Finite Group Databasebeta

← #25028047

Subgroups — #25028047

Order 11008.

2558 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×C4×C22⋊D43C211yesmaximal, characteristic
2C2×#14582818C211yesmaximal, characteristic, complemented
3C2×#14582810C211yesmaximal, characteristic, complemented
4C2×#14582770C212yesmaximal, complemented
5#19132845C211yesmaximal, characteristic, complemented
6#19132838C212yesmaximal, complemented
7#19132837C211yesmaximal, characteristic, complemented
8#19132834C212yesmaximal
9#19132827C212yesmaximal, complemented
10#19132818C211yesmaximal, characteristic, complemented
11C22×C22⋊Q8×C43C211yesmaximal, characteristic, complemented
12C23×C22⋊D43C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C2×C4×C22⋊D43—24no—
15C2×C4×C22⋊D43—24no—
16C2×C4×C22⋊D43—24no—
17C22×Dic43⋊C4C2212yes—
18C22×Dic43⋊C4C2211yescharacteristic
19C22×C22⋊Dic43C2211yescharacteristic
20C22×C22⋊Dic43C2212yes—
21C22×(C2×D43)⋊C4C2212yes—
22C22×(C2×D43)⋊C4C2212yes—
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×C4×Dic43C2211yescharacteristic
25#14582818—24no—
26#14582810—24no—
27#14582770—28no—
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2212yes—
36C23×Q8×C43C2211yescharacteristic
37C24×C4×C43C2211yescharacteristic
38C2×C22⋊Q8×C43—24no—
39C2×C22⋊Q8×C43—28no—
40C22×C4⋊C4×C43C2211yescharacteristic
41C22×C4⋊C4×C43C2212yes—
42C22×C22⋊C4×C43C2212yes—
43C24×D43C2311yescharacteristic
44C22×C22⋊D43—22no—
45C22×C22⋊D43—22no—
46C22×C22⋊D43—22no—
47C22×C22⋊D43—22no—
48C22×C22⋊D43—22no—
49C22×C22⋊D43—22no—
50C22×C22⋊D43Q814yescomplemented
51C23×Dic43C2312yes—
52C23×Dic43C2311yescharacteristic
53C23×Dic43C2311yescharacteristic
54C23×Dic43C2312yes—
55C23×Dic43C2311yescharacteristic
56C22×C4×D43—22no—
57C22×C4×D43—22no—
58C22×C4×D43—22no—
59C22×C4×D43—24no—
60C22×C4×D43—42no—
61C4×C22⋊D43—232no—
62C2×Dic43⋊C4—22no—
63C2×Dic43⋊C4—22no—
64C2×Dic43⋊C4—24no—
65C2×Dic43⋊C4—24no—
66C2×Dic43⋊C4—42no—
67C2×Dic43⋊C4D414yes—
68C2×C22⋊Dic43—22no—
69C2×C22⋊Dic43—22no—
70C2×C22⋊Dic43—22no—
71C2×C22⋊Dic43—24no—
72C2×C22⋊Dic43—24no—
73C2×C22⋊Dic43—42no—
74C2×(C2×D43)⋊C4—24no—
75C2×(C2×D43)⋊C4—22no—
76C2×(C2×D43)⋊C4—22no—
77C2×(C2×D43)⋊C4—24no—
78C2×(C2×D43)⋊C4—24no—
79C2×(C2×D43)⋊C4—24no—
80C2×(C2×D43)⋊C4—24no—
81C2×(C2×D43)⋊C4—42no—
82C2×(C2×D43)⋊C4D414yes—
83C2×C4×Dic43—22no—
84C2×C4×Dic43—22no—
85C2×C4×Dic43—22no—
86C43⋊#95—22no—
87C43⋊#95—22no—
88C43⋊#95—24no—
89C43⋊#95—24no—
90C43⋊#95—24no—
91C43⋊#95—24no—
92C43⋊#95—24no—
93C43⋊#95—24no—
94C25×C43C2311yescharacteristic
95C22×Q8×C43—24no—
96C22×Q8×C43—22no—
97C22×Q8×C43—22no—
98C22×Q8×C43—22no—
99C22×Q8×C43—42no—
100C23×C4×C43—24no—
101C23×C4×C43—22no—
102C23×C4×C43—22no—
103C23×C4×C43—42no—
104C23×C4×C43D414yes—
105C23×C4×C43C2312yes—
106C23×C4×C43C2312yes—
107C23×C4×C43C2311yescharacteristic
108C23×C4×C43C2311yescharacteristic
109C22⋊Q8×C43—232no—
110C2×C4⋊C4×C43—24no—
111C2×C4⋊C4×C43—22no—
112C2×C4⋊C4×C43—24no—
113C2×C4⋊C4×C43—24no—
114C2×C4⋊C4×C43D418yescomplemented
115C2×C22⋊C4×C43—24no—
116C2×C22⋊C4×C43—24no—
117C2×C22⋊C4×C43—24no—
