Finite Group Databasebeta

← #25019313

Subgroups — #25019313

Order 11008.

2590 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063287C211yesmaximal, characteristic
2C2×#14582777C212yesmaximal
3C2×#14582756C211yesmaximal, characteristic, complemented
4C2×#95×D43C211yesmaximal, characteristic, complemented
5#19132848C211yesmaximal, characteristic, complemented
6#19132841C211yesmaximal, characteristic, complemented
7#19132837C211yesmaximal, characteristic, complemented
8#19132821C212yesmaximal, complemented
9(C2×D43)⋊#95C212yesmaximal, complemented
10(C2×D43)⋊#95C212yesmaximal, complemented
11C43×#1441C211yesmaximal, characteristic, complemented
12C23×D172C2211yescharacteristic
13C23×C4×D43C2212yes—
14C23×C4×D43C2211yescharacteristic
15C23×C4×D43C2211yescharacteristic
16C2×#13063287—24no—
17C2×#13063287—24no—
18C2×#13063287C418yescomplemented
19C22×C4⋊Dic43C2211yescharacteristic
20C22×(C2×D43)⋊C4C2212yes—
21C22×(C2×D43)⋊C4C2212yes—
22C22×(C2×D43)⋊C4C2212yes—
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×C4×Dic43C2211yescharacteristic
26#14582777—28no—
27#14582756—24no—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2212yes—
35#95×D43—24no—
36C22×C4⋊C4×C43C2211yescharacteristic
37C22×C4⋊C4×C43C2211yescharacteristic
38C2×#95×C43C2212yes—
39C2×#95×C43C2211yescharacteristic
40C2×#95×C43C2212yes—
41C24×D43C2311yescharacteristic
42C24×D43C2311yescharacteristic
43C22×D172—22no—
44C22×D172—22no—
45C22×D172—22no—
46C22×D172—22no—
47C22×D172C2×C414yes—
48C22×D172D414yes—
49C22×D172Q814yes—
50C23×Dic43C2312yes—
51C23×Dic43C2311yescharacteristic
52C23×Dic43C2312yes—
53C23×Dic43C2311yescharacteristic
54C22×C4×D43—24no—
55C22×C4×D43—24no—
56C22×C4×D43—22no—
57C22×C4×D43—22no—
58C22×C4×D43—24no—
59C22×C4×D43—24no—
60C22×C4×D43—24no—
61C22×C4×D43—42no—
62C22×C4×D43—42no—
63C22×C4×D43—42no—
64C22×C4×D43—42no—
65C22×C4×D43—42no—
66C22×C4×D43—42no—
67C22×C4×D43C2×C414yes—
68C22×C4×D43C2×C414yescomplemented
69C22×C4×D43D414yes—
70C22×C4×D43D414yes—
71#13063287—232no—
72C2×C4⋊Dic43—22no—
73C2×C4⋊Dic43—42no—
74C2×(C2×D43)⋊C4—22no—
75C2×(C2×D43)⋊C4—22no—
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)⋊C4—42no—
86C2×(C2×D43)⋊C4—42no—
87C2×(C2×D43)⋊C4C2×C414yes—
88C2×(C2×D43)⋊C4C2×C414yescomplemented
89C2×C4×Dic43—22no—
90C2×C4×Dic43—22no—
91C2×C4×Dic43C2×C414yescomplemented
92C43⋊#95—22no—
93C43⋊#95—24no—
94C43⋊#95—24no—
95C43⋊#95—24no—
96C43⋊#95—24no—
97C43⋊#95—24no—
98C43⋊#95—42no—
99C23×C4×C43C2312yes—
100C23×C4×C43C2311yescharacteristic
101C23×C4×C43C2312yes—
102C23×C4×C43C2311yescharacteristic
103C23×C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43—22no—
105C2×C4⋊C4×C43—22no—
106C2×C4⋊C4×C43—22no—
107C2×C4⋊C4×C43—42no—
108C2×C4⋊C4×C43C2×C414yescomplemented
109#95×C43—22no—
110#95×C43—24no—
111#95×C43—42no—
112C24×C43C2411yescharacteristic
113C23×D43—22no—
114C23×D43—22no—
115C23×D43—22no—
116C23×D43—22no—
117C23×D43—21no—
118C23×D43—21no—
119C23×D43—22no—
120C23×D43—22no—
121C23×D43—21no—
122C23×D43—21no—
123C23×D43—22no—
124C23×D43—22no—
125C23×D43C22×C412yes—
126C23×D43C22×C412yes—
