Finite Group Databasebeta

← #25153676

Subgroups — #25153676

Order 11008.

966 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583183C211yesmaximal, characteristic, complemented
2C2×#14582896C211yesmaximal, characteristic
3#19138287C211yesmaximal, characteristic, complemented
4#19137432C211yesmaximal, characteristic
5#19136117C211yesmaximal, characteristic, complemented
6#19135970C211yesmaximal, characteristic, complemented
7#19135964C211yesmaximal, characteristic, complemented
8#19135730C211yesmaximal, characteristic, complemented
9#19134860C211yesmaximal, characteristic, complemented
10#19134850C211yesmaximal, characteristic, complemented
11#19134792C211yesmaximal, characteristic, complemented
12#19134773C211yesmaximal, characteristic, complemented
13#19134609C211yesmaximal, characteristic, complemented
14#19134533C211yesmaximal, characteristic
15C43×#1807C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21#14583183—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26#14582896—24no—
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36#14582822—21no—
37#14582811—21no—
38#14582803—21no—
39#14582800C2211yescharacteristic
40#14582800C2211yescharacteristic
41#14582799—21no—
42#14582799—21no—
43#14582798C2211yescharacteristic
44#14582795C2211yescharacteristic
45#14582782—21no—
46#14582764C2211yescharacteristic
47#14582758—21no—
48C4×C22⋊Dic43C2211yescharacteristic
49#14582746—21no—
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C23×C8×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C2×#10621898—22no—
62C2×#10621898—22no—
63C2×#10621898—22no—
64C2×#10621898—41no—
65C2×#10621898—41no—
66C2×#10621898Q814yescomplemented
67C22×Dic86—21no—
68C22×Dic86C2311yescharacteristic
69C22×D172C2311yescharacteristic
70C22×C22⋊D43—21no—
71C22×C4×D43—21no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063324—22no—
75#13063324—41no—
76#13063290—22no—
77#13063290—22no—
78#13063290—41no—
79#13063290—41no—
80#13063284—22no—
81#13063284—41no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43D411yescharacteristic
91C2×C22⋊Dic43D411yescharacteristic
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43C2311yescharacteristic
100C2×C4×Dic43C2311yescharacteristic
101#13063258—41no—
102#13063256—22no—
103Dic43⋊C8—22no—
104Dic43⋊C8—41no—
105#13063250—22no—
106#13063250D414yes—
107#13063248—22no—
108#13063248—22no—
109#13063247—22no—
110#13063247—22no—
111#13063245—41no—
112#13063245—41no—
113C22⋊(C43⋊C8)—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95D411yescharacteristic
119C43⋊#95D411yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C22×C8×C43—22no—
122C22×C8×C43—22no—
123C22×C8×C43—41no—
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132#106×C43—22no—
133#106×C43—41no—
134#95×C43—21no—
135#95×C43—21no—
136C24×C43C2×D411yescharacteristic
137C23×D43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×Q812yes—
148C22×C4×C43#4112yes—
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—24no—
151C2×C22⋊D43—42no—
152C2×C22⋊D43—42no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160#10621898—28no—
161#10621898—44no—
162#10621898—44no—
163#10621898—44no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172C2×Q812yes—
170C2×C4×D43—24no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—42no—
177C2×Dic86—42no—
178C2×Dic86—81no—
179C2×Dic86C2×D412yes—
180C2×Dic86C2×Q812yes—
181C2×Dic86#4112yes—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—44no—
188C2×C8×C43C2×D412yes—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C22⋊C4×C43—81no—
198C22⋊C4×C43—81no—
199C22⋊Dic43—22no—
200C22⋊Dic43—41no—
201C22⋊Dic43—42no—
202(C2×D43)⋊C4—42no—
203(C2×D43)⋊C4—42no—
204(C2×D43)⋊C4—81no—
205(C2×D43)⋊C4—81no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—42no—
210C4⋊Dic43C2×D412yes—
211Dic43⋊C4—42no—
212Dic43⋊C4—42no—
213Dic43⋊C4—42no—
214Dic43⋊C4—81no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—42no—
220C4×Dic43—42no—
221C4×Dic43—42no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43C22⋊Q812yes—
235C23×C43C22×D411yescharacteristic
236C22×D43—22no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—41no—
