Finite Group Databasebeta

← #25156527

Subgroups — #25156527

Order 11008.

854 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583241C211yesmaximal, characteristic, complemented
2C2×#14582941C211yesmaximal, characteristic, complemented
3#19138046C211yesmaximal, characteristic
4#19137544C211yesmaximal, characteristic
5#19136137C211yesmaximal, characteristic, complemented
6#19136073C211yesmaximal, characteristic, complemented
7#19136028C211yesmaximal, characteristic, complemented
8#19135792C211yesmaximal, characteristic, complemented
9#19135237C211yesmaximal, characteristic, complemented
10#19135188C211yesmaximal, characteristic, complemented
11#19135028C211yesmaximal, characteristic, complemented
12#19134905C211yesmaximal, characteristic, complemented
13#19134796C211yesmaximal, characteristic, complemented
14#19134790C211yesmaximal, characteristic, complemented
15C43×#1870C211yesmaximal, characteristic
16C2×#13063304C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21#14583241—24no—
22#14582941—24no—
23C2×#13063259C2211yescharacteristic
24C2×#13063259C2211yescharacteristic
25C2×#13063257C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27C2×#13063257C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33#14582832—21no—
34#14582822—21no—
35#14582805C2211yescharacteristic
36#14582802—21no—
37#14582797C2211yescharacteristic
38#14582792—21no—
39#14582792—21no—
40#14582779—21no—
41#14582769C2211yescharacteristic
42#14582759C2211yescharacteristic
43#14582759C2211yescharacteristic
44#14582759C2211yescharacteristic
45#14582757—21no—
46C4⋊C4×Dic43—21no—
47C4×C4⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C22×M16×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C23×Dic43—21no—
63#13063304—22no—
64#13063304—22no—
65#13063304—22no—
66#13063304—41no—
67#13063284—22no—
68#13063284—22no—
69#13063284—41no—
70#13063284—41no—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—41no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96#13063259—22no—
97#13063259D414yescomplemented
98#13063257—22no—
99#13063257—22no—
100#13063257—22no—
101#13063257—41no—
102#13063250—22no—
103#13063250—22no—
104#13063250—22no—
105#13063250—41no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×D4×C43D411yescharacteristic
114C23×C4×C43C2311yescharacteristic
115C23×C4×C43C2311yescharacteristic
116C2×M16×C43—22no—
117C2×M16×C43—22no—
118C2×M16×C43—22no—
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C4×D4×C43—22no—
124C4×D4×C43—22no—
125C2×C4⋊C4×C43D411yescharacteristic
126C2×C22⋊C4×C43D411yescharacteristic
127C2×C22⋊C4×C43D411yescharacteristic
128C2×C42×C43C2311yescharacteristic
129C22⋊C8×C43—22no—
130C22⋊C8×C43—22no—
131C22⋊C8×C43—22no—
132C24×C43C2×D411yescharacteristic
133C24×C43C2×D411yescharacteristic
134C2×D4×C43—22no—
135C2×D4×C43—22no—
136C2×D4×C43—41no—
137C22×C4×C43—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×C43—21no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43#4112yes—
152C22×C4×C43#4112yes—
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—42no—
163C22×Dic43—42no—
164C22×Dic43—81no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171M16×C43—28no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43C2×D412yes—
183C2×C8×C43#4112yes—
184C4⋊C4×C43—22no—
185C22⋊C4×C43—22no—
186C22⋊C4×C43—22no—
187C42×C43—21no—
188C42×C43—21no—
189C22⋊Dic43—42no—
190C22⋊Dic43—42no—
191C22⋊Dic43—42no—
192C22⋊Dic43—42no—
193C22⋊Dic43—81no—
194C22⋊Dic43—81no—
195C22⋊Dic43—81no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—42no—
209C4⋊Dic43—42no—
210C4⋊Dic43—81no—
211C4⋊Dic43C2×D412yes—
