Finite Group Databasebeta

← #25019367

Subgroups — #25019367

Order 11008.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063294C211yesmaximal, characteristic
2C22×C4×C22⋊D43C211yesmaximal, characteristic, complemented
3C2×#14582778C211yesmaximal, characteristic, complemented
4C2×#14582775C212yesmaximal, complemented
5C2×#14582755C211yesmaximal, characteristic, complemented
6#19132838C212yesmaximal, complemented
7#19132834C212yesmaximal, complemented
8#19132832C212yesmaximal, complemented
9#19132818C211yesmaximal, characteristic, complemented
10#19132818C211yesmaximal, characteristic, complemented
11C23×C22⋊C4×C43C211yesmaximal, characteristic, complemented
12C23×C22⋊D43C2212yes—
13C23×C22⋊D43C2211yescharacteristic
14C23×C4×D43C2211yescharacteristic, complemented
15C2×#13063294—24no—
16C2×#13063294—24no—
17C2×#13063294C418yescomplemented
18C2×C4×C22⋊D43—24no—
19C2×C4×C22⋊D43—24no—
20C2×C4×C22⋊D43—24no—
21C22×Dic43⋊C4C2211yescharacteristic, complemented
22C22×C22⋊Dic43C2211yescharacteristic
23C22×C22⋊Dic43C2212yes—
24C22×C22⋊Dic43C2212yes—
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2212yes—
27C22×C22⋊Dic43C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic, complemented
29C22×(C2×D43)⋊C4C2212yescomplemented
30C22×C4×Dic43C2211yescharacteristic, complemented
31#14582778—24no—
32#14582775—28no—
33#14582755—24no—
34C2×C43⋊#95C2212yescomplemented
35C2×C43⋊#95C2212yescomplemented
36C2×C43⋊#95C2212yescomplemented
37C2×C43⋊#95C2212yescomplemented
38C2×C43⋊#95C2212yescomplemented
39C26×C43C2211yescharacteristic
40C24×C4×C43C2211yescharacteristic
41C24×C4×C43C2211yescharacteristic
42C22×C22⋊C4×C43—24no—
43C22×C22⋊C4×C43—28no—
44C22×C22⋊C4×C43C2212yes—
45C22×C22⋊C4×C43C2212yes—
46C24×D43C2311yescharacteristic
47C22×C22⋊D43—22no—
48C22×C22⋊D43—22no—
49C22×C22⋊D43—22no—
50C22×C22⋊D43—22no—
51C22×C22⋊D43—24no—
52C22×C22⋊D43—24no—
53C22×C22⋊D43—24no—
54C22×C22⋊D43—24no—
55C22×C22⋊D43—42no—
56C22×C22⋊D43—42no—
57C22×C22⋊D43C2×C414yes—
58C22×C22⋊D43C2×C418yescomplemented
59C22×C22⋊D43D414yes—
60C22×C22⋊D43D414yes—
61C23×Dic43C2312yes—
62C23×Dic43C2312yes—
63C23×Dic43C2311yescharacteristic
64C23×Dic43C2311yescharacteristic
65C23×Dic43C2311yescharacteristic
66C22×C4×D43—22no—
67C22×C4×D43—22no—
68C22×C4×D43—22no—
69C22×C4×D43—24no—
70C22×C4×D43—42no—
71#13063294—232no—
72C4×C22⋊D43—232no—
73C2×Dic43⋊C4—22no—
74C2×Dic43⋊C4—22no—
75C2×Dic43⋊C4—22no—
76C2×C22⋊Dic43—22no—
77C2×C22⋊Dic43—22no—
78C2×C22⋊Dic43—22no—
79C2×C22⋊Dic43—22no—
80C2×C22⋊Dic43—24no—
81C2×C22⋊Dic43—24no—
82C2×C22⋊Dic43—22no—
83C2×C22⋊Dic43—24no—
84C2×C22⋊Dic43—22no—
85C2×C22⋊Dic43—24no—
86C2×C22⋊Dic43—22no—
87C2×C22⋊Dic43—24no—
88C2×C22⋊Dic43—24no—
89C2×C22⋊Dic43—42no—
90C2×C22⋊Dic43—42no—
91C2×C22⋊Dic43C2×C418yescomplemented
