Finite Group Databasebeta

← #25153692

Subgroups — #25153692

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×#14583203C211yesmaximal, characteristic, complemented
2C2×#14582892C211yesmaximal, characteristic
3#19138304C211yesmaximal, characteristic, complemented
4#19137434C211yesmaximal, characteristic
5#19136126C211yesmaximal, characteristic, complemented
6#19135979C211yesmaximal, characteristic, complemented
7#19135969C211yesmaximal, characteristic, complemented
8#19134866C211yesmaximal, characteristic, complemented
9#19134864C211yesmaximal, characteristic, complemented
10#19134795C211yesmaximal, characteristic, complemented
11#19134774C211yesmaximal, characteristic, complemented
12#19134619C211yesmaximal, characteristic, complemented
13#19134599C211yesmaximal, characteristic, complemented
14#19134532C211yesmaximal, characteristic
15C43×#2025C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21#14583203—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28#14582892—24no—
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36#14582834—21no—
37#14582821—21no—
38#14582802C2211yescharacteristic
39#14582799—21no—
40#14582799—21no—
41#14582798C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582795—21no—
44#14582780—21no—
45#14582768C2211yescharacteristic
46#14582757—21no—
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49C22⋊C4×Dic43—21no—
50C4×(C2×D43)⋊C4C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#125×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C2×#10621900—22no—
62C2×#10621900—22no—
63C2×#10621900—22no—
64C2×#10621900—41no—
65C2×#10621900—41no—
66C2×#10621900Q814yes—
67C22×Dic86C2311yescharacteristic
68C22×C22⋊D43—21no—
69C23×Dic43—21no—
70C22×C4×D43C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C2×C8×D43—22no—
74C2×C8×D43—22no—
75C2×C8×D43—41no—
76C4×Dic86—22no—
77C4×Dic86—41no—
78#13063290—22no—
79#13063290—41no—
80#13063283—22no—
81#13063283—41no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4D411yescharacteristic
97C2×(C2×D43)⋊C4D411yescharacteristic
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43C2311yescharacteristic
102#13063258—22no—
103#13063257—41no—
104#13063256—22no—
105#13063256—41no—
106C4⋊(C43⋊C8)—22no—
107Dic43⋊C8—41no—
108#13063250—22no—
109#13063250—22no—
110#13063248—22no—
111#13063248D414yes—
112#13063246—22no—
113#13063246—41no—
114(C2×D43)⋊C8—22no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95D411yescharacteristic
120C43⋊#95D411yescharacteristic
121C22×D4×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124#125×C43—22no—
125#125×C43—41no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#102×C43—22no—
135#102×C43—41no—
136C24×C43—21no—
137C23×D43C2×D411yescharacteristic
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43C2×Q812yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—24no—
151C2×C22⋊D43—42no—
152C2×C22⋊D43—42no—
153C22×Dic43—24no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—42no—
159C22×Dic43—42no—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163#10621900—28no—
164#10621900—44no—
165#10621900—44no—
166#10621900—44no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43C2×Q812yes—
172C2×C4×D43#4112yes—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86C2×D412yes—
177C2×Dic86C2×Q812yes—
178C2×Dic86#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—42no—
191C4⋊C4×C43—42no—
192C4⋊C4×C43C2×D412yes—
193C22⋊C4×C43—42no—
194C22⋊C4×C43—81no—
195C42×C43—21no—
196C42×C43—21no—
197C22⋊Dic43—42no—
198C22⋊Dic43—81no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—41no—
201(C2×D43)⋊C4—42no—
202(C2×D43)⋊C4—81no—
203(C2×D43)⋊C4—81no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—42no—
211Dic43⋊C4—42no—
212Dic43⋊C4—42no—
213Dic43⋊C4—42no—
214Dic43⋊C4—81no—
215Dic43⋊C4—81no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—42no—