240C22×D43—41no—
241C22×D43—41no—
242C22×D43—41no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
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×C43C22⋊Q812yes—
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—22no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—22no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43#13512yes—
290D172—22no—
291D172—22no—
292D172—41no—
293D172—41no—
294C4×D43—48no—
295Dic86—22no—
296Dic86—22no—
297Dic86—22no—
298Dic86—84no—
299Dic86C22⋊Q814yes—
300C8×C43—22no—
301C8×C43—41no—
302C43⋊C8—41no—
303C43⋊C8—41no—
304#25951—431nomaximal, Sylow
305C22×C43—22no—
306C22×C43—22no—
307C22×C43—22no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43C2×C22⋊Q811yescharacteristic
313C22×C43D4211yescharacteristic
314C22×C43#54611yescharacteristic
315C22×C43C2×#13511yescharacteristic
316C22×C43#57511yescharacteristic
317C22×C43#57711yescharacteristic
318C22×C43#57711yescharacteristic
319C2×D43—42no—
320C2×D43—42no—
321C2×D43—42no—
322C2×D43—81no—
323C2×D43—81no—
324C2×D43—81no—
325C2×D43—81no—
326C4×C43—22no—
327C4×C43—81no—
328C4×C43—81no—
329C4×C43—81no—
330C4×C43—81no—
331C4×C43C2×C22⋊Q811yescharacteristic
332C4×C43#54311yescharacteristic
333C4×C43#54611yescharacteristic
334C4×C43#55111yescharacteristic
335Dic43—24no—
336Dic43—22no—
337Dic43—41no—
338Dic43—42no—
339Dic43—41no—
340Dic43—41no—
341Dic43—81no—
342C2×#475—431no—
343C2×#416—431no—
344#2439—431no—
345#2341—431no—
346#2092—431no—
347#2065—431no—
348#2065—431no—
349#2023—431no—
350#1865—431no—
351#1863—431no—
352#1854—431no—
353#1850—431no—
354#1807D4311yescharacteristic, complemented
355#1805—431no—
356#1788—431no—
357C2×C43—42no—
358C2×C43#243711yescharacteristic
359C2×C43#307611yescharacteristic
360C2×C43#308411yescharacteristic
361C2×C43#327111yescharacteristic
362C2×C43#328211yescharacteristic
363C2×C43#330411yescharacteristic
364C2×C43#332111yescharacteristic
365D43—82no—
366C22×#41—431no—
367C23×C8C2×D4311yescharacteristic
368C2×C4⋊Q8—431no—
369C2×C4×Q8—431no—
370C2×C4×Q8—431no—
371C2×#117—431no—
372#475—864no—
373C2×#107—431no—
374C2×#106—431no—
375C2×#106C2×D4311yescharacteristic
376C2×#106C2×D4311yescharacteristic
377C2×C4⋊C8—431no—
378C2×C4⋊C8—431no—
379#416—864no—
380C2×#103—431no—
381C2×#103—431no—
382C2×#103—431no—
383C2×#103—431no—
384C2×#102—431no—
385C2×#102—431no—
386C2×#102—431no—
387C2×#102—431no—
388C2×C22⋊C8—431no—
389#396—861no—
390#393—861no—
391#391—861no—
392#390—431no—
393#390—431no—
394#390—861no—
395#390—861no—
396#389—431no—
397#389—431no—
398#387—861no—
399#382—431no—
400#380—861no—
401#380C2×D4311yescharacteristic
402#380C2×D4311yescharacteristic
403C4×C22⋊C4—431no—
404C4×C22⋊C4—861no—
405#340—431no—
406#340—431no—
407#340C2×D4311yescharacteristic
408#340C2×D4311yescharacteristic
409#336—431no—
410#336—431no—
411C43#2595111yescharacteristic, complemented, Sylow
412C2×#41—434no—
413C2×#41—862no—
414C2×#41—862no—
415C2×#41—862no—
416C2×#41—1721no—
417C2×#41—1721no—
418C22×Q8—431no—
419C22×Q8—861no—
420C22×D4—431no—
421C22×D4—861no—
422C23×C4—861no—
423C23×C4C22×D4311yescharacteristic
424C22×C8—22no—
425C22×C8—22no—
426C22×C8—41no—
427C22×C8—431no—
428C22×C8—431no—
429C22×C8C22×D4311yescharacteristic
430C22×C8C22×D4311yescharacteristic
431C4⋊Q8—862no—
432C4⋊Q8—1721no—
433C4×Q8—862no—
434C4×Q8—862no—
435C4×Q8—1721no—
436C4×Q8—1721no—
437#117—862no—
438#117—1721no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C4⋊C4C22×D4311yescharacteristic
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—431no—
453C2×C22⋊C4—431no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—861no—
462C2×C42—861no—
463C2×C42—861no—
464#107—1721no—
465#106—22no—
466#106—41no—
467#106—862no—
468C4⋊C8—862no—
469C4⋊C8—1721no—
470#103—434no—
471#103—862no—
472#103—862no—
473#103—862no—
474#102—862no—
475#102—862no—
476#102—1721no—
477#102—1721no—
478C22⋊C8—862no—
479#95—21no—
480#95—21no—
481#95—431no—
482#95—431no—
483#95—861no—
484#95—861no—
485#95—861no—
486#95—861no—
487C24—861no—
488C24D4×D4311yescharacteristic
489#41—868no—
490#41—1724no—
491#41—1724no—
492#41—1724no—
493C2×Q8—432no—
494C2×Q8—432no—
