Finite Group Databasebeta

← #25130752

Subgroups — #25130752

Order 11008.

1154 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×#14583595C211yesmaximal, characteristic
2C2×#14583206C211yesmaximal, characteristic, complemented
3C2×#14582997C211yesmaximal, characteristic, complemented
4#19135784C211yesmaximal, characteristic, complemented
5#19135777C211yesmaximal, characteristic, complemented
6#19135596C211yesmaximal, characteristic, complemented
7#19135596C211yesmaximal, characteristic, complemented
8#19135563C211yesmaximal, characteristic, complemented
9#19135394C211yesmaximal, characteristic, complemented
10#19134908C211yesmaximal, characteristic, complemented
11#19134903C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic, complemented
13#19134782C211yesmaximal, characteristic, complemented
14#19134592C211yesmaximal, characteristic, complemented
15C43×#2538C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17#14583595—24no—
18#14583595—24no—
19C2×#13063320—21no—
20C2×#13063317C2211yescharacteristic
21C2×#13063307—21no—
22C2×#13063299C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063297—21no—
25C2×C4×D172C2211yescharacteristic
26C2×(C22⋊D43)⋊C4—21no—
27C2×#13063284C2211yescharacteristic
28C22×C4⋊Dic43C2211yescharacteristic
29#14583206—24no—
30#14582997—24no—
31C2×#13063258C2211yescharacteristic
32C2×#13063258C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×#13063236C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C2×C22⋊Q8×C43C2211yescharacteristic
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C43×#396—21no—
57C43×#396—21no—
58C43×#390—21no—
59C43×#389—21no—
60C43×#384C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#380C2211yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C23×Dic43—21no—
67C22×C4×D43—21no—
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063320—28no—
76#13063317—22no—
77#13063317D414yes—
78#13063307—28no—
79#13063299—22no—
80#13063299—22no—
81#13063299—22no—
82#13063299—22no—
83#13063297—28no—
84C4×D172—22no—
85C4×D172D414yes—
86(C22⋊D43)⋊C4—28no—
87#13063284—22no—
88#13063284—22no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×C22⋊Dic43—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×C4×Dic43—21no—
102#13063258—22no—
103#13063258—22no—
104#13063256—22no—
105C4⋊(C43⋊C8)—22no—
106#13063249—22no—
107#13063249—22no—
108#13063249—22no—
109#13063245—22no—
110#13063245—41no—
111#13063245—41no—
112C22⋊(C43⋊C8)—22no—
113C22⋊(C43⋊C8)—22no—
114C22⋊(C43⋊C8)—41no—
115C22⋊(C43⋊C8)—41no—
116#13063236—22no—
117C22×Q8×C43C2311yescharacteristic
118C22×D4×C43D411yescharacteristic
119C23×C4×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C22⋊Q8×C43—22no—
122C22⋊Q8×C43—22no—
123C22⋊Q8×C43—41no—
124C22⋊Q8×C43—41no—
125C4×Q8×C43—22no—
126C4×Q8×C43—22no—
127C4×D4×C43—22no—
128C4×D4×C43—22no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43D411yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43D411yescharacteristic
143C2×C22⋊C4×C43D411yescharacteristic
144C2×C42×C43—21no—
145C2×C42×C43C2311yescharacteristic
146#95×C43—21no—
147#95×C43—21no—
148C24×C43C2×D411yescharacteristic
149C24×C43C2×D411yescharacteristic
150C23×D43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43#4112yes—
157C2×D4×C43—22no—
158C2×D4×C43—22no—
159C2×D4×C43—41no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
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—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2411yescharacteristic
181C2×C22⋊D43—24no—
182C2×C22⋊D43—24no—
183C2×C22⋊D43—42no—
184C2×C22⋊D43—42no—
185C2×C22⋊D43—81no—
186C2×C22⋊D43—81no—
187C22×Dic43—24no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—81no—
192C22×Dic43—81no—
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—81no—
201C2×C4×D43—81no—
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—
209C4⋊C4×C43—42no—
210C4⋊C4×C43—42no—
211C4⋊C4×C43—42no—
212C4⋊C4×C43—42no—
213C4⋊C4×C43—81no—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—22no—
216C22⋊C4×C43—42no—
217C22⋊C4×C43—42no—
218C22⋊C4×C43—81no—
219C22⋊C4×C43—81no—
220C42×C43—42no—
221C42×C43C2×D412yes—
222C42×C43C2×D412yes—
223C22⋊Dic43—24no—
224#10621884—28no—
225(C2×D43)⋊C4—24no—
226(C2×D43)⋊C4—24no—
227(C2×D43)⋊C4—24no—
228C4⋊Dic43—24no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43C2×D412yes—
233C4⋊Dic43C2×D412yes—
