Finite Group Databasebeta

← #24988465

Subgroups — #24988465

Order 11008.

758 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134405C211yesmaximal, characteristic, complemented
2#19133202C211yesmaximal, characteristic, complemented
3#19133103C211yesmaximal, characteristic, complemented
4#19133081C211yesmaximal, characteristic, complemented
5#19133029C211yesmaximal, characteristic, complemented
6#19133012C211yesmaximal, characteristic, complemented
7C43×#3517C211yesmaximal, characteristic
8#14582956C2211yescharacteristic
9#14582952C2211yescharacteristic
10C2×#13063252—21no—
11C4×#10621877C2211yescharacteristic
12#14582745C2211yescharacteristic
13#14582658—21no—
14#14582641—21no—
15#14582639—21no—
16#14582636—21no—
17#14582633—21no—
18#14582633—22no—
19Q8⋊(C43⋊C8)—21no—
20D4⋊(C43⋊C8)—22no—
21D4⋊(C43⋊C8)—21no—
22C43×#557C411yescharacteristic, complemented
23C43×#553—22no—
24C43×#553—21no—
25C43×#550—21no—
26C43×#550—21no—
27C43×#550C411yescharacteristic, complemented
28C43×#550C411yescharacteristic, complemented
29C43×#547—21no—
30C43×#547C411yescharacteristic, complemented
31C43×#540—22no—
32C43×#540—21no—
33C43×#532—21no—
34C43×#532C2211yescharacteristic
35C43×#529—21no—
36C43×#529C2211yescharacteristic
37C43×#520—21no—
38C4×#41×C43C2211yescharacteristic
39C2×#10621877—21no—
40C2×C4×Dic43—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43#13063252—24no—
44C22⋊(C43⋊C8)—21no—
45C22⋊(C43⋊C8)—21no—
46#13063236—21no—
47#13063236—21no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C2×#41×C43—21no—
53C2×#41×C43—21no—
54C2×#41×C43—21no—
55C2×#41×C43—21no—
56C2×#41×C43D411yescharacteristic
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43C2×C411yescharacteristic
59#127×C43—22no—
60#127×C43—21no—
61#127×C43—21no—
62#127×C43C2×C411yescharacteristic
63#126×C43—22no—
64#126×C43—21no—
65#125×C43—22no—
66#125×C43—21no—
67#125×C43D411yescharacteristic
68#124×C43—21no—
69#124×C43D411yescharacteristic
70#123×C43—22no—
71#123×C43—22no—
72#123×C43—22no—
73#123×C43—21no—
74#123×C43—22no—
75C22⋊Q8×C43—21no—
76C22⋊Q8×C43D411yescharacteristic
77#121×C43—22no—
78#121×C43—22no—
79#121×C43—22no—
80#121×C43—22no—
81#121×C43—22no—
82#121×C43—21no—
83#121×C43—22no—
84#121×C43—22no—
85#121×C43—21no—
86#121×C43—21no—
87#121×C43—21no—
88#121×C43D411yescharacteristic
89#121×C43D412yes—
90C4×Q8×C43—21no—
91C4×Q8×C43—21no—
92C4×Q8×C43C2×C411yescharacteristic
93C4×Q8×C43C2×C411yescharacteristic
94C4×Q8×C43D411yescharacteristic
95C4×D4×C43—22no—
96C4×D4×C43—22no—
97C4×D4×C43—22no—
98C4×D4×C43—22no—
99C4×D4×C43—21no—
100C4×D4×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43C2×C411yescharacteristic
106C4×D4×C43C2×C411yescharacteristic
107C4×D4×C43D411yescharacteristic
108C4×D4×C43D412yes—
109#117×C43—22no—
110#117×C43—21no—
111#117×C43—21no—
112#117×C43D411yescharacteristic
113C2×C4⋊C4×C43—22no—
114C2×C4⋊C4×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#41×C43—22no—
118#41×C43—41no—
119#41×C43—42no—
120#41×C43—42no—
121#41×C43—82no—
122#41×C43—82no—
123#41×C43—82no—
124C2×Q8×C43—21no—
125C2×Q8×C43C22⋊C411yescharacteristic
126C2×Q8×C43C22⋊C411yescharacteristic
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43—22no—
130C2×D4×C43—22no—
131C2×D4×C43—22no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—22no—
137C2×D4×C43C22⋊C411yescharacteristic
138C2×D4×C43C22⋊C411yescharacteristic
139C2×D4×C43C22⋊C412yes—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×Dic43—41no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—21no—
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×C43C22⋊C411yescharacteristic
164C4⋊C4×C43C22⋊C411yescharacteristic
165C4⋊C4×C43C22⋊C411yescharacteristic
166C4⋊C4×C43C22⋊C412yes—
167C4⋊C4×C43C22⋊C411yescharacteristic
