Finite Group Databasebeta

← #25129880

Subgroups — #25129880

Order 11008.

1352 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×#14583444C211yesmaximal, characteristic
2C2×#14583224C211yesmaximal, characteristic, complemented
3C2×#14583220C211yesmaximal, characteristic, complemented
4#19137079C211yesmaximal, characteristic, complemented
5#19135927C211yesmaximal, characteristic, complemented
6#19135922C211yesmaximal, characteristic, complemented
7#19135828C211yesmaximal, characteristic, complemented
8#19135828C211yesmaximal, characteristic, complemented
9#19134917C211yesmaximal, characteristic, complemented
10#19134858C211yesmaximal, characteristic, complemented
11#19134857C211yesmaximal, characteristic, complemented
12#19134844C211yesmaximal, characteristic, complemented
13#19134843C211yesmaximal, characteristic, complemented
14#19134661C211yesmaximal, characteristic, complemented
15C43×#1875C211yesmaximal, characteristic, complemented
16C22×#10621900—21no—
17#14583444—24no—
18#14583444—24no—
19C2×#13063324C2211yescharacteristic
20C2×#13063321C2211yescharacteristic
21C2×#13063311—21no—
22C2×#13063299C2211yescharacteristic
23C2×#13063297—21no—
24C2×D4×Dic43C2211yescharacteristic
25C2×#13063287C2211yescharacteristic
26C2×(C22⋊D43)⋊C4—21no—
27C2×#13063284C2211yescharacteristic
28C22×C4×Dic43C2211yescharacteristic
29#14583224—24no—
30#14583220—24no—
31C2×#13063259C2211yescharacteristic
32C2×#13063258C2211yescharacteristic
33C2×#13063257C2211yescharacteristic
34C2×#13063256C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42#14582798C2211yescharacteristic
43#14582798C2211yescharacteristic
44#14582798C2211yescharacteristic
45#14582798C2211yescharacteristic
46#14582774—21no—
47#14582774—21no—
48C4×C4⋊Dic43—21no—
49C4×C4⋊Dic43—21no—
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C2×#117×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C2×#10621900—28no—
64C2×#10621900—44no—
65C2×#10621900—44no—
66C22×Dic86—21no—
67C22×D172C2311yescharacteristic
68C22×C22⋊D43—21no—
69C22×C22⋊D43—21no—
70C22×C22⋊D43—21no—
71C23×Dic43—21no—
72C23×Dic43D411yescharacteristic
73C23×Dic43D411yescharacteristic
74C22×C4×D43—21no—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063324—22no—
78#13063324—22no—
79#13063321—22no—
80#13063321—22no—
81#13063311—28no—
82#13063299—22no—
83#13063299D414yes—
84#13063297—28no—
85D4×Dic43—22no—
86D4×Dic43—22no—
87#13063287—22no—
88#13063287—22no—
89(C22⋊D43)⋊C4—28no—
90#13063284—22no—
91#13063284—22no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×C4×Dic43—22no—
105C2×C4×Dic43—22no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43C2311yescharacteristic
110C2×C4×Dic43C2311yescharacteristic
111#13063259—22no—
112#13063258—22no—
113#13063257—22no—
114#13063256—22no—
115#13063247—22no—
116#13063247—22no—
117#13063246—22no—
118#13063246—22no—
119#13063245—22no—
120#13063245—22no—
121C22⋊(C43⋊C8)—22no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C22×D4×C43—21no—
127C22×D4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131#121×C43—22no—
132#121×C43D414yes—
133#117×C43—22no—
134#117×C43—22no—
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C42×C43—21no—
141#102×C43—22no—
142#102×C43—22no—
143C22⋊C8×C43—22no—
144C24×C43—21no—
145C24×C43C2×D411yescharacteristic
146C23×D43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—24no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—42no—
154C2×D4×C43—42no—
