Finite Group Databasebeta

← #24991977

Subgroups — #24991977

Order 11008.

964 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C8×D43C211yesmaximal, characteristic
2C2×#14582773C211yesmaximal, characteristic
3#19134504C211yesmaximal, characteristic
4C2×#14582624C211yesmaximal, characteristic, complemented
5C2×#14582624C211yesmaximal, characteristic, complemented
6#19132438C211yesmaximal, characteristic, complemented
7C43×#1280C211yesmaximal, characteristic, complemented
8C23×C4×D43C2211yescharacteristic
9C22×C8×D43—21no—
10C22×C4⋊Dic43C411yescharacteristic
11C22×Dic43⋊C4C2211yescharacteristic
12C22×(C2×D43)⋊C4C411yescharacteristic
13C22×(C2×D43)⋊C4C411yescharacteristic
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16C2×(C2×D43)⋊C8—21no—
17C2×(C2×D43)⋊C8—21no—
18C2×(C2×D43)⋊C8—21no—
19C22⋊C8×D43—22no—
20C22⋊C8×D43—22no—
21#14582773—21no—
22#14582773—21no—
23#14582773—21no—
24#14582773—21no—
25C2×C43⋊#95C411yescharacteristic
26#14582624—22no—
27#14582624—22no—
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C2×#95×C43C2211yescharacteristic
31C24×D43C2×C411yescharacteristic
32C23×Dic43C2×C411yescharacteristic
33C23×Dic43C2×C411yescharacteristic
34C23×Dic43C2×C411yescharacteristic
35C22×C4×D43—21no—
36C22×C4×D43—21no—
37C22×C4×D43—21no—
38C22×C4×D43—21no—
39C22×C4×D43—42no—
40C22×C4×D43—42no—
41C22×C4×D43D411yescharacteristic
42C22×C4×D43D411yescharacteristic
43C22×C4×D43D411yescharacteristic
44C22×C4×D43D411yescharacteristic
45C22×C43⋊C8—21no—
46C22×C43⋊C8—21no—
47C2×C8×D43—24no—
48C2×C8×D43—42no—
49C2×C8×D43—42no—
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—42no—
53C2×Dic43⋊C4—21no—
54C2×Dic43⋊C4—21no—
55C2×Dic43⋊C4—21no—
56C2×Dic43⋊C4—21no—
57C2×Dic43⋊C4—21no—
58C2×Dic43⋊C4—21no—
59C2×(C2×D43)⋊C4—21no—
60C2×(C2×D43)⋊C4—21no—
61C2×(C2×D43)⋊C4—22no—
62C2×(C2×D43)⋊C4—21no—
63C2×(C2×D43)⋊C4—21no—
64C2×(C2×D43)⋊C4—42no—
65C2×(C2×D43)⋊C4C814yescomplemented
66C22⋊(C43⋊C8)—21no—
67C22⋊(C43⋊C8)—21no—
68C22⋊(C43⋊C8)—21no—
69C22⋊(C43⋊C8)D412yes—
70(C2×D43)⋊C8—24no—
71(C2×D43)⋊C8—42no—
72(C2×D43)⋊C8—42no—
73C43⋊#95—21no—
74C43⋊#95—21no—
75C23×C4×C43C2×C411yescharacteristic
76C23×C4×C43C2×C411yescharacteristic
77C23×C4×C43C2311yescharacteristic
78C22×C8×C43—21no—
79C22×C8×C43—21no—
80C22⋊C8×C43—21no—
81C22⋊C8×C43—21no—
82C22⋊C8×C43—21no—
83C22⋊C8×C43D412yes—
84#95×C43—21no—
85#95×C43—21no—
86C24×C43C22×C411yescharacteristic
87C23×D43—21no—
88C23×D43—21no—
89C23×D43—21no—
90C23×D43—21no—
91C23×D43—22no—
92C23×D43—22no—
93C23×D43—41no—
94C23×D43—41no—
95C23×D43C22⋊C411yescharacteristic
96C23×D43C22⋊C411yescharacteristic
97C23×D43C2×C812yes—
98C23×D43M1612yes—
99C22×C4×C43—21no—
100C22×C4×C43—21no—
101C22×C4×C43—21no—
102C22×C4×C43—21no—
103C22×C4×C43—21no—
104C22×C4×C43—41no—
105C22×C4×C43—41no—
106C22×C4×C43—41no—
107C22×C4×C43—41no—
108C22×C4×C43—41no—
109C22×C4×C43—41no—
110C22×C4×C43C2×C812yescomplemented
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43#4111yescharacteristic
116C22×C4×C43#4111yescharacteristic
117C22×Dic43—22no—
118C22×Dic43—21no—
119C22×Dic43—21no—
120C22×Dic43—21no—
121C22×Dic43—21no—
122C22×Dic43—21no—
123C22×Dic43—21no—
124C22×Dic43—21no—
