Finite Group Databasebeta

← #24992329

Subgroups — #24992329

Order 11008.

1348 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142874C211yesmaximal, characteristic
2C2×#95×D43C211yesmaximal, characteristic, complemented
3#19134504C211yesmaximal, characteristic, complemented
4C2×#14582633C211yesmaximal, characteristic, complemented
5#19132475C211yesmaximal, characteristic, complemented
6#19132474C211yesmaximal, characteristic, complemented
7C2×C43×#327C211yesmaximal, characteristic, complemented
8C23×C4×D43—21no—
9C23×C4×D43C2211yescharacteristic
10C2×#13063296C412yescomplemented
11C2×#13063293—21no—
12C2×C22⋊(C43⋊C8)C2211yescharacteristic
13C2×(C2×D43)⋊C8—22no—
14#14582779—21no—
15#14582775—22no—
16#14582759C2211yescharacteristic
17#14582756C412yescomplemented
18C2×C43⋊#95—21no—
19C2×C43⋊#95C2211yescharacteristic
20#95×D43—22no—
21#95×D43—22no—
22#14582633—22no—
23C2×#121×C43C2211yescharacteristic
24C2×C22⋊C8×C43C2211yescharacteristic
25C2×#95×C43C2211yescharacteristic
26C43×#327—22no—
27C24×D43D411yescharacteristic
28C22×C22⋊D43—22no—
29C23×Dic43—21no—
30C23×Dic43D411yescharacteristic
31C22×C4×D43—28no—
32C22×C4×D43—24no—
33C22×C4×D43—21no—
34C22×C4×D43—21no—
35C22×C4×D43—21no—
36C22×C4×D43—21no—
37C22×C4×D43—44no—
38C22×C4×D43—44no—
39C22×C4×D43—42no—
40C22×C4×D43—42no—
41C22×C4×D43C2×C412yes—
42C22×C4×D43D412yes—
43C22×C43⋊C8—21no—
44#13063296—44no—
45#13063293—42no—
46#13063293—42no—
47C2×C4⋊Dic43C2×C412yescomplemented
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43—22no—
50C2×(C2×D43)⋊C4—22no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53(C2×D43)⋊C8—44no—
54C43⋊#95—24no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95—22no—
58C43⋊#95D412yescomplemented
59C22×D4×C43—21no—
60C22×D4×C43C2×C411yescharacteristic, complemented
61C23×C4×C43—21no—
62C23×C4×C43C2311yescharacteristic
63C22×C8×C43—21no—
64#121×C43—21no—
65#121×C43—21no—
66#121×C43—21no—
67#121×C43—21no—
68C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
69C2×C22⋊C4×C43—21no—
70C22⋊C8×C43—21no—
71C22⋊C8×C43—21no—
72#95×C43—21no—
73#95×C43D412yescomplemented
74C24×C43—21no—
75C24×C43C2×D411yescharacteristic
76C23×D43—21no—
77C23×D43—21no—
78C23×D43—21no—
79C23×D43—21no—
80C23×D43—24no—
81C23×D43—24no—
82C23×D43C22⋊C412yes—
83C23×D43D812yes—
84C23×D43SD1612yes—
85C2×D4×C43—21no—
86C2×D4×C43—21no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—41no—
91C2×D4×C43—41no—
92C2×D4×C43—41no—
93C2×D4×C43—42no—
94C22×C4×C43—24no—
95C22×C4×C43—21no—
96C22×C4×C43—22no—
97C22×C4×C43—42no—
98C22×C4×C43—42no—
99C22×C4×C43—41no—
100C22×C4×C43—41no—
101C22×C4×C43C22×C411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43#4111yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C2×C22⋊D43—44no—
108C2×C22⋊D43—44no—
109C2×C22⋊D43—44no—
110C22×Dic43—24no—
111C22×Dic43—22no—
112C22×Dic43—21no—
113C22×Dic43—22no—
114C22×Dic43—21no—
115C22×Dic43—42no—
116C22×Dic43—42no—
117C22×Dic43—41no—
118C22×Dic43—41no—
119C22×Dic43C22⋊C412yes—