118C24×C43—22no—
119C24×C43—21no—
120C24×C43—21no—
121C24×C43—22no—
122C24×C43—21no—
123C24×C43—21no—
124C24×C43—22no—
125C24×C43—22no—
126C24×C43C2×D412yes—
127C24×C43C2×Q812yes—
128C24×C43#4112yes—
129C24×C43C2411yescharacteristic
130C23×D43—22no—
131C23×D43—21no—
132C23×D43—21no—
133C23×D43—22no—
134C23×D43—21no—
135C23×D43—21no—
136C23×D43—22no—
137C23×D43—22no—
138C23×D43C2×D412yes—
139C23×D43C2×Q812yes—
140C23×D43#4112yes—
141C2×Q8×C43—28no—
142C2×Q8×C43—48no—
143C2×Q8×C43—48no—
144C2×Q8×C43—44no—
145C2×Q8×C43—44no—
146C22×C4×C43—28no—
147C22×C4×C43—28no—
148C22×C4×C43—22no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—22no—
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—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—48no—
167C22×C4×C43—48no—
168C22×C4×C43C2×D412yes—
169C22×C4×C43C2×D412yes—
170C22×C4×C43C2×D414yes—
171C22×C4×C43C2×D414yes—
172C22×C4×C43C2×D412yes—
173C22×C4×C43C2×D414yes—
174C22×C4×C43C2×D412yes—
175C2×C22⋊D43—28no—
176C2×C22⋊D43—28no—
177C2×C22⋊D43—28no—
178C2×C22⋊D43—28no—
179C2×C22⋊D43—28no—
180C2×C22⋊D43—28no—
181C2×C22⋊D43—28no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43C2×D412yes—
208C22×Dic43C2×D412yes—
209C22×Dic43C2×D412yes—
210C22×Dic43C2×Q812yes—
211C22×Dic43#4114yes—
212C22×Dic43#4112yes—
213C2×C4×D43—28no—
214C2×C4×D43—48no—
215C2×C4×D43—48no—
216C2×C4×D43—44no—
217C2×C4×D43—44no—
218C4⋊C4×C43—28no—
219C4⋊C4×C43—216no—
220C22⋊C4×C43—216no—
221C22⋊Dic43—28no—
222C22⋊Dic43—48no—
223(C2×D43)⋊C4—216no—
224(C2×D43)⋊C4—28no—
225(C2×D43)⋊C4—48no—
226Dic43⋊C4—28no—
227Dic43⋊C4—48no—
228C4×Dic43—28no—
229C23×C43—22no—
230C23×C43—22no—
231C23×C43—22no—
232C23×C43—22no—
233C23×C43—22no—
234C23×C43—22no—
235C23×C43—22no—
236C23×C43—22no—
237C23×C43—22no—
238C23×C43—22no—
239C23×C43—24no—
240C23×C43—24no—
241C23×C43—24no—
242C23×C43—24no—
243C23×C43—42no—
244C23×C43—42no—
245C23×C43—42no—
246C23×C43—42no—
247C23×C43—42no—
248C23×C43—42no—
249C23×C43—42no—
250C23×C43—42no—
251C23×C43C22⋊Q814yes—
252C23×C43C22×D411yescharacteristic
253C23×C43C22×D411yescharacteristic
254C23×C43C22×D411yescharacteristic
255C23×C43C22×D412yes—
256C23×C43C22×Q811yescharacteristic
257C23×C43C2×#4111yescharacteristic
258C23×C43C2×#4111yescharacteristic
259C23×C43C2×#4112yes—
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—22no—
268C22×D43—22no—
269C22×D43—22no—
270C22×D43—24no—
271C22×D43—24no—
272C22×D43—24no—
273C22×D43—24no—
274C22×D43—24no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—42no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—42no—
281C22×D43—42no—
282C22×D43—42no—
283C22×D43—42no—
284C22×D43—42no—
285C22×D43C22⋊Q814yescomplemented
286Q8×C43—416no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
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—24no—
298C2×C4×C43—24no—
299C2×C4×C43—24no—
300C2×C4×C43—24no—
301C2×C4×C43—416no—
302C2×C4×C43—42no—
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×C43—42no—
310C2×C4×C43#12014yes—
311C2×C4×C43#12014yes—
