Finite Group Databasebeta

← #25033350

Subgroups — #25033350

Order 11008.

1922 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582836C211yesmaximal, characteristic, complemented
2C2×#14582835C211yesmaximal, characteristic, complemented
3C2×#14582799C211yesmaximal, characteristic
4C2×#14582799C212yesmaximal
5C2×#14582796C212yesmaximal, complemented
6C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
7#19132840C212yesmaximal, complemented
8#19132839C212yesmaximal, complemented
9#19132837C211yesmaximal, characteristic, complemented
10Dic43⋊#95C211yesmaximal, characteristic, complemented
11C43×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D43C2211yescharacteristic
13C22×C4⋊Dic43C2212yes—
14C22×C4⋊Dic43C2211yescharacteristic
15C22×Dic43⋊C4C2211yescharacteristic
16C22×Dic43⋊C4C2212yes—
17C22×Dic43⋊C4C2212yes—
18C22×C22⋊Dic43C2212yes—
19C22×C22⋊Dic43C2211yescharacteristic
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2212yes—
22C22×(C2×D43)⋊C4C2212yes—
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×C4×Dic43C2212yes—
25C22×C4×Dic43C2211yescharacteristic
26#14582836—24no—
27#14582835—24no—
28#14582799—28no—
29#14582799—24no—
30#14582796—28no—
31C4⋊C4×Dic43—24no—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2212yes—
36C22×C4⋊C4×C43C2211yescharacteristic
37C22×C22⋊C4×C43C2211yescharacteristic
38C22×C22⋊C4×C43C2212yes—
39C2×#95×C43C2212yes—
40C2×#95×C43C2211yescharacteristic
41C24×D43C2311yescharacteristic
42C22×C22⋊D43—22no—
43C22×C22⋊D43—24no—
44C22×C22⋊D43—24no—
45C22×C22⋊D43—22no—
46C22×C22⋊D43Q814yes—
47C23×Dic43C2311yescharacteristic
48C23×Dic43C2312yes—
49C23×Dic43C2311yescharacteristic
50C23×Dic43C2312yes—
51C23×Dic43C2311yescharacteristic
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—24no—
55C2×C4⋊Dic43—24no—
56C2×C4⋊Dic43—42no—
57C2×C4⋊Dic43D414yescomplemented
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—24no—
60C2×Dic43⋊C4—24no—
61C2×Dic43⋊C4—24no—
62C2×Dic43⋊C4—22no—
63C2×Dic43⋊C4—24no—
64C2×Dic43⋊C4—42no—
65C2×Dic43⋊C4D418yes—
66C2×C22⋊Dic43—24no—
67C2×C22⋊Dic43—22no—
68C2×C22⋊Dic43—24no—
69C2×C22⋊Dic43—42no—
70C2×C22⋊Dic43—42no—
71C2×(C2×D43)⋊C4—24no—
72C2×(C2×D43)⋊C4—22no—
73C2×(C2×D43)⋊C4—22no—
74C2×(C2×D43)⋊C4—22no—
75C2×(C2×D43)⋊C4—24no—
76C2×(C2×D43)⋊C4—24no—
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4—24no—
79C2×(C2×D43)⋊C4—42no—
80C2×(C2×D43)⋊C4—42no—
81C2×(C2×D43)⋊C4—42no—
82C2×C4×Dic43—24no—
83C2×C4×Dic43—24no—
84C2×C4×Dic43—24no—
85C2×C4×Dic43—24no—
86C2×C4×Dic43D414yes—
87C43⋊#95—22no—
88C43⋊#95—24no—
89C43⋊#95—24no—
90C43⋊#95—42no—
91C25×C43C2311yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2312yes—
94C23×C4×C43C2312yes—
95C23×C4×C43C2311yescharacteristic
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43—24no—
98C2×C22⋊C4×C43—24no—
99C2×C22⋊C4×C43—22no—
100C2×C22⋊C4×C43—22no—
101C2×C22⋊C4×C43—22no—
102C2×C22⋊C4×C43—24no—
103C2×C22⋊C4×C43—42no—
104#95×C43—24no—
105#95×C43—22no—
106C24×C43—21no—
107C24×C43—21no—
108C24×C43—22no—
109C24×C43—21no—
110C24×C43—22no—
