Finite Group Databasebeta

← #25023801

Subgroups — #25023801

Order 11008.

2150 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C2×#14582761C211yesmaximal, characteristic, complemented
3C2×#14582756C211yesmaximal, characteristic, complemented
4#19132849C211yesmaximal, characteristic, complemented
5#19132845C211yesmaximal, characteristic, complemented
6#19132843C212yesmaximal, complemented
7#19132840C211yesmaximal, characteristic, complemented
8#19132834C212yesmaximal
9#19132821C212yesmaximal, complemented
10#19132817C212yesmaximal, complemented
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)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2212yes—
23C22×(C2×D43)⋊C4C2212yes—
24C22×C4×Dic43C2211yescharacteristic
25#14582761—24no—
26#14582756—24no—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C22⋊C4×C43C2211yescharacteristic
37C22×C22⋊C4×C43C2212yes—
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2212yes—
40C24×D43C2311yescharacteristic
41C22×C22⋊D43—22no—
42C22×C22⋊D43—22no—
43C22×C22⋊D43—22no—
44C22×C22⋊D43—22no—
45C22×C22⋊D43—22no—
46C22×C22⋊D43—22no—
47C22×C22⋊D43C2×C414yes—
48C23×Dic43—22no—
49C23×Dic43—22no—
50C23×Dic43—42no—
51C23×Dic43—42no—
52C23×Dic43C2×C414yes—
53C23×Dic43C2312yes—
54C23×Dic43C2312yes—
55C23×Dic43C2311yescharacteristic
56C23×Dic43C2311yescharacteristic
57C23×Dic43C2311yescharacteristic
58C22×C4×D43—42no—
59C22×C4×D43—42no—
60C22×C4×D43C2×C414yes—
61C22×C4×D43D414yes—
62C22×C4×D43D414yes—
63(C22⋊D43)⋊C4—232no—
64C2×C4⋊Dic43—22no—
65C2×C4⋊Dic43—42no—
66C2×Dic43⋊C4—22no—
67C2×Dic43⋊C4—22no—
68C2×Dic43⋊C4C2×C414yes—
69C2×C22⋊Dic43—24no—
70C2×C22⋊Dic43—42no—
71C2×C22⋊Dic43—42no—
72C2×(C2×D43)⋊C4—22no—
73C2×(C2×D43)⋊C4—22no—
74C2×(C2×D43)⋊C4—24no—
75C2×(C2×D43)⋊C4—24no—
76C2×(C2×D43)⋊C4—42no—
77C2×(C2×D43)⋊C4—42no—
78C2×(C2×D43)⋊C4—42no—
79C2×(C2×D43)⋊C4—42no—
80C2×(C2×D43)⋊C4C2×C414yes—
81C2×C4×Dic43—22no—
82C2×C4×Dic43—22no—
83C2×C4×Dic43C2×C414yes—
84C43⋊#95—22no—
85C43⋊#95—24no—
86C43⋊#95—24no—
87C43⋊#95—24no—
88C43⋊#95—24no—
89C43⋊#95—42no—
90C43⋊#95—42no—
91C43⋊#95—42no—
92C25×C43C2311yescharacteristic
93C23×C4×C43C2312yes—
94C23×C4×C43C2312yes—
95C23×C4×C43C2311yescharacteristic
96C23×C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—42no—
99C2×C22⋊C4×C43—22no—
100C2×C22⋊C4×C43—22no—
101C2×C22⋊C4×C43—24no—
102C2×C22⋊C4×C43—42no—
103C2×C22⋊C4×C43—42no—
104C2×C22⋊C4×C43C2×C414yes—
105#95×C43—22no—
106#95×C43—42no—
107C24×C43—21no—
108C24×C43—21no—
109C24×C43—21no—
110C24×C43—21no—
111C24×C43—22no—
112C24×C43—22no—
113C24×C43—22no—
114C24×C43—22no—
115C24×C43C22×C412yes—
116C24×C43#4112yes—
117C24×C43#4112yes—
118C24×C43C2411yescharacteristic
119C23×D43—21no—
120C23×D43—21no—
121C23×D43—21no—
122C23×D43—21no—
123C23×D43—22no—
124C23×D43—22no—
125C23×D43—22no—
126C23×D43—22no—
127C23×D43C22×C412yes—
128C23×D43C2×D412yes—
129C23×D43C2×D412yes—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
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—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43C22×C412yes—
151C22×C4×C43C22×C412yes—
152C22×C4×C43C2×D412yes—
153C22×C4×C43C2×D412yes—
154C2×C22⋊D43—28no—
155C2×C22⋊D43—28no—
156C2×C22⋊D43—28no—
157C2×C22⋊D43—28no—
158C2×C22⋊D43—28no—
159C2×C22⋊D43—28no—
160C2×C22⋊D43—28no—
161C22×Dic43—28no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
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×Dic43—22no—
186C22×Dic43—48no—
187C22×Dic43—48no—
188C22×Dic43—44no—
189C22×Dic43—44no—
190C22×Dic43C22×C412yes—
191C22×Dic43C22×C412yes—
192C22×Dic43C22×C412yes—