312C22⋊D43—232no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—24no—
322C2×Dic43—24no—
323C2×Dic43—24no—
324C2×Dic43—24no—
325C2×Dic43—24no—
326C2×Dic43—41no—
327C2×Dic43—42no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43—42no—
339C2×Dic43—42no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43C22⋊Q814yescomplemented
344C4×D43—416no—
345#14723—431nomaximal, Sylow
346C22×C43—24no—
347C22×C43—24no—
348C22×C43—24no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—44no—
354C22×C43—44no—
355C22×C43—44no—
356C22×C43—44no—
357C22×C43C2×#12011yescharacteristic
358C22×C43C2×#12011yescharacteristic
359C22×C43C2×C22⋊Q811yescharacteristic
360C22×C43C2×C22⋊Q811yescharacteristic
361C22×C43C2×C22⋊Q811yescharacteristic
362C22×C43#52511yescharacteristic
363C22×C43#52512yes—
364C22×C43#52511yescharacteristic
365C22×C43#52511yescharacteristic
366C22×C43#53211yescharacteristic
367C22×C43#53212yes—
368C22×C43#53411yescharacteristic
369C22×C43#53611yescharacteristic
370C22×C43#53912yes—
371C22×C43#54212yes—
372C22×C43D4212yes—
373C22×C43D4212yes—
374C22×C43#54712yes—
375C22×C43#54812yes—
376C22×C43#54812yes—
377C22×C43D4×Q812yes—
378C22×C43#55112yes—
379C22×C43#55412yes—
380C2×D43—24no—
381C2×D43—28no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—44no—
389C2×D43—44no—
390C2×D43—44no—
391C4×C43—24no—
392C4×C43—24no—
393C4×C43—44no—
394C4×C43—44no—
395Dic43—24no—
396Dic43—42no—
397Dic43—42no—
398Dic43—44no—
399Dic43—82no—
400C22×C22⋊Q8D4311yescharacteristic, complemented
401C22×C4×D4—431no—
402C2×#395—431no—
403C2×#393—431no—
404C2×#385—432no—
405#1441—431no—
406#1439—431no—
407#1439—432no—
408#1438—432no—
409#1436—432no—
410C22⋊#95—431no—
411C2×C43—44no—
412C2×C43#238811yescharacteristic
413C2×C43#240311yescharacteristic
414C2×C43#240911yescharacteristic
415C2×C43#243211yescharacteristic
416C2×C43#244912yes—
417C2×C43#245212yes—
418C2×C43#246112yes—
419C2×C43#246312yes—
420C2×C43#256411yescharacteristic
421C2×C43#263811yescharacteristic
422C2×C43#284811yescharacteristic
423D43—44no—
424C23×Q8C2×D4311yescharacteristic
425C23×D4—431no—
426C24×C4—431no—
427C24×C4C2×D4311yescharacteristic
428C2×C22⋊Q8—24no—
429C2×C22⋊Q8—28no—
430C2×C4×D4—864no—
431C2×C4×D4—864no—
432C2×C4×D4—864no—
433C22×C4⋊C4—431no—
434C22×C4⋊C4—432no—
435C22×C4⋊C4C2×D4311yescharacteristic
436C22×C4⋊C4C2×D4312yes—
437C22×C22⋊C4—431no—
438C22×C22⋊C4—431no—
439C22×C22⋊C4—432no—
440C22×C22⋊C4—432no—
441C22×C22⋊C4—432no—
442C22×C22⋊C4C2×D4312yes—
443C22×C42—431no—
444#395—864no—
445#393—864no—
446#385—868no—
447C2×#95—431no—
448C2×#95—432no—
449C2×#95—431no—
450C2×#95—432no—
451C2×#95—432no—
452C2×#95—432no—
453C2×#95—432no—
454C2×#95—432no—
455C43#1472311yescharacteristic, complemented, Sylow
456C25—431no—
457C25C22×D4311yescharacteristic
458C22×Q8—22no—
459C22×Q8—22no—
460C22×Q8—24no—
461C22×Q8—22no—
462C22×Q8—42no—
463C22×D4—434no—
464C22×D4—862no—
465C22×D4—862no—
466C22×D4—862no—
467C22×D4—862no—
468C22×D4—862no—
469C22×D4—862no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—24no—
473C23×C4—42no—
474C23×C4—431no—
