Finite Group Databasebeta

← #25018332

Subgroups — #25018332

Order 11008.

2574 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic43C212yesmaximal, complemented
4C2×#14582746C212yesmaximal, complemented
5C2×#14582744C211yesmaximal, characteristic, complemented
6#19132861C212yesmaximal, complemented
7#19132841C211yesmaximal, characteristic, complemented
8#19132840C211yesmaximal, characteristic, complemented
9#19132837C211yesmaximal, characteristic, complemented
10#19132834C212yesmaximal
11C43×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D43C2211yescharacteristic
13C24×Dic43C2211yescharacteristic
14C23×C4×D43C2211yescharacteristic
15C2×(C22⋊D43)⋊C4—24no—
16C2×(C22⋊D43)⋊C4—24no—
17C2×(C22⋊D43)⋊C4C418yescomplemented
18C22×C4⋊Dic43C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×C22⋊Dic43C2212yes—
21C22×(C2×D43)⋊C4C2212yes—
22C22×(C2×D43)⋊C4C2212yes—
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×C4×Dic43C2212yes—
25C22×C4×Dic43C2212yes—
26C22×C4×Dic43C2211yescharacteristic
27C4⋊C4×Dic43—24no—
28C22⋊C4×Dic43—28no—
29#14582746—28no—
30#14582744—24no—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2212yes—
36C2×C43⋊#95C2212yes—
37C22×C4⋊C4×C43C2211yescharacteristic
38C22×C22⋊C4×C43C2212yes—
39C22×C22⋊C4×C43C2211yescharacteristic
40C2×#95×C43C2211yescharacteristic
41C2×#95×C43C2212yes—
42C24×D43C2311yescharacteristic
43C22×C22⋊D43—22no—
44C22×C22⋊D43—22no—
45C22×C22⋊D43—22no—
46C22×C22⋊D43—22no—
47C22×C22⋊D43—22no—
48C22×C22⋊D43—22no—
49C22×C22⋊D43C2×C414yes—
50C23×Dic43—22no—
51C23×Dic43—22no—
52C23×Dic43—24no—
53C23×Dic43—24no—
54C23×Dic43C2×C414yes—
55C23×Dic43C2311yescharacteristic
56C23×Dic43C2312yes—
57C23×Dic43C2312yes—
58C23×Dic43C2311yescharacteristic
59C23×Dic43C2311yescharacteristic
60C22×C4×D43—22no—
61C22×C4×D43—22no—
62C22×C4×D43—24no—
63C22×C4×D43—24no—
64C22×C4×D43C2×C414yes—
65(C22⋊D43)⋊C4—232no—
66C2×C4⋊Dic43—22no—
67C2×C4⋊Dic43—24no—
68C2×Dic43⋊C4—22no—
69C2×Dic43⋊C4—22no—
70C2×Dic43⋊C4C2×C414yes—
71C2×C22⋊Dic43—24no—
72C2×C22⋊Dic43—24no—
73C2×C22⋊Dic43—24no—
74C2×(C2×D43)⋊C4—24no—
75C2×(C2×D43)⋊C4—24no—
76C2×(C2×D43)⋊C4—22no—
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4—24no—
79C2×(C2×D43)⋊C4—24no—
80C2×(C2×D43)⋊C4—24no—
81C2×(C2×D43)⋊C4—24no—
82C2×(C2×D43)⋊C4C2×C414yes—
83C2×C4×Dic43—24no—
84C2×C4×Dic43—24no—
85C2×C4×Dic43—24no—
86C2×C4×Dic43—24no—
87C2×C4×Dic43—24no—
88C2×C4×Dic43C2×C414yes—
89C2×C4×Dic43D414yes—
90C2×C4×Dic43D414yes—
91C2×C4×Dic43D418yescomplemented
92C43⋊#95—22no—
93C43⋊#95—24no—
94C43⋊#95—24no—
95C43⋊#95—24no—
96C43⋊#95—24no—
97C43⋊#95—24no—
98C25×C43C2311yescharacteristic
99C23×C4×C43C2311yescharacteristic
100C23×C4×C43C2312yes—
101C23×C4×C43C2312yes—
102C23×C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43—22no—
104C2×C4⋊C4×C43—24no—
105C2×C22⋊C4×C43—24no—
106C2×C22⋊C4×C43—22no—
107C2×C22⋊C4×C43—22no—
108C2×C22⋊C4×C43—24no—
109C2×C22⋊C4×C43—24no—
110C2×C22⋊C4×C43C2×C414yes—
111#95×C43—22no—
112#95×C43—24no—
113C24×C43—22no—
114C24×C43—21no—
115C24×C43—21no—
116C24×C43—22no—
117C24×C43—22no—
118C24×C43—22no—
