Finite Group Databasebeta

← #25080473

Subgroups — #25080473

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145180C211yesmaximal, characteristic
2#19144727C211yesmaximal, characteristic
3#19144724C211yesmaximal, characteristic
4C8×Q8×D43C211yesmaximal, characteristic
5#19134026C211yesmaximal, characteristic, complemented
6#19134025C211yesmaximal, characteristic, complemented
7#19134022C211yesmaximal, characteristic, complemented
8#19133988C211yesmaximal, characteristic, complemented
9#19133987C211yesmaximal, characteristic, complemented
10#19133964C211yesmaximal, characteristic, complemented
11#19133963C211yesmaximal, characteristic, complemented
12#19133355C211yesmaximal, characteristic
13#19133294C211yesmaximal, characteristic
14#19133292C211yesmaximal, characteristic
15C43×#1680C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583278C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583231—21no—
23#14583228—21no—
24#14583185C2211yescharacteristic
25#14583184C2211yescharacteristic
26#14583181C2211yescharacteristic
27#14583139—21no—
28#14583139—21no—
29#14583110C2211yescharacteristic
30#14583109C2211yescharacteristic
31#14583106C2211yescharacteristic
32#14583056—21no—
33#14583053—21no—
34Q8×C43⋊C8C2211yescharacteristic
35C8×Dic86—21no—
36C8×Dic86C2211yescharacteristic
37#14583023—21no—
38#14583023C2211yescharacteristic
39#14583006—21no—
40#14583005—21no—
41#14583003—21no—
42#14583003—21no—
43#14582991—21no—
44#14582991—21no—
45#14582955C2211yescharacteristic
46#14582955C2211yescharacteristic
47C4⋊C8×D43—21no—
48C4⋊C8×D43C2211yescharacteristic
49C4×C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582650C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#475C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q8×D43D411yescharacteristic
68C2×Dic172—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621885—21no—
73C2×C8×D43—21no—
74C2×C8×D43D411yescharacteristic
75C2×C8×D43D411yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063316—21no—
79#13063316—21no—
80#13063305—21no—
81#13063305—21no—
82#13063301—21no—
83#13063301—21no—
84Q8×Dic43—21no—
85Q8×Dic43—21no—
86Q8×Dic43D411yescharacteristic
87C4×Dic86—21no—
88C4×Dic86C2311yescharacteristic
89#13063290—21no—
90#13063290—21no—
91#13063290—21no—
92#13063290D411yescharacteristic
93#13063283—21no—
94#13063283—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43D411yescharacteristic
97C42×D43—21no—
98C42×D43C2311yescharacteristic
99#13063258—21no—
100#13063258—21no—
101#13063257—21no—
102#13063256—21no—
103#13063256—21no—
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063250—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063249—21no—
116#13063249—21no—
117#13063248—21no—
118#13063248—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063235—21no—
122#13063235—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C2×Q16×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131C4⋊Q8×C43C2311yescharacteristic
132C4×Q8×C43C2311yescharacteristic
133#106×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147Q8×D43—22no—
148Q8×D43—22no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43C2×D411yescharacteristic
152C2×C4×D43C2×D411yescharacteristic
153C2×C4×D43#4111yescharacteristic
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86C2×D411yescharacteristic
158Q16×C43—42no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C2×D411yescharacteristic
170C42×C43—21no—
171C42×C43C2411yescharacteristic
172#10621885—42no—
173#10621885—42no—
174#10621885—42no—
175#10621885—42no—
176(C2×D43)⋊C4—41no—
177(C2×D43)⋊C4—41no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—41no—
184C4⋊Dic43—41no—
185C4⋊Dic43C2×D411yescharacteristic
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—41no—
195C4×Dic43—41no—
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204Dic172—42no—
205C8×D43—22no—
206C8×D43—41no—
207C8×D43—42no—
208C22×D43#12111yescharacteristic
209Q8×C43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43#13512yes—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43#12111yescharacteristic
227C2×Dic43#12111yescharacteristic
228C2×Dic43#12111yescharacteristic
229C4×D43—24no—
230C4×D43—22no—
231C4×D43—21no—
232C4×D43—21no—
233C4×D43—21no—
234C4×D43—21no—
235C4×D43—42no—
236Dic86—24no—
237Dic86—21no—
238Dic86—41no—
239Dic86—41no—
240Dic86—41no—
241Dic86—41no—
242Dic86#13512yes—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248C43⋊C8—21no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8#13712yes—
253#19265—431nomaximal, Sylow
254C22×C43C2×#12111yescharacteristic
255C2×D43—21no—
256C2×D43—21no—
257C2×D43#47312yes—
258C4×C43—22no—
259C4×C43—21no—
260C4×C43—41no—
261C4×C43—81no—
262C4×C43—81no—
263C4×C43C2×#13511yescharacteristic
264C4×C43C2×#13511yescharacteristic
265C4×C43C2×#13711yescharacteristic
266C4×C43#57511yescharacteristic
267Dic43—21no—
268Dic43—21no—
269Dic43—22no—
270Dic43—21no—
271Dic43—41no—
272Dic43—81no—
273Dic43—81no—
274#3170—431no—
275#3113—431no—
276#3113—431no—
277C2×C8×Q8—431no—
278#1680—431no—
279#1680—431no—
280#1680—431no—
281#1680D4311yescharacteristic, complemented
282#1674—431no—
283#1674—431no—
284#1670—431no—
285#1670—431no—