193C22×Dic43C2×D412yes—
194C22×Dic43C2×D412yes—
195C22×Dic43#4112yes—
196C22×Dic43#4112yes—
197C2×C4×D43—48no—
198C2×C4×D43—48no—
199C2×C4×D43—44no—
200C2×C4×D43—44no—
201C2×C4×D43C22⋊C4116yescomplemented
202C4⋊C4×C43—44no—
203C22⋊C4×C43—28no—
204C22⋊C4×C43—48no—
205C22⋊Dic43—48no—
206(C2×D43)⋊C4—28no—
207(C2×D43)⋊C4—48no—
208(C2×D43)⋊C4—48no—
209C4⋊Dic43—44no—
210Dic43⋊C4—28no—
211C4×Dic43—28no—
212C23×C43—22no—
213C23×C43—22no—
214C23×C43—24no—
215C23×C43—24no—
216C23×C43—22no—
217C23×C43—22no—
218C23×C43—22no—
219C23×C43—22no—
220C23×C43—24no—
221C23×C43—24no—
222C23×C43—24no—
223C23×C43—24no—
224C23×C43—42no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—42no—
230C23×C43—42no—
231C23×C43—42no—
232C23×C43—42no—
233C23×C43—42no—
234C23×C43#11714yes—
235C23×C43C23×C411yescharacteristic
236C23×C43C22×D411yescharacteristic
237C23×C43C22×D411yescharacteristic
238C23×C43C2×#4111yescharacteristic
239C23×C43C2×#4111yescharacteristic
240C23×C43C2×#4111yescharacteristic
241C23×C43C2×#4111yescharacteristic
242C23×C43H(5,𝔽2)12yes—
243C23×C43H(5,𝔽2)12yes—
244C23×C43H(5,𝔽2)12yes—
245C23×C432−1+412yes—
246C22×D43—22no—
247C22×D43—22no—
248C22×D43—24no—
249C22×D43—24no—
250C22×D43—22no—
251C22×D43—22no—
252C22×D43—22no—
253C22×D43—22no—
254C22×D43—24no—
255C22×D43—22no—
256C22×D43—22no—
257C22×D43—22no—
258C22×D43—22no—
259C22×D43—24no—
260C22×D43—42no—
261C22×D43—42no—
262C22×D43—42no—
263C22×D43—42no—
264C22×D43—42no—
265C22×D43—42no—
266C22×D43—42no—
267C22×D43—42no—
268C22×D43C2×C22⋊C414yes—
269C2×C4×C43—24no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—24no—
273C2×C4×C43—22no—
274C2×C4×C43—24no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—42no—
278C2×C4×C43—42no—
279C2×C4×C43—42no—
280C2×C4×C43—42no—
281C2×C4×C43—42no—
282C2×C4×C43—42no—
283C2×C4×C43—42no—
284C2×C4×C43—42no—
285C2×C4×C43—42no—
286C2×C4×C43—42no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43—42no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43C2×C22⋊C414yes—
293C22⋊D43—232no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—24no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—24no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—24no—
306C2×Dic43—416no—
307C2×Dic43—42no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43C2×C22⋊C414yes—
325C2×Dic43#11714yes—
326C4×D43—416no—
327#14344—431nomaximal, Sylow
328C22×C43—28no—
329C22×C43—24no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—44no—
333C22×C43—44no—
334C22×C43—44no—
335C22×C43—42no—
336C22×C43—42no—
337C22×C43—42no—
338C22×C43—42no—
339C22×C43C22×C22⋊C411yescharacteristic
340C22×C43C2×#11711yescharacteristic
341C22×C43C2×#11711yescharacteristic
342C22×C43#51812yes—
343C22×C43#52012yes—
344C22×C43#52511yescharacteristic
345C22×C43#52511yescharacteristic
346C22×C43#52511yescharacteristic
347C22×C43#52511yescharacteristic
348C22×C43#53412yes—
349C22×C43#53411yescharacteristic
350C22×C43#53411yescharacteristic
351C22×C43#53511yescharacteristic
352C22×C43#53611yescharacteristic
353C22×C43#53712yes—
354C22×C43#53812yes—
355C22×C43#53812yes—
356C22×C43#53912yes—
357C22×C43#53912yes—
358C22×C43#54012yes—
359C22×C43#54012yes—
360C22×C43#54212yes—
361C22×C43#54212yes—
362C2×D43—24no—
363C2×D43—24no—
364C2×D43—24no—
365C2×D43—44no—
366C2×D43—44no—
367C2×D43—44no—
368C2×D43—44no—
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—42no—
373C4×C43—24no—
374C4×C43—42no—
375C4×C43—82no—
376C4×C43—82no—
377Dic43—24no—
378Dic43—24no—
379Dic43—42no—
380Dic43—82no—
381Dic43—82no—
382C22×C4×D4—431no—
383C2×#381—431no—
384C2×#380—431no—