212C4⋊Dic43C2×D412yes—
213Dic43⋊C4—42no—
214Dic43⋊C4—42no—
215Dic43⋊C4—81no—
216C4×Dic43—42no—
217C4×Dic43—42no—
218C4×Dic43—42no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43#12312yes—
233C23×C43C22×D411yescharacteristic
234D4×C43—44no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43#12312yes—
254C2×C4×C43#13712yes—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
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—84no—
286Dic86—41no—
287Dic86—41no—
288Dic86—41no—
289Dic86—41no—
290C8×C43—22no—
291C8×C43—22no—
292C8×C43—41no—
293C8×C43—41no—
294#26155—431nomaximal, Sylow
295C22×C43—22no—
296C22×C43—22no—
297C22×C43—22no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43—41no—
303C22×C43—41no—
304C22×C43—41no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43C2×#12311yescharacteristic
310C22×C43D4211yescharacteristic
311C22×C43#54711yescharacteristic
312C22×C43C2×#13711yescharacteristic
313C22×C43#57511yescharacteristic
314C22×C43#57711yescharacteristic
315C22×C43#57711yescharacteristic
316C4×C43—22no—
317C4×C43—22no—
318C4×C43—41no—
319C4×C43—41no—
320C4×C43#52511yescharacteristic
321C4×C43#53911yescharacteristic
322C4×C43#54811yescharacteristic
323C4×C43#55311yescharacteristic
324Dic43—42no—
325Dic43—42no—
326Dic43—81no—
327Dic43—81no—
328Dic43—81no—
329Dic43—81no—
330Dic43—81no—
331Dic43—81no—
332C2×#485—431no—
333C2×#428—431no—
334#2417—431no—
335#2354—431no—
336#2096—431no—
337#2084—431no—
338#2077—431no—
339#2035—431no—
340#1928—431no—
341#1921—431no—
342#1894—431no—
343#1873—431no—
344#1870D4311yescharacteristic
345#1854—431no—
346#1853—431no—
347C2×C43—42no—
348C2×C43—81no—
349C2×C43#244311yescharacteristic
350C2×C43#309511yescharacteristic
351C2×C43#309911yescharacteristic
352C2×C43#326711yescharacteristic
353C2×C43#327811yescharacteristic
354C2×C43#334811yescharacteristic
355C2×C43#335611yescharacteristic
356C22×M16C2×D4311yescharacteristic
357C2×C22⋊Q8—431no—
358C2×C22⋊Q8—431no—
359C2×C4×D4C2×D4311yescharacteristic
360C2×#117—431no—
361C2×#117—431no—
362C22×C4⋊C4—431no—
363#485—864no—
364#428—864no—
365C2×#107—431no—
366C2×#107—431no—
367C2×#106—431no—
368C2×#106—431no—
369C2×#106—431no—
370C2×#106—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×C22⋊C8C2×D4311yescharacteristic
376C2×C22⋊C8C2×D4311yescharacteristic
377C2×C22⋊C8C2×D4311yescharacteristic
378#398—861no—
379#396—861no—
380#391—431no—
381#390—861no—
382#389—431no—
383#388—861no—
384#388—861no—
385#386—861no—
386#384—431no—
387#380—431no—
388#380—431no—
389#380—431no—
390#380—861no—
391C4×C4⋊C4—431no—
392C4×C4⋊C4—861no—
393#340—431no—
394#340—431no—
395#340—431no—
396#340—431no—
397#340—431no—
398#340—431no—
399#336C2×D4311yescharacteristic
400#336C2×D4311yescharacteristic
401C43#2615511yescharacteristic, complemented, Sylow
402C22×Q8—431no—
403C22×D4D17211yescharacteristic
404C23×C4—861no—
405C23×C4C22×D4311yescharacteristic
406C23×C4C22×D4311yescharacteristic
407C2×M16—22no—
408C2×M16—22no—
409C2×M16—22no—
410C22×C8C22×D4311yescharacteristic
411C22×C8C22×D4311yescharacteristic
412C22×C8C22×D4311yescharacteristic
413C22×C8C22×D4311yescharacteristic
414C22⋊Q8—862no—
415C22⋊Q8—862no—
416C22⋊Q8—862no—
417C22⋊Q8—1721no—
418C4×D4—22no—
419C4×D4—22no—
420#117—862no—
421#117—862no—
422#117—1721no—
423#117—1721no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—862no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—1721no—
439C2×C4⋊C4D17211yescharacteristic
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4D17211yescharacteristic
448C2×C22⋊C4D17211yescharacteristic
449C2×C42—861no—
450C2×C42—861no—
