Finite Group Databasebeta

← #25169208

Subgroups — #25169208

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#19138465C211yesmaximal, characteristic
2#19137691C211yesmaximal, characteristic, complemented
3#19135984C211yesmaximal, characteristic
4#19135935C211yesmaximal, characteristic, complemented
5#19135933C211yesmaximal, characteristic, complemented
6#19135742C211yesmaximal, characteristic
7#19135549C211yesmaximal, characteristic, complemented
8#19135337C211yesmaximal, characteristic, complemented
9#19135220C211yesmaximal, characteristic
10#19135215C211yesmaximal, characteristic
11#19135169C211yesmaximal, characteristic, complemented
12#19135160C211yesmaximal, characteristic, complemented
13#19134853C211yesmaximal, characteristic
14#19134419C211yesmaximal, characteristic
15C43×#1919C211yesmaximal, characteristic, complemented
16C2×#13063317C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28#14582836—21no—
29#14582821—21no—
30#14582801C2211yescharacteristic
31#14582800C2211yescharacteristic
32#14582798C2211yescharacteristic
33#14582796—21no—
34#14582795C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582786—21no—
37#14582783—21no—
38#14582773—21no—
39#14582756—21no—
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×Dic43⋊C4—21no—
43C4×C4⋊Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C4×D43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063317—22no—
64#13063317—22no—
65#13063316—22no—
66#13063316—41no—
67#13063287—22no—
68#13063287—41no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43D411yescharacteristic
72C2×C4⋊Dic43D411yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063258—22no—
91#13063258—41no—
92#13063256—22no—
93Dic43⋊C8—41no—
94#13063247—22no—
95#13063247—22no—
96#13063245—41no—
97#13063245Q814yes—
98#13063235—41no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C42×C43—21no—
114C2×C42×C43C2311yescharacteristic
115#106×C43—22no—
116#95×C43—21no—
117#95×C43—21no—
118C23×D43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2411yescharacteristic
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43C2×D411yescharacteristic
130C22×Dic43C2×D411yescharacteristic
131C22×Dic43C2×D411yescharacteristic
132C22×Dic43C2×D411yescharacteristic
133C2×D172—21no—
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172C2×Q812yes—
139C2×C4×D43—42no—
140C2×C4×D43—42no—
141C2×C4×D43—81no—
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—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—81no—
155C4⋊C4×C43C2×Q812yes—
156C4⋊C4×C43#4112yes—
157C42×C43—21no—
158C42×C43—21no—
159C42×C43—81no—
160(C2×D43)⋊C4—42no—
161(C2×D43)⋊C4—42no—
162(C2×D43)⋊C4—81no—
163(C2×D43)⋊C4—81no—
164(C2×D43)⋊C4—81no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—41no—
170C4⋊Dic43—41no—
171C4⋊Dic43—42no—
172C4⋊Dic43—81no—
173C4⋊Dic43#4112yes—
174C4⋊Dic43#4112yes—
175Dic43⋊C4—24no—
176Dic43⋊C4—24no—
177Dic43⋊C4—42no—
178Dic43⋊C4—42no—
179Dic43⋊C4—81no—
180C4×Dic43—21no—
181C4×Dic43—21no—
182C4×Dic43—21no—
183C4×Dic43—21no—
184C4×Dic43—42no—
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×C43C22×D411yescharacteristic
193C22×D43—22no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—41no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
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×C43C22×Q811yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43H(5,𝔽2)11yescharacteristic
223C2×C4×C432−1+411yescharacteristic
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245D172—22no—
246D172—22no—
247D172—41no—
248D172—41no—
249C4×D43—84no—
250C8×C43—41no—
251C8×C43—41no—
252C43⋊C8—22no—
253C43⋊C8—41no—
254#27027—431nomaximal, Sylow
255C22×C43#52511yescharacteristic
256C22×C43#54611yescharacteristic
257C22×C43D4×Q811yescharacteristic
258C22×C43#57511yescharacteristic
259C22×C43#57511yescharacteristic
260C22×C43#57611yescharacteristic
261C22×C43#57711yescharacteristic
262C2×D43—42no—
263C2×D43—42no—
264C2×D43—42no—
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—81no—
268C2×D43—81no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—42no—
272C4×C43—42no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43#53311yescharacteristic
276C4×C43#54211yescharacteristic
277C4×C43#55411yescharacteristic
278C4×C43#55611yescharacteristic
279Dic43—42no—
280Dic43—42no—
281Dic43—41no—
282Dic43—41no—
283Dic43—41no—
284Dic43—41no—
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#1919D4311yescharacteristic, complemented
297#1918—431no—
298#1917—431no—
299#1864—431no—
300#1762—431no—
301C2×C43#246511yescharacteristic
302C2×C43#311111yescharacteristic
303C2×C43#311911yescharacteristic
304C2×C43#330911yescharacteristic
