Finite Group Databasebeta

← #25019358

Subgroups — #25019358

Order 11008.

1862 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582758C211yesmaximal, characteristic
2C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
3C2×#95×D43C211yesmaximal, characteristic
4#19132853C212yesmaximal, complemented
5#19132850C212yesmaximal, complemented
6#19132822C211yesmaximal, characteristic, complemented
7#19132821C211yesmaximal, characteristic, complemented
8#19132821C211yesmaximal, characteristic, complemented
9(C2×D43)⋊#95C212yesmaximal
10(C2×D43)⋊#95C212yesmaximal
11C43×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D43C2212yes—
13C23×C4×D43C2211yescharacteristic
14C22×Dic43⋊C4C2212yes—
15C22×(C2×D43)⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2211yescharacteristic
17C22×(C2×D43)⋊C4C2211yescharacteristic
18C22×C4×Dic43C2211yescharacteristic
19#14582758—24no—
20C4×(C2×D43)⋊C4C418yescomplemented
21C2×C43⋊#95C2212yes—
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2211yescharacteristic
25C2×C43⋊#95C2211yescharacteristic
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2211yescharacteristic
32#95×D43—24no—
33C22×C42×C43C2211yescharacteristic
34C2×#95×C43C2212yes—
35C2×#95×C43C2211yescharacteristic
36C2×#95×C43C2211yescharacteristic
37C2×#95×C43C2212yes—
38C24×D43C2311yescharacteristic
39C23×Dic43C2312yes—
40C23×Dic43C2311yescharacteristic
41C23×Dic43C2311yescharacteristic
42C23×Dic43C2312yes—
43C23×Dic43C2311yescharacteristic
44C22×C4×D43—24no—
45C22×C4×D43—24no—
46C22×C4×D43—24no—
47C22×C4×D43—24no—
48C22×C4×D43—24no—
49C22×C4×D43—42no—
50C22×C4×D43—42no—
51C22×C4×D43—42no—
52C22×C4×D43—42no—
53C22×C4×D43C2×C414yes—
54C22×C4×D43D414yes—
55C22×C4×D43Q814yes—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—42no—
58C2×Dic43⋊C4—42no—
59C2×(C2×D43)⋊C4—22no—
60C2×(C2×D43)⋊C4—22no—
61C2×(C2×D43)⋊C4—22no—
62C2×(C2×D43)⋊C4—22no—
63C2×(C2×D43)⋊C4—24no—
64C2×(C2×D43)⋊C4—24no—
65C2×(C2×D43)⋊C4—24no—
66C2×(C2×D43)⋊C4C2×C414yes—
67C2×(C2×D43)⋊C4C2×C414yes—
68C2×C4×Dic43—42no—
69C2×C4×Dic43C2×C414yescomplemented
70C43⋊#95—22no—
71C43⋊#95—22no—
72C43⋊#95—24no—
73C43⋊#95—24no—
74C43⋊#95—24no—
75C43⋊#95—24no—
76C43⋊#95—42no—
77C43⋊#95—42no—
78C43⋊#95—42no—
79C43⋊#95C2×C414yescomplemented
80C43⋊#95C2×C414yescomplemented
81C23×C4×C43C2312yes—
82C23×C4×C43C2311yescharacteristic
83C23×C4×C43C2311yescharacteristic
84C23×C4×C43C2312yes—
85C23×C4×C43C2311yescharacteristic
86C2×C42×C43—42no—
87C2×C42×C43C2×C414yescomplemented
88#95×C43—22no—
89#95×C43—22no—
90#95×C43—24no—
91#95×C43—42no—
92C24×C43C2411yescharacteristic
93C23×D43—22no—
94C23×D43—22no—
95C23×D43—22no—
96C23×D43—22no—
97C23×D43C22×C412yes—
98C23×D43C2×D412yes—
99C23×D43C2×Q812yes—
100C23×D43#4112yes—
101C23×D43#4112yes—
102C23×D43#4112yes—
103C23×D43#4112yes—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43C22×C412yes—
128C22×C4×C43C22×C412yes—
129C22×C4×C43C22×C412yes—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×Q812yes—
