Finite Group Databasebeta

← #25160141

Subgroups — #25160141

Order 11008.

902 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138293C211yesmaximal, characteristic, complemented
2#19137616C211yesmaximal, characteristic
3#19136155C211yesmaximal, characteristic, complemented
4#19136087C211yesmaximal, characteristic, complemented
5#19135983C211yesmaximal, characteristic, complemented
6#19135548C211yesmaximal, characteristic, complemented
7#19135167C211yesmaximal, characteristic, complemented
8#19135020C211yesmaximal, characteristic
9#19134909C211yesmaximal, characteristic
10#19134844C211yesmaximal, characteristic, complemented
11#19134784C211yesmaximal, characteristic, complemented
12#19134774C211yesmaximal, characteristic, complemented
13#19134593C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#2023C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17C2×#13063301—21no—
18C2×#13063296C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×(C22⋊D43)⋊C4—21no—
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23C2×#13063259C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30#14582832—21no—
31#14582818—21no—
32#14582798C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582787—21no—
36#14582775—21no—
37#14582771—21no—
38#14582770—21no—
39#14582768C2211yescharacteristic
40#14582756C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42C4×(C2×D43)⋊C4C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4⋊Q8×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C22⋊D43—21no—
60C23×Dic43—21no—
61C22×C4×D43—21no—
62C22×C4×D43—21no—
63C22×C4×D43C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C2×C8×D43—22no—
67C2×C8×D43—41no—
68C2×C8×D43—41no—
69#13063301—44no—
70#13063296—22no—
71#13063296Q814yescomplemented
72D4×Dic43—22no—
73D4×Dic43—41no—
74(C22⋊D43)⋊C4—44no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C4⋊C4×D43—22no—
87C4⋊C4×D43—22no—
88C4⋊C4×D43—41no—
89C4⋊C4×D43—41no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4D411yescharacteristic
94C2×(C2×D43)⋊C4D411yescharacteristic
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97#13063259—22no—
98#13063258—41no—
99C4⋊(C43⋊C8)—41no—
100Dic43⋊C8—41no—
101#13063246—41no—
102#13063246—41no—
103(C2×D43)⋊C8—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C22×Q8×C43—21no—
112C22×D4×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C4⋊Q8×C43—22no—
116C4⋊Q8×C43—41no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C42×C43C2311yescharacteristic
124#102×C43—22no—
125#102×C43—41no—
126C24×C43—21no—
127C23×D43C2×D411yescharacteristic
128C2×Q8×C43—42no—
129C2×Q8×C43—42no—
130C2×Q8×C43—81no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43C2×Q812yes—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2411yescharacteristic
143C2×C22⋊D43—24no—
144C2×C22⋊D43—42no—
145C2×C22⋊D43—42no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—81no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43—81no—
165C2×C4×D43—81no—
166C2×C4×D43C2×Q812yes—
167C2×C4×D43#4112yes—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×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#4112yes—
181C22⋊C4×C43—42no—
182C22⋊C4×C43—81no—
183C42×C43—21no—
184C42×C43—21no—
185C22⋊Dic43—24no—
186C22⋊Dic43—42no—
187(C2×D43)⋊C4—22no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4D814yes—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—42no—
197C4⋊Dic43C2×Q812yes—
198C4⋊Dic43#4112yes—
199Dic43⋊C4—42no—
200Dic43⋊C4—42no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204Dic43⋊C4—81no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—42no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C8×D43—44no—
215C23×C43—22no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43C22×D411yescharacteristic
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—21no—
