Finite Group Databasebeta

← #25087474

Subgroups — #25087474

Order 11008.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147646C211yesmaximal, characteristic, complemented
2#19147470C211yesmaximal, characteristic, complemented
3#19147255C211yesmaximal, characteristic
4#19134218C211yesmaximal, characteristic, complemented
5#19134120C211yesmaximal, characteristic, complemented
6#19134013C211yesmaximal, characteristic, complemented
7#19133979C211yesmaximal, characteristic, complemented
8#19133936C211yesmaximal, characteristic
9#19133809C211yesmaximal, characteristic, complemented
10#19133751C211yesmaximal, characteristic, complemented
11#19133715C211yesmaximal, characteristic, complemented
12#19133667C211yesmaximal, characteristic
13#19133431C211yesmaximal, characteristic, complemented
14#19133414C211yesmaximal, characteristic, complemented
15C43×#3338C211yesmaximal, characteristic, complemented
16#14583634C2211yescharacteristic
17#14583627C2211yescharacteristic
18#14583298—21no—
19#14583295C2211yescharacteristic
20#14583292—21no—
21#14583273C2211yescharacteristic
22#14583272C2211yescharacteristic
23#14583256—21no—
24#14583249C2211yescharacteristic
25#14583247C2211yescharacteristic
26#14583203—21no—
27#14583199—21no—
28#14583196—21no—
29#14583191C2211yescharacteristic
30#14583191C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583124—21no—
33#14583114—21no—
34#14583109C2211yescharacteristic
35#14583103—21no—
36#14583099C2211yescharacteristic
37#14583094C2211yescharacteristic
38#14583029C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40Q8×C43⋊C8C2211yescharacteristic
41#14582998—21no—
42C4×#10621883—21no—
43C4×#10621883C2211yescharacteristic
44C4×#10621882—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#554C2211yescharacteristic
57C43×#554C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#484—21no—
60C43×#484—21no—
61C43×#477C2211yescharacteristic
62C43×#477C2211yescharacteristic
63C43×#467—21no—
64C4×Q16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#107×C43—21no—
67C2×#10621885—21no—
68C2×#10621873—21no—
69C2×#10621873—21no—
70C2×#10621883D411yescharacteristic
71C2×#10621884—21no—
72C2×#10621884—41no—
73C2×#10621882—21no—
74#13063325C2311yescharacteristic
75#13063323—21no—
76#13063322C2311yescharacteristic
77#13063317—21no—
78#13063315—41no—
79#13063314—21no—
80#13063313—21no—
81#13063310—41no—
82C4×Dic86—21no—
83C4×Dic86C2311yescharacteristic
84#13063290—21no—
85C4×D172—21no—
86#13063287—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256D411yescharacteristic
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98Dic43⋊C8—21no—
99#13063249—41no—
100#13063248—21no—
101#13063248—21no—
102#13063248—21no—
103#13063248D411yescharacteristic
104#13063246—21no—
105#13063246D411yescharacteristic
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—21no—
110#13063235—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×Q16×C43D411yescharacteristic
116C22×C8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119#125×C43—21no—
120#125×C43—21no—
121C22⋊Q8×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—41no—
124C22⋊Q8×C43—41no—
125C4×Q8×C43C2311yescharacteristic
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134#107×C43—21no—
135#107×C43—21no—
136#107×C43D411yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#103×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—41no—
151C22×C4×C43—41no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×C4×D43—41no—
156C2×Dic86—21no—
157C2×Dic86C2×D411yescharacteristic
158Q16×C43—22no—
159C2×C8×C43—21no—
160C2×C8×C43—42no—