111C24×C43—22no—
112C24×C43—21no—
113C24×C43—21no—
114C24×C43—22no—
115C24×C43—21no—
116C24×C43C2×Q812yes—
117C24×C43C2411yescharacteristic
118C23×D43—21no—
119C23×D43—21no—
120C23×D43—22no—
121C23×D43—21no—
122C23×D43—22no—
123C23×D43—22no—
124C23×D43—21no—
125C23×D43—22no—
126C23×D43—21no—
127C23×D43—21no—
128C23×D43C2×Q812yes—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—21no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43C2×D414yes—
149C22×C4×C43C2×D412yes—
150C22×C4×C43C2×D412yes—
151C22×C4×C43#4112yes—
152C22×C4×C43#4114yes—
153C2×C22⋊D43—28no—
154C2×C22⋊D43—216no—
155C2×C22⋊D43—44no—
156C2×C22⋊D43—48no—
157C2×C22⋊D43—44no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—22no—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—22no—
178C22×Dic43—21no—
179C22×Dic43C2×D412yes—
180C22×Dic43C2×D414yes—
181C22×Dic43C2×D414yes—
182C22×Dic43C2×D412yes—
183C22×Dic43C2×D414yes—
184C22×Dic43C2×Q812yes—
185C22×Dic43#4114yes—
186C22×Dic43#4112yes—
187C4⋊C4×C43—28no—
188C22⋊C4×C43—48no—
189C22⋊C4×C43—44no—
190C22⋊Dic43—48no—
191C22⋊Dic43—44no—
192(C2×D43)⋊C4—48no—
193(C2×D43)⋊C4—48no—
194(C2×D43)⋊C4—44no—
195(C2×D43)⋊C4—44no—
196C4⋊Dic43—28no—
197C4⋊Dic43—48no—
198Dic43⋊C4—216no—
199Dic43⋊C4—48no—
200Dic43⋊C4—44no—
201C4×Dic43—28no—
202C4×Dic43—48no—
203C23×C43—22no—
204C23×C43—24no—
205C23×C43—22no—
206C23×C43—22no—
207C23×C43—24no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—42no—
211C23×C43—41no—
212C23×C43—42no—
213C23×C43—41no—
214C23×C43—42no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—42no—
218C23×C43—42no—
219C23×C43—42no—
220C23×C43—42no—
221C23×C43—42no—
222C23×C43—41no—
223C23×C43—42no—
224C23×C43—41no—
225C23×C43—42no—
226C23×C43C22×D411yescharacteristic
227C23×C43C22×D411yescharacteristic
228C23×C43C22×D412yes—
229C23×C43C22×Q811yescharacteristic
230C23×C43C2×#4112yes—
231C23×C43C2×#4111yescharacteristic
232C23×C43C2×#4112yes—
233C23×C43C2×#4111yescharacteristic
234C23×C43H(5,𝔽2)11yescharacteristic
235C23×C43H(5,𝔽2)12yes—
236C23×C432−1+411yescharacteristic
237C22×D43—22no—
238C22×D43—24no—
239C22×D43—22no—
240C22×D43—22no—
241C22×D43—24no—
242C22×D43—41no—
243C22×D43—41no—
244C22×D43—42no—
245C22×D43—41no—
246C22×D43—42no—
247C22×D43—41no—
248C22×D43—42no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—42no—
252C22×D43—42no—
253C22×D43—42no—
254C22×D43—42no—
255C22×D43—42no—
256C22×D43—41no—
257C22×D43—42no—
258C22×D43—41no—
259C22×D43—42no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—24no—
263C2×C4×C43—24no—
264C2×C4×C43—24no—
265C2×C4×C43—24no—
266C2×C4×C43—24no—
267C2×C4×C43—24no—
268C2×C4×C43—24no—
269C2×C4×C43—24no—
270C2×C4×C43—42no—
271C2×C4×C43—42no—
272C2×C4×C43—42no—
273C2×C4×C43—42no—
274C2×C4×C43—42no—
275C2×C4×C43—42no—
276C2×C4×C43—42no—
277C2×C4×C43—42no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—42no—
282C2×C4×C43—42no—
283C2×C4×C43#12114yes—
284C22⋊D43—416no—
285C2×Dic43—24no—
286C2×Dic43—22no—
287C2×Dic43—24no—
288C2×Dic43—22no—
289C2×Dic43—22no—
290C2×Dic43—24no—
291C2×Dic43—24no—