92C2×C22⋊Dic43C2×C414yescomplemented
93C2×C22⋊Dic43D414yescomplemented
94C2×(C2×D43)⋊C4—22no—
95C2×(C2×D43)⋊C4—22no—
96C2×(C2×D43)⋊C4—22no—
97C2×(C2×D43)⋊C4—24no—
98C2×(C2×D43)⋊C4—24no—
99C2×(C2×D43)⋊C4—42no—
100C2×C4×Dic43—22no—
101C2×C4×Dic43—22no—
102C2×C4×Dic43—22no—
103C43⋊#95—24no—
104C43⋊#95—24no—
105C43⋊#95—24no—
106C43⋊#95—42no—
107C43⋊#95—42no—
108C25×C43—24no—
109C25×C43—22no—
110C25×C43—24no—
111C25×C43—22no—
112C25×C43—22no—
113C25×C43—22no—
114C25×C43—22no—
115C25×C43—22no—
116C25×C43—42no—
117C25×C43—42no—
118C25×C43C2×C414yescomplemented
119C25×C43C2312yes—
120C25×C43C2311yescharacteristic
121C23×C4×C43—22no—
122C23×C4×C43—22no—
123C23×C4×C43—22no—
124C23×C4×C43—24no—
125C23×C4×C43—24no—
126C23×C4×C43—22no—
127C23×C4×C43—22no—
128C23×C4×C43—42no—
129C23×C4×C43—42no—
130C23×C4×C43D414yescomplemented
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2312yes—
133C23×C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—232no—
135C2×C22⋊C4×C43—24no—
136C2×C22⋊C4×C43—24no—
137C2×C22⋊C4×C43—24no—
138C2×C22⋊C4×C43—24no—
139C2×C22⋊C4×C43—24no—
140C2×C22⋊C4×C43D418yescomplemented
141C24×C43—22no—
142C24×C43—22no—
143C24×C43—22no—
144C24×C43—22no—
145C24×C43—28no—
146C24×C43—28no—
147C24×C43—216no—
148C24×C43—28no—
149C24×C43—216no—
150C24×C43—22no—
151C24×C43—22no—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43—22no—
157C24×C43—22no—
158C24×C43—22no—
159C24×C43—22no—
160C24×C43—22no—
161C24×C43—22no—
162C24×C43—28no—
163C24×C43—28no—
164C24×C43—48no—
165C24×C43—48no—
166C24×C43—48no—
167C24×C43—48no—
168C24×C43—48no—
169C24×C43—48no—
170C24×C43—48no—
171C24×C43—48no—
172C24×C43—48no—
173C24×C43—44no—
174C24×C43—44no—
175C24×C43—48no—
176C24×C43—44no—
177C24×C43—44no—
178C24×C43—44no—
179C24×C43—44no—
180C24×C43C22×C414yes—
181C24×C43C22×C412yes—
182C24×C43C2×D414yes—
183C24×C43C2×D412yes—
184C24×C43C2×D412yes—
185C24×C43C2×D412yes—
186C24×C43C2×D412yes—
187C24×C43#4114yes—
188C24×C43#4112yes—
189C24×C43#4112yes—
190C24×C43C2411yescharacteristic
191C23×D43—21no—
192C23×D43—21no—
193C23×D43—22no—
194C23×D43—21no—
195C23×D43—21no—
196C23×D43—22no—
197C23×D43—22no—
198C23×D43—22no—
199C23×D43C22×C412yes—
200C23×D43C2×D412yes—
201C23×D43C2×D412yes—
202C22×C4×C43—28no—
203C22×C4×C43—28no—
204C22×C4×C43—28no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—22no—
208C22×C4×C43—22no—
209C22×C4×C43—22no—
210C22×C4×C43—22no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—22no—
214C22×C4×C43—22no—
215C22×C4×C43—22no—
216C22×C4×C43—22no—
217C22×C4×C43—22no—
218C22×C4×C43—44no—
219C22×C4×C43—48no—
220C22×C4×C43—48no—
221C22×C4×C43—48no—
222C22×C4×C43—48no—
223C22×C4×C43—44no—
224C22×C4×C43—44no—
225C22×C4×C43C2×D412yes—
226C22×C4×C43C2×D414yes—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D414yes—