227C22×D43C22⋊Q812yes—
228C22×D43C2×D812yes—
229C22×D43#13712yes—
230Q8×C43—84no—
231D4×C43—22no—
232D4×C43—22no—
233D4×C43—41no—
234D4×C43—41no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43C2×D812yes—
250C2×C4×C43C22×Q811yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C22⋊D43—48no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—22no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—21no—
265C2×Dic43—21no—
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—84no—
277C2×Dic43C22⋊Q812yes—
278C2×Dic43C2×D812yes—
279C4×D43—22no—
280C4×D43—22no—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—84no—
284C4×D43—84no—
285C8×C43—41no—
286C8×C43—41no—
287C43⋊C8—41no—
288C43⋊C8—41no—
289#26408—431nomaximal, Sylow
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43C2×C22⋊Q811yescharacteristic
298C22×C43#54611yescharacteristic
299C22×C43#54611yescharacteristic
300C22×C43C22×D811yescharacteristic
301C22×C43C2×#13711yescharacteristic
302C22×C43#57711yescharacteristic
303C22×C43#57711yescharacteristic
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—22no—
308C2×D43—22no—
309C2×D43—22no—
310C2×D43#47414yes—
311C4×C43—22no—
312C4×C43—42no—
313C4×C43—41no—
314C4×C43—81no—
315C4×C43—81no—
316C4×C43#52911yescharacteristic
317C4×C43#53811yescharacteristic
318C4×C43#55411yescharacteristic
319C4×C43#55411yescharacteristic
320Dic43—22no—
321Dic43—22no—
322Dic43—42no—
323Dic43—41no—
324Dic43—42no—
325Dic43—81no—
326Dic43—81no—
327#2440—431no—
328#2361—431no—
329#2099—431no—
330#2086—431no—
331#2067—431no—
332#2023D4311yescharacteristic, complemented
333#1988—431no—
334#1918—431no—
335#1893—431no—
336#1874—431no—
337#1862—431no—
338#1852—431no—
339#1850—431no—
340#1802—431no—
341C2×#340—431no—
342C2×C43—82no—
343C2×C43#245011yescharacteristic
344C2×C43C2×#47411yescharacteristic
345C2×C43#308411yescharacteristic
346C2×C43#329411yescharacteristic
347C2×C43#329411yescharacteristic
348C2×C43#331611yescharacteristic
349C2×C43#332011yescharacteristic
350D43—24no—
351C23×C8—431no—
352C2×C4⋊Q8C2×D4311yescharacteristic
353C2×C22⋊Q8—861no—
354C2×#121—431no—
355C2×C4×D4—431no—
356C2×C4×D4—861no—
357C22×C4⋊C4—431no—
358C22×C4⋊C4—431no—
359C2×#107—431no—
360C2×#107—431no—
361C2×C4⋊C8—431no—
362C2×C4⋊C8—431no—
363C2×#102—431no—
364C2×#102—431no—
365C2×#102C2×D4311yescharacteristic
366C2×#102C2×D4311yescharacteristic
367C2×C22⋊C8—431no—
368#398—861no—
369#395—861no—
370#390C2×D4311yescharacteristic
371#389—431no—
372#389—431no—
373#389—431no—
374#388—861no—
375#386—861no—
376#385—861no—
377#385—861no—
378#384—431no—
379#380—431no—
380C4×C4⋊C4—431no—
381C4×C22⋊C4—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#340C2×D4311yescharacteristic
391#340C2×D4311yescharacteristic
392#336—431no—
393#336C2×D4311yescharacteristic
394C43#2640811yescharacteristic, complemented, Sylow
395C22×Q8—21no—
396C22×D4—861no—
397C22×D4C22×D4311yescharacteristic
398C23×C4—431no—
399C23×C4—861no—
400C23×C4—861no—
401C23×C4—861no—
402C22×C8—431no—
403C22×C8—431no—
404C22×C8—862no—
405C22×C8—1721no—
406C22×C8—1721no—
407C22×C8C22×D4311yescharacteristic
408C22×C8C22×D4311yescharacteristic
409C4⋊Q8—22no—
410C4⋊Q8—41no—
411C22⋊Q8—1724no—
412#121—434no—
413#121—862no—
414C4×D4—862no—
415C4×D4—1721no—
416C4×D4—1724no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—862no—
423C2×C4⋊C4—862no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—1721no—
432C2×C4⋊C4—1721no—
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C4⋊C4C22×D4311yescharacteristic
435C2×C4⋊C4C22×D4311yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—431no—
439C2×C22⋊C4—431no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C42—431no—
444C2×C42—861no—
445C2×C42C22×D4311yescharacteristic
446#107—862no—
447#107—1721no—
448C4⋊C8—1721no—
449C4⋊C8—1721no—
450#102—22no—
451#102—41no—
