Finite Group Databasebeta

← #25150772

Subgroups — #25150772

Order 11008.

1028 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583621C211yesmaximal, characteristic
2C2×#14583261C211yesmaximal, characteristic
3#19139804C211yesmaximal, characteristic, complemented
4#19135839C212yesmaximal, complemented
5#19135832C212yesmaximal
6#19135534C211yesmaximal, characteristic, complemented
7#19135525C211yesmaximal, characteristic
8#19134860C212yesmaximal, complemented
9#19134853C212yesmaximal
10#19134425C211yesmaximal, characteristic, complemented
11C2×C43×#475C211yesmaximal, characteristic, complemented
12#14583621—24no—
13#14583621—24no—
14C2×#13063323C2211yescharacteristic
15C2×#13063320—21no—
16C2×#13063319—21no—
17C2×#13063314C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×#13063303—21no—
20C2×C4×Dic86C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23C2×#13063282—21no—
24#14583261—24no—
25C2×#13063250C2212yes—
26C2×#13063249C2212yes—
27C2×#13063248C2212yes—
28C2×#13063247C2212yes—
29C2×#13063245C2212yes—
30C2×#13063236C2211yescharacteristic
31#14582818—21no—
32#14582818—21no—
33#14582804—21no—
34#14582795C2212yes—
35#14582795C2212yes—
36#14582768—21no—
37C4×C4⋊Dic43C2211yescharacteristic
38#14582661C2212yes—
39#14582653C2212yes—
40#14582653C2212yes—
41C2×C4⋊Q8×C43C2211yescharacteristic
42C2×C4×Q8×C43C2211yescharacteristic
43C43×#475—24no—
44C2×#106×C43C2212yes—
45C2×C4⋊C8×C43C2211yescharacteristic
46C2×#103×C43C2212yes—
47C22×Dic86D411yescharacteristic
48C22×Dic86C2311yescharacteristic
49C22×D172C2311yescharacteristic
50C22×C4×D43—21no—
51C22×C43⋊C8C2312yes—
52#13063323—22no—
53#13063323—22no—
54#13063320—28no—
55#13063319—28no—
56#13063314—22no—
57#13063314—22no—
58#13063313—22no—
59#13063313D414yes—
60#13063303—28no—
61C4×Dic86—22no—
62C4×Dic86—22no—
63#13063290—22no—
64#13063290—22no—
65#13063287—22no—
66#13063287—22no—
67#13063282—28no—
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43C2312yes—
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—22no—
74C2×Dic43⋊C4—22no—
75C2×Dic43⋊C4D411yescharacteristic
76C2×Dic43⋊C4D411yescharacteristic
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43C2311yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86#13063250—24no—
87#13063249—24no—
88#13063248—24no—
89#13063247—24no—
90#13063245—24no—
91#13063236—22no—
92C43⋊#95—21no—
93C43⋊#95—22no—
94C43⋊#95—22no—
95C22×Q8×C43—21no—
96C22×Q8×C43C2311yescharacteristic
97C22×C8×C43C2312yes—
98C4⋊Q8×C43—22no—
99C4⋊Q8×C43—22no—
100C4×Q8×C43—22no—
101C4×Q8×C43D414yes—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43C2312yes—
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C42×C43—21no—
107C2×C42×C43C2311yescharacteristic
108#106×C43—24no—
109C4⋊C8×C43—22no—
110#103×C43—24no—
111C23×D43—21no—
