Finite Group Databasebeta

← #25156523

Subgroups — #25156523

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×#14583240C211yesmaximal, characteristic, complemented
2C2×#14582942C211yesmaximal, characteristic, complemented
3#19138046C211yesmaximal, characteristic
4#19136139C211yesmaximal, characteristic, complemented
5#19136072C211yesmaximal, characteristic, complemented
6#19136032C211yesmaximal, characteristic, complemented
7#19135791C211yesmaximal, characteristic, complemented
8#19135236C211yesmaximal, characteristic, complemented
9#19135187C211yesmaximal, characteristic, complemented
10#19135026C211yesmaximal, characteristic, complemented
11#19134907C211yesmaximal, characteristic, complemented
12#19134893C211yesmaximal, characteristic
13#19134794C211yesmaximal, characteristic, complemented
14#19134787C211yesmaximal, characteristic, complemented
15C43×#2354C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20#14583240—24no—
21#14582942—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35#14582832—21no—
36#14582822—21no—
37#14582805C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582779—21no—
40#14582759C2211yescharacteristic
41#14582757—21no—
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×C4×D4×C43C2211yescharacteristic
51C2×#117×C43C2211yescharacteristic
52C2×#117×C43C2211yescharacteristic
53C43×#390—21no—
54C43×#388—21no—
55C43×#388—21no—
56C43×#384C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C4×C4⋊C4×C43—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C23×Dic43—21no—
63C2×#10621877—22no—
64C2×#10621877—22no—
65C2×#10621877—22no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063304—22no—
71#13063304—22no—
72#13063304—22no—
73#13063304—41no—
74C2×C4⋊Dic43—22no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—41no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86#13063258—22no—
87#13063258D414yescomplemented
88#13063256—22no—
89#13063256—22no—
90#13063256—22no—
91#13063256—41no—
92#13063248—22no—
93#13063248—22no—
94#13063248—22no—
95#13063248—41no—
96C22⋊(C43⋊C8)—22no—
97C22⋊(C43⋊C8)—22no—
98C22⋊(C43⋊C8)—22no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C22×D4×C43D411yescharacteristic
104C23×C4×C43C2311yescharacteristic
105C23×C4×C43C2311yescharacteristic
106C4×D4×C43—22no—
107C4×D4×C43—22no—
108#117×C43—22no—
109#117×C43—22no—
110#117×C43—41no—
111#117×C43—41no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43D411yescharacteristic
124C2×C22⋊C4×C43D411yescharacteristic
125C2×C42×C43—21no—
126C2×C42×C43—21no—
127C2×C42×C43—21no—
128C2×C42×C43C2311yescharacteristic
129#95×C43—21no—
130#95×C43—21no—
131#95×C43—21no—
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×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43#4112yes—
156C22×C4×C43#4112yes—
157C22×C4×C43C2411yescharacteristic
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—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—42no—
180C4⋊C4×C43—81no—
181C4⋊C4×C43C2×D412yes—
182C22⋊C4×C43—22no—
183C22⋊C4×C43—22no—
184C22⋊C4×C43—42no—
185C22⋊C4×C43—42no—
186C22⋊C4×C43—81no—
187C22⋊C4×C43—81no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—42no—
191C42×C43—42no—
192C42×C43—42no—
193C22⋊Dic43—42no—
194C22⋊Dic43—42no—
195C22⋊Dic43—81no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—42no—
202C4⋊Dic43C2×D412yes—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205Dic43⋊C4—81no—
206#10621877—28no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8C2×D412yes—
218C2×C43⋊C8#4112yes—
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—22no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
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×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43#12312yes—
266C2×C4×C43#13712yes—
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43H(5,𝔽2)11yescharacteristic
272C2×C4×C432−1+411yescharacteristic
273C2×Dic43—22no—
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—
290C43⋊C8—22no—
291C43⋊C8—22no—
292C43⋊C8—41no—
293C43⋊C8—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—42no—
321C4×C43—81no—
322C4×C43—81no—
323C4×C43—81no—
324C4×C43#52511yescharacteristic
325C4×C43#53911yescharacteristic
326C4×C43#54811yescharacteristic
327C4×C43#55311yescharacteristic
328Dic43—42no—
329Dic43—81no—
330Dic43—81no—
331Dic43—81no—
332C2×#485—431no—
333C2×#428—431no—
334#2417—431no—
335#2354D4311yescharacteristic
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#1870—431no—
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×M16—431no—
357C2×C22⋊Q8—431no—
358C2×C22⋊Q8—431no—
359C2×C4×D4C2×D4311yescharacteristic
360C2×#117C2×D4311yescharacteristic
361C2×#117C2×D4311yescharacteristic
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⋊C8—431no—
