Finite Group Databasebeta

← #25018576

Subgroups — #25018576

Order 11008.

2006 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063283C211yesmaximal, characteristic
2C2×#14582768C211yesmaximal, characteristic, complemented
3C2×#14582756C211yesmaximal, characteristic
4C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
5#19132839C214yesmaximal
6#19132826C214yesmaximal, complemented
7#19132825C211yesmaximal, characteristic, complemented
8#19132824C211yesmaximal, characteristic, complemented
9C2×C43×#382C211yesmaximal, characteristic, complemented
10C23×C4×D43C2211yescharacteristic
11C2×#13063283—24no—
12C2×#13063283—24no—
13C2×#13063283—24no—
14C22×C4⋊Dic43C2211yescharacteristic
15C22×C4⋊Dic43C2211yescharacteristic
16C22×Dic43⋊C4C2214yes—
17C22×(C2×D43)⋊C4C2212yes—
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2212yes—
20C22×C4×Dic43C2212yes—
21C22×C4×Dic43C2211yescharacteristic
22#14582768—24no—
23#14582756—24no—
24C4×(C2×D43)⋊C4C418yescomplemented
25C2×C43⋊#95C2214yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2214yes—
28C2×C43⋊#95C2212yes—
29C22×C4⋊C4×C43C2211yescharacteristic
30C22×C4⋊C4×C43C2211yescharacteristic
31C22×C42×C43C2211yescharacteristic
32C43×#382—24no—
33C2×#95×C43C2214yes—
34C24×D43C2311yescharacteristic
35C23×Dic43C2312yes—
36C23×Dic43C2312yes—
37C23×Dic43C2311yescharacteristic
38C23×Dic43C2312yes—
39C22×C4×D43—22no—
40C22×C4×D43—22no—
41C22×C4×D43—22no—
42C22×C4×D43—22no—
43C22×C4×D43C2×C414yes—
44C22×C4×D43D414yes—
45C22×C4×D43Q814yes—
46#13063283—232no—
47C2×C4⋊Dic43—22no—
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43—22no—
50C2×C4⋊Dic43—22no—
51C2×C4⋊Dic43—22no—
52C2×C4⋊Dic43D414yes—
53C2×Dic43⋊C4—28no—
54C2×Dic43⋊C4—28no—
55C2×Dic43⋊C4—44no—
56C2×(C2×D43)⋊C4—24no—
57C2×(C2×D43)⋊C4—24no—
58C2×(C2×D43)⋊C4—24no—
59C2×(C2×D43)⋊C4—24no—
60C2×(C2×D43)⋊C4—24no—
61C2×(C2×D43)⋊C4—24no—
62C2×(C2×D43)⋊C4—44no—
63C2×(C2×D43)⋊C4C2×C418yes—
64C2×C4×Dic43—24no—
65C2×C4×Dic43—22no—
66C2×C4×Dic43—22no—
67C2×C4×Dic43—24no—
68C2×C4×Dic43—24no—
69C2×C4×Dic43C2×C414yes—
70C43⋊#95—24no—
71C43⋊#95—28no—
72C43⋊#95—44no—
73C43⋊#95C2×C418yes—
74C23×C4×C43C2312yes—
75C23×C4×C43C2312yes—
76C23×C4×C43C2312yes—
77C23×C4×C43C2311yescharacteristic
78C2×C4⋊C4×C43—22no—
79C2×C4⋊C4×C43—22no—
80C2×C4⋊C4×C43—22no—
81C2×C4⋊C4×C43—22no—
82C2×C4⋊C4×C43—22no—
83C2×C4⋊C4×C43D414yes—
84C2×C42×C43—22no—
85C2×C42×C43—22no—
86C2×C42×C43C2×C414yes—
87#95×C43—28no—
88C24×C43C2411yescharacteristic
89C23×D43—21no—
90C23×D43—21no—
91C23×D43—22no—
92C23×D43—22no—
93C23×D43—21no—
94C23×D43—21no—
95C23×D43—22no—
96C23×D43—22no—
97C23×D43C22×C412yes—
98C23×D43C2×D412yes—
99C23×D43C2×Q812yes—
100C22×C4×C43—22no—
101C22×C4×C43—22no—
102C22×C4×C43—22no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—24no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—24no—
111C22×C4×C43—22no—
112C22×C4×C43—24no—
113C22×C4×C43—22no—
114C22×C4×C43—24no—
115C22×C4×C43C22×C414yes—
116C22×C4×C43C22×C412yes—
117C22×C4×C43C2×D412yes—
118C22×C4×C43C2×D412yes—
119C22×C4×C43C2×D414yes—
120C22×C4×C43C2×D412yes—
121C22×C4×C43C2×Q812yes—
122C22×C4×C43#4112yes—
123C22×C4×C43#4112yes—
124C22×Dic43—21no—
125C22×Dic43—21no—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—24no—
