Finite Group Databasebeta

← #25113722

Subgroups — #25113722

Order 11008.

966 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582892C211yesmaximal, characteristic
2#19137484C211yesmaximal, characteristic, complemented
3#19137434C211yesmaximal, characteristic
4#19135295C211yesmaximal, characteristic, complemented
5#19135289C211yesmaximal, characteristic, complemented
6#19135217C211yesmaximal, characteristic, complemented
7#19134852C211yesmaximal, characteristic, complemented
8#19134846C211yesmaximal, characteristic, complemented
9#19134689C211yesmaximal, characteristic, complemented
10#19134621C211yesmaximal, characteristic, complemented
11#19134532C211yesmaximal, characteristic
12#19134428C211yesmaximal, characteristic, complemented
13#19134424C211yesmaximal, characteristic, complemented
14#19134370C211yesmaximal, characteristic, complemented
15C43×#1925C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22#14582892C418yescomplemented
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32#14582802C2211yescharacteristic
33#14582799—21no—
34#14582799—21no—
35#14582797C2211yescharacteristic
36#14582795C2211yescharacteristic
37#14582790—21no—
38#14582788—21no—
39#14582766—21no—
40#14582757—21no—
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×Dic43⋊C4—21no—
45C22⋊C4×Dic43—21no—
46C4×(C2×D43)⋊C4C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C2×#10621900—22no—
61C2×#10621900—22no—
62C2×#10621900—22no—
63C2×#10621900—41no—
64C2×#10621900—41no—
65C2×#10621900C2×C414yes—
66C22×Dic86C2311yescharacteristic
67C22×C22⋊D43—21no—
68C23×Dic43—21no—
69C22×C4×D43C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C2×C8×D43—41no—
73C2×C8×D43—41no—
74C2×C8×D43C2×C414yes—
75C4×Dic86—22no—
76C4×Dic86—41no—
77#13063290—22no—
78#13063290—41no—
79#13063283—22no—
80#13063283C2×C414yes—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4D411yescharacteristic
94C2×(C2×D43)⋊C4D411yescharacteristic
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43C2311yescharacteristic
100#13063259—41no—
101#13063250—22no—
102#13063250C2×C414yes—
103#13063248—22no—
104#13063248C2×C414yes—
105#13063246—41no—
106#13063246C2×C414yes—
107(C2×D43)⋊C8—22no—
108#13063236—41no—
109#13063235—41no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C22×D4×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C42×C43—21no—
126C2×C42×C43C2311yescharacteristic
127#107×C43—41no—
128#102×C43—41no—
129#102×C43C2×C414yes—
130#95×C43—21no—
131C24×C43—21no—
132C23×D43C2×D411yescharacteristic
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43C22×C412yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C2×C22⋊D43—24no—
146C2×C22⋊D43—42no—
147C2×C22⋊D43—42no—
148C22×Dic43—24no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—42no—
154C22×Dic43—42no—
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158#10621900—28no—
159#10621900—44no—
160#10621900—44no—
161#10621900—44no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43C22×C412yes—
167C2×C4×D43#4112yes—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86C22×C412yes—
172C2×Dic86#4112yes—
173C2×Dic86#4112yes—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C22×C412yes—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43C22×C412yes—
186C22⋊C4×C43—42no—
187C22⋊C4×C43—81no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—81no—
191C22⋊Dic43—42no—
192C22⋊Dic43—81no—
193(C2×D43)⋊C4—24no—
194(C2×D43)⋊C4—41no—
195(C2×D43)⋊C4—41no—
196(C2×D43)⋊C4—81no—
197(C2×D43)⋊C4—81no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43C22×C412yes—
204Dic43⋊C4—42no—
205Dic43⋊C4—42no—
206Dic43⋊C4—42no—
207Dic43⋊C4—42no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—24no—
211C4×Dic43—42no—
212C4×Dic43—42no—
213C4×Dic43—81no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8C22×C412yes—
220C8×D43—44no—
221C23×C43—22no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43C22×D411yescharacteristic
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—21no—
