Finite Group Databasebeta

← #25019714

Subgroups — #25019714

Order 11008.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063309C211yesmaximal, characteristic
2C2×#14582778C211yesmaximal, characteristic
3C2×#14582776C211yesmaximal, characteristic
4C2×#14582774C211yesmaximal, characteristic, complemented
5C2×#14582760C211yesmaximal, characteristic, complemented
6C22×C43⋊#95C211yesmaximal, characteristic, complemented
7#19132862C212yesmaximal, complemented
8#19132841C212yesmaximal, complemented
9#19132833C212yesmaximal, complemented
10#19132825C212yesmaximal, complemented
11C2×C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
12C23×C22⋊D43C2211yescharacteristic
13C24×Dic43C2211yescharacteristic
14C24×Dic43C2211yescharacteristic
15C2×#13063309—24no—
16C2×#13063309—24no—
17C2×#13063309C418yescomplemented
18C22×C4⋊Dic43C2212yes—
19C22×C4⋊Dic43C2212yes—
20C22×C22⋊Dic43C2211yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2212yes—
23C22×(C2×D43)⋊C4C2212yes—
24C22×(C2×D43)⋊C4C2211yescharacteristic
25#14582778—24no—
26#14582776—24no—
27#14582774—24no—
28#14582760—24no—
29C2×C43⋊#95—24no—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2212yes—
36C2×C43⋊#95C2212yes—
37C2×C43⋊#95C2211yescharacteristic
38C24×C4×C43C2211yescharacteristic
39C22×C22⋊C4×C43C2211yescharacteristic
40C22×C22⋊C4×C43C2211yescharacteristic
41C22×C42×C43C2212yes—
42C4×C22⋊C4×C43—24no—
43C2×#95×C43C2212yes—
44C24×D43C2311yescharacteristic
45C22×C22⋊D43—22no—
46C22×C22⋊D43—22no—
47C22×C22⋊D43—22no—
48C22×C22⋊D43—22no—
49C22×C22⋊D43—22no—
50C22×C22⋊D43—22no—
51C22×C22⋊D43C2×C414yes—
52C23×Dic43—22no—
53C23×Dic43—22no—
54C23×Dic43—22no—
55C23×Dic43—22no—
56C23×Dic43—22no—
57C23×Dic43—22no—
58C23×Dic43—22no—
59C23×Dic43—24no—
60C23×Dic43—22no—
61C23×Dic43—22no—
62C23×Dic43—42no—
63C23×Dic43C2×C414yes—
64C23×Dic43C2311yescharacteristic
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2312yes—
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2312yes—
69#13063309—232no—
70C2×C4⋊Dic43—24no—
71C2×C4⋊Dic43—24no—
72C2×C4⋊Dic43—24no—
73C2×C4⋊Dic43—24no—
74C2×C4⋊Dic43—42no—
75C2×C4⋊Dic43C2×C418yescomplemented
76C2×C22⋊Dic43—22no—
77C2×C22⋊Dic43—22no—
78C2×C22⋊Dic43—22no—
79C2×(C2×D43)⋊C4—24no—
80C2×(C2×D43)⋊C4—24no—
81C2×(C2×D43)⋊C4—24no—
82C2×(C2×D43)⋊C4—22no—
83C2×(C2×D43)⋊C4—22no—
84C2×(C2×D43)⋊C4—24no—
85C2×(C2×D43)⋊C4—24no—
86C2×(C2×D43)⋊C4—42no—
87C2×(C2×D43)⋊C4—42no—
88C2×(C2×D43)⋊C4C2×C418yescomplemented
89C43⋊#95—24no—
90C43⋊#95—24no—
91C43⋊#95—24no—
92C43⋊#95—24no—
93C43⋊#95—24no—
94C43⋊#95—24no—
95C43⋊#95—22no—
96C43⋊#95—22no—
97C25×C43C2311yescharacteristic
98C23×C4×C43—22no—
99C23×C4×C43—22no—
100C23×C4×C43—24no—
101C23×C4×C43—42no—
102C23×C4×C43D414yes—
103C23×C4×C43C2312yes—
104C23×C4×C43C2311yescharacteristic
105C23×C4×C43C2312yes—
106C23×C4×C43C2311yescharacteristic
107C2×C22⋊C4×C43—22no—
108C2×C22⋊C4×C43—22no—
109C2×C22⋊C4×C43C2×C414yes—
110C2×C22⋊C4×C43D414yes—
111C2×C22⋊C4×C43D414yes—
112C2×C22⋊C4×C43D414yes—
113C2×C42×C43—24no—
114C2×C42×C43—24no—
115C2×C42×C43—42no—
116#95×C43—24no—
117C24×C43—22no—
118C24×C43—22no—
119C24×C43—22no—
120C24×C43—22no—
121C24×C43C22×C412yes—
122C24×C43C2×D412yes—
123C24×C43C2×D412yes—
