Finite Group Databasebeta

← #25140952

Subgroups — #25140952

Order 11008.

754 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138886C211yesmaximal, characteristic
2#19137525C211yesmaximal, characteristic
3#19136165C211yesmaximal, characteristic, complemented
4#19136082C211yesmaximal, characteristic, complemented
5#19136033C211yesmaximal, characteristic, complemented
6#19136020C211yesmaximal, characteristic, complemented
7#19135185C211yesmaximal, characteristic, complemented
8#19135165C211yesmaximal, characteristic, complemented
9#19134887C211yesmaximal, characteristic
10#19134794C211yesmaximal, characteristic, complemented
11#19134784C211yesmaximal, characteristic, complemented
12#19134690C211yesmaximal, characteristic, complemented
13#19134684C211yesmaximal, characteristic, complemented
14#19134624C211yesmaximal, characteristic, complemented
15C43×#1735C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊D43C2211yescharacteristic
17C2×C4⋊C4×D43C2211yescharacteristic
18C2×#13063259C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×C22⋊(C43⋊C8)C2211yescharacteristic
23C2×(C2×D43)⋊C8C2211yescharacteristic
24C2×(C2×D43)⋊C8C2211yescharacteristic
25#14582827—21no—
26#14582814—21no—
27#14582795C2211yescharacteristic
28#14582795C2211yescharacteristic
29#14582793—21no—
30#14582790—21no—
31#14582783—21no—
32#14582783—21no—
33#14582775—21no—
34#14582764C2211yescharacteristic
35#14582759C2211yescharacteristic
36#14582759C2211yescharacteristic
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4×(C2×D43)⋊C4—21no—
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C23×C8×C43C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×C22⋊D43D411yescharacteristic
60C22×C4×D43—21no—
61C22×C4×D43C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C4×C22⋊D43—22no—
65C4×C22⋊D43—22no—
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4D411yescharacteristic
74C4⋊C4×D43—22no—
75C4⋊C4×D43—41no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43D411yescharacteristic
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4D411yescharacteristic
83C2×C4×Dic43—21no—
84C2×C4×Dic43C2311yescharacteristic
85#13063259—22no—
86#13063259—41no—
87#13063258—22no—
88#13063256—41no—
89C22⋊(C43⋊C8)—22no—
90(C2×D43)⋊C8—22no—
91(C2×D43)⋊C8—41no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C23×C4×C43C2311yescharacteristic
103C22×C8×C43—22no—
104C22×C8×C43—22no—
105C22×C8×C43—41no—
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108#117×C43—22no—
109#117×C43—22no—
110#117×C43—22no—
111#117×C43—41no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C42×C43—21no—
119C2×C42×C43—21no—
120C24×C43C2×D411yescharacteristic
121C23×D43C2×D411yescharacteristic
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43#4112yes—
132C22×C4×C43#4112yes—
133C22×C4×C43C2411yescharacteristic
134C2×C22⋊D43—22no—
135C2×C22⋊D43—22no—
136C2×C22⋊D43—41no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—42no—
151C2×C4×D43—42no—
152C2×C4×D43—81no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—44no—
159C2×C8×C43#4112yes—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43#4112yes—
168C22⋊C4×C43—42no—
169C22⋊C4×C43—42no—
170C42×C43—42no—
171C42×C43—42no—
172C22⋊Dic43—22no—
173C22⋊Dic43—81no—
174C22⋊Dic43—81no—
175(C2×D43)⋊C4—22no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—42no—
178(C2×D43)⋊C4—81no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187Dic43⋊C4—22no—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190Dic43⋊C4—81no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—81no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43#12312yes—
207C23×C43C22×D411yescharacteristic
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43#13512yes—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43#12312yes—
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C2×C4×C432−1+411yescharacteristic
240C22⋊D43—44no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—84no—
267C8×C43—22no—
268C8×C43—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271#24934—431nomaximal, Sylow
272C22×C43—22no—
273C22×C43—22no—
274C22×C43—22no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43C2×#12311yescharacteristic
280C22×C43#54611yescharacteristic
281C22×C43#54711yescharacteristic
282C22×C43C2×#13511yescharacteristic
283C22×C43#57511yescharacteristic
284C22×C43#57611yescharacteristic
285C22×C43#57811yescharacteristic
286C2×D43—22no—
287C2×D43—22no—
288C2×D43—22no—
289C2×D43—41no—
290C2×D43—41no—
291C2×D43—41no—
292C2×D43—41no—
293C4×C43—22no—
294C4×C43—42no—
295C4×C43—81no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43#52911yescharacteristic
299C4×C43#53911yescharacteristic
300C4×C43#55111yescharacteristic
301C4×C43#55211yescharacteristic
302Dic43—41no—
303Dic43—41no—
304Dic43—41no—
305Dic43—81no—
306Dic43—81no—
307Dic43—81no—
308Dic43—81no—
309#2485—431no—
310#2352—431no—
311#2101—431no—
312#2085—431no—
313#2077—431no—
314#2075—431no—
315#1921—431no—
316#1918—431no—
317#1869—431no—
318#1854—431no—
319#1852—431no—
320#1825—431no—
321#1824—431no—
322#1808—431no—
323#1735D4311yescharacteristic, complemented
324C2×C43—42no—
325C2×C43#241911yescharacteristic
326C2×C43#309111yescharacteristic
