Finite Group Databasebeta

← #25124763

Subgroups — #25124763

Order 11008.

1272 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583430C211yesmaximal, characteristic, complemented
2C2×#14582990C211yesmaximal, characteristic, complemented
3C2×D8×Dic43C211yesmaximal, characteristic, complemented
4#121×Dic43C211yesmaximal, characteristic, complemented
5#19135936C211yesmaximal, characteristic, complemented
6#19135835C211yesmaximal, characteristic, complemented
7#19135799C211yesmaximal, characteristic, complemented
8#19135781C211yesmaximal, characteristic, complemented
9#19135739C211yesmaximal, characteristic, complemented
10#19135670C211yesmaximal, characteristic, complemented
11#19135598C211yesmaximal, characteristic, complemented
12#19134414C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
15C43×#1999C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17#14583430—24no—
18#14583430—24no—
19C2×#13063318—21no—
20C2×#13063316C2211yescharacteristic
21C2×#13063312C2211yescharacteristic
22C2×#13063306—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063290C2211yescharacteristic
25C2×D4×Dic43—21no—
26C2×D4×Dic43—21no—
27C2×D4×Dic43C2211yescharacteristic
28C2×D4×Dic43C2211yescharacteristic
29C2×#13063281—21no—
30C22×C4×Dic43C2211yescharacteristic
31#14582990—24no—
32D8×Dic43—24no—
33C2×#13063259C2211yescharacteristic
34C2×#13063256C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C8×Dic43C2211yescharacteristic
43C2×C8×Dic43C2211yescharacteristic
44#14582802C2211yescharacteristic
45#14582798C2211yescharacteristic
46#14582792—21no—
47#14582779—21no—
48#14582759C2211yescharacteristic
49C4⋊C4×Dic43C2211yescharacteristic
50C22⋊C4×Dic43—21no—
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×D8×C43C2211yescharacteristic
57C2×#121×C43C2211yescharacteristic
58C2×#121×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C23×Dic43—21no—
65C23×Dic43—21no—
66C23×Dic43D411yescharacteristic
67C23×Dic43D411yescharacteristic
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883—22no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063318—28no—
74#13063316—22no—
75#13063316—22no—
76#13063312—22no—
77#13063312—22no—
78#13063306—28no—
79#13063304—22no—
80#13063304—22no—
81#13063290—22no—
82#13063290D414yescomplemented
83D4×Dic43—28no—
84D4×Dic43—22no—
85D4×Dic43—22no—
86D4×Dic43—22no—
87D4×Dic43—44no—
88D4×Dic43D414yescomplemented
89#13063281—28no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—22no—
108C2×C4×Dic43—22no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43D411yescharacteristic
111C2×C4×Dic43D411yescharacteristic
112C2×C4×Dic43C2311yescharacteristic
113C2×C4×Dic43C2311yescharacteristic
114#13063259—22no—
115#13063256—22no—
116#13063250—22no—
117#13063250—22no—
118#13063248—22no—
119#13063246—22no—
120#13063246—22no—
121#13063246—22no—
122C22⋊(C43⋊C8)—22no—
123C8×Dic43—22no—
124C8×Dic43—22no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C22×D4×C43—21no—
129C22×D4×C43—21no—
130C22×D4×C43C2311yescharacteristic
131C22×D4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C2×D8×C43—22no—
134C2×D8×C43—22no—
135C2×D8×C43—22no—
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138#121×C43—22no—
139#121×C43—22no—
140#121×C43—22no—
141#121×C43—22no—
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146#102×C43—22no—
147#102×C43—22no—
148C22⋊C8×C43—22no—
149C24×C43—21no—
150C24×C43—21no—
151C24×C43C2×D411yescharacteristic
152C2×D4×C43—24no—
153C2×D4×C43—24no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43—42no—
168C2×D4×C43C2×D412yes—
169C2×D4×C43#4112yes—
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×C43C2×D411yescharacteristic
179C22×C4×C43C2411yescharacteristic
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—24no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—41no—
191C22×Dic43—42no—
192C22×Dic43—42no—
193C22×Dic43—42no—
194C22×Dic43—42no—
195C22×Dic43—42no—
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199C22×Dic43C2×D411yescharacteristic
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86C2×D412yes—
206D8×C43—28no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43#4112yes—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43C2×D412yes—
216C4⋊C4×C43#4112yes—
217C22⋊C4×C43—24no—
218C22⋊C4×C43—24no—
219C22⋊Dic43—24no—
220C22⋊Dic43—24no—
