Finite Group Databasebeta

← #25166486

Subgroups — #25166486

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×#14583260C211yesmaximal, characteristic, complemented
2C2×#14583002C211yesmaximal, characteristic, complemented
3#19138443C211yesmaximal, characteristic, complemented
4#19138391C211yesmaximal, characteristic, complemented
5#19135980C211yesmaximal, characteristic, complemented
6#19135922C211yesmaximal, characteristic, complemented
7#19135910C211yesmaximal, characteristic, complemented
8#19135673C211yesmaximal, characteristic
9#19135461C211yesmaximal, characteristic
10#19135293C211yesmaximal, characteristic, complemented
11#19135293C211yesmaximal, characteristic, complemented
12#19134944C211yesmaximal, characteristic
13#19134851C211yesmaximal, characteristic, complemented
14#19134462C211yesmaximal, characteristic, complemented
15C43×#1933C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×D344C2211yescharacteristic
18C2×#13063324C2211yescharacteristic
19C2×#13063314C2211yescharacteristic
20C2×#13063305—21no—
21C2×Q8×Dic43C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23#14583260—24no—
24#14583002—24no—
25C2×#13063259C2211yescharacteristic
26C2×#13063258C2211yescharacteristic
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063235C2211yescharacteristic
35C2×#13063235C2211yescharacteristic
36#14582836—21no—
37#14582826—21no—
38#14582821—21no—
39#14582812—21no—
40#14582801C2211yescharacteristic
41#14582801C2211yescharacteristic
42#14582800C2211yescharacteristic
43#14582800C2211yescharacteristic
44#14582798C2211yescharacteristic
45#14582798C2211yescharacteristic
46#14582791—21no—
47#14582791—21no—
48#14582773—21no—
49C4×C4⋊Dic43C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×D172C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×D344—22no—
69C2×D344—22no—
70C2×D344—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063324—22no—
74#13063324—41no—
75#13063314—22no—
76#13063314—41no—
77#13063305—44no—
78Q8×Dic43—22no—
79Q8×Dic43—41no—
80#13063287—22no—
81#13063287—41no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43D411yescharacteristic
86C2×C4⋊Dic43D411yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×Dic43⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43C2311yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104#13063259—41no—
105#13063258—22no—
106C4⋊(C43⋊C8)—22no—
107#13063249—22no—
108#13063247—22no—
109#13063247—22no—
110#13063245—22no—
111#13063245—22no—
112#13063245—22no—
113#13063235—22no—
114#13063235—22no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95D411yescharacteristic
118C43⋊#95D411yescharacteristic
119C22×Q8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127#103×C43—22no—
128#103×C43D414yes—
129C4×C8×C43—22no—
130#95×C43—21no—
131#95×C43—21no—
132#95×C43—21no—
133C23×D43—21no—
134C23×D43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43C2×D412yes—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172#4112yes—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×C4×D43—81no—
169C2×Dic86—42no—
170C2×Dic86—42no—
171C2×Dic86—81no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43C2×D412yes—
177C2×C8×C43#4112yes—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—42no—
184C4⋊C4×C43C2×D412yes—
185C42×C43—21no—
186C42×C43—21no—
187#10621884—28no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—81no—
197(C2×D43)⋊C4—81no—
198(C2×D43)⋊C4—81no—
199C4⋊Dic43—22no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—41no—
205C4⋊Dic43—42no—
206C4⋊Dic43—42no—
207C4⋊Dic43—81no—
208Dic43⋊C4—42no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—42no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8#4112yes—
220D344—44no—
221C23×C43C22×D411yescharacteristic
222C22×D43—22no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236Q8×C43—22no—
237Q8×C43—22no—
238Q8×C43—41no—
239Q8×C43—41no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
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×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43AGL(1,ℤ/8)12yes—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C2×C4×C432−1+411yescharacteristic
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
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—
282D172—22no—
283D172—22no—
284D172—41no—
285D172—41no—
286D172—41no—
287D172—41no—
288D172—41no—
289D172—41no—
290C4×D43—84no—
291Dic86—84no—
292C8×C43—22no—
293C8×C43—22no—
294C43⋊C8—22no—
295C43⋊C8—41no—
296#26844—431nomaximal, Sylow
297C22×C43#53211yescharacteristic
298C22×C43D4211yescharacteristic
299C22×C43#54811yescharacteristic
300C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
301C22×C43#57511yescharacteristic
302C22×C43#57611yescharacteristic
303C22×C43#57811yescharacteristic
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C2×D43—81no—
315C2×D43—81no—
316C2×D43—81no—
317C2×D43—81no—
318C4×C43—22no—
319C4×C43—41no—
320C4×C43—42no—
321C4×C43—42no—
322C4×C43—81no—
323C4×C43—81no—
324C4×C43#52511yescharacteristic
325C4×C43#54211yescharacteristic
326C4×C43#54711yescharacteristic
327C4×C43#55111yescharacteristic
328Dic43—41no—
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#1970—431no—
343#1936—431no—
344#1936—431no—
345#1933D4311yescharacteristic, complemented
346#1879—431no—
347#1863—431no—
348#1770—431no—
349C2×C43#246111yescharacteristic
350C2×C43#317511yescharacteristic
351C2×C43#318011yescharacteristic
352C2×C43#327411yescharacteristic