451C2×C42—861no—
452C2×C42C22×D4311yescharacteristic
453#107—434no—
454#107—862no—
455#106—862no—
456#106—862no—
457#106—862no—
458#106—1721no—
459#103—862no—
460#103—862no—
461#103—862no—
462#103—1721no—
463C22⋊C8—22no—
464C22⋊C8—22no—
465C22⋊C8—22no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473C24C2×D17211yescharacteristic
474C24C2×D17211yescharacteristic
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—41no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—3441no—
503C22×C4—1722no—
504C22×C4—1722no—
505C22×C4C2×D17211yescharacteristic
506C22×C4C2×D17211yescharacteristic
507C22×C4C2×D17211yescharacteristic
508C22×C4C2×D17211yescharacteristic
509C22×C4#1062190012yes—
510C22×C4#1062190012yes—
511C22×C4C23×D4311yescharacteristic
512M16—28no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8D4×D4312yes—
524C2×C8#1062190012yes—
525C4⋊C4—22no—
526C4⋊C4—432no—
527C4⋊C4—432no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—3441no—
541C4⋊C4—3441no—
542C4⋊C4—1722no—
543C4⋊C4—1722no—
544C4⋊C4—1722no—
545C4⋊C4—1722no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—3441no—
549C22⋊C4—3441no—
550C22⋊C4—3441no—
551C22⋊C4—1722no—
552C22⋊C4—1722no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C42—21no—
556C42—21no—
557C42—1722no—
558C42—1722no—
559C42—1722no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23#1306330912yes—
574C23C22×D17211yescharacteristic
575Q8—1721no—
576Q8—1721no—
577Q8—1721no—
578Q8—1721no—
579D4—44no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—3444no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4#1306330912yes—
624C2×C4#1306335812yes—
625C2×C4C2×D4×D4311yescharacteristic
626C2×C4C2×#1062190011yescharacteristic
627C2×C4C2×#1062190011yescharacteristic
628C2×C4C2×#1062190011yescharacteristic
629C2×C4#1306337111yescharacteristic
630C2×C4#1306337211yescharacteristic
631C8—22no—
632C8—22no—
633C8—41no—
634C8—41no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22C2×#1306330911yescharacteristic
650C22D4×D17211yescharacteristic
651C22#1458355311yescharacteristic
652C22C2×#1306335811yescharacteristic
653C22#1458369911yescharacteristic
654C22#1458371111yescharacteristic
655C22#1458371111yescharacteristic
656C4—22no—
657C4—22no—
658C4—41no—
659C4—41no—
660C4—3441no—
661C4—3441no—
662C4—3441no—
663C4—3441no—
664C4—3441no—
665C4—3441no—
666C4—1722no—
667C4—1722no—
668C4#1458340511yescharacteristic
669C4#1458349311yescharacteristic
670C4#1458355511yescharacteristic
671C4#1458360111yescharacteristic
672C2—42no—
673C2—81no—
674C2#1913832811yescharacteristic
675C2#1914454411yescharacteristic
676C2#1914458611yescharacteristic
677C2#1914612511yescharacteristic
678C2#1914626311yescharacteristic
679C2#1914711211yescharacteristic
680C2#1914721111yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1870C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenter#1870D43
hypocenterC43#26155
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×#14583241C2semidirect
2. C2×#14582941C2semidirect
5. #19136137C2semidirect
6. #19136073C2semidirect
7. #19136028C2semidirect
8. #19135792C2semidirect
9. #19135237C2semidirect
10. #19135188C2semidirect
11. #19135028C2semidirect
12. #19134905C2semidirect
13. #19134796C2semidirect
14. #19134790C2semidirect
97. #13063259D4semidirect
401. C43#26155semidirect

Maximal subgroups

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

subgroupindex
C2×#145832412
C2×#145829412
#191380462
#191375442
#191361372
#191360732
#191360282
#191357922
#191352372
#191351882
#191350282
#191349052
#191347962
#191347902
C43×#18702
#2615543