Finite Group Databasebeta

← #25140123

Subgroups — #25140123

Order 11008.

1064 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583227C211yesmaximal, characteristic, complemented
2C2×#14582900C211yesmaximal, characteristic, complemented
3D4×C4⋊Dic43C211yesmaximal, characteristic, complemented
4#19136128C211yesmaximal, characteristic, complemented
5#19136003C211yesmaximal, characteristic, complemented
6#19135788C211yesmaximal, characteristic, complemented
7#19135774C211yesmaximal, characteristic, complemented
8#19135233C211yesmaximal, characteristic, complemented
9#19135219C211yesmaximal, characteristic, complemented
10#19134913C211yesmaximal, characteristic, complemented
11#19134893C211yesmaximal, characteristic, complemented
12#19134787C211yesmaximal, characteristic, complemented
13#19134626C211yesmaximal, characteristic, complemented
14#19134535C211yesmaximal, characteristic, complemented
15C43×#2407C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×D4×Dic43—21no—
18C22×C4⋊Dic43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20#14583227—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25#14582900—24no—
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37#14582798—21no—
38#14582774—21no—
39#14582774—21no—
40#14582769C2211yescharacteristic
41#14582759C2211yescharacteristic
42#14582759C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C22×#41×C43C2211yescharacteristic
51C2×C22⋊Q8×C43C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C43×#394—21no—
55C43×#392—21no—
56C43×#391C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#386—21no—
59C43×#385—21no—
60C43×#380C2211yescharacteristic
61C23×Dic43—21no—
62C23×Dic43—21no—
63C2×#10621877—22no—
64C2×#10621877—22no—
65C2×#10621877—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70D4×Dic43—44no—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43—22no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—41no—
78C2×C4⋊Dic43—41no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C4×Dic43—21no—
86#13063258—41no—
87#13063256—22no—
88#13063256—22no—
89#13063256—41no—
90#13063249—22no—
91#13063249—22no—
92#13063249—41no—
93#13063249D414yescomplemented
94#13063246—22no—
95#13063246—22no—
96#13063246—22no—
97#13063246—41no—
98C22⋊(C43⋊C8)—22no—
99C22⋊(C43⋊C8)—22no—
100C22⋊(C43⋊C8)—41no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C2×#41×C43—22no—
105C2×#41×C43—22no—
106C2×#41×C43—22no—
107C2×#41×C43—22no—
108C2×#41×C43—41no—
109C2×#41×C43—41no—
110C22×Q8×C43C2311yescharacteristic
111C22×D4×C43—21no—
112C22×D4×C43—21no—
113C22×D4×C43D411yescharacteristic
114C22×D4×C43C2311yescharacteristic
115C23×C4×C43—21no—
116C23×C4×C43C2311yescharacteristic
117C23×C4×C43C2311yescharacteristic
118C22⋊Q8×C43—22no—
119C22⋊Q8×C43—41no—
120#121×C43—22no—
121#121×C43—41no—
122C4×D4×C43—22no—
123C4×D4×C43—22no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43D411yescharacteristic
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×C43C2311yescharacteristic
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139C24×C43—21no—
140C24×C43C2×D411yescharacteristic
141C24×C43C2×D411yescharacteristic
142#41×C43—28no—
143#41×C43—44no—
144#41×C43—44no—
145#41×C43—44no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43C2×D412yes—
152C2×D4×C43—22no—
153C2×D4×C43—21no—
154C2×D4×C43—22no—
155C2×D4×C43—22no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—81no—
166C2×D4×C43#4112yes—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—42no—
181C22×C4×C43—42no—
182C22×C4×C43—42no—
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43#4112yes—
188C22×C4×C43#4112yes—
189C22×C4×C43C2411yescharacteristic
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—42no—
195C22×Dic43—42no—
196C22×Dic43—42no—
197C22×Dic43—42no—
198C22×Dic43—81no—
199C22×Dic43—81no—
200C4⋊C4×C43—22no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—42no—
206C22⋊C4×C43—22no—
207C22⋊C4×C43—22no—
208C22⋊C4×C43—42no—
209C22⋊C4×C43—42no—
210C22⋊C4×C43—42no—
211C22⋊C4×C43—81no—
212C22⋊C4×C43—81no—
213C42×C43—21no—
214C42×C43—21no—
215C22⋊Dic43—42no—
216C22⋊Dic43—42no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—42no—