452#102—1721no—
453#102—1721no—
454C22⋊C8—862no—
455#95—431no—
456#95—431no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462C24—21no—
463C24—431no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—81no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—864no—
473C2×D4—1722no—
474C2×D4—1722no—
475C2×D4Q8×D4312yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—432no—
482C22×C4—432no—
483C22×C4—431no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—3441no—
493C22×C4—3441no—
494C22×C4—3441no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4—1722no—
498C22×C4—1722no—
499C22×C4—1722no—
500C22×C4—1722no—
501C22×C4D4×D4311yescharacteristic
502C22×C4D4×D4311yescharacteristic
503C22×C4C23×D4311yescharacteristic
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—1724no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—42no—
523C4⋊C4—432no—
524C4⋊C4—432no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—3441no—
532C4⋊C4—1722no—
533C4⋊C4—1722no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4#1062190012yes—
539C22⋊C4—42no—
540C22⋊C4—81no—
541C22⋊C4—434no—
542C22⋊C4—862no—
543C22⋊C4—864no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C42—21no—
547C42—21no—
548C42—861no—
549C42—861no—
550C42—1722no—
551C23—22no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—432no—
559C23—432no—
560C23—432no—
561C23—861no—
562C23—861no—
563C23—861no—
564C23—861no—
565C23C2×D4×D4311yescharacteristic
566Q8—84no—
567D4—22no—
568D4—22no—
569D4—41no—
570D4—41no—
571D4—1728no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—432no—
587C2×C4—432no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—862no—
601C2×C4—3444no—
602C2×C4—3444no—
603C2×C4—3444no—
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×C4D8×D4312yes—
615C2×C4C2×Q8×D4311yescharacteristic
616C2×C4#41×D4311yescharacteristic
617C2×C4#41×D4311yescharacteristic
618C2×C4C2×#1062190011yescharacteristic
619C2×C4#1306337011yescharacteristic
620C2×C4#1306337111yescharacteristic
621C8—41no—
622C8—41no—
623C8—1721no—
624C8—1721no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—434no—
633C22—862no—
634C22—862no—
635C22—862no—
636C22—862no—
637C22—862no—
638C22—862no—
639C22C22⋊Q8×D4311yescharacteristic
640C22#1458353611yescharacteristic
641C22#1458354211yescharacteristic
642C22C2×D8×D4311yescharacteristic
643C22#137×D4311yescharacteristic
644C22#1458370511yescharacteristic
645C22#1458370911yescharacteristic
646C4—22no—
647C4—41no—
648C4—42no—
649C4—81no—
650C4—81no—
651C4—862no—
652C4—862no—
653C4—3441no—
654C4—3441no—
655C4—1722no—
656C4—1722no—
657C4—1721no—
658C4#1458342811yescharacteristic
659C4#1458348311yescharacteristic
660C4#1458360311yescharacteristic
661C4#1458360711yescharacteristic
662C2—82no—
663C2—864no—
664C2#1913841211yescharacteristic
665C2#474×D4311yescharacteristic
666C2#1914445211yescharacteristic
667C2#1914640111yescharacteristic
668C2#1914640711yescharacteristic
669C2#1914670511yescharacteristic
670C2#1914675911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2023C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#2023D43
hypocenterC43#26408
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. #19138293C2semidirect
3. #19136155C2semidirect
4. #19136087C2semidirect
5. #19135983C2semidirect
6. #19135548C2semidirect
7. #19135167C2semidirect
10. #19134844C2semidirect
11. #19134784C2semidirect
12. #19134774C2semidirect
13. #19134593C2semidirect
14. #340×D43C2semidirect
15. C43×#2023C2semidirect
71. #13063296Q8semidirect
332. #2023D43semidirect
394. C43#26408semidirect

Maximal subgroups

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

subgroupindex
#191382932
#191376162
#191361552
#191360872
#191359832
#191355482
#191351672
#191350202
#191349092
#191348442
#191347842
#191347742
#191345932
#340×D432
C43×#20232
#2640843