233C22×D43—21no—
234C22×D43—21no—
235C22×D43C4×D412yes—
236D4×C43—22no—
237D4×C43—22no—
238D4×C43—41no—
239D4×C43—41no—
240C2×C4×C43—22no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
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×C43C23×C411yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C22⋊D43—48no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—48no—
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×Dic43C4×D412yes—
284C4×D43—22no—
285C4×D43—22no—
286C4×D43—22no—
287C4×D43—22no—
288Dic86—22no—
289Dic86—22no—
290Dic86—22no—
291Dic86#11714yes—
292C8×C43—22no—
293C8×C43—41no—
294C43⋊C8—22no—
295C43⋊C8—41no—
296#22569—431nomaximal, Sylow
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43C2×C4×D411yescharacteristic
305C22×C43#54611yescharacteristic
306C22×C43#54611yescharacteristic
307C22×C43#57511yescharacteristic
308C22×C43#57511yescharacteristic
309C22×C43#57611yescharacteristic
310C22×C43#57811yescharacteristic
311C2×D43—22no—
312C2×D43—22no—
313C2×D43—22no—
314C2×D43—41no—
315C2×D43—41no—
316C2×D43—41no—
317C2×D43—41no—
318C4×C43—42no—
319C4×C43—41no—
320C4×C43—41no—
321C4×C43—81no—
322C4×C43—81no—
323C4×C43C2×#11711yescharacteristic
324C4×C43#51811yescharacteristic
325C4×C43#55111yescharacteristic
326C4×C43#55111yescharacteristic
327Dic43—24no—
328Dic43—22no—
329Dic43—42no—
330Dic43—41no—
331Dic43—41no—
332Dic43—81no—
333Dic43—81no—
334C2×#416—431no—
335#2347—431no—
336#2341—431no—
337#1936—431no—
338#1936—431no—
339#1925—431no—
340#1925D4311yescharacteristic, complemented
341#1863—431no—
342#1863—431no—
343#1825—431no—
344#1808—431no—
345#1788—431no—
346#1763—431no—
347#1763—431no—
348#1752—431no—
349C2×C43—82no—
350C2×C43#234211yescharacteristic
351C2×C43#294311yescharacteristic
352C2×C43#295111yescharacteristic
353C2×C43#330911yescharacteristic
354C2×C43#330911yescharacteristic
355C2×C43#331311yescharacteristic
356C2×C43#331311yescharacteristic
357D43—42no—
358C22×#41—431no—
359C23×C8—431no—
360C2×C4×Q8—431no—
361C2×C4×Q8—431no—
362C2×#117—431no—
363C2×#107—431no—
364C2×#107C2×D4311yescharacteristic
365#416—438no—
366C2×#103—431no—
367C2×#103—431no—
368C2×#103—431no—
369C2×#103—431no—
370C2×#102—431no—
371C2×#102—431no—
372C2×#102C2×D4311yescharacteristic
373C2×#102C2×D4311yescharacteristic
374C2×C22⋊C8—431no—
375C2×#97—431no—
376C2×#97—431no—
377#390—431no—
378#390—861no—
379#390—861no—
380#390C2×D4311yescharacteristic
381#389—431no—
382#389—431no—
383#388—861no—
384#388—861no—
385#383—861no—
386#380—431no—
387#380—431no—
388#380—861no—
389C4×C4⋊C4—431no—
390C4×C4⋊C4—861no—
391C4×C4⋊C4C2×D4311yescharacteristic
392C4×C22⋊C4—431no—
393C4×C22⋊C4—861no—
394#340—431no—
395#340—431no—
396#340—431no—
397#340—431no—
398#340—431no—
399#340C2×D4311yescharacteristic
400#336—431no—
401#336C2×D4311yescharacteristic
402C43#2256911yescharacteristic, complemented, Sylow
403C2×#41—434no—
404C2×#41—862no—
405C2×#41—862no—
406C2×#41—862no—
407C2×#41—1721no—
408C2×#41—1721no—
409C22×Q8—431no—
410C22×D4—861no—
411C22×D4C22×D4311yescharacteristic
412C23×C4—431no—
413C23×C4—861no—
414C22×C8—431no—
415C22×C8—434no—
416C22×C8—431no—
417C22×C8—1721no—
418C22×C8—1721no—
419C22×C8C22×D4311yescharacteristic
420C22×C8C22×D4311yescharacteristic
421C4×Q8—862no—
422C4×Q8—862no—
423C4×Q8—1721no—
424C4×Q8—1721no—
425#117—434no—
426#117—862no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4C22×D4311yescharacteristic
435C2×C4⋊C4C22×D4311yescharacteristic
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—431no—
440C2×C22⋊C4—431no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C42—21no—
447C2×C42—431no—
448C2×C42—861no—
449C2×C42—861no—
450C2×C42—861no—
451C2×C42—861no—
452C2×C42C22×D4311yescharacteristic
453#107—41no—
454#107—1721no—
455#103—434no—
456#103—434no—
457#103—862no—
458#103—862no—
459#102—41no—
460#102—434no—
461#102—1721no—
462#102C4×D4314yes—
463C22⋊C8—862no—
464#97—1721no—
465#97—1721no—
466#95—21no—
467#95—431no—
