Finite Group Databasebeta

← #25131128

Subgroups — #25131128

Order 11008.

1142 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583516C211yesmaximal, characteristic, complemented
2C2×#14583177C211yesmaximal, characteristic, complemented
3C2×#14583112C211yesmaximal, characteristic, complemented
4#19137290C211yesmaximal, characteristic, complemented
5#19135799C211yesmaximal, characteristic, complemented
6#19135774C211yesmaximal, characteristic, complemented
7#19135598C211yesmaximal, characteristic, complemented
8#19135541C211yesmaximal, characteristic, complemented
9#19135526C211yesmaximal, characteristic, complemented
10#19134947C211yesmaximal, characteristic, complemented
11#19134945C211yesmaximal, characteristic, complemented
12#19134850C211yesmaximal, characteristic, complemented
13#19134844C211yesmaximal, characteristic, complemented
14#19134577C211yesmaximal, characteristic, complemented
15C43×#1999C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17#14583516—24no—
18#14583516—24no—
19C2×#13063324C2211yescharacteristic
20C2×#13063318—21no—
21C2×#13063312—21no—
22C2×#13063312C2211yescharacteristic
23C2×#13063306—21no—
24C2×#13063304C2211yescharacteristic
25C2×#13063302—21no—
26C2×#13063290C2211yescharacteristic
27C2×D4×Dic43C2211yescharacteristic
28C2×D4×Dic43C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30#14583177—24no—
31#14583112—24no—
32C2×#13063259C2211yescharacteristic
33C2×#13063258C2211yescharacteristic
34C2×Dic43⋊C8C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43#14582802—21no—
44#14582802C2211yescharacteristic
45#14582798C2211yescharacteristic
46#14582792—21no—
47#14582779—21no—
48#14582774—21no—
49#14582759C2211yescharacteristic
50C4⋊C4×Dic43C2211yescharacteristic
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×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C23×Dic43—21no—
66C23×Dic43—21no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—41no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063324—22no—
73#13063324D414yescomplemented
74#13063318—28no—
75#13063312—28no—
76#13063312—22no—
77#13063312D414yescomplemented
78#13063306—28no—
79#13063304—22no—
80#13063304—22no—
81#13063302—28no—
82#13063290—22no—
83#13063290—22no—
84D4×Dic43—22no—
85D4×Dic43—22no—
86D4×Dic43—22no—
87D4×Dic43—22no—
88#13063284—22no—
89#13063284—22no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43D411yescharacteristic
92C2×C4⋊Dic43D411yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—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×C22⋊Dic43—21no—
107C2×C22⋊Dic43D411yescharacteristic
108C2×C22⋊Dic43D411yescharacteristic
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43C2311yescharacteristic
112C2×C4×Dic43C2311yescharacteristic
113#13063259—22no—
114#13063258—22no—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117#13063250—22no—
118#13063250—41no—
119#13063248—22no—
120#13063246—22no—
121#13063246—22no—
122#13063246—41no—
123C22⋊(C43⋊C8)—41no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C22×D4×C43—21no—
128C22×D4×C43—21no—
129C22×D4×C43C2311yescharacteristic
130C22×D4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C2×D8×C43—22no—
133C2×D8×C43—22no—
134C2×D8×C43—41no—
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137#121×C43—22no—
138#121×C43—22no—
139#121×C43—22no—
140#121×C43—22no—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145#102×C43—22no—
146#102×C43—22no—
147C22⋊C8×C43—41no—
148C24×C43—21no—
149C24×C43—21no—
150C24×C43C2×D411yescharacteristic
151C2×D4×C43—24no—
152C2×D4×C43—24no—
153C2×D4×C43—21no—
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—81no—
164C2×D4×C43—81no—
165C2×D4×C43—81no—
166C2×D4×C43—81no—
167C2×D4×C43C2×D412yes—
168C2×D4×C43#4112yes—
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×C43C2×D411yescharacteristic
178C22×C4×C43C2411yescharacteristic
179C22×Dic43—24no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—42no—
185C22×Dic43—81no—
186C22×Dic43—81no—
187C22×Dic43—81no—
188C22×Dic43—81no—
189C22×Dic43C2×D411yescharacteristic
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—24no—
199C2×Dic86—81no—
200C2×Dic86—81no—
201C2×Dic86C2×D412yes—
202D8×C43—44no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43C2×D412yes—
212C4⋊C4×C43#4112yes—
213C22⋊C4×C43—24no—
214C22⋊C4×C43—24no—
215C22⋊Dic43—24no—
216C22⋊Dic43—24no—
217C22⋊Dic43—24no—
218C22⋊Dic43—24no—
219C22⋊Dic43—22no—
220C22⋊Dic43—22no—
221C22⋊Dic43—42no—
222C22⋊Dic43—81no—
223C22⋊Dic43—81no—
224C22⋊Dic43—81no—
225#10621883—44no—
