Finite Group Databasebeta

← #25133291

Subgroups — #25133291

Order 11008.

1078 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148398C211yesmaximal, characteristic
2#19140408C212yesmaximal, complemented
3#19135948C212yesmaximal, complemented
4#19135762C212yesmaximal, complemented
5#19135580C212yesmaximal, complemented
6#19135009C212yesmaximal
7#19134875C212yesmaximal
8#19134583C211yesmaximal, characteristic
9C43×#2322C211yesmaximal, characteristic
10#14583608—24no—
11#14583606—22no—
12D4×Dic86—22no—
13#14583530—21no—
14#14583525—21no—
15#14583525C2212yes—
16#14583456—21no—
17C2×#13063304—21no—
18C2×#13063304C2212yes—
19#14583374C2212yes—
20C2×#13063240C2212yes—
21#14582838—22no—
22#14582832—24no—
23#14582819—22no—
24#14582772C2214yes—
25#14582762C2214yes—
26#14582759C2212yes—
27#14582666C2212yes—
28#14582665C2214yes—
29#14582665C2214yes—
30C2×#123×C43C2211yescharacteristic
31C2×C4×D4×C43C2211yescharacteristic
32C22×C4⋊C4×C43C2211yescharacteristic
33C43×#389—21no—
34C43×#388—21no—
35C43×#387—21no—
36C43×#386C2211yescharacteristic
37C43×#385—21no—
38C43×#385C2211yescharacteristic
39C43×#381C2211yescharacteristic
40C4×C22⋊C4×C43C2211yescharacteristic
41C22×Dic86—21no—
42C22×Dic86D412yes—
43#13063325—21no—
44#13063325—21no—
45#13063324—24no—
46#13063317—22no—
47#13063316—24no—
48#13063304—22no—
49#13063304—22no—
50#13063304—22no—
51#13063304—22no—
52#13063304—22no—
53#13063304—22no—
54#13063304—22no—
55#13063304—22no—
56#13063302—24no—
57#13063302—24no—
58#13063302—24no—
59#13063302—24no—
60C4×Dic86—22no—
61C4×Dic86—22no—
62D4×Dic43—24no—
63D4×Dic43—24no—
64#13063284—22no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—22no—
67C2×C4⋊Dic43D412yes—
68C2×Dic43⋊C4—22no—
69C2×Dic43⋊C4—24no—
70C2×Dic43⋊C4D414yes—
71C2×C22⋊Dic43—22no—
72C2×C22⋊Dic43C2314yes—
73C2×C22⋊Dic43C2314yes—
74#13063240—24no—
75C43⋊#95—22no—
76C43⋊#95—24no—
77C43⋊#95—24no—
78C43⋊#95—24no—
79C22×D4×C43C2311yescharacteristic
80C23×C4×C43D411yescharacteristic
81C23×C4×C43C2311yescharacteristic
82C23×C4×C43C2311yescharacteristic
83C23×C4×C43C2311yescharacteristic
84#123×C43—22no—
85#123×C43Q814yescomplemented
86C4×D4×C43—22no—
87C4×D4×C43—22no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—22no—
90C2×C4⋊C4×C43—22no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43D411yescharacteristic
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43D411yescharacteristic
98C2×C22⋊C4×C43C2311yescharacteristic
99C2×C22⋊C4×C43C2311yescharacteristic
100C2×C22⋊C4×C43C2311yescharacteristic
101C2×C42×C43—21no—
102C2×C42×C43D411yescharacteristic
103#95×C43—21no—
104#95×C43—21no—
105#95×C43—21no—
106#95×C43—21no—
107#95×C43—21no—
108C24×C43C2×D411yescharacteristic
109C24×C43C2411yescharacteristic
110C2×D4×C43—22no—
111C2×D4×C43—22no—
112C2×D4×C43C2×Q812yes—
113C2×D4×C43#4112yes—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—22no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—22no—
124C22×C4×C43—81no—
125C22×C4×C43—81no—
126C22×C4×C43—81no—
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2×D412yes—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×Q812yescomplemented
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—24no—
138C22×Dic43C2×D414yes—
139C22×Dic43C2×D414yes—
140C2×Dic86—22no—
141C2×Dic86—22no—
142C2×Dic86—22no—
143C2×Dic86—22no—
144C2×Dic86—82no—
145C2×Dic86—82no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—24no—
148C4⋊C4×C43—41no—
149C4⋊C4×C43—42no—
150C4⋊C4×C43—41no—
151C4⋊C4×C43—81no—
152C22⋊C4×C43—22no—
153C22⋊C4×C43—24no—
154C22⋊C4×C43—22no—
155C22⋊C4×C43—21no—
156C22⋊C4×C43—22no—
157C22⋊C4×C43—81no—
158C22⋊C4×C43C2×Q812yescomplemented
159C42×C43—21no—
160C42×C43—21no—
161C42×C43—81no—
162C22⋊Dic43—24no—
163C22⋊Dic43—24no—
164C22⋊Dic43—24no—
165C22⋊Dic43—24no—
166C22⋊Dic43—24no—
