Finite Group Databasebeta

← #25102372

Subgroups — #25102372

Order 11008.

1400 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583376C211yesmaximal, characteristic, complemented
2C2×#14583037C211yesmaximal, characteristic
3C2×#14582999C211yesmaximal, characteristic, complemented
4C2×C4×#10621883C211yesmaximal, characteristic, complemented
5#19134953C211yesmaximal, characteristic, complemented
6#19134953C211yesmaximal, characteristic, complemented
7#19134918C211yesmaximal, characteristic
8#19134862C211yesmaximal, characteristic, complemented
9#19134848C211yesmaximal, characteristic, complemented
10#19134792C211yesmaximal, characteristic, complemented
11#19134529C211yesmaximal, characteristic, complemented
12#19134428C211yesmaximal, characteristic, complemented
13C4×#13063248C211yesmaximal, characteristic, complemented
14#19134361C211yesmaximal, characteristic, complemented
15C43×#2324C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19#14583376—24no—
20#14583376—24no—
21C2×C4×Dic86C2211yescharacteristic
22C2×C4×Dic86C2211yescharacteristic
23C2×C4×Dic86C2211yescharacteristic
24C2×C4×Dic86C2211yescharacteristic
25C2×#13063290—21no—
26C2×#13063290—21no—
27C2×#13063284C2211yescharacteristic
28C2×#13063281—21no—
29C2×#13063281—21no—
30#14583037C418yescomplemented
31#14582999—24no—
32C4×#10621883—24no—
33C2×#13063258C2211yescharacteristic
34C2×#13063256C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×#13063236C2211yescharacteristic
46C2×C4×C43⋊C8C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582654C2211yescharacteristic
53C2×#121×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×#117×C43C2211yescharacteristic
56C43×#390—21no—
57C43×#390C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#388—21no—
60C43×#386—21no—
61C43×#385—21no—
62C43×#380C2211yescharacteristic
63C4×C4⋊C4×C43C2211yescharacteristic
64C22×Dic86—21no—
65C22×Dic86—22no—
66C22×Dic86—22no—
67C22×Dic86—22no—
68C22×Dic86—22no—
69C22×Dic86—22no—
70C22×Dic86C2×C414yescomplemented
71C22×Dic86C2311yescharacteristic
72C22×Dic86C2311yescharacteristic
73C23×Dic43—21no—
74C2×#10621883—22no—
75C2×#10621883—22no—
76C2×#10621883—22no—
77C2×#10621883—22no—
78C2×#10621883C2×C414yes—
79C2×#10621883C2×C414yes—
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C4×Dic86—22no—
85C4×Dic86—22no—
86C4×Dic86—22no—
87C4×Dic86—22no—
88C4×Dic86—22no—
89C4×Dic86—22no—
90C4×Dic86D414yescomplemented
91C4×Dic86D414yescomplemented
92#13063290—28no—
93#13063290—28no—
94#13063284—22no—
95#13063284—22no—
96#13063281—28no—
97#13063281—28no—
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×C22⋊Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110#13063258—22no—
111#13063256—22no—
112#13063248—22no—
113#13063248—22no—
114#13063248—22no—
115#13063248—22no—
116#13063248C2×C414yescomplemented
117#13063248C2×C414yescomplemented
118#13063246—22no—
119#13063246—22no—
120C22⋊(C43⋊C8)—22no—
121C22⋊(C43⋊C8)C2×C414yescomplemented
122#13063236—22no—
123C4×C43⋊C8—22no—
124C22×D4×C43—21no—
125C22×D4×C43C2311yescharacteristic
126C23×C4×C43—21no—
127C23×C4×C43C2311yescharacteristic
128#121×C43—22no—
129#121×C43C2×C414yes—
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132#117×C43—22no—
133#117×C43—22no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43D411yescharacteristic
136C2×C4⋊C4×C43D411yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C22⋊C4×C43D411yescharacteristic