229C2×C22⋊D43—28no—
230C2×C22⋊D43—28no—
231C2×C22⋊D43—216no—
232C2×C22⋊D43—28no—
233C2×C22⋊D43—28no—
234C2×C22⋊D43—28no—
235C2×C22⋊D43—28no—
236C2×C22⋊D43—216no—
237C2×C22⋊D43—48no—
238C2×C22⋊D43—48no—
239C2×C22⋊D43—48no—
240C2×C22⋊D43—48no—
241C2×C22⋊D43—48no—
242C2×C22⋊D43C22⋊C4116yescomplemented
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—22no—
246C22×Dic43—22no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—22no—
250C22×Dic43—22no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—22no—
254C22×Dic43—22no—
255C22×Dic43—22no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—22no—
259C22×Dic43—22no—
260C22×Dic43—22no—
261C22×Dic43—22no—
262C22×Dic43—22no—
263C22×Dic43—22no—
264C22×Dic43—22no—
265C22×Dic43—22no—
266C22×Dic43—22no—
267C22×Dic43—22no—
268C22×Dic43C22×C414yes—
269C22×Dic43C22×C412yes—
270C22×Dic43C2×D412yes—
271C22×Dic43C2×D412yes—
272C22×Dic43C2×D412yes—
273C22×Dic43C2×D412yes—
274C2×C4×D43—28no—
275C2×C4×D43—48no—
276C2×C4×D43—48no—
277C2×C4×D43—44no—
278C2×C4×D43—44no—
279C22⋊C4×C43—216no—
280C22⋊C4×C43—216no—
281C22⋊Dic43—216no—
282C22⋊Dic43—28no—
283C22⋊Dic43—28no—
284C22⋊Dic43—48no—
285C22⋊Dic43—48no—
286C22⋊Dic43—44no—
287(C2×D43)⋊C4—28no—
288(C2×D43)⋊C4—48no—
289Dic43⋊C4—28no—
290C4×Dic43—28no—
291C23×C43—24no—
292C23×C43—24no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—24no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—24no—
299C23×C43—24no—
300C23×C43—24no—
301C23×C43—24no—
302C23×C43—24no—
303C23×C43—24no—
304C23×C43—24no—
305C23×C43—24no—
306C23×C43—24no—
307C23×C43—232no—
308C23×C43—24no—
309C23×C43—24no—
310C23×C43—24no—
311C23×C43—24no—
312C23×C43—24no—
313C23×C43—24no—
314C23×C43—24no—
315C23×C43—24no—
316C23×C43—24no—
317C23×C43—24no—
318C23×C43—24no—
319C23×C43—24no—
320C23×C43—24no—
321C23×C43—24no—
322C23×C43—24no—
323C23×C43—24no—
324C23×C43—24no—
325C23×C43—24no—
326C23×C43—432no—
327C23×C43—432no—
328C23×C43—416no—
329C23×C43—416no—
330C23×C43—416no—
331C23×C43—416no—
332C23×C43—432no—
333C23×C43—432no—
334C23×C43—416no—
335C23×C43—42no—
336C23×C43—42no—
337C23×C43—42no—
338C23×C43—42no—
339C23×C43—42no—
340C23×C43—42no—
341C23×C43—42no—
342C23×C43—42no—
343C23×C43—42no—
344C23×C43—42no—
345C23×C43—42no—
346C23×C43—42no—
347C23×C43—42no—
348C23×C43—42no—
349C23×C43—42no—
350C23×C43—42no—
351C23×C43—416no—
352C23×C43C2×C22⋊C414yes—
353C23×C43C4×D414yes—
354C23×C43C4×D414yes—
355C23×C43C4×D418yescomplemented
356C23×C43#12014yes—
357C23×C43#12114yes—
358C23×C43#12114yes—
359C23×C43#12314yes—
360C23×C43C23×C411yescharacteristic
361C23×C43C22×D411yescharacteristic
362C23×C43C22×D411yescharacteristic
363C23×C43C22×D411yescharacteristic
364C23×C43C22×D411yescharacteristic
365C23×C43C22×D412yes—