119C24×C43—21no—
120C24×C43—21no—
121C24×C43C22×C412yes—
122C24×C43#4112yes—
123C24×C43#4112yes—
124C24×C43C2411yescharacteristic
125C23×D43—22no—
126C23×D43—21no—
127C23×D43—21no—
128C23×D43—22no—
129C23×D43—22no—
130C23×D43—22no—
131C23×D43—21no—
132C23×D43—21no—
133C23×D43C22×C412yes—
134C23×D43#4112yes—
135C23×D43#4112yes—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43C22×C412yes—
155C22×C4×C43C22×C412yes—
156C22×C4×C43C2×D414yes—
157C22×C4×C43C2×D412yes—
158C22×C4×C43C2×D412yes—
159C22×C4×C43#4114yes—
160C2×C22⋊D43—28no—
161C2×C22⋊D43—28no—
162C2×C22⋊D43—28no—
163C2×C22⋊D43—28no—
164C2×C22⋊D43—28no—
165C2×C22⋊D43—28no—
166C2×C22⋊D43—28no—
167C22×Dic43—28no—
168C22×Dic43—216no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—22no—
173C22×Dic43—22no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—48no—
190C22×Dic43—44no—
191C22×Dic43—44no—
192C22×Dic43C22×C412yes—
193C22×Dic43C22×C412yes—
194C22×Dic43C22×C412yes—
195C22×Dic43C2×D414yes—
196C22×Dic43C2×D412yes—
197C22×Dic43C2×D412yes—
198C22×Dic43C2×D412yes—
199C22×Dic43C2×D412yes—
200C22×Dic43C2×D414yes—
201C22×Dic43#4114yes—
202C22×Dic43#4114yes—
203C2×C4×D43—28no—
204C2×C4×D43—216no—
205C2×C4×D43—48no—
206C2×C4×D43—44no—
207C2×C4×D43—44no—
208C4⋊C4×C43—28no—
209C22⋊C4×C43—216no—
210C22⋊C4×C43—28no—
211C22⋊Dic43—216no—
212(C2×D43)⋊C4—216no—
213(C2×D43)⋊C4—216no—
214(C2×D43)⋊C4—28no—
215C4⋊Dic43—28no—
216Dic43⋊C4—28no—
217C4×Dic43—216no—
218C4×Dic43—48no—
219C4×Dic43C22⋊C4116yescomplemented
220C23×C43—22no—
221C23×C43—22no—
222C23×C43—24no—
223C23×C43—24no—
224C23×C43—24no—
225C23×C43—24no—
226C23×C43—22no—
227C23×C43—22no—
228C23×C43—22no—
229C23×C43—22no—
230C23×C43—24no—
231C23×C43—24no—
232C23×C43—42no—
233C23×C43—41no—
234C23×C43—42no—
235C23×C43—41no—
236C23×C43—42no—
237C23×C43—41no—
238C23×C43—42no—
239C23×C43—42no—
240C23×C43—41no—
241C23×C43—42no—
242C23×C43#11714yes—
243C23×C43C23×C411yescharacteristic
244C23×C43C22×D411yescharacteristic
245C23×C43C22×D411yescharacteristic
246C23×C43C22×D412yes—
247C23×C43C2×#4111yescharacteristic
248C23×C43C2×#4111yescharacteristic
249C23×C43C2×#4112yes—
250C23×C43C2×#4112yes—
251C23×C43C2×#4111yescharacteristic
252C23×C43C2×#4112yes—
253C23×C43C2×#4111yescharacteristic
254C22×D43—22no—
255C22×D43—22no—
256C22×D43—24no—
257C22×D43—24no—
258C22×D43—24no—
259C22×D43—24no—
260C22×D43—22no—
261C22×D43—22no—
262C22×D43—22no—
263C22×D43—22no—
264C22×D43—24no—
265C22×D43—24no—
266C22×D43—42no—
267C22×D43—42no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—42no—
271C22×D43—41no—
272C22×D43—42no—
273C22×D43—42no—
274C22×D43—41no—
275C22×D43—42no—
276C22×D43#11714yes—
277C2×C4×C43—24no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—24no—
281C2×C4×C43—22no—
282C2×C4×C43—24no—
283C2×C4×C43—24no—
284C2×C4×C43—24no—
285C2×C4×C43—24no—
286C2×C4×C43—24no—
287C2×C4×C43—24no—
288C2×C4×C43—24no—
289C2×C4×C43—42no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43—41no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—41no—
299C2×C4×C43—42no—
300C2×C4×C43C2×C22⋊C414yes—
