Finite Group Databasebeta

← #25153749

Subgroups — #25153749

Order 11008.

986 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583200C211yesmaximal, characteristic, complemented
2C2×#14582896C211yesmaximal, characteristic
3#19138308C211yesmaximal, characteristic, complemented
4#19137426C211yesmaximal, characteristic
5#19136132C211yesmaximal, characteristic, complemented
6#19135989C211yesmaximal, characteristic, complemented
7#19135975C211yesmaximal, characteristic, complemented
8#19135747C211yesmaximal, characteristic, complemented
9#19134845C211yesmaximal, characteristic, complemented
10#19134845C211yesmaximal, characteristic, complemented
11#19134796C211yesmaximal, characteristic, complemented
12#19134624C211yesmaximal, characteristic, complemented
13#19134596C211yesmaximal, characteristic, complemented
14#19134536C211yesmaximal, characteristic
15C43×#1850C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21#14583200—24no—
22C2×#13063259C2211yescharacteristic
23C2×#13063259C2211yescharacteristic
24C2×#13063259C2211yescharacteristic
25C2×#13063257C2211yescharacteristic
26#14582896—24no—
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35#14582835—21no—
36#14582822—21no—
37#14582805C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582796—21no—
42#14582782—21no—
43#14582775—21no—
44#14582775—21no—
45#14582769C2211yescharacteristic
46#14582761—21no—
47#14582759C2211yescharacteristic
48#14582759C2211yescharacteristic
49#95×D43—21no—
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C23×C8×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C2×#10621898—22no—
62C2×#10621898—22no—
63C2×#10621898—22no—
64C2×#10621898—41no—
65C2×#10621898—41no—
66C2×#10621898Q814yes—
67C22×Dic86C2311yescharacteristic
68C22×D172C2311yescharacteristic
69C22×C22⋊D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73#13063317—22no—
74#13063317—41no—
75C4×D172—22no—
76C4×D172—22no—
77C4×D172—41no—
78C4×D172—41no—
79#13063284—22no—
80#13063284—41no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×C4×Dic43—21no—
99#13063259—22no—
100#13063259—41no—
101#13063259—41no—
102#13063257—22no—
103#13063250—22no—
104#13063250—22no—
105#13063250—41no—
106#13063250—41no—
107#13063247—22no—
108#13063247—22no—
109#13063247—22no—
110#13063247D414yes—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C23×C4×C43C2311yescharacteristic
120C22×C8×C43—22no—
121C22×C8×C43—22no—
122C22×C8×C43—41no—
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C2×C22⋊C4×C43D411yescharacteristic
128C2×C22⋊C4×C43D411yescharacteristic
129C2×C42×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—22no—
132C4⋊C8×C43—41no—
133C22⋊C8×C43—22no—
134#95×C43D411yescharacteristic
135#95×C43D411yescharacteristic
136C24×C43C2×D411yescharacteristic
137C23×D43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
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×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160#10621898—28no—
161#10621898—44no—
162#10621898—44no—
163#10621898—44no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172C2×D412yes—
168C2×D172C2×Q812yes—
169C2×D172#4112yes—
170C2×C4×D43—24no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×C4×D43—42no—
174C2×C4×D43—42no—
175C2×C4×D43—42no—
176C2×C4×D43—42no—
177C2×C4×D43—81no—
178C2×C4×D43—81no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86C2×Q812yes—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—44no—
197C2×C8×C43C2×D412yes—
198C22⋊C4×C43—22no—
199C22⋊C4×C43—41no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—21no—
203C42×C43—21no—
204C22⋊Dic43—42no—
205C22⋊Dic43—81no—
206C22⋊Dic43—81no—
207(C2×D43)⋊C4—42no—
208(C2×D43)⋊C4—42no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—42no—
221C4⋊Dic43—81no—
222C4⋊Dic43C2×D412yes—
223Dic43⋊C4—42no—
224Dic43⋊C4—42no—
225Dic43⋊C4—42no—
226Dic43⋊C4—81no—
227C4×Dic43—42no—
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—22no—
238C22×D43—22no—
239C22×D43—41no—
240C22×D43—41no—
241C22×D43—41no—