292C2×Dic43—24no—
293C2×Dic43—24no—
294C2×Dic43—42no—
295C2×Dic43—42no—
296C2×Dic43—42no—
297C2×Dic43—42no—
298C2×Dic43—42no—
299C2×Dic43—42no—
300C2×Dic43—42no—
301C2×Dic43—42no—
302C2×Dic43—42no—
303C2×Dic43—42no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—42no—
308C2×Dic43—42no—
309C2×Dic43C22⋊Q814yes—
310C2×Dic43C22⋊Q818yes—
311C2×Dic43#12314yes—
312C2×Dic43#12318yes—
313C2×Dic43#12714yes—
314#15148—431nomaximal, Sylow
315C22×C43—42no—
316C22×C43—42no—
317C22×C43—44no—
318C22×C43—44no—
319C22×C43—42no—
320C22×C43—81no—
321C22×C43—81no—
322C22×C43—82no—
323C22×C43—82no—
324C22×C43—81no—
325C22×C43—81no—
326C22×C43C2×#12111yescharacteristic
327C22×C43C2×C22⋊Q811yescharacteristic
328C22×C43C2×C22⋊Q812yes—
329C22×C43C2×#12311yescharacteristic
330C22×C43C2×#12312yes—
331C22×C43#52511yescharacteristic
332C22×C43#52912yes—
333C22×C43C2×#12711yescharacteristic
334C22×C43#53212yes—
335C22×C43#53511yescharacteristic
336C22×C43#53711yescharacteristic
337C22×C43#54012yes—
338C22×C43#54212yes—
339C22×C43D4212yes—
340C22×C43#54612yes—
341C22×C43#54812yes—
342C22×C43D4×Q811yescharacteristic
343C22×C43#55011yescharacteristic
344C22×C43#55012yes—
345C22×C43#55411yescharacteristic
346C22×C43#55412yes—
347C22×C43#55611yescharacteristic
348C22×C43#55912yes—
349C2×D43—42no—
350C2×D43—42no—
351C2×D43—44no—
352C2×D43—44no—
353C2×D43—42no—
354C2×D43—81no—
355C2×D43—81no—
356C2×D43—82no—
357C2×D43—82no—
358C2×D43—81no—
359C2×D43—81no—
360C4×C43—24no—
361C4×C43—44no—
362C4×C43—44no—
363C4×C43—81no—
364Dic43—42no—
365Dic43—44no—
366Dic43—44no—
367Dic43—81no—
368Dic43#39918yescomplemented
369C2×#399—431no—
370C2×#399—431no—
371C2×#390—431no—
372C2×#390—432no—
373C2×#389—432no—
374C2×C4×C4⋊C4—431no—
375#1439—432no—
376#1439—431no—
377#1439—432no—
378#1439D4311yescharacteristic, complemented
379C4⋊#95—431no—
380C2×C43—82no—
381C2×C43C2×#39911yescharacteristic
382C2×C43#244512yes—
383C2×C43#244812yes—
384C2×C43#245212yes—
385C2×C43#245412yes—
386C2×C43#253811yescharacteristic
387C2×C43#254011yescharacteristic
388C2×C43#254111yescharacteristic
389C2×C43#258011yescharacteristic
390C2×C43#262411yescharacteristic
391C2×C43#285411yescharacteristic
392D43—82no—
393C23×D4—431no—
394C22×C4⋊C4—432no—
395C22×C4⋊C4—431no—
396C22×C4⋊C4—431no—
397C22×C4⋊C4—432no—
398C22×C4⋊C4—432no—
399C22×C4⋊C4C2×D4311yescharacteristic
400C22×C22⋊C4—431no—
401C22×C22⋊C4—432no—
402C22×C22⋊C4—432no—
403C22×C22⋊C4—432no—
404C22×C22⋊C4—431no—
405C22×C22⋊C4—431no—
406C22×C22⋊C4C2×D4311yescharacteristic
407C22×C22⋊C4C2×D4312yes—
408C22×C42—431no—
409C22×C42—432no—
410#399—864no—
411#399—864no—
412#390—864no—
413#390—868no—
414#389—868no—
415C4×C4⋊C4—864no—
416C2×#95—431no—
417C2×#95—432no—
418C2×#95—432no—
419C2×#95—432no—
420C2×#95C2×D4311yescharacteristic
421C2×#95C2×D4312yes—
422C43#1514811yescharacteristic, complemented, Sylow
423C25—431no—
424C25C22×D4311yescharacteristic
425C22×D4—434no—
426C22×D4—862no—
427C22×D4—864no—
428C22×D4—864no—
429C22×D4—862no—
430C23×C4—431no—
431C23×C4—432no—
432C23×C4—432no—
