Finite Group Databasebeta

← #25149720

Subgroups — #25149720

Order 11008.

1108 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583583C211yesmaximal, characteristic
2C2×#14583237C211yesmaximal, characteristic, complemented
3#19138047C211yesmaximal, characteristic
4#19135935C211yesmaximal, characteristic, complemented
5#19135796C211yesmaximal, characteristic, complemented
6#19135744C211yesmaximal, characteristic, complemented
7#19135602C211yesmaximal, characteristic, complemented
8#19134938C211yesmaximal, characteristic, complemented
9#19134903C211yesmaximal, characteristic, complemented
10#19134899C211yesmaximal, characteristic, complemented
11#19134892C211yesmaximal, characteristic
12#19134861C211yesmaximal, characteristic, complemented
13#19134786C211yesmaximal, characteristic, complemented
14#19134315C211yesmaximal, characteristic, complemented
15C2×C43×#470C211yesmaximal, characteristic, complemented
16#14583583—24no—
17#14583583—24no—
18C2×#13063318—21no—
19C2×#13063316C2211yescharacteristic
20C2×#13063315—21no—
21C2×#13063307—21no—
22C2×#13063301C2211yescharacteristic
23C2×#13063301C2211yescharacteristic
24C2×Q8×Dic43C2211yescharacteristic
25C2×C4×C22⋊D43C2211yescharacteristic
26C2×#13063284C2211yescharacteristic
27C2×#13063283—21no—
28C22×C4⋊Dic43C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30#14583237—24no—
31C2×#13063258C2211yescharacteristic
32C2×#13063256C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×(C2×D43)⋊C8C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40#14582832—21no—
41#14582821—21no—
42#14582806C2211yescharacteristic
43#14582795C2211yescharacteristic
44#14582776—21no—
45#14582757—21no—
46#14582756C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×Q16×C43C2211yescharacteristic
56C22×M16×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×C22⋊Q8×C43C2211yescharacteristic
59C43×#470—24no—
60C2×#106×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C22×C22⋊D43D411yescharacteristic
64C23×Dic43—21no—
65C22×C4×D43—21no—
66C22×C4×D43C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063318—28no—
70#13063316—22no—
71#13063316—22no—
72#13063315—28no—
73#13063307—28no—
74#13063301—22no—
75#13063301—22no—
76#13063301—22no—
77#13063301—41no—
78Q8×Dic43—22no—
79Q8×Dic43—22no—
80C4×C22⋊D43—22no—
81C4×C22⋊D43—22no—
82#13063284—22no—
83#13063284D414yes—
84#13063283—28no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—41no—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4D411yescharacteristic
100C4⋊C4×D43—22no—
101C4⋊C4×D43—22no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43D411yescharacteristic
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4D411yescharacteristic
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43C2311yescharacteristic
111#13063258—22no—
112#13063256—22no—
113#13063249—22no—
114#13063249—22no—
115#13063249—22no—
116#13063249—41no—
117C22⋊(C43⋊C8)—22no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—41no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C22×Q8×C43C2311yescharacteristic
125C22×Q8×C43C2311yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C2×Q16×C43—22no—
128C2×Q16×C43—22no—
129C2×Q16×C43—41no—
130C2×M16×C43—22no—
131C2×M16×C43—22no—
132C2×M16×C43—41no—
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C22⋊Q8×C43—22no—
136C22⋊Q8×C43—22no—
137C22⋊Q8×C43—22no—
138C22⋊Q8×C43D414yes—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145#106×C43—22no—
146#103×C43—22no—
147#103×C43—22no—
148C24×C43C2×D411yescharacteristic
149C23×D43C2×D411yescharacteristic
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43C2×D412yes—
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×C43C2×D412yes—
171C22×C4×C43C2×D412yes—
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2411yescharacteristic
174C2×C22⋊D43—22no—
175C2×C22⋊D43—22no—
176C2×C22⋊D43—41no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—42no—
182C22×Dic43—42no—
183C22×Dic43—81no—
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187C2×C4×D43—24no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—42no—
195C2×C4×D43—42no—
196Q16×C43—44no—
197M16×C43—44no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43#4112yes—
204C4⋊C4×C43—24no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—42no—
209C4⋊C4×C43C2×D412yes—
210C22⋊C4×C43—24no—
211C22⋊C4×C43—42no—
212C22⋊Dic43—24no—
213C22⋊Dic43—22no—
214(C2×D43)⋊C4—24no—
215(C2×D43)⋊C4—22no—
216(C2×D43)⋊C4—42no—