301C22⋊D43—232no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—24no—
310C2×Dic43—24no—
311C2×Dic43—24no—
312C2×Dic43—24no—
313C2×Dic43—24no—
314C2×Dic43—24no—
315C2×Dic43—24no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—41no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—41no—
326C2×Dic43—42no—
327C2×Dic43—416no—
328C2×Dic43C2×C22⋊C414yes—
329C2×Dic43C2×C22⋊C414yes—
330C2×Dic43C4×D418yes—
331C2×Dic43#12118yes—
332C2×Dic43#12414yes—
333C2×Dic43#12714yes—
334C4×D43—416no—
335#13847—431nomaximal, Sylow
336C22×C43—24no—
337C22×C43—28no—
338C22×C43—44no—
339C22×C43—44no—
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—44no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43C22×C22⋊C411yescharacteristic
348C22×C43C2×#11711yescharacteristic
349C22×C43C2×#11711yescharacteristic
350C22×C43C2×C4×D412yes—
351C22×C43C4×#4112yes—
352C22×C43C2×#12112yes—
353C22×C43#52512yes—
354C22×C43#52511yescharacteristic
355C22×C43#52512yes—
356C22×C43#52511yescharacteristic
357C22×C43#52511yescharacteristic
358C22×C43#52512yes—
359C22×C43#52511yescharacteristic
360C22×C43#52511yescharacteristic
361C22×C43#52512yes—
362C22×C43#52511yescharacteristic
363C22×C43C2×#12411yescharacteristic
364C22×C43#52912yes—
365C22×C43#52912yes—
366C22×C43#52912yes—
367C22×C43#52912yes—
368C22×C43C2×#12711yescharacteristic
369C22×C43#53212yes—
370C2×D43—24no—
371C2×D43—28no—
372C2×D43—44no—
373C2×D43—44no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—44no—
379C2×D43—42no—
380C2×D43—42no—
381C4×C43—24no—
382C4×C43—44no—
383C4×C43—44no—
384C4×C43—42no—
385Dic43—24no—
386Dic43—44no—
387Dic43—44no—
388Dic43—42no—
389Dic43#39018yes—
390C22×C4×D4—431no—
391C2×C4×C4⋊C4—431no—
392C2×C4×C22⋊C4—432no—
393C2×C4×C22⋊C4—432no—
394C2×#376—431no—
395#1445—432no—
396#1439—431no—
397#1439—431no—
398#1439—431no—
399#1439D4311yescharacteristic, complemented
400#1438—432no—
401C2×C43—44no—
402C2×C43#228011yescharacteristic
403C2×C43#229012yes—
404C2×C43#229012yes—
405C2×C43C2×#39011yescharacteristic
406C2×C43#229711yescharacteristic
407C2×C43#239212yes—
408C2×C43#239212yes—
409C2×C43#239711yescharacteristic
410C2×C43#239711yescharacteristic
411C2×C43#239811yescharacteristic
412C2×C43#239811yescharacteristic
413D43—44no—
414C23×D4—431no—
415C24×C4—431no—
416C24×C4—431no—
417C2×C4×D4—438no—
418C2×C4×D4—864no—
419C2×C4×D4—864no—
420C22×C4⋊C4—431no—
421C22×C4⋊C4—431no—
422C22×C4⋊C4C2×D4311yescharacteristic
423C22×C22⋊C4—431no—
424C22×C22⋊C4—432no—
425C22×C22⋊C4—432no—
426C22×C22⋊C4—432no—
427C22×C22⋊C4C2×D4312yes—
428C22×C22⋊C4C2×D4311yescharacteristic
429C22×C42—431no—
430C22×C42—432no—
431C22×C42—432no—
432C4×C4⋊C4—864no—
433C4×C22⋊C4—868no—
434C4×C22⋊C4—868no—
435#376—864no—
436C2×#95—432no—
437C2×#95—432no—
438C2×#95—431no—
439C2×#95—432no—
440C2×#95—432no—
441C2×#95—432no—
442C2×#95C2×D4311yescharacteristic
443C2×#95C2×D4312yes—
444C43#1384711yescharacteristic, complemented, Sylow
445C25—431no—
446C25C22×D4311yescharacteristic
447C22×D4—434no—
448C22×D4—862no—
449C22×D4—862no—
450C22×D4—862no—
451C22×D4—862no—