132C22×C4×C43#4114yes—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43C22×C412yes—
157C22×Dic43C22×C412yes—
158C22×Dic43C22×C412yes—
159C22×Dic43C2×D412yes—
160C22×Dic43C2×Q812yes—
161C22×Dic43#4114yes—
162C2×C4×D43—216no—
163C2×C4×D43—44no—
164C2×C4×D43—44no—
165C2×C4×D43—48no—
166C2×C4×D43—48no—
167C2×C4×D43—48no—
168C2×C4×D43—48no—
169C2×C4×D43—48no—
170C2×C4×D43—48no—
171C2×C4×D43—48no—
172C2×C4×D43—48no—
173C2×C4×D43C4⋊C4116yes—
174C42×C43—44no—
175(C2×D43)⋊C4—28no—
176(C2×D43)⋊C4—28no—
177(C2×D43)⋊C4—48no—
178Dic43⋊C4—48no—
179C4×Dic43—44no—
180C23×C43C23×C411yescharacteristic
181C23×C43C22×D411yescharacteristic
182C23×C43C22×Q811yescharacteristic
183C23×C43C2×#4111yescharacteristic
184C23×C43C2×#4111yescharacteristic
185C23×C43C2×#4111yescharacteristic
186C23×C43C2×#4111yescharacteristic
187C23×C43C2×#4112yes—
188C23×C43C2×#4112yes—
189C23×C43H(5,𝔽2)12yes—
190C23×C43H(5,𝔽2)12yes—
191C22×D43—22no—
192C22×D43—22no—
193C22×D43—22no—
194C22×D43—22no—
195C22×D43—24no—
196C22×D43—24no—
197C22×D43—24no—
198C22×D43—24no—
199C22×D43—24no—
200C22×D43—24no—
201C22×D43—24no—
202C22×D43—24no—
203C22×D43—24no—
204C22×D43—24no—
205C22×D43—24no—
206C22×D43—24no—
207C22×D43C2×C4⋊C414yes—
208C22×D43#11714yes—
209C22×D43#11714yes—
210C22×D43#12414yes—
211C22×D43#12414yes—
212C22×D43#12514yes—
213C22×D43#12514yes—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—24no—
217C2×C4×C43—24no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—24no—
225C2×C4×C43—24no—
226C2×C4×C43—24no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43C2×C4⋊C414yes—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—24no—
246C2×Dic43—24no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—24no—
254C2×Dic43—24no—
255C2×Dic43—24no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43C2×C4⋊C414yes—
272C4×D43—416no—
273C4×D43—432no—
274#13966—431nomaximal, Sylow
275C22×C43C22×C4⋊C411yescharacteristic
276C22×C43C2×#11711yescharacteristic
277C22×C43C2×#11711yescharacteristic
278C22×C43C4×#4111yescharacteristic
279C22×C43C4×#4111yescharacteristic
280C22×C43#51811yescharacteristic
281C22×C43#51811yescharacteristic
282C22×C43#52512yes—
283C22×C43C2×#12411yescharacteristic
284C22×C43C2×#12411yescharacteristic
285C22×C43C2×#12511yescharacteristic
286C22×C43C2×#12511yescharacteristic
287C22×C43#53312yes—
288C22×C43#53412yes—
289C22×C43#54312yes—
290C22×C43#55112yes—
291C22×C43#55112yes—
292C22×C43#55112yes—
293C22×C43#55112yes—
294C22×C43#55312yes—
295C22×C43#55312yes—
296C22×C43#55312yes—
297C22×C43#55312yes—
298C2×D43—28no—
299C2×D43—28no—
300C2×D43—28no—
301C2×D43—24no—
302C2×D43—28no—
303C2×D43—24no—
304C2×D43—24no—
305C2×D43—24no—
306C2×D43—24no—
307C2×D43—24no—
308C2×D43#38218yes—
309C4×C43—24no—
310C4×C43—44no—
311C4×C43—42no—
312C4×C43—42no—
313C4×C43—82no—
314Dic43—24no—
315Dic43—44no—
316Dic43—42no—
317Dic43—42no—
318Dic43—82no—
319C2×#380—431no—
320C2×C4×C22⋊C4—431no—