242C22×D43—41no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43C22⋊Q812yes—
261C2×C4×C43#13512yes—
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—22no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
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×Dic43—41no—
290D172—22no—
291D172—22no—
292D172—22no—
293D172C22⋊Q814yes—
294C4×D43—48no—
295C4×D43—84no—
296C4×D43—84no—
297Dic86—22no—
298Dic86—22no—
299Dic86—41no—
300Dic86—41no—
301C8×C43—22no—
302C8×C43—41no—
303C8×C43—41no—
304C8×C43—41no—
305#25956—431nomaximal, Sylow
306C22×C43—22no—
307C22×C43—22no—
308C22×C43—22no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43C2×C22⋊Q811yescharacteristic
314C22×C43D4211yescharacteristic
315C22×C43#54611yescharacteristic
316C22×C43C2×#13511yescharacteristic
317C22×C43#57511yescharacteristic
318C22×C43#57611yescharacteristic
319C22×C43#57811yescharacteristic
320C2×D43—24no—
321C2×D43—42no—
322C2×D43—42no—
323C2×D43—42no—
324C2×D43—42no—
325C2×D43—42no—
326C2×D43—42no—
327C4×C43—22no—
328C4×C43—22no—
329C4×C43—41no—
330C4×C43—41no—
331C4×C43—41no—
332C4×C43C2×C22⋊Q811yescharacteristic
333C4×C43#54311yescharacteristic
334C4×C43#54611yescharacteristic
335C4×C43#55111yescharacteristic
336Dic43—42no—
337Dic43—42no—
338Dic43—81no—
339Dic43—81no—
340Dic43—81no—
341Dic43—81no—
342Dic43—81no—
343C2×#478—431no—
344C2×#416—431no—
345#2441—431no—
346#2339—431no—
347#2095—431no—
348#2068—431no—
349#2066—431no—
350#2026—431no—
351#1862—431no—
352#1862—431no—
353#1854—431no—
354#1850D4311yescharacteristic, complemented
355#1808—431no—
356#1802—431no—
357#1788—431no—
358C2×C43—42no—
359C2×C43#243711yescharacteristic
360C2×C43#307611yescharacteristic
361C2×C43#308311yescharacteristic
362C2×C43#326811yescharacteristic
363C2×C43#328311yescharacteristic
364C2×C43#329711yescharacteristic
365C2×C43#331511yescharacteristic
366D43—44no—
367C22×#41—431no—
368C23×C8C2×D4311yescharacteristic
369C2×#125—431no—
370C2×C4×D4—431no—
371C2×C4×D4—431no—
372C2×#117—431no—
373#478—864no—
374C2×#107—431no—
375C2×#107—431no—
376C2×#107—431no—
377C2×#106—431no—
378C2×C4⋊C8C2×D4311yescharacteristic
379C2×C4⋊C8C2×D4311yescharacteristic
380#416—864no—
381C2×#103—431no—
382C2×#103—431no—
383C2×#103—431no—
384C2×#103—431no—
385C2×#102—431no—
386C2×#102—431no—
387C2×#102—431no—
388C2×#102—431no—
389C2×C22⋊C8C2×D4311yescharacteristic
390#399—861no—
391#396—861no—
392#391—431no—
393#391—431no—
394#389—431no—
395#389—431no—
396#389—861no—
397#387—861no—
398#386—861no—
399#386—861no—
400#384—431no—
401#381—861no—
402#380—431no—
403#380—431no—
404C4×C22⋊C4C2×D4311yescharacteristic
405C2×#95—861no—
406#340—431no—
407#340—431no—
408#340—431no—
409#340—431no—
410#336C2×D4311yescharacteristic
411#336C2×D4311yescharacteristic
412C43#2595611yescharacteristic, complemented, Sylow
413C2×#41—434no—
414C2×#41—862no—
415C2×#41—862no—
416C2×#41—862no—
417C2×#41—1721no—
418C2×#41—1721no—
419C22×Q8—431no—
420C22×D4—431no—
421C22×D4—861no—
422C23×C4—861no—
423C23×C4—861no—
424C23×C4—861no—
425C23×C4C22×D4311yescharacteristic
426C22×C8—22no—
427C22×C8—22no—
428C22×C8—41no—
429C22×C8C22×D4311yescharacteristic
430C22×C8C22×D4311yescharacteristic
431C22×C8C22×D4311yescharacteristic
432C22×C8C22×D4311yescharacteristic
433#125—862no—
434#125—1721no—
435C4×D4—862no—
436C4×D4—862no—
437C4×D4—1721no—
438C4×D4—1721no—
439#117—862no—
440#117—1721no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—431no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4D17211yescharacteristic
459C2×C22⋊C4D17211yescharacteristic
460C2×C42—861no—
461C2×C42C22×D4311yescharacteristic
462C2×C42C22×D4311yescharacteristic
463#107—862no—
464#107—1721no—
465#107—1721no—
466#106—862no—
467C4⋊C8—22no—
468C4⋊C8—41no—
469#103—862no—
470#103—862no—
471#103—1721no—
472#103—1721no—
473#102—434no—
474#102—862no—
475#102—862no—
476#102—862no—
477C22⋊C8—22no—
478#95—861no—
479#95—861no—
480#95—861no—
481#95—861no—
482#95—861no—
483#95—861no—
484#95—861no—
485#95—861no—
486#95D17211yescharacteristic
