Finite Group Databasebeta

← #25018278

Subgroups — #25018278

Order 11008.

2702 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063287C211yesmaximal, characteristic
2C22×#13063283C211yesmaximal, characteristic, complemented
3C2×#14582746C211yesmaximal, characteristic, complemented
4C2×#14582746C212yesmaximal, complemented
5#19132848C211yesmaximal, characteristic, complemented
6#19132843C212yesmaximal, complemented
7#19132841C211yesmaximal, characteristic, complemented
8#19132837C211yesmaximal, characteristic, complemented
9#19132835C212yesmaximal
10#95×Dic43C212yesmaximal, complemented
11C43×#1441C211yesmaximal, characteristic, complemented
12C23×D172C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C23×C4×D43C2211yescharacteristic
15C2×#13063287—24no—
16C2×#13063287—24no—
17C2×#13063287C418yescomplemented
18C2×#13063283—24no—
19C2×#13063283—28no—
20C22×C4⋊Dic43C2211yescharacteristic
21C22×(C2×D43)⋊C4C2212yes—
22C22×(C2×D43)⋊C4C2212yes—
23C22×(C2×D43)⋊C4C2212yes—
24C22×(C2×D43)⋊C4C2212yes—
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×C4×Dic43C2212yes—
28C22×C4×Dic43C2211yescharacteristic
29C22×C4×Dic43C2212yes—
30#14582746—24no—
31#14582746—28no—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2211yescharacteristic
36C2×C43⋊#95C2212yes—
37C22×C4⋊C4×C43C2211yescharacteristic
38C22×C4⋊C4×C43C2211yescharacteristic
39C2×#95×C43C2212yes—
40C2×#95×C43C2211yescharacteristic
41C2×#95×C43C2212yes—
42C24×D43C2311yescharacteristic
43C24×D43C2311yescharacteristic
44C22×D172—22no—
45C22×D172—22no—
46C22×D172—22no—
47C22×D172—22no—
48C22×D172—22no—
49C22×D172—22no—
50C22×D172C2×C414yes—
51C23×Dic43C2311yescharacteristic
52C23×Dic43C2312yes—
53C23×Dic43C2312yes—
54C23×Dic43C2311yescharacteristic
55C22×C4×D43—24no—
56C22×C4×D43—24no—
57C22×C4×D43—22no—
58C22×C4×D43—22no—
59C22×C4×D43—24no—
60C22×C4×D43—24no—
61C22×C4×D43C2×C414yes—
62C22×C4×D43C2×C414yes—
63C22×C4×D43D414yes—
64C22×C4×D43D414yes—
65#13063287—232no—
66#13063283—232no—
67C2×C4⋊Dic43—22no—
68C2×C4⋊Dic43—24no—
69C2×(C2×D43)⋊C4—24no—
70C2×(C2×D43)⋊C4—22no—
71C2×(C2×D43)⋊C4—22no—
72C2×(C2×D43)⋊C4—24no—
73C2×(C2×D43)⋊C4—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)⋊C4—24no—
83C2×(C2×D43)⋊C4—24no—
84C2×(C2×D43)⋊C4—24no—
85C2×(C2×D43)⋊C4C2×C414yes—
86C2×(C2×D43)⋊C4C2×C414yes—
87C2×C4×Dic43—24no—
88C2×C4×Dic43—24no—
89C2×C4×Dic43—22no—
90C2×C4×Dic43—22no—
91C2×C4×Dic43—24no—
92C2×C4×Dic43—24no—
93C2×C4×Dic43—24no—
94C2×C4×Dic43C2×C414yes—
95C2×C4×Dic43D418yescomplemented
96C43⋊#95—22no—
97C43⋊#95—24no—
98C43⋊#95—24no—
99C43⋊#95—24no—
100C43⋊#95—24no—
101C23×C4×C43C2311yescharacteristic
102C23×C4×C43C2312yes—
103C23×C4×C43C2312yes—
104C23×C4×C43C2311yescharacteristic
105C23×C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43—24no—
107C2×C4⋊C4×C43—22no—
108C2×C4⋊C4×C43—22no—
109C2×C4⋊C4×C43—22no—
110C2×C4⋊C4×C43C2×C414yes—
111#95×C43—24no—
112#95×C43—22no—
113#95×C43—24no—
114C24×C43C2411yescharacteristic
115C23×D43—22no—
116C23×D43—22no—
117C23×D43—21no—
118C23×D43—21no—
119C23×D43—22no—
120C23×D43—22no—