168C22⋊C4×C43—22no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—22no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C42×C43—22no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43C22×C411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C4×Dic43—22no—
191C4×Dic43—41no—
192#10621877—22no—
193#10621877—41no—
194C2×C43⋊C8—41no—
195C2×C43⋊C8—41no—
196C2×C43⋊C8—41no—
197C23×C43—21no—
198C23×C43—22no—
199C23×C43—21no—
200C23×C43#12011yescharacteristic
201Q8×C43—21no—
202Q8×C43—41no—
203Q8×C43—42no—
204Q8×C43#10412yes—
205D4×C43—21no—
206D4×C43—21no—
207D4×C43—42no—
208D4×C43—42no—
209D4×C43—41no—
210D4×C43—44no—
211D4×C43—42no—
212D4×C43—41no—
213D4×C43—41no—
214D4×C43—81no—
215D4×C43—82no—
216D4×C43—82no—
217D4×C43—82no—
218D4×C43—82no—
219D4×C43—82no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—22no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—42no—
232C2×C4×C43—44no—
233C2×C4×C43—42no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—81no—
237C2×C4×C43—82no—
238C2×C4×C43—82no—
239C2×C4×C43—82no—
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43#12011yescharacteristic
244C2×C4×C43#12011yescharacteristic
245C2×C4×C43#12011yescharacteristic
246C2×Dic43—42no—
247C2×Dic43—81no—
248C2×Dic43—81no—
249C43⋊C8—42no—
250C43⋊C8—81no—
251C43⋊C8—81no—
252#8414—431nomaximal, Sylow
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—41no—
257C22×C43—42no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—42no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—42no—
264C22×C43—41no—
265C22×C43#37911yescharacteristic
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—22no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—42no—
277C4×C43—41no—
278C4×C43C2×#10411yescharacteristic
279C4×C43#42111yescharacteristic
280Dic43—82no—
281#3517D4311yescharacteristic
282#1759—431no—
283#1529—431no—
284#1505—431no—
285#1500—431no—
286#1488—431no—
287#1484—431no—
288C2×C43—41no—
289C2×C43—81no—
290C2×C43—82no—
291C2×C43—81no—
292C2×C43#178911yescharacteristic
293C2×C43#179411yescharacteristic
294C2×C43#179511yescharacteristic
295#557Dic4311yescharacteristic, complemented
296#553—22no—
297#553—21no—
298#550—21no—
299#550—21no—
300#550Dic4311yescharacteristic, complemented
301#550Dic4311yescharacteristic, complemented
302#547—21no—
303#547Dic4311yescharacteristic, complemented
304#540—22no—
305#540—21no—
306#532—21no—
307#532C2×D4311yescharacteristic
308#529—21no—
309#529C2×D4311yescharacteristic
310#520—21no—
311C4×#41C2×D4311yescharacteristic
312#432—431no—
313#431—431no—
314C2×#104—861no—
315C4×M16—431no—
316#376—431no—
317#339—861no—
318#330—861no—
319#329—861no—
320#328—861no—
321#327—861no—
322#327—862no—
323Q8⋊C8—861no—
324D4⋊C8—862no—
325D4⋊C8—861no—
326C43#841411yescharacteristic, complemented, Sylow
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41C22⋊D4311yescharacteristic
332C2×M16—861no—
333C4⋊Q8—21no—
334C4⋊Q8C2×Dic4311yescharacteristic
335#127—22no—
336#127—21no—
337#127—21no—
338#127C2×Dic4311yescharacteristic
339#126—22no—
340#126—21no—
341#125—22no—
342#125—21no—
343#125C22⋊D4311yescharacteristic
344#124—21no—
345#124C22⋊D4311yescharacteristic
346#123—22no—
347#123—22no—
348#123—22no—
349#123—21no—
350#123—22no—
351C22⋊Q8—21no—
352C22⋊Q8C22⋊D4311yescharacteristic
353#121—22no—
354#121—22no—
355#121—22no—
356#121—22no—
357#121—22no—
358#121—21no—
359#121—22no—
360#121—22no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121C22⋊D4311yescharacteristic
365#121C22⋊D4312yes—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8C2×Dic4311yescharacteristic
369C4×Q8C2×Dic4311yescharacteristic
370C4×Q8C22⋊D4311yescharacteristic
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4C2×Dic4311yescharacteristic