134C22×Dic43—24no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—24no—
139C22×Dic43—24no—
140C22×Dic43—22no—
141C22×Dic43C22×C412yes—
142C22×Dic43C22×C414yes—
143C22×Dic43C2×D414yes—
144C22×Dic43C2×D412yes—
145C22×Dic43C2×Q812yes—
146C22×Dic43#4114yes—
147C22×Dic43#4114yes—
148C2×C4×D43—28no—
149C2×C4×D43—28no—
150C2×C4×D43—28no—
151C2×C4×D43—28no—
152C2×C4×D43—28no—
153C2×C4×D43—28no—
154C2×C4×D43C4⋊C4116yescomplemented
155C4⋊C4×C43—28no—
156C4⋊C4×C43—44no—
157C42×C43—28no—
158(C2×D43)⋊C4—216no—
159(C2×D43)⋊C4—216no—
160(C2×D43)⋊C4—48no—
161C4⋊Dic43—28no—
162C4⋊Dic43—44no—
163Dic43⋊C4—416no—
164C4×Dic43—216no—
165C4×Dic43—28no—
166C23×C43C23×C411yescharacteristic
167C23×C43C22×D411yescharacteristic
168C23×C43C22×D411yescharacteristic
169C23×C43C22×D411yescharacteristic
170C23×C43C22×Q811yescharacteristic
171C23×C43C2×#4112yes—
172C23×C43C2×#4112yes—
173C23×C43C2×#4111yescharacteristic
174C23×C43C2×#4111yescharacteristic
175C23×C43H(5,𝔽2)12yes—
176C23×C432−1+412yes—
177C22×D43—24no—
178C22×D43—22no—
179C22×D43—22no—
180C22×D43—24no—
181C22×D43—22no—
182C22×D43—22no—
183C22×D43—22no—
184C22×D43—22no—
185C22×D43—22no—
186C22×D43—22no—
187C22×D43—24no—
188C22×D43—22no—
189C22×D43—22no—
190C22×D43—24no—
191C22×D43—42no—
192C22×D43—42no—
193C22×D43—42no—
194C22×D43—42no—
195C22×D43—42no—
196C22×D43—42no—
197C22×D43—42no—
198C22×D43—42no—
199C22×D43C2×C4⋊C414yes—
200C2×C4×C43—24no—
201C2×C4×C43—24no—
202C2×C4×C43—24no—
203C2×C4×C43—24no—
204C2×C4×C43—28no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—44no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—44no—
216C2×C4×C43—44no—
217C2×C4×C43C2×C4⋊C414yes—
218C2×C4×C43C4×D414yes—
219C2×C4×C43C4×D414yes—
220C2×C4×C43#12014yes—
221C2×C4×C43C22⋊Q814yes—
222C2×C4×C43C22⋊Q814yes—
223C2×C4×C43#12314yes—
224C2×Dic43—24no—
225C2×Dic43—22no—
226C2×Dic43—22no—
227C2×Dic43—24no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—24no—
233C2×Dic43—24no—
234C2×Dic43—24no—
235C2×Dic43—24no—
236C2×Dic43—24no—
237C2×Dic43—28no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—44no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—44no—
245C2×Dic43—44no—
246C2×Dic43C2×C4⋊C414yes—
247C2×Dic43#11718yescomplemented
248C4×D43—232no—
249#13879—431nomaximal, Sylow
250C22×C43C22×C4⋊C411yescharacteristic
251C22×C43C2×#11712yes—
252C22×C43C2×C4×D411yescharacteristic
253C22×C43C2×C4×D411yescharacteristic
254C22×C43#52012yes—
255C22×C43C2×#12011yescharacteristic
256C22×C43C2×C22⋊Q811yescharacteristic
257C22×C43C2×C22⋊Q811yescharacteristic
258C22×C43C2×#12311yescharacteristic
259C22×C43#53211yescharacteristic
260C22×C43#53211yescharacteristic
261C22×C43#53312yes—
262C22×C43#53511yescharacteristic
263C22×C43#53611yescharacteristic
264C22×C43#54412yes—
265C22×C43#54612yes—
266C22×C43#54712yes—
267C22×C43#54812yes—
268C22×C43#55012yes—
269C22×C43#55212yes—
270C22×C43#55312yes—
271C22×C43#55512yes—
272C22×C43#55612yes—
273C2×D43—24no—
274C2×D43—24no—
275C2×D43—24no—
276C2×D43—44no—
277C2×D43—44no—
278C2×D43—42no—
279C2×D43—42no—
280C2×D43—44no—
281C2×D43—44no—
282C2×D43—42no—
283C2×D43—42no—
284C4×C43—44no—
285C4×C43—44no—
286C4×C43—82no—
287C4×C43#38518yes—
288Dic43—28no—
289Dic43—24no—
290Dic43—44no—
291Dic43—82no—
292C22×#117—431no—
293C2×#384—431no—
294C2×#382D4311yescharacteristic, complemented
