Finite Group Databasebeta

← #25130589

Subgroups — #25130589

Order 11008.

1152 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583589C211yesmaximal, characteristic, complemented
2C2×#14583199C211yesmaximal, characteristic, complemented
3C2×C4×#10621883C211yesmaximal, characteristic, complemented
4#19135798C211yesmaximal, characteristic, complemented
5#19135791C211yesmaximal, characteristic, complemented
6#19135598C211yesmaximal, characteristic, complemented
7#19135598C211yesmaximal, characteristic, complemented
8#19135559C211yesmaximal, characteristic, complemented
9#19135390C211yesmaximal, characteristic, complemented
10#19134918C211yesmaximal, characteristic, complemented
11#19134913C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic, complemented
13#19134787C211yesmaximal, characteristic, complemented
14#19134607C211yesmaximal, characteristic, complemented
15C43×#2535C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17#14583589—24no—
18#14583589—24no—
19C2×#13063318—21no—
20C2×#13063317C2211yescharacteristic
21C2×#13063315—21no—
22C2×#13063306—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063304C2211yescharacteristic
25C2×C4×Dic86C2211yescharacteristic
26C2×#13063284C2211yescharacteristic
27C2×#13063281—21no—
28C22×C4⋊Dic43C2211yescharacteristic
29#14583199—24no—
30C4×#10621883—24no—
31C2×#13063258C2211yescharacteristic
32C2×#13063256C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×C4×C43⋊C8C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×#121×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C43×#397—21no—
57C43×#392—21no—
58C43×#386—21no—
59C43×#386—21no—
60C43×#382C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#380C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C23×Dic43—21no—
65C2×#10621883—22no—
66C2×#10621883—22no—
67C2×#10621883—22no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063318—28no—
73#13063317—22no—
74#13063317D414yescomplemented
75#13063315—28no—
76#13063306—28no—
77#13063304—22no—
78#13063304—22no—
79#13063304—22no—
80#13063304—22no—
81C4×Dic86—22no—
82C4×Dic86D414yescomplemented
83#13063284—22no—
84#13063284—22no—
85#13063281—28no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102#13063258—22no—
103#13063256—22no—
104#13063256—22no—
105C4⋊(C43⋊C8)—22no—
106#13063248—22no—
107#13063248—41no—
108#13063248—41no—
109#13063246—22no—
110#13063246—22no—
111#13063246—22no—
112C22⋊(C43⋊C8)—22no—
113C22⋊(C43⋊C8)—22no—
114C22⋊(C43⋊C8)—41no—
115C22⋊(C43⋊C8)—41no—
116C4×C43⋊C8—22no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119C22×D4×C43D411yescharacteristic
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43—21no—
122C23×C4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124#121×C43—22no—
125#121×C43—22no—
126#121×C43—41no—
127#121×C43—41no—
128C4×D4×C43—22no—
129C4×D4×C43—22no—
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132C2×C4⋊C4×C43D411yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43D411yescharacteristic
142C2×C22⋊C4×C43D411yescharacteristic
143C2×C42×C43C2311yescharacteristic
144#95×C43—21no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148C24×C43—21no—
149C24×C43C2×D411yescharacteristic
150C24×C43C2×D411yescharacteristic
151C2×D4×C43—22no—
152C2×D4×C43—21no—
153C2×D4×C43—22no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—41no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—81no—
164C2×D4×C43—81no—
165C2×D4×C43#4112yes—
166C22×C4×C43—21no—
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—21no—
181C22×C4×C43—42no—
182C22×C4×C43—81no—
183C22×C4×C43—81no—
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2411yescharacteristic
189C22×Dic43—24no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—42no—
195C22×Dic43—42no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86C2×D412yes—
202C4⋊C4×C43—22no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C22⋊C4×C43—22no—
210C22⋊C4×C43—22no—
211C22⋊C4×C43—42no—
212C22⋊C4×C43—42no—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—81no—
215C22⋊C4×C43—81no—
216C42×C43C2×D412yes—
217C42×C43C2×D412yes—
218C22⋊Dic43—24no—
219C22⋊Dic43—24no—
220C22⋊Dic43—24no—
221#10621883—28no—
222C4⋊Dic43—24no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43C2×D412yes—
227C4⋊Dic43C2×D412yes—