124C24×C43C2×D412yes—
125C24×C43C2×D412yes—
126C24×C43#4112yes—
127C24×C43#4112yes—
128C24×C43C2411yescharacteristic
129C23×D43—21no—
130C23×D43—21no—
131C23×D43—21no—
132C23×D43—21no—
133C23×D43—22no—
134C23×D43—22no—
135C23×D43—21no—
136C23×D43—21no—
137C23×D43—22no—
138C23×D43—22no—
139C23×D43C22×C412yes—
140C22×C4×C43—28no—
141C22×C4×C43—28no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—21no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—44no—
160C22×C4×C43—48no—
161C22×C4×C43—48no—
162C22×C4×C43C22×C414yes—
163C22×C4×C43C2×D414yes—
164C22×C4×C43C2×D412yes—
165C22×C4×C43C2×D414yes—
166C22×C4×C43C2×D412yes—
167C22×C4×C43C2×D414yes—
168C22×C4×C43#4114yes—
169C2×C22⋊D43—28no—
170C2×C22⋊D43—28no—
171C2×C22⋊D43—28no—
172C2×C22⋊D43—44no—
173C2×C22⋊D43—44no—
174C2×C22⋊D43—44no—
175C2×C22⋊D43—44no—
176C22×Dic43—28no—
177C22×Dic43—28no—
178C22×Dic43—28no—
179C22×Dic43—28no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—48no—
209C22×Dic43—48no—
210C22×Dic43—44no—
211C22×Dic43—44no—
212C22×Dic43—44no—
213C22×Dic43—44no—
214C22×Dic43—44no—
215C22×Dic43—44no—
216C22×Dic43C22×C414yes—
217C22×Dic43C22×C412yes—
218C22×Dic43#4114yes—
219C22⋊C4×C43—28no—
220C22⋊C4×C43C22⋊C4116yescomplemented
221C42×C43—48no—
222C22⋊Dic43—44no—
223(C2×D43)⋊C4—216no—
224(C2×D43)⋊C4—48no—
225(C2×D43)⋊C4—44no—
226(C2×D43)⋊C4—44no—
227C4⋊Dic43—216no—
228C4⋊Dic43—48no—
229C23×C43—24no—
230C23×C43—24no—
231C23×C43—22no—
232C23×C43—22no—
233C23×C43—24no—
234C23×C43—22no—
235C23×C43—22no—
236C23×C43—24no—
237C23×C43—24no—
238C23×C43—24no—
239C23×C43—24no—
240C23×C43—24no—
241C23×C43—24no—
242C23×C43—24no—
243C23×C43—24no—
244C23×C43—24no—
245C23×C43C2×C22⋊C414yes—
246C23×C43C4×D414yes—
247C23×C43C4×D414yes—
248C23×C43#12114yes—
249C23×C43#12114yes—
250C23×C43#12414yes—
251C23×C43#12714yes—
252C23×C43C23×C411yescharacteristic
253C23×C43C22×D411yescharacteristic
254C23×C43C22×D411yescharacteristic
255C23×C43C22×D411yescharacteristic
256C23×C43C22×D411yescharacteristic
257C23×C43C2×#4112yes—
258C23×C43C2×#4112yes—
259C23×C43C2×#4111yescharacteristic
260C23×C43C2×#4111yescharacteristic
261C23×C43H(5,𝔽2)12yes—
262C23×C432−1+412yes—
263C22×D43—22no—
264C22×D43—22no—
265C22×D43—22no—
266C22×D43—24no—
267C22×D43—24no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—42no—
274C22×D43—41no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—42no—
278C22×D43—42no—
279C22×D43—42no—
280C22×D43—42no—
281C22×D43—42no—
282C22×D43—42no—
283C22×D43—42no—
284C22×D43—42no—
285C22×D43—42no—
286C2×C4×C43—24no—
287C2×C4×C43—24no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—24no—
291C2×C4×C43—24no—
292C2×C4×C43—24no—
293C2×C4×C43—24no—
294C2×C4×C43—24no—
295C2×C4×C43—24no—
296C2×C4×C43—24no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—24no—
301C2×C4×C43—24no—
302C2×C4×C43—416no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43—42no—
309C2×C4×C43C2×C22⋊C418yes—
310C2×C4×C43#12314yescomplemented
311C22⋊D43—416no—
312C2×Dic43—22no—
313C2×Dic43—24no—
314C2×Dic43—24no—
315C2×Dic43—24no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—24no—
319C2×Dic43—24no—
320C2×Dic43—24no—
321C2×Dic43—416no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—42no—
