Finite Group Databasebeta

← #25166494

Subgroups — #25166494

Order 11008.

868 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×#14583257C211yesmaximal, characteristic, complemented
2C2×#14582996C211yesmaximal, characteristic, complemented
3#19138448C211yesmaximal, characteristic, complemented
4#19138396C211yesmaximal, characteristic, complemented
5#19135983C211yesmaximal, characteristic, complemented
6#19135921C211yesmaximal, characteristic, complemented
7#19135912C211yesmaximal, characteristic, complemented
8#19135670C211yesmaximal, characteristic
9#19135289C211yesmaximal, characteristic, complemented
10#19135289C211yesmaximal, characteristic, complemented
11#19135271C211yesmaximal, characteristic, complemented
12#19134945C211yesmaximal, characteristic
13#19134846C211yesmaximal, characteristic, complemented
14#19134462C211yesmaximal, characteristic, complemented
15C43×#1970C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063312C2211yescharacteristic
19C2×#13063302—21no—
20C2×#13063290C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22#14583257—24no—
23#14582996—24no—
24C2×#13063258C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33C2×#13063235C2211yescharacteristic
34#14582835—21no—
35#14582827—21no—
36#14582822—21no—
37#14582811—21no—
38#14582805C2211yescharacteristic
39#14582802C2211yescharacteristic
40#14582802C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582795C2211yescharacteristic
44#14582793—21no—
45#14582792—21no—
46#14582771—21no—
47C4×C4⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×D8×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#390C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C2×#10621883—22no—
65C2×#10621883—22no—
66C2×#10621883—22no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063324—22no—
70#13063324—41no—
71#13063312—22no—
72#13063312—41no—
73#13063302—44no—
74#13063290—22no—
75#13063290—41no—
76D4×Dic43—22no—
77D4×Dic43—41no—
78C2×C4⋊Dic43D411yescharacteristic
79C2×C4⋊Dic43D411yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
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×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98#13063258—22no—
99C4⋊(C43⋊C8)—22no—
100#13063250—22no—
101#13063250D414yes—
102#13063248—22no—
103#13063246—22no—
104#13063246—22no—
105#13063246—22no—
106#13063235—22no—
107#13063235—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95D411yescharacteristic
114C43⋊#95D411yescharacteristic
115C22×D4×C43C2311yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C2×D8×C43—22no—
118C2×D8×C43—22no—
119C2×D8×C43—41no—
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C42×C43C2311yescharacteristic
129#107×C43—41no—
130#102×C43—22no—
131#102×C43—22no—
132C4×C8×C43—22no—
133C24×C43—21no—
134C24×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43#4112yes—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—42no—
157C22×Dic43—42no—
158C22×Dic43—81no—
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—42no—
169C2×Dic86—42no—
170C2×Dic86—81no—
171C2×Dic86C2×D412yes—
172D8×C43—44no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43C2×D412yes—
178C2×C8×C43#4112yes—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C22⋊C4×C43—42no—
184C22⋊C4×C43—42no—
185C22⋊C4×C43—81no—
186C22⋊C4×C43—81no—
187C42×C43—21no—
188C42×C43—21no—
189C22⋊Dic43—42no—
190C22⋊Dic43—42no—
191C22⋊Dic43—42no—
192C22⋊Dic43—42no—
193C22⋊Dic43—42no—
194C22⋊Dic43—42no—
195C22⋊Dic43—81no—
196#10621883—28no—
197C4⋊Dic43—22no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—41no—
204C4⋊Dic43C2×D412yes—
205Dic43⋊C4—42no—
206Dic43⋊C4—42no—
207Dic43⋊C4—42no—
208Dic43⋊C4—42no—
