Finite Group Databasebeta

← #25154202

Subgroups — #25154202

Order 11008.

802 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138298C211yesmaximal, characteristic
2#19137464C211yesmaximal, characteristic
3#19136156C211yesmaximal, characteristic, complemented
4#19136087C211yesmaximal, characteristic, complemented
5#19136085C211yesmaximal, characteristic, complemented
6#19135922C211yesmaximal, characteristic, complemented
7#19135545C211yesmaximal, characteristic, complemented
8#19135352C211yesmaximal, characteristic, complemented
9#19135169C211yesmaximal, characteristic, complemented
10#19135165C211yesmaximal, characteristic, complemented
11#19134785C211yesmaximal, characteristic
12#19134772C211yesmaximal, characteristic
13#19134622C211yesmaximal, characteristic
14C2×#14582661C211yesmaximal, characteristic
15C43×#1823C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063302—21no—
19C2×#13063284—21no—
20C22×C4⋊Dic43C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063259C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27#14582833—21no—
28#14582820—21no—
29#14582798C2211yescharacteristic
30#14582798C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582785—21no—
34#14582785—21no—
35#14582771—21no—
36#14582768C2211yescharacteristic
37#14582762—21no—
38#14582759C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4×C22⋊Dic43C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×C4⋊C4×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C43×#380C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86—21no—
60C23×Dic43—21no—
61C22×C43⋊C8—22no—
62C22×C43⋊C8—22no—
63C22×C43⋊C8—41no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063324—22no—
67#13063324—41no—
68#13063302—44no—
69#13063284—44no—
70C2×C4⋊Dic43—22no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—41no—
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×C22⋊Dic43—21no—
85C2×C22⋊Dic43D411yescharacteristic
86C2×C22⋊Dic43D411yescharacteristic
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063259—22no—
92#13063259—41no—
93#13063258—22no—
94#13063258—41no—
95Dic43⋊C8—22no—
96Dic43⋊C8—41no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C23×C4×C43—21no—
107C23×C4×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—22no—
112C2×C4⋊C4×C43Q814yescomplemented
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43—21no—
118C22⋊C8×C43—22no—
119#95×C43—21no—
120C24×C43C2×D411yescharacteristic
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—24no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—42no—
131C22×C4×C43—42no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×Q812yes—
134C22×C4×C43#4112yes—
135C22×C4×C43C2411yescharacteristic
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—42no—
141C22×Dic43—42no—
142C22×Dic43—81no—
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×Dic86—42no—
148C2×Dic86—42no—
149C2×Dic86—81no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C4⋊C4×C43—24no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43C2×Q812yes—
164C4⋊C4×C43C2×Q812yes—
165C22⋊C4×C43—42no—
166C22⋊Dic43—22no—
167C22⋊Dic43—42no—
168C22⋊Dic43D814yes—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—42no—
177C4⋊Dic43—42no—
178C4⋊Dic43—42no—
179C4⋊Dic43—42no—
180C4⋊Dic43#4112yes—
181Dic43⋊C4—42no—
182Dic43⋊C4—42no—
183Dic43⋊C4—42no—
184Dic43⋊C4—81no—
185C4×Dic43—21no—
186C4×Dic43—21no—
187C4×Dic43—21no—
188C4×Dic43—21no—
189C4×Dic43—42no—
190C4×Dic43—42no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—44no—
197C2×C43⋊C8#4112yes—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43C22⋊Q812yes—
203C23×C43C2×D812yes—
204C23×C43#13712yes—
205C23×C43C22×D411yescharacteristic
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—48no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43C22⋊Q812yes—
226C2×C4×C43C22×Q811yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43H(5,𝔽2)11yescharacteristic
231C2×C4×C432−1+411yescharacteristic
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—22no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—84no—
255C2×Dic43C2×D812yes—
256C2×Dic43C2×D812yes—
257Dic86—84no—
258C8×C43—41no—
259C8×C43—41no—
260C43⋊C8—22no—
261C43⋊C8—41no—
262#25988—431nomaximal, Sylow
263C22×C43—22no—
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—22no—
269C22×C43#47414yes—
270C22×C43C2×C22⋊Q811yescharacteristic
271C22×C43#54611yescharacteristic
272C22×C43#54711yescharacteristic
273C22×C43C22×D811yescharacteristic
274C22×C43C2×#13711yescharacteristic
275C22×C43#57711yescharacteristic
276C22×C43#57811yescharacteristic
277C4×C43—22no—
278C4×C43—42no—
279C4×C43—42no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43#53311yescharacteristic
283C4×C43#54411yescharacteristic
284C4×C43#55111yescharacteristic
285C4×C43#55211yescharacteristic
286Dic43—22no—
287Dic43—22no—
288Dic43—41no—
289Dic43—42no—
290Dic43—41no—
291Dic43—81no—
292Dic43—81no—
293Dic43—81no—
294#2440—431no—
295#2344—431no—
296#2099—431no—
297#2086—431no—
298#2086—431no—
299#2057—431no—
300#1988—431no—
301#1947—431no—
302#1918—431no—
303#1918—431no—
304#1852—431no—
305#1850—431no—
306#1823D4311yescharacteristic
307#1808—431no—
308C2×#340—431no—
309C2×C43—24no—