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43C2411yescharacteristic
182#10621885—81no—
183#10621884—81no—
184#10621884—82no—
185#10621883—22no—
186#10621882—42no—
187(C2×D43)⋊C4—41no—
188(C2×D43)⋊C4—41no—
189(C2×D43)⋊C4—41no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197C4×Dic43—21no—
198C4×Dic43—41no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205#10621873—42no—
206#10621873—81no—
207C23×C43—21no—
208C22×D43—41no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—81no—
214Q8×C43—81no—
215D4×C43—21no—
216D4×C43#13712yes—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—161no—
227C2×C4×C43—161no—
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43H(5,𝔽2)11yescharacteristic
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—41no—
234D172—41no—
235D172—41no—
236D172—41no—
237D172—41no—
238D172—81no—
239C4×D43—161no—
240Dic86—21no—
241Dic86—21no—
242Dic86—41no—
243Dic86—41no—
244C8×C43—21no—
245C8×C43—41no—
246C8×C43#13512yes—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253#19857—431nomaximal, Sylow
254C22×C43—22no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43D4211yescharacteristic
258C2×D43—81no—
259C2×D43—81no—
260C2×D43—81no—
261C4×C43—21no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—81no—
268C4×C43—81no—
269C4×C43C2×#13511yescharacteristic
270C4×C43C2×#13711yescharacteristic
271C4×C43#57711yescharacteristic
272C4×C43#57811yescharacteristic
273Dic43—41no—
274Dic43—41no—
275Dic43—81no—
276#3400—431no—
277#3381—431no—
278#3361—431no—
279#3338D4311yescharacteristic, complemented
280#1714—431no—
281#1696—431no—
282#1678—431no—
283#1672—431no—
284#1665—431no—
285#1644—431no—
286#1636—431no—
287#1630—431no—
288#1622—431no—
289#1582—431no—
290#1579—431no—
291C2×C43—42no—
292C2×C43#327011yescharacteristic
293C2×C43#328411yescharacteristic
294C2×C43#328811yescharacteristic
295D43—161no—
296#559—431no—
297#557—431no—
298#554C2×D4311yescharacteristic
299#554C2×D4311yescharacteristic
300#500C2×D4311yescharacteristic
301#499—861no—
302#498—431no—
303#497—861no—
304#492—431no—
305#492—431no—
306#488—861no—
307#487—431no—
308#486—431no—
309#484—21no—
310#484—21no—
311#479—861no—
312#478—861no—
313#478—861no—
314#477—431no—
315#477—431no—
316#477C2×D4311yescharacteristic
317#477C2×D4311yescharacteristic
318#474—431no—
319#467—21no—
320#464—861no—
321#463—861no—
322#462—431no—
323#461—861no—
324#460—431no—
325#459—431no—
326#446—431no—
327C8×Q8—431no—
328C8×Q8—431no—
329#440—861no—
330C4×Q16C2×D4311yescharacteristic
331C4×SD16—431no—
332C4×SD16—861no—
333C4×D8—861no—
334C8×D4C2×D4311yescharacteristic
335C2×#107—21no—
336#334—431no—
337#334—431no—
338#333—431no—
339#333—431no—
340#332—431no—
341#331—431no—
342Q8⋊C8—431no—
343Q8⋊C8—431no—
344Q8⋊C8—431no—
345D4⋊C8—431no—
346#322—431no—
347C43#1985711yescharacteristic, complemented, Sylow
348C2×Q16—861no—
349C2×Q16C22⋊D4311yescharacteristic
350C2×SD16—431no—
351C2×SD16—861no—
352C2×SD16—861no—
353C2×SD16—861no—
354C2×SD16—1721no—
355C2×D8—861no—
356C22×C8—21no—
357C4⋊Q8—431no—
358C4⋊Q8—861no—
359C4⋊Q8C22×D4311yescharacteristic
360C4⋊Q8C22×D4311yescharacteristic
361#127—431no—
362#125—21no—
363#125—21no—
364#125—861no—
365#125—1721no—
366#124—861no—
367#124—861no—
368#123—1721no—
369C22⋊Q8—21no—
370C22⋊Q8—21no—
371C22⋊Q8—41no—
372C22⋊Q8—41no—
373C4×Q8—431no—
374C4×Q8—861no—
375C4×Q8—861no—
376C4×Q8C22×D4311yescharacteristic
377C4×Q8C22×D4311yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—861no—
381C4×D4—861no—
382C4×D4C22×D4311yescharacteristic
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#107—861no—