327C2×Dic43—41no—
328C2×Dic43—42no—
329C2×Dic43—42no—
330C2×Dic43—41no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—416no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345#13996—431nomaximal, Sylow
346C22×C43—24no—
347C22×C43—28no—
348C22×C43—28no—
349C22×C43—24no—
350C22×C43—24no—
351C22×C43—28no—
352C22×C43—28no—
353C22×C43—24no—
354C22×C43—24no—
355C22×C43—24no—
356C22×C43#39018yes—
357C22×C43C22×C22⋊C411yescharacteristic
358C22×C43C2×C4×D411yescharacteristic
359C22×C43C2×C4×D411yescharacteristic
360C22×C43C4×#4112yes—
361C22×C43#52012yes—
362C22×C43C2×#12111yescharacteristic
363C22×C43C2×#12111yescharacteristic
364C22×C43C2×#12311yescharacteristic
365C22×C43#52511yescharacteristic
366C22×C43C2×#12411yescharacteristic
367C22×C43#52912yes—
368C22×C43C2×#12711yescharacteristic
369C22×C43#53411yescharacteristic
370C22×C43#53611yescharacteristic
371C22×C43#53912yes—
372C22×C43#54612yes—
373C22×C43#54612yes—
374C22×C43#54612yes—
375C22×C43#54712yes—
376C22×C43#54712yes—
377C22×C43#54712yes—
378C22×C43#55112yes—
379C22×C43#55212yes—
380C2×D43—42no—
381C2×D43—44no—
382C2×D43—44no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—81no—
386C2×D43—81no—
387C2×D43—82no—
388C2×D43—82no—
389C2×D43—81no—
390C2×D43—81no—
391C4×C43—28no—
392C4×C43—24no—
393C4×C43—42no—
394C4×C43—44no—
395Dic43—44no—
396Dic43—44no—
397Dic43—42no—
398Dic43—81no—
399Dic43—81no—
400C22×#123—431no—
401C2×#386—431no—
402C2×#386—431no—
403C2×#385—431no—
404C2×#381—431no—
405C2×C4×C22⋊C4D4311yescharacteristic, complemented
406C22×#95—431no—
407#1445—432no—
408#1439—432no—
409#1437—432no—
410C4⋊#95—432no—
411C2×C43—28no—
412C2×C43C2×#39011yescharacteristic
413C2×C43C4×#12311yescharacteristic
414C2×C43#232211yescharacteristic
415C2×C43#233912yes—
416C2×C43#235912yes—
417C2×C43#241211yescharacteristic
418C2×C43#241311yescharacteristic
419C2×C43#242512yes—
420C2×C43#248812yes—
421C2×C43#250111yescharacteristic
422C2×C43#253911yescharacteristic
423D43—82no—
424C23×D4—431no—
425C24×C4—431no—
426C24×C4—431no—
427C24×C4C2×D4311yescharacteristic
428C2×#123—438no—
429C2×#123—864no—
430C2×#123—864no—
431C22×C4⋊C4—432no—
432C22×C4⋊C4—432no—
433C22×C22⋊C4—432no—
434C22×C22⋊C4—431no—
435C22×C22⋊C4—431no—
436C22×C22⋊C4—432no—
437C22×C22⋊C4—431no—
438C22×C22⋊C4C2×D4311yescharacteristic
439C22×C22⋊C4C2×D4311yescharacteristic
440C22×C42C2×D4312yes—
441#386—864no—
442#386—864no—
443#385—864no—
444#381—864no—
445C4×C22⋊C4—24no—
446C2×#95—431no—
447C2×#95—432no—
448C2×#95—432no—
449C2×#95—432no—
450C2×#95—432no—
451C2×#95—432no—
452C2×#95—432no—
453C2×#95—431no—
454C2×#95—864no—
455C2×#95C2×D4312yes—
456C43#1399611yescharacteristic, complemented, Sylow
457C25—431no—
458C25C22×D4311yescharacteristic
459C22×D4—434no—
460C22×D4—862no—
461C22×D4—862no—
462C22×D4—862no—
463C22×D4—862no—
464C22×D4—862no—
465C22×D4—862no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—24no—
469C23×C4—42no—
470C23×C4—434no—
471C23×C4—432no—
472C23×C4—432no—
473C23×C4—431no—
474C23×C4—431no—
475C23×C4—431no—
476C23×C4—864no—
477C23×C4—862no—
478C23×C4—862no—
479C23×C4—862no—
480C23×C4—862no—
481C23×C4—862no—
482C23×C4—862no—
483C23×C4—862no—
484C23×C4—862no—
485C23×C4—862no—