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149C2×C42×C43C2311yescharacteristic
150#95×C43—21no—
151#95×C43—21no—
152#95×C43—21no—
153C24×C43—21no—
154C24×C43C2×D411yescharacteristic
155C2×D4×C43—21no—
156C2×D4×C43—24no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—81no—
162C2×D4×C43—81no—
163C2×D4×C43C22×C412yes—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—42no—
172C22×C4×C43—81no—
173C22×C4×C43—81no—
174C22×C4×C43C22×C412yes—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43#4112yes—
181C22×C4×C43C2411yescharacteristic
182C22×Dic43—24no—
183C22×Dic43—24no—
184C22×Dic43—24no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C2×Dic86—24no—
190C2×Dic86—24no—
191C2×Dic86—28no—
192C2×Dic86—28no—
193C2×Dic86—24no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—28no—
201C2×Dic86—28no—
202C2×Dic86C22×C412yes—
203C2×Dic86C22×C412yes—
204C2×Dic86C2×D412yes—
205C2×Dic86C2×D412yes—
206C2×Dic86#4112yes—
207C2×Dic86#4112yes—
208C4⋊C4×C43—22no—
209C4⋊C4×C43—22no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—81no—
216C4⋊C4×C43C22×C412yes—
217C22⋊C4×C43—24no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—22no—
220C22⋊C4×C43—42no—
221C22⋊C4×C43—81no—
222C22⋊C4×C43—81no—
223C22⋊C4×C43—81no—
224C42×C43—21no—
225C42×C43—21no—
226C42×C43—81no—
227C42×C43C2×D412yes—
228C42×C43C2×D412yes—
229C22⋊Dic43—24no—
230#10621883—28no—
231#10621883—28no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43C2×D412yes—
235C4⋊Dic43C2×D412yes—
236Dic43⋊C4—24no—
237Dic43⋊C4—24no—
238Dic43⋊C4—24no—
239Dic43⋊C4—24no—
240C4×Dic43—24no—
241C4×Dic43—24no—
242C4×Dic43—24no—
243C4×Dic43—24no—
244C4×Dic43—24no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8C22×C412yes—
256C2×C43⋊C8C22×C412yes—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—22no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43C4×D412yes—
271C23×C43C22×D411yescharacteristic
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—41no—
275D4×C43—41no—
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—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
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—84no—
303C2×C4×C43C4×D412yes—
304C2×C4×C43#12012yes—
305C2×C4×C43#12012yes—
306C2×C4×C43C23×C411yescharacteristic
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C2×C4×C43C2×#4111yescharacteristic
312C2×Dic43—216no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325Dic86—216no—
326Dic86—22no—
327Dic86—22no—
328Dic86—22no—
329Dic86—22no—
330Dic86—22no—
331Dic86—22no—
332Dic86C4×D414yes—
333Dic86C4×D414yes—
334C43⋊C8—22no—
335C43⋊C8—22no—
336C43⋊C8—41no—
337C43⋊C8—41no—
338#21462—431nomaximal, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43C2×C4×D411yescharacteristic
354C22×C43C2×#12011yescharacteristic
355C22×C43#52511yescharacteristic
356C22×C43#57711yescharacteristic
357C22×C43#57711yescharacteristic
358C22×C43#57711yescharacteristic
359C22×C43#57811yescharacteristic
360C4×C43—22no—
361C4×C43—22no—
362C4×C43—22no—
363C4×C43—42no—
364C4×C43—41no—
365C4×C43—41no—
366C4×C43—81no—
367C4×C43—81no—
368C4×C43C2×C4×D411yescharacteristic
369C4×C43C2×C4×D411yescharacteristic
370C4×C43#52511yescharacteristic
371C4×C43#52511yescharacteristic
372Dic43—24no—
373Dic43—24no—
374Dic43—42no—
375Dic43—42no—
376C2×#519—431no—
377C2×#448—431no—
378C2×#440—431no—
379C2×C4×SD16—431no—
380#2324D4311yescharacteristic
381#1880—431no—
382#1880—431no—