155C2×D4×C43C2×D412yes—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43C2×D412yes—
164C22×C4×C43C2×D412yes—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2411yescharacteristic
167C2×C22⋊D43—24no—
168C2×C22⋊D43—24no—
169C2×C22⋊D43—24no—
170C2×C22⋊D43—42no—
171C2×C22⋊D43—42no—
172C2×C22⋊D43—42no—
173C2×C22⋊D43—42no—
174C2×C22⋊D43—42no—
175C2×C22⋊D43—42no—
176C22×Dic43—22no—
177C22×Dic43—22no—
178C22×Dic43—24no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—41no—
186C22×Dic43—42no—
187C22×Dic43—42no—
188C22×Dic43C2×D411yescharacteristic
189C22×Dic43C2×D411yescharacteristic
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192#10621900—432no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—21no—
198C2×D172C2×D412yes—
199C2×C4×D43—24no—
200C2×C4×D43—42no—
201C2×C4×D43—42no—
202C2×Dic86—24no—
203C2×Dic86—42no—
204C2×Dic86—42no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43C2×D412yes—
215C4⋊C4×C43#4112yescomplemented
216C4⋊C4×C43#4112yescomplemented
217C22⋊C4×C43—24no—
218C22⋊C4×C43—24no—
219C42×C43—24no—
220C22⋊Dic43—24no—
221C22⋊Dic43—42no—
222(C2×D43)⋊C4—24no—
223(C2×D43)⋊C4—24no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—42no—
230C4⋊Dic43—42no—
231C4⋊Dic43—42no—
232C4⋊Dic43—42no—
233C4⋊Dic43C2×D412yes—
234Dic43⋊C4—24no—
235C4×Dic43—22no—
236C4×Dic43—22no—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C4×Dic43—42no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—22no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43#12012yes—
262C23×C43C22×D411yescharacteristic
263C22×D43—22no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—48no—
273D4×C43—41no—
274D4×C43—41no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43#12012yes—
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C22×D411yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×C4×C432−1+411yescharacteristic
296C2×C4×C432−1+411yescharacteristic
297C22⋊D43—48no—
298C22⋊D43—48no—
299C22⋊D43—48no—
300C2×Dic43—28no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—22no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—44no—
312C2×Dic43—48no—
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#13512yes—
322C2×Dic43AGL(1,ℤ/8)12yes—
323C2×Dic43AGL(1,ℤ/8)12yes—
324D172—22no—
325D172—22no—
326D172—41no—
327D172—41no—
328C4×D43—48no—
329Dic86—48no—
330C8×C43—41no—
331C8×C43—41no—
332C43⋊C8—41no—
333C43⋊C8—41no—
334#24062—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—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43C2×#12011yescharacteristic
350C22×C43#52511yescharacteristic
351C22×C43#53611yescharacteristic
352C22×C43C2×#13511yescharacteristic
353C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C43#57511yescharacteristic
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—81no—
360C2×D43—81no—
361C2×D43—81no—
362C2×D43—81no—
363C4×C43—22no—
364C4×C43—42no—
365C4×C43—42no—
366C4×C43—42no—
367C4×C43#54711yescharacteristic
368C4×C43#54711yescharacteristic
369C4×C43#54711yescharacteristic
370C4×C43#54711yescharacteristic
371Dic43—22no—
372Dic43—22no—
373Dic43—22no—
374Dic43—41no—
375Dic43—42no—
376Dic43—81no—
377Dic43—81no—
378C2×#532—431no—
379C2×#482—431no—
380C2×#482—431no—
381#2296—431no—
382#2058—431no—
383#2057—431no—
384#2041—431no—
385#2041—431no—
386#1875—431no—
387#1875D4311yescharacteristic, complemented
388#1864—431no—
389#1864—431no—
390#1862—431no—
391#1862—431no—
392#1817—431no—
393C2×C43—42no—
394C2×C43—82no—