234C4⋊Dic43C2×D412yes—
235Dic43⋊C4—24no—
236Dic43⋊C4—24no—
237C4×Dic43—24no—
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—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8#4112yes—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43#13712yes—
264C23×C43C22×D411yescharacteristic
265C22×D43—22no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272Q8×C43—22no—
273Q8×C43—22no—
274Q8×C43—41no—
275Q8×C43—41no—
276D4×C43—44no—
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—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
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—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43#12012yes—
308C2×C4×C43#12012yes—
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C2×#4111yescharacteristic
312C2×C4×C43C2×#4111yescharacteristic
313C2×C4×C43H(5,𝔽2)11yescharacteristic
314C2×C4×C432−1+411yescharacteristic
315C22⋊D43—48no—
316C22⋊D43—84no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—84no—
327D172—22no—
328D172—22no—
329D172—41no—
330D172—41no—
331C4×D43—84no—
332C43⋊C8—22no—
333C43⋊C8—41no—
334C43⋊C8—41no—
335C43⋊C8—41no—
336#24138—431nomaximal, Sylow
337C22×C43—22no—
338C22×C43—22no—
339C22×C43—22no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43C2×#12011yescharacteristic
352C22×C43#54611yescharacteristic
353C22×C43#54711yescharacteristic
354C22×C43C2×#13711yescharacteristic
355C22×C43#57511yescharacteristic
356C22×C43#57611yescharacteristic
357C22×C43#57711yescharacteristic
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—81no—
362C2×D43—81no—
363C2×D43—81no—
364C2×D43—81no—
365C4×C43—22no—
366C4×C43—22no—
367C4×C43—41no—
368C4×C43—41no—
369C4×C43—42no—
370C4×C43—81no—
371C4×C43—81no—
372C4×C43—81no—
373C4×C43#52511yescharacteristic
374C4×C43#53711yescharacteristic
375C4×C43#54811yescharacteristic
376C4×C43#55011yescharacteristic
377Dic43—42no—
378Dic43—42no—
379Dic43—42no—
380C2×#553—431no—
381C2×#479—431no—
382C2×#440—431no—
383#2538D4311yescharacteristic, complemented
384#2034—431no—
385#2033—431no—
386#2000—431no—
387#2000—431no—
388#1992—431no—
389#1955—431no—
390#1873—431no—
391#1872—431no—
392#1854—431no—
393#1852—431no—
394#1802—431no—
395C2×C43—42no—
396C2×C43—81no—
397C2×C43#240711yescharacteristic
398C2×C43#300711yescharacteristic
399C2×C43#301211yescharacteristic
400C2×C43#330911yescharacteristic
401C2×C43#332011yescharacteristic
402C2×C43#334611yescharacteristic
403C2×C43#335011yescharacteristic
404D43—82no—
405C22×SD16—431no—
406#553—864no—
407#553—864no—
408C2×#126—861no—
409C2×#125—431no—
410C2×#123—861no—
411C2×C22⋊Q8C2×D4311yescharacteristic
412C2×C22⋊Q8C2×D4311yescharacteristic
413C2×#121—431no—
414C2×#121—431no—
415C2×#121—861no—
416C2×C4×Q8C2×D4311yescharacteristic
417C2×C4×D4—431no—
418C2×C4×D4—861no—
419C2×C4×D4C2×D4311yescharacteristic
420C2×#117—431no—
421C22×C4⋊C4—431no—
422#479—864no—
423#440—864no—
424C2×#107—431no—
425C2×#107—431no—
426C2×#106—431no—
427C2×C4⋊C8—431no—
428C2×#103—431no—
429C2×#103—431no—
430C2×#103—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—431no—
434C2×C22⋊C8—431no—
435C2×C22⋊C8—431no—
436C2×C22⋊C8—431no—
437C2×C22⋊C8—431no—
438C2×#97—431no—
439#396—21no—
440#396—21no—
441#390—21no—
442#389—21no—
443#384C2×D4311yescharacteristic
444#380C2×D4311yescharacteristic
445#380C2×D4311yescharacteristic
446#340—431no—
447#340—431no—
448#340—431no—
449#340—431no—
450#340—431no—
451#340—431no—
452C43#2413811yescharacteristic, complemented, Sylow
453C22×Q8C22×D4311yescharacteristic
454C22×D4—431no—
455C22×D4—861no—
456C22×D4—861no—
457C22×D4C22⋊D4311yescharacteristic
458C23×C4—861no—
459C23×C4—861no—
460C23×C4C22×D4311yescharacteristic
461C23×C4C22×D4311yescharacteristic
462C2×SD16—862no—
463C2×SD16—862no—
464C2×SD16—862no—
465C22×C8—431no—
466C22×C8—431no—
467C22×C8—431no—
468C22×C8—431no—
469#126—868no—
470#125—434no—
471#125—862no—
472#123—868no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—41no—
476C22⋊Q8—41no—
477#121—862no—
478#121—862no—
479#121—862no—
480#121—862no—
481#121—868no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—434no—
487C4×D4—868no—
488C4×D4—862no—
489#117—862no—
490#117—862no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—862no—
500C2×C4⋊C4—862no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4C22⋊D4311yescharacteristic
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4C22⋊D4311yescharacteristic