382C4×D4C2×Dic4311yescharacteristic
383C4×D4C22⋊D4311yescharacteristic
384C4×D4C22⋊D4312yes—
385#117—22no—
386#117—21no—
387#117—21no—
388#117C22⋊D4311yescharacteristic
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C42—21no—
392C2×C42—861no—
393C2×C42C22×D4311yescharacteristic
394C4⋊C8—861no—
395C4⋊C8—861no—
396#104—864no—
397C22⋊C8—861no—
398C22⋊C8—861no—
399#97—861no—
400#97—861no—
401C4×C8—861no—
402C4×C8—861no—
403#95—861no—
404#95—861no—
405#41—22no—
406#41—41no—
407#41—42no—
408#41—42no—
409#41—82no—
410#41—82no—
411#41—82no—
412C2×Q8—21no—
413C2×Q8C22⋊Dic4311yescharacteristic
414C2×Q8C22⋊Dic4311yescharacteristic
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4C22⋊Dic4311yescharacteristic
426C2×D4C22⋊Dic4311yescharacteristic
427C2×D4C22⋊Dic4312yes—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—1721no—
437C22×C4C2×C22⋊D4311yescharacteristic
438C22×C4C2×C22⋊D4311yescharacteristic
439C22×C4C2×C22⋊D4311yescharacteristic
440M16—862no—
441M16—1721no—
442C2×C8—1721no—
443C2×C8—1721no—
444C2×C8—1721no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4C22⋊Dic4311yescharacteristic
457C4⋊C4C22⋊Dic4311yescharacteristic
458C4⋊C4C22⋊Dic4311yescharacteristic
459C4⋊C4C22⋊Dic4312yes—
460C4⋊C4C22⋊Dic4311yescharacteristic
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—21no—
469C22⋊C4—21no—
470C22⋊C4—22no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—22no—
474C42—22no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—862no—
480C42—1721no—
481C42C22×Dic4311yescharacteristic
482C42C2×C22⋊D4311yescharacteristic
483C42C2×C22⋊D4311yescharacteristic
484C42C2×C22⋊D4311yescharacteristic
485C23—21no—
486C23—22no—
487C23—21no—
488C23#1306329411yescharacteristic
489Q8—21no—
490Q8—41no—
491Q8—42no—
492Q8#1306325212yes—
493D4—21no—
494D4—21no—
495D4—42no—
496D4—41no—
497D4—42no—
498D4—44no—
499D4—42no—
500D4—41no—
501D4—41no—
502D4—82no—
503D4—81no—
504D4—82no—
505D4—82no—
506D4—82no—
507D4—82no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—82no—
525C2×C4—81no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—3441no—
529C2×C4—3441no—
530C2×C4—1722no—
531C2×C4C2×C22⋊Dic4311yescharacteristic
532C2×C4C2×C22⋊Dic4311yescharacteristic
533C2×C4C2×C22⋊Dic4311yescharacteristic
534C2×C4#1306329411yescharacteristic
535C2×C4#1306329411yescharacteristic
536C2×C4#1306329411yescharacteristic
537C8—3441no—
538C8—3441no—
539C8—1722no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—42no—
545C22—41no—
546C22—41no—
547C22—42no—
548C22—41no—
549C22—41no—
550C22—42no—
551C22—41no—
552C22#1458275511yescharacteristic
553C4—21no—
554C4—22no—
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—42no—
564C4—41no—
565C4—3442no—
566C4C2×#1306325211yescharacteristic
567C4#1458291611yescharacteristic
568C2—41no—
569C2—81no—
570C2—82no—
571C2—81no—
572C2#1913453911yescharacteristic
573C2#1913455911yescharacteristic
574C2#1913456511yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3517C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3517D43
hypocenterC43#8414
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3517

Complements

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

NH ≅ G/Ntype
1. #19134405C2semidirect
2. #19133202C2semidirect
3. #19133103C2semidirect
4. #19133081C2semidirect
5. #19133029C2semidirect
6. #19133012C2semidirect
22. C43×#557C4semidirect
27. C43×#550C4semidirect
28. C43×#550C4semidirect
30. C43×#547C4semidirect
295. #557Dic43semidirect
300. #550Dic43semidirect
301. #550Dic43semidirect
303. #547Dic43semidirect
326. C43#8414semidirect

Maximal subgroups

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

subgroupindex
#191344052
#191332022
#191331032
#191330812
#191330292
#191330122
C43×#35172
#841443