112C2×Q8×C43—21no—
113C2×Q8×C43—22no—
114C2×Q8×C43—22no—
115C2×Q8×C43—42no—
116C2×Q8×C43—82no—
117C2×Q8×C43C2×D412yes—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—22no—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2411yescharacteristic
124C22×Dic43—22no—
125C22×Dic43—21no—
126C22×Dic43C2×D411yescharacteristic
127C22×Dic43C2×D411yescharacteristic
128C22×Dic43C2×D411yescharacteristic
129C22×Dic43C2×D411yescharacteristic
130C2×D172—21no—
131C2×D172—22no—
132C2×D172—22no—
133C2×D172C2×D412yes—
134C2×C4×D43—24no—
135C2×C4×D43—42no—
136C2×C4×D43—42no—
137C2×Dic86—22no—
138C2×Dic86—22no—
139C2×Dic86—22no—
140C2×Dic86—21no—
141C2×Dic86—22no—
142C2×Dic86—41no—
143C2×Dic86C2×D412yes—
144C2×C8×C43—22no—
145C2×C8×C43—22no—
146C2×C8×C43—22no—
147C4⋊C4×C43—24no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—42no—
152C4⋊C4×C43C2×D412yes—
153C42×C43—24no—
154C42×C43C2×D412yes—
155C42×C43C2×D412yes—
156(C2×D43)⋊C4—24no—
157(C2×D43)⋊C4—24no—
158(C2×D43)⋊C4—24no—
159(C2×D43)⋊C4—24no—
160(C2×D43)⋊C4—24no—
161C4⋊Dic43—22no—
162C4⋊Dic43—22no—
163C4⋊Dic43#4114yes—
164Dic43⋊C4—24no—
165Dic43⋊C4—24no—
166Dic43⋊C4—24no—
167Dic43⋊C4—22no—
168Dic43⋊C4—22no—
169Dic43⋊C4—82no—
170Dic43⋊C4—82no—
171C4×Dic43—24no—
172C4×Dic43—21no—
173C4×Dic43—21no—
174C4×Dic43—21no—
175C4×Dic43—21no—
176C4×Dic43—42no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—22no—
180C23×C43C22×D411yescharacteristic
181C22×D43—22no—
182C22×D43—42no—
183C22×D43—41no—
184C22×D43—41no—
185C22×D43—42no—
186Q8×C43—22no—
187Q8×C43—22no—
188Q8×C43—42no—
189Q8×C43—84no—
190C2×C4×C43—21no—
191C2×C4×C43—21no—
192C2×C4×C43—22no—
193C2×C4×C43—22no—
194C2×C4×C43—22no—
195C2×C4×C43—42no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—42no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43#12012yes—
202C2×C4×C43#12012yes—
203C2×C4×C43C22×D411yescharacteristic
204C2×C4×C43C22×D411yescharacteristic
205C2×C4×C43C2×#4112yes—
206C2×C4×C432−1+412yes—
207C2×Dic43—21no—
208C2×Dic43—21no—
209C2×Dic43—21no—
210C2×Dic43—21no—
211C2×Dic43—21no—
212C2×Dic43—22no—
213C2×Dic43—24no—
214C2×Dic43—21no—
215C2×Dic43—21no—
216C2×Dic43—22no—
217C2×Dic43—22no—
218C2×Dic43—42no—
219C2×Dic43—42no—
220C2×Dic43—42no—
221C2×Dic43#13712yes—
222D172—24no—
223D172—41no—
224D172—41no—
225C4×D43—48no—
226Dic86—24no—
227Dic86—44no—
228Dic86—41no—
229Dic86—41no—
230C8×C43—42no—
231C43⋊C8—42no—
232#25662—431nomaximal, Sylow
233C22×C43C2×#12011yescharacteristic
234C22×C43#54812yes—
235C22×C43C2×#13711yescharacteristic
236C22×C43#57511yescharacteristic
237C22×C43#57712yes—
238C2×D43—42no—
239C2×D43—42no—
240C2×D43—42no—
241C2×D43—82no—
242C2×D43—82no—
243C4×C43—22no—
244C4×C43—22no—
245C4×C43—42no—
246C4×C43—42no—
247C4×C43—82no—
248C4×C43#53211yescharacteristic
249C4×C43#53611yescharacteristic