486C23×C4—1722no—
487C23×C4D17214yes—
488C23×C4C22×D4312yes—
489C23×C4C22×D4311yescharacteristic
490C23×C4C22×D4312yes—
491C23×C4C22×D4311yescharacteristic
492#123—8632no—
493C2×C4⋊C4—438no—
494C2×C4⋊C4—864no—
495C2×C4⋊C4—864no—
496C2×C4⋊C4—864no—
497C2×C4⋊C4—864no—
498C2×C4⋊C4—1722no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—438no—
502C2×C22⋊C4—864no—
503C2×C22⋊C4—864no—
504C2×C22⋊C4—864no—
505C2×C22⋊C4—862no—
506C2×C22⋊C4—862no—
507C2×C22⋊C4—862no—
508C2×C22⋊C4—864no—
509C2×C22⋊C4—862no—
510C2×C22⋊C4—862no—
511C2×C22⋊C4—864no—
512C2×C22⋊C4—1722no—
513C2×C22⋊C4—1722no—
514C2×C22⋊C4C4×D4314yes—
515C2×C22⋊C4D17214yes—
516C2×C22⋊C4D17214yes—
517C2×C22⋊C4C22⋊D4314yes—
518C2×C42—24no—
519C2×C42—24no—
520C2×C42—42no—
521#95—24no—
522#95—864no—
523#95—864no—
524#95—864no—
525#95—864no—
526#95—864no—
527#95—864no—
528#95—862no—
529#95—862no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—432no—
535C24—861no—
536C24—861no—
537C24—861no—
538C24—861no—
539C24—862no—
540C24—862no—
541C24—861no—
542C24—861no—
543C24—862no—
544C24—862no—
545C24C2×C4×D4312yes—
546C24C2×D17212yes—
547C24C2×D17212yes—
548C24C2×D17212yes—
549C24#1062189812yes—
550C24#1062189812yes—
551C24C2×C22⋊D4312yes—
552C24C23×D4311yescharacteristic
553C2×D4—868no—
554C2×D4—868no—
555C2×D4—868no—
556C2×D4—1724no—
557C2×D4—1724no—
558C2×D4—1724no—
559C2×D4—1724no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—28no—
579C22×C4—44no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—434no—
583C22×C4—432no—
584C22×C4—434no—
585C22×C4—868no—
586C22×C4—868no—
587C22×C4—868no—
588C22×C4—868no—
589C22×C4—862no—
590C22×C4—861no—
591C22×C4—862no—
592C22×C4—862no—
593C22×C4—862no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—861no—
600C22×C4—862no—
601C22×C4—862no—
602C22×C4—862no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—862no—
606C22×C4—862no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—1728no—
618C22×C4—1728no—
619C22×C4—1724no—
620C22×C4—1724no—
621C22×C4—1724no—
622C22×C4—1724no—
623C22×C4—1724no—
624C22×C4—1724no—
625C22×C4C2×C4×D4314yes—
626C22×C4C2×D17214yes—
627C22×C4C2×D17212yes—
628C22×C4C2×D17214yes—
629C22×C4C2×D17212yes—
630C22×C4#1062190014yes—
631C22×C4C2×C22⋊D4314yes—
632C4⋊C4—8616no—
633C4⋊C4—1728no—
634C22⋊C4—28no—
635C22⋊C4—8616no—
636C22⋊C4—1728no—
637C22⋊C4—1724no—
638C22⋊C4—1724no—
639C22⋊C4—1724no—
640C22⋊C4(C2×D43)⋊C4116yescomplemented
641C42—48no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—862no—
659C23—862no—
660C23—862no—
661C23—864no—
662C23—864no—
663C23—1722no—
664C23—1722no—
665C23—1722no—
666C23—1722no—
667C23—1721no—
668C23—1721no—
669C23—1721no—
670C23—1721no—
671C23—1721no—
672C23—1722no—
673C23—1721no—
674C23—1721no—
675C23—1721no—
676C23—1722no—
677C23—1722no—
678C23—1722no—
679C23—1722no—
680C23—1722no—
681C23C2×(C2×D43)⋊C414yes—
682C23C4×D17214yes—
683C23C4×D17214yes—
684C23#1306329914yes—
685C23#1306329914yes—
686C23#1306331314yes—
687C23#1306332214yes—
688C23C22×C4×D4311yescharacteristic
689C23C22×C22⋊D4311yescharacteristic
690C23C22×D17211yescharacteristic
691C23C22×D17211yescharacteristic
692C23C22×D17211yescharacteristic
693C23#41×D4312yes—
694C23C2×#1062190012yes—
