Finite Group Databasebeta

← #25019716

Subgroups — #25019716

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×#13063308C211yesmaximal, characteristic
2C2×#14582776C211yesmaximal, characteristic
3C2×#14582776C211yesmaximal, characteristic
4C2×#14582771C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
6C22×C43⋊#95C211yesmaximal, characteristic, complemented
7#19132861C212yesmaximal, complemented
8#19132839C212yesmaximal, complemented
9#19132831C212yesmaximal, complemented
10Dic43⋊#95C212yesmaximal, complemented
11C2×C43×#381C211yesmaximal, characteristic, complemented
12C23×C22⋊D43C2211yescharacteristic
13C24×Dic43C2211yescharacteristic
14C24×Dic43C2211yescharacteristic
15C2×#13063308—24no—
16C2×#13063308—24no—
17C2×#13063308C418yescomplemented
18C22×Dic43⋊C4C2212yes—
19C22×Dic43⋊C4C2212yes—
20C22×C22⋊Dic43C2211yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2212yes—
23C22×(C2×D43)⋊C4C2212yes—
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×C4×Dic43C2212yes—
26#14582776—24no—
27#14582776—24no—
28#14582771—24no—
29C22⋊C4×Dic43—24no—
30C2×C43⋊#95—24no—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2212yes—
36C2×C43⋊#95C2212yes—
37C2×C43⋊#95C2211yescharacteristic
38C24×C4×C43C2211yescharacteristic
39C22×C22⋊C4×C43C2211yescharacteristic
40C22×C22⋊C4×C43C2211yescharacteristic
41C43×#381—24no—
42C2×#95×C43C2212yes—
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—24no—
56C23×Dic43—24no—
57C23×Dic43—22no—
58C23×Dic43—22no—
59C23×Dic43—42no—
60C23×Dic43—42no—
61C23×Dic43D414yes—
62C23×Dic43C2311yescharacteristic
63C23×Dic43C2311yescharacteristic
64C23×Dic43C2312yes—
65C23×Dic43C2312yes—
66C23×Dic43C2311yescharacteristic
67#13063308—232no—
68C2×Dic43⋊C4—24no—
69C2×Dic43⋊C4—24no—
70C2×Dic43⋊C4—24no—
71C2×Dic43⋊C4—24no—
72C2×Dic43⋊C4—42no—
73C2×Dic43⋊C4C2×C418yescomplemented
74C2×C22⋊Dic43C2×C414yes—
75C2×C22⋊Dic43D414yes—
76C2×C22⋊Dic43D414yes—
77C2×(C2×D43)⋊C4—24no—
78C2×(C2×D43)⋊C4—24no—
79C2×(C2×D43)⋊C4—24no—
80C2×(C2×D43)⋊C4—22no—
81C2×(C2×D43)⋊C4—22no—
82C2×(C2×D43)⋊C4—24no—
83C2×(C2×D43)⋊C4—24no—
84C2×(C2×D43)⋊C4—42no—
85C2×(C2×D43)⋊C4—42no—
86C2×(C2×D43)⋊C4C2×C418yescomplemented
87C2×C4×Dic43—24no—
88C2×C4×Dic43—24no—
89C2×C4×Dic43—42no—
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—22no—
101C23×C4×C43—22no—
102C23×C4×C43—22no—
103C23×C4×C43—22no—
104C23×C4×C43C2×C414yes—
105C23×C4×C43C2311yescharacteristic
106C23×C4×C43C2311yescharacteristic
107C23×C4×C43C2312yes—
108C23×C4×C43C2312yes—
109C2×C22⋊C4×C43—22no—
110C2×C22⋊C4×C43—22no—
111C2×C22⋊C4×C43—22no—
112C2×C22⋊C4×C43—22no—
113C2×C22⋊C4×C43—22no—
114C2×C22⋊C4×C43D414yes—
115#95×C43—24no—
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—28no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—44no—
166C22×C4×C43—44no—
167C22×C4×C43—44no—
168C22×C4×C43—44no—
169C22×C4×C43C22×C414yes—
170C22×C4×C43C2×D414yes—
171C2×C22⋊D43—28no—
172C2×C22⋊D43—28no—
173C2×C22⋊D43—28no—
174C2×C22⋊D43—44no—
175C2×C22⋊D43—44no—
176C2×C22⋊D43—44no—
177C2×C22⋊D43—44no—
178C22×Dic43—28no—
179C22×Dic43—28no—
180C22×Dic43—28no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—22no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—21no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—44no—
205C22×Dic43—48no—
206C22×Dic43—48no—
207C22×Dic43—48no—
208C22×Dic43—48no—
209C22×Dic43—44no—
210C22×Dic43—44no—
211C22×Dic43C22×C412yes—
212C22×Dic43C22×C414yes—
213C22×Dic43C2×D412yes—
214C22×Dic43C2×D414yes—
215C22×Dic43C2×D414yes—
216C22×Dic43C2×D412yes—
217C22×Dic43#4114yes—
218C22×Dic43#4114yes—
219C22⋊C4×C43—28no—
220C22⋊C4×C43—44no—
221C22⋊Dic43C22⋊C4116yescomplemented
222(C2×D43)⋊C4—216no—
223(C2×D43)⋊C4—48no—
224(C2×D43)⋊C4—44no—
225(C2×D43)⋊C4—44no—
