Finite Group Databasebeta

← #25169198

Subgroups — #25169198

Order 11008.

726 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138439C211yesmaximal, characteristic
2#19137690C211yesmaximal, characteristic, complemented
3#19135967C211yesmaximal, characteristic
4#19135932C211yesmaximal, characteristic, complemented
5#19135926C211yesmaximal, characteristic, complemented
6#19135739C211yesmaximal, characteristic
7#19135545C211yesmaximal, characteristic, complemented
8#19135330C211yesmaximal, characteristic, complemented
9#19135225C211yesmaximal, characteristic
10#19135218C211yesmaximal, characteristic
11#19135182C211yesmaximal, characteristic, complemented
12#19135181C211yesmaximal, characteristic, complemented
13#19135157C211yesmaximal, characteristic, complemented
14#19134420C211yesmaximal, characteristic
15C43×#1864C211yesmaximal, characteristic
16C2×#13063324C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063304—21no—
19C2×#13063258C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063236C2211yescharacteristic
26#14582822—21no—
27#14582811—21no—
28#14582802C2211yescharacteristic
29#14582802C2211yescharacteristic
30#14582798C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582794—21no—
34#14582784—21no—
35#14582781—21no—
36#14582772—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×Dic86—21no—
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62#13063324—22no—
63#13063324—41no—
64#13063316—22no—
65#13063316—22no—
66#13063304—44no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4D411yescharacteristic
78C2×Dic43⋊C4D411yescharacteristic
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43C2311yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88#13063258—22no—
89#13063257—22no—
90#13063256—41no—
91Dic43⋊C8—41no—
92#13063246—22no—
93#13063246Q814yescomplemented
94#13063236—41no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95D411yescharacteristic
102C43⋊#95D411yescharacteristic
103C22×D4×C43C2311yescharacteristic
104C23×C4×C43—21no—
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C4×D4×C43—22no—
108C4×D4×C43—41no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C42×C43C2311yescharacteristic
115#106×C43—22no—
116#102×C43—22no—
117#102×C43—41no—
118#95×C43—21no—
119C24×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43C2×Q812yes—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—42no—
130C22×C4×C43—42no—
131C22×C4×C43—81no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C2×Dic86—42no—
144C2×Dic86—42no—
145C2×Dic86—81no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—42no—
157C4⋊C4×C43#4112yes—
158C4⋊C4×C43#4112yes—
159C22⋊C4×C43—42no—
160C42×C43—21no—
161C42×C43—21no—
162C22⋊Dic43—42no—
163C22⋊Dic43—42no—
164C22⋊Dic43—42no—
165C22⋊Dic43—81no—
166C4⋊Dic43—24no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—42no—
174C4⋊Dic43C2×Q812yes—
175C4⋊Dic43#4112yes—
176Dic43⋊C4—24no—
177Dic43⋊C4—22no—
178Dic43⋊C4—41no—
179Dic43⋊C4—42no—
180Dic43⋊C4—42no—
181Dic43⋊C4—81no—
182C4×Dic43—21no—
183C4×Dic43—21no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C4×Dic43—42no—
187C4×Dic43—81no—
188C4×Dic43—81no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8C2×Q812yes—
195C23×C43—22no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43C22×D411yescharacteristic
203D4×C43—22no—
204D4×C43—22no—
205D4×C43—41no—
206D4×C43—41no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—84no—
223C2×C4×C43C22×Q811yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43H(5,𝔽2)11yescharacteristic
228C2×C4×C432−1+411yescharacteristic
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—22no—
234C2×Dic43—21no—
235C2×Dic43—22no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—41no—
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×Dic43AGL(1,ℤ/8)12yes—
253Dic86—84no—
254C8×C43—41no—
255C8×C43—41no—
256C43⋊C8—22no—
257C43⋊C8—41no—
258#27026—431nomaximal, Sylow
259C22×C43—42no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43#52511yescharacteristic
267C22×C43#54611yescharacteristic
268C22×C43D4×Q811yescharacteristic
269C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C43#57511yescharacteristic
271C22×C43#57711yescharacteristic
272C22×C43#57711yescharacteristic
273C4×C43—42no—
274C4×C43—42no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—81no—
278C4×C43#53311yescharacteristic
279C4×C43#54211yescharacteristic
280C4×C43#55411yescharacteristic
281C4×C43#55611yescharacteristic
282Dic43—22no—
283Dic43—41no—
284Dic43—41no—
285Dic43—42no—
286Dic43—42no—
287Dic43—41no—
288Dic43—81no—
289Dic43—81no—
290#2452—431no—
291#2370—431no—
292#2065—431no—
293#2059—431no—
294#2058—431no—
295#2025—431no—
296#1988—431no—
297#1943—431no—
298#1926—431no—
299#1925—431no—
300#1920—431no—
301#1920—431no—
302#1917—431no—
303#1864D4311yescharacteristic
304#1762—431no—
305C2×C43—82no—