295C2×#380—431no—
296C2×C4×C22⋊C4—431no—
297#1439—434no—
298#1436—434no—
299C4⋊#95—431no—
300C4⋊#95—431no—
301C2×C43#228511yescharacteristic
302C2×C43C2×#38511yescharacteristic
303C2×C43#231711yescharacteristic
304C2×C43#235212yes—
305C2×C43#235412yes—
306C2×C43#243111yescharacteristic
307C2×C43#243211yescharacteristic
308C2×C43#243912yes—
309C2×C43#244112yes—
310C2×C43#249911yescharacteristic
311C2×C43#250011yescharacteristic
312D43—44no—
313C24×C4—431no—
314C2×#117—864no—
315C2×#117—864no—
316C2×#117—864no—
317C22×C4⋊C4—431no—
318C22×C4⋊C4—431no—
319C22×C4⋊C4—434no—
320C22×C4⋊C4C2×D4311yescharacteristic
321C22×C4⋊C4C2×D4311yescharacteristic
322C22×C22⋊C4—432no—
323C22×C22⋊C4—432no—
324C22×C22⋊C4—432no—
325C22×C42—431no—
326C22×C42—432no—
327C22×C42C2×D4311yescharacteristic
328#384—864no—
329#382—24no—
330#380—864no—
331C4×C22⋊C4—438no—
332C2×#95—432no—
333C2×#95—434no—
334C2×#95—432no—
335C2×#95—434no—
336C2×#95C2×D4314yes—
337C43#1387911yescharacteristic, complemented, Sylow
338C25—431no—
339C23×C4—432no—
340C23×C4—431no—
341C23×C4—434no—
342C23×C4—434no—
343C23×C4—434no—
344C23×C4—432no—
345C23×C4—432no—
346C23×C4—862no—
347C23×C4—862no—
348C23×C4—862no—
349C23×C4—862no—
350C23×C4C22×D4312yes—
351C23×C4C22×D4312yes—
352C23×C4C22×D4312yes—
353C23×C4C22×D4311yescharacteristic
354#117—8632no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—434no—
361C2×C4⋊C4—862no—
362C2×C4⋊C4—862no—
363C2×C4⋊C4—868no—
364C2×C4⋊C4—868no—
365C2×C4⋊C4—862no—
366C2×C4⋊C4—862no—
367C2×C4⋊C4—862no—
368C2×C4⋊C4—1724no—
369C2×C4⋊C4C22⋊D4314yes—
370C2×C22⋊C4—438no—
371C2×C22⋊C4—864no—
372C2×C22⋊C4—864no—
373C2×C22⋊C4—864no—
374C2×C22⋊C4—864no—
375C2×C22⋊C4—864no—
376C2×C22⋊C4—864no—
377C2×C22⋊C4—1724no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—434no—
381C2×C42—864no—
382C2×C42—864no—
383C2×C42—862no—
384C2×C42—862no—
385C2×C42—864no—
386C2×C42C4×D4314yes—
387#95—28no—
388#95—438no—
389#95—868no—
390#95—864no—
391#95—1724no—
392C24—432no—
393C24—432no—
394C24—432no—
395C24—861no—
396C24—861no—
397C24—862no—
398C24—862no—
399C24—861no—
400C24—861no—
401C24—862no—
402C24—862no—
403C24C23×D4311yescharacteristic
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—432no—
420C22×C4—434no—
421C22×C4—432no—
422C22×C4—432no—
423C22×C4—434no—
424C22×C4—434no—
425C22×C4—4316no—
426C22×C4—434no—
427C22×C4—861no—
428C22×C4—862no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—862no—
432C22×C4—861no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4—868no—
436C22×C4—868no—
437C22×C4—868no—
438C22×C4—868no—
439C22×C4—868no—
440C22×C4—868no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—864no—
444C22×C4—864no—
445C22×C4—862no—
446C22×C4—864no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—864no—
450C22×C4C2×C4×D4314yes—
451C22×C4C2×C4×D4312yes—
452C22×C4#1062189812yes—
453C22×C4D4×D4312yes—
454C22×C4D4×D4312yes—
455C22×C4Q8×D4312yes—
456C22×C4#1062190212yes—
457C22×C4C2×C22⋊D4314yes—
458C22×C4C2×C22⋊D4312yes—
459C4⋊C4—28no—
460C4⋊C4—44no—
461C4⋊C4—868no—
462C4⋊C4—17216no—
463C4⋊C4—1724no—
464C22⋊C4—8616no—
465C22⋊C4—8616no—
466C22⋊C4—1728no—
467C42—28no—
468C42—8616no—
469C42—868no—
470C23—434no—
471C23—864no—
472C23—862no—
473C23—862no—
474C23—864no—
475C23—862no—
476C23—862no—
477C23—862no—