250C4×C43#54712yes—
251Dic43—22no—
252Dic43—44no—
253Dic43—42no—
254Dic43—41no—
255Dic43—41no—
256Dic43—41no—
257C2×#556—431no—
258C2×#489—431no—
259C2×#475D4311yescharacteristic, complemented
260#2567—431no—
261#2043—432no—
262#2042—432no—
263#1985—431no—
264#1983—431no—
265#1865—432no—
266#1864—432no—
267#1763—431no—
268C2×C43#243211yescharacteristic
269C2×C43#300711yescharacteristic
270C2×C43#301011yescharacteristic
271C2×C43#336912yes—
272C2×C43#337612yes—
273D43—82no—
274#556—864no—
275#556—864no—
276C2×C4⋊Q8—431no—
277C2×C4⋊Q8C2×D4311yescharacteristic
278C2×#126—861no—
279C2×#126—861no—
280C2×#124—431no—
281C2×#124—431no—
282C2×C22⋊Q8—861no—
283C2×C4×Q8—431no—
284C2×C4×Q8—431no—
285C2×C4×Q8C2×D4311yescharacteristic
286C2×C4×D4—431no—
287C2×#117—861no—
288#489—864no—
289#475—24no—
290C2×#106C2×D4312yes—
291C2×C4⋊C8C2×D4311yescharacteristic
292C2×#103—432no—
293C2×#103—432no—
294C2×#103—432no—
295C2×#103C2×D4312yes—
296C2×#102—432no—
297C2×#102—432no—
298C2×#97—431no—
299#395—861no—
300#395—861no—
301#391—861no—
302#389—432no—
303#389—432no—
304#384—861no—
305C4×C4⋊C4—431no—
306#340—432no—
307#336—432no—
308#336—432no—
309C43#2566211yescharacteristic, complemented, Sylow
310C22×Q8—21no—
311C22×Q8—431no—
312C22×Q8—431no—
313C22×Q8C22×D4311yescharacteristic
314C22×D4—431no—
315C23×C4—861no—
316C22×C8—432no—
317C22×C8C22×D4312yes—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320C4⋊Q8—862no—
321C4⋊Q8—862no—
322#126—868no—
323#126—868no—
324#124—434no—
325#124—862no—
326#124—862no—
327#124—862no—
328C22⋊Q8—868no—
329C4×Q8—22no—
330C4×Q8—862no—
331C4×Q8—862no—
332C4×Q8—862no—
333C4×Q8—862no—
334C4×Q8C22⋊D4314yes—
335C4×D4—862no—
336C4×D4—862no—
337#117—868no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—432no—
341C2×C4⋊C4—431no—
342C2×C4⋊C4—431no—
343C2×C4⋊C4—431no—
344C2×C4⋊C4—861no—
345C2×C4⋊C4—861no—
346C2×C4⋊C4—861no—
347C2×C4⋊C4—862no—
348C2×C4⋊C4—862no—
349C2×C4⋊C4C22×D4312yes—
350C2×C4⋊C4C22×D4311yescharacteristic
351C2×C22⋊C4—861no—
352C2×C22⋊C4—861no—
353C2×C22⋊C4—861no—
354C2×C22⋊C4—861no—
355C2×C22⋊C4—861no—
356C2×C42—21no—
357C2×C42—431no—
358C2×C42—431no—
359C2×C42—861no—
360C2×C42—861no—
361C2×C42C22×D4311yescharacteristic
362#106—24no—
363C4⋊C8—22no—
364#103—24no—
365#103—864no—
366#103—864no—
367#103—864no—
368#102—864no—
369#102—864no—
370#97—862no—
371#95—862no—
372#95—862no—
373#95—861no—
374C24—861no—
375C2×Q8—21no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—42no—
379C2×Q8—82no—
380C2×Q8—432no—
381C2×Q8—862no—
382C2×Q8—862no—
383C2×Q8—861no—
384C2×Q8—862no—
385C2×Q8—862no—
386C2×Q8—1721no—
387C2×Q8C2×C22⋊D4312yes—
388C2×D4—432no—
389C2×D4—861no—
390C2×D4—862no—
391C2×D4—862no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—431no—
396C22×C4—431no—
397C22×C4—431no—
398C22×C4—431no—