286#1568—431no—
287#1552—431no—
288#1552—431no—
289C2×C43#303711yescharacteristic
290C2×C43#305011yescharacteristic
291C2×C43C2×#47311yescharacteristic
292D43—22no—
293#533—431no—
294#533—431no—
295C2×C4×Q8—431no—
296#500—431no—
297#494—431no—
298#487—431no—
299#487C2×D4311yescharacteristic
300#483—861no—
301#483—861no—
302#475—431no—
303#475—431no—
304#475—431no—
305#475C2×D4311yescharacteristic
306#467—861no—
307#467—861no—
308#462—431no—
309#462—431no—
310#462—431no—
311#462C2×D4311yescharacteristic
312#451—861no—
313#451—861no—
314C8×Q8—431no—
315C8×Q8—431no—
316C8×Q8—431no—
317C8×Q8—861no—
318C8×Q8—861no—
319C8×Q8C2×D4311yescharacteristic
320#441—861no—
321#441—861no—
322#441—861no—
323#441—861no—
324C4×Q16—861no—
325C4×Q16—861no—
326#432—431no—
327#432—431no—
328C2×C4⋊C8—431no—
329C2×C4⋊C8—861no—
330C2×C4×C8—431no—
331C2×C4×C8—861no—
332#335—431no—
333#335—431no—
334#334—431no—
335#334C2×D4311yescharacteristic
336#332—431no—
337#332—431no—
338#332—431no—
339#332—431no—
340#332—431no—
341#332—431no—
342#332C2×D4311yescharacteristic
343#332C2×D4311yescharacteristic
344C43#1926511yescharacteristic, complemented, Sylow
345C22×Q8—431no—
346C2×Q16—21no—
347C2×Q16—861no—
348C2×Q16—861no—
349C2×Q16—861no—
350C2×Q16—861no—
351C2×Q16—861no—
352C22×C8—431no—
353C22×C8—431no—
354C22×C8—861no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8C22×D4311yescharacteristic
358C4⋊Q8C22×D4311yescharacteristic
359#125—861no—
360#125—861no—
361C22⋊Q8—861no—
362C22⋊Q8—861no—
363C22⋊Q8—861no—
364C22⋊Q8—861no—
365C4×Q8—431no—
366C4×Q8—431no—
367C4×Q8—431no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×Q8—861no—
371C4×Q8—861no—
372C4×Q8—861no—
373C4×Q8—861no—
374C4×Q8C22×D4311yescharacteristic
375#117—861no—
376#117—861no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—861no—
379C2×C42—431no—
380C2×C42—861no—
381#107—861no—
382#107—861no—
383#106—21no—
384#106—861no—
385#106—861no—
386#106—861no—
387C4⋊C8—21no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8C22×D4311yescharacteristic
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410C22⋊C8—861no—
411C22⋊C8—861no—
412#97—861no—
413#97—861no—
414C4×C8—21no—
415C4×C8—431no—
416C4×C8—431no—
417C4×C8—431no—
418C4×C8—861no—
419C4×C8—861no—
420C4×C8—861no—
421C4×C8C22×D4311yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—431no—
425C2×Q8—861no—
426C2×Q8—862no—
427C2×Q8—862no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×Q8D4×D4311yescharacteristic
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—431no—
434C22×C4—861no—
435C22×C4—861no—
436Q16—42no—
437Q16—1722no—
438Q16—1722no—
439Q16—1722no—
440Q16—1722no—
441Q16—1722no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—431no—
446C2×C8—431no—
447C2×C8—862no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—1721no—
452C2×C8—1722no—
453C2×C8D4×D4311yescharacteristic
454C2×C8D4×D4311yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—431no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—1721no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4—1721no—
473C4⋊C4D4×D4311yescharacteristic
474C22⋊C4—1721no—
475C22⋊C4—1721no—
476C42—21no—
477C42—431no—
478C42—431no—
479C42—431no—
480C42—861no—
481C42—861no—
482C42—861no—
483C42—1721no—
484C42—1721no—
485C42C23×D4311yescharacteristic
486C23—431no—
487Q8—21no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—432no—
493Q8—864no—
494Q8—861no—
495Q8—1721no—
496Q8—1721no—
497Q8—1721no—
498Q8—1721no—
499Q8#1306334612yes—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—431no—
505C2×C4—431no—
506C2×C4—431no—
507C2×C4—862no—
508C2×C4—864no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—1722no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4C2×D4×D4311yescharacteristic
519C2×C4C2×D4×D4311yescharacteristic
520C2×C4#41×D4311yescharacteristic
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—432no—
527C8—861no—
528C8—1721no—
529C8—1721no—
530C8—1721no—
531C22—432no—
532C22—861no—
533C22—861no—
534C22#121×D4311yescharacteristic
535C4—21no—
536C4—22no—
537C4—41no—
538C4—81no—
539C4—81no—
540C4—861no—
541C4—861no—
542C4—861no—
543C4—862no—
544C4—3441no—
545C4—3441no—
546C4—1721no—
547C4#135×D4311yescharacteristic
548C4C2×#1306334611yescharacteristic
549C4#137×D4311yescharacteristic
550C4#1458369611yescharacteristic
551C2—862no—
552C2#1914406511yescharacteristic
553C2#1914417111yescharacteristic
554C2#473×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1680C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1680D43
hypocenterC43#19265
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1680

Complements

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

NH ≅ G/Ntype
5. #19134026C2semidirect
6. #19134025C2semidirect
7. #19134022C2semidirect
8. #19133988C2semidirect
9. #19133987C2semidirect
10. #19133964C2semidirect
11. #19133963C2semidirect
15. C43×#1680C2semidirect
281. #1680D43semidirect
344. C43#19265semidirect

Maximal subgroups

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

subgroupindex
#191451802
#191447272
#191447242
C8×Q8×D432
#191340262
#191340252
#191340222
#191339882
#191339872
#191339642
#191339632
#191333552
#191332942
#191332922
C43×#16802
#1926543