306C2×C43#246511yescharacteristic
307C2×C43#311511yescharacteristic
308C2×C43#312511yescharacteristic
309C2×C43#331011yescharacteristic
310C2×C43#332611yescharacteristic
311C2×C43#338411yescharacteristic
312C2×C43#338811yescharacteristic
313C2×C4⋊Q8—431no—
314C2×#125—431no—
315C2×C22⋊Q8—861no—
316C2×C4×D4C2×D4311yescharacteristic
317C2×#107—431no—
318C2×#106—431no—
319C2×#106—431no—
320C2×#106C2×D4311yescharacteristic
321C2×C4⋊C8—431no—
322C2×#102—431no—
323C2×#102—431no—
324C2×#102C2×D4311yescharacteristic
325C2×#102C2×D4311yescharacteristic
326C2×#97—431no—
327#396—861no—
328#393—861no—
329#390—431no—
330#390—431no—
331#389—431no—
332#389—431no—
333#389—431no—
334#389—861no—
335#389C2×D4311yescharacteristic
336#387—861no—
337#387—861no—
338#385—861no—
339C4×C4⋊C4—431no—
340C4×C4⋊C4—431no—
341C4×C4⋊C4—431no—
342C4×C4⋊C4—431no—
343C4×C4⋊C4—861no—
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340C2×D4311yescharacteristic
352#336—431no—
353#336—431no—
354#336—431no—
355#336C2×D4311yescharacteristic
356C43#2702611yescharacteristic, complemented, Sylow
357C22×Q8—861no—
358C22×D4C22×D4311yescharacteristic
359C23×C4—21no—
360C22×C8—431no—
361C22×C8—431no—
362C22×C8C22×D4311yescharacteristic
363C22×C8C22×D4311yescharacteristic
364C4⋊Q8—862no—
365C4⋊Q8—1721no—
366#125—862no—
367#125—862no—
368C22⋊Q8—1724no—
369C4×D4—22no—
370C4×D4—41no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C42—431no—
393C2×C42—431no—
394C2×C42—861no—
395C2×C42—861no—
396C2×C42—861no—
397C2×C42C22×D4311yescharacteristic
398#107—862no—
399#106—22no—
400#106—862no—
401#106—1721no—
402C4⋊C8—1721no—
403#102—22no—
404#102—41no—
405#102—434no—
406#102—862no—
407#97—1721no—
408#95—21no—
409#95—431no—
410#95—431no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417C24—21no—
418C2×Q8—3441no—
419C2×Q8—1722no—
420C2×Q8—1722no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4Q8×D4312yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—81no—
433C22×C4—431no—
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4D4×D4311yescharacteristic
442C22×C4D4×D4311yescharacteristic
443C22×C4C23×D4311yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—432no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—42no—
461C4⋊C4—432no—
462C4⋊C4—432no—
463C4⋊C4—862no—
464C4⋊C4—864no—
465C4⋊C4—864no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—3441no—
473C4⋊C4—1721no—
474C4⋊C4—1722no—
475C4⋊C4—1722no—
476C4⋊C4—1722no—
477C4⋊C4#1062189812yes—
478C4⋊C4#1062190012yes—
479C22⋊C4—42no—
480C22⋊C4—3441no—
481C22⋊C4—1722no—
482C22⋊C4—1722no—
483C22⋊C4—1722no—
484C42—21no—
485C42—21no—
486C42—861no—
487C42—861no—
488C42—861no—
489C42—861no—
490C42—3441no—
491C42—3441no—
492C42—1722no—
493C23—22no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23C2×D4×D4311yescharacteristic
501Q8—3444no—
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—84no—
522C2×C4—432no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—862no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—862no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4C2×Q8×D4311yescharacteristic
547C2×C4#41×D4311yescharacteristic
548C2×C4C2×#1062190011yescharacteristic
549C2×C4C2×#1062189811yescharacteristic
550C2×C4#1306337011yescharacteristic
551C2×C4#1306337211yescharacteristic
552C8—41no—
553C8—41no—
554C8—862no—
555C8—1721no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22#1458340811yescharacteristic
564C22#1458353611yescharacteristic
565C22#1458356211yescharacteristic
566C22AGL(1,ℤ/8)×D4311yescharacteristic
567C22#1458369511yescharacteristic
568C22#1458370511yescharacteristic
569C22#1458370611yescharacteristic
570C4—42no—
571C4—41no—
572C4—41no—
573C4—42no—
574C4—81no—
575C4—862no—
576C4—3441no—
577C4—3441no—
578C4—1721no—
579C4—1721no—
580C4—1721no—
581C4—1722no—
582C4—1722no—
583C4#1458345111yescharacteristic
584C4#1458351711yescharacteristic
585C4#1458360411yescharacteristic
586C4#1458361911yescharacteristic
587C2—82no—
588C2#1913862011yescharacteristic
589C2#1914474211yescharacteristic
590C2#1914487811yescharacteristic
591C2#1914660911yescharacteristic
592C2#1914684111yescharacteristic
593C2#1914749711yescharacteristic
594C2#1914753311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1864C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1864D43
hypocenterC43#27026
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. #19135932C2semidirect
5. #19135926C2semidirect
7. #19135545C2semidirect
8. #19135330C2semidirect
11. #19135182C2semidirect
12. #19135181C2semidirect
13. #19135157C2semidirect
93. #13063246Q8semidirect
356. C43#27026semidirect

Maximal subgroups

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

subgroupindex
#191384392
#191376902
#191359672
#191359322
#191359262
#191357392
#191355452
#191353302
#191352252
#191352182
#191351822
#191351812
#191351572
#191344202
C43×#18642
#2702643