Finite Group Databasebeta

← #25153705

Subgroups — #25153705

Order 11008.

958 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583208C211yesmaximal, characteristic, complemented
2C2×#14582894C211yesmaximal, characteristic
3#19138311C211yesmaximal, characteristic, complemented
4#19137433C211yesmaximal, characteristic
5#19136129C211yesmaximal, characteristic, complemented
6#19135982C211yesmaximal, characteristic, complemented
7#19135970C211yesmaximal, characteristic, complemented
8#19135740C211yesmaximal, characteristic, complemented
9#19134863C211yesmaximal, characteristic, complemented
10#19134861C211yesmaximal, characteristic, complemented
11#19134797C211yesmaximal, characteristic, complemented
12#19134771C211yesmaximal, characteristic, complemented
13#19134619C211yesmaximal, characteristic, complemented
14#19134534C211yesmaximal, characteristic
15C43×#1803C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063316C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21#14583208—24no—
22C2×#13063259C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27#14582894—24no—
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35#14582834—21no—
36#14582821—21no—
37#14582801—21no—
38#14582801C2211yescharacteristic
39#14582800—21no—
40#14582800C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582794—21no—
44#14582785—21no—
45#14582756—21no—
46#14582756C2211yescharacteristic
47#14582756C2211yescharacteristic
48C4×(C2×D43)⋊C4—21no—
49C4×(C2×D43)⋊C4C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C43×#384C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C2×#10621902—22no—
62C2×#10621902—22no—
63C2×#10621902—22no—
64C2×#10621902—41no—
65C2×#10621902—41no—
66C2×#10621902Q814yes—
67C22×D172—21no—
68C22×D172C2311yescharacteristic
69C22×C4×D43—21no—
70C22×C4×D43C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C2×C8×D43—22no—
74C2×C8×D43—22no—
75C2×C8×D43—41no—
76#13063316—22no—
77#13063316—41no—
78Q8×Dic43—22no—
79Q8×Dic43—41no—
80#13063283—22no—
81#13063283—41no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4D411yescharacteristic
98C2×(C2×D43)⋊C4D411yescharacteristic
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43C2311yescharacteristic
102#13063259—22no—
103#13063256—22no—
104#13063256—41no—
105#13063256—41no—
106Dic43⋊C8—22no—
107#13063249—22no—
108#13063249D414yes—
109#13063247—22no—
110#13063247—41no—
111#13063245—22no—
112#13063245—41no—
113(C2×D43)⋊C8—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95D411yescharacteristic
119C43⋊#95D411yescharacteristic
120C22×Q8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C4×Q8×C43—22no—
124C4×Q8×C43—41no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133C4⋊C8×C43—41no—
134#103×C43—22no—
135#103×C43—22no—
136C23×D43—21no—
137C23×D43C2×D411yescharacteristic
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43C2×D412yes—
142C2×Q8×C43C2×Q812yes—
143C2×Q8×C43#4112yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157#10621902—28no—
158#10621902—44no—
159#10621902—44no—
160#10621902—44no—
161C2×D172—21no—
162C2×D172—24no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—42no—
168C2×D172—42no—
169C2×D172C2×Q812yes—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—24no—
175C2×C4×D43—42no—
176C2×C4×D43—42no—
177C2×C4×D43C2×Q812yes—
178C2×C4×D43#4112yes—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—42no—
192C4⋊C4×C43—42no—
193C4⋊C4×C43—81no—
194C42×C43—21no—
195C42×C43—21no—
196C42×C43—42no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—41no—
199(C2×D43)⋊C4—42no—
200(C2×D43)⋊C4—42no—
201(C2×D43)⋊C4—42no—
202(C2×D43)⋊C4—81no—
203(C2×D43)⋊C4—81no—
204(C2×D43)⋊C4—81no—
205(C2×D43)⋊C4—81no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—42no—
212C4⋊Dic43—42no—
213C4⋊Dic43C2×D412yes—
214Dic43⋊C4—42no—
215Dic43⋊C4—42no—
216Dic43⋊C4—81no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—42no—
220C4×Dic43—42no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8C2×D412yes—
227C8×D43—44no—
228C23×C43C22×D411yescharacteristic
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—21no—
233C22×D43—21no—
234C22×D43—21no—