209Dic43⋊C4—81no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—42no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8#4112yes—
221C23×C43—22no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43C22×D411yescharacteristic
236D4×C43—22no—
237D4×C43—22no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
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—41no—
254C2×C4×C43—41no—
255C2×C4×C43AGL(1,ℤ/8)12yes—
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C2×C4×C432−1+411yescharacteristic
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
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—84no—
287Dic86—22no—
288Dic86—22no—
289Dic86—41no—
290Dic86—41no—
291Dic86—84no—
292C8×C43—22no—
293C8×C43—22no—
294C43⋊C8—22no—
295C43⋊C8—41no—
296#26844—431nomaximal, Sylow
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43#53211yescharacteristic
312C22×C43D4211yescharacteristic
313C22×C43#54811yescharacteristic
314C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C43#57511yescharacteristic
316C22×C43#57611yescharacteristic
317C22×C43#57811yescharacteristic
318C4×C43—22no—
319C4×C43—41no—
320C4×C43—81no—
321C4×C43—81no—
322C4×C43#52511yescharacteristic
323C4×C43#54211yescharacteristic
324C4×C43#54711yescharacteristic
325C4×C43#55111yescharacteristic
326Dic43—42no—
327Dic43—41no—
328Dic43—42no—
329Dic43—41no—
330Dic43—41no—
331Dic43—41no—
332Dic43—81no—
333Dic43—81no—
334C2×#489—431no—
335C2×#440—431no—
336#2452—431no—
337#2448—431no—
338#2067—431no—
339#2057—431no—
340#2055—431no—
341#2012—431no—
342#1970D4311yescharacteristic
343#1936—431no—
344#1936—431no—
345#1933—431no—
346#1879—431no—
347#1863—431no—
348#1770—431no—
349C2×C43—82no—
350C2×C43—161no—
351C2×C43#246111yescharacteristic
352C2×C43#317511yescharacteristic
353C2×C43#318011yescharacteristic
354C2×C43#327411yescharacteristic
355C2×C43#327711yescharacteristic
356C2×C43#336711yescharacteristic
357C2×C43#337011yescharacteristic
358C22×SD16—431no—
359C22×D8C2×D4311yescharacteristic
360C2×C4⋊Q8—431no—
361C2×#124—431no—
362C2×C22⋊Q8—861no—
363C2×C4×Q8—431no—
364C2×C4×D4—431no—
365#489—864no—
366#440—864no—
367C2×#107—431no—
368C2×#107C2×D4311yescharacteristic
369C2×C4⋊C8—431no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102C2×D4311yescharacteristic
377C2×#102C2×D4311yescharacteristic
378C2×#97—431no—
379C2×#97—431no—
380C2×C4×C8C2×D4311yescharacteristic
381#399—861no—
382#397—861no—
383#396—861no—
384#393—861no—
385#391—431no—
386#390—431no—
387#390—431no—
388#390C2×D4311yescharacteristic
389#390C2×D4311yescharacteristic
390#389—431no—
391#389—431no—
392#389—431no—
393#388—861no—
394#388—861no—
395#385—861no—
396C4×C4⋊C4—431no—
397#340—431no—
398#340—431no—
399#340—431no—
400#340—431no—
401#336—431no—
402#336—431no—
403C43#2684411yescharacteristic, complemented, Sylow
404C22×Q8—431no—
405C22×Q8—861no—
406C22×D4C22×D4311yescharacteristic
407C22×D4C22×D4311yescharacteristic
408C23×C4—861no—
409C2×SD16—862no—
410C2×SD16—862no—
411C2×SD16—862no—
412C2×D8—22no—
413C2×D8—22no—
414C2×D8—41no—
415C22×C8—431no—
416C22×C8—431no—
417C22×C8C22×D4311yescharacteristic
418C22×C8C22×D4311yescharacteristic
419C4⋊Q8—862no—
420C4⋊Q8—1721no—
421#124—862no—
422#124—1721no—
423C22⋊Q8—1724no—
424C4×Q8—862no—
425C4×Q8—1721no—
426C4×D4—862no—
427C4×D4—1721no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
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⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C42—431no—
452C2×C42—431no—
453C2×C42—861no—
454C2×C42C22×D4311yescharacteristic
455#107—41no—
456#107—862no—
457C4⋊C8—862no—
458#103—434no—
459#103—862no—
460#103—862no—
461#102—22no—
462#102—22no—
463#102—862no—
464#102—862no—