452C22×D4—862no—
453C22×D4—862no—
454C23×C4—431no—
455C23×C4—431no—
456C23×C4—434no—
457C23×C4—432no—
458C23×C4—432no—
459C23×C4—431no—
460C23×C4—434no—
461C23×C4—862no—
462C23×C4—862no—
463C23×C4—864no—
464C23×C4—864no—
465C23×C4—862no—
466C23×C4—862no—
467C23×C4—864no—
468C23×C4—864no—
469C23×C4C22×D4311yescharacteristic
470C23×C4C22×D4312yes—
471C23×C4C22×D4312yes—
472C23×C4C22×D4311yescharacteristic
473C4×D4—8632no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—434no—
477C2×C4⋊C4—862no—
478C2×C4⋊C4—862no—
479C2×C4⋊C4—864no—
480C2×C4⋊C4—862no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—434no—
487C2×C22⋊C4—864no—
488C2×C22⋊C4—864no—
489C2×C22⋊C4—864no—
490C2×C22⋊C4—864no—
491C2×C22⋊C4—864no—
492C2×C22⋊C4—864no—
493C2×C22⋊C4—864no—
494C2×C22⋊C4—862no—
495C2×C22⋊C4—862no—
496C2×C22⋊C4—864no—
497C2×C22⋊C4—864no—
498C2×C22⋊C4C4×D4314yes—
499C2×C42—434no—
500C2×C42—434no—
501C2×C42—434no—
502C2×C42—438no—
503C2×C42—864no—
504C2×C42—864no—
505C2×C42—864no—
506C2×C42—864no—
507C2×C42—864no—
508#95—22no—
509#95—24no—
510#95—864no—
511#95—864no—
512#95—864no—
513#95—864no—
514#95—862no—
515#95—864no—
516C24—22no—
517C24—21no—
518C24—21no—
519C24—22no—
520C24—22no—
521C24—21no—
522C24—21no—
523C24—22no—
524C24—432no—
525C24—432no—
526C24—432no—
527C24—862no—
528C24—861no—
529C24—861no—
530C24—862no—
531C24—862no—
532C24—862no—
533C24—861no—
534C24—861no—
535C24C2×C4×D4312yes—
536C24#1062190012yes—
537C24#1062190212yes—
538C24C23×D4311yescharacteristic
539C2×D4—868no—
540C2×D4—868no—
541C2×D4—868no—
542C2×D4—868no—
543C2×D4—868no—
544C2×D4—868no—
545C2×D4—868no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—432no—
565C22×C4—432no—
566C22×C4—432no—
567C22×C4—434no—
568C22×C4—434no—
569C22×C4—432no—
570C22×C4—432no—
571C22×C4—432no—
572C22×C4—432no—
573C22×C4—434no—
574C22×C4—434no—
575C22×C4—868no—
576C22×C4—8616no—
577C22×C4—868no—
578C22×C4—8616no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—862no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—1728no—
600C22×C4—1724no—
601C22×C4—1724no—
602C22×C4—1728no—
603C22×C4—1724no—
604C22×C4—1724no—
605C22×C4C2×C4×D4312yes—
606C22×C4C2×C4×D4312yes—
607C22×C4D4×D4314yes—
608C22×C4D4×D4312yes—
609C22×C4D4×D4312yes—
610C22×C4#1062190014yes—
611C4⋊C4—28no—
612C4⋊C4—868no—
613C4⋊C4—868no—
614C22⋊C4—216no—
615C22⋊C4—28no—
616C22⋊C4—8616no—
617C22⋊C4—8616no—
618C22⋊C4—8616no—
619C22⋊C4—868no—
620C42—4316no—
621C42—8616no—
622C42—1728no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—22no—
629C23—22no—
630C23—24no—
631C23—22no—
632C23—22no—
633C23—24no—
634C23—24no—
635C23—42no—
636C23—41no—
637C23—42no—
638C23—41no—
639C23—42no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—41no—
644C23—42no—
645C23—434no—
646C23—862no—
647C23—862no—
648C23—864no—
649C23—864no—
650C23—864no—
651C23—864no—
652C23—862no—
653C23—862no—
654C23—862no—
655C23—862no—
656C23—864no—
657C23—864no—
658C23—1722no—
659C23—1722no—
660C23—1721no—
661C23—1721no—
662C23—1722no—
663C23—1721no—
664C23—1722no—
665C23—1722no—
666C23—1721no—
667C23—1722no—