228C4⋊Dic43C2×D412yes—
229Dic43⋊C4—24no—
230Dic43⋊C4—24no—
231Dic43⋊C4—24no—
232Dic43⋊C4—24no—
233Dic43⋊C4—24no—
234C4×Dic43—24no—
235C4×Dic43—24no—
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—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8#4112yes—
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—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43#13512yes—
269C23×C43C22×D411yescharacteristic
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—44no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43—84no—
276D4×C43—84no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
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—84no—
305C2×C4×C43#12012yes—
306C2×C4×C43#12012yes—
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C2×C4×C43H(5,𝔽2)11yescharacteristic
312C2×C4×C432−1+411yescharacteristic
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—48no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326Dic86—22no—
327Dic86—22no—
328Dic86—41no—
329Dic86—41no—
330C43⋊C8—22no—
331C43⋊C8—41no—
332C43⋊C8—41no—
333C43⋊C8—41no—
334#24125—431nomaximal, Sylow
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
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—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—42no—
350C22×C43—41no—
351C22×C43—42no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43C2×#12011yescharacteristic
357C22×C43#54611yescharacteristic
358C22×C43#54711yescharacteristic
359C22×C43C2×#13511yescharacteristic
360C22×C43#57511yescharacteristic
361C22×C43#57711yescharacteristic
362C22×C43#57711yescharacteristic
363C4×C43—22no—
364C4×C43—22no—
365C4×C43—41no—
366C4×C43—41no—
367C4×C43—81no—
368C4×C43—81no—
369C4×C43—81no—
370C4×C43#52511yescharacteristic
371C4×C43#53711yescharacteristic
372C4×C43#54811yescharacteristic
373C4×C43#55011yescharacteristic
374Dic43—42no—
375Dic43—42no—
376Dic43—42no—
377Dic43—42no—
378C2×#552—431no—
379C2×#478—431no—
380C2×C4×SD16—431no—
381#2535D4311yescharacteristic
382#2036—431no—
383#2035—431no—
384#2000—431no—
385#2000—431no—
386#1991—431no—
387#1954—431no—
388#1875—431no—
389#1874—431no—
390#1854—431no—
391#1853—431no—
392#1805—431no—
393C2×C43—42no—
394C2×C43—81no—
395C2×C43—82no—
396C2×C43#240711yescharacteristic
397C2×C43#300211yescharacteristic
398C2×C43#301011yescharacteristic
399C2×C43#329611yescharacteristic
400C2×C43#332311yescharacteristic
401C2×C43#333711yescharacteristic
402C2×C43#335111yescharacteristic
403C22×SD16—431no—
404#552—864no—
405#552—864no—
406C2×#126—861no—
407C2×#125—431no—
408C2×#125—861no—
409C2×#123—861no—
410C2×C22⋊Q8—431no—
411C2×C22⋊Q8—431no—
412C2×#121C2×D4311yescharacteristic
413C2×#121C2×D4311yescharacteristic
414C2×C4×Q8—431no—
415C2×C4×D4C2×D4311yescharacteristic
416C2×C4×D4C2×D4311yescharacteristic
417C2×#117—431no—
418C2×#117—861no—
419C22×C4⋊C4—431no—
420#478—864no—
421C4×SD16—864no—
422C2×#107—431no—
423C2×#106—431no—
424C2×#106—431no—
425C2×C4⋊C8—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102—431no—
432C2×C22⋊C8—431no—
433C2×C22⋊C8—431no—
434C2×C22⋊C8—431no—
435C2×C22⋊C8—431no—
436C2×C4×C8—431no—
437#397—21no—
438#392—21no—
439#386—21no—
440#386—21no—
441#382C2×D4311yescharacteristic
442#380C2×D4311yescharacteristic
443#380C2×D4311yescharacteristic
444#340—431no—
445#340—431no—
446#340—431no—
447#340—431no—
448#340—431no—
449#340—431no—
450C43#2412511yescharacteristic, complemented, Sylow
451C22×Q8—431no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4C22⋊D4311yescharacteristic
455C22×D4C22×D4311yescharacteristic
456C23×C4—21no—
457C23×C4—861no—
458C23×C4C22×D4311yescharacteristic
459C23×C4C22×D4311yescharacteristic
460C2×SD16—862no—
461C2×SD16—862no—
462C2×SD16—862no—
463C22×C8—431no—
464C22×C8—431no—
465C22×C8—431no—
466C22×C8—431no—
467#126—868no—
468#125—434no—
469#125—868no—
470#125—862no—
471#123—868no—
472C22⋊Q8—862no—
473C22⋊Q8—862no—
474C22⋊Q8—862no—
475C22⋊Q8—862no—
476#121—22no—
477#121—22no—
478#121—41no—
479#121—41no—
480C4×Q8—434no—
481C4×Q8—862no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486#117—868no—
487#117—862no—
488#117—862no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—862no—
493C2×C4⋊C4—862no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4C22⋊D4311yescharacteristic