321C22×#95—431no—
322#1442—432no—
323#1442—432no—
324#1434—431no—
325#1434—431no—
326#1434—431no—
327#1434D4311yescharacteristic, complemented
328C22⋊#95—432no—
329C22⋊#95—432no—
330C2×C43C2×#38211yescharacteristic
331C2×C43#229611yescharacteristic
332C2×C43#231511yescharacteristic
333C2×C43#235311yescharacteristic
334C2×C43#235311yescharacteristic
335C2×C43#235311yescharacteristic
336C2×C43#235311yescharacteristic
337C2×C43#256112yes—
338C2×C43#256912yes—
339C2×C43#256912yes—
340C2×C43#259112yes—
341D43—28no—
342C24×C4—431no—
343C24×C4—432no—
344C22×C4⋊C4—432no—
345C22×C22⋊C4—431no—
346C22×C22⋊C4—431no—
347C22×C22⋊C4—432no—
348C22×C42—431no—
349C22×C42C2×D4311yescharacteristic
350#380—864no—
351C4×C22⋊C4—438no—
352C2×#95—431no—
353C2×#95—431no—
354C2×#95—432no—
355C2×#95—432no—
356C2×#95—432no—
357C2×#95—431no—
358C2×#95—431no—
359C2×#95—432no—
360C2×#95—432no—
361C2×#95—432no—
362C2×#95—432no—
363C2×#95—864no—
364C2×#95C2×D4312yes—
365C2×#95C2×D4311yescharacteristic
366C2×#95C2×D4311yescharacteristic
367C2×#95C2×D4312yes—
368C43#1396611yescharacteristic, complemented, Sylow
369C25—431no—
370C23×C4—431no—
371C23×C4—434no—
372C23×C4—434no—
373C23×C4—434no—
374C23×C4—431no—
375C23×C4—431no—
376C23×C4—432no—
377C23×C4—432no—
378C23×C4—864no—
379C23×C4—864no—
380C23×C4—864no—
381C23×C4—864no—
382C23×C4—864no—
383C23×C4—1722no—
384C23×C4—1722no—
385C23×C4—1722no—
386C23×C4—1722no—
387C23×C4C22×D4312yes—
388C23×C4C22×D4311yescharacteristic
389C23×C4C22×D4311yescharacteristic
390C23×C4C22×D4312yes—
391C23×C4C22×D4311yescharacteristic
392C2×C4⋊C4—864no—
393C2×C4⋊C4—1722no—
394C2×C4⋊C4—1722no—
395C2×C22⋊C4—434no—
396C2×C22⋊C4—434no—
397C2×C22⋊C4—862no—
398C2×C22⋊C4—862no—
399C2×C22⋊C4—862no—
400C2×C22⋊C4—862no—
401C2×C22⋊C4—864no—
402C2×C22⋊C4—864no—
403C2×C22⋊C4—864no—
404C2×C42—42no—
405C2×C42—434no—
406C2×C42—1722no—
407C2×C42C4×D4314yescomplemented
408#95—24no—
409#95—22no—
410#95—22no—
411#95—42no—
412#95—434no—
413#95—434no—
414#95—864no—
415#95—864no—
416#95—864no—
417#95—864no—
418#95—862no—
419#95—862no—
420#95—1722no—
421#95—1722no—
422#95—1722no—
423C24—432no—
424C24—432no—
425C24—432no—
426C24—432no—
427C24—432no—
428C24—432no—
429C24—432no—
430C24—862no—
431C24—862no—
432C24—862no—
433C24—862no—
434C24C23×D4311yescharacteristic
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—432no—
459C22×C4—432no—
460C22×C4—432no—
461C22×C4—4316no—
462C22×C4—432no—
463C22×C4—432no—
464C22×C4—434no—
465C22×C4—8616no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—1724no—
490C22×C4—1724no—
491C22×C4—1728no—
492C22×C4—1728no—
493C22×C4—1728no—
494C22×C4—1728no—
495C22×C4—1728no—
496C22×C4—1728no—
497C22×C4—1728no—
498C22×C4—1728no—
499C22×C4C2×C4×D4312yes—
500C22×C4C2×C4×D4312yes—
501C22×C4C2×C4×D4312yes—
502C22×C4#1062189814yes—
503C22×C4D4×D4312yes—
504C22×C4Q8×D4312yes—
505C4⋊C4—1728no—
506C22⋊C4—868no—
507C22⋊C4—868no—
508C22⋊C4—1728no—
509C42—44no—
510C42—1724no—
511C23—434no—
512C23—434no—