366C23×C43C2×#4111yescharacteristic
367C23×C43C2×#4111yescharacteristic
368C23×C43C2×#4112yes—
369C23×C43H(5,𝔽2)12yes—
370C23×C43H(5,𝔽2)12yes—
371C22×D43—22no—
372C22×D43—24no—
373C22×D43—22no—
374C22×D43—24no—
375C22×D43—22no—
376C22×D43—22no—
377C22×D43—22no—
378C22×D43—22no—
379C22×D43—24no—
380C22×D43—24no—
381C22×D43—24no—
382C22×D43—24no—
383C22×D43—41no—
384C22×D43—41no—
385C22×D43—42no—
386C22×D43—41no—
387C22×D43—41no—
388C22×D43—42no—
389C22×D43—42no—
390C22×D43—42no—
391C22×D43—42no—
392C22×D43—42no—
393C22×D43C2×C22⋊C414yescomplemented
394C2×C4×C43—22no—
395C2×C4×C43—22no—
396C2×C4×C43—24no—
397C2×C4×C43—24no—
398C2×C4×C43—22no—
399C2×C4×C43—22no—
400C2×C4×C43—24no—
401C2×C4×C43—22no—
402C2×C4×C43—24no—
403C2×C4×C43—24no—
404C2×C4×C43—416no—
405C2×C4×C43—416no—
406C2×C4×C43—42no—
407C2×C4×C43—42no—
408C2×C4×C43—42no—
409C2×C4×C43—42no—
410C2×C4×C43—42no—
411C2×C4×C43—42no—
412C2×C4×C43#12014yescomplemented
413C22⋊D43—232no—
414C22⋊D43—432no—
415C2×Dic43—22no—
416C2×Dic43—22no—
417C2×Dic43—22no—
418C2×Dic43—22no—
419C2×Dic43—22no—
420C2×Dic43—22no—
421C2×Dic43—24no—
422C2×Dic43—24no—
423C2×Dic43—24no—
424C2×Dic43—22no—
425C2×Dic43—22no—
426C2×Dic43—24no—
427C2×Dic43—24no—
428C2×Dic43—41no—
429C2×Dic43—41no—
430C2×Dic43—41no—
431C2×Dic43—41no—
432C2×Dic43—42no—
433C2×Dic43—42no—
434C2×Dic43—42no—
435C2×Dic43—42no—
436C2×Dic43—42no—
437C2×Dic43—42no—
438C2×Dic43—42no—
439C2×Dic43—42no—
440C2×Dic43—42no—
441C2×Dic43—42no—
442C2×Dic43—42no—
443C2×Dic43—42no—
444C2×Dic43—42no—
445C2×Dic43C2×C22⋊C414yescomplemented
446C4×D43—416no—
447#13967—431nomaximal, Sylow
448C22×C43—24no—
449C22×C43—28no—
450C22×C43—28no—
451C22×C43—24no—
452C22×C43—24no—
453C22×C43—24no—
454C22×C43—28no—
455C22×C43—28no—
456C22×C43—24no—
457C22×C43—24no—
458C22×C43—28no—
459C22×C43—28no—
460C22×C43—28no—
461C22×C43—464no—
462C22×C43—44no—
463C22×C43—44no—
464C22×C43—44no—
465C22×C43—44no—
466C22×C43—44no—
467C22×C43—44no—
468C22×C43—44no—
469C22×C43—44no—
470C22×C43—44no—
471C22×C43—44no—
472C22×C43—44no—
473C22×C43—44no—
474C22×C43#38618yescomplemented
475C22×C43C22×C22⋊C411yescharacteristic
476C22×C43C2×C4×D411yescharacteristic
477C22×C43C2×C4×D411yescharacteristic
478C22×C43C2×C4×D412yes—
479C22×C43#51812yes—
480C22×C43C2×#12011yescharacteristic
481C22×C43C2×#12011yescharacteristic
482C22×C43C2×#12111yescharacteristic
483C22×C43C2×#12111yescharacteristic
484C22×C43C2×#12311yescharacteristic
485C22×C43#52511yescharacteristic
486C22×C43#52512yes—
487C22×C43#53411yescharacteristic
488C22×C43#53511yescharacteristic
489C22×C43#53812yes—
490C22×C43D4212yes—
491C22×C43D4212yes—
492C22×C43D4212yes—
493C22×C43#54612yes—
494C22×C43#54612yes—
495C22×C43#54612yes—
496C22×C43#54612yes—
497C22×C43#55112yes—
498C2×D43—28no—