487#95D17211yescharacteristic
488C24—861no—
489C24C2×D17211yescharacteristic
490#41—868no—
491#41—1724no—
492#41—1724no—
493#41—1724no—
494C2×Q8—432no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8—861no—
500C2×D4—432no—
501C2×D4—432no—
502C2×D4—432no—
503C2×D4—864no—
504C2×D4—861no—
505C2×D4—861no—
506C2×D4—861no—
507C2×D4—1722no—
508C2×D4—1722no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—864no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—3441no—
522C22×C4—3441no—
523C22×C4—1722no—
524C22×C4—1722no—
525C22×C4—1722no—
526C22×C4—1722no—
527C22×C4—1722no—
528C22×C4—1722no—
529C22×C4C2×D17211yescharacteristic
530C22×C4C2×D17211yescharacteristic
531C22×C4C2×D17211yescharacteristic
532C22×C4C2×D17211yescharacteristic
533C22×C4C2×D17211yescharacteristic
534C22×C4#1062190012yes—
535C22×C4Q8×D4312yes—
536C22×C4C23×D4311yescharacteristic
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—44no—
549C2×C8D4×D4312yes—
550C4⋊C4—432no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—861no—
560C4⋊C4—861no—
561C4⋊C4—861no—
562C4⋊C4—3441no—
563C4⋊C4—3441no—
564C4⋊C4—1722no—
565C4⋊C4—1722no—
566C4⋊C4—1722no—
567C4⋊C4—1722no—
568C22⋊C4—22no—
569C22⋊C4—41no—
570C22⋊C4—3441no—
571C22⋊C4—3441no—
572C22⋊C4—1722no—
573C22⋊C4—1722no—
574C22⋊C4—1722no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—1722no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—862no—
587C23—862no—
588C23—862no—
589C23—1721no—
590C23—1721no—
591C23—1721no—
592C23—1721no—
593C23#1306330512yes—
594C23C22×D17211yescharacteristic
595Q8—862no—
596Q8—862no—
597Q8—1721no—
598Q8—1721no—
599D4—434no—
600D4—862no—
601D4—862no—
602D4—862no—
603D4—1728no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—3444no—
624C2×C4—3444no—
625C2×C4—1728no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
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×C4—1721no—
644C2×C4—1721no—
645C2×C4#1306330512yes—
646C2×C4#1306334712yes—
647C2×C4C2×D4×D4311yescharacteristic
648C2×C4C2×Q8×D4311yescharacteristic
649C2×C4#41×D4311yescharacteristic
650C2×C4C2×#1062190011yescharacteristic
651C2×C4#1306337011yescharacteristic
652C2×C4#1306337111yescharacteristic
653C8—22no—
654C8—41no—
655C8—41no—
656C8—41no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—864no—
665C22—1722no—
666C22—1722no—
667C22—1722no—
668C22—1722no—
669C22—1722no—
670C22—1722no—
671C22C2×#1306330511yescharacteristic
672C22D4×D17211yescharacteristic
673C22#1458354411yescharacteristic
674C22C2×#1306334711yescharacteristic
675C22#1458369911yescharacteristic
676C22#1458370411yescharacteristic
677C22#1458371611yescharacteristic
678C4—22no—
679C4—22no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4—3441no—
684C4—3441no—
685C4—3441no—
686C4—3441no—
687C4—3441no—
688C4—1722no—
689C4—1722no—
690C4C22⋊Q8×D4311yescharacteristic
691C4#1458352411yescharacteristic
692C4#1458353611yescharacteristic
693C4#1458357211yescharacteristic
694C2—42no—
695C2—1724no—
696C2#1913825911yescharacteristic
697C2#1914438511yescharacteristic
698C2#1914444811yescharacteristic
699C2#1914614011yescharacteristic
700C2#1914631711yescharacteristic
701C2#1914644711yescharacteristic
702C2#1914669311yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1850C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
hypercenter#1850D43
hypocenterC43#25956
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×#14583200C2semidirect
3. #19138308C2semidirect
5. #19136132C2semidirect
6. #19135989C2semidirect
7. #19135975C2semidirect
8. #19135747C2semidirect
9. #19134845C2semidirect
10. #19134845C2semidirect
11. #19134796C2semidirect
12. #19134624C2semidirect
13. #19134596C2semidirect
15. C43×#1850C2semidirect
354. #1850D43semidirect
412. C43#25956semidirect

Maximal subgroups

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

subgroupindex
C2×#145832002
C2×#145828962
#191383082
#191374262
#191361322
#191359892
#191359752
#191357472
#191348452
#191347962
#191346242
#191345962
#191345362
C43×#18502
#2595643