125C22×Dic43—21no—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—41no—
130C22×Dic43—41no—
131C22×Dic43—41no—
132C22×Dic43C22⋊C411yescharacteristic
133C22×Dic43C22⋊C411yescharacteristic
134C22×Dic43C2×C812yescomplemented
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—22no—
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43—21no—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—41no—
148C2×C4×D43—41no—
149C2×C4×D43—41no—
150C2×C4×D43—41no—
151C2×C4×D43—44no—
152C2×C4×D43—44no—
153C2×C4×D43—44no—
154C2×C4×D43—44no—
155C2×C8×C43—22no—
156C2×C8×C43—41no—
157C2×C8×C43—41no—
158C2×C8×C43—41no—
159C2×C8×C43—41no—
160C2×C8×C43—41no—
161(C2×D43)⋊C4—24no—
162(C2×D43)⋊C4—24no—
163(C2×D43)⋊C4—42no—
164(C2×D43)⋊C4—42no—
165C4⋊Dic43—42no—
166C4⋊Dic43—42no—
167Dic43⋊C4—41no—
168Dic43⋊C4—41no—
169Dic43⋊C4—41no—
170Dic43⋊C4—41no—
171C2×C43⋊C8—22no—
172C2×C43⋊C8—41no—
173C2×C43⋊C8—41no—
174C2×C43⋊C8—41no—
175C2×C43⋊C8—41no—
176C2×C43⋊C8—41no—
177C8×D43—48no—
178C23×C43—21no—
179C23×C43—21no—
180C23×C43—21no—
181C23×C43—21no—
182C23×C43C2×C22⋊C411yescharacteristic
183C23×C43C4×D411yescharacteristic
184C23×C43C4×D411yescharacteristic
185C23×C43C22×C811yescharacteristic
186C23×C43C2×M1611yescharacteristic
187C23×C43#13111yescharacteristic
188C23×C43#13111yescharacteristic
189C22×D43—21no—
190C22×D43—21no—
191C22×D43—21no—
192C22×D43—21no—
193C22×D43—21no—
194C22×D43—21no—
195C22×D43—21no—
196C22×D43—21no—
197C22×D43—21no—
198C22×D43—21no—
199C22×D43—22no—
200C22×D43—22no—
201C22×D43—22no—
202C22×D43—22no—
203C22×D43—24no—
204C22×D43—24no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43—42no—
212C22×D43—42no—
213C22×D43—42no—
214C22×D43—42no—
215C22×D43C22⋊C812yes—
216C22×D43C22⋊C812yes—
217C22×D43#9912yes—
218C22×D43#10112yes—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—22no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—42no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—42no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—81no—
236C2×C4×C43—81no—
237C2×C4×C43#12011yescharacteristic
238C2×C4×C43#12111yescharacteristic
239C2×C4×C43#12111yescharacteristic
240C2×C4×C43#12311yescharacteristic
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—22no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—81no—
259C2×Dic43—81no—
260C2×Dic43#9912yes—
261C4×D43—24no—
262C4×D43—24no—
263C4×D43—42no—
264C4×D43—42no—
265C4×D43—42no—
266C4×D43—42no—
267C4×D43—42no—
268C4×D43—42no—
269C8×C43—42no—
270C8×C43—81no—
271C43⋊C8—42no—
272C43⋊C8—81no—
273#9081—431nomaximal, Sylow
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—21no—
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—21no—
286C22×C43#38611yescharacteristic
287C22×C43C2×C22⋊C811yescharacteristic
288C22×C43#40811yescharacteristic
289C22×C43C2×#9911yescharacteristic
290C22×C43C2×#9911yescharacteristic
291C22×C43C2×#10111yescharacteristic
292C22×C43#41311yescharacteristic
293C22×C43C8×D411yescharacteristic
294C22×C43C8×D411yescharacteristic
295C22×C43#43511yescharacteristic
296C22×C43#43511yescharacteristic
297C2×D43—22no—
298C2×D43—22no—
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—22no—
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—44no—