383#1875—431no—
384#1865—431no—
385#1863—431no—
386#1854—431no—
387#1787—431no—
388#1763—431no—
389C4×#103—431no—
390#1750—431no—
391C2×C43—42no—
392C2×C43—82no—
393C2×C43C4×#12011yescharacteristic
394C2×C43#294711yescharacteristic
395C2×C43#294911yescharacteristic
396C2×C43#301011yescharacteristic
397C2×C43#301311yescharacteristic
398C2×C43#312111yescharacteristic
399C2×C43#312611yescharacteristic
400C23×Q8—431no—
401C22×SD16—431no—
402C22×SD16—431no—
403C2×#121C2×D4311yescharacteristic
404#519—864no—
405#519—864no—
406C2×C4×Q8—431no—
407C2×C4×Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—861no—
411C2×C4×Q8—861no—
412C2×C4×D4C2×D4311yescharacteristic
413C2×#117—431no—
414C2×#117—861no—
415C2×#117—861no—
416C2×#117C2×D4311yescharacteristic
417#448—438no—
418#440—864no—
419C4×SD16—864no—
420C2×#107—431no—
421C2×#106—431no—
422C2×#103—431no—
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#102—431no—
429C2×#102—431no—
430C2×C22⋊C8—431no—
431C2×C22⋊C8—431no—
432C2×#97—431no—
433C2×C4×C8—431no—
434#390—21no—
435#390C2×D4311yescharacteristic
436#389C2×D4311yescharacteristic
437#388—21no—
438#386—21no—
439#385—21no—
440#380C2×D4311yescharacteristic
441C4×C4⋊C4C2×D4311yescharacteristic
442#340—431no—
443#340—431no—
444#340—431no—
445#340—431no—
446#336—431no—
447#336—431no—
448C43#2146211yescharacteristic, complemented, Sylow
449C22×Q8—434no—
450C22×Q8—431no—
451C22×Q8—431no—
452C22×Q8—862no—
453C22×Q8—862no—
454C22×Q8—862no—
455C22×Q8—862no—
456C22×Q8—862no—
457C22×Q8—861no—
458C22×D4—21no—
459C22×D4C22×D4311yescharacteristic
460C23×C4—21no—
461C23×C4—861no—
462C23×C4C22×D4311yescharacteristic
463C2×SD16—434no—
464C2×SD16—434no—
465C2×SD16—862no—
466C2×SD16—862no—
467C2×SD16—862no—
468C2×SD16—862no—
469C22×C8—431no—
470C22×C8—431no—
471C22×C8—431no—
472C22×C8—431no—
473#121—22no—
474#121C4×D4314yes—
475C4×Q8—434no—
476C4×Q8—434no—
477C4×Q8—862no—
478C4×Q8—862no—
479C4×Q8—862no—
480C4×Q8—862no—
481C4×Q8—868no—
482C4×Q8—868no—
483C4×Q8—862no—
484C4×Q8—862no—
485C4×D4—22no—
486C4×D4—22no—
487#117—22no—
488#117—22no—
489#117—868no—
490#117—868no—
491#117—862no—
492#117—862no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
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×C4⋊C4C22×D4311yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4C22⋊D4311yescharacteristic
512C2×C22⋊C4C22⋊D4311yescharacteristic
513C2×C42—21no—
514C2×C42—861no—
515C2×C42—861no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42C22×D4311yescharacteristic
520C2×C42C22×D4311yescharacteristic
521#107—862no—
522#106—862no—
523#103—434no—
524#103—434no—
525#103—862no—
526#103—862no—
527#103—862no—
528#103—862no—
529#102—862no—
530#102—862no—
531C22⋊C8—434no—
532C22⋊C8—862no—
533#97—862no—
534C4×C8—862no—
535#95—21no—
536#95—21no—
537#95—21no—
538C24—21no—
539C24C2×C22⋊D4311yescharacteristic
540C2×Q8—432no—
541C2×Q8—432no—
542C2×Q8—432no—
543C2×Q8—432no—
544C2×Q8—432no—
545C2×Q8—432no—
546C2×Q8—868no—
547C2×Q8—868no—
548C2×Q8—864no—
549C2×Q8—864no—
550C2×Q8—868no—
551C2×Q8—868no—
552C2×Q8—864no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—861no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4C2×C4×D4312yes—
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—864no—
580C22×C4—864no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4C2×C4×D4312yes—
586C22×C4#1062189812yes—
587C22×C4C2×C22⋊D4311yescharacteristic
588C22×C4C2×C22⋊D4311yescharacteristic
