Finite Group Databasebeta

← #25169321

Subgroups — #25169321

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139015C211yesmaximal, characteristic
2#19137602C211yesmaximal, characteristic
3#19136005C211yesmaximal, characteristic, complemented
4#19135973C211yesmaximal, characteristic, complemented
5#19135794C211yesmaximal, characteristic
6#19135794C211yesmaximal, characteristic
7#19135358C211yesmaximal, characteristic, complemented
8#19135322C211yesmaximal, characteristic, complemented
9#19135202C211yesmaximal, characteristic
10#19135183C211yesmaximal, characteristic, complemented
11#19134860C211yesmaximal, characteristic, complemented
12#19134786C211yesmaximal, characteristic
13#19134684C211yesmaximal, characteristic
14#19134414C211yesmaximal, characteristic, complemented
15C43×#1919C211yesmaximal, characteristic, complemented
16C2×#13063320—21no—
17C2×#13063305C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×C4⋊C4×D43C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582838—21no—
32#14582826—21no—
33#14582805C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582797—21no—
36#14582795C2211yescharacteristic
37#14582784—21no—
38#14582782—21no—
39#14582773—21no—
40#14582769C2211yescharacteristic
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×(C2×D43)⋊C4—21no—
45C4×(C2×D43)⋊C4C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C4×D43—21no—
61C22×C4×D43C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063320—44no—
65#13063305—22no—
66#13063305—22no—
67#13063290—22no—
68#13063290—41no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C4⋊C4×D43—22no—
80C4⋊C4×D43—41no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4D411yescharacteristic
85C2×(C2×D43)⋊C4D411yescharacteristic
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89#13063256—22no—
90#13063256—22no—
91#13063256—41no—
92C4⋊(C43⋊C8)—22no—
93#13063250—22no—
94#13063250—22no—
95#13063248—22no—
96#13063248—41no—
97(C2×D43)⋊C8—22no—
98(C2×D43)⋊C8—41no—
99C8×Dic43—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C42×C43—21no—
117C2×C42×C43C2311yescharacteristic
118#106×C43—22no—
119#95×C43—21no—
120#95×C43—21no—
121C23×D43C2×D411yescharacteristic
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2411yescharacteristic
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C22×Dic43C2×D411yescharacteristic
136C2×C4×D43—21no—
137C2×C4×D43—21no—
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—42no—
143C2×C4×D43—42no—
144C2×C4×D43—81no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86#4112yes—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×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×C43—42no—
164C4⋊C4×C43#4112yes—
165C4⋊C4×C43#4112yes—
166C42×C43—21no—
167C42×C43—21no—
168C42×C43—81no—
169(C2×D43)⋊C4—24no—
170(C2×D43)⋊C4—41no—
171(C2×D43)⋊C4—42no—
172(C2×D43)⋊C4—42no—
173(C2×D43)⋊C4SD1614yes—
174C4⋊Dic43—24no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—42no—
182C4⋊Dic43—42no—
183C4⋊Dic43—81no—
184Dic43⋊C4—42no—
185Dic43⋊C4—42no—
186Dic43⋊C4—42no—
187C4×Dic43—21no—
188C4×Dic43—21no—
189C4×Dic43—42no—
190C4×Dic43—42no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8#4112yes—
197C23×C43C22×D411yescharacteristic
198C22×D43—21no—
199C22×D43—21no—
200C22×D43—21no—
201C22×D43—21no—
202C22×D43—21no—
203C22×D43—21no—
204C22×D43C2×SD1612yes—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
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×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43C2×SD1612yes—
223C2×C4×C43C2×#4111yescharacteristic
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—22no—
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—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43C2×SD1612yes—
250C4×D43—41no—
251C4×D43—41no—
252C4×D43—41no—
253C4×D43—41no—
254C4×D43—84no—
255Dic86—22no—
256Dic86—22no—
257Dic86—41no—
258Dic86—41no—
259C8×C43—41no—
260C8×C43—41no—
261C43⋊C8—22no—
262C43⋊C8—41no—
263#27034—431nomaximal, Sylow
264C22×C43#52511yescharacteristic
265C22×C43#54611yescharacteristic
266C22×C43#54711yescharacteristic
267C22×C43C22×SD1611yescharacteristic
268C22×C43#57511yescharacteristic
269C22×C43#57711yescharacteristic
270C22×C43#57811yescharacteristic
271C2×D43—22no—
272C2×D43—22no—
273C2×D43—22no—
274C2×D43—41no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—41no—
278C4×C43—22no—
279C4×C43—41no—
280C4×C43—42no—
281C4×C43—42no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43#52911yescharacteristic
285C4×C43#53911yescharacteristic
286C4×C43#55311yescharacteristic
287C4×C43#55611yescharacteristic
288Dic43—22no—
289Dic43—42no—
290Dic43—41no—
291Dic43—41no—
292Dic43—81no—
293Dic43—81no—
294Dic43—81no—
295#2496—431no—
296#2360—431no—
297#2072—431no—
298#2066—431no—
299#2035—431no—
300#2035—431no—
301#1948—431no—
302#1941—431no—
303#1923—431no—
304#1920—431no—
305#1919D4311yescharacteristic, complemented
306#1865—431no—
307#1853—431no—
308#1824—431no—
309C4×#103—431no—
310C2×C43#246611yescharacteristic
311C2×C43#310311yescharacteristic
312C2×C43#312011yescharacteristic
313C2×C43#329811yescharacteristic