307C2×D43—44no—
308C2×D43—44no—
309C2×D43—44no—
310C2×D43—41no—
311C2×D43—41no—
312C2×D43—41no—
313C2×D43—41no—
314C2×D43#32414yescomplemented
315C4×C43—21no—
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—21no—
319C4×C43—42no—
320C4×C43—81no—
321Dic43—22no—
322Dic43—42no—
323Dic43—41no—
324Dic43—81no—
325C22×C22⋊C8—431no—
326C2×#385—431no—
327#1779—431no—
328C2×#324—431no—
329C2×#324—431no—
330#1280—431no—
331#1280D4311yescharacteristic, complemented
332C2×C43—21no—
333C2×C43—21no—
334C2×C43—21no—
335C2×C43—21no—
336C2×C43C2×#32411yescharacteristic
337C2×C43#145911yescharacteristic
338C2×C43#146811yescharacteristic
339C2×C43#147211yescharacteristic
340C2×C43#186911yescharacteristic
341C2×C43#189811yescharacteristic
342C2×C43#190111yescharacteristic
343D43—24no—
344D43—42no—
345C24×C4—431no—
346C23×C8—861no—
347C22×C4⋊C4—431no—
348C22×C4⋊C4—431no—
349C22×C22⋊C4—431no—
350C22×C22⋊C4—431no—
351C2×C22⋊C8—431no—
352C2×C22⋊C8—431no—
353C2×C22⋊C8—862no—
354C2×C22⋊C8—861no—
355C2×C22⋊C8—862no—
356C2×C22⋊C8—861no—
357C2×C22⋊C8—861no—
358C2×C22⋊C8C2×D4311yescharacteristic
359C2×C22⋊C8C2×D4311yescharacteristic
360#385—861no—
361#385—861no—
362#385—861no—
363#385—861no—
364C2×#95—431no—
365C2×#95C2×D4311yescharacteristic
366#324—862no—
367#324—862no—
368C43#908111yescharacteristic, complemented, Sylow
369C25—431no—
370C23×C4—431no—
371C23×C4—431no—
372C23×C4—431no—
373C23×C4—431no—
374C23×C4—431no—
375C23×C4—431no—
376C23×C4—431no—
377C23×C4—861no—
378C23×C4—861no—
379C23×C4—861no—
380C23×C4—861no—
381C23×C4—1722no—
382C23×C4—1722no—
383C23×C4C4×D4311yescharacteristic
384C23×C4C4×D4311yescharacteristic
385C23×C4C22×D4311yescharacteristic
386C22×C8—21no—
387C22×C8—21no—
388C22×C8—864no—
389C22×C8—861no—
390C22×C8—861no—
391C22×C8—1722no—
392C22×C8—1722no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—1722no—
402C2×C22⋊C4—434no—
403C2×C22⋊C4—862no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—1722no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—432no—
413C22⋊C8—864no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416C22⋊C8—861no—
417C22⋊C8—1722no—
418C22⋊C8—1722no—
419C22⋊C8D17212yes—
420#95—21no—
421#95—21no—
422#95—861no—
423#95—861no—
424C24—431no—
425C24—431no—
426C24—432no—
427C24—432no—
428C24—862no—
429C24—862no—
430C24—861no—
431C24—861no—
432C24—861no—
433C24—861no—
434C24—1721no—
435C24—1721no—
436C24C2×C4×D4311yescharacteristic
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—432no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—1721no—
476C22×C4—1721no—
477C22×C4—1721no—
478C22×C4—1721no—
479C22×C4—1724no—
480C22×C4—1724no—
481C22×C4—1724no—
482C22×C4—1724no—
483C22×C4—1721no—
484C22×C4—1721no—
485C22×C4—1721no—
486C22×C4C8×D4312yescomplemented
487C22×C4C2×D17211yescharacteristic
488C22×C4#1062189811yescharacteristic
489C22×C4D4×D4311yescharacteristic
490C22×C4D4×D4311yescharacteristic
491C22×C4D4×D4311yescharacteristic
492C22×C4#1062190211yescharacteristic
493C2×C8—22no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—862no—
500C2×C8—1728no—
501C2×C8—1721no—
502C2×C8—1721no—
503C2×C8—1721no—
504C2×C8—1721no—
505C2×C8—1721no—
506C4⋊C4—1722no—
507C4⋊C4—1722no—
508C4⋊C4—1721no—