385#1441—431no—
386#1441—431no—
387#1440—432no—
388#1439—431no—
389#1439D4311yescharacteristic, complemented
390#1438—432no—
391#1434—432no—
392C22⋊#95—432no—
393C2×C43—44no—
394C2×C43#228011yescharacteristic
395C2×C43#230811yescharacteristic
396C2×C43#231111yescharacteristic
397C2×C43#231812yes—
398C2×C43#231912yes—
399C2×C43#263012yes—
400C2×C43#263012yes—
401C2×C43#263511yescharacteristic
402C2×C43#263511yescharacteristic
403C2×C43#263811yescharacteristic
404C2×C43#263811yescharacteristic
405D43—44no—
406C23×D4—431no—
407C24×C4—431no—
408C24×C4—431no—
409C2×C4×D4—438no—
410C2×C4×D4—864no—
411C2×C4×D4—864no—
412C22×C4⋊C4—431no—
413C22×C4⋊C4—431no—
414C22×C4⋊C4C2×D4311yescharacteristic
415C22×C22⋊C4—431no—
416C22×C22⋊C4—432no—
417C22×C22⋊C4—432no—
418C22×C22⋊C4—432no—
419C22×C22⋊C4C2×D4311yescharacteristic
420C22×C22⋊C4C2×D4312yes—
421C22×C42—431no—
422#381—864no—
423#380—864no—
424C2×#95—432no—
425C2×#95—432no—
426C2×#95—432no—
427C2×#95—432no—
428C2×#95—431no—
429C2×#95—432no—
430C2×#95—432no—
431C2×#95—432no—
432C2×#95C2×D4311yescharacteristic
433C2×#95C2×D4312yes—
434C43#1434411yescharacteristic, complemented, Sylow
435C25—431no—
436C25C22×D4311yescharacteristic
437C22×D4—434no—
438C22×D4—862no—
439C22×D4—862no—
440C22×D4—862no—
441C22×D4—862no—
442C22×D4—862no—
443C22×D4—862no—
444C23×C4—431no—
445C23×C4—431no—
446C23×C4—434no—
447C23×C4—434no—
448C23×C4—434no—
449C23×C4—431no—
450C23×C4—434no—
451C23×C4—432no—
452C23×C4—432no—
453C23×C4—862no—
454C23×C4—862no—
455C23×C4—1722no—
456C23×C4—1722no—
457C23×C4—1722no—
458C23×C4—1722no—
459C23×C4C22×D4312yes—
460C23×C4C22×D4312yes—
461C23×C4C22×D4311yescharacteristic
462C23×C4C22×D4311yescharacteristic
463C4×D4—8632no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—434no—
467C2×C4⋊C4—862no—
468C2×C4⋊C4—862no—
469C2×C4⋊C4—862no—
470C2×C4⋊C4—1722no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—434no—
477C2×C22⋊C4—862no—
478C2×C22⋊C4—862no—
479C2×C22⋊C4—864no—
480C2×C22⋊C4—864no—
481C2×C22⋊C4—864no—
482C2×C22⋊C4—1722no—
483C2×C22⋊C4—1722no—
484C2×C22⋊C4—1722no—
485C2×C22⋊C4—1722no—
486C2×C22⋊C4—1722no—
487C2×C22⋊C4—1722no—
488C2×C22⋊C4C4×D4314yes—
489C2×C42—434no—
490C2×C42—862no—
491C2×C42—862no—
492#95—22no—
493#95—42no—
494#95—864no—
495#95—864no—
496#95—864no—
497#95—864no—
498#95—862no—
499#95—1722no—
500#95—1722no—
501#95—1722no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—432no—
511C24—432no—
512C24—432no—
513C24—861no—
514C24—861no—
515C24—861no—
516C24—861no—
517C24—862no—
518C24—862no—
519C24—862no—
520C24—862no—
521C24C2×C4×D4312yes—
522C24#1062190012yes—
523C24#1062190212yes—
524C24C23×D4311yescharacteristic
525C2×D4—868no—
526C2×D4—868no—
527C2×D4—868no—
528C2×D4—868no—
529C2×D4—868no—
530C2×D4—868no—
531C2×D4—868no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—432no—
553C22×C4—432no—
554C22×C4—432no—
555C22×C4—432no—
556C22×C4—432no—
557C22×C4—432no—
558C22×C4—4316no—
559C22×C4—432no—
560C22×C4—868no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—862no—
566C22×C4—862no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—862no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4—862no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—1728no—
586C22×C4—1728no—
587C22×C4—1724no—
588C22×C4—1724no—
589C22×C4—1728no—
590C22×C4—1728no—
591C22×C4—1724no—
592C22×C4—1724no—
593C22×C4C2×C4×D4312yes—
594C22×C4C2×C4×D4312yes—
595C22×C4D4×D4312yes—
596C22×C4D4×D4312yes—
597C4⋊C4—44no—
598C4⋊C4—868no—
599C4⋊C4—1724no—
600C22⋊C4—28no—
601C22⋊C4—48no—
602C22⋊C4—868no—
603C22⋊C4—1728no—