217(C2×D43)⋊C4—81no—
218C4⋊Dic43—24no—
219C4⋊Dic43—24no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—42no—
226C4⋊Dic43C2×D412yes—
227C4⋊Dic43C2×D412yes—
228C4⋊Dic43#4112yes—
229Dic43⋊C4—24no—
230Dic43⋊C4—24no—
231Dic43⋊C4—24no—
232Dic43⋊C4—22no—
233Dic43⋊C4—42no—
234Dic43⋊C4—81no—
235C4×Dic43—24no—
236C4×Dic43—24no—
237C4×Dic43—21no—
238C4×Dic43—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—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43#12012yes—
252C23×C43C22×D411yescharacteristic
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43#13712yes—
260Q8×C43—22no—
261Q8×C43—22no—
262Q8×C43—41no—
263Q8×C43—41no—
264Q8×C43—41no—
265Q8×C43—41no—
266Q8×C43—41no—
267Q8×C43—41no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43#12012yes—
287C2×C4×C43C22×D411yescharacteristic
288C2×C4×C43C22×D411yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43H(5,𝔽2)11yescharacteristic
292C2×C4×C432−1+411yescharacteristic
293C22⋊D43—44no—
294C2×Dic43—21no—
295C2×Dic43—22no—
296C2×Dic43—21no—
297C2×Dic43—22no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—22no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—84no—
316C4×D43—48no—
317C4×D43—41no—
318C4×D43—41no—
319C4×D43—41no—
320C4×D43—41no—
321C8×C43—22no—
322C8×C43—41no—
323C43⋊C8—41no—
324C43⋊C8—41no—
325#25562—431nomaximal, Sylow
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—22no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43C2×#12011yescharacteristic
334C22×C43#54611yescharacteristic
335C22×C43#54711yescharacteristic
336C22×C43C2×#13711yescharacteristic
337C22×C43#57511yescharacteristic
338C22×C43#57711yescharacteristic
339C22×C43#57811yescharacteristic
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—22no—
343C2×D43—41no—
344C2×D43—41no—
345C2×D43—41no—
346C2×D43—41no—
347C4×C43—22no—
348C4×C43—42no—
349C4×C43—42no—
350C4×C43—81no—
351C4×C43—81no—
352C4×C43#53211yescharacteristic
353C4×C43#53711yescharacteristic
354C4×C43#54611yescharacteristic
355C4×C43#54711yescharacteristic
356Dic43—41no—
357Dic43—42no—
358Dic43—41no—
359Dic43—41no—
360Dic43—42no—
361Dic43—42no—
362Dic43—81no—
363C2×#552—431no—
364C2×#485—431no—
365C2×#470D4311yescharacteristic, complemented
366#2417—431no—
367#2059—431no—
368#2036—431no—
369#2026—431no—
370#2001—431no—
371#1878—431no—
372#1872—431no—
373#1872—431no—
374#1870—431no—
375#1865—431no—
376#1853—431no—
377#1736—431no—
378C2×C43—42no—
379C2×C43#243011yescharacteristic
380C2×C43#300711yescharacteristic
381C2×C43#301311yescharacteristic
382C2×C43#331211yescharacteristic
383C2×C43#332311yescharacteristic
384C2×C43#334411yescharacteristic
385C2×C43#335211yescharacteristic
386D43—42no—
387C22×Q16C2×D4311yescharacteristic
388C22×M16C2×D4311yescharacteristic
389#552—864no—
390#552—864no—
391C2×#126—861no—
392C2×#125—431no—
393C2×#125—861no—
394C2×#123—861no—
395C2×C22⋊Q8—431no—
396C2×C22⋊Q8—431no—
397C2×C22⋊Q8C2×D4311yescharacteristic
398C2×C22⋊Q8C2×D4311yescharacteristic
399C2×C4×Q8—431no—
400C2×C4×D4—431no—
401C2×#117—431no—
402C2×#117—861no—
403C22×C4⋊C4—431no—
404C22×C4⋊C4—431no—
405#485—864no—
406#470—24no—
407C2×#107—431no—
408C2×#106—431no—
409C2×#106C2×D4311yescharacteristic
410C2×#103—431no—
411C2×#103—431no—
412C2×#103—431no—
413C2×#103—431no—
414C2×#103C2×D4311yescharacteristic
415C2×#103C2×D4311yescharacteristic
416C2×C22⋊C8—431no—
417C2×C22⋊C8—431no—
418C2×C22⋊C8—431no—
419#398—861no—
420#396—861no—
421#391—431no—
422#389—431no—
423#386—861no—
424#380—431no—
425#380—861no—
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#340—431no—
431#340—431no—
432#336—431no—
433#336—431no—
434C43#2556211yescharacteristic, complemented, Sylow
435C22×Q8C22×D4311yescharacteristic
436C22×Q8C22×D4311yescharacteristic
437C22×D4—431no—
438C23×C4—431no—
439C23×C4—861no—
440C23×C4—861no—
441C23×C4C22×D4311yescharacteristic
442C2×Q16—22no—
443C2×Q16—22no—
444C2×Q16—41no—
445C2×M16—22no—
446C2×M16—22no—
447C2×M16—41no—
448C22×C8—431no—
449C22×C8—431no—
450C22×C8C22×D4311yescharacteristic
451C22×C8C22×D4311yescharacteristic
452#126—868no—
453#125—862no—
454#125—868no—
455#125—862no—
456#123—868no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460C22⋊Q8—862no—
461C22⋊Q8—862no—
462C22⋊Q8—862no—
463C22⋊Q8—1721no—
464C22⋊Q8C22⋊D4314yes—
465C4×Q8—862no—
466C4×Q8—862no—
467C4×D4—862no—
468C4×D4—862no—
469#117—434no—
470#117—868no—
471#117—862no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—862no—