465#102—862no—
466#97—862no—
467#97—862no—
468C4×C8—22no—
469#95—431no—
470#95—431no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476C24—21no—
477C24—21no—
478C2×Q8—432no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8—861no—
483C2×Q8—861no—
484C2×Q8—3441no—
485C2×Q8—1722no—
486C2×Q8—1722no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4#1062189812yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—3441no—
510C22×C4—1722no—
511C22×C4—1722no—
512C22×C4D4×D4311yescharacteristic
513C22×C4D4×D4311yescharacteristic
514C22×C4C23×D4311yescharacteristic
515SD16—868no—
516D8—44no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—432no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8D4×D4312yes—
528C2×C8#1062190012yes—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—432no—
534C4⋊C4—862no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—3441no—
541C4⋊C4—1721no—
542C4⋊C4—1722no—
543C4⋊C4—1722no—
544C4⋊C4—1722no—
545C4⋊C4—1722no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—81no—
549C22⋊C4—81no—
550C22⋊C4—3441no—
551C22⋊C4—1722no—
552C22⋊C4—1722no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C22⋊C4—1722no—
556C22⋊C4—1722no—
557C42—21no—
558C42—21no—
559C42—861no—
560C42—861no—
561C42—861no—
562C42—861no—
563C42—1722no—
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23C2×D4×D4311yescharacteristic
579Q8—862no—
580Q8—862no—
581Q8—3444no—
582Q8—1721no—
583Q8—1721no—
584D4—22no—
585D4—22no—
586D4—41no—
587D4—41no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—862no—
616C2×C4—862no—
617C2×C4—3444no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4#1306334912yes—
629C2×C4C2×D4×D4311yescharacteristic
630C2×C4#41×D4311yescharacteristic
631C2×C4C2×#1062190011yescharacteristic
632C2×C4C2×#1062189811yescharacteristic
633C2×C4#1306337011yescharacteristic
634C2×C4#1306337211yescharacteristic
635C8—22no—
636C8—22no—
637C8—862no—
638C8—1721no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22#1458344411yescharacteristic
654C22#1458353411yescharacteristic
655C22#1458355811yescharacteristic
656C22C2×#1306334911yescharacteristic
657C22#1458369611yescharacteristic
658C22#1458370011yescharacteristic
659C22#1458371311yescharacteristic
660C4—22no—
661C4—41no—
662C4—81no—
663C4—81no—
664C4—3441no—
665C4—3441no—
666C4—1722no—
667C4—1721no—
668C4—1721no—
669C4—1721no—
670C4—1721no—
671C4—1722no—
672C4#1458340811yescharacteristic
673C4#1458351311yescharacteristic
674C4#1458354911yescharacteristic
675C4#1458357511yescharacteristic
676C2—82no—
677C2—161no—
678C2#1913856811yescharacteristic
679C2#1914522711yescharacteristic
680C2#1914528811yescharacteristic
681C2#1914621411yescharacteristic
682C2#1914625011yescharacteristic
683C2#1914731111yescharacteristic
684C2#1914734411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1970C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
hypercenter#1970D43
hypocenterC43#26844
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1970

Complements

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

NH ≅ G/Ntype
1. C2×#14583257C2semidirect
2. C2×#14582996C2semidirect
3. #19138448C2semidirect
4. #19138396C2semidirect
5. #19135983C2semidirect
6. #19135921C2semidirect
7. #19135912C2semidirect
9. #19135289C2semidirect
10. #19135289C2semidirect
11. #19135271C2semidirect
13. #19134846C2semidirect
14. #19134462C2semidirect
403. C43#26844semidirect

Maximal subgroups

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

subgroupindex
C2×#145832572
C2×#145829962
#191384482
#191383962
#191359832
#191359212
#191359122
#191356702
#191352892
#191352712
#191349452
#191348462
#191344622
C43×#19702
#2684443