327C2×C43#309811yescharacteristic
328C2×C43#330011yescharacteristic
329C2×C43#331911yescharacteristic
330C2×C43#333911yescharacteristic
331C2×C43#334911yescharacteristic
332D43—42no—
333C23×C8C2×D4311yescharacteristic
334C2×C4×D4—431no—
335C2×#117C2×D4311yescharacteristic
336C2×#117C2×D4311yescharacteristic
337C22×C4⋊C4—431no—
338C2×#107—431no—
339C2×#107—431no—
340C2×#107—431no—
341C2×#106—431no—
342C2×C22⋊C8—431no—
343C2×C22⋊C8—431no—
344C2×C22⋊C8—431no—
345#397—861no—
346#394—861no—
347#389—431no—
348#389—431no—
349#388—861no—
350#388—861no—
351#387—861no—
352#387—861no—
353#386—861no—
354#382—431no—
355#380—431no—
356#380—431no—
357#380—431no—
358#380—431no—
359#380—431no—
360C4×C4⋊C4—431no—
361C4×C22⋊C4—861no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340C2×D4311yescharacteristic
371#340C2×D4311yescharacteristic
372#340C2×D4311yescharacteristic
373#340C2×D4311yescharacteristic
374#336—431no—
375#336—431no—
376C43#2493411yescharacteristic, complemented, Sylow
377C22×D4—431no—
378C23×C4—431no—
379C23×C4—861no—
380C23×C4C22×D4311yescharacteristic
381C22×C8—22no—
382C22×C8—22no—
383C22×C8—41no—
384C22×C8—431no—
385C22×C8—431no—
386C22×C8C22×D4311yescharacteristic
387C22×C8C22×D4311yescharacteristic
388C4×D4—862no—
389C4×D4—862no—
390#117—22no—
391#117—22no—
392#117—22no—
393#117—41no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—862no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—1721no—
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—431no—
411C2×C22⋊C4—431no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—431no—
420C2×C42—861no—
421#107—862no—
422#107—862no—
423#107—1721no—
424#106—1721no—
425C22⋊C8—862no—
426C22⋊C8—862no—
427C22⋊C8—1721no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438C24—431no—
439C24D4×D4311yescharacteristic
440C2×D4—862no—
441C2×D4—862no—
442C2×D4—1721no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—861no—
455C22×C4—861no—
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—3441no—
465C22×C4—1722no—
466C22×C4—1722no—
467C22×C4#1062189812yes—
468C22×C4D4×D4311yescharacteristic
469C22×C4#1062190012yes—
470C22×C4C23×D4311yescharacteristic
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—44no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8#1062189812yes—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—862no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—3441no—
501C4⋊C4—1722no—
502C4⋊C4—1722no—
503C4⋊C4#1062189812yes—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—862no—
507C22⋊C4—862no—
508C22⋊C4—3441no—
509C22⋊C4—3441no—
510C22⋊C4—3441no—
511C22⋊C4—1722no—
512C22⋊C4—1722no—
513C42—42no—
514C42—42no—
515C42—861no—
516C42—861no—
517C42—3441no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—432no—
525C23—861no—
526C23—861no—
527C23—861no—
528C23—861no—
529C23—861no—
530C23—861no—
531C23#1306330712yes—
532C23C2×D4×D4311yescharacteristic
533D4—1724no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—3444no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4#1306330712yes—
579C2×C4C2×#1062190011yescharacteristic
580C2×C4C2×#1062189811yescharacteristic
581C2×C4C2×#1062189811yescharacteristic
582C2×C4C2×#1062189811yescharacteristic
583C2×C4#1306337011yescharacteristic
584C2×C4#1306337311yescharacteristic
585C8—22no—
586C8—41no—
587C8—1721no—
588C8—1721no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—862no—
597C22—862no—
598C22—862no—
599C22—1721no—
600C22—1721no—
601C22—1721no—
602C22—1721no—
603C22C2×#1306330711yescharacteristic
604C22#1458353911yescharacteristic
605C22#1458355011yescharacteristic
606C22#135×D4311yescharacteristic
607C22#1458369611yescharacteristic
608C22#1458370111yescharacteristic
609C22#1458371311yescharacteristic
610C4—22no—
611C4—42no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4—3441no—
616C4—3441no—
617C4—3441no—
618C4—3441no—
619C4—1721no—
620C4—1721no—
621C4—1721no—
622C4#1458343311yescharacteristic
623C4#1458349611yescharacteristic
624C4#1458357511yescharacteristic
625C4#1458358411yescharacteristic
626C2—42no—
627C2—1722no—
628C2#1913807211yescharacteristic
629C2#1914450611yescharacteristic
630C2#1914457111yescharacteristic
631C2#1914648311yescharacteristic
632C2#1914674711yescharacteristic
633C2#1914699711yescharacteristic
634C2#1914712111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1735C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#1735D43
hypocenterC43#24934
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1735

Complements

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

NH ≅ G/Ntype
3. #19136165C2semidirect
4. #19136082C2semidirect
5. #19136033C2semidirect
6. #19136020C2semidirect
7. #19135185C2semidirect
8. #19135165C2semidirect
10. #19134794C2semidirect
11. #19134784C2semidirect
12. #19134690C2semidirect
13. #19134684C2semidirect
14. #19134624C2semidirect
15. C43×#1735C2semidirect
323. #1735D43semidirect
376. C43#24934semidirect

Maximal subgroups

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

subgroupindex
#191388862
#191375252
#191361652
#191360822
#191360332
#191360202
#191351852
#191351652
#191348872
#191347942
#191347842
#191346902
#191346842
#191346242
C43×#17352
#2493443