513C23—434no—
514C23—434no—
515C23—434no—
516C23—434no—
517C23—434no—
518C23—864no—
519C23—864no—
520C23—864no—
521C23—864no—
522C23—864no—
523C23—864no—
524C23—864no—
525C23—864no—
526C23—862no—
527C23—862no—
528C23—862no—
529C23—862no—
530C23—864no—
531C23—864no—
532C23—864no—
533C23—864no—
534C23C22×C4×D4311yescharacteristic
535C23C2×D4×D4311yescharacteristic
536C23C2×Q8×D4311yescharacteristic
537C23#41×D4311yescharacteristic
538C23#41×D4311yescharacteristic
539C23#41×D4312yes—
540C23#41×D4311yescharacteristic
541C23#41×D4311yescharacteristic
542C23C2×#1062189812yes—
543C23#1306337012yes—
544C23#1306337112yes—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—434no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—864no—
577C2×C4—864no—
578C2×C4—864no—
579C2×C4—864no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—864no—
587C2×C4—17216no—
588C2×C4—17232no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4C4⋊C4×D4314yes—
605C22—438no—
606C22—864no—
607C22—864no—
608C22—864no—
609C22—868no—
610C22—864no—
611C22—868no—
612C22—868no—
613C22—868no—
614C22—864no—
615C22—864no—
616C22C2×C4⋊C4×D4311yescharacteristic
617C22#117×D4311yescharacteristic
618C22#117×D4311yescharacteristic
619C22#1458336711yescharacteristic
620C22C4×#1062189811yescharacteristic
621C22#1458337211yescharacteristic
622C22#1458337311yescharacteristic
623C22#1458340812yes—
624C22#124×D4311yescharacteristic
625C22#124×D4311yescharacteristic
626C22#125×D4311yescharacteristic
627C22#125×D4311yescharacteristic
628C22#1458345312yes—
629C22#1458345712yes—
630C22#1458352412yes—
631C22#1458357312yes—
632C22#1458357412yes—
633C22#1458357712yes—
634C22#1458357812yes—
635C22#1458359312yes—
636C22#1458359412yes—
637C22#1458359912yes—
638C22#1458360012yes—
639C4—24no—
640C4—42no—
641C4—44no—
642C4—42no—
643C4—82no—
644C4—864no—
645C4—3442no—
646C4—1722no—
647C4—1724no—
648C4—1722no—
649C2—868no—
650C2#382×D4311yescharacteristic
651C2#1913707511yescharacteristic
652C2#1913720811yescharacteristic
653C2#1913752811yescharacteristic
654C2#1913753211yescharacteristic
655C2#1913753611yescharacteristic
656C2#1913753811yescharacteristic
657C2#1913975112yes—
658C2#1913981712yes—
659C2#1913981812yes—
660C2#1914007312yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1434C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1434D43
hypocenterC43#13966
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
4. #19132853C2semidirect
5. #19132850C2semidirect
6. #19132822C2semidirect
7. #19132821C2semidirect
8. #19132821C2semidirect
11. C43×#1434C2semidirect
20. C4×(C2×D43)⋊C4C4semidirect
69. C2×C4×Dic43C2×C4semidirect
79. C43⋊#95C2×C4semidirect
80. C43⋊#95C2×C4semidirect
87. C2×C42×C43C2×C4semidirect
327. #1434D43semidirect
368. C43#13966semidirect
407. C2×C42C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827582
C2×C4×(C2×D43)⋊C42
C2×#95×D432
#191328532
#191328502
#191328222
#191328212
(C2×D43)⋊#952
C43×#14342
#1396643