120C2×C4×D43—216no—
121C2×C4×D43—22no—
122C2×C4×D43—22no—
123C2×C4×D43—22no—
124C2×C4×D43—22no—
125C2×C4×D43—24no—
126C2×C4×D43—24no—
127C2×C4×D43—42no—
128C2×C4×D43—42no—
129C2×C4×D43—44no—
130C2×C4×D43—44no—
131C2×C4×D43—48no—
132C2×C4×D43—44no—
133C2×C4×D43—44no—
134C2×C4×D43—416no—
135C2×C4×D43—48no—
136C2×C4×D43—416no—
137C2×C8×C43—42no—
138C2×C8×C43—41no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C22⋊C4×C43—41no—
142C22⋊C4×C43—41no—
143C22⋊Dic43—44no—
144C22⋊Dic43—41no—
145C22⋊Dic43—41no—
146(C2×D43)⋊C4—44no—
147C4⋊Dic43—42no—
148C2×C43⋊C8—42no—
149C2×C43⋊C8—41no—
150C23×C43—22no—
151C23×C43—22no—
152C23×C43—41no—
153C23×C43—42no—
154C23×C43—41no—
155C23×C43—41no—
156C23×C43—42no—
157C23×C43C2×C22⋊C411yescharacteristic
158C23×C43#12011yescharacteristic
159C23×C43#12311yescharacteristic
160C23×C43C2×D811yescharacteristic
161C23×C43C2×SD1611yescharacteristic
162C23×C43AGL(1,ℤ/8)11yescharacteristic
163C23×C43#13711yescharacteristic
164C22×D43—24no—
165C22×D43—24no—
166C22×D43—24no—
167C22×D43—28no—
168C22×D43—24no—
169C22×D43—28no—
170C22×D43—22no—
171C22×D43—22no—
172C22×D43—22no—
173C22×D43—22no—
174C22×D43—22no—
175C22×D43—22no—
176C22×D43—22no—
177C22×D43—22no—
178C22×D43—28no—
179C22×D43—28no—
180C22×D43#9914yes—
181C22×D43#10214yes—
182C22×D43#10414yes—
183D4×C43—81no—
184D4×C43—81no—
185D4×C43—81no—
186D4×C43—81no—
187D4×C43—81no—
188D4×C43—81no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—24no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—42no—
197C2×C4×C43—44no—
198C2×C4×C43—44no—
199C2×C4×C43—42no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43C4×D411yescharacteristic
204C2×C4×C43C4×D411yescharacteristic
205C2×C4×C43#12111yescharacteristic
206C2×C4×C43#12111yescharacteristic
207C22⋊D43—88no—
208C2×Dic43—24no—
209C2×Dic43—22no—
210C2×Dic43—22no—
211C2×Dic43—22no—
212C2×Dic43—42no—
213C2×Dic43—44no—
214C2×Dic43—44no—
215C2×Dic43—42no—
216C2×Dic43—42no—
217C2×Dic43—42no—
218C2×Dic43—42no—
219C2×Dic43—42no—
220C2×Dic43—42no—
221C4×D43—44no—
222C4×D43—44no—
223C4×D43—44no—
224C4×D43—44no—
225C4×D43—432no—
226C8×C43—81no—
227C43⋊C8—81no—
228#9147—431nomaximal, Sylow
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—22no—
234C22×C43—22no—
235C22×C43—22no—
236C22×C43—22no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43—81no—
240C22×C43—82no—
241C22×C43—82no—
242C22×C43#38611yescharacteristic
243C22×C43C2×#9912yes—
244C22×C43C2×#10211yescharacteristic
245C22×C43#41711yescharacteristic
246C22×C43C2×#10412yes—
247C22×C43#44711yescharacteristic
248C22×C43#44811yescharacteristic
249C22×C43#48011yescharacteristic
250C22×C43#48111yescharacteristic
251C2×D43—28no—
252C2×D43—28no—
253C2×D43—28no—
254C2×D43—28no—
255C2×D43—24no—
256C2×D43—24no—
257C2×D43—24no—
258C2×D43—24no—
259C2×D43—24no—
260C2×D43—24no—
261C2×D43#32718yescomplemented
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—44no—
267C4×C43—81no—
268Dic43—44no—
269Dic43—42no—
270Dic43—82no—