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C4⋊C4C22×D4311yescharacteristic
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4C22⋊D4311yescharacteristic
513C2×C22⋊C4C22⋊D4311yescharacteristic
514C2×C42—861no—
515C2×C42—861no—
516C2×C42C22×D4311yescharacteristic
517#107—862no—
518#106—862no—
519#106—862no—
520C4⋊C8—862no—
521#103—862no—
522#103—1721no—
523#103—1721no—
524#102—862no—
525#102—862no—
526#102—862no—
527C22⋊C8—862no—
528C22⋊C8—862no—
529C22⋊C8—1721no—
530C22⋊C8—1721no—
531C4×C8—862no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536C24—21no—
537C24C2×C22⋊D4311yescharacteristic
538C24C2×C22⋊D4311yescharacteristic
539C2×Q8—432no—
540C2×Q8—861no—
541C2×Q8—861no—
542C2×Q8—861no—
543C2×Q8—861no—
544C2×Q8—861no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—41no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4#1062190012yes—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—42no—
576C22×C4—81no—
577C22×C4—81no—
578C22×C4—864no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—1722no—
584C22×C4—1722no—
585C22×C4C2×C22⋊D4311yescharacteristic
586C22×C4C2×C22⋊D4311yescharacteristic
587C22×C4C2×C22⋊D4311yescharacteristic
588C22×C4C2×C22⋊D4311yescharacteristic
589C22×C4C23×D4311yescharacteristic
590SD16—868no—
591C2×C8—432no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C4⋊C4—22no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—432no—
611C4⋊C4—432no—
612C4⋊C4—432no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4—864no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—864no—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C42—864no—
633C42—864no—
634C42D4×D4312yes—
635C42D4×D4312yes—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23#1306334512yes—
657C23C22×C22⋊D4311yescharacteristic
658Q8—862no—
659Q8—862no—
660Q8—1721no—
661Q8—1721no—
662D4—22no—
663D4—22no—
664D4—44no—
665D4—41no—
666D4—41no—
667D4—84no—
668D4—84no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
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—41no—
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—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—1728no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4#1306329312yes—
711C2×C4#1306329312yes—
712C2×C4C2×D4×D4311yescharacteristic
713C2×C4C2×D4×D4311yescharacteristic
714C2×C4#41×D4311yescharacteristic
715C2×C4C2×#1062190011yescharacteristic
716C2×C4#1306337011yescharacteristic
717C2×C4#1306337211yescharacteristic
718C8—862no—
719C8—1721no—
720C8—1721no—
721C8—1721no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—42no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22C2×#1306329311yescharacteristic
744C22#1458354311yescharacteristic
745C22#1458354811yescharacteristic
746C22C2×#1306334511yescharacteristic
747C22#1458369711yescharacteristic
748C22#1458371011yescharacteristic
749C22#1458371011yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—81no—
755C4—81no—
756C4—81no—
757C4—1722no—
758C4—1722no—
759C4—1722no—
760C4—1722no—
761C4#1458340911yescharacteristic
762C4#1458347811yescharacteristic
763C4#1458355511yescharacteristic
764C4#1458356711yescharacteristic
765C2—42no—
766C2—81no—
767C2—82no—
768C2#1913793611yescharacteristic
769C2#1914381111yescharacteristic
770C2#1914387911yescharacteristic
771C2#1914643011yescharacteristic
772C2#1914681111yescharacteristic
773C2#1914696811yescharacteristic
774C2#1914714911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2535C2
socleC23×C43C22×D4
hypercenter#2535D43
hypocenterC43#24125
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×#14583589C2semidirect
2. C2×#14583199C2semidirect
3. C2×C4×#10621883C2semidirect
4. #19135798C2semidirect
5. #19135791C2semidirect
6. #19135598C2semidirect
7. #19135598C2semidirect
8. #19135559C2semidirect
9. #19135390C2semidirect
10. #19134918C2semidirect
11. #19134913C2semidirect
12. #19134792C2semidirect
13. #19134787C2semidirect
14. #19134607C2semidirect
74. #13063317D4semidirect
82. C4×Dic86D4semidirect
450. C43#24125semidirect

Maximal subgroups

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

subgroupindex
C2×#145835892
C2×#145831992
C2×C4×#106218832
#191357982
#191357912
#191355982
#191355592
#191353902
#191349182
#191349132
#191347922
#191347872
#191346072
C43×#25352
#2412543