127C23×D43C2×D412yes—
128C23×D43C2×D412yes—
129C23×D43C2×D412yes—
130C23×D43C2×D412yes—
131C23×D43C2×Q812yes—
132C23×D43C2×Q812yes—
133C23×D43#4112yes—
134C23×D43#4112yes—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
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×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43C22×C412yes—
159C22×C4×C43C22×C412yes—
160C22×C4×C43C22×C412yes—
161C22×C4×C43C2×D412yes—
162C22×C4×C43C2×D412yes—
163C22×C4×C43C2×D412yes—
164C22×C4×C43C2×Q812yes—
165C22×C4×C43#4114yes—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—22no—
171C22×Dic43—22no—
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×Dic43—22no—
185C22×Dic43C22×C412yes—
186C22×Dic43C22×C412yes—
187C22×Dic43C2×D412yes—
188C22×Dic43C2×D412yes—
189C22×Dic43#4114yes—
190C2×D172—28no—
191C2×D172—28no—
192C2×D172—28no—
193C2×D172—28no—
194C2×D172—28no—
195C2×D172—28no—
196C2×D172C4⋊C4116yescomplemented
197C2×C4×D43—216no—
198C2×C4×D43—28no—
199C2×C4×D43—48no—
200C2×C4×D43—48no—
201C2×C4×D43—48no—
202C2×C4×D43—44no—
203C2×C4×D43—44no—
204C2×C4×D43—48no—
205C2×C4×D43—48no—
206C2×C4×D43—48no—
207C2×C4×D43—48no—
208C2×C4×D43—48no—
209C2×C4×D43—48no—
210C2×C4×D43—44no—
211C2×C4×D43—44no—
212C2×C4×D43—48no—
213C2×C4×D43C22⋊C4116yescomplemented
214C4⋊C4×C43—28no—
215C4⋊C4×C43—44no—
216(C2×D43)⋊C4—28no—
217(C2×D43)⋊C4—28no—
218(C2×D43)⋊C4—48no—
219(C2×D43)⋊C4—48no—
220(C2×D43)⋊C4—48no—
221C4⋊Dic43—44no—
222C4×Dic43—28no—
223C23×C43C23×C411yescharacteristic
224C23×C43C22×D411yescharacteristic
225C23×C43C22×D411yescharacteristic
226C23×C43C22×D411yescharacteristic
227C23×C43C22×Q811yescharacteristic
228C23×C43C2×#4111yescharacteristic
229C23×C43C2×#4111yescharacteristic
230C23×C43C2×#4112yes—
231C23×C43C2×#4112yes—
232C23×C43H(5,𝔽2)12yes—
233C23×C43H(5,𝔽2)12yes—
234C22×D43—24no—
235C22×D43—24no—
236C22×D43—24no—
237C22×D43—22no—
238C22×D43—22no—
239C22×D43—24no—
240C22×D43—22no—
241C22×D43—22no—
242C22×D43—24no—
243C22×D43—24no—
244C22×D43—24no—
245C22×D43—24no—
246C22×D43—24no—
247C22×D43—24no—
248C22×D43—24no—
249C22×D43—24no—
250C22×D43—22no—
251C22×D43—22no—
252C22×D43—24no—
253C22×D43—24no—
254C22×D43—22no—
255C22×D43—22no—
256C22×D43—22no—
257C22×D43—22no—
258C22×D43—24no—
259C22×D43—24no—
260C22×D43—24no—
261C22×D43—24no—
262C22×D43—42no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—42no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—42no—
269C22×D43—42no—
270C22×D43—42no—
271C22×D43—42no—
272C22×D43C2×C22⋊C414yes—
273C22×D43C2×C4⋊C414yes—
274C22×D43C2×C4⋊C414yes—
275C22×D43#11714yes—
276C22×D43#12114yes—
277C22×D43#12114yes—
278C22×D43C22⋊Q814yes—
279C22×D43C22⋊Q814yes—
280C2×C4×C43—22no—
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—22no—
291C2×C4×C43—24no—
292C2×C4×C43—24no—
293C2×C4×C43—24no—
294C2×C4×C43—24no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—41no—
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×C43—42no—
308C2×C4×C43—42no—
309C2×C4×C43C2×C22⋊C414yes—
310C2×C4×C43C2×C4⋊C414yes—
311C2×Dic43—24no—
312C2×Dic43—24no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—24no—