475C23×C4—432no—
476C23×C4—431no—
477C23×C4—431no—
478C23×C4—432no—
479C23×C4—862no—
480C23×C4—862no—
481C23×C4—862no—
482C23×C4—864no—
483C23×C4—1722no—
484C23×C4C22⋊D4314yes—
485C23×C4C22×D4312yes—
486C23×C4C22×D4312yes—
487C23×C4C22×D4311yescharacteristic
488C23×C4C22×D4311yescharacteristic
489C22⋊Q8—232no—
490C4×D4—8632no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—434no—
496C2×C4⋊C4—862no—
497C2×C4⋊C4—862no—
498C2×C4⋊C4—864no—
499C2×C4⋊C4—864no—
500C2×C4⋊C4—1722no—
501C2×C4⋊C4C22⋊D4318yescomplemented
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—434no—
506C2×C22⋊C4—864no—
507C2×C22⋊C4—864no—
508C2×C22⋊C4—862no—
509C2×C22⋊C4—862no—
510C2×C22⋊C4—862no—
511C2×C22⋊C4—862no—
512C2×C22⋊C4—862no—
513C2×C22⋊C4—864no—
514C2×C22⋊C4—864no—
515C2×C22⋊C4—864no—
516C2×C22⋊C4—864no—
517C2×C22⋊C4—864no—
518C2×C22⋊C4—1722no—
519C2×C22⋊C4—1722no—
520C2×C42—862no—
521C2×C42—862no—
522C2×C42—862no—
523#95—864no—
524#95—864no—
525#95—864no—
526#95—864no—
527#95—862no—
528#95—862no—
529#95—864no—
530#95—864no—
531C24—21no—
532C24—21no—
533C24—22no—
534C24—22no—
535C24—21no—
536C24—21no—
537C24—22no—
538C24—22no—
539C24—432no—
540C24—432no—
541C24—432no—
542C24—861no—
543C24—862no—
544C24—861no—
545C24—862no—
546C24—861no—
547C24—861no—
548C24—862no—
549C24—862no—
550C24Q8×D4312yes—
551C24#1062190212yes—
552C24C2×C22⋊D4312yes—
553C24C23×D4311yescharacteristic
554C2×Q8—28no—
555C2×Q8—48no—
556C2×Q8—48no—
557C2×Q8—44no—
558C2×Q8—44no—
559C2×D4—868no—
560C2×D4—868no—
561C2×D4—868no—
562C2×D4—868no—
563C2×D4—868no—
564C2×D4—868no—
565C2×D4—868no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—44no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—432no—
589C22×C4—432no—
590C22×C4—432no—
591C22×C4—432no—
592C22×C4—432no—
593C22×C4—434no—
594C22×C4—868no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—862no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—862no—
603C22×C4—862no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—1728no—
621C22×C4—1728no—
622C22×C4—1724no—
623C22×C4—1724no—
624C22×C4D4×D4312yes—
625C22×C4D4×D4312yes—
626C22×C4C2×C22⋊D4314yes—
627C22×C4C2×C22⋊D4314yes—
628C22×C4C2×C22⋊D4312yes—
629C22×C4C2×C22⋊D4314yes—
630C22×C4C2×C22⋊D4312yes—
631C4⋊C4—28no—
632C4⋊C4—216no—
633C4⋊C4—868no—
634C4⋊C4—1728no—
635C22⋊C4—216no—
636C22⋊C4—8616no—
637C22⋊C4—868no—
638C22⋊C4—868no—
639C22⋊C4—1728no—
640C22⋊C4—1728no—
641C42—868no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—434no—
665C23—864no—
666C23—864no—
667C23—862no—
668C23—862no—
669C23—862no—
670C23—864no—
671C23—862no—
672C23—862no—
673C23—862no—
674C23—864no—
675C23—864no—
676C23—864no—
677C23—1722no—
678C23—1722no—
679C23—1722no—
680C23—1721no—
681C23—1722no—
682C23—1721no—
683C23—1721no—
684C23—1721no—
685C23—1722no—
686C23—1722no—
687C23#1306330114yes—
688C23C2×D4×D4311yescharacteristic
689C23C2×D4×D4311yescharacteristic
690C23C22×C22⋊D4312yes—
691C23C22×C22⋊D4311yescharacteristic
692C23C2×Q8×D4311yescharacteristic
693C23#41×D4312yes—
694C23#41×D4311yescharacteristic