499C2×D43—24no—
500C2×D43—42no—
501C2×D43—44no—
502C2×D43—42no—
503C2×D43—42no—
504C2×D43—42no—
505C2×D43—44no—
506C2×D43—44no—
507C2×D43—42no—
508C2×D43—42no—
509C4×C43—24no—
510C4×C43—42no—
511C4×C43—44no—
512Dic43—24no—
513Dic43—44no—
514Dic43—42no—
515Dic43—42no—
516Dic43—82no—
517C22×#120—431no—
518C22×C4×D4—431no—
519C23×C22⋊C4D4311yescharacteristic, complemented
520C2×#386—431no—
521C2×#386—432no—
522C2×#379—431no—
523#1439—432no—
524#1438—432no—
525#1437—432no—
526C22⋊#95—431no—
527C22⋊#95—431no—
528C2×C43—28no—
529C2×C43—48no—
530C2×C43C2×#38611yescharacteristic
531C2×C43C4×#12011yescharacteristic
532C2×C43#232111yescharacteristic
533C2×C43D4×C22⋊C412yes—
534C2×C43#235812yes—
535C2×C43#240311yescharacteristic
536C2×C43#240411yescharacteristic
537C2×C43#240811yescharacteristic
538C2×C43#241812yes—
539C2×C43#242412yes—
540C2×C43#253411yescharacteristic
541D43—44no—
542C26C2×D4311yescharacteristic
543C23×D4—431no—
544C23×D4—432no—
545C24×C4—431no—
546C24×C4C2×D4311yescharacteristic
547C24×C4C2×D4311yescharacteristic
548C2×#120—438no—
549C2×#120—864no—
550C2×#120—864no—
551C2×C4×D4—864no—
552C2×C4×D4—864no—
553C2×C4×D4—864no—
554C22×C4⋊C4—431no—
555C22×C22⋊C4—24no—
556C22×C22⋊C4—28no—
557C22×C22⋊C4—431no—
558C22×C22⋊C4—431no—
559C22×C22⋊C4—432no—
560C22×C22⋊C4—431no—
561C22×C22⋊C4—431no—
562C22×C22⋊C4—432no—
563C22×C22⋊C4—432no—
564C22×C22⋊C4—432no—
565C22×C22⋊C4C2×D4312yes—
566C22×C22⋊C4C2×D4312yes—
567C22×C42—431no—
568#386—864no—
569#386—868no—
570#379—864no—
571C2×#95—432no—
572C2×#95—432no—
573C2×#95—432no—
574C2×#95—432no—
575C2×#95—432no—
576C43#1396711yescharacteristic, complemented, Sylow
577C25—24no—
578C25—22no—
579C25—24no—
580C25—22no—
581C25—22no—
582C25—22no—
583C25—22no—
584C25—22no—
585C25—42no—
586C25—42no—
587C25—431no—
588C25C4×D4314yescomplemented
589C25C22×D4312yes—
590C25C22×D4311yescharacteristic
591C22×D4—434no—
592C22×D4—434no—
593C22×D4—434no—
594C22×D4—438no—
595C22×D4—862no—
596C22×D4—862no—
597C22×D4—862no—
598C22×D4—862no—
599C22×D4—864no—
600C22×D4—864no—
601C22×D4—864no—
602C22×D4—864no—
603C22×D4—1722no—
604C22×D4—1722no—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—22no—
608C23×C4—24no—
609C23×C4—24no—
610C23×C4—22no—
611C23×C4—22no—
612C23×C4—42no—
613C23×C4—42no—
614C23×C4—431no—
615C23×C4—431no—
616C23×C4—431no—
617C23×C4—432no—
618C23×C4—432no—
619C23×C4—862no—
620C23×C4—862no—
621C23×C4—862no—
622C23×C4—864no—
623C23×C4—1722no—
624C23×C4C22⋊D4314yescomplemented
625C23×C4C22×D4311yescharacteristic
626C23×C4C22×D4312yes—
627C23×C4C22×D4311yescharacteristic
628#120—8632no—
629C4×D4—8632no—
630C2×C4⋊C4—862no—
631C2×C4⋊C4—862no—
632C2×C4⋊C4—862no—
633C2×C22⋊C4—232no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—438no—
640C2×C22⋊C4—434no—