395C2×C43#240611yescharacteristic
396C2×C43#300211yescharacteristic
397C2×C43#300311yescharacteristic
398C2×C43#310611yescharacteristic
399C2×C43#311511yescharacteristic
400C2×C43#322811yescharacteristic
401C2×C43#323511yescharacteristic
402D43—82no—
403C22×#41—861no—
404#532—864no—
405#532—864no—
406C2×C4⋊Q8—431no—
407C2×#127—431no—
408C2×#124—861no—
409C2×#121—431no—
410C2×#121—861no—
411C2×#121C2×D4311yescharacteristic
412C2×C4×D4—431no—
413C2×C4×D4—431no—
414C2×C4×D4—861no—
415C2×#117—431no—
416C2×#117C2×D4311yescharacteristic
417C22×C42—431no—
418#482—864no—
419#482—864no—
420C2×#107—431no—
421C2×#107—431no—
422C2×#106—431no—
423C2×#106—431no—
424C2×#102—431no—
425C2×#102—431no—
426C2×#102—431no—
427C2×#102—431no—
428C2×#102—431no—
429C2×#102—431no—
430C2×#102C2×D4311yescharacteristic
431C2×#102C2×D4311yescharacteristic
432C2×C22⋊C8—431no—
433C2×C22⋊C8C2×D4311yescharacteristic
434#389—431no—
435#389—431no—
436#389—431no—
437#389—431no—
438#385—861no—
439#385—861no—
440C4×C4⋊C4—861no—
441C4×C4⋊C4—861no—
442#340—431no—
443#340—431no—
444#340C2×D4311yescharacteristic
445#340C2×D4311yescharacteristic
446#336—431no—
447#336—431no—
448#336—431no—
449#336—431no—
450C43#2406211yescharacteristic, complemented, Sylow
451C2×#41—868no—
452C2×#41—1724no—
453C2×#41—1724no—
454C22×Q8—861no—
455C22×D4—21no—
456C22×D4—431no—
457C22×D4—861no—
458C22×D4—861no—
459C22×D4—861no—
460C22×D4C22×D4311yescharacteristic
461C23×C4—431no—
462C23×C4—431no—
463C23×C4—861no—
464C23×C4—861no—
465C23×C4C22×D4311yescharacteristic
466C22×C8—431no—
467C22×C8—431no—
468C22×C8C22×D4311yescharacteristic
469C22×C8C22×D4311yescharacteristic
470C4⋊Q8—862no—
471C4⋊Q8—862no—
472#127—862no—
473#127—862no—
474#124—868no—
475#121—22no—
476#121—434no—
477#121—868no—
478#121—862no—
479#121D17214yes—
480C4×D4—868no—
481C4×D4—862no—
482C4×D4—862no—
483C4×D4—862no—
484C4×D4—862no—
485#117—22no—
486#117—22no—
487#117—862no—
488#117—862no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4C22×D4311yescharacteristic
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C4⋊C4C22×D4311yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C42—21no—
507C2×C42—431no—
508C2×C42—431no—
509C2×C42—431no—
510C2×C42—431no—
511C2×C42—862no—
512C2×C42—862no—
513C2×C42—861no—
514#107—862no—
515#107—862no—
516#106—862no—
517#106—862no—
518#102—22no—
519#102—22no—
520#102—862no—
521#102—862no—
522#102—862no—
523#102—862no—
524#102—862no—
525#102—862no—
526C22⋊C8—22no—
527C22⋊C8—862no—
528#95—861no—
529#95—861no—
530#95—861no—
531#95—861no—
532C24—21no—
533C24—861no—
534C24D4×D4311yescharacteristic
535#41—17232no—
536C2×Q8—864no—
537C2×Q8—1722no—
538C2×Q8—1722no—
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—432no—
548C2×D4—864no—
549C2×D4—864no—
550C2×D4—864no—
551C2×D4—861no—
552C2×D4—861no—
553C2×D4—861no—
554C2×D4—861no—
555C2×D4—861no—
556C2×D4—1722no—
557C2×D4—1722no—
558C2×D4—1722no—
559C2×D4—1722no—
560C2×D4—1722no—
561C2×D4—1722no—
562C2×D4C2×D17212yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—431no—
571C22×C4—431no—
572C22×C4—431no—
573C22×C4—431no—
574C22×C4—864no—
575C22×C4—862no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—864no—
580C22×C4—862no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—1722no—
585C22×C4—1722no—
586C22×C4—1722no—
587C22×C4—1721no—
588C22×C4—1722no—
589C22×C4C2×D17212yes—
590C22×C4D4×D4311yescharacteristic
591C22×C4D4×D4312yes—
592C22×C4C23×D4311yescharacteristic