399C22×C4—864no—
400C22×C4—862no—
401C22×C4—861no—
402C22×C4—1722no—
403C22×C4—1722no—
404C22×C4D4×D4311yescharacteristic
405C22×C4D4×D4311yescharacteristic
406C22×C4C23×D4311yescharacteristic
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—862no—
411C2×C8—862no—
412C2×C8—862no—
413C4⋊C4—24no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—42no—
418C4⋊C4—434no—
419C4⋊C4—864no—
420C4⋊C4—864no—
421C4⋊C4—864no—
422C4⋊C4—862no—
423C4⋊C4—862no—
424C4⋊C4—862no—
425C4⋊C4—862no—
426C4⋊C4—3442no—
427C4⋊C4—3442no—
428C4⋊C4C2×C22⋊D4312yes—
429C22⋊C4—864no—
430C22⋊C4—864no—
431C22⋊C4—864no—
432C22⋊C4—864no—
433C22⋊C4—864no—
434C42—24no—
435C42—864no—
436C42—861no—
437C42—861no—
438C42—861no—
439C42—861no—
440C42—1722no—
441C42D4×D4312yes—
442C42C2×C22⋊D4312yes—
443C23—862no—
444C23—1722no—
445C23—1721no—
446C23—1721no—
447C23—1722no—
448C23C2×D4×D4311yescharacteristic
449Q8—22no—
450Q8—22no—
451Q8—42no—
452Q8—84no—
453Q8—864no—
454Q8—1724no—
455Q8—1721no—
456Q8—1721no—
457D4—864no—
458D4—1721no—
459D4—1721no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—432no—
472C2×C4—861no—
473C2×C4—861no—
474C2×C4—864no—
475C2×C4—861no—
476C2×C4—861no—
477C2×C4—861no—
478C2×C4—862no—
479C2×C4—861no—
480C2×C4—861no—
481C2×C4—862no—
482C2×C4—862no—
483C2×C4—1728no—
484C2×C4—1722no—
485C2×C4—1722no—
486C2×C4—1722no—
487C2×C4#1306329312yes—
488C2×C4#1306329312yes—
489C2×C4C2×D4×D4311yescharacteristic
490C2×C4C22×C22⋊D4311yescharacteristic
491C2×C4#41×D4312yes—
492C2×C4#1306337312yes—
493C8—42no—
494C8—1722no—
495C22—3442no—
496C22—3442no—
497C22—1722no—
498C22—1722no—
499C22—1722no—
500C22C2×#1306329311yescharacteristic
501C22#1458355912yes—
502C22#137×D4311yescharacteristic
503C22#1458369811yescharacteristic
504C22#1458370512yes—
505C4—22no—
506C4—22no—
507C4—42no—
508C4—42no—
509C4—82no—
510C4—862no—
511C4—1724no—
512C4—1721no—
513C4—1722no—
514C4—1721no—
515C4—1721no—
516C4#1458344511yescharacteristic
517C4#1458347311yescharacteristic
518C4#1458355112yes—
519C2—3442no—
520C2#1913822411yescharacteristic
521C2#1914385111yescharacteristic
522C2#1914387711yescharacteristic
523C2#1914733812yes—
524C2#1914742912yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#475C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenterC2×#475D43
hypocenterC43#25662
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #19139804C2semidirect
4. #19135839C2semidirect
6. #19135534C2semidirect
8. #19134860C2semidirect
10. #19134425C2semidirect
11. C2×C43×#475C2semidirect
259. C2×#475D43semidirect
309. C43#25662semidirect

Maximal subgroups

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

subgroupindex
C2×#145836212
C2×#145832612
#191398042
#191358392
#191358322
#191355342
#191355252
#191348602
#191348532
#191344252
C2×C43×#4752
#2566243