317C2×Dic43—24no—
318C2×Dic43—24no—
319C2×Dic43—24no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43—42no—
330C2×Dic43—42no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43C2×C22⋊C414yes—
335D172—232no—
336C4×D43—416no—
337C4×D43—416no—
338C4×D43—432no—
339#13960—431nomaximal, Sylow
340C22×C43C22×C22⋊C411yescharacteristic
341C22×C43C22×C4⋊C411yescharacteristic
342C22×C43C2×#11711yescharacteristic
343C22×C43C4×#4112yes—
344C22×C43#51812yes—
345C22×C43C2×#12111yescharacteristic
346C22×C43C2×#12111yescharacteristic
347C22×C43C2×C22⋊Q811yescharacteristic
348C22×C43C2×C22⋊Q811yescharacteristic
349C22×C43#52512yes—
350C22×C43#53211yescharacteristic
351C22×C43#53211yescharacteristic
352C22×C43#53412yes—
353C22×C43#53411yescharacteristic
354C22×C43#53411yescharacteristic
355C22×C43#54612yes—
356C22×C43#54612yes—
357C22×C43#55112yes—
358C22×C43#55112yes—
359C22×C43#55312yes—
360C22×C43#55312yes—
361C22×C43#55412yes—
362C22×C43#55412yes—
363C2×D43—24no—
364C2×D43—24no—
365C2×D43—24no—
366C2×D43—28no—
367C2×D43—28no—
368C2×D43—28no—
369C2×D43—28no—
370C2×D43—24no—
371C2×D43—24no—
372C2×D43—24no—
373C2×D43—28no—
374C2×D43—24no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—44no—
379C2×D43—44no—
380C2×D43—44no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43#38018yes—
385C4×C43—24no—
386C4×C43—24no—
387C4×C43—42no—
388C4×C43—44no—
389C4×C43—82no—
390Dic43—24no—
391Dic43—44no—
392Dic43—42no—
393Dic43—82no—
394C22×C4×D4—431no—
395C2×#386—432no—
396C2×#380—431no—
397C22×#95—431no—
398#1441—431no—
399#1441D4311yescharacteristic, complemented
400#1439—431no—
401#1439—431no—
402#1434—432no—
403C22⋊#95—432no—
404C22⋊#95—432no—
405C2×C43C2×#38011yescharacteristic
406C2×C43#229711yescharacteristic
407C2×C43#230811yescharacteristic
408C2×C43#234912yes—
409C2×C43#235312yes—
410C2×C43#253412yes—
411C2×C43#254311yescharacteristic
412C2×C43#254311yescharacteristic
413C2×C43#256411yescharacteristic
414C2×C43#256411yescharacteristic
415C2×C43#257912yes—
416D43—28no—
417D43—44no—
418C23×D4—431no—
419C24×C4—431no—
420C24×C4—431no—
421C24×C4—432no—
422C2×C4×D4—438no—
423C2×C4×D4—864no—
424C2×C4×D4—864no—
425C22×C4⋊C4—431no—
426C22×C4⋊C4C2×D4311yescharacteristic
427C22×C4⋊C4C2×D4311yescharacteristic
428C22×C22⋊C4—431no—
429C22×C22⋊C4—431no—
430C22×C22⋊C4—432no—
431C22×C22⋊C4—432no—
432C22×C22⋊C4—432no—
433C22×C42—431no—
434#386—868no—
435#380—864no—
436C2×#95—432no—
437C2×#95—432no—
438C2×#95—432no—
439C2×#95—432no—
440C2×#95—432no—
441C2×#95—431no—
442C2×#95—432no—
443C2×#95—864no—
444C2×#95C2×D4312yes—
445C2×#95C2×D4311yescharacteristic
446C2×#95C2×D4312yes—
447C43#1396011yescharacteristic, complemented, Sylow
448C25—431no—
449C25—431no—
450C22×D4—434no—
451C22×D4—434no—
452C22×D4—434no—
453C22×D4—862no—
454C22×D4—862no—
455C22×D4—862no—
456C22×D4—862no—
457C23×C4—431no—
458C23×C4—434no—
459C23×C4—434no—
460C23×C4—434no—
461C23×C4—431no—
462C23×C4—432no—
463C23×C4—434no—
464C23×C4—432no—
465C23×C4—862no—
466C23×C4—862no—
467C23×C4—864no—
468C23×C4—864no—
469C23×C4—864no—
470C23×C4—864no—
471C23×C4—864no—