480C2×C4⋊C4—862no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—862no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—1721no—
491C2×C4⋊C4C22×D4311yescharacteristic
492C2×C4⋊C4C22×D4311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—431no—
496C2×C22⋊C4—431no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C42—431no—
502C2×C42—861no—
503C2×C42—861no—
504#107—862no—
505#106—22no—
506#106—862no—
507#103—22no—
508#103—22no—
509#103—862no—
510#103—862no—
511#103—862no—
512#103—1721no—
513C22⋊C8—862no—
514C22⋊C8—862no—
515C22⋊C8—1721no—
516#95—861no—
517#95—861no—
518#95—861no—
519#95—861no—
520C24—431no—
521C24D4×D4311yescharacteristic
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8C2×C22⋊D4312yes—
534C2×D4—862no—
535C2×D4—862no—
536C2×D4—1721no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—431no—
546C22×C4—431no—
547C22×C4—431no—
548C22×C4—864no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—3441no—
560C22×C4—1722no—
561C22×C4—1722no—
562C22×C4—1722no—
563C22×C4—1722no—
564C22×C4D4×D4311yescharacteristic
565C22×C4D4×D4312yes—
566C22×C4C2×C22⋊D4312yes—
567C22×C4C23×D4311yescharacteristic
568Q16—44no—
569M16—44no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8#1062190012yes—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—42no—
587C4⋊C4—432no—
588C4⋊C4—432no—
589C4⋊C4—432no—
590C4⋊C4—864no—
591C4⋊C4—864no—
592C4⋊C4—864no—
593C4⋊C4—864no—
594C4⋊C4—864no—
595C4⋊C4—862no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—3441no—
602C4⋊C4—1722no—
603C4⋊C4—1722no—
604C4⋊C4C2×C22⋊D4312yes—
605C22⋊C4—24no—
606C22⋊C4—42no—
607C22⋊C4—864no—
608C22⋊C4—862no—
609C22⋊C4—864no—
610C22⋊C4—862no—
611C22⋊C4—3441no—
612C22⋊C4—1722no—
613C42—864no—
614C42—864no—
615C42—861no—
616C42—861no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—432no—
624C23—861no—
625C23—861no—
626C23—861no—
627C23—861no—
628C23—861no—
629C23—861no—
630C23#1306329312yes—
631C23C2×D4×D4311yescharacteristic
632Q8—22no—
633Q8—22no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640D4—1724no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—861no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—861no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—862no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—3444no—
672C2×C4—1728no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4#1306329312yes—
687C2×C4C2×D4×D4311yescharacteristic
688C2×C4C22×C22⋊D4311yescharacteristic
689C2×C4#41×D4311yescharacteristic
690C2×C4C2×#1062190011yescharacteristic
691C2×C4#1306337011yescharacteristic
692C2×C4#1306337211yescharacteristic
693C8—22no—
694C8—41no—
695C8—1721no—
696C8—1721no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—862no—
705C22—862no—
706C22—862no—
707C22—1721no—
708C22—1721no—
709C22—1721no—
710C22—1721no—
711C22C2×#1306329311yescharacteristic
712C22#1458353811yescharacteristic
713C22#1458354911yescharacteristic
714C22#137×D4311yescharacteristic
715C22#1458369811yescharacteristic
716C22#1458370811yescharacteristic
717C22#1458371511yescharacteristic
718C4—22no—
719C4—42no—
720C4—42no—
721C4—81no—
722C4—81no—
723C4—3441no—
724C4—1722no—
725C4—1721no—
726C4—1721no—
727C4—1722no—
728C4—1721no—
729C4—1722no—
730C4#1458344411yescharacteristic
731C4#1458347611yescharacteristic
732C4#1458354311yescharacteristic
733C4#1458354811yescharacteristic
734C2—42no—
735C2—1722no—
736C2#1913820111yescharacteristic
737C2#1914385111yescharacteristic
738C2#1914390911yescharacteristic
739C2#1914664111yescharacteristic
740C2#1914681711yescharacteristic
741C2#1914704511yescharacteristic
742C2#1914716511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#470C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC2×#470D43
hypocenterC43#25562
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
2. C2×#14583237C2semidirect
4. #19135935C2semidirect
5. #19135796C2semidirect
6. #19135744C2semidirect
7. #19135602C2semidirect
8. #19134938C2semidirect
9. #19134903C2semidirect
10. #19134899C2semidirect
12. #19134861C2semidirect
13. #19134786C2semidirect
14. #19134315C2semidirect
15. C2×C43×#470C2semidirect
365. C2×#470D43semidirect
434. C43#25562semidirect

Maximal subgroups

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

subgroupindex
C2×#145835832
C2×#145832372
#191380472
#191359352
#191357962
#191357442
#191356022
#191349382
#191349032
#191348992
#191348922
#191348612
#191347862
#191343152
C2×C43×#4702
#2556243