225C4⋊Dic43—42no—
226C4⋊Dic43—42no—
227C4⋊Dic43—81no—
228C4⋊Dic43C2×D412yes—
229C4×Dic43—42no—
230#10621877—44no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—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⋊C8C2×D412yes—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—22no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43#12312yes—
263C23×C43AGL(1,ℤ/8)12yes—
264C23×C43C22×D411yescharacteristic
265Q8×C43—22no—
266Q8×C43—22no—
267Q8×C43—41no—
268Q8×C43—41no—
269D4×C43—28no—
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—48no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43—84no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—22no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—48no—
292C2×C4×C43—41no—
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—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43#12312yes—
305C2×C4×C43#13712yes—
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C2×C4×C43C2×#4111yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43H(5,𝔽2)11yescharacteristic
311C2×C4×C43H(5,𝔽2)11yescharacteristic
312C2×Dic43—22no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—84no—
325C2×Dic43—84no—
326C43⋊C8—22no—
327C43⋊C8—41no—
328C43⋊C8—41no—
329C43⋊C8—41no—
330#24879—431nomaximal, Sylow
331C22×C43—22no—
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43C2×#12311yescharacteristic
353C22×C43D4211yescharacteristic
354C22×C43#54611yescharacteristic
355C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C43C2×#13711yescharacteristic
357C22×C43#57711yescharacteristic
358C22×C43#57711yescharacteristic
359C4×C43—22no—
360C4×C43—22no—
361C4×C43—41no—
362C4×C43—41no—
363C4×C43—42no—
364C4×C43—81no—
365C4×C43—81no—
366C4×C43#52511yescharacteristic
367C4×C43#53811yescharacteristic
368C4×C43#54611yescharacteristic
369C4×C43#55111yescharacteristic
370Dic43—42no—
371Dic43—81no—
372Dic43—81no—
373Dic43—81no—
374C2×#483—431no—
375C2×#417—431no—
376#2407D4311yescharacteristic
377D4×C4⋊C4—431no—
378#2094—431no—
379#2072—431no—
380#2035—431no—
381#2033—431no—
382#1928—431no—
383#1926—431no—
384#1874—431no—
385#1870—431no—
386#1853—431no—
387#1809—431no—
388#1788—431no—
389C2×C43—42no—
390C2×C43—42no—
391C2×C43—82no—
392C2×C43#241811yescharacteristic
393C2×C43#309211yescharacteristic
394C2×C43#309911yescharacteristic
395C2×C43#326511yescharacteristic
396C2×C43#327811yescharacteristic
397C2×C43#330611yescharacteristic
398C2×C43#333111yescharacteristic
399C22×#41C2×D4311yescharacteristic
400C22×M16—431no—
401C2×C22⋊Q8C2×D4311yescharacteristic
402C2×#121C2×D4311yescharacteristic
403C2×C4×D4—861no—
404C2×C4×D4C2×D4311yescharacteristic
405C22×C4⋊C4—431no—
406C22×C4⋊C4—431no—
407#483—864no—
408C2×#107—431no—
409C2×#106—431no—
410C2×#106—431no—
411C2×#106—431no—
412#417—864no—
413C2×#103—431no—
414C2×#103—431no—
415C2×#103—431no—
416C2×#103—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×C22⋊C8—431no—
422C2×C22⋊C8—431no—
423C2×C22⋊C8—431no—
424#394—21no—
425#392—21no—
426#391C2×D4311yescharacteristic
427#390C2×D4311yescharacteristic
428#389—861no—
429#386—21no—
430#385—21no—
431#385—861no—
432#385—861no—
433#384—431no—
434#380—431no—
435#380—431no—
436#380C2×D4311yescharacteristic
437C4×C4⋊C4—431no—
438#340—431no—
439#340—431no—
440#340—431no—
441#340—431no—
442#336—431no—
443#336—431no—
444C43#2487911yescharacteristic, complemented, Sylow
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—22no—
449C2×#41—41no—
450C2×#41—41no—
451C22×Q8C22×D4311yescharacteristic
452C22×D4—21no—
453C22×D4—21no—
454C22×D4C22⋊D4311yescharacteristic
455C22×D4C22×D4311yescharacteristic
456C23×C4—21no—
457C23×C4—861no—
458C23×C4—861no—
459C23×C4C22×D4311yescharacteristic
460C23×C4C22×D4311yescharacteristic
461C2×M16—862no—
462C2×M16—862no—
463C2×M16—1721no—
464C22×C8—431no—
465C22×C8—431no—
466C22×C8—431no—
467C22×C8—431no—
468C22⋊Q8—22no—
469C22⋊Q8—41no—
470#121—22no—
471#121—41no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—1724no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—862no—
481C2×C4⋊C4—862no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—1721no—
487C2×C4⋊C4—1721no—
488C2×C4⋊C4C22⋊D4311yescharacteristic