353C2×C43#327711yescharacteristic
354C2×C43#336711yescharacteristic
355C2×C43#337011yescharacteristic
356D43—82no—
357D43—161no—
358C22×SD16—431no—
359C22×D8—431no—
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×#107—431no—
369C2×C4⋊C8—431no—
370C2×#103—431no—
371C2×#103C2×D4311yescharacteristic
372C2×#103C2×D4311yescharacteristic
373C2×#102—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×#97—431no—
379C2×#97—431no—
380C2×C4×C8C2×D4311yescharacteristic
381#399—861no—
382#397—861no—
383#396—861no—
384#393—861no—
385#391C2×D4311yescharacteristic
386#390—431no—
387#390—431no—
388#390—431no—
389#390—431no—
390#389—431no—
391#389—431no—
392#389C2×D4311yescharacteristic
393#388—861no—
394#388—861no—
395#385—861no—
396C4×C4⋊C4—431no—
397#340—431no—
398#340—431no—
399#340C2×D4311yescharacteristic
400#340C2×D4311yescharacteristic
401#336—431no—
402#336—431no—
403C43#2684411yescharacteristic, complemented, Sylow
404C22×Q8—861no—
405C22×Q8C22×D4311yescharacteristic
406C22×D4—431no—
407C22×D4—431no—
408C23×C4—861no—
409C2×SD16—862no—
410C2×SD16—862no—
411C2×SD16—862no—
412C2×D8—862no—
413C2×D8—862no—
414C2×D8—1721no—
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—21no—
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⋊C4C22×D4311yescharacteristic
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C4⋊C4C22×D4311yescharacteristic
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⋊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—862no—
456#107—1721no—
457C4⋊C8—862no—
458#103—22no—
459#103—862no—
460#103D17214yes—
461#102—862no—
462#102—862no—
463#102—862no—
464#102—862no—
465#102—862no—
466#97—862no—
467#97—862no—
468C4×C8—22no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—431no—
473#95—431no—
474#95—861no—
475#95—861no—
476C24—861no—
477C24—861no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—3441no—
484C2×Q8—1722no—
485C2×Q8—1722no—
486C2×Q8C2×D17212yes—
487C2×D4—432no—
488C2×D4—861no—
489C2×D4—861no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C2×D4—861no—
496C2×D4—861no—
497C2×D4—861no—
498C2×D4—861no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—431no—
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—1724no—
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×C8C2×D17212yes—
528C2×C8#1062190012yes—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—862no—
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⋊C4C2×D17212yes—
546C22⋊C4—3441no—
547C22⋊C4—3441no—
548C22⋊C4—3441no—
549C22⋊C4—1722no—
550C22⋊C4—1722no—
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—862no—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23—1721no—
571C23—1721no—
572C23—1721no—
573C23—1721no—
574C23—1721no—
575C23—1721no—
576C23—1721no—
577C23—1721no—
578C23C2×D4×D4311yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—41no—
582Q8—41no—
583Q8—3444no—
584D4—862no—
585D4—862no—
586D4—1721no—
587D4—1721no—
588D4—1721no—
589D4—1721no—
590D4—1721no—
591D4—1721no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
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—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—3444no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4#1306335212yes—
629C2×C4C22×D17211yescharacteristic
630C2×C4#41×D4311yescharacteristic
631C2×C4#41×D4311yescharacteristic
632C2×C4C2×#1062190011yescharacteristic
633C2×C4#1306337111yescharacteristic
634C2×C4#1306337211yescharacteristic
635C8—22no—
636C8—22no—
637C8—862no—
638C8—1721no—
639C22—3441no—
640C22—3441no—
641C22—3441no—
642C22—3441no—
643C22—3441no—
644C22—3441no—
645C22—3441no—
646C22—3441no—
647C22—3441no—
648C22—3441no—
649C22—3441no—
650C22—1722no—
651C22—1722no—
652C22—1722no—
653C22#1458344411yescharacteristic
654C22D4×D17211yescharacteristic
655C22#1458355711yescharacteristic
656C22C2×#1306335211yescharacteristic
657C22#1458369611yescharacteristic
658C22#1458370111yescharacteristic
659C22#1458371211yescharacteristic
660C4—22no—
661C4—42no—
662C4—41no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—3441no—
667C4—3441no—
668C4—1721no—
669C4—1721no—
670C4—1721no—
671C4—1721no—
672C4#1458341111yescharacteristic
673C4#1458351511yescharacteristic
674C4#1458355311yescharacteristic
675C4#1458357211yescharacteristic
676C2—3442no—
677C2—6881no—
678C2#1913856011yescharacteristic
679C2#1914523511yescharacteristic
680C2#1914528611yescharacteristic
681C2#1914621611yescharacteristic
682C2#1914625111yescharacteristic
683C2#1914731811yescharacteristic
684C2#1914735411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1933C2
socleC23×C43C22×D4
prime radicalC22×D344C22
hypercenter#1933D43
hypocenterC43#26844
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1933

Complements

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

NH ≅ G/Ntype
1. C2×#14583260C2semidirect
2. C2×#14583002C2semidirect
3. #19138443C2semidirect
4. #19138391C2semidirect
5. #19135980C2semidirect
6. #19135922C2semidirect
7. #19135910C2semidirect
10. #19135293C2semidirect
11. #19135293C2semidirect
13. #19134851C2semidirect
14. #19134462C2semidirect
15. C43×#1933C2semidirect
345. #1933D43semidirect
403. C43#26844semidirect

Maximal subgroups

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

subgroupindex
C2×#145832602
C2×#145830022
#191384432
#191383912
#191359802
#191359222
#191359102
#191356732
#191354612
#191352932
#191349442
#191348512
#191344622
C43×#19332
#2684443