589C22×C4C2×C22⋊D4311yescharacteristic
590C22×C4C2×C22⋊D4311yescharacteristic
591C22×C4C2×C22⋊D4311yescharacteristic
592C22×C4C23×D4311yescharacteristic
593SD16—868no—
594SD16—868no—
595C2×C8—432no—
596C2×C8—432no—
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—861no—
606C2×C8—861no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—81no—
615C4⋊C4—432no—
616C4⋊C4—432no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4C2×C4×D4312yes—
624C22⋊C4—24no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—42no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—864no—
632C42—21no—
633C42—21no—
634C42—81no—
635C42—864no—
636C42—864no—
637C42—864no—
638C42—864no—
639C42—864no—
640C42D4×D4312yes—
641C42D4×D4312yes—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23C4×C22⋊D4312yes—
656C23C22×C22⋊D4311yescharacteristic
657Q8—434no—
658Q8—434no—
659Q8—8616no—
660Q8—862no—
661Q8—862no—
662Q8—862no—
663Q8—862no—
664Q8—862no—
665Q8—862no—
666D4—22no—
667D4—22no—
668D4—41no—
669D4—41no—
670D4—84no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
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—8616no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4C4×C22⋊D4312yes—
711C2×C4#1306329312yes—
712C2×C4#1306329312yes—
713C2×C4C22×C4×D4311yescharacteristic
714C2×C4C2×D4×D4311yescharacteristic
715C2×C4C2×D4×D4311yescharacteristic
716C2×C4#41×D4311yescharacteristic
717C2×C4#41×D4311yescharacteristic
718C2×C4C2×#1062189811yescharacteristic
719C8—862no—
720C8—862no—
721C8—1721no—
722C8—1721no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22C2×C4×C22⋊D4311yescharacteristic
738C22C2×#1306329311yescharacteristic
739C22#1458340611yescharacteristic
740C22#1458371011yescharacteristic
741C22#1458371011yescharacteristic
742C22#1458371011yescharacteristic
743C22#1458371411yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—42no—
748C4—41no—
749C4—41no—
750C4—81no—
751C4—81no—
752C4—864no—
753C4—864no—
754C4—1722no—
755C4—1722no—
756C4C4×D4×D4311yescharacteristic
757C4C4×D4×D4311yescharacteristic
758C4#1458340811yescharacteristic
759C4#1458340811yescharacteristic
760C2—42no—
761C2—82no—
762C2C4×#1306329311yescharacteristic
763C2#1914343411yescharacteristic
764C2#1914345211yescharacteristic
765C2#1914387911yescharacteristic
766C2#1914390711yescharacteristic
767C2#1914481811yescharacteristic
768C2#1914488111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2324C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
cosocleC22×C4×C43C24
hypercenter#2324D43
hypocenterC43#21462
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
1. C2×#14583376C2semidirect
3. C2×#14582999C2semidirect
4. C2×C4×#10621883C2semidirect
5. #19134953C2semidirect
6. #19134953C2semidirect
8. #19134862C2semidirect
9. #19134848C2semidirect
10. #19134792C2semidirect
11. #19134529C2semidirect
12. #19134428C2semidirect
13. C4×#13063248C2semidirect
14. #19134361C2semidirect
30. #14583037C4semidirect
70. C22×Dic86C2×C4semidirect
90. C4×Dic86D4semidirect
91. C4×Dic86D4semidirect
116. #13063248C2×C4semidirect
117. #13063248C2×C4semidirect
121. C22⋊(C43⋊C8)C2×C4semidirect
448. C43#21462semidirect

Maximal subgroups

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

subgroupindex
C2×#145833762
C2×#145830372
C2×#145829992
C2×C4×#106218832
#191349532
#191349182
#191348622
#191348482
#191347922
#191345292
#191344282
C4×#130632482
#191343612
C43×#23242
#2146243