226C4⋊Dic43—21no—
227C4⋊Dic43—22no—
228C4⋊Dic43—22no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—81no—
234C4⋊Dic43C2×D412yes—
235Dic43⋊C4—24no—
236Dic43⋊C4—24no—
237Dic43⋊C4—24no—
238C4×Dic43—24no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C4×Dic43—81no—
242C4×Dic43C2×D412yes—
243C4×Dic43C2×D412yes—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C23×C43—21no—
251C23×C43—22no—
252C23×C43—22no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—41no—
260C23×C43—41no—
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×C43C22×D411yescharacteristic
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—22no—
275D4×C43—22no—
276D4×C43—41no—
277D4×C43—41no—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43—84no—
281D4×C43—84no—
282C2×C4×C43—22no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—22no—
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×C43C22×D411yescharacteristic
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C43H(5,𝔽2)11yescharacteristic
300C2×C4×C432−1+411yescharacteristic
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
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—84no—
324C2×Dic43—84no—
325C2×Dic43#12012yes—
326C2×Dic43#12012yes—
327Dic86—22no—
328Dic86—22no—
329Dic86—41no—
330Dic86—41no—
331Dic86—84no—
332C8×C43—41no—
333C8×C43—41no—
334C43⋊C8—41no—
335C43⋊C8—41no—
336#24167—431nomaximal, Sylow
337C22×C43—41no—
338C22×C43—42no—
339C22×C43—41no—
340C22×C43—42no—
341C22×C43—41no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—42no—
348C22×C43—41no—
349C22×C43—42no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43C2×#12011yescharacteristic
359C22×C43#52511yescharacteristic
360C22×C43#53711yescharacteristic
361C22×C43#57611yescharacteristic
362C22×C43#57611yescharacteristic
363C22×C43#57711yescharacteristic
364C22×C43#57811yescharacteristic
365C4×C43—42no—
366C4×C43—41no—
367C4×C43—42no—
368C4×C43#54611yescharacteristic
369C4×C43#54711yescharacteristic
370C4×C43#54811yescharacteristic
371C4×C43#55011yescharacteristic
372Dic43—22no—
373Dic43—22no—
374Dic43—42no—
375Dic43—42no—
376Dic43—41no—
377Dic43—41no—
378Dic43—81no—
379Dic43—81no—
380C2×#542—431no—
381C2×#474—431no—
382C2×#463—431no—
383#2324—431no—
384#2036—431no—
385#2033—431no—
386#2000—431no—
387#1999D4311yescharacteristic
388#1987—431no—
389#1983—431no—
390#1880—431no—
391#1879—431no—
392#1863—431no—
393#1862—431no—
394#1798—431no—
395C2×C43—81no—
396C2×C43—82no—
397C2×C43—82no—
398C2×C43#240711yescharacteristic
399C2×C43#300811yescharacteristic
400C2×C43#301311yescharacteristic
401C2×C43#311811yescharacteristic
402C2×C43#312411yescharacteristic
403C2×C43#325711yescharacteristic
404C2×C43#326211yescharacteristic
405C22×SD16—431no—
406C22×D8C2×D4311yescharacteristic
407#542—864no—
408#542—864no—
409C2×C4⋊Q8—431no—
410C2×#126—861no—
411C2×#124—431no—
412C2×#124—861no—
413C2×#123—861no—
414C2×C22⋊Q8—431no—
415C2×C22⋊Q8—861no—
416C2×#121C2×D4311yescharacteristic
417C2×#121C2×D4311yescharacteristic
418C2×C4×Q8—431no—
419C2×C4×D4—431no—
420C2×C4×D4—431no—
421C2×#117—431no—
422#474—864no—
423#463—864no—
424C2×#107—431no—
425C2×#107—431no—
426C2×C4⋊C8—431no—
427C2×C4⋊C8—431no—
428C2×#103—431no—
429C2×#103—431no—
430C2×#103—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—431no—
434C2×#102C2×D4311yescharacteristic
435C2×#102C2×D4311yescharacteristic
436C2×C22⋊C8—431no—
437C2×C22⋊C8C2×D4311yescharacteristic
438#390—431no—
439#390—861no—
440#389—431no—
441#388—861no—
442#386—861no—
443#385—861no—
444#380—431no—
445C4×C4⋊C4—431no—
446#340—431no—
447#340—431no—
448#340—431no—
449#340C2×D4311yescharacteristic
450#336—431no—
451#336—431no—
452C43#2416711yescharacteristic, complemented, Sylow
453C22×Q8—431no—
454C22×Q8—861no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4C22×D4311yescharacteristic
458C22×D4C22×D4311yescharacteristic
459C23×C4—861no—
460C23×C4—861no—
461C23×C4C22×D4311yescharacteristic
462C2×SD16—862no—
463C2×SD16—862no—
464C2×SD16—1721no—
465C2×D8—22no—
466C2×D8—22no—
467C2×D8—41no—
468C22×C8—431no—
469C22×C8—431no—
470C22×C8C22×D4311yescharacteristic
471C22×C8C22×D4311yescharacteristic
472C4⋊Q8—434no—
473C4⋊Q8—862no—
474#126—868no—
475#124—434no—
476#124—862no—
477#124—868no—
478#123—868no—
479C22⋊Q8—868no—
480C22⋊Q8—862no—
481C22⋊Q8—862no—
482#121—22no—
483#121—22no—
484#121—22no—
485#121—22no—
486C4×Q8—862no—
487C4×Q8—862no—
488C4×D4—862no—
489C4×D4—862no—
490C4×D4—862no—
491C4×D4—862no—
492#117—862no—
493#117—862no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—431no—