641C2×C22⋊C4—434no—
642C2×C22⋊C4—862no—
643C2×C22⋊C4—862no—
644C2×C22⋊C4—864no—
645C2×C22⋊C4—864no—
646C2×C22⋊C4—862no—
647C2×C22⋊C4—862no—
648C2×C22⋊C4—862no—
649C2×C22⋊C4—862no—
650C2×C22⋊C4—862no—
651C2×C22⋊C4—864no—
652C2×C22⋊C4—864no—
653C2×C22⋊C4—864no—
654C2×C22⋊C4—864no—
655C2×C22⋊C4—862no—
656C2×C22⋊C4—862no—
657C2×C22⋊C4—862no—
658C2×C22⋊C4—864no—
659C2×C22⋊C4—864no—
660C2×C22⋊C4—1722no—
661C2×C22⋊C4—1722no—
662C2×C22⋊C4—1722no—
663C2×C22⋊C4C22⋊D4318yescomplemented
664C2×C42—862no—
665C2×C42—862no—
666C2×C42—862no—
667#95—864no—
668#95—864no—
669#95—864no—
670#95—1722no—
671#95—1722no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—28no—
677C24—216no—
678C24—28no—
679C24—28no—
680C24—216no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—28no—
694C24—28no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—48no—
700C24—48no—
701C24—48no—
702C24—48no—
703C24—48no—
704C24—44no—
705C24—44no—
706C24—48no—
707C24—44no—
708C24—44no—
709C24—44no—
710C24—44no—
711C24—432no—
712C24—432no—
713C24—432no—
714C24—861no—
715C24—861no—
716C24—862no—
717C24—861no—
718C24—861no—
719C24—862no—
720C24—862no—
721C24—862no—
722C24C2×C4×D4314yes—
723C24C2×C4×D4312yes—
724C24#1062189814yes—
725C24#1062189812yes—
726C24D4×D4312yes—
727C24D4×D4312yes—
728C24D4×D4312yes—
729C24#1062190012yes—
730C24C2×C22⋊D4314yes—
731C24C2×C22⋊D4312yes—
732C24C23×D4311yescharacteristic
733C2×D4—4316no—
734C2×D4—868no—
735C2×D4—868no—
736C2×D4—868no—
737C2×D4—868no—
738C2×D4—868no—
739C2×D4—868no—
740C2×D4—8616no—
741C2×D4—8616no—
742C2×D4—1728no—
743C2×D4—1728no—
744C2×D4—1728no—
745C2×D4—1728no—
746C2×D4—1728no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—28no—
751C22×C4—28no—
752C22×C4—22no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—28no—
763C22×C4—44no—
764C22×C4—48no—
765C22×C4—48no—
766C22×C4—48no—
767C22×C4—48no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—432no—
771C22×C4—432no—
772C22×C4—432no—
773C22×C4—434no—
774C22×C4—432no—
775C22×C4—432no—
776C22×C4—868no—
777C22×C4—861no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—861no—
781C22×C4—861no—
782C22×C4—862no—
783C22×C4—862no—
784C22×C4—861no—
785C22×C4—862no—
786C22×C4—862no—
787C22×C4—861no—
788C22×C4—861no—
789C22×C4—862no—
790C22×C4—862no—
791C22×C4—862no—
792C22×C4—862no—
793C22×C4—862no—
794C22×C4—862no—
795C22×C4—862no—
796C22×C4—862no—
797C22×C4—862no—
798C22×C4—862no—
799C22×C4—862no—
800C22×C4—862no—
801C22×C4—862no—
802C22×C4—1728no—
803C22×C4—1728no—
804C22×C4—1724no—
805C22×C4—1724no—
806C22×C4C2×C22⋊D4314yes—
807C22×C4C2×C22⋊D4312yes—
808C22×C4C2×C22⋊D4314yes—
809C22×C4C2×C22⋊D4312yes—
810C4⋊C4—868no—
811C22⋊C4—216no—
812C22⋊C4—216no—
813C22⋊C4—868no—
814C22⋊C4—8616no—
815C22⋊C4—868no—
816C22⋊C4—868no—