226Dic43⋊C4—216no—
227Dic43⋊C4—48no—
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—24no—
289C2×C4×C43—24no—
290C2×C4×C43—24no—
291C2×C4×C43—24no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—416no—
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—42no—
308C2×C4×C43—42no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C22⋊D43—416no—
312C2×Dic43—24no—
313C2×Dic43—24no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—24no—
317C2×Dic43—24no—
318C2×Dic43—24no—
319C2×Dic43—24no—
320C2×Dic43—24no—
321C2×Dic43—24no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—24no—
328C2×Dic43—22no—
329C2×Dic43—24no—
330C2×Dic43—24no—
331C2×Dic43—416no—
332C2×Dic43—416no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—42no—
337C2×Dic43—41no—
338C2×Dic43—42no—
339C2×Dic43—42no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43C2×C22⋊C418yes—
344C2×Dic43#12314yescomplemented
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—44no—
392C4×C43—44no—
393C4×C43—81no—
394C4×C43—81no—
395Dic43—28no—
396Dic43—24no—
397Dic43—42no—
398Dic43—44no—
399Dic43—42no—
400C22×#123—431no—
401C2×#386—431no—
402C2×#386—431no—
403C2×#385—431no—
404C2×#381D4311yescharacteristic, complemented
405C2×C4×C22⋊C4—431no—
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—431no—
434C22×C22⋊C4—432no—
435C22×C22⋊C4—431no—
436C22×C22⋊C4—432no—
437C22×C22⋊C4—431no—
438C22×C22⋊C4C2×D4311yescharacteristic
439C22×C22⋊C4C2×D4311yescharacteristic
440C22×C42—432no—
441#386—864no—
442#386—864no—
443#385—864no—
444#381—24no—
445C4×C22⋊C4—864no—
446C2×#95—431no—
447C2×#95—432no—
448C2×#95—432no—
449C2×#95—432no—
450C2×#95—432no—
451C2×#95—432no—
452C2×#95—431no—
453C2×#95—864no—
454C2×#95C2×D4312yes—
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—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—432no—
473C23×C4—431no—
474C23×C4—432no—
475C23×C4—431no—
476C23×C4—431no—
477C23×C4—434no—
478C23×C4—864no—
479C23×C4—864no—
480C23×C4—862no—
481C23×C4—862no—
482C23×C4—862no—
483C23×C4—862no—
484C23×C4—862no—
485C23×C4—1722no—
486C23×C4—1722no—
487C23×C4C4×D4314yes—
488C23×C4C22×D4311yescharacteristic
489C23×C4C22×D4311yescharacteristic
490C23×C4C22×D4312yes—
491C23×C4C22×D4312yes—
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—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—434no—
505C2×C22⋊C4—434no—
506C2×C22⋊C4—434no—
507C2×C22⋊C4—438no—
508C2×C22⋊C4—864no—
509C2×C22⋊C4—864no—
510C2×C22⋊C4—864no—
511C2×C22⋊C4—864no—
512C2×C22⋊C4—862no—
513C2×C22⋊C4—862no—
514C2×C22⋊C4—864no—
515C2×C22⋊C4—1722no—
516C2×C22⋊C4—1722no—
517C2×C22⋊C4C22⋊D4314yes—
518C2×C42—864no—
519C2×C42—864no—
520C2×C42—1722no—
521#95—24no—
522#95—24no—
523#95—864no—
524#95—864no—
525#95—864no—
526#95—864no—
527#95—862no—
528#95—862no—
529#95—864no—
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—
546C24#1062189812yes—
547C24D4×D4312yes—
548C24D4×D4312yes—
549C24D4×D4312yes—
550C24#1062190012yes—
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—28no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—434no—
590C22×C4—432no—
591C22×C4—434no—
592C22×C4—434no—
593C22×C4—434no—
594C22×C4—432no—
595C22×C4—432no—
596C22×C4—434no—
597C22×C4—868no—
598C22×C4—861no—
599C22×C4—862no—
600C22×C4—862no—
601C22×C4—861no—
602C22×C4—862no—
603C22×C4—862no—
604C22×C4—862no—
605C22×C4—868no—
606C22×C4—868no—
607C22×C4—861no—
608C22×C4—862no—
609C22×C4—861no—
610C22×C4—862no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—862no—
621C22×C4—862no—
622C22×C4—862no—
623C22×C4—1724no—
624C22×C4—1728no—
625C22×C4—1728no—
626C22×C4—1728no—
627C22×C4—1728no—
628C22×C4—1724no—
629C22×C4—1724no—
630C22×C4C2×C4×D4314yes—
631C22×C4C2×C22⋊D4314yes—
632C4⋊C4—8616no—