472C23×C4—1722no—
473C23×C4—1722no—
474C23×C4—1722no—
475C23×C4—1722no—
476C23×C4—1722no—
477C23×C4—1722no—
478C23×C4C22×D4312yes—
479C23×C4C22×D4311yescharacteristic
480C23×C4C22×D4312yes—
481C23×C4C22×D4311yescharacteristic
482C23×C4C22×D4311yescharacteristic
483C4×D4—8632no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—862no—
489C2×C4⋊C4—1722no—
490C2×C4⋊C4C4×D4314yescomplemented
491C2×C22⋊C4—434no—
492C2×C22⋊C4—434no—
493C2×C22⋊C4—862no—
494C2×C22⋊C4—862no—
495C2×C22⋊C4—862no—
496C2×C22⋊C4—862no—
497C2×C22⋊C4—864no—
498C2×C22⋊C4—864no—
499C2×C22⋊C4—864no—
500C2×C22⋊C4—864no—
501C2×C22⋊C4—864no—
502C2×C22⋊C4—864no—
503C2×C22⋊C4—864no—
504C2×C22⋊C4—1722no—
505C2×C22⋊C4—1722no—
506C2×C42—434no—
507C2×C42—862no—
508C2×C42—862no—
509#95—22no—
510#95—24no—
511#95—42no—
512#95—864no—
513#95—864no—
514#95—864no—
515#95—862no—
516#95—864no—
517#95—864no—
518#95—1722no—
519C24—432no—
520C24—432no—
521C24—432no—
522C24—432no—
523C24—432no—
524C24—432no—
525C24—432no—
526C24—432no—
527C24—432no—
528C24—432no—
529C24—862no—
530C24—862no—
531C24—862no—
532C24—862no—
533C24—861no—
534C24—861no—
535C24—862no—
536C24—861no—
537C24—861no—
538C24—862no—
539C24—862no—
540C24—862no—
541C24C23×D4311yescharacteristic
542C2×D4—4316no—
543C2×D4—868no—
544C2×D4—868no—
545C2×D4—868no—
546C2×D4—868no—
547C2×D4—868no—
548C2×D4—868no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
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—22no—
571C22×C4—22no—
572C22×C4—432no—
573C22×C4—432no—
574C22×C4—432no—
575C22×C4—4316no—
576C22×C4—432no—
577C22×C4—434no—
578C22×C4—868no—
579C22×C4—8616no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
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—1728no—
600C22×C4—1728no—
601C22×C4—1724no—
602C22×C4—1724no—
603C22×C4—1728no—
604C22×C4—1728no—
605C22×C4—1728no—
606C22×C4—1728no—
607C22×C4—1728no—
608C22×C4—1728no—
609C22×C4—1724no—
610C22×C4—1724no—
611C22×C4—1728no—
612C22×C4—1728no—
613C22×C4C2×C4×D4312yes—
614C22×C4C2×C4×D4312yes—
615C22×C4C2×C4×D4312yes—
616C22×C4D4×D4312yes—
617C22×C4D4×D4312yes—
618C22×C4D4×D4312yes—
619C22×C4Q8×D4312yes—
620C22×C4#1062190214yes—
621C4⋊C4—28no—
622C4⋊C4—44no—
623C4⋊C4—1724no—
624C22⋊C4—868no—
625C22⋊C4—868no—
626C22⋊C4—1728no—
627C22⋊C4—1728no—
628C22⋊C4—1728no—
629C42—868no—
630C23—434no—
631C23—434no—
632C23—434no—
633C23—434no—
634C23—434no—
635C23—434no—
636C23—434no—
637C23—434no—
638C23—864no—
639C23—864no—
640C23—864no—
641C23—864no—
642C23—864no—
643C23—864no—
644C23—864no—
645C23—864no—
646C23—864no—
647C23—862no—
648C23—862no—
649C23—864no—
650C23—862no—
651C23—862no—
652C23—864no—
653C23—864no—
654C23—862no—
655C23—864no—
656C23—862no—
657C23—864no—
658C23—864no—
659C23—864no—
660C23—862no—
661C23—862no—
662C23—862no—
663C23—862no—
664C23—864no—
665C23—864no—
666C23—1722no—
667C23—1722no—
668C23—1722no—
669C23—1722no—
670C23—1722no—
671C23—1721no—
672C23—1721no—
673C23—1722no—
674C23—1721no—
675C23—1721no—
676C23C22×C4×D4311yescharacteristic
677C23C2×D4×D4311yescharacteristic
678C23C2×D4×D4311yescharacteristic