305C2×C43#332311yescharacteristic
306C2×C43#338811yescharacteristic
307C2×C43#338911yescharacteristic
308D43—82no—
309C2×#125—431no—
310C2×#125—431no—
311C2×C4×D4—431no—
312C2×#107—431no—
313C2×#107—431no—
314C2×#106—431no—
315C2×#106C2×D4311yescharacteristic
316C2×C4⋊C8—431no—
317C2×#102—431no—
318C2×#102—431no—
319C2×#102—431no—
320C2×#102—431no—
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—861no—
339C4×C4⋊C4C2×D4311yescharacteristic
340#340—431no—
341#340—431no—
342#340—431no—
343#340—431no—
344#340—431no—
345#340C2×D4311yescharacteristic
346#340C2×D4311yescharacteristic
347#340C2×D4311yescharacteristic
348#336—431no—
349#336—431no—
350#336—431no—
351#336C2×D4311yescharacteristic
352C43#2702711yescharacteristic, complemented, Sylow
353C22×D4—431no—
354C23×C4—861no—
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—862no—
364C4×D4—1721no—
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—861no—
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⋊C4C22×D4311yescharacteristic
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C4⋊C4C22×D4311yescharacteristic
381C2×C4⋊C4C22×D4311yescharacteristic
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C42—21no—
388C2×C42—431no—
389C2×C42—431no—
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—434no—
399#102—862no—
400#102—862no—
401#102—1721no—
402#97—1721no—
403#95—21no—
404#95—21no—
405#95—431no—
406#95—431no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412C24—861no—
413C2×D4—432no—
414C2×D4—861no—
415C2×D4—861no—
416C2×D4—861no—
417C2×D4—861no—
418C2×D4—861no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—431no—
424C22×C4—431no—
425C22×C4—431no—
426C22×C4—431no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—3441no—
431C22×C4—1722no—
432C22×C4—1722no—
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—21no—
453C4⋊C4—21no—
454C4⋊C4—81no—
455C4⋊C4—432no—
456C4⋊C4—432no—
457C4⋊C4—864no—
458C4⋊C4—864no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—3441no—
464C4⋊C4—3441no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C4⋊C4—1722no—
468C4⋊C4—1722no—
469C4⋊C4—1722no—
470C4⋊C4#1062189812yes—
471C4⋊C4Q8×D4312yes—
472C22⋊C4—3441no—
473C22⋊C4—3441no—
474C22⋊C4—3441no—
475C22⋊C4—1722no—
476C22⋊C4—1722no—
477C42—21no—
478C42—21no—
479C42—81no—
480C42—861no—
481C42—861no—
482C42—861no—
483C42—861no—
484C42—3441no—
485C42—1722no—
486C23—862no—
487C23—1721no—
488C23—1721no—
489C23—1721no—
490C23—1721no—
491C23—1721no—
492C23—1721no—
493C23C2×D4×D4311yescharacteristic
494D4—862no—
495D4—862no—
496D4—1721no—
497D4—1721no—
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—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—862no—
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—861no—
529C2×C4—861no—
530C2×C4—3444no—
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×C4#41×D4311yescharacteristic
541C2×C4C2×#1062189811yescharacteristic
542C2×C4#1306337111yescharacteristic
543C2×C4#1306337211yescharacteristic
544C8—41no—
545C8—41no—
546C8—862no—
547C8—1721no—
548C22—3441no—
549C22—3441no—
550C22—3441no—
551C22—3441no—
552C22—1722no—
553C22—1722no—
554C22—1722no—
555C22#1458340711yescharacteristic
556C22#1458354511yescharacteristic
557C22#1458356211yescharacteristic
558C22#1458369611yescharacteristic
559C22#1458369811yescharacteristic
560C22#1458370311yescharacteristic
561C22#1458370511yescharacteristic
562C4—41no—
563C4—42no—
564C4—42no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—3441no—
569C4—1722no—
570C4—1721no—
571C4—1721no—
572C4—1722no—
573C4—1721no—
574C4—1721no—
575C4#1458345311yescharacteristic
576C4#1458351511yescharacteristic
577C4#1458360511yescharacteristic
578C4#1458361711yescharacteristic
579C2—3442no—
580C2#1913861511yescharacteristic
581C2#1914470711yescharacteristic
582C2#1914478911yescharacteristic
583C2#1914660611yescharacteristic
584C2#1914681611yescharacteristic
585C2#1914754711yescharacteristic
586C2#1914755311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1919C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1919D43
hypocenterC43#27027
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
2. #19137691C2semidirect
4. #19135935C2semidirect
5. #19135933C2semidirect
7. #19135549C2semidirect
8. #19135337C2semidirect
11. #19135169C2semidirect
12. #19135160C2semidirect
15. C43×#1919C2semidirect
296. #1919D43semidirect
352. C43#27027semidirect

Maximal subgroups

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

subgroupindex
#191384652
#191376912
#191359842
#191359352
#191359332
#191357422
#191355492
#191353372
#191352202
#191352152
#191351692
#191351602
#191348532
#191344192
C43×#19192
#2702743