310C2×C43#243811yescharacteristic
311C2×C43C2×#47411yescharacteristic
312C2×C43#308211yescharacteristic
313C2×C43#329411yescharacteristic
314C2×C43#331211yescharacteristic
315C2×C43#333411yescharacteristic
316C2×C43#334411yescharacteristic
317C23×C8—431no—
318C2×C4⋊Q8—431no—
319C2×C22⋊Q8—861no—
320C2×#117—861no—
321C22×C4⋊C4—431no—
322C22×C4⋊C4C2×D4311yescharacteristic
323C2×#107—431no—
324C2×#107—431no—
325C2×#107—431no—
326C2×#107—431no—
327C2×C4⋊C8—431no—
328C2×C4⋊C8—431no—
329C2×C22⋊C8C2×D4311yescharacteristic
330#398—861no—
331#395—861no—
332#389—431no—
333#389—431no—
334#389—431no—
335#389—431no—
336#387—861no—
337#387—861no—
338#385—861no—
339#384—431no—
340#381—861no—
341#380—431no—
342#380C2×D4311yescharacteristic
343C4×C4⋊C4—431no—
344C4×C4⋊C4—431no—
345C4×C22⋊C4—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340C2×D4311yescharacteristic
355#340C2×D4311yescharacteristic
356#340C2×D4311yescharacteristic
357#340C2×D4311yescharacteristic
358#336—431no—
359#336—431no—
360C43#2598811yescharacteristic, complemented, Sylow
361C22×Q8—861no—
362C23×C4—21no—
363C23×C4—861no—
364C23×C4C22×D4311yescharacteristic
365C22×C8—431no—
366C22×C8—431no—
367C22×C8—862no—
368C22×C8—862no—
369C22×C8—1721no—
370C22×C8C22×D4311yescharacteristic
371C22×C8C22×D4311yescharacteristic
372C4⋊Q8—862no—
373C4⋊Q8—1721no—
374C22⋊Q8—1724no—
375#117—1724no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—862no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—1721no—
392C2×C4⋊C4Dic8614yescomplemented
393C2×C4⋊C4C22×D4311yescharacteristic
394C2×C4⋊C4C22×D4311yescharacteristic
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—431no—
399C2×C22⋊C4—431no—
400C2×C22⋊C4—861no—
401C2×C42—431no—
402C2×C42—431no—
403C2×C42—861no—
404C2×C42—861no—
405#107—862no—
406#107—862no—
407#107—1721no—
408#107—1721no—
409C4⋊C8—862no—
410C4⋊C8—1721no—
411C22⋊C8—22no—
412#95—21no—
413#95—431no—
414#95—431no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422C24D4×D4311yescharacteristic
423C2×Q8—3441no—
424C2×Q8—1722no—
425C2×Q8—1722no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—3441no—
446C22×C4—1722no—
447C22×C4—1722no—
448C22×C4C2×Dic8612yes—
449C22×C4D4×D4311yescharacteristic
450C22×C4#1062190012yes—
451C22×C4C23×D4311yescharacteristic
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—432no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—1724no—
465C4⋊C4—24no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—432no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—3441no—
481C4⋊C4—1722no—
482C4⋊C4—1722no—
483C4⋊C4—1722no—
484C4⋊C4—1722no—
485C4⋊C4—1722no—
486C4⋊C4—1722no—
487C4⋊C4—1722no—
488C4⋊C4C2×Dic8612yes—
489C4⋊C4C2×Dic8612yes—
490C22⋊C4—42no—
491C22⋊C4—434no—
492C22⋊C4—862no—
493C22⋊C4—1722no—
494C42—861no—
495C42—861no—
496C42—861no—
497C42—861no—
498C42—1722no—
499C42—1722no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23#1306330212yes—
505C23D8×D4312yes—
506C23#1306335412yes—
507C23C2×D4×D4311yescharacteristic
508Q8—3444no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—48no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—432no—
529C2×C4—432no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—862no—
540C2×C4—861no—
541C2×C4—3444no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4#1306330212yes—
554C2×C4C22×Dic8611yescharacteristic
555C2×C4#41×D4311yescharacteristic
556C2×C4#41×D4311yescharacteristic
557C2×C4C2×#1062190011yescharacteristic
558C2×C4#1306337111yescharacteristic
559C2×C4#1306337211yescharacteristic
560C8—41no—
561C8—41no—
562C8—862no—
563C8—1721no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22#1458317714yes—
571C22C2×#1306330211yescharacteristic
572C22#1458354111yescharacteristic
573C22#1458354711yescharacteristic
574C22C2×D8×D4311yescharacteristic
575C22C2×#1306335411yescharacteristic
576C22#1458370811yescharacteristic
577C22#1458371511yescharacteristic
578C4—22no—
579C4—42no—
580C4—42no—
581C4—81no—
582C4—81no—
583C4—862no—
584C4—862no—
585C4—3441no—
586C4—3441no—
587C4—3441no—
588C4—1721no—
589C4—1721no—
590C4—1722no—
591C4#1458345211yescharacteristic
592C4#1458352711yescharacteristic
593C4#1458357211yescharacteristic
594C4#1458358611yescharacteristic
595C2—24no—
596C2#1913827311yescharacteristic
597C2C2×#1458317711yescharacteristic
598C2#1914443911yescharacteristic
599C2#1914640611yescharacteristic
600C2#1914664411yescharacteristic
601C2#1914693711yescharacteristic
602C2#1914705411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1823C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1823D43
hypocenterC43#25988
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
3. #19136156C2semidirect
4. #19136087C2semidirect
5. #19136085C2semidirect
6. #19135922C2semidirect
7. #19135545C2semidirect
8. #19135352C2semidirect
9. #19135169C2semidirect
10. #19135165C2semidirect
112. C2×C4⋊C4×C43Q8semidirect
360. C43#25988semidirect
392. C2×C4⋊C4Dic86semidirect

Maximal subgroups

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

subgroupindex
#191382982
#191374642
#191361562
#191360872
#191360852
#191359222
#191355452
#191353522
#191351692
#191351652
#191347852
#191347722
#191346222
C2×#145826612
C43×#18232
#2598843