668C23#1306328314yes—
669C23C22×C4×D4311yescharacteristic
670C23C2×D4×D4311yescharacteristic
671C23C2×D4×D4311yescharacteristic
672C23C2×D4×D4312yes—
673C23#41×D4311yescharacteristic
674C23#41×D4311yescharacteristic
675C23#41×D4312yes—
676C23#41×D4312yes—
677C23C2×#1062190011yescharacteristic
678C23C2×#1062190012yes—
679C23C2×#1062190211yescharacteristic
680D4—8632no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—434no—
705C2×C4—438no—
706C2×C4—438no—
707C2×C4—434no—
708C2×C4—434no—
709C2×C4—434no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—864no—
718C2×C4—864no—
719C2×C4—864no—
720C2×C4—864no—
721C2×C4—864no—
722C2×C4—864no—
723C2×C4—864no—
724C2×C4—17216no—
725C2×C4—17216no—
726C2×C4—1722no—
727C2×C4—1722no—
728C2×C4—1722no—
729C2×C4—1722no—
730C2×C4—1722no—
731C2×C4—1721no—
732C2×C4—1722no—
733C2×C4—1722no—
734C2×C4—1722no—
735C2×C4—1721no—
736C2×C4—1722no—
737C2×C4C22⋊C4×D4314yes—
738C22—28no—
739C22—24no—
740C22—44no—
741C22—42no—
742C22—44no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—868no—
750C22—864no—
751C22—1724no—
752C22—1722no—
753C22—1724no—
754C22—1724no—
755C22—1722no—
756C22—1722no—
757C22—1722no—
758C22—1722no—
759C22—1722no—
760C22C2×C22⋊C4×D4311yescharacteristic
761C22#117×D4311yescharacteristic
762C22C2×#1306328311yescharacteristic
763C22C4×D4×D4312yes—
764C22C4×#1062190012yes—
765C22#121×D4312yes—
766C22#1458340512yes—
767C22#1458340511yescharacteristic
768C22#1458340712yes—
769C22#1458340711yescharacteristic
770C22#1458340912yes—
771C22#1458340911yescharacteristic
772C22#1458340911yescharacteristic
773C22#1458341212yes—
774C22#1458341211yescharacteristic
775C22#1458341211yescharacteristic
776C22#124×D4311yescharacteristic
777C22#1458342612yes—
778C22#1458342812yes—
779C22#1458343212yes—
780C22#1458343512yes—
781C22#127×D4311yescharacteristic
782C22#1458344412yes—
783C4—24no—
784C4—42no—
785C4—44no—
786C4—44no—
787C4—438no—
788C4—864no—
789C4—1722no—
790C4—1724no—
791C4—1724no—
792C2—44no—
793C2—1724no—
794C2#1913697711yescharacteristic
795C2#1913703112yes—
796C2#1913703712yes—
797C2#390×D4311yescharacteristic
798C2#1913708011yescharacteristic
799C2#1913783812yes—
800C2#1913784012yes—
801C2#1913787311yescharacteristic
802C2#1913787511yescharacteristic
803C2#1913787711yescharacteristic
804C2#1913788011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1439C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenter#1439D43
hypocenterC43#13847
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic43C2semidirect
3. C2×C22⋊C4×Dic43C2semidirect
4. C2×#14582746C2semidirect
5. C2×#14582744C2semidirect
6. #19132861C2semidirect
7. #19132841C2semidirect
8. #19132840C2semidirect
9. #19132837C2semidirect
11. C43×#1439C2semidirect
17. C2×(C22⋊D43)⋊C4C4semidirect
91. C2×C4×Dic43D4semidirect
219. C4×Dic43C22⋊C4semidirect
399. #1439D43semidirect
444. C43#13847semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
C2×C4⋊C4×Dic432
C2×C22⋊C4×Dic432
C2×#145827462
C2×#145827442
#191328612
#191328412
#191328402
#191328372
#191328342
C43×#14392
#1384743