314C2×C43#331111yescharacteristic
315C2×C43#333511yescharacteristic
316C2×C43#335211yescharacteristic
317D43—42no—
318C2×#126—861no—
319C2×C22⋊Q8—431no—
320C2×C4×Q8—431no—
321C22×C4⋊C4—431no—
322C2×#106—431no—
323C2×#106—431no—
324C2×#106—431no—
325C2×#106C2×D4311yescharacteristic
326C2×C4⋊C8—431no—
327C2×#103—431no—
328C2×#103—431no—
329C2×#103—431no—
330C2×#103—431no—
331C2×C22⋊C8—431no—
332C2×C22⋊C8—431no—
333C2×C4×C8—431no—
334#400—861no—
335#397—861no—
336#391—431no—
337#389—431no—
338#389—431no—
339#389—861no—
340#389C2×D4311yescharacteristic
341#387—861no—
342#387—861no—
343#385—861no—
344#384—431no—
345#380—431no—
346#380—431no—
347C4×C4⋊C4—431no—
348C4×C4⋊C4C2×D4311yescharacteristic
349C4×C22⋊C4—431no—
350C4×C22⋊C4—861no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340C2×D4311yescharacteristic
357#340C2×D4311yescharacteristic
358#340C2×D4311yescharacteristic
359#336—431no—
360#336C2×D4311yescharacteristic
361C43#2703411yescharacteristic, complemented, Sylow
362C22×Q8—431no—
363C23×C4—431no—
364C23×C4—861no—
365C22×C8—431no—
366C22×C8—431no—
367C22×C8C22×D4311yescharacteristic
368C22×C8C22×D4311yescharacteristic
369#126—1724no—
370C22⋊Q8—862no—
371C22⋊Q8—862no—
372C4×Q8—862no—
373C4×Q8—1721no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—862no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—1721no—
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C4⋊C4C22×D4311yescharacteristic
389C2×C4⋊C4C22×D4311yescharacteristic
390C2×C4⋊C4C22×D4311yescharacteristic
391C2×C22⋊C4—431no—
392C2×C22⋊C4—431no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C42—21no—
397C2×C42—431no—
398C2×C42—861no—
399C2×C42—861no—
400C2×C42C22×D4311yescharacteristic
401#106—22no—
402#106—862no—
403#106—862no—
404#106—1721no—
405C4⋊C8—862no—
406#103—862no—
407#103—862no—
408#103—862no—
409#103—1721no—
410C22⋊C8—862no—
411C22⋊C8—1721no—
412C4×C8—1721no—
413#95—21no—
414#95—21no—
415#95—431no—
416#95—431no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424C24—431no—
425C2×Q8—432no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×Q8—861no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—3441no—
449C22×C4—1722no—
450C22×C4—1722no—
451C22×C4D4×D4311yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4C23×D4311yescharacteristic
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—432no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—42no—
473C4⋊C4—864no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—3441no—
481C4⋊C4—1722no—
482C4⋊C4—1722no—
483C4⋊C4—1722no—
484C4⋊C4—1722no—
485C4⋊C4—1722no—
486C4⋊C4#1062189812yes—
487C4⋊C4#1062190212yes—
488C22⋊C4—434no—
489C22⋊C4—864no—
490C22⋊C4—1721no—
491C22⋊C4—1722no—
492C22⋊C4—1722no—
493C42—21no—
494C42—21no—
495C42—81no—
496C42—861no—
497C42—861no—
498C42—1722no—
499C42—1722no—
500C23—432no—
501C23—861no—
502C23—861no—
503C23—861no—
504C23—861no—
505C23—861no—
506C23—861no—
507C23C2×D4×D4311yescharacteristic
508Q8—862no—
509Q8—862no—
510Q8—1721no—
511Q8—1721no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—432no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—862no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—3444no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4SD16×D4312yes—
556C2×C4#41×D4311yescharacteristic
557C2×C4#41×D4311yescharacteristic
558C2×C4C2×#1062189811yescharacteristic
559C2×C4C2×#1062190211yescharacteristic
560C2×C4#1306337111yescharacteristic
561C2×C4#1306337211yescharacteristic
562C8—41no—
563C8—41no—
564C8—862no—
565C8—1721no—
566C22—862no—
567C22—862no—
568C22—862no—
569C22—1721no—
570C22—1721no—
571C22—1721no—
572C22—1721no—
573C22#1458341211yescharacteristic
574C22#1458354511yescharacteristic
575C22#1458354711yescharacteristic
576C22C2×SD16×D4311yescharacteristic
577C22#1458369811yescharacteristic
578C22#1458370911yescharacteristic
579C22#1458371311yescharacteristic
580C4—22no—
581C4—42no—
582C4—42no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—862no—
587C4—3441no—
588C4—3441no—
589C4—3441no—
590C4—1721no—
591C4—1722no—
592C4—1721no—
593C4#1458342711yescharacteristic
594C4#1458349011yescharacteristic
595C4#1458360211yescharacteristic
596C4#1458362211yescharacteristic
597C2—1722no—
598C2#1913863811yescharacteristic
599C2#1914462811yescharacteristic
600C2#1914481411yescharacteristic
601C2#1914646211yescharacteristic
602C2#1914663611yescharacteristic
603C2#1914695011yescharacteristic
604C2#1914716311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1919C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1919D43
hypocenterC43#27034
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
3. #19136005C2semidirect
4. #19135973C2semidirect
7. #19135358C2semidirect
8. #19135322C2semidirect
10. #19135183C2semidirect
11. #19134860C2semidirect
14. #19134414C2semidirect
15. C43×#1919C2semidirect
305. #1919D43semidirect
361. C43#27034semidirect

Maximal subgroups

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

subgroupindex
#191390152
#191376022
#191360052
#191359732
#191357942
#191353582
#191353222
#191352022
#191351832
#191348602
#191347862
#191346842
#191344142
C43×#19192
#2703443