817C22⋊C4—1728no—
818C22⋊C4—1728no—
819C22⋊C4—1728no—
820C22⋊C4—1724no—
821C42—868no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—22no—
826C23—24no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—232no—
839C23—24no—
840C23—24no—
841C23—24no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—432no—
858C23—432no—
859C23—432no—
860C23—432no—
861C23—416no—
862C23—416no—
863C23—416no—
864C23—416no—
865C23—416no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—416no—
882C23—42no—
883C23—434no—
884C23—862no—
885C23—864no—
886C23—862no—
887C23—864no—
888C23—862no—
889C23—862no—
890C23—862no—
891C23—862no—
892C23—864no—
893C23—864no—
894C23—864no—
895C23—864no—
896C23—1722no—
897C23—1721no—
898C23—1722no—
899C23—1721no—
900C23—1721no—
901C23—1721no—
902C23—1722no—
903C23—1722no—
904C23—1722no—
905C23—1722no—
906C23C22⋊C4×D4314yes—
907C23(C22⋊D43)⋊C414yes—
908C23C4×C22⋊D4314yes—
909C23C4×C22⋊D4318yescomplemented
910C23#1306329314yes—
911C23#1306329614yes—
912C23#1306329814yes—
913C23#1306330714yes—
914C23C22×C4×D4311yescharacteristic
915C23C2×D4×D4311yescharacteristic
916C23C2×D4×D4311yescharacteristic
917C23C2×D4×D4311yescharacteristic
918C23C22×C22⋊D4311yescharacteristic
919C23C22×C22⋊D4312yes—
920C23C2×#1062190011yescharacteristic
921C23C2×#1062189812yes—
922C23C2×#1062189811yescharacteristic
923C23#1306337012yes—
924C23#1306337012yes—
925D4—8632no—
926D4—17232no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—416no—
938C2×C4—416no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—434no—
946C2×C4—862no—
947C2×C4—862no—
948C2×C4—862no—
949C2×C4—862no—
950C2×C4—862no—
951C2×C4—862no—
952C2×C4—864no—
953C2×C4—864no—
954C2×C4—864no—
955C2×C4—862no—
956C2×C4—862no—
957C2×C4—864no—
958C2×C4—864no—
959C2×C4—17216no—
960C2×C4—1722no—
961C2×C4—1722no—
962C2×C4—1722no—
963C2×C4—1722no—
964C2×C4—1722no—
965C2×C4—1722no—
966C2×C4—1722no—
967C2×C4—1721no—
968C2×C4—1721no—
969C2×C4—1721no—
970C2×C4—1721no—
971C2×C4—1722no—
972C2×C4—1722no—
973C2×C4—1722no—
974C2×C4—1722no—
975C2×C4—1722no—
976C2×C4—1722no—
977C2×C4#1306329414yescomplemented
978C22—28no—
979C22—28no—
980C22—24no—
981C22—28no—
982C22—24no—
983C22—24no—
984C22—28no—
985C22—24no—
986C22—24no—
987C22—24no—
988C22—28no—
989C22—28no—
990C22—28no—
991C22—464no—
992C22—44no—
993C22—44no—
994C22—44no—
995C22—44no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—44no—
1000C22—44no—
1001C22—44no—
1002C22—44no—
1003C22—44no—
1004C22—868no—
1005C22—864no—
1006C22—1724no—
1007C22—1724no—
1008C22—1722no—
1009C22—1724no—
1010C22—1722no—
1011C22—1722no—
1012C22—1722no—
1013C22—1722no—
1014C22—1722no—
1015C22#1458277518yescomplemented
1016C22C2×C22⋊C4×D4311yescharacteristic
1017C22C2×(C22⋊D43)⋊C411yescharacteristic
1018C22C2×C4×C22⋊D4312yes—