235C22×D43—22no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—41no—
240C22×D43—41no—
241C22×D43—41no—
242C22×D43C22⋊Q812yes—
243Q8×C43—22no—
244Q8×C43—22no—
245Q8×C43—22no—
246Q8×C43C22⋊Q814yes—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—21no—
250C2×C4×C43—22no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43#13512yes—
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C22×Q811yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43H(5,𝔽2)11yescharacteristic
270C2×C4×C43H(5,𝔽2)11yescharacteristic
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—22no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43C22⋊Q812yes—
289D172—22no—
290D172—22no—
291D172—48no—
292D172—41no—
293D172—41no—
294C4×D43—22no—
295C4×D43—22no—
296C4×D43—22no—
297C4×D43—22no—
298C4×D43—48no—
299C8×C43—41no—
300C8×C43—41no—
301C43⋊C8—22no—
302C43⋊C8—41no—
303#25953—431nomaximal, Sylow
304C22×C43C2×C22⋊Q811yescharacteristic
305C22×C43D4211yescharacteristic
306C22×C43#54611yescharacteristic
307C22×C43C2×#13511yescharacteristic
308C22×C43#57511yescharacteristic
309C22×C43#57711yescharacteristic
310C22×C43#57711yescharacteristic
311C2×D43—22no—
312C2×D43—22no—
313C2×D43—22no—
314C2×D43—41no—
315C2×D43—41no—
316C2×D43—41no—
317C2×D43—41no—
318C2×D43—42no—
319C2×D43—42no—
320C2×D43—42no—
321C2×D43—81no—
322C2×D43—81no—
323C2×D43—81no—
324C2×D43—81no—
325C4×C43—24no—
326C4×C43—22no—
327C4×C43—41no—
328C4×C43—81no—
329C4×C43—81no—
330C4×C43—81no—
331C4×C43C2×C22⋊Q811yescharacteristic
332C4×C43#54311yescharacteristic
333C4×C43#54611yescharacteristic
334C4×C43#55111yescharacteristic
335Dic43—22no—
336Dic43—41no—
337Dic43—41no—
338Dic43—42no—
339Dic43—81no—
340Dic43—81no—
341C2×#479—431no—
342C2×#416—431no—
343#2441—431no—
344#2341—431no—
345#2094—431no—
346#2067—431no—
347#2065—431no—
348#2025—431no—
349#1865—431no—
350#1865—431no—
351#1854—431no—
352#1850—431no—
353#1807—431no—
354#1803D4311yescharacteristic, complemented
355#1788—431no—
356C2×C43#243711yescharacteristic
357C2×C43#307611yescharacteristic
358C2×C43#308411yescharacteristic
359C2×C43#327111yescharacteristic
360C2×C43#328411yescharacteristic
361C2×C43#330111yescharacteristic
362C2×C43#331711yescharacteristic
363D43—42no—
364D43—82no—
365C22×#41—431no—
366C23×C8—431no—
367C2×#125—431no—
368C2×C4×Q8—431no—
369C2×C4×Q8C2×D4311yescharacteristic
370C2×#117—431no—
371#479—864no—
372C2×#107—431no—
373C2×#106—431no—
374C2×#106—431no—
375C2×#106—431no—
376C2×C4⋊C8—431no—
377C2×C4⋊C8C2×D4311yescharacteristic
378#416—864no—
379C2×#103—431no—
380C2×#103—431no—
381C2×#103C2×D4311yescharacteristic
382C2×#103C2×D4311yescharacteristic
383C2×#102—431no—
384C2×#102—431no—
385C2×#102—431no—
386C2×#102—431no—
387C2×C22⋊C8—431no—
388#399—861no—
389#396—861no—
390#390—431no—
391#390—431no—
392#390—861no—
393#390—861no—
394#389—431no—
395#389—431no—
396#389—861no—
397#387—861no—
398#384C2×D4311yescharacteristic
399#380—431no—
400#380—431no—
401#380—861no—
402C4×C22⋊C4—431no—
403C4×C22⋊C4—861no—
404#340—431no—
405#340—431no—
406#340C2×D4311yescharacteristic
407#340C2×D4311yescharacteristic
408#336—431no—
409#336—431no—
410C43#2595311yescharacteristic, complemented, Sylow
411C2×#41—434no—
412C2×#41—862no—
413C2×#41—862no—
414C2×#41—862no—
415C2×#41—1721no—
416C2×#41—1721no—
417C22×Q8C22×D4311yescharacteristic
418C22×D4—431no—
419C22×D4—861no—
420C23×C4—431no—
421C23×C4—861no—
422C22×C8—431no—
423C22×C8—431no—
424C22×C8—862no—
425C22×C8—862no—
426C22×C8—1721no—
427C22×C8C22×D4311yescharacteristic
428C22×C8C22×D4311yescharacteristic
429#125—862no—
430#125—1721no—
431C4×Q8—22no—
432C4×Q8—41no—
433C4×Q8—862no—
434C4×Q8—1721no—
435#117—862no—
436#117—1721no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4C22×D4311yescharacteristic
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C4⋊C4C22×D4311yescharacteristic
451C2×C22⋊C4—431no—
452C2×C22⋊C4—431no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C22⋊C4—861no—
460C2×C42—21no—
461C2×C42—431no—
462C2×C42—861no—
463C2×C42—861no—
464C2×C42C22×D4311yescharacteristic
465#107—862no—
466#106—862no—
467#106—1721no—
468#106—1721no—
469C4⋊C8—41no—
470C4⋊C8—862no—
471#103—22no—
472#103—22no—
473#103—434no—