495C2×Q8—432no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8—3441no—
500C2×Q8—1722no—
501C2×Q8—1722no—
502C2×D4—432no—
503C2×D4—864no—
504C2×D4—861no—
505C2×D4—861no—
506C2×D4—861no—
507C2×D4—861no—
508C2×D4—861no—
509C2×D4—1722no—
510C2×D4—1722no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—431no—
520C22×C4—431no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—864no—
526C22×C4—861no—
527C22×C4—1722no—
528C22×C4—1722no—
529C22×C4#1062189812yes—
530C22×C4D4×D4311yescharacteristic
531C22×C4Q8×D4312yes—
532C22×C4C23×D4311yescharacteristic
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—44no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8D4×D4312yes—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—432no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—861no—
558C4⋊C4—3441no—
559C4⋊C4—1722no—
560C4⋊C4—1722no—
561C4⋊C4—1722no—
562C4⋊C4—1722no—
563C22⋊C4—81no—
564C22⋊C4—81no—
565C22⋊C4—862no—
566C22⋊C4—3441no—
567C22⋊C4—3441no—
568C22⋊C4—1722no—
569C22⋊C4—1722no—
570C22⋊C4—1721no—
571C22⋊C4—1722no—
572C42—861no—
573C42—861no—
574C42—861no—
575C42—861no—
576C42—1722no—
577C42—1722no—
578C42—1722no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—862no—
586C23—1721no—
587C23—1721no—
588C23—1721no—
589C23—1721no—
590C23—1721no—
591C23—1721no—
592C23#1306330312yes—
593C23C2×D4×D4311yescharacteristic
594Q8—434no—
595Q8—862no—
596Q8—862no—
597Q8—862no—
598Q8—3444no—
599D4—862no—
600D4—862no—
601D4—1728no—
602D4—1721no—
603D4—1721no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
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—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—432no—
623C2×C4—862no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—862no—
627C2×C4—862no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—861no—
634C2×C4—861no—
635C2×C4—862no—
636C2×C4—861no—
637C2×C4—861no—
638C2×C4—1728no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4#1306330312yes—
645C2×C4C2×D4×D4311yescharacteristic
646C2×C4C2×Q8×D4311yescharacteristic
647C2×C4#41×D4311yescharacteristic
648C2×C4C2×#1062189811yescharacteristic
649C2×C4#1306337011yescharacteristic
650C2×C4#1306337111yescharacteristic
651C8—22no—
652C8—41no—
653C8—1721no—
654C8—1721no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—3441no—
663C22—3441no—
664C22—3441no—
665C22—3441no—
666C22—1722no—
667C22—1722no—
668C22—1722no—
669C22C2×#1306330311yescharacteristic
670C22#1458353311yescharacteristic
671C22#1458353811yescharacteristic
672C22#135×D4311yescharacteristic
673C22#1458369611yescharacteristic
674C22#1458370511yescharacteristic
675C22#1458370511yescharacteristic
676C4—22no—
677C4—81no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—862no—
682C4—864no—
683C4—3441no—
684C4—1721no—
685C4—1721no—
686C4—1722no—
687C4—1721no—
688C4C22⋊Q8×D4311yescharacteristic
689C4#1458352411yescharacteristic
690C4#1458353911yescharacteristic
691C4#1458357311yescharacteristic
692C2—42no—
693C2—3442no—
694C2#1913826311yescharacteristic
695C2#1914438111yescharacteristic
696C2#1914446211yescharacteristic
697C2#1914617711yescharacteristic
698C2#1914630911yescharacteristic
699C2#1914652911yescharacteristic
700C2#1914678711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1807C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
hypercenter#1807D43
hypocenterC43#25951
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1807

Complements

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

NH ≅ G/Ntype
1. C2×#14583183C2semidirect
3. #19138287C2semidirect
5. #19136117C2semidirect
6. #19135970C2semidirect
7. #19135964C2semidirect
8. #19135730C2semidirect
9. #19134860C2semidirect
10. #19134850C2semidirect
11. #19134792C2semidirect
12. #19134773C2semidirect
13. #19134609C2semidirect
15. C43×#1807C2semidirect
66. C2×#10621898Q8semidirect
354. #1807D43semidirect
411. C43#25951semidirect

Maximal subgroups

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

subgroupindex
C2×#145831832
C2×#145828962
#191382872
#191374322
#191361172
#191359702
#191359642
#191357302
#191348602
#191348502
#191347922
#191347732
#191346092
#191345332
C43×#18072
#2595143