478C23—862no—
479C23—862no—
480C23—862no—
481C23—864no—
482C23—862no—
483C23—862no—
484C23—864no—
485C23—1722no—
486C23—1722no—
487C23—1722no—
488C23—1722no—
489C23—1722no—
490C23—1722no—
491C23—1722no—
492C23—1722no—
493C23C22×C4×D4311yescharacteristic
494C23C2×D4×D4311yescharacteristic
495C23C2×D4×D4311yescharacteristic
496C23C22×C22⋊D4311yescharacteristic
497C23C2×Q8×D4311yescharacteristic
498C23#41×D4312yes—
499C23#41×D4312yes—
500C23C2×#1062189811yescharacteristic
501C23C2×#1062190211yescharacteristic
502C23#1306337112yes—
503C23#1306337212yes—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—28no—
509C2×C4—44no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—44no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—434no—
522C2×C4—438no—
523C2×C4—864no—
524C2×C4—864no—
525C2×C4—864no—
526C2×C4—862no—
527C2×C4—864no—
528C2×C4—862no—
529C2×C4—864no—
530C2×C4—862no—
531C2×C4—862no—
532C2×C4—862no—
533C2×C4—862no—
534C2×C4—864no—
535C2×C4—8632no—
536C2×C4—864no—
537C2×C4—868no—
538C2×C4—1724no—
539C2×C4—1724no—
540C2×C4—1722no—
541C2×C4—1722no—
542C2×C4—1722no—
543C2×C4—1724no—
544C2×C4—1722no—
545C2×C4—1722no—
546C2×C4C4⋊C4×D4314yes—
547C2×C4C4×C22⋊D4314yes—
548C2×C4#1306328714yes—
549C2×C4#1306329314yes—
550C2×C4#1306330114yes—
551C2×C4#1306330314yes—
552C2×C4#1306331014yes—
553C22—864no—
554C22—864no—
555C22—864no—
556C22—1724no—
557C22—1724no—
558C22—1722no—
559C22—1722no—
560C22—1722no—
561C22—1724no—
562C22—1724no—
563C22—1722no—
564C22C2×C4⋊C4×D4311yescharacteristic
565C22#117×D4312yes—
566C22C2×C4×C22⋊D4311yescharacteristic
567C22C2×#1306328711yescharacteristic
568C22#1458337912yes—
569C22C2×#1306329311yescharacteristic
570C22C2×#1306330111yescharacteristic
571C22C2×#1306330311yescharacteristic
572C22C2×#1306331011yescharacteristic
573C22#1458344811yescharacteristic
574C22#1458344811yescharacteristic
575C22#1458345512yes—
576C22#1458346711yescharacteristic
577C22#1458346911yescharacteristic
578C22#1458352912yes—
579C22#1458354212yes—
580C22#1458354812yes—
581C22#1458355712yes—
582C22#1458356812yes—
583C22#1458358712yes—
584C22#1458360212yes—
585C22#1458361212yes—
586C22#1458361712yes—
587C4—44no—
588C4—44no—
589C4—82no—
590C4—864no—
591C4—868no—
592C4—3442no—
593C4—1724no—
594C4#1458277018yes—
595C2—1724no—
596C2#1913700111yescharacteristic
597C2C2×#1458277011yescharacteristic
598C2#1913722011yescharacteristic
599C2#1913752112yes—
600C2#1913754512yes—
601C2#1913821711yescharacteristic
602C2#1913822611yescharacteristic
603C2#1913828912yes—
604C2#1913830412yes—
605C2#1913905111yescharacteristic
606C2#1913906011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#382C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×#382D43
hypocenterC43#13879
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. C2×#14582768C2semidirect
6. #19132826C2semidirect
7. #19132825C2semidirect
8. #19132824C2semidirect
9. C2×C43×#382C2semidirect
24. C4×(C2×D43)⋊C4C4semidirect
154. C2×C4×D43C4⋊C4semidirect
247. C2×Dic43#117semidirect
294. C2×#382D43semidirect
337. C43#13879semidirect

Maximal subgroups

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

subgroupindex
C22×#130632832
C2×#145827682
C2×#145827562
C2×C4×(C2×D43)⋊C42
#191328392
#191328262
#191328252
#191328242
C2×C43×#3822
#1387943