Finite Group Databasebeta

← #25169213

Subgroups — #25169213

Order 11008.

690 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138461C211yesmaximal, characteristic
2#19137690C211yesmaximal, characteristic, complemented
3#19135981C211yesmaximal, characteristic
4#19135936C211yesmaximal, characteristic, complemented
5#19135935C211yesmaximal, characteristic, complemented
6#19135739C211yesmaximal, characteristic
7#19135549C211yesmaximal, characteristic, complemented
8#19135335C211yesmaximal, characteristic, complemented
9#19135225C211yesmaximal, characteristic
10#19135218C211yesmaximal, characteristic
11#19135175C211yesmaximal, characteristic, complemented
12#19135167C211yesmaximal, characteristic, complemented
13#19135157C211yesmaximal, characteristic, complemented
14#19134420C211yesmaximal, characteristic
15C43×#1864C211yesmaximal, characteristic
16C2×#13063316C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063259C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063236C2211yescharacteristic
25#14582835—21no—
26#14582822—21no—
27#14582802C2211yescharacteristic
28#14582802C2211yescharacteristic
29#14582798C2211yescharacteristic
30#14582797C2211yescharacteristic
31#14582795C2211yescharacteristic
32#14582794—21no—
33#14582784—21no—
34#14582781—21no—
35#14582772—21no—
36#14582759—21no—
37C4⋊C4×Dic43—21no—
38C4⋊C4×Dic43C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4×Dic43⋊C4C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C43⋊C8C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61#13063316—22no—
62#13063316—22no—
63#13063316—22no—
64#13063316—41no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4D411yescharacteristic
77C2×Dic43⋊C4D411yescharacteristic
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43C2311yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87#13063259—22no—
88#13063258—41no—
89#13063256—22no—
90Dic43⋊C8—41no—
91#13063246—22no—
92#13063246Q814yes—
93#13063236—41no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95D411yescharacteristic
101C43⋊#95D411yescharacteristic
102C22×D4×C43C2311yescharacteristic
103C23×C4×C43—21no—
104C22×C8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C4×D4×C43—22no—
107C4×D4×C43—41no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C42×C43C2311yescharacteristic
114#106×C43—22no—
115#102×C43—22no—
116#102×C43—41no—
117#95×C43—21no—
118C24×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43C2×Q812yes—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—42no—
129C22×C4×C43—42no—
130C22×C4×C43—81no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—42no—
153C4⋊C4×C43#4112yes—
154C4⋊C4×C43#4112yes—
155C22⋊C4×C43—42no—
156C42×C43—21no—
157C42×C43—21no—
158C22⋊Dic43—42no—
159C22⋊Dic43—81no—
160C22⋊Dic43—81no—
161C22⋊Dic43—81no—
162C4⋊Dic43—24no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—42no—
170C4⋊Dic43—81no—
171C4⋊Dic43C2×Q812yes—
172C4⋊Dic43#4112yes—
173Dic43⋊C4—24no—
174Dic43⋊C4—41no—
175Dic43⋊C4—41no—
176Dic43⋊C4—42no—
177Dic43⋊C4—81no—
178Dic43⋊C4—81no—
179C4×Dic43—21no—
180C4×Dic43—21no—
181C4×Dic43—21no—
182C4×Dic43—21no—
183C4×Dic43—42no—
184C4×Dic43—81no—
185C4×Dic43—81no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8C2×Q812yes—
192C23×C43—22no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43C22×D411yescharacteristic
200D4×C43—22no—
201D4×C43—22no—
202D4×C43—41no—
203D4×C43—41no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—84no—
220C2×C4×C43C22×Q811yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43H(5,𝔽2)11yescharacteristic
225C2×C4×C432−1+411yescharacteristic
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—22no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—22no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C8×C43—41no—
251C8×C43—41no—
252C43⋊C8—22no—
253C43⋊C8—41no—
254#27027—431nomaximal, Sylow
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43#52511yescharacteristic
263C22×C43#54611yescharacteristic
264C22×C43D4×Q811yescharacteristic
265C22×C43#57511yescharacteristic
266C22×C43#57511yescharacteristic
267C22×C43#57611yescharacteristic
268C22×C43#57711yescharacteristic
269C4×C43—42no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—42no—
273C4×C43—81no—
274C4×C43#53311yescharacteristic
275C4×C43#54211yescharacteristic
276C4×C43#55411yescharacteristic
277C4×C43#55611yescharacteristic
278Dic43—41no—
279Dic43—41no—
280Dic43—42no—
281Dic43—42no—
282Dic43—41no—
283Dic43—41no—
284Dic43—81no—
285Dic43—81no—
286#2454—431no—
287#2370—431no—
288#2067—431no—
289#2059—431no—
290#2059—431no—
291#2025—431no—
292#1989—431no—
293#1944—431no—
294#1926—431no—
295#1925—431no—
296#1919—431no—
297#1918—431no—
298#1917—431no—
299#1864D4311yescharacteristic
300#1762—431no—
301C2×C43—82no—
302C2×C43#246511yescharacteristic
303C2×C43#311111yescharacteristic
304C2×C43#311911yescharacteristic
305C2×C43#330911yescharacteristic
306C2×C43#332311yescharacteristic