695C23C2×#1062189811yescharacteristic
696C23C2×#1062189811yescharacteristic
697C23#1306337012yes—
698C23#1306337212yes—
699D4—17216no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—416no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—864no—
724C2×C4—862no—
725C2×C4—864no—
726C2×C4—864no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—864no—
730C2×C4—864no—
731C2×C4—864no—
732C2×C4—1722no—
733C2×C4—1722no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4—1722no—
741C2×C4—1722no—
742C2×C4—17216no—
743C2×C4—17216no—
744C2×C4—1722no—
745C2×C4—1722no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1722no—
749C2×C4—1721no—
750C2×C4—1722no—
751C2×C4—1722no—
752C2×C4—1721no—
753C2×C4—1722no—
754C2×C4—1722no—
755C2×C4—1722no—
756C2×C4C2×(C2×D43)⋊C418yes—
757C2×C4#1306330914yescomplemented
758C22—28no—
759C22—28no—
760C22—24no—
761C22—28no—
762C22—28no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—3442no—
769C22—3442no—
770C22—3441no—
771C22—3441no—
772C22—3441no—
773C22—3441no—
774C22—1722no—
775C22—1724no—
776C22—1722no—
777C22—1724no—
778C22—1722no—
779C22#1458280118yes—
780C22C22×(C2×D43)⋊C411yescharacteristic
781C22C2×C4×D17211yescharacteristic
782C22C2×C4×D17211yescharacteristic
783C22C4×#1062190012yes—
784C22#1458337812yes—
785C22C2×#1306329911yescharacteristic
786C22C2×#1306329911yescharacteristic
787C22C2×#1306330911yescharacteristic
788C22#1458341111yescharacteristic
789C22C2×#1306331311yescharacteristic
790C22#1458342912yes—
791C22C2×#1306332211yescharacteristic
792C22#1458346111yescharacteristic
793C22#1458347511yescharacteristic
794C22#1458349112yes—
795C22#1458354312yes—
796C22#1458354412yes—
797C22#1458354412yes—
798C22#1458354812yes—
799C22#1458355312yes—
800C22#1458355312yes—
801C22#1458357512yes—
802C22#1458358212yes—
803C4—28no—
804C4—24no—
805C4—44no—
806C4—42no—
807C4—3441no—
808C4—3441no—
809C4—1724no—
810C4—1722no—
811C4—1724no—
812C2—28no—
813C2—3442no—
814C2C2×#1458280111yescharacteristic
815C2C4×#1306330911yescharacteristic
816C2#1913726611yescharacteristic
817C2#1913742012yes—
818C2#1913758912yes—
819C2#1913798511yescharacteristic
820C2#1913799611yescharacteristic
821C2#1913814012yes—
822C2#1913891512yes—
823C2#1913906611yescharacteristic
824C2#1913952111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C4×C22⋊C4×C43C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×C4×C22⋊C4D43
hypocenterC43#13996
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#14582774C2semidirect
5. C2×#14582760C2semidirect
6. C22×C43⋊#95C2semidirect
7. #19132862C2semidirect
8. #19132841C2semidirect
9. #19132833C2semidirect
10. #19132825C2semidirect
11. C2×C4×C22⋊C4×C43C2semidirect
17. C2×#13063309C4semidirect
75. C2×C4⋊Dic43C2×C4semidirect
88. C2×(C2×D43)⋊C4C2×C4semidirect
220. C22⋊C4×C43C22⋊C4semidirect
310. C2×C4×C43#123semidirect
405. C2×C4×C22⋊C4D43semidirect
456. C43#13996semidirect
640. C22⋊C4(C2×D43)⋊C4semidirect
757. C2×C4#13063309semidirect

Maximal subgroups

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

subgroupindex
C22×#130633092
C2×#145827782
C2×#145827762
C2×#145827742
C2×#145827602
C22×C43⋊#952
#191328622
#191328412
#191328332
#191328252
C2×C4×C22⋊C4×C432
#1399643