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×C43—22no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43C22×D411yescharacteristic
236C22×D43—21no—
237C22×D43—21no—
238C22×D43—21no—
239C22×D43—21no—
240C22×D43—21no—
241C22×D43—21no—
242C22×D43C22⋊Q812yes—
243D4×C43—22no—
244D4×C43—22no—
245D4×C43—41no—
246D4×C43—41no—
247C2×C4×C43—21no—
248C2×C4×C43—22no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
263C2×C4×C43C22×Q811yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×C4×C43H(5,𝔽2)11yescharacteristic
268C22⋊D43—48no—
269C2×Dic43—22no—
270C2×Dic43—21no—
271C2×Dic43—22no—
272C2×Dic43—21no—
273C2×Dic43—22no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—48no—
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×Dic43—41no—
289C2×Dic43C22⋊Q812yes—
290C2×Dic43#13512yes—
291C4×D43—22no—
292C4×D43—22no—
293C4×D43—22no—
294C4×D43—22no—
295Dic86—22no—
296Dic86—22no—
297Dic86—22no—
298Dic86C22⋊Q814yes—
299C8×C43—41no—
300C8×C43—41no—
301C43⋊C8—22no—
302C43⋊C8—41no—
303#25953—431nomaximal, Sylow
304C22×C43—42no—
305C22×C43—42no—
306C22×C43—42no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43C2×C22⋊Q811yescharacteristic
312C22×C43D4211yescharacteristic
313C22×C43#54611yescharacteristic
314C22×C43C2×#13511yescharacteristic
315C22×C43#57511yescharacteristic
316C22×C43#57711yescharacteristic
317C22×C43#57711yescharacteristic
318C2×D43—22no—
319C2×D43—22no—
320C2×D43—22no—
321C2×D43—41no—
322C2×D43—41no—
323C2×D43—41no—
324C2×D43—41no—
325C4×C43—41no—
326C4×C43—41no—
327C4×C43—42no—
328C4×C43—81no—
329C4×C43—81no—
330C4×C43C2×C22⋊Q811yescharacteristic
331C4×C43#54311yescharacteristic
332C4×C43#54611yescharacteristic
333C4×C43#55111yescharacteristic
334Dic43—24no—
335Dic43—22no—
336Dic43—22no—
337Dic43—41no—
338Dic43—81no—
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#2025D4311yescharacteristic, complemented
349#1865—431no—
350#1865—431no—
351#1854—431no—
352#1850—431no—
353#1807—431no—
354#1803—431no—
355#1788—431no—
356C2×C43—82no—
357C2×C43#243711yescharacteristic
358C2×C43#307611yescharacteristic
359C2×C43#308411yescharacteristic
360C2×C43#327111yescharacteristic
361C2×C43#328411yescharacteristic
362C2×C43#330111yescharacteristic
363C2×C43#331711yescharacteristic
364D43—42no—
365C22×#41—431no—
366C23×C8—431no—
367C2×#125C2×D4311yescharacteristic
368C2×C4×Q8—431no—
369C2×C4×Q8—431no—
370C2×#117—431no—
371#479—864no—
372C2×#107—431no—
373C2×#106—431no—
374C2×#106—431no—
375C2×#106—431no—
376C2×C4⋊C8—431no—
377C2×C4⋊C8—431no—
378#416—864no—
379C2×#103—431no—
380C2×#103—431no—
381C2×#103—431no—
382C2×#103—431no—
383C2×#102—431no—
384C2×#102—431no—
385C2×#102C2×D4311yescharacteristic
386C2×#102C2×D4311yescharacteristic
387C2×C22⋊C8—431no—
388#399—861no—
389#396—861no—
390#390—431no—
391#390—861no—
392#390—861no—
393#390C2×D4311yescharacteristic
394#389—431no—
395#389—431no—
396#389—861no—
397#387—861no—
398#384—431no—
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#336C2×D4311yescharacteristic
410C43#2595311yescharacteristic, complemented, Sylow
411C2×#41—434no—
412C2×#41—862no—
413C2×#41—862no—
414C2×#41—862no—
415C2×#41—1721no—
416C2×#41—1721no—
417C22×Q8—431no—
418C22×D4—861no—
419C22×D4C22×D4311yescharacteristic
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—22no—
430#125—41no—
431C4×Q8—862no—
432C4×Q8—862no—
433C4×Q8—1721no—
434C4×Q8—1721no—
435#117—862no—
436#117—1721no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—861no—
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—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—431no—
454C2×C22⋊C4—431no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C22⋊C4—861no—
460C2×C42—431no—
461C2×C42—861no—
462C2×C42—861no—
463C2×C42—861no—
464C2×C42C22×D4311yescharacteristic
465#107—862no—
466#106—862no—
467#106—1721no—
468#106—1721no—
469C4⋊C8—862no—
470C4⋊C8—1721no—