679C23C2×D4×D4311yescharacteristic
680C23C2×Q8×D4311yescharacteristic
681C23#41×D4311yescharacteristic
682C23#41×D4312yes—
683C23#41×D4311yescharacteristic
684C23C2×#1062190212yes—
685C23#1306337012yes—
686C23#1306337112yes—
687D4—8632no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—434no—
718C2×C4—864no—
719C2×C4—864no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—864no—
723C2×C4—862no—
724C2×C4—864no—
725C2×C4—864no—
726C2×C4—864no—
727C2×C4—17216no—
728C2×C4—17216no—
729C2×C4—17232no—
730C2×C4—1722no—
731C2×C4—1722no—
732C2×C4—1722no—
733C2×C4—1722no—
734C2×C4—1722no—
735C2×C4—1722no—
736C2×C4—1722no—
737C2×C4—1722no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1722no—
743C2×C4—1722no—
744C2×C4C22⋊C4×D4314yes—
745C2×C4C4⋊C4×D4314yes—
746C22—438no—
747C22—864no—
748C22—868no—
749C22—864no—
750C22—868no—
751C22—864no—
752C22—864no—
753C22—868no—
754C22—864no—
755C22—864no—
756C22—868no—
757C22—864no—
758C22—868no—
759C22—1722no—
760C22—1724no—
761C22—1722no—
762C22—1724no—
763C22—1722no—
764C22—1722no—
765C22—1722no—
766C22—1722no—
767C22—1724no—
768C22C2×C22⋊C4×D4311yescharacteristic
769C22C2×C4⋊C4×D4311yescharacteristic
770C22#117×D4311yescharacteristic
771C22C4×#1062190212yes—
772C22#1458337112yes—
773C22#121×D4311yescharacteristic
774C22#121×D4311yescharacteristic
775C22C22⋊Q8×D4311yescharacteristic
776C22C22⋊Q8×D4311yescharacteristic
777C22#1458341212yes—
778C22#1458344811yescharacteristic
779C22#1458345011yescharacteristic
780C22#1458345712yes—
781C22#1458345911yescharacteristic
782C22#1458346011yescharacteristic
783C22#1458354012yes—
784C22#1458354612yes—
785C22#1458357412yes—
786C22#1458357612yes—
787C22#1458359412yes—
788C22#1458360212yes—
789C22#1458360512yes—
790C22#1458361012yes—
791C4—24no—
792C4—24no—
793C4—42no—
794C4—44no—
795C4—82no—
796C4—864no—
797C4—3442no—
798C4—1722no—
799C4—1724no—
800C2—868no—
801C2—1724no—
802C2#380×D4311yescharacteristic
803C2#1913708411yescharacteristic
804C2#1913716911yescharacteristic
805C2#1913750412yes—
806C2#1913753412yes—
807C2#1913948612yes—
808C2#1913955611yescharacteristic
809C2#1913955811yescharacteristic
810C2#1913977611yescharacteristic
811C2#1913977811yescharacteristic
812C2#1913994312yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1441C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1441D43
hypocenterC43#13960
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. C2×#14582756C2semidirect
4. C2×#95×D43C2semidirect
5. #19132848C2semidirect
6. #19132841C2semidirect
7. #19132837C2semidirect
8. #19132821C2semidirect
9. (C2×D43)⋊#95C2semidirect
10. (C2×D43)⋊#95C2semidirect
11. C43×#1441C2semidirect
18. C2×#13063287C4semidirect
68. C22×C4×D43C2×C4semidirect
88. C2×(C2×D43)⋊C4C2×C4semidirect
91. C2×C4×Dic43C2×C4semidirect
108. C2×C4⋊C4×C43C2×C4semidirect
196. C2×D172C4⋊C4semidirect
213. C2×C4×D43C22⋊C4semidirect
399. #1441D43semidirect
447. C43#13960semidirect
490. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130632872
C2×#145827772
C2×#145827562
C2×#95×D432
#191328482
#191328412
#191328372
#191328212
(C2×D43)⋊#952
C43×#14412
#1396043