Finite Group Databasebeta

← #25149956

Subgroups — #25149956

Order 11008.

1126 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583269C211yesmaximal, characteristic, complemented
2C2×#14583109C211yesmaximal, characteristic, complemented
3#19139548C211yesmaximal, characteristic
4#19135603C212yesmaximal, complemented
5#19135603C212yesmaximal, complemented
6#19135553C211yesmaximal, characteristic, complemented
7#19135394C211yesmaximal, characteristic
8#19134907C212yesmaximal, complemented
9#19134902C212yesmaximal, complemented
10#19134425C211yesmaximal, characteristic, complemented
11C2×C43×#552C211yesmaximal, characteristic
12C22×#10621885C2212yes—
13C2×#13063325C2211yescharacteristic
14C2×#13063304C2212yes—
15C2×#13063304C2212yes—
16#14583269—24no—
17#14583109—24no—
18C2×C4⋊(C43⋊C8)C2211yescharacteristic
19C2×#13063249C2212yes—
20C2×#13063248C2212yes—
21C2×#13063248C2212yes—
22C2×#13063248C2212yes—
23C2×C22⋊(C43⋊C8)C2212yes—
24C2×C22⋊(C43⋊C8)C2212yes—
25C2×#13063236C2211yescharacteristic
26#14582835—21no—
27#14582835—21no—
28#14582802—21no—
29#14582768—21no—
30C4×C4⋊Dic43C2211yescharacteristic
31#14582661C2212yes—
32#14582661C2212yes—
33#14582661C2212yes—
34C43×#552—24no—
35C43×#552—24no—
36C2×#126×C43—21no—
37C2×#125×C43—21no—
38C2×#125×C43C2211yescharacteristic
39C2×#123×C43—21no—
40C2×C22⋊Q8×C43C2211yescharacteristic
41C2×C22⋊Q8×C43C2211yescharacteristic
42C2×C4×Q8×C43C2211yescharacteristic
43C2×C4×D4×C43C2211yescharacteristic
44C2×#117×C43—21no—
45C2×#117×C43C2211yescharacteristic
46C22×C4⋊C4×C43C2211yescharacteristic
47C22×Dic86C2312yes—
48C2×#10621885—24no—
49C2×#10621885—42no—
50C2×#10621885—42no—
51C22×C43⋊C8C2312yes—
52C22×C43⋊C8C2312yes—
53#13063325—22no—
54#13063325—22no—
55#13063304—24no—
56#13063304—24no—
57#13063304—42no—
58#13063304—42no—
59C2×C4⋊Dic43—21no—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43C2312yes—
62C2×Dic43⋊C4—22no—
63C2×Dic43⋊C4—22no—
64C2×C22⋊Dic43—22no—
65C2×C22⋊Dic43—22no—
66C2×C4×Dic43—21no—
67C4⋊(C43⋊C8)—22no—
68#13063249—24no—
69#13063248—24no—
70#13063248—24no—
71#13063248—24no—
72C22⋊(C43⋊C8)—42no—
73C22⋊(C43⋊C8)—42no—
74#13063236—22no—
75C43⋊#95—21no—
76C22×Q8×C43C2311yescharacteristic
77C22×D4×C43D411yescharacteristic
78C23×C4×C43—21no—
79C23×C4×C43C2311yescharacteristic
80C23×C4×C43C2311yescharacteristic
81#126×C43—28no—
82#125×C43—28no—
83#125×C43—22no—
84#125×C43D414yes—
85#123×C43—28no—
86C22⋊Q8×C43—22no—
87C22⋊Q8×C43—22no—
88C22⋊Q8×C43—22no—
89C22⋊Q8×C43—22no—
90C4×Q8×C43—22no—
91C4×Q8×C43D414yes—
92C4×D4×C43—22no—
93C4×D4×C43—22no—
94#117×C43—28no—
95#117×C43—22no—
96#117×C43—22no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—22no—
104C2×C4⋊C4×C43—22no—
105C2×C4⋊C4×C43D411yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43D411yescharacteristic
113C2×C22⋊C4×C43D411yescharacteristic
114C2×C42×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117C24×C43C2×D411yescharacteristic
118C24×C43C2×D411yescharacteristic
119C2×Q8×C43—21no—
120C2×Q8×C43—22no—
121C2×Q8×C43—22no—
122C2×Q8×C43C2×D412yes—
123C2×D4×C43—22no—
124C2×D4×C43—22no—
125C2×D4×C43—41no—
126C22×C4×C43—24no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—42no—
140C22×C4×C43—42no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—22no—
147C22×Dic43—22no—
148C2×Dic86—22no—
149C2×Dic86—22no—
150C2×Dic86—22no—
151C2×Dic86—22no—
152C2×Dic86—22no—
153C2×Dic86—22no—
154C4⋊C4×C43—24no—
155C4⋊C4×C43—24no—
156C4⋊C4×C43—24no—
157C4⋊C4×C43—24no—
158C4⋊C4×C43—24no—
159C4⋊C4×C43—24no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43C2×D412yes—
165C4⋊C4×C43C2×D412yes—
166C4⋊C4×C43C2×D412yes—
167C22⋊C4×C43—24no—