121C23×D43—22no—
122C23×D43—22no—
123C23×D43—22no—
124C23×D43—22no—
125C23×D43—21no—
126C23×D43—21no—
127C23×D43—21no—
128C23×D43—21no—
129C23×D43—21no—
130C23×D43—21no—
131C23×D43C22×C412yes—
132C23×D43C22×C412yes—
133C23×D43C2×D412yes—
134C23×D43C2×D412yes—
135C23×D43#4112yes—
136C23×D43#4112yes—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—22no—
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×C43C22×C412yes—
160C22×C4×C43C22×C412yes—
161C22×C4×C43C22×C412yes—
162C22×C4×C43C2×D414yes—
163C22×C4×C43C2×D412yes—
164C22×C4×C43C2×D412yes—
165C22×C4×C43#4112yes—
166C22×C4×C43#4114yes—
167C22×C4×C43#4112yes—
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—22no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43C22×C412yes—
185C22×Dic43C22×C412yes—
186C22×Dic43C2×D414yes—
187C22×Dic43C2×D412yes—
188C22×Dic43C2×D412yes—
189C22×Dic43C2×D414yes—
190C22×Dic43#4114yes—
191C22×Dic43#4114yes—
192C2×D172—28no—
193C2×D172—28no—
194C2×D172—28no—
195C2×D172—28no—
196C2×D172—28no—
197C2×D172—28no—
198C2×D172—28no—
199C2×C4×D43—216no—
200C2×C4×D43—28no—
201C2×C4×D43—216no—
202C2×C4×D43—28no—
203C2×C4×D43—28no—
204C2×C4×D43—216no—
205C2×C4×D43—44no—
206C2×C4×D43—48no—
207C2×C4×D43—44no—
208C2×C4×D43C22⋊C4116yescomplemented
209C4⋊C4×C43—28no—
210C4⋊C4×C43—28no—
211(C2×D43)⋊C4—216no—
212(C2×D43)⋊C4—216no—
213(C2×D43)⋊C4—216no—
214(C2×D43)⋊C4—216no—
215(C2×D43)⋊C4—28no—
216(C2×D43)⋊C4—28no—
217C4⋊Dic43—28no—
218C4×Dic43—28no—
219C4×Dic43—216no—
220C4×Dic43—48no—
221C23×C43C23×C411yescharacteristic
222C23×C43C22×D411yescharacteristic
223C23×C43C22×D411yescharacteristic
224C23×C43C22×D412yes—
225C23×C43C2×#4111yescharacteristic
226C23×C43C2×#4111yescharacteristic
227C23×C43C2×#4112yes—
228C23×C43C2×#4112yes—
229C23×C43C2×#4111yescharacteristic
230C23×C43C2×#4111yescharacteristic
231C23×C43C2×#4112yes—
232C22×D43—22no—
233C22×D43—22no—
234C22×D43—22no—
235C22×D43—22no—
236C22×D43—24no—
237C22×D43—24no—
238C22×D43—24no—
239C22×D43—24no—
240C22×D43—22no—
241C22×D43—24no—
242C22×D43—22no—
243C22×D43—24no—
244C22×D43—24no—
245C22×D43—24no—
246C22×D43—22no—
247C22×D43—22no—
248C22×D43—22no—
249C22×D43—22no—
250C22×D43—22no—
251C22×D43—22no—
252C22×D43—22no—
253C22×D43—22no—
254C22×D43—24no—
255C22×D43—24no—
256C22×D43—22no—
257C22×D43—22no—
258C22×D43—41no—
259C22×D43—42no—
260C22×D43—41no—
261C22×D43—42no—
262C22×D43—42no—
263C22×D43—42no—
264C22×D43—42no—
265C22×D43—42no—
266C22×D43—42no—
267C22×D43—42no—
268C22×D43—42no—
269C22×D43—42no—
270C22×D43—42no—
271C22×D43—42no—
272C22×D43—41no—
273C22×D43—42no—
274C22×D43—42no—
275C22×D43—41no—
276C22×D43C2×C22⋊C414yes—
277C22×D43#11714yescomplemented
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—24no—
281C2×C4×C43—22no—
282C2×C4×C43—24no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—24no—
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—41no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—41no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43C2×C22⋊C414yes—
308C2×C4×C43#11714yescomplemented
309C2×Dic43—22no—