271#2847—431no—
272C22×#95—431no—
273#1779—431no—
274C2×#327—431no—
275C2×#327D4311yescharacteristic, complemented
276#1294—431no—
277#1294—431no—
278C2×C43—21no—
279C2×C43—21no—
280C2×C43—21no—
281C2×C43—21no—
282C2×C43—161no—
283C2×C43C2×#32712yes—
284C2×C43#150412yes—
285C2×C43#187411yescharacteristic
286C2×C43#189611yescharacteristic
287C2×C43#189811yescharacteristic
288D43—28no—
289C24×C4—431no—
290C24×C4—861no—
291C2×#121—432no—
292C2×#121C2×D4311yescharacteristic
293C2×#120—861no—
294C2×C22⋊C8—431no—
295C2×C22⋊C8—862no—
296C2×C22⋊C8C2×D4311yescharacteristic
297#386—862no—
298#386—861no—
299#380—431no—
300#380—432no—
301C2×#95—431no—
302C2×#95—862no—
303C2×#95—861no—
304C2×#95—862no—
305C2×#95C2×D4311yescharacteristic
306#327—22no—
307#327—862no—
308C43#914711yescharacteristic, complemented, Sylow
309C25—431no—
310C22×D4—21no—
311C22×D4—862no—
312C22×D4C4×D4311yescharacteristic, complemented
313C23×C4—21no—
314C23×C4—431no—
315C23×C4—432no—
316C23×C4—432no—
317C23×C4—864no—
318C23×C4—868no—
319C23×C4—861no—
320C23×C4—861no—
321C23×C4—861no—
322C23×C4—861no—
323C23×C4—861no—
324C23×C4—1724no—
325C23×C4—1722no—
326C23×C4—1724no—
327C23×C4—1722no—
328C23×C4C22×D4311yescharacteristic
329C22×C8—21no—
330C22×C8—861no—
331#121—21no—
332#121—21no—
333#121—21no—
334#121—21no—
335#121—1724no—
336#120—1722no—
337#120—1722no—
338C2×C4⋊C4—432no—
339C2×C4⋊C4C4×D4311yescharacteristic, complemented
340C2×C22⋊C4—21no—
341C2×C22⋊C4—862no—
342C2×C22⋊C4—862no—
343C2×C22⋊C4—861no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—861no—
347C22⋊C8—861no—
348C22⋊C8—1724no—
349#95—21no—
350#95—432no—
351#95—862no—
352#95—864no—
353#95—861no—
354#95—861no—
355#95C22⋊D4312yescomplemented
356C24—21no—
357C24—432no—
358C24—432no—
359C24—432no—
360C24—864no—
361C24—864no—
362C24—861no—
363C24—861no—
364C24—861no—
365C24—861no—
366C24D4×D4311yescharacteristic
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—42no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—1724no—
377C2×D4—1724no—
378C2×D4—1724no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—432no—
387C22×C4—864no—
388C22×C4—864no—
389C22×C4—8616no—
390C22×C4—864no—
391C22×C4—862no—
392C22×C4—861no—
393C22×C4—861no—
394C22×C4—862no—
395C22×C4—862no—
396C22×C4—862no—
397C22×C4—862no—
398C22×C4—862no—
399C22×C4—1722no—
400C22×C4—1722no—
401C22×C4—1724no—
402C22×C4—1724no—
403C22×C4—1724no—
404C22×C4—1724no—
405C22×C4—17216no—
406C22×C4—1728no—
407C22×C4—17216no—
408C22×C4—1728no—
409C22×C4—1722no—
410C22×C4—1722no—
411C22×C4—1721no—
412C22×C4—1721no—
413C22×C4C2×C4×D4311yescharacteristic
414C22×C4#1062189811yescharacteristic
415C22×C4D4×D4311yescharacteristic
416C22×C4D4×D4311yescharacteristic
417C22×C4#1062190011yescharacteristic
418C22×C4C2×C22⋊D4311yescharacteristic
419C2×C8—42no—
420C2×C8—41no—
421C2×C8—1722no—
422C2×C8—1721no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—1722no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—1724no—
429C22⋊C4—1724no—