517C2×C22⋊C4C22⋊D4311yescharacteristic
518C2×C42—21no—
519C2×C42—861no—
520C2×C42C22×D4311yescharacteristic
521#107—862no—
522#107—862no—
523#106—862no—
524C4⋊C8—862no—
525#103—862no—
526#103—862no—
527#103—862no—
528#102—862no—
529#102—1721no—
530#102—1721no—
531C22⋊C8—862no—
532C22⋊C8—862no—
533C22⋊C8—1721no—
534C22⋊C8—1721no—
535#97—862no—
536#95—21no—
537#95—21no—
538C24—861no—
539C24C2×C22⋊D4311yescharacteristic
540C24C2×C22⋊D4311yescharacteristic
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8#1062190012yes—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—41no—
550C2×D4—432no—
551C2×D4—864no—
552C2×D4—864no—
553C2×D4—861no—
554C2×D4—861no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—3441no—
559C2×D4—3441no—
560C2×D4—1722no—
561C2×D4—1722no—
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—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—864no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—864no—
583C22×C4—3441no—
584C22×C4—3441no—
585C22×C4—3441no—
586C22×C4—3441no—
587C22×C4C2×C22⋊D4311yescharacteristic
588C22×C4C2×C22⋊D4311yescharacteristic
589C22×C4C2×C22⋊D4311yescharacteristic
590C22×C4C2×C22⋊D4311yescharacteristic
591C22×C4C23×D4311yescharacteristic
592SD16—868no—
593C2×C8—432no—
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—
603C2×C8—861no—
604C2×C8—861no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—81no—
617C4⋊C4—432no—
618C4⋊C4—432no—
619C4⋊C4—432no—
620C4⋊C4—864no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C42—42no—
637C42—864no—
638C42D4×D4312yes—
639C42D4×D4312yes—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—862no—
654C23—1721no—
655C23—1721no—
656C23—1721no—
657C23—1721no—
658C23—1721no—
659C23—1721no—
660C23#1306335612yes—
661C23C22×C22⋊D4311yescharacteristic
662Q8—22no—
663Q8—22no—
664Q8—41no—
665Q8—41no—
666D4—44no—
667D4—862no—
668D4—862no—
669D4—3444no—
670D4—1728no—
671D4—1721no—
672D4—1721no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
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—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—3444no—
707C2×C4—3444no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4#1306329312yes—
715C2×C4#1306329312yes—
716C2×C4C2×D4×D4311yescharacteristic
717C2×C4C2×D4×D4311yescharacteristic
718C2×C4#41×D4311yescharacteristic
719C2×C4C2×#1062190011yescharacteristic
720C2×C4#1306337011yescharacteristic
721C2×C4#1306337211yescharacteristic
722C8—862no—
723C8—1721no—
724C8—1721no—
725C8—1721no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—3441no—
741C22—3441no—
742C22—3441no—
743C22—3441no—
744C22—1722no—
745C22—1722no—
746C22—1722no—
747C22C2×#1306329311yescharacteristic
748C22#1458354311yescharacteristic
749C22#1458354811yescharacteristic
750C22C2×#1306335611yescharacteristic
751C22#1458369711yescharacteristic
752C22#1458370211yescharacteristic
753C22#1458370711yescharacteristic
754C4—22no—
755C4—22no—
756C4—41no—
757C4—41no—
758C4—42no—
759C4—81no—
760C4—81no—
761C4—81no—
762C4—1722no—
763C4—1722no—
764C4—1722no—
765C4#1458340911yescharacteristic
766C4#1458347811yescharacteristic
767C4#1458355511yescharacteristic
768C4#1458356711yescharacteristic
769C2—42no—
770C2—81no—
771C2—3442no—
772C2#1913793611yescharacteristic
773C2#1914385311yescharacteristic
774C2#1914389611yescharacteristic
775C2#1914660111yescharacteristic
776C2#1914676611yescharacteristic
777C2#1914707411yescharacteristic
778C2#1914714011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2538C2
socleC23×C43C22×D4
prime radicalC2×#14583595C2
hypercenter#2538D43
hypocenterC43#24138
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
2. C2×#14583206C2semidirect
3. C2×#14582997C2semidirect
4. #19135784C2semidirect
5. #19135777C2semidirect
6. #19135596C2semidirect
7. #19135596C2semidirect
8. #19135563C2semidirect
9. #19135394C2semidirect
10. #19134908C2semidirect
11. #19134903C2semidirect
12. #19134792C2semidirect
13. #19134782C2semidirect
14. #19134592C2semidirect
15. C43×#2538C2semidirect
383. #2538D43semidirect
452. C43#24138semidirect

Maximal subgroups

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

subgroupindex
C2×#145835952
C2×#145832062
C2×#145829972
#191357842
#191357772
#191355962
#191355632
#191353942
#191349082
#191349032
#191347922
#191347822
#191345922
C43×#25382
#2413843