508C2×C22⋊C4—431no—
509C2×C22⋊C4—861no—
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×C42—431no—
518C2×C42—431no—
519C2×C42—861no—
520C2×C42—861no—
521#107—862no—
522#107—862no—
523C4⋊C8—862no—
524C4⋊C8—862no—
525#103—862no—
526#103—862no—
527#103—1721no—
528#102—22no—
529#102—22no—
530#102—862no—
531#102—862no—
532#102—1721no—
533C22⋊C8—41no—
534C22⋊C8—1721no—
535#95—861no—
536#95—861no—
537#95—861no—
538C24—21no—
539C24—21no—
540C24D4×D4311yescharacteristic
541C2×Q8—432no—
542C2×Q8—864no—
543C2×Q8—861no—
544C2×Q8—861no—
545C2×Q8—861no—
546C2×Q8—861no—
547C2×Q8—861no—
548C2×Q8—3441no—
549C2×Q8—3441no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
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—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4D4×D4312yes—
567C2×D4#1062190012yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—431no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—864no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—3441no—
586C22×C4—3441no—
587C22×C4—3441no—
588C22×C4—3441no—
589C22×C4—1722no—
590C22×C4D4×D4311yescharacteristic
591C22×C4C23×D4311yescharacteristic
592SD16—1724no—
593D8—44no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—432no—
609C4⋊C4—862no—
610C4⋊C4—862no—
611C4⋊C4—864no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—3441no—
620C4⋊C4D4×D4312yes—
621C4⋊C4#1062190012yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—862no—
625C22⋊C4—862no—
626C22⋊C4—864no—
627C22⋊C4—864no—
628C22⋊C4—864no—
629C22⋊C4—864no—
630C22⋊C4—3441no—
631C22⋊C4—3441no—
632C22⋊C4—3441no—
633C22⋊C4—1722no—
634C42—432no—
635C42—432no—
636C42—864no—
637C42—861no—
638C42—861no—
639C42—3441no—
640C23—22no—
641C23—21no—
642C23—22no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23C2×D4×D4311yescharacteristic
662Q8—862no—
663Q8—862no—
664Q8—3444no—
665Q8—1721no—
666Q8—1721no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—22no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—84no—
676D4—84no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
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—432no—
691C2×C4—432no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—862no—
698C2×C4—861no—
699C2×C4—862no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—3444no—
705C2×C4—3444no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4C2×D4×D4311yescharacteristic
717C2×C4C2×D4×D4311yescharacteristic
718C2×C4C2×#1062190011yescharacteristic
719C2×C4C2×#1062190011yescharacteristic
720C2×C4#1306337011yescharacteristic
721C2×C4#1306337211yescharacteristic
722C8—41no—
723C8—41no—
724C8—1721no—
725C8—1721no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—42no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—41no—
734C22—42no—
735C22—42no—
736C22—41no—
737C22—41no—
738C22—42no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22#120×D4311yescharacteristic
748C22#1458340511yescharacteristic
749C22#1458347611yescharacteristic
750C22#1458370011yescharacteristic
751C22#1458370311yescharacteristic
752C22#1458370911yescharacteristic
753C22#1458371311yescharacteristic
754C4—42no—
755C4—41no—
756C4—42no—
757C4—862no—
758C4—862no—
759C4—3441no—
760C4—3441no—
761C4—1722no—
762C4—1721no—
763C4—1722no—
764C4—1721no—
765C4#1458353611yescharacteristic
766C4#1458354911yescharacteristic
767C4#1458355511yescharacteristic
768C4#1458356911yescharacteristic
769C2—81no—
770C2—82no—
771C2—82no—
772C2#1913793311yescharacteristic
773C2#1914385811yescharacteristic
774C2#1914390811yescharacteristic
775C2#1914477211yescharacteristic
776C2#1914485011yescharacteristic
777C2#1914600711yescharacteristic
778C2#1914605011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#1999C2
socleC23×C43C22×D4
hypercenter#1999D43
hypocenterC43#24167
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×#14583516C2semidirect
2. C2×#14583177C2semidirect
3. C2×#14583112C2semidirect
4. #19137290C2semidirect
5. #19135799C2semidirect
6. #19135774C2semidirect
7. #19135598C2semidirect
8. #19135541C2semidirect
9. #19135526C2semidirect
10. #19134947C2semidirect
11. #19134945C2semidirect
12. #19134850C2semidirect
13. #19134844C2semidirect
14. #19134577C2semidirect
73. #13063324D4semidirect
77. #13063312D4semidirect
452. C43#24167semidirect

Maximal subgroups

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

subgroupindex
C2×#145835162
C2×#145831772
C2×#145831122
#191372902
#191357992
#191357742
#191355982
#191355412
#191355262
#191349472
#191349452
#191348502
#191348442
#191345772
C43×#19992
#2416743