310C2×Dic43—24no—
311C2×Dic43—24no—
312C2×Dic43—24no—
313C2×Dic43—24no—
314C2×Dic43—24no—
315C2×Dic43—24no—
316C2×Dic43—24no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—41no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—41no—
328C2×Dic43C2×C22⋊C414yes—
329C2×Dic43C4×D418yes—
330C2×Dic43#12014yes—
331C2×Dic43#12118yes—
332C2×Dic43#12314yes—
333D172—232no—
334C4×D43—232no—
335C4×D43—416no—
336#13839—431nomaximal, Sylow
337C22×C43C22×C22⋊C411yescharacteristic
338C22×C43C2×#11711yescharacteristic
339C22×C43C2×#11711yescharacteristic
340C22×C43C2×C4×D412yes—
341C22×C43C4×#4112yes—
342C22×C43C2×#12011yescharacteristic
343C22×C43C2×#12112yes—
344C22×C43C2×#12311yescharacteristic
345C22×C43#52512yes—
346C22×C43#52511yescharacteristic
347C22×C43#52511yescharacteristic
348C22×C43#52512yes—
349C22×C43#52511yescharacteristic
350C22×C43#52511yescharacteristic
351C22×C43#52512yes—
352C22×C43#52912yes—
353C22×C43#52912yes—
354C22×C43#52912yes—
355C22×C43#52912yes—
356C22×C43#53212yes—
357C22×C43#53211yescharacteristic
358C22×C43#53212yes—
359C22×C43#53211yescharacteristic
360C2×D43—24no—
361C2×D43—24no—
362C2×D43—24no—
363C2×D43—28no—
364C2×D43—24no—
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—44no—
370C2×D43—44no—
371C2×D43—44no—
372C2×D43—44no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—44no—
379C2×D43—44no—
380C2×D43—44no—
381C2×D43—42no—
382C4×C43—24no—
383C4×C43—24no—
384C4×C43—44no—
385C4×C43—44no—
386C4×C43—42no—
387Dic43—44no—
388Dic43—44no—
389Dic43—42no—
390Dic43#38618yes—
391C22×C4×D4—431no—
392C22×#117—431no—
393C2×C4×C22⋊C4—432no—
394C2×C4×C22⋊C4—431no—
395#1441—431no—
396#1441D4311yescharacteristic, complemented
397#1440—432no—
398#1439—431no—
399#1439—431no—
400#1438—432no—
401C4×#95—432no—
402C2×C43#228011yescharacteristic
403C2×C43C2×#38611yescharacteristic
404C2×C43#229012yes—
405C2×C43#229312yes—
406C2×C43#229711yescharacteristic
407C2×C43#238811yescharacteristic
408C2×C43#238811yescharacteristic
409C2×C43#239212yes—
410C2×C43#239212yes—
411C2×C43#239511yescharacteristic
412C2×C43#239511yescharacteristic
413D43—44no—
414D43—44no—
415C23×D4—431no—
416C24×C4—431no—
417C24×C4—431no—
418C2×C4×D4—438no—
419C2×C4×D4—864no—
420C2×C4×D4—864no—
421C2×#117—868no—
422C2×#117—864no—
423C22×C4⋊C4—431no—
424C22×C4⋊C4C2×D4311yescharacteristic
425C22×C4⋊C4C2×D4311yescharacteristic
426C22×C22⋊C4—431no—
427C22×C22⋊C4—431no—
428C22×C22⋊C4—432no—
429C22×C22⋊C4—432no—
430C22×C22⋊C4—432no—
431C22×C22⋊C4—432no—
432C22×C42—432no—
433C22×C42—431no—
434C22×C42—432no—
435C4×C22⋊C4—868no—
436C4×C22⋊C4—864no—
437C2×#95—432no—
438C2×#95—432no—
439C2×#95—432no—
440C2×#95—431no—
441C2×#95—432no—
442C2×#95C2×D4312yes—
443C2×#95C2×D4311yescharacteristic
444C2×#95C2×D4312yes—
445C43#1383911yescharacteristic, complemented, Sylow
446C25—431no—
447C25—431no—
448C22×D4—434no—
449C22×D4—862no—
450C22×D4—862no—
451C22×D4—862no—
452C22×D4—862no—
453C22×D4—862no—
454C22×D4—862no—
455C23×C4—431no—
456C23×C4—434no—
457C23×C4—434no—
458C23×C4—434no—
459C23×C4—432no—
460C23×C4—431no—