468#95—431no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474C24—21no—
475C24—431no—
476#41—868no—
477#41—1724no—
478#41—1724no—
479#41—1724no—
480C2×Q8—432no—
481C2×Q8—432no—
482C2×Q8—432no—
483C2×Q8—861no—
484C2×Q8—861no—
485C2×Q8—861no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—864no—
492C2×D4—1722no—
493C2×D4—1722no—
494C2×D4C2×C4×D4312yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—431no—
499C22×C4—432no—
500C22×C4—432no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—864no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—1722no—
513C22×C4—1722no—
514C22×C4D4×D4311yescharacteristic
515C22×C4D4×D4311yescharacteristic
516C22×C4C23×D4311yescharacteristic
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—432no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—1724no—
529C2×C8C2×C4×D4312yes—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—432no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—1722no—
542C4⋊C4—1722no—
543C4⋊C4—1722no—
544C4⋊C4—1722no—
545C4⋊C4C2×C4×D4312yes—
546C22⋊C4—42no—
547C22⋊C4—81no—
548C22⋊C4—864no—
549C22⋊C4—3441no—
550C22⋊C4—3441no—
551C22⋊C4—3441no—
552C22⋊C4—1721no—
553C22⋊C4—1721no—
554C22⋊C4—1722no—
555C42—21no—
556C42—21no—
557C42—81no—
558C42—864no—
559C42—861no—
560C42—861no—
561C42—3441no—
562C42—1722no—
563C42—1722no—
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—432no—
572C23—861no—
573C23—861no—
574C23—861no—
575C23—861no—
576C23—861no—
577C23—861no—
578C23C2×D4×D4311yescharacteristic
579Q8—434no—
580Q8—862no—
581Q8—862no—
582Q8—862no—
583D4—22no—
584D4—22no—
585D4—41no—
586D4—41no—
587D4—1728no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
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—432no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—861no—
607C2×C4—862no—
608C2×C4—861no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—1728no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4C22×C4×D4311yescharacteristic
630C2×C4#41×D4311yescharacteristic
631C2×C4#41×D4311yescharacteristic
632C2×C4#41×D4311yescharacteristic
633C2×C4#1306337011yescharacteristic
634C2×C4#1306337111yescharacteristic
635C8—22no—
636C8—41no—
637C8—862no—
638C8—1721no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—862no—
647C22—862no—
648C22—862no—
649C22—1721no—
650C22—1721no—
651C22—1721no—
652C22—1721no—
653C22C4×D4×D4311yescharacteristic
654C22#1458354111yescharacteristic
655C22#1458354611yescharacteristic
656C22#1458369511yescharacteristic
657C22#1458369811yescharacteristic
658C22#1458370011yescharacteristic
659C22#1458371311yescharacteristic
660C4—42no—
661C4—41no—
662C4—41no—
663C4—81no—
664C4—81no—
665C4—862no—
666C4—864no—
667C4—3441no—
668C4—3441no—
669C4—1721no—
670C4—1721no—
671C4—1722no—
672C4#117×D4311yescharacteristic
673C4#1458337111yescharacteristic
674C4#1458357411yescharacteristic
675C4#1458357911yescharacteristic
676C2—82no—
677C2—1722no—
678C2#1913743911yescharacteristic
679C2#1914339011yescharacteristic
680C2#1914346511yescharacteristic
681C2#1914660411yescharacteristic
682C2#1914660811yescharacteristic
683C2#1914666411yescharacteristic
684C2#1914666811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1925C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
cosocleC22×C4×C43C24
hypercenter#1925D43
hypocenterC43#22569
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
2. #19137484C2semidirect
4. #19135295C2semidirect
5. #19135289C2semidirect
6. #19135217C2semidirect
7. #19134852C2semidirect
8. #19134846C2semidirect
9. #19134689C2semidirect
10. #19134621C2semidirect
12. #19134428C2semidirect
13. #19134424C2semidirect
14. #19134370C2semidirect
15. C43×#1925C2semidirect
22. #14582892C4semidirect
340. #1925D43semidirect
402. C43#22569semidirect

Maximal subgroups

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

subgroupindex
C2×#145828922
#191374842
#191374342
#191352952
#191352892
#191352172
#191348522
#191348462
#191346892
#191346212
#191345322
#191344282
#191344242
#191343702
C43×#19252
#2256943