221C22⋊Dic43—24no—
222C22⋊Dic43—24no—
223C22⋊Dic43—42no—
224C22⋊Dic43—42no—
225C22⋊Dic43—42no—
226C22⋊Dic43—42no—
227#10621883—28no—
228C4⋊Dic43—24no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—42no—
235C4⋊Dic43C2×D412yes—
236Dic43⋊C4—24no—
237Dic43⋊C4—24no—
238Dic43⋊C4—24no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C4×Dic43—22no—
242C4×Dic43—22no—
243C4×Dic43—24no—
244C4×Dic43—42no—
245C4×Dic43C2×D412yes—
246C4×Dic43C2×D412yes—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8#4112yes—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43#13512yes—
274C23×C43C22×D411yescharacteristic
275D4×C43—22no—
276D4×C43—22no—
277D4×C43—22no—
278D4×C43—22no—
279D4×C43—48no—
280D4×C43—48no—
281D4×C43—41no—
282D4×C43—41no—
283D4×C43—41no—
284D4×C43—41no—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
287C2×C4×C43—21no—
288C2×C4×C43—22no—
289C2×C4×C43—21no—
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×C43C22×D411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—44no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—44no—
320C2×Dic43—48no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—84no—
328C2×Dic43#12012yes—
329C2×Dic43#12012yes—
330C2×Dic43#13512yes—
331C2×Dic43AGL(1,ℤ/8)12yes—
332Dic86—22no—
333Dic86—22no—
334Dic86—41no—
335Dic86—41no—
336C8×C43—22no—
337C8×C43—41no—
338C43⋊C8—22no—
339C43⋊C8—41no—
340#23569—431nomaximal, Sylow
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43C2×#12011yescharacteristic
363C22×C43#52511yescharacteristic
364C22×C43#53211yescharacteristic
365C22×C43C2×#13511yescharacteristic
366C22×C43C2×#13511yescharacteristic
367C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C43#57511yescharacteristic
369C4×C43—42no—
370C4×C43—41no—
371C4×C43—42no—
372C4×C43#52511yescharacteristic
373C4×C43#52511yescharacteristic
374C4×C43#53211yescharacteristic
375C4×C43#53211yescharacteristic
376Dic43—22no—
377Dic43—42no—
378Dic43—41no—
379Dic43—42no—
380Dic43—41no—
381Dic43—81no—
382Dic43—81no—
383Dic43#44914yes—
384C2×#529—431no—
385C2×C4×SD16—431no—
386C2×C4×D8—431no—
387C4×#121—431no—
388#2059—431no—
389#2042—431no—
390#2036—431no—
391#2034—431no—
392#2025—431no—
393#2012—431no—
394#2000—431no—
395#1999D4311yescharacteristic
396C4×#103—431no—
397C4×#102—431no—
398C4×C22⋊C8—431no—
399C2×C43—42no—
400C2×C43—82no—
401C2×C43—82no—
402C2×C43#238811yescharacteristic
403C2×C43C2×#44911yescharacteristic
404C2×C43#300211yescharacteristic
405C2×C43#310211yescharacteristic
406C2×C43#310511yescharacteristic
407C2×C43#316811yescharacteristic
408C2×C43#317111yescharacteristic
409C22×SD16—431no—
410C22×D8C2×D4311yescharacteristic
411#529—864no—
412#529—864no—
413C2×#126—861no—
414C2×#125—431no—
415C2×#124—431no—
416C2×#123—861no—
417C2×C22⋊Q8—431no—
418C2×#121C2×D4311yescharacteristic
419C2×#121C2×D4311yescharacteristic
420C2×C4×Q8—431no—
421C2×C4×D4—431no—
422C2×C4×D4—431no—
423C2×C4×D4—861no—
424C2×C4×D4—861no—
425C2×#117—861no—
426C22×C42—431no—
427C4×SD16—864no—
428C4×D8—864no—
429C2×#107—431no—
430C2×#106—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#102—431no—
435C2×#102—431no—
436C2×#102—431no—
437C2×#102C2×D4311yescharacteristic
438C2×#102C2×D4311yescharacteristic
439C2×C22⋊C8—431no—
440C2×C22⋊C8C2×D4311yescharacteristic
441C2×C4×C8—431no—
442C2×C4×C8—431no—
443#390—431no—
444#389—431no—
445#388—861no—
446#386—861no—
447#380—431no—
448C4×C4⋊C4—431no—
449C4×C22⋊C4—861no—
450#340—431no—
451#340—431no—
452#340—431no—
453#340C2×D4311yescharacteristic
454#336—431no—
455#336—431no—
456C43#2356911yescharacteristic, complemented, Sylow
457C22×Q8—431no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4C22×D4311yescharacteristic
461C22×D4C22×D4311yescharacteristic
462C23×C4—431no—
463C23×C4—431no—
464C23×C4—861no—
465C23×C4—861no—
466C23×C4C22×D4311yescharacteristic
467C2×SD16—862no—
468C2×SD16—862no—
469C2×SD16—862no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—22no—
473C22×C8—431no—
474C22×C8—431no—
475C22×C8C22×D4311yescharacteristic
476C22×C8C22×D4311yescharacteristic
477#126—868no—
478#125—862no—
479#125—862no—
480#124—862no—
481#124—862no—
482#123—868no—
483C22⋊Q8—862no—
484C22⋊Q8—862no—
485#121—22no—
486#121—22no—
487#121—22no—
488#121—22no—
489C4×Q8—434no—
490C4×Q8—862no—
491C4×D4—434no—
492C4×D4—862no—
493C4×D4—862no—
494C4×D4—862no—
495C4×D4—868no—