461C23×C4—432no—
462C23×C4—434no—
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
473C23×C4C22×D4311yescharacteristic
474C4×D4—8632no—
475#117—8632no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—864no—
481C2×C4⋊C4—862no—
482C2×C4⋊C4C4×D4314yes—
483C2×C22⋊C4—434no—
484C2×C22⋊C4—434no—
485C2×C22⋊C4—864no—
486C2×C22⋊C4—864no—
487C2×C22⋊C4—864no—
488C2×C22⋊C4—864no—
489C2×C22⋊C4—864no—
490C2×C22⋊C4—862no—
491C2×C22⋊C4—862no—
492C2×C22⋊C4—864no—
493C2×C22⋊C4—864no—
494C2×C22⋊C4—864no—
495C2×C22⋊C4—864no—
496C2×C22⋊C4—862no—
497C2×C22⋊C4—862no—
498C2×C22⋊C4—864no—
499C2×C22⋊C4—864no—
500C2×C22⋊C4—864no—
501C2×C42—434no—
502C2×C42—438no—
503C2×C42—864no—
504C2×C42—864no—
505C2×C42—862no—
506C2×C42—862no—
507C2×C42—864no—
508C2×C42—864no—
509C2×C42—864no—
510#95—24no—
511#95—22no—
512#95—24no—
513#95—864no—
514#95—864no—
515#95—862no—
516#95—864no—
517#95—864no—
518C24—432no—
519C24—432no—
520C24—432no—
521C24—432no—
522C24—432no—
523C24—432no—
524C24—862no—
525C24—862no—
526C24—861no—
527C24—861no—
528C24—862no—
529C24—862no—
530C24—862no—
531C24—862no—
532C24—861no—
533C24—861no—
534C24—861no—
535C24—861no—
536C24—862no—
537C24—862no—
538C24—861no—
539C24—861no—
540C24C23×D4311yescharacteristic
541C2×D4—868no—
542C2×D4—868no—
543C2×D4—868no—
544C2×D4—868no—
545C2×D4—868no—
546C2×D4—868no—
547C2×D4—868no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—432no—
571C22×C4—434no—
572C22×C4—432no—
573C22×C4—432no—
574C22×C4—434no—
575C22×C4—4316no—
576C22×C4—432no—
577C22×C4—434no—
578C22×C4—434no—
579C22×C4—868no—
580C22×C4—8616no—
581C22×C4—8616no—
582C22×C4—868no—
583C22×C4—868no—
584C22×C4—8616no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—862no—
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—862no—
600C22×C4—862no—
601C22×C4—1724no—
602C22×C4—1728no—
603C22×C4—1724no—
604C22×C4C2×C4×D4312yes—
605C22×C4C2×C4×D4312yes—
606C22×C4C2×C4×D4312yes—
607C22×C4D4×D4314yes—
608C22×C4D4×D4312yes—
609C22×C4D4×D4312yes—
610C22×C4#1062190012yes—
611C22×C4#1062190214yes—
612C22×C4#1062190212yes—
613C4⋊C4—28no—
614C4⋊C4—28no—
615C4⋊C4—868no—
616C22⋊C4—868no—
617C22⋊C4—8616no—
618C22⋊C4—8616no—
619C22⋊C4—8616no—
620C22⋊C4—8616no—
621C22⋊C4—868no—
622C42—8616no—
623C42—868no—
624C42—1728no—
625C23—434no—
626C23—434no—
627C23—862no—
628C23—862no—
629C23—862no—
630C23—862no—
631C23—864no—
632C23—864no—
633C23—864no—
634C23—864no—
635C23—862no—
636C23—864no—
637C23—862no—
638C23—864no—
639C23—862no—
640C23—862no—
641C23—862no—
642C23—862no—
643C23—864no—
644C23—864no—
645C23—862no—
646C23—862no—
647C23—862no—
648C23—862no—
649C23—864no—
650C23—864no—
651C23—862no—
652C23—862no—
653C23—1721no—
654C23—1722no—
655C23—1721no—
656C23—1722no—
657C23—1722no—
658C23—1722no—
659C23—1722no—
660C23—1722no—
661C23—1722no—
662C23—1722no—
663C23—1722no—
664C23—1722no—
665C23—1722no—
666C23—1722no—
667C23—1721no—
668C23—1722no—
669C23—1722no—
670C23—1721no—
671C23C22×C4×D4311yescharacteristic
672C23C2×D4×D4311yescharacteristic
673C23C2×D4×D4311yescharacteristic
674C23C2×D4×D4312yes—