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—432no—
609C4⋊C4—864no—
610C4⋊C4—861no—
611C4⋊C4—861no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—1722no—
616C4⋊C4—1722no—
617C4⋊C4—1722no—
618C4⋊C4—1722no—
619C4⋊C4C2×D17212yes—
620C4⋊C4#1062190012yescomplemented
621C4⋊C4#1062190012yescomplemented
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—864no—
625C22⋊C4—864no—
626C22⋊C4—864no—
627C22⋊C4—1722no—
628C42—24no—
629C42—862no—
630C42—862no—
631C42—861no—
632C42—861no—
633C42—861no—
634C42—861no—
635C42—1722no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—862no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23—1721no—
654C23—1721no—
655C23—1721no—
656C23#1306329512yes—
657C23C2×D4×D4311yescharacteristic
658Q8—1728no—
659D4—22no—
660D4—22no—
661D4—48no—
662D4—41no—
663D4—41no—
664D4—862no—
665D4—862no—
666D4—1728no—
667D4—1728no—
668D4—1728no—
669D4—1721no—
670D4—1721no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—432no—
687C2×C4—432no—
688C2×C4—432no—
689C2×C4—868no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—862no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—1728no—
701C2×C4—1724no—
702C2×C4—1728no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4#1306329512yes—
712C2×C4C2×D4×D4311yescharacteristic
713C2×C4C22×D17211yescharacteristic
714C2×C4C2×#1062190011yescharacteristic
715C2×C4C2×#1062190011yescharacteristic
716C2×C4#1306337211yescharacteristic
717C2×C4#1306337211yescharacteristic
718C8—41no—
719C8—41no—
720C8—1721no—
721C8—1721no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—3441no—
737C22—3441no—
738C22—3441no—
739C22—3441no—
740C22—1722no—
741C22—1722no—
742C22—1722no—
743C22C2×#1306329511yescharacteristic
744C22#1458340511yescharacteristic
745C22#1458347111yescharacteristic
746C22#135×D4311yescharacteristic
747C22AGL(1,ℤ/8)×D4311yescharacteristic
748C22AGL(1,ℤ/8)×D4311yescharacteristic
749C22#1458369611yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—862no—
755C4—862no—
756C4—862no—
757C4—3441no—
758C4—3441no—
759C4—1721no—
760C4—1722no—
761C4#1458354911yescharacteristic
762C4#1458354911yescharacteristic
763C4#1458355311yescharacteristic
764C4#1458355311yescharacteristic
765C2—42no—
766C2—82no—
767C2—3442no—
768C2#1913792911yescharacteristic
769C2#1914381511yescharacteristic
770C2#1914382411yescharacteristic
771C2#1914464811yescharacteristic
772C2#1914473911yescharacteristic
773C2#1914572911yescharacteristic
774C2#1914579011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1875C2
socleC23×C43C22×D4
prime radicalC2×#14583444C2
hypercenter#1875D43
hypocenterC43#24062
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
2. C2×#14583224C2semidirect
3. C2×#14583220C2semidirect
4. #19137079C2semidirect
5. #19135927C2semidirect
6. #19135922C2semidirect
7. #19135828C2semidirect
8. #19135828C2semidirect
9. #19134917C2semidirect
10. #19134858C2semidirect
11. #19134857C2semidirect
12. #19134844C2semidirect
13. #19134843C2semidirect
14. #19134661C2semidirect
15. C43×#1875C2semidirect
215. C4⋊C4×C43#41semidirect
216. C4⋊C4×C43#41semidirect
387. #1875D43semidirect
450. C43#24062semidirect
620. C4⋊C4#10621900semidirect
621. C4⋊C4#10621900semidirect

Maximal subgroups

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

subgroupindex
C2×#145834442
C2×#145832242
C2×#145832202
#191370792
#191359272
#191359222
#191358282
#191349172
#191348582
#191348572
#191348442
#191348432
#191346612
C43×#18752
#2406243