063245D4semidirect
106. C22⋊(C43⋊C8)C2×C4semidirect
119. #121×C43C2×C4semidirect
380. #2363D43semidirect
448. C43#22860semidirect
479. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830422
C2×#145830092
C2×#145828932
#191374262
#191354752
#191352842
#191352292
#191350242
#191349462
#191349292
#191348412
#191347942
#191344232
#191343732
C43×#23632
#2286043