430C22⋊C4—1721no—
431C22⋊C4—1721no—
432C23—22no—
433C23—22no—
434C23—42no—
435C23—41no—
436C23—41no—
437C23—42no—
438C23—41no—
439C23—434no—
440C23—434no—
441C23—434no—
442C23—868no—
443C23—868no—
444C23—864no—
445C23—864no—
446C23—864no—
447C23—868no—
448C23—864no—
449C23—868no—
450C23—862no—
451C23—862no—
452C23—862no—
453C23—862no—
454C23—862no—
455C23—862no—
456C23—862no—
457C23—862no—
458C23C22⋊C4×D4311yescharacteristic
459C23#1306329311yescharacteristic
460C23#1306330711yescharacteristic
461C23D8×D4311yescharacteristic
462C23SD16×D4311yescharacteristic
463C23#1306334911yescharacteristic
464C23#1306335411yescharacteristic
465D4—81no—
466D4—81no—
467D4—81no—
468D4—81no—
469D4—81no—
470D4—81no—
471D4—3448no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—864no—
487C2×C4—862no—
488C2×C4—862no—
489C2×C4—862no—
490C2×C4—1724no—
491C2×C4—1724no—
492C2×C4—1724no—
493C2×C4—1724no—
494C2×C4—17232no—
495C2×C4—1722no—
496C2×C4—1722no—
497C2×C4—1722no—
498C2×C4—1722no—
499C2×C4—1724no—
500C2×C4—1724no—
501C2×C4—1722no—
502C2×C4—1722no—
503C2×C4—1722no—
504C2×C4(C22⋊D43)⋊C411yescharacteristic
505C2×C4C4×C22⋊D4311yescharacteristic
506C2×C4#1306329611yescharacteristic
507C2×C4#1306329811yescharacteristic
508C8—81no—
509C8—3441no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—22no—
518C22—81no—
519C22—81no—
520C22—82no—
521C22—82no—
522C22—81no—
523C22—438no—
524C22—868no—
525C22—868no—
526C22—868no—
527C22—868no—
528C22—864no—
529C22—864no—
530C22—864no—
531C22—864no—
532C22—864no—
533C22—864no—
534C22#1458277511yescharacteristic
535C22#99×D4312yes—
536C22#102×D4311yescharacteristic
537C22#1458289711yescharacteristic
538C22#104×D4312yes—
539C22#1458303111yescharacteristic
540C22#1458303611yescharacteristic
541C22#1458321111yescharacteristic
542C22#1458321611yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—44no—
548C4—81no—
549C4—3442no—
550C4—1724no—
551C4—1722no—
552C2—21no—
553C2—21no—
554C2—21no—
555C2—21no—
556C2—161no—
557C2—868no—
558C2#327×D4312yes—
559C2#1913309612yes—
560C2#1913490911yescharacteristic
561C2#1913503511yescharacteristic
562C2#1913504511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#327C2
socleC23×C43C2×C22⋊C4
prime radical#19142874C2
cosocleC23×C4×C43C23
hypercenterC2×#327D43
hypocenterC43#9147
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#95×D43C2semidirect
3. #19134504C2semidirect
4. C2×#14582633C2semidirect
5. #19132475C2semidirect
6. #19132474C2semidirect
7. C2×C43×#327C2semidirect
10. C2×#13063296C4semidirect
17. #14582756C4semidirect
47. C2×C4⋊Dic43C2×C4semidirect
58. C43⋊#95D4semidirect
60. C22×D4×C43C2×C4semidirect
68. C2×C4⋊C4×C43C2×C4semidirect
73. #95×C43D4semidirect
261. C2×D43#327semidirect
275. C2×#327D43semidirect
308. C43#9147semidirect
312. C22×D4C4×D43semidirect
339. C2×C4⋊C4C4×D43semidirect
355. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191428742
C2×#95×D432
#191345042
C2×#145826332
#191324752
#191324742
C2×C43×#3272
#914743