1019C22C2×C4×C22⋊D4311yescharacteristic
1020C22#1458337212yes—
1021C22C2×#1306329311yescharacteristic
1022C22C2×#1306329411yescharacteristic
1023C22C2×#1306329611yescharacteristic
1024C22C2×#1306329811yescharacteristic
1025C22C2×#1306330711yescharacteristic
1026C22#1458341012yes—
1027C22#1458341011yescharacteristic
1028C22#1458345811yescharacteristic
1029C22#1458346611yescharacteristic
1030C22#1458348712yes—
1031C22D4×C22⋊D4312yes—
1032C22D4×C22⋊D4312yes—
1033C22D4×C22⋊D4312yes—
1034C22#1458353912yes—
1035C22#1458353912yes—
1036C22#1458353912yes—
1037C22#1458354312yes—
1038C22#1458357512yes—
1039C4—24no—
1040C4—42no—
1041C4—44no—
1042C4—864no—
1043C4—3442no—
1044C4—1722no—
1045C4—1722no—
1046C4—1724no—
1047C2—28no—
1048C2—48no—
1049C2—1724no—
1050C2C2×#1458277511yescharacteristic
1051C2C4×#1306329411yescharacteristic
1052C2#1913725311yescharacteristic
1053C2C22⋊C4×C22⋊D4312yes—
1054C2#1913757412yes—
1055C2#1913790511yescharacteristic
1056C2#1913791411yescharacteristic
1057C2#1913794511yescharacteristic
1058C2#1913805712yes—
1059C2#1913813112yes—
1060C2#1913948511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC23×C22⋊C4×C43C2
socle, cosocleC24×C43C24
prime radicalC22×#13063294C2
hypercenterC23×C22⋊C4D43
hypocenterC43#13967
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D43C2semidirect
3. C2×#14582778C2semidirect
4. C2×#14582775C2semidirect
5. C2×#14582755C2semidirect
6. #19132838C2semidirect
7. #19132834C2semidirect
8. #19132832C2semidirect
9. #19132818C2semidirect
10. #19132818C2semidirect
11. C23×C22⋊C4×C43C2semidirect
14. C23×C4×D43C22semidirect
17. C2×#13063294C4semidirect
21. C22×Dic43⋊C4C22semidirect
28. C22×(C2×D43)⋊C4C22semidirect
29. C22×(C2×D43)⋊C4C22semidirect
30. C22×C4×Dic43C22semidirect
34. C2×C43⋊#95C22semidirect
35. C2×C43⋊#95C22semidirect
36. C2×C43⋊#95C22semidirect
37. C2×C43⋊#95C22semidirect
38. C2×C43⋊#95C22semidirect
58. C22×C22⋊D43C2×C4semidirect
91. C2×C22⋊Dic43C2×C4semidirect
92. C2×C22⋊Dic43C2×C4semidirect
93. C2×C22⋊Dic43D4semidirect
118. C25×C43C2×C4semidirect
130. C23×C4×C43D4semidirect
140. C2×C22⋊C4×C43D4semidirect
242. C2×C22⋊D43C22⋊C4semidirect
355. C23×C43C4×D4semidirect
393. C22×D43C2×C22⋊C4semidirect
412. C2×C4×C43#120semidirect
445. C2×Dic43C2×C22⋊C4semidirect
474. C22×C43#386semidirect
519. C23×C22⋊C4D43semidirect
576. C43#13967semidirect
588. C25C4×D43semidirect
624. C23×C4C22⋊D43semidirect
663. C2×C22⋊C4C22⋊D43semidirect
909. C23C4×C22⋊D43semidirect
977. C2×C4#13063294semidirect
1015. C22#14582775semidirect

Maximal subgroups

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

subgroupindex
C22×#130632942
C22×C4×C22⋊D432
C2×#145827782
C2×#145827752
C2×#145827552
#191328382
#191328342
#191328322
#191328182
C23×C22⋊C4×C432
#1396743