307C2×C43#338811yescharacteristic
308C2×C43#338911yescharacteristic
309C2×#125—431no—
310C2×#125—431no—
311C2×C4×D4C2×D4311yescharacteristic
312C2×#107—431no—
313C2×#107—431no—
314C2×#106—431no—
315C2×#106C2×D4311yescharacteristic
316C2×C4⋊C8—431no—
317C2×#102—431no—
318C2×#102—431no—
319C2×#102C2×D4311yescharacteristic
320C2×#102C2×D4311yescharacteristic
321C2×#97—431no—
322#399—861no—
323#396—861no—
324#390—431no—
325#390—431no—
326#389—431no—
327#389—431no—
328#389—431no—
329#389—861no—
330#389C2×D4311yescharacteristic
331#387—861no—
332#387—861no—
333#385—861no—
334#380—861no—
335C4×C4⋊C4—431no—
336C4×C4⋊C4—431no—
337C4×C4⋊C4—431no—
338C4×C4⋊C4—431no—
339C4×C4⋊C4—861no—
340#340—431no—
341#340—431no—
342#340—431no—
343#340—431no—
344#340—431no—
345#340—431no—
346#340—431no—
347#340C2×D4311yescharacteristic
348#336—431no—
349#336—431no—
350#336—431no—
351#336C2×D4311yescharacteristic
352C43#2702711yescharacteristic, complemented, Sylow
353C22×D4C22×D4311yescharacteristic
354C23×C4—21no—
355C22×C8—431no—
356C22×C8—431no—
357C22×C8C22×D4311yescharacteristic
358C22×C8C22×D4311yescharacteristic
359#125—862no—
360#125—862no—
361#125—862no—
362#125—1721no—
363C4×D4—22no—
364C4×D4—41no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—431no—
368C2×C4⋊C4—431no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C4⋊C4C22×D4311yescharacteristic
381C2×C4⋊C4C22×D4311yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C42—431no—
388C2×C42—431no—
389C2×C42—861no—
390C2×C42—861no—
391C2×C42—861no—
392C2×C42C22×D4311yescharacteristic
393#107—862no—
394#107—1721no—
395#106—22no—
396#106—862no—
397C4⋊C8—1721no—
398#102—22no—
399#102—41no—
400#102—434no—
401#102—862no—
402#97—1721no—
403#95—21no—
404#95—431no—
405#95—431no—
406#95—861no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412C24—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4Q8×D4312yes—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—81no—
425C22×C4—431no—
426C22×C4—431no—
427C22×C4—431no—
428C22×C4—431no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4D4×D4311yescharacteristic
434C22×C4D4×D4311yescharacteristic
435C22×C4C23×D4311yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—432no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—42no—
453C4⋊C4—432no—
454C4⋊C4—432no—
455C4⋊C4—864no—
456C4⋊C4—864no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—3441no—
464C4⋊C4—3441no—
465C4⋊C4—3441no—
466C4⋊C4—1721no—
467C4⋊C4—1721no—
468C4⋊C4—1722no—
469C4⋊C4—1722no—
470C4⋊C4#1062189812yes—
471C4⋊C4#1062190012yes—
472C22⋊C4—42no—
473C22⋊C4—3441no—
474C22⋊C4—3441no—
475C22⋊C4—3441no—
476C22⋊C4—1722no—
477C42—21no—
478C42—21no—
479C42—861no—
480C42—861no—
481C42—861no—
482C42—861no—
483C42—3441no—
484C42—3441no—
485C42—1722no—
486C23—22no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23C2×D4×D4311yescharacteristic
494D4—22no—
495D4—22no—
496D4—41no—
497D4—41no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—84no—
514C2×C4—862no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—862no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4C2×Q8×D4311yescharacteristic
539C2×C4#41×D4311yescharacteristic
540C2×C4C2×#1062190011yescharacteristic
541C2×C4C2×#1062189811yescharacteristic
542C2×C4#1306337011yescharacteristic
543C2×C4#1306337211yescharacteristic
544C8—41no—
545C8—41no—
546C8—862no—
547C8—1721no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22#1458340811yescharacteristic
556C22#1458353611yescharacteristic
557C22#1458356211yescharacteristic
558C22#1458369511yescharacteristic
559C22#1458369511yescharacteristic
560C22#1458370111yescharacteristic
561C22#1458370511yescharacteristic
562C4—41no—
563C4—42no—
564C4—41no—
565C4—42no—
566C4—81no—
567C4—3441no—
568C4—3441no—
569C4—1722no—
570C4—1721no—
571C4—1721no—
572C4—1722no—
573C4—1721no—
574C4—1721no—
575C4#1458345111yescharacteristic
576C4#1458351711yescharacteristic
577C4#1458360411yescharacteristic
578C4#1458361911yescharacteristic
579C2—82no—
580C2#1913862011yescharacteristic
581C2#1914470011yescharacteristic
582C2#1914480011yescharacteristic
583C2#1914659411yescharacteristic
584C2#1914681511yescharacteristic
585C2#1914753311yescharacteristic
586C2#1914755211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1864C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1864D43
hypocenterC43#27027
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. #19137690C2semidirect
4. #19135936C2semidirect
5. #19135935C2semidirect
7. #19135549C2semidirect
8. #19135335C2semidirect
11. #19135175C2semidirect
12. #19135167C2semidirect
13. #19135157C2semidirect
352. C43#27027semidirect

Maximal subgroups

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

subgroupindex
#191384612
#191376902
#191359812
#191359362
#191359352
#191357392
#191355492
#191353352
#191352252
#191352182
#191351752
#191351672
#191351572
#191344202
C43×#18642
#2702743