604C22⋊C4—1728no—
605C22⋊C4—1728no—
606C42—868no—
607C23—22no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—42no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—434no—
630C23—862no—
631C23—862no—
632C23—864no—
633C23—864no—
634C23—862no—
635C23—862no—
636C23—862no—
637C23—862no—
638C23—864no—
639C23—862no—
640C23—862no—
641C23—862no—
642C23—862no—
643C23—864no—
644C23—1722no—
645C23—1722no—
646C23—1722no—
647C23—1722no—
648C23—1722no—
649C23—1722no—
650C23—1722no—
651C23—1722no—
652C23#1306328314yes—
653C23C22×C4×D4311yescharacteristic
654C23C2×D4×D4311yescharacteristic
655C23C2×D4×D4311yescharacteristic
656C23#41×D4311yescharacteristic
657C23#41×D4311yescharacteristic
658C23C2×#1062190011yescharacteristic
659C23C2×#1062190211yescharacteristic
660C23#1306337012yes—
661C23#1306337012yes—
662C23#1306337112yes—
663C23#1306337212yes—
664D4—8632no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—434no—
689C2×C4—434no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—864no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—864no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—864no—
702C2×C4—17216no—
703C2×C4—17216no—
704C2×C4—1722no—
705C2×C4—1722no—
706C2×C4—1722no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4—1722no—
710C2×C4—1722no—
711C2×C4—1722no—
712C2×C4—1722no—
713C2×C4—1722no—
714C2×C4—1722no—
715C2×C4—1722no—
716C2×C4—1722no—
717C2×C4—1722no—
718C2×C4—1722no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4C22⋊C4×D4314yes—
722C22—28no—
723C22—24no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—44no—
733C22—864no—
734C22—864no—
735C22—864no—
736C22—1724no—
737C22—1724no—
738C22—1722no—
739C22—1722no—
740C22—1722no—
741C22—1722no—
742C22—1724no—
743C22—1724no—
744C22C2×C22⋊C4×D4311yescharacteristic
745C22#117×D4311yescharacteristic
746C22C2×#1306328311yescharacteristic
747C22#1458337112yes—
748C22#1458337812yes—
749C22#1458340911yescharacteristic
750C22#1458340911yescharacteristic
751C22#1458341211yescharacteristic
752C22#1458341211yescharacteristic
753C22#1458345712yes—
754C22#1458345911yescharacteristic
755C22#1458346011yescharacteristic
756C22#1458346211yescharacteristic
757C22#1458346911yescharacteristic
758C22#1458347812yes—
759C22#1458348412yes—
760C22#1458348912yes—
761C22#1458349312yes—
762C22#1458349812yes—
763C22#1458349912yes—
764C22#1458350112yes—
765C22#1458351312yes—
766C22#1458351512yes—
767C4—24no—
768C4—42no—
769C4—82no—
770C4—82no—
771C4—864no—
772C4—864no—
773C4—3442no—
774C4—3442no—
775C4—1722no—
776C2—44no—
777C2—1724no—
778C2#1913697711yescharacteristic
779C2#1913716911yescharacteristic
780C2#1913718511yescharacteristic
781C2#1913722312yes—
782C2#1913723612yes—
783C2#1914043912yes—
784C2#1914044112yes—
785C2#1914048411yescharacteristic
786C2#1914048511yescharacteristic
787C2#1914051711yescharacteristic
788C2#1914051811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1439C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenter#1439D43
hypocenterC43#14344
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#14582761C2semidirect
3. C2×#14582756C2semidirect
4. #19132849C2semidirect
5. #19132845C2semidirect
6. #19132843C2semidirect
7. #19132840C2semidirect
9. #19132821C2semidirect
10. #19132817C2semidirect
11. C43×#1439C2semidirect
17. C2×(C22⋊D43)⋊C4C4semidirect
201. C2×C4×D43C22⋊C4semidirect
389. #1439D43semidirect
434. C43#14344semidirect

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×#145827612
C2×#145827562
#191328492
#191328452
#191328432
#191328402
#191328342
#191328212
#191328172
C43×#14392
#1434443