376C2×C22⋊C8—431no—
377C2×C22⋊C8—431no—
378#398—861no—
379#396—861no—
380#391—431no—
381#390—21no—
382#389—431no—
383#388—21no—
384#388—21no—
385#386—861no—
386#384C2×D4311yescharacteristic
387#380—431no—
388#380—861no—
389#380C2×D4311yescharacteristic
390#380C2×D4311yescharacteristic
391C4×C4⋊C4—21no—
392C4×C4⋊C4C2×D4311yescharacteristic
393#340—431no—
394#340—431no—
395#340—431no—
396#340—431no—
397#340—431no—
398#340—431no—
399#336—431no—
400#336—431no—
401C43#2615511yescharacteristic, complemented, Sylow
402C22×Q8—431no—
403C22×D4C22⋊D4311yescharacteristic
404C23×C4—861no—
405C23×C4C22×D4311yescharacteristic
406C23×C4C22×D4311yescharacteristic
407C2×M16—862no—
408C2×M16—862no—
409C2×M16—862no—
410C22×C8—431no—
411C22×C8—431no—
412C22×C8—431no—
413C22×C8—431no—
414C22⋊Q8—862no—
415C22⋊Q8—862no—
416C22⋊Q8—862no—
417C22⋊Q8—1721no—
418C4×D4—22no—
419C4×D4—22no—
420#117—22no—
421#117—22no—
422#117—41no—
423#117—41no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—862no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—1721no—
435C2×C4⋊C4C22⋊D4311yescharacteristic
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4C22⋊D4311yescharacteristic
448C2×C22⋊C4C22⋊D4311yescharacteristic
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
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—862no—
464C22⋊C8—862no—
465C22⋊C8—862no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473C24C2×C22⋊D4311yescharacteristic
474C24C2×C22⋊D4311yescharacteristic
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—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—3441no—
503C22×C4—1722no—
504C22×C4—1722no—
505C22×C4#1062189812yes—
506C22×C4#1062189812yes—
507C22×C4C2×C22⋊D4311yescharacteristic
508C22×C4C2×C22⋊D4311yescharacteristic
509C22×C4C2×C22⋊D4311yescharacteristic
510C22×C4C2×C22⋊D4311yescharacteristic
511C22×C4C23×D4311yescharacteristic
512M16—868no—
513C2×C8—432no—
514C2×C8—432no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C4⋊C4—22no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—42no—
534C4⋊C4—81no—
535C4⋊C4—432no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—3441no—
542C4⋊C4—1722no—
543C4⋊C4—1722no—
544C4⋊C4—1722no—
545C4⋊C4D4×D4312yes—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—81no—
551C22⋊C4—81no—
552C22⋊C4—3441no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C42—21no—
556C42—21no—
557C42—42no—
558C42—42no—
559C42—42no—
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#1306330812yes—
574C23C22×C22⋊D4311yescharacteristic
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—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—862no—
611C2×C4—3444no—
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#1306330812yes—
624C2×C4#1306335512yes—
625C2×C4C2×D4×D4311yescharacteristic
626C2×C4#41×D4311yescharacteristic
627C2×C4C2×#1062189811yescharacteristic
628C2×C4C2×#1062189811yescharacteristic
629C2×C4#1306337011yescharacteristic
630C2×C4#1306337211yescharacteristic
631C8—862no—
632C8—862no—
633C8—1721no—
634C8—1721no—
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×#1306330811yescharacteristic
650C22D4×C22⋊D4311yescharacteristic
651C22#1458354811yescharacteristic
652C22C2×#1306335511yescharacteristic
653C22#1458369711yescharacteristic
654C22#1458370711yescharacteristic
655C22#1458371011yescharacteristic
656C4—22no—
657C4—22no—
658C4—41no—
659C4—41no—
660C4—42no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4—3441no—
665C4—3441no—
666C4—3441no—
667C4—1722no—
668C4#1458340811yescharacteristic
669C4#1458349111yescharacteristic
670C4#1458355811yescharacteristic
671C4#1458359811yescharacteristic
672C2—42no—
673C2—81no—
674C2#1913832411yescharacteristic
675C2#1914454311yescharacteristic
676C2#1914458411yescharacteristic
677C2#1914612111yescharacteristic
678C2#1914626111yescharacteristic
679C2#1914711011yescharacteristic
680C2#1914720411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2354C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenter#2354D43
hypocenterC43#26155
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
1. C2×#14583240C2semidirect
2. C2×#14582942C2semidirect
4. #19136139C2semidirect
5. #19136072C2semidirect
6. #19136032C2semidirect
7. #19135791C2semidirect
8. #19135236C2semidirect
9. #19135187C2semidirect
10. #19135026C2semidirect
11. #19134907C2semidirect
13. #19134794C2semidirect
14. #19134787C2semidirect
87. #13063258D4semidirect
401. C43#26155semidirect

Maximal subgroups

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

subgroupindex
C2×#145832402
C2×#145829422
#191380462
#191361392
#191360722
#191360322
#191357912
#191352362
#191351872
#191350262
#191349072
#191348932
#191347942
#191347872
C43×#23542
#2615543