471#103—434no—
472#103—862no—
473#103—862no—
474#103—862no—
475#102—22no—
476#102—41no—
477#102—862no—
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—21no—
487C24—431no—
488#41—868no—
489#41—1724no—
490#41—1724no—
491#41—1724no—
492C2×Q8—432no—
493C2×Q8—432no—
494C2×Q8—432no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—864no—
504C2×D4—1722no—
505C2×D4—1722no—
506C2×D4Q8×D4312yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—432no—
513C22×C4—432no—
514C22×C4—431no—
515C22×C4—864no—
516C22×C4—861no—
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—42no—
548C4⋊C4—42no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—3441no—
556C4⋊C4—3441no—
557C4⋊C4—1722no—
558C4⋊C4—1722no—
559C4⋊C4—1722no—
560C4⋊C4—1722no—
561C4⋊C4D4×D4312yes—
562C22⋊C4—42no—
563C22⋊C4—81no—
564C22⋊C4—862no—
565C22⋊C4—3441no—
566C22⋊C4—3441no—
567C22⋊C4—3441no—
568C22⋊C4—1721no—
569C22⋊C4—1722no—
570C22⋊C4—1722no—
571C42—21no—
572C42—21no—
573C42—861no—
574C42—861no—
575C42—1722no—
576C42—1722no—
577C42—1722no—
578C23—22no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—432no—
586C23—861no—
587C23—861no—
588C23—861no—
589C23—861no—
590C23—861no—
591C23—861no—
592C23C2×D4×D4311yescharacteristic
593Q8—434no—
594Q8—862no—
595Q8—862no—
596Q8—862no—
597D4—22no—
598D4—22no—
599D4—41no—
600D4—41no—
601D4—1728no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—432no—
618C2×C4—432no—
619C2×C4—862no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—862no—
623C2×C4—861no—
624C2×C4—862no—
625C2×C4—861no—
626C2×C4—862no—
627C2×C4—862no—
628C2×C4—862no—
629C2×C4—862no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—861no—
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—1721no—
643C2×C4C2×D4×D4311yescharacteristic
644C2×C4C2×Q8×D4311yescharacteristic
645C2×C4#41×D4311yescharacteristic
646C2×C4#41×D4311yescharacteristic
647C2×C4#1306337011yescharacteristic
648C2×C4#1306337111yescharacteristic
649C8—41no—
650C8—41no—
651C8—862no—
652C8—1721no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—862no—
661C22—862no—
662C22—862no—
663C22—1721no—
664C22—1721no—
665C22—1721no—
666C22—1721no—
667C22C22⋊Q8×D4311yescharacteristic
668C22#1458353111yescharacteristic
669C22#1458354211yescharacteristic
670C22#135×D4311yescharacteristic
671C22#1458369511yescharacteristic
672C22#1458370611yescharacteristic
673C22#1458370911yescharacteristic
674C4—41no—
675C4—42no—
676C4—41no—
677C4—81no—
678C4—81no—
679C4—862no—
680C4—862no—
681C4—864no—
682C4—3441no—
683C4—3441no—
684C4—3441no—
685C4—1721no—
686C4C22⋊Q8×D4311yescharacteristic
687C4#1458352411yescharacteristic
688C4#1458354211yescharacteristic
689C4#1458357911yescharacteristic
690C2—82no—
691C2—1722no—
692C2#1913825511yescharacteristic
693C2#1914438011yescharacteristic
694C2#1914445811yescharacteristic
695C2#1914617811yescharacteristic
696C2#1914632311yescharacteristic
697C2#1914649611yescharacteristic
698C2#1914672011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2025C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
hypercenter#2025D43
hypocenterC43#25953
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2025

Complements

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

NH ≅ G/Ntype
1. C2×#14583203C2semidirect
3. #19138304C2semidirect
5. #19136126C2semidirect
6. #19135979C2semidirect
7. #19135969C2semidirect
8. #19134866C2semidirect
9. #19134864C2semidirect
10. #19134795C2semidirect
11. #19134774C2semidirect
12. #19134619C2semidirect
13. #19134599C2semidirect
15. C43×#2025C2semidirect
348. #2025D43semidirect
410. C43#25953semidirect

Maximal subgroups

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

subgroupindex
C2×#145832032
C2×#145828922
#191383042
#191374342
#191361262
#191359792
#191359692
#191348662
#191348642
#191347952
#191347742
#191346192
#191345992
#191345322
C43×#20252
#2595343