496C4×D4—1724no—
497#117—868no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C42—431no—
519C2×C42—431no—
520C2×C42—431no—
521C2×C42—431no—
522C2×C42—862no—
523C2×C42—862no—
524C2×C42—861no—
525C2×C42—861no—
526#107—862no—
527#106—862no—
528#103—862no—
529#103—862no—
530#103—862no—
531#102—22no—
532#102—22no—
533#102—862no—
534#102—862no—
535#102—862no—
536C22⋊C8—22no—
537C22⋊C8—862no—
538C4×C8—862no—
539C4×C8—862no—
540#95—861no—
541#95—861no—
542#95—861no—
543C24—21no—
544C24—21no—
545C24D4×D4311yescharacteristic
546C2×Q8—432no—
547C2×Q8—861no—
548C2×Q8—861no—
549C2×Q8—861no—
550C2×Q8—861no—
551C2×Q8—861no—
552C2×D4—24no—
553C2×D4—24no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4D4×D4312yes—
569C2×D4#1062190012yes—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—864no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—1722no—
593C22×C4—1722no—
594C22×C4—1722no—
595C22×C4—1722no—
596C22×C4—1722no—
597C22×C4—1721no—
598C22×C4D4×D4311yescharacteristic
599C22×C4C23×D4311yescharacteristic
600SD16—868no—
601D8—28no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—432no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8#1062190012yes—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—432no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—1722no—
627C4⋊C4D4×D4312yes—
628C4⋊C4#1062190012yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—864no—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—1722no—
636C22⋊C4—1722no—
637C22⋊C4—1722no—
638C22⋊C4—1722no—
639C42—432no—
640C42—432no—
641C42—862no—
642C42—862no—
643C42—864no—
644C42—861no—
645C42—861no—
646C42—1722no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23#1306334412yes—
668C23C2×D4×D4311yescharacteristic
669Q8—862no—
670Q8—862no—
671Q8—1721no—
672Q8—1721no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—22no—
677D4—48no—
678D4—48no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—22no—
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—432no—
697C2×C4—432no—
698C2×C4—432no—
699C2×C4—432no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—3444no—
711C2×C4—1724no—
712C2×C4—1728no—
713C2×C4—1724no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4C2×D4×D4311yescharacteristic
725C2×C4C2×D4×D4311yescharacteristic
726C2×C4#41×D4311yescharacteristic
727C2×C4C2×#1062190011yescharacteristic
728C2×C4C2×#1062190011yescharacteristic
729C2×C4C2×#1062190011yescharacteristic
730C8—22no—
731C8—41no—
732C8—862no—
733C8—1721no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22#120×D4311yescharacteristic
756C22#1458340511yescharacteristic
757C22#1458344411yescharacteristic
758C22#135×D4311yescharacteristic
759C22C2×#1306334411yescharacteristic
760C22AGL(1,ℤ/8)×D4311yescharacteristic
761C22#1458369511yescharacteristic
762C4—41no—
763C4—42no—
764C4—42no—
765C4—434no—
766C4—862no—
767C4—3441no—
768C4—3441no—
769C4—1722no—
770C4—1721no—
771C4—1722no—
772C4—1721no—
773C4#1458340511yescharacteristic
774C4#1458340911yescharacteristic
775C4#1458344411yescharacteristic
776C4#1458344711yescharacteristic
777C2—42no—
778C2—82no—
779C2—82no—
780C2#1913780711yescharacteristic
781C2#449×D4311yescharacteristic
782C2#1914380811yescharacteristic
783C2#1914460611yescharacteristic
784C2#1914463711yescharacteristic
785C2#1914516011yescharacteristic
786C2#1914518511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#1999C2
socleC23×C43C22×D4
hypercenter#1999D43
hypocenterC43#23569
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1999

Complements

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

NH ≅ G/Ntype
1. C2×#14583430C2semidirect
2. C2×#14582990C2semidirect
3. C2×D8×Dic43C2semidirect
4. #121×Dic43C2semidirect
5. #19135936C2semidirect
6. #19135835C2semidirect
7. #19135799C2semidirect
8. #19135781C2semidirect
9. #19135739C2semidirect
10. #19135670C2semidirect
11. #19135598C2semidirect
12. #19134414C2semidirect
13. #102×Dic43C2semidirect
14. C22⋊C8×Dic43C2semidirect
82. #13063290D4semidirect
88. D4×Dic43D4semidirect
456. C43#23569semidirect

Maximal subgroups

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

subgroupindex
C2×#145834302
C2×#145829902
C2×D8×Dic432
#121×Dic432
#191359362
#191358352
#191357992
#191357812
#191357392
#191356702
#191355982
#191344142
#102×Dic432
C22⋊C8×Dic432
C43×#19992
#2356943