489C2×C4⋊C4C22×D4311yescharacteristic
490C2×C4⋊C4C22×D4311yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4C22⋊D4311yescharacteristic
499C2×C22⋊C4C22⋊D4311yescharacteristic
500C2×C42—861no—
501C2×C42C22×D4311yescharacteristic
502#107—1721no—
503#106—862no—
504#106—862no—
505#106—1721no—
506#103—434no—
507#103—862no—
508#103—862no—
509#103—1721no—
510#102—862no—
511#102—862no—
512#102—862no—
513#102—1721no—
514C22⋊C8—862no—
515C22⋊C8—862no—
516C22⋊C8—1721no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—861no—
521#95—861no—
522#95—861no—
523C24—21no—
524C24C2×C22⋊D4311yescharacteristic
525C24C2×C22⋊D4311yescharacteristic
526#41—28no—
527#41—44no—
528#41—44no—
529#41—44no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8D4×D4312yes—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—81no—
550C2×D4#1062190012yes—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—3441no—
572C22×C4—3441no—
573C22×C4—1722no—
574C22×C4—1722no—
575C22×C4—1722no—
576C22×C4—1722no—
577C22×C4#1062190012yes—
578C22×C4#1062190012yes—
579C22×C4C2×C22⋊D4311yescharacteristic
580C22×C4C2×C22⋊D4311yescharacteristic
581C22×C4C2×C22⋊D4311yescharacteristic
582C22×C4C2×C22⋊D4311yescharacteristic
583C22×C4C23×D4311yescharacteristic
584M16—1724no—
585C2×C8—432no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—432no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—861no—
611C4⋊C4—3441no—
612C4⋊C4—1722no—
613C4⋊C4—1722no—
614C4⋊C4—1722no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—81no—
621C22⋊C4—81no—
622C22⋊C4—1722no—
623C22⋊C4—1722no—
624C42—21no—
625C42—21no—
626C42—1722no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
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#1306330612yes—
647C23#1306335012yes—
648C23C22×C22⋊D4311yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—41no—
652Q8—41no—
653D4—28no—
654D4—22no—
655D4—22no—
656D4—48no—
657D4—41no—
658D4—41no—
659D4—84no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—48no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—862no—
689C2×C4—3444no—
690C2×C4—3444no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4#1306330612yes—
703C2×C4#1306335512yes—
704C2×C4C2×D4×D4311yescharacteristic
705C2×C4C2×#1062190011yescharacteristic
706C2×C4C2×#1062190011yescharacteristic
707C2×C4C2×#1062190011yescharacteristic
708C2×C4#1306337011yescharacteristic
709C2×C4#1306337011yescharacteristic
710C8—862no—
711C8—1721no—
712C8—1721no—
713C8—1721no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22C2×#1306330611yescharacteristic
736C22D4×C22⋊D4311yescharacteristic
737C22#1458354311yescharacteristic
738C22C2×#1306335011yescharacteristic
739C22C2×#1306335511yescharacteristic
740C22#1458370711yescharacteristic
741C22#1458371011yescharacteristic
742C4—22no—
743C4—22no—
744C4—41no—
745C4—42no—
746C4—41no—
747C4—81no—
748C4—81no—
749C4—3441no—
750C4—3441no—
751C4—3441no—
752C4—1722no—
753C4#1458340511yescharacteristic
754C4#1458348411yescharacteristic
755C4#1458353611yescharacteristic
756C4#1458358011yescharacteristic
757C2—42no—
758C2—42no—
759C2—82no—
760C2#1913805311yescharacteristic
761C2#1914451511yescharacteristic
762C2#1914458011yescharacteristic
763C2#1914609111yescharacteristic
764C2#1914626111yescharacteristic
765C2#1914655611yescharacteristic
766C2#1914691111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2407C2
socleC23×C43C22×D4
hypercenter#2407D43
hypocenterC43#24879
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C2×#14583227C2semidirect
2. C2×#14582900C2semidirect
3. D4×C4⋊Dic43C2semidirect
4. #19136128C2semidirect
5. #19136003C2semidirect
6. #19135788C2semidirect
7. #19135774C2semidirect
8. #19135233C2semidirect
9. #19135219C2semidirect
10. #19134913C2semidirect
11. #19134893C2semidirect
12. #19134787C2semidirect
13. #19134626C2semidirect
14. #19134535C2semidirect
93. #13063249D4semidirect
444. C43#24879semidirect

Maximal subgroups

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

subgroupindex
C2×#145832272
C2×#145829002
D4×C4⋊Dic432
#191361282
#191360032
#191357882
#191357742
#191352332
#191352192
#191349132
#191348932
#191347872
#191346262
#191345352
C43×#24072
#2487943