168C22⋊C4×C43—24no—
169C22⋊C4×C43—24no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—22no—
172C42×C43—24no—
173C42×C43—24no—
174C42×C43C2×D412yes—
175C42×C43C2×D412yes—
176C22⋊Dic43—44no—
177C22⋊Dic43—44no—
178#10621885—48no—
179C4⋊Dic43—22no—
180C4⋊Dic43—42no—
181C4⋊Dic43—42no—
182C4⋊Dic43#4114yes—
183Dic43⋊C4—44no—
184Dic43⋊C4—44no—
185C4×Dic43—42no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—22no—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C23×C43—21no—
193C23×C43—22no—
194C23×C43—21no—
195C23×C43—22no—
196C23×C43—21no—
197C23×C43—22no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43—22no—
201C23×C43#13712yes—
202C23×C43C22×D411yescharacteristic
203Q8×C43—22no—
204Q8×C43—22no—
205Q8×C43—42no—
206D4×C43—44no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—22no—
210C2×C4×C43—21no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—48no—
219C2×C4×C43—42no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—42no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43#12012yes—
232C2×C4×C43#12012yes—
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4112yes—
236C2×C4×C43H(5,𝔽2)12yes—
237C2×Dic43—24no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243Dic86—42no—
244Dic86—42no—
245Dic86—42no—
246Dic86—42no—
247C43⋊C8—42no—
248C43⋊C8—42no—
249#25584—431nomaximal, Sylow
250C22×C43—22no—
251C22×C43—24no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43—42no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43C2×#12011yescharacteristic
261C22×C43#54612yes—
262C22×C43C2×#13711yescharacteristic
263C22×C43#57511yescharacteristic
264C22×C43#57812yes—
265C4×C43—22no—
266C4×C43—22no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—42no—
270C4×C43—42no—
271C4×C43—42no—
272C4×C43—42no—
273C4×C43#53211yescharacteristic
274C4×C43#53511yescharacteristic
275C4×C43#55012yes—
276Dic43—44no—
277Dic43—82no—
278C2×#552D4311yescharacteristic
279C2×#491—431no—
280C2×#462—431no—
281#2542—431no—
282#2001—432no—
283#2001—432no—
284#1989—431no—
285#1955—431no—
286#1873—432no—
287#1872—432no—
288#1763—431no—
289C2×C43—42no—
290C2×C43—81no—
291C2×C43#243111yescharacteristic
292C2×C43#300711yescharacteristic
293C2×C43#301111yescharacteristic
294C2×C43#331212yes—
295C2×C43#331512yes—
296C22×Q16—432no—
297#552—24no—
298#552—24no—
299C2×C4⋊Q8—431no—
300C2×#126—21no—
301C2×#125—21no—
302C2×#125C2×D4311yescharacteristic
303C2×#123—21no—
304C2×C22⋊Q8—432no—
305C2×C22⋊Q8—432no—
306C2×C22⋊Q8C2×D4311yescharacteristic
307C2×C22⋊Q8C2×D4311yescharacteristic
308C2×C4×Q8C2×D4311yescharacteristic
309C2×C4×D4C2×D4311yescharacteristic
310C2×#117—21no—
311C2×#117C2×D4311yescharacteristic
312C22×C4⋊C4C2×D4311yescharacteristic
313#491—864no—
314#462—864no—
315C2×C4⋊C8—431no—
316C2×#103—432no—
317C2×#103—432no—
318C2×#103—432no—
319C2×#103—432no—
320C2×C22⋊C8—432no—
321C2×C22⋊C8—432no—
322C2×#97—431no—
323#399—861no—
324#399—861no—
325#390—861no—
326#384—861no—
327C4×C4⋊C4—431no—
328#340—432no—
329#340—432no—
330#340—432no—
331C43#2558411yescharacteristic, complemented, Sylow
332C22×Q8—432no—
333C22×Q8C22×D4311yescharacteristic
334C22×D4C22⋊D4311yescharacteristic
335C23×C4—21no—
336C23×C4C22×D4311yescharacteristic
337C23×C4C22×D4311yescharacteristic
338C2×Q16—864no—
339C2×Q16—1722no—
340C2×Q16—1722no—
341C22×C8—432no—
342C22×C8—432no—
343C4⋊Q8—862no—
344C4⋊Q8—862no—
345#126—28no—
346#125—28no—
347#125—22no—
348#125C22⋊D4314yes—
349#123—28no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8—864no—
355C22⋊Q8—864no—
356C22⋊Q8—1722no—
357C22⋊Q8—1722no—
358C4×Q8—22no—
359C4×Q8C22⋊D4314yes—
360C4×D4—22no—
361C4×D4—22no—
362#117—28no—
363#117—22no—