675C23#41×D4311yescharacteristic
676C23#41×D4311yescharacteristic
677C23#41×D4312yes—
678C23#41×D4312yes—
679C23C2×#1062190011yescharacteristic
680C23C2×#1062190211yescharacteristic
681C23C2×#1062190212yes—
682D4—8632no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—434no—
713C2×C4—438no—
714C2×C4—434no—
715C2×C4—438no—
716C2×C4—434no—
717C2×C4—8632no—
718C2×C4—862no—
719C2×C4—864no—
720C2×C4—864no—
721C2×C4—864no—
722C2×C4—864no—
723C2×C4—864no—
724C2×C4—864no—
725C2×C4—864no—
726C2×C4—17216no—
727C2×C4—1722no—
728C2×C4—1722no—
729C2×C4—1722no—
730C2×C4—1722no—
731C2×C4—1722no—
732C2×C4—1722no—
733C2×C4—1721no—
734C2×C4—1722no—
735C2×C4—1722no—
736C2×C4—1722no—
737C2×C4—1721no—
738C2×C4C22⋊C4×D4314yes—
739C2×C4#1306328314yescomplemented
740C22—868no—
741C22—864no—
742C22—864no—
743C22—864no—
744C22—864no—
745C22—1724no—
746C22—1722no—
747C22—1722no—
748C22—1722no—
749C22—1722no—
750C22—1724no—
751C22—1724no—
752C22—1724no—
753C22—1724no—
754C22—1724no—
755C22—1724no—
756C22—1722no—
757C22—1722no—
758C22—1722no—
759C22—1722no—
760C22—1722no—
761C22—1722no—
762C22C2×C22⋊C4×D4311yescharacteristic
763C22#117×D4311yescharacteristic
764C22C2×#1306328311yescharacteristic
765C22C4×D4×D4312yes—
766C22C4×#1062190212yes—
767C22#120×D4311yescharacteristic
768C22#121×D4312yes—
769C22#123×D4311yescharacteristic
770C22#1458340712yes—
771C22#1458340911yescharacteristic
772C22#1458340911yescharacteristic
773C22#1458341212yes—
774C22#1458341211yescharacteristic
775C22#1458341211yescharacteristic
776C22#1458341212yes—
777C22#1458343212yes—
778C22#1458343412yes—
779C22#1458343412yes—
780C22#1458343512yes—
781C22#1458344412yes—
782C22#1458344811yescharacteristic
783C22#1458345012yes—
784C22#1458345011yescharacteristic
785C4—24no—
786C4—24no—
787C4—44no—
788C4—44no—
789C4—42no—
790C4—438no—
791C4—1724no—
792C4—1724no—
793C4—1722no—
794C2—1724no—
795C2—1724no—
796C2#1913697711yescharacteristic
797C2#386×D4311yescharacteristic
798C2#1913703312yes—
799C2#1913705312yes—
800C2#1913708411yescharacteristic
801C2#1913780911yescharacteristic
802C2#1913781311yescharacteristic
803C2#1913783612yes—
804C2#1913784012yes—
805C2#1913785911yescharacteristic
806C2#1913786111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1441C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1441D43
hypocenterC43#13839
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C22×#13063283C2semidirect
3. C2×#14582746C2semidirect
4. C2×#14582746C2semidirect
5. #19132848C2semidirect
6. #19132843C2semidirect
7. #19132841C2semidirect
8. #19132837C2semidirect
10. #95×Dic43C2semidirect
11. C43×#1441C2semidirect
17. C2×#13063287C4semidirect
95. C2×C4×Dic43D4semidirect
208. C2×C4×D43C22⋊C4semidirect
277. C22×D43#117semidirect
308. C2×C4×C43#117semidirect
396. #1441D43semidirect
445. C43#13839semidirect
739. C2×C4#13063283semidirect

Maximal subgroups

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

subgroupindex
C22×#130632872
C22×#130632832
C2×#145827462
#191328482
#191328432
#191328412
#191328372
#191328352
#95×Dic432
C43×#14412
#1383943