433C23×C4—431no—
434C23×C4—431no—
435C23×C4C22×D4311yescharacteristic
436C23×C4C22×D4312yes—
437C23×C4C22×D4312yes—
438C23×C4C22×D4311yescharacteristic
439C2×C4⋊C4—22no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—438no—
442C2×C4⋊C4—434no—
443C2×C4⋊C4—864no—
444C2×C4⋊C4—864no—
445C2×C4⋊C4—862no—
446C2×C4⋊C4—862no—
447C2×C4⋊C4—864no—
448C2×C4⋊C4—864no—
449C2×C4⋊C4—862no—
450C2×C4⋊C4—864no—
451C2×C4⋊C4—864no—
452C2×C4⋊C4—864no—
453C2×C4⋊C4—1722no—
454C2×C4⋊C4—1722no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—864no—
462C2×C22⋊C4—862no—
463C2×C22⋊C4—864no—
464C2×C22⋊C4—864no—
465C2×C22⋊C4—862no—
466C2×C22⋊C4—864no—
467C2×C22⋊C4—862no—
468C2×C22⋊C4—864no—
469C2×C22⋊C4—862no—
470C2×C22⋊C4—862no—
471C2×C22⋊C4—864no—
472C2×C22⋊C4—1722no—
473C2×C22⋊C4—1722no—
474C2×C22⋊C4—1722no—
475C2×C22⋊C4—1722no—
476C2×C22⋊C4—1722no—
477C2×C42—434no—
478C2×C42—864no—
479C2×C42—864no—
480C2×C42—864no—
481C2×C42—864no—
482#95—24no—
483#95—22no—
484#95—864no—
485#95—864no—
486#95—862no—
487#95—1722no—
488C24—21no—
489C24—22no—
490C24—21no—
491C24—21no—
492C24—22no—
493C24—22no—
494C24—21no—
495C24—21no—
496C24—22no—
497C24—21no—
498C24—432no—
499C24—861no—
500C24—862no—
501C24—861no—
502C24—861no—
503C24—862no—
504C24—862no—
505C24—861no—
506C24—861no—
507C24—862no—
508C24—861no—
509C24Q8×D4312yes—
510C24C23×D4311yescharacteristic
511C2×D4—868no—
512C2×D4—8616no—
513C2×D4—1724no—
514C2×D4—1728no—
515C2×D4—1724no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—432no—
536C22×C4—434no—
537C22×C4—432no—
538C22×C4—434no—
539C22×C4—432no—
540C22×C4—432no—
541C22×C4—434no—
542C22×C4—434no—
543C22×C4—862no—
544C22×C4—862no—
545C22×C4—862no—
546C22×C4—862no—
547C22×C4—862no—
548C22×C4—862no—
549C22×C4—862no—
550C22×C4—862no—
551C22×C4—862no—
552C22×C4—861no—
553C22×C4—862no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—861no—
559C22×C4—862no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—862no—
564C22×C4#1062189812yes—
565C22×C4D4×D4314yes—
566C22×C4D4×D4312yes—
567C22×C4D4×D4312yes—
568C22×C4#1062190014yes—
569C4⋊C4—28no—
570C4⋊C4—8616no—
571C4⋊C4—868no—
572C4⋊C4—1728no—
573C4⋊C4—1724no—
574C4⋊C4—1728no—
575C22⋊C4—48no—
576C22⋊C4—44no—
577C22⋊C4—1728no—
578C22⋊C4—1728no—
579C22⋊C4—1724no—
580C22⋊C4—1728no—
581C22⋊C4—1724no—
582C22⋊C4—1724no—
583C42—868no—
584C42—1728no—
585C23—22no—
586C23—22no—
587C23—24no—
588C23—22no—
589C23—24no—
590C23—42no—
591C23—41no—
592C23—42no—
593C23—41no—
594C23—42no—
595C23—41no—
596C23—41no—
597C23—42no—
598C23—41no—
599C23—42no—
600C23—41no—
601C23—42no—
602C23—41no—
603C23—41no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—862no—
609C23—862no—
610C23—864no—
611C23—862no—
612C23—864no—
613C23—1722no—
614C23—1721no—
615C23—1722no—
616C23—1721no—
617C23—1722no—
618C23—1721no—
619C23—1721no—
620C23—1722no—
621C23—1721no—
622C23—1722no—
623C23—1721no—
624C23—1722no—
625C23—1721no—
626C23—1721no—
627C23—1722no—
628C23—1722no—
629C23—1722no—
630C23—1722no—
631C23C2×D4×D4312yes—
632C23C2×D4×D4311yescharacteristic