509C4⋊C4—1721no—
510C4⋊C4—1721no—
511C4⋊C4—1721no—
512C22⋊C4—864no—
513C22⋊C4—864no—
514C22⋊C4—1722no—
515C22⋊C4—1722no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—432no—
521C23—432no—
522C23—432no—
523C23—432no—
524C23—864no—
525C23—864no—
526C23—861no—
527C23—861no—
528C23—861no—
529C23—861no—
530C23—861no—
531C23—861no—
532C23—861no—
533C23—861no—
534C23—861no—
535C23—862no—
536C23—862no—
537C23—862no—
538C23—862no—
539C23—861no—
540C23—1722no—
541C23—1722no—
542C23—1722no—
543C23—1722no—
544C23—1722no—
545C23—1722no—
546C23—1722no—
547C23—1722no—
548C23—1722no—
549C23—1722no—
550C23C22⋊C4×D4311yescharacteristic
551C23#1306328711yescharacteristic
552C23C4×D17211yescharacteristic
553C23C2×C8×D4311yescharacteristic
554C23M16×D4311yescharacteristic
555C23#1306333111yescharacteristic
556C23#1306333311yescharacteristic
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—81no—
574C2×C4—81no—
575C2×C4—432no—
576C2×C4—864no—
577C2×C4—864no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—862no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—861no—
586C2×C4—3441no—
587C2×C4—3441no—
588C2×C4—1722no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4#1306329511yescharacteristic
604C2×C4#1306329811yescharacteristic
605C2×C4#1306330011yescharacteristic
606C2×C4#1306331011yescharacteristic
607C8—42no—
608C8—81no—
609C8—3441no—
610C8—1722no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—434no—
624C22—862no—
625C22—862no—
626C22—862no—
627C22—862no—
628C22—862no—
629C22—862no—
630C22—862no—
631C22—862no—
632C22—862no—
633C22—1724no—
634C22—1724no—
635C22—1724no—
636C22—1724no—
637C22—1721no—
638C22—1721no—
639C22—1721no—
640C22—1721no—
641C22#1458277711yescharacteristic
642C22C22⋊C8×D4311yescharacteristic
643C22#1458286411yescharacteristic
644C22#99×D4311yescharacteristic
645C22#99×D4311yescharacteristic
646C22#101×D4311yescharacteristic
647C22#1458288011yescharacteristic
648C22#1458296411yescharacteristic
649C22C8×D17211yescharacteristic
650C22#1458296911yescharacteristic
651C22#1458297211yescharacteristic
652C4—21no—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—42no—
657C4—81no—
658C4—862no—
659C4—3441no—
660C4—1721no—
661C4—1722no—
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—864no—
667C2—1722no—
668C2#324×D4311yescharacteristic
669C2#1913291011yescharacteristic
670C2#1913294011yescharacteristic
671C2#1913295711yescharacteristic
672C2#1913488611yescharacteristic
673C2#1913504711yescharacteristic
674C2#1913506211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC23×C43C22×C8
FrattiniC23×C4C22×D43
FittingC43×#1280C2
socleC23×C43C2×C22⋊C4
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenter#1280D43
hypocenterC43#9081
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
4. C2×#14582624C2semidirect
5. C2×#14582624C2semidirect
6. #19132438C2semidirect
7. C43×#1280C2semidirect
65. C2×(C2×D43)⋊C4C8semidirect
110. C22×C4×C43C2×C8semidirect
134. C22×Dic43C2×C8semidirect
314. C2×D43#324semidirect
331. #1280D43semidirect
368. C43#9081semidirect
486. C22×C4C8×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C8×D432
C2×#145827732
#191345042
C2×#145826242
#191324382
C43×#12802
#908143