695C23#41×D4311yescharacteristic
696C23C2×#1062190211yescharacteristic
697C23#1306337012yes—
698C23#1306337312yes—
699Q8—416no—
700D4—8632no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—416no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—434no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—864no—
732C2×C4—864no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—864no—
736C2×C4—864no—
737C2×C4—864no—
738C2×C4—17216no—
739C2×C4—1722no—
740C2×C4—1722no—
741C2×C4—1722no—
742C2×C4—1722no—
743C2×C4—1722no—
744C2×C4—1722no—
745C2×C4—1722no—
746C2×C4—1722no—
747C2×C4—1722no—
748C2×C4—1721no—
749C2×C4—1722no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1722no—
754C2×C4—1722no—
755C2×C4—1722no—
756C2×C4#1306329314yes—
757C2×C4#1306329414yes—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—44no—
762C22—42no—
763C22—44no—
764C22—44no—
765C22—42no—
766C22—44no—
767C22—42no—
768C22—42no—
769C22—868no—
770C22—864no—
771C22—1724no—
772C22—1722no—
773C22—1724no—
774C22—1722no—
775C22—1724no—
776C22—1722no—
777C22—1722no—
778C22—1722no—
779C22—1722no—
780C22C2×#1306329311yescharacteristic
781C22C2×#1306329411yescharacteristic
782C22C22⋊Q8×D4311yescharacteristic
783C22C22⋊Q8×D4311yescharacteristic
784C22C2×#1306330111yescharacteristic
785C22#1458340612yes—
786C22#1458340611yescharacteristic
787C22#1458341211yescharacteristic
788C22#1458341211yescharacteristic
789C22#1458344512yes—
790C22#1458344511yescharacteristic
791C22#1458345811yescharacteristic
792C22#1458347311yescharacteristic
793C22#1458349512yes—
794C22#1458351912yes—
795C22D4×C22⋊D4312yes—
796C22D4×C22⋊D4312yes—
797C22#1458355112yes—
798C22#1458355912yes—
799C22#1458356012yes—
800C22Q8×C22⋊D4312yes—
801C22#1458357612yes—
802C22#1458360312yes—
803C4—24no—
804C4—24no—
805C4—44no—
806C4—44no—
807C4—864no—
808C4—3442no—
809C4—1724no—
810C4—1722no—
811C4—1722no—
812C2—44no—
813C2—1724no—
814C2#1913780811yescharacteristic
815C2#1913790511yescharacteristic
816C2#1913795411yescharacteristic
817C2#1913822411yescharacteristic
818C2#1913840112yes—
819C2#1913844412yes—
820C2#1913856912yes—
821C2#1913858812yes—
822C2#1913977711yescharacteristic
823C2#1914051311yescharacteristic
824C2#1914287911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, cosocleC24×C43C24
FittingC22×C22⋊Q8×C43C2
prime radicalC23×C22⋊D43C22
hypercenterC22×C22⋊Q8D43
hypocenterC43#14723
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#14582818C2semidirect
3. C2×#14582810C2semidirect
4. C2×#14582770C2semidirect
5. #19132845C2semidirect
6. #19132838C2semidirect
7. #19132837C2semidirect
9. #19132827C2semidirect
10. #19132818C2semidirect
11. C22×C22⋊Q8×C43C2semidirect
50. C22×C22⋊D43Q8semidirect
114. C2×C4⋊C4×C43D4semidirect
285. C22×D43C22⋊Q8semidirect
343. C2×Dic43C22⋊Q8semidirect
400. C22×C22⋊Q8D43semidirect
455. C43#14723semidirect
501. C2×C4⋊C4C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D432
C2×#145828182
C2×#145828102
C2×#145827702
#191328452
#191328382
#191328372
#191328342
#191328272
#191328182
C22×C22⋊Q8×C432
#1472343