633C23C2×D4×D4311yescharacteristic
634C23C2×Q8×D4311yescharacteristic
635C23#41×D4311yescharacteristic
636C23#41×D4312yes—
637C23C2×#1062190012yes—
638C23C2×#1062189811yescharacteristic
639C23#1306337011yescharacteristic
640C23#1306337112yes—
641C23#1306337211yescharacteristic
642D4—17216no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—434no—
667C2×C4—438no—
668C2×C4—434no—
669C2×C4—438no—
670C2×C4—434no—
671C2×C4—864no—
672C2×C4—862no—
673C2×C4—864no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—864no—
677C2×C4—864no—
678C2×C4—864no—
679C2×C4—864no—
680C2×C4—1722no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1722no—
685C2×C4—1722no—
686C2×C4—1722no—
687C2×C4—1722no—
688C2×C4—1722no—
689C2×C4—1722no—
690C2×C4—1722no—
691C2×C4—1722no—
692C2×C4—1722no—
693C2×C4—1722no—
694C2×C4—1722no—
695C2×C4#1306329814yes—
696C22—42no—
697C22—42no—
698C22—44no—
699C22—44no—
700C22—42no—
701C22—81no—
702C22—81no—
703C22—82no—
704C22—82no—
705C22—81no—
706C22—81no—
707C22—3441no—
708C22—3441no—
709C22—3442no—
710C22—3442no—
711C22—3441no—
712C22—3441no—
713C22—1722no—
714C22—1722no—
715C22—1724no—
716C22—1724no—
717C22—1722no—
718C22C2×#1306329811yescharacteristic
719C22C22⋊Q8×D4311yescharacteristic
720C22C22⋊Q8×D4312yes—
721C22#123×D4311yescharacteristic
722C22#123×D4312yes—
723C22#1458340511yescharacteristic
724C22#1458342912yes—
725C22#127×D4311yescharacteristic
726C22#1458344412yes—
727C22#1458346711yescharacteristic
728C22#1458347811yescharacteristic
729C22#1458350112yes—
730C22#1458351512yes—
731C22#1458353312yes—
732C22#1458353612yes—
733C22#1458355512yes—
734C22#1458356211yescharacteristic
735C22#1458356711yescharacteristic
736C22#1458357012yes—
737C22#1458360411yescharacteristic
738C22#1458360712yes—
739C22#1458361711yescharacteristic
740C22#1458363112yes—
741C4—24no—
742C4—44no—
743C4—44no—
744C4—81no—
745C4—438no—
746C4—3441no—
747C4—1722no—
748C4—1724no—
749C4—1724no—
750C2—82no—
751C2—3442no—
752C2#399×D4311yescharacteristic
753C2#1913835312yes—
754C2#1913839012yes—
755C2#1913843812yes—
756C2#1913846412yes—
757C2#1913951911yescharacteristic
758C2#1913952811yescharacteristic
759C2#1913954011yescharacteristic
760C2#1913994811yescharacteristic
761C2#1914039011yescharacteristic
762C2#1914292311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, cosocleC24×C43C24
FittingC43×#1439C2
prime radicalC23×C22⋊D43C22
hypercenter#1439D43
hypocenterC43#15148
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#14582836C2semidirect
2. C2×#14582835C2semidirect
5. C2×#14582796C2semidirect
6. C2×C4⋊C4×Dic43C2semidirect
7. #19132840C2semidirect
8. #19132839C2semidirect
9. #19132837C2semidirect
10. Dic43⋊#95C2semidirect
11. C43×#1439C2semidirect
57. C2×C4⋊Dic43D4semidirect
368. Dic43#399semidirect
378. #1439D43semidirect
422. C43#15148semidirect

Maximal subgroups

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

subgroupindex
C2×#145828362
C2×#145828352
C2×#145827992
C2×#145827962
C2×C4⋊C4×Dic432
#191328402
#191328392
#191328372
Dic43⋊#952
C43×#14392
#1514843