390#107—861no—
391#107—861no—
392#107C22⋊D4311yescharacteristic
393#106—431no—
394#106—861no—
395#106—861no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8C22×D4311yescharacteristic
403#103—21no—
404#103—21no—
405#103—431no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—1721no—
410#103C22⋊D4311yescharacteristic
411#103C22⋊D4311yescharacteristic
412#102—431no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418C22⋊C8—21no—
419#97—861no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8—861no—
423C4×C8—861no—
424C4×C8C22×D4311yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—431no—
428C2×Q8—861no—
429C2×Q8C2×C22⋊D4311yescharacteristic
430C2×Q8C2×C22⋊D4311yescharacteristic
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4D4×D4311yescharacteristic
435C22×C4—21no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—1721no—
439Q16—22no—
440Q16—3441no—
441SD16—862no—
442SD16—3441no—
443SD16—3442no—
444SD16—3441no—
445SD16—1722no—
446D8—1722no—
447C2×C8—21no—
448C2×C8—42no—
449C2×C8—431no—
450C2×C8—431no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8C2×C22⋊D4311yescharacteristic
456C2×C8C2×C22⋊D4311yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—431no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—1721no—
472C4⋊C4—1721no—
473C4⋊C4—1721no—
474C4⋊C4D4×D4311yescharacteristic
475C4⋊C4C2×C22⋊D4311yescharacteristic
476C4⋊C4C2×C22⋊D4311yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—1721no—
481C22⋊C4—1721no—
482C22⋊C4—1721no—
483C42—21no—
484C42—21no—
485C42—861no—
486C42—1721no—
487C42C23×D4311yescharacteristic
488C23—21no—
489C23—1721no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—81no—
496Q8—861no—
497Q8—861no—
498Q8—1721no—
499Q8—1721no—
500D4—21no—
501D4—3441no—
502D4—1721no—
503D4—1721no—
504D4—1721no—
505D4—1721no—
506D4#1306335712yes—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—161no—
517C2×C4—161no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—1721no—
521C2×C4—6881no—
522C2×C4C2×D4×D4311yescharacteristic
523C2×C4C22×C22⋊D4311yescharacteristic
524C2×C4#1306337011yescharacteristic
525C8—21no—
526C8—41no—
527C8—861no—
528C8—861no—
529C8—1721no—
530C8—1721no—
531C8—1721no—
532C8—1721no—
533C8#1306334512yes—
534C22—22no—
535C22—41no—
536C22—41no—
537C22—3441no—
538C22—3441no—
539C22—3441no—
540C22D4×C22⋊D4311yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—81no—
548C4—81no—
549C4—3441no—
550C4—1721no—
551C4—1721no—
552C4C2×#1306334511yescharacteristic
553C4C2×#1306335711yescharacteristic
554C4#1458370711yescharacteristic
555C4#1458371211yescharacteristic
556C2—42no—
557C2—6881no—
558C2#1914616511yescharacteristic
559C2#1914632111yescharacteristic
560C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3338C2
socleC22×C43D42
prime radical#14583094C22
hypercenter#3338D43
hypocenterC43#19857
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3338

Complements

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

NH ≅ G/Ntype
1. #19147646C2semidirect
2. #19147470C2semidirect
4. #19134218C2semidirect
5. #19134120C2semidirect
6. #19134013C2semidirect
7. #19133979C2semidirect
9. #19133809C2semidirect
10. #19133751C2semidirect
11. #19133715C2semidirect
13. #19133431C2semidirect
14. #19133414C2semidirect
15. C43×#3338C2semidirect
279. #3338D43semidirect
347. C43#19857semidirect

Maximal subgroups

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

subgroupindex
#191476462
#191474702
#191472552
#191342182
#191341202
#191340132
#191339792
#191339362
#191338092
#191337512
#191337152
#191336672
#191334312
#191334142
C43×#33382
#1985743