633C4⋊C4—1728no—
634C22⋊C4—28no—
635C22⋊C4—44no—
636C22⋊C4—4316no—
637C22⋊C4—8616no—
638C22⋊C4—1728no—
639C22⋊C4—1724no—
640C22⋊C4—1724no—
641C42—1728no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—24no—
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—1721no—
666C23—1721no—
667C23—1721no—
668C23—1721no—
669C23—1721no—
670C23—1722no—
671C23—1721no—
672C23—1721no—
673C23—1721no—
674C23—1722no—
675C23—1722no—
676C23—1722no—
677C23—1722no—
678C23—1722no—
679C23—1722no—
680C23—1722no—
681C23C22⋊C4×D4314yes—
682C23(C22⋊D43)⋊C414yes—
683C23C4×C22⋊D4314yes—
684C23#1306329714yes—
685C23#1306329814yes—
686C23#1306331114yes—
687C23#1306332114yes—
688C23C22×C4×D4311yescharacteristic
689C23C2×D4×D4311yescharacteristic
690C23C2×D4×D4311yescharacteristic
691C23C2×D4×D4311yescharacteristic
692C23C22×C22⋊D4311yescharacteristic
693C23#41×D4312yes—
694C23#41×D4312yes—
695C23C2×#1062190011yescharacteristic
696C23C2×#1062189811yescharacteristic
697C23#1306337112yes—
698C23#1306337212yes—
699D4—17216no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—416no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—438no—
726C2×C4—434no—
727C2×C4—864no—
728C2×C4—864no—
729C2×C4—864no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—864no—
733C2×C4—864no—
734C2×C4—864no—
735C2×C4—864no—
736C2×C4—864no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—864no—
743C2×C4—862no—
744C2×C4—864no—
745C2×C4—864no—
746C2×C4—17216no—
747C2×C4—17216no—
748C2×C4—1722no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1722no—
753C2×C4—1721no—
754C2×C4—1722no—
755C2×C4—1722no—
756C2×C4—1722no—
757C2×C4—1722no—
758C22—28no—
759C22—24no—
760C22—28no—
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#1458279918yes—
780C22C2×C22⋊C4×D4311yescharacteristic
781C22C2×(C22⋊D43)⋊C411yescharacteristic
782C22C2×C4×C22⋊D4311yescharacteristic
783C22#1458336712yes—
784C22#1458337912yes—
785C22C2×#1306329711yescharacteristic
786C22C2×#1306329811yescharacteristic
787C22#123×D4311yescharacteristic
788C22#1458340711yescharacteristic
789C22C2×#1306331111yescharacteristic
790C22#1458342612yes—
791C22C2×#1306332111yescharacteristic
792C22#1458346011yescharacteristic
793C22#1458347111yescharacteristic
794C22#1458349312yes—
795C22#1458353712yes—
796C22#1458354112yes—
797C22#1458354112yes—
798C22#1458354712yes—
799C22#1458354712yes—
800C22#1458354812yes—
801C22#1458357312yes—
802C22#1458358212yes—
803C4—44no—
804C4—44no—
805C4—81no—
806C4—81no—
807C4—868no—
808C4—864no—
809C4—1722no—
810C4—1724no—
811C4—1722no—
812C2—28no—
813C2—3442no—
814C2C2×#1458279911yescharacteristic
815C2#1913711211yescharacteristic
816C2#1913726111yescharacteristic
817C2#1913741912yes—
818C2#1913758712yes—
819C2#1913799311yescharacteristic
820C2#1913800411yescharacteristic
821C2#1913815012yes—
822C2#1913891712yes—
823C2#1913906411yescharacteristic
824C2#1913952511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#381C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#381D43
hypocenterC43#13996
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
4. C2×#14582771C2semidirect
5. C2×C22⋊C4×Dic43C2semidirect
6. C22×C43⋊#95C2semidirect
7. #19132861C2semidirect
8. #19132839C2semidirect
9. #19132831C2semidirect
10. Dic43⋊#95C2semidirect
11. C2×C43×#381C2semidirect
17. C2×#13063308C4semidirect
73. C2×Dic43⋊C4C2×C4semidirect
86. C2×(C2×D43)⋊C4C2×C4semidirect
221. C22⋊Dic43C22⋊C4semidirect
344. C2×Dic43#123semidirect
404. C2×#381D43semidirect
456. C43#13996semidirect

Maximal subgroups

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

subgroupindex
C22×#130633082
C2×#145827762
C2×#145827712
C2×C22⋊C4×Dic432
C22×C43⋊#952
#191328612
#191328392
#191328312
Dic43⋊#952
C2×C43×#3812
#1399643