474#103—862no—
475#102—862no—
476#102—862no—
477#102—1721no—
478#102—1721no—
479C22⋊C8—862no—
480#95—431no—
481#95—431no—
482#95—861no—
483#95—861no—
484#95—861no—
485#95—861no—
486C24—431no—
487C24—861no—
488#41—868no—
489#41—1724no—
490#41—1724no—
491#41—1724no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8#1062189812yes—
496C2×Q8D4×D4312yes—
497C2×Q8Q8×D4312yes—
498C2×D4—432no—
499C2×D4—864no—
500C2×D4—861no—
501C2×D4—861no—
502C2×D4—861no—
503C2×D4—861no—
504C2×D4—861no—
505C2×D4—1722no—
506C2×D4—1722no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—431no—
512C22×C4—432no—
513C22×C4—432no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—864no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—1722no—
525C22×C4—1722no—
526C22×C4D4×D4311yescharacteristic
527C22×C4D4×D4311yescharacteristic
528C22×C4C23×D4311yescharacteristic
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—432no—
536C2×C8—861no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8—1724no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—81no—
551C4⋊C4—432no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—3441no—
558C4⋊C4—1722no—
559C4⋊C4—1722no—
560C4⋊C4—1722no—
561C4⋊C4—1722no—
562C22⋊C4—862no—
563C22⋊C4—3441no—
564C22⋊C4—3441no—
565C22⋊C4—3441no—
566C22⋊C4—3441no—
567C22⋊C4—1721no—
568C22⋊C4—1722no—
569C22⋊C4—1722no—
570C22⋊C4—1722no—
571C42—21no—
572C42—21no—
573C42—42no—
574C42—861no—
575C42—861no—
576C42—1722no—
577C42—1722no—
578C23—432no—
579C23—861no—
580C23—861no—
581C23—861no—
582C23—861no—
583C23—861no—
584C23—861no—
585C23—862no—
586C23—1721no—
587C23—1721no—
588C23—1721no—
589C23—1721no—
590C23—1721no—
591C23—1721no—
592C23C2×D4×D4311yescharacteristic
593Q8—22no—
594Q8—22no—
595Q8—22no—
596Q8#1306330314yes—
597D4—862no—
598D4—862no—
599D4—1728no—
600D4—1721no—
601D4—1721no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—432no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—862no—
633C2×C4—1728no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4#1306334812yes—
643C2×C4C2×D4×D4311yescharacteristic
644C2×C4C2×Q8×D4311yescharacteristic
645C2×C4#41×D4311yescharacteristic
646C2×C4C2×#1062189811yescharacteristic
647C2×C4#1306337011yescharacteristic
648C2×C4#1306337111yescharacteristic
649C8—41no—
650C8—41no—
651C8—862no—
652C8—1721no—
653C22—862no—
654C22—862no—
655C22—862no—
656C22—3441no—
657C22—3441no—
658C22—3441no—
659C22—3441no—
660C22—1722no—
661C22—1722no—
662C22—1722no—
663C22—1721no—
664C22—1721no—
665C22—1721no—
666C22—1721no—
667C22C22⋊Q8×D4311yescharacteristic
668C22#1458353311yescharacteristic
669C22#1458353911yescharacteristic
670C22C2×#1306334811yescharacteristic
671C22#1458369511yescharacteristic
672C22#1458370511yescharacteristic
673C22#1458370811yescharacteristic
674C4—24no—
675C4—22no—
676C4—41no—
677C4—81no—
678C4—81no—
679C4—81no—
680C4—862no—
681C4—3441no—
682C4—3441no—
683C4—1721no—
684C4—1722no—
685C4—1721no—
686C4C2×#1306330311yescharacteristic
687C4#1458352411yescharacteristic
688C4#1458353811yescharacteristic
689C4#1458357311yescharacteristic
690C2—3442no—
691C2—1722no—
692C2#1913826311yescharacteristic
693C2#1914438611yescharacteristic
694C2#1914445411yescharacteristic
695C2#1914617511yescharacteristic
696C2#1914632011yescharacteristic
697C2#1914649311yescharacteristic
698C2#1914672211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1803C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
hypercenter#1803D43
hypocenterC43#25953
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
1. C2×#14583208C2semidirect
3. #19138311C2semidirect
5. #19136129C2semidirect
6. #19135982C2semidirect
7. #19135970C2semidirect
8. #19135740C2semidirect
9. #19134863C2semidirect
10. #19134861C2semidirect
11. #19134797C2semidirect
12. #19134771C2semidirect
13. #19134619C2semidirect
15. C43×#1803C2semidirect
354. #1803D43semidirect
410. C43#25953semidirect

Maximal subgroups

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

subgroupindex
C2×#145832082
C2×#145828942
#191383112
#191374332
#191361292
#191359822
#191359702
#191357402
#191348632
#191348612
#191347972
#191347712
#191346192
#191345342
C43×#18032
#2595343