364#117—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—432no—
374C2×C4⋊C4—862no—
375C2×C4⋊C4—862no—
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—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—862no—
386C2×C22⋊C4—862no—
387C2×C22⋊C4C22⋊D4311yescharacteristic
388C2×C22⋊C4C22⋊D4311yescharacteristic
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—861no—
392C2×C42C22×D4311yescharacteristic
393C4⋊C8—862no—
394#103—864no—
395#103—864no—
396#103—864no—
397#103—864no—
398C22⋊C8—1722no—
399C22⋊C8—1722no—
400#97—862no—
401#95—861no—
402C24C2×C22⋊D4311yescharacteristic
403C24C2×C22⋊D4311yescharacteristic
404C2×Q8—21no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—862no—
408C2×Q8—862no—
409C2×Q8—862no—
410C2×Q8—862no—
411C2×Q8—862no—
412C2×Q8—862no—
413C2×Q8C2×C22⋊D4312yes—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—41no—
417C22×C4—24no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4C2×C22⋊D4311yescharacteristic
435C22×C4C2×C22⋊D4311yescharacteristic
436C22×C4C2×C22⋊D4311yescharacteristic
437C22×C4C2×C22⋊D4311yescharacteristic
438C22×C4C23×D4311yescharacteristic
439Q16—1728no—
440C2×C8—862no—
441C2×C8—862no—
442C2×C8—862no—
443C2×C8—862no—
444C2×C8—862no—
445C2×C8—862no—
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—434no—
457C4⋊C4—862no—
458C4⋊C4—1724no—
459C4⋊C4—1724no—
460C4⋊C4—1722no—
461C4⋊C4—1722no—
462C4⋊C4C2×C22⋊D4312yes—
463C4⋊C4C2×C22⋊D4312yes—
464C4⋊C4C2×C22⋊D4312yes—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—1724no—
471C22⋊C4—1724no—
472C42—24no—
473C42—24no—
474C42—1722no—
475C42C2×C22⋊D4312yes—
476C42C2×C22⋊D4312yes—
477C23—21no—
478C23—21no—
479C23—22no—
480C23—22no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—22no—
485C23—22no—
486C23#1306335512yes—
487C23C22×C22⋊D4311yescharacteristic
488Q8—22no—
489Q8—22no—
490Q8—42no—
491Q8—1722no—
492Q8—1722no—
493Q8—1722no—
494Q8—1722no—
495D4—44no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—48no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—864no—
521C2×C4—1722no—
522C2×C4—1722no—
523C2×C4—1722no—
524C2×C4—1722no—
525C2×C4—1722no—
526C2×C4#1306329412yes—
527C2×C4#1306329412yes—
528C2×C4C22×C22⋊D4311yescharacteristic
529C2×C4C22×C22⋊D4311yescharacteristic
530C2×C4#41×D4312yes—
531C2×C4#1306337112yes—
532C8—1722no—
533C8—1722no—
534C22—24no—
535C22—22no—
536C22—41no—
537C22—42no—
538C22—41no—
539C22—42no—
540C22—41no—
541C22—41no—
542C22—42no—
543C22—41no—
544C22C2×#1306329411yescharacteristic
545C22#1458353712yes—
546C22C2×#1306335511yescharacteristic
547C22#1458369711yescharacteristic
548C22#1458371412yes—
549C4—22no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—42no—
554C4—42no—
555C4—42no—
556C4—42no—
557C4—3442no—
558C4—1724no—
559C4#1458344511yescharacteristic
560C4#1458346311yescharacteristic
561C4#1458356812yes—
562C2—42no—
563C2—81no—
564C2#1913821011yescharacteristic
565C2#1914385511yescharacteristic
566C2#1914389011yescharacteristic
567C2#1914664012yes—
568C2#1914668512yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#552C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenterC2×#552D43
hypocenterC43#25584
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#14583269C2semidirect
2. C2×#14583109C2semidirect
4. #19135603C2semidirect
5. #19135603C2semidirect
6. #19135553C2semidirect
8. #19134907C2semidirect
9. #19134902C2semidirect
10. #19134425C2semidirect
331. C43#25584semidirect

Maximal subgroups

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

subgroupindex
C2×#145832692
C2×#145831092
#191395482
#191356032
#191355532
#191353942
#191349072
#191349022
#191344252
C2×C43×#5522
#2558443