167C4⋊Dic43—22no—
168C4⋊Dic43—22no—
169C4⋊Dic43—22no—
170C4⋊Dic43—22no—
171C4⋊Dic43—22no—
172C4⋊Dic43—22no—
173C4⋊Dic43—82no—
174Dic43⋊C4—24no—
175Dic43⋊C4—24no—
176Dic43⋊C4—24no—
177Dic43⋊C4—24no—
178Dic43⋊C4—84no—
179C4×Dic43—24no—
180C23×C43—21no—
181C23×C43—21no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—41no—
185C23×C43—41no—
186C23×C43C22⋊Q812yes—
187C23×C43C22×D412yes—
188C23×C43C22×D411yescharacteristic
189C23×C43C22×Q811yescharacteristic
190C23×C43C2×#4111yescharacteristic
191C23×C432−1+412yes—
192D4×C43—24no—
193D4×C43—24no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—24no—
201C2×C4×C43—42no—
202C2×C4×C43—41no—
203C2×C4×C43—42no—
204C2×C4×C43—41no—
205C2×C4×C43—42no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—42no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—44no—
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—81no—
221C2×C4×C43#12011yescharacteristic
222C2×C4×C43#12012yes—
223C2×C4×C43#12011yescharacteristic
224C2×C4×C43C22⋊Q812yes—
225C2×Dic43—24no—
226C2×Dic43—24no—
227C2×Dic43—44no—
228C2×Dic43—44no—
229C2×Dic43—44no—
230C2×Dic43—44no—
231C2×Dic43—44no—
232C2×Dic43—82no—
233C2×Dic43—82no—
234Dic86—44no—
235Dic86—82no—
236Dic86—82no—
237Dic86—82no—
238#24353—431nomaximal, Sylow
239C22×C43—21no—
240C22×C43—22no—
241C22×C43—21no—
242C22×C43—22no—
243C22×C43—22no—
244C22×C43—41no—
245C22×C43—41no—
246C22×C43—42no—
247C22×C43—42no—
248C22×C43—41no—
249C22×C43—41no—
250C22×C43—81no—
251C22×C43C2×#12011yescharacteristic
252C22×C43C2×C22⋊Q811yescharacteristic
253C22×C43#53611yescharacteristic
254C22×C43#54812yes—
255C22×C43D4×Q812yes—
256C4×C43—22no—
257C4×C43—21no—
258C4×C43—22no—
259C4×C43—21no—
260C4×C43—42no—
261C4×C43—42no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—81no—
265C4×C43—81no—
266Dic43—44no—
267Dic43—44no—
268Dic43—84no—
269#3501—431no—
270#2627—432no—
271#2322D4311yescharacteristic
272#2062—432no—
273#2030—432no—
274#1996—432no—
275#1890—432no—
276#1867—432no—
277#1799—431no—
278C2×C43—22no—
279C2×C43—21no—
280C2×C43—21no—
281C2×C43—22no—
282C2×C43—42no—
283C2×C43#240911yescharacteristic
284C2×C43#302611yescharacteristic
285C2×C43#302811yescharacteristic
286#554—862no—
287#554—864no—
288D4×Q8—862no—
289#544—861no—
290#543—432no—
291#543—861no—
292#533—861no—
293C2×#123C2×D4311yescharacteristic
294C2×C22⋊Q8—432no—
295C2×C22⋊Q8—861no—
296#518—432no—
297C2×C4×D4C2×D4311yescharacteristic
298C22×C4⋊C4C2×D4311yescharacteristic
299C2×#99—432no—
300#400—862no—
301#398—864no—
302#395—862no—
303#389—21no—
304#388—21no—
305#387—21no—
306#386C2×D4311yescharacteristic
307#385—21no—
308#385—434no—
309#385C2×D4311yescharacteristic
310#381—434no—
311#381C2×D4311yescharacteristic
312#380—432no—
313C4×C22⋊C4C2×D4311yescharacteristic
314#342—432no—
315#342—434no—
316#342—434no—
317C43#2435311yescharacteristic, complemented, Sylow
318C22×Q8—432no—
319C22×Q8—861no—
320C22×D4C22×D4311yescharacteristic
321C23×C4C22⋊D4311yescharacteristic
322C23×C4C22×D4311yescharacteristic
323C23×C4C22×D4311yescharacteristic
324C23×C4C22×D4311yescharacteristic
325C4⋊Q8—861no—
326C4⋊Q8—861no—
327C4⋊Q8—864no—
328#125—862no—
329#125—864no—
330#123—22no—
331#123Dic8614yescomplemented
332C22⋊Q8—864no—
333C22⋊Q8—864no—
334C22⋊Q8—864no—
335C22⋊Q8—864no—
336C22⋊Q8—862no—
337C22⋊Q8—862no—
338C22⋊Q8—862no—
339C22⋊Q8—862no—
340C22⋊Q8—862no—
341C22⋊Q8—862no—
342C22⋊Q8—862no—
343C22⋊Q8—862no—
344C4×Q8—862no—
345C4×Q8—862no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—864no—
349C4×D4—864no—
350#117—862no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—434no—
358C2×C4⋊C4—432no—
359C2×C4⋊C4—862no—
360C2×C4⋊C4—861no—
361C2×C4⋊C4—864no—
362C2×C4⋊C4—862no—
363C2×C4⋊C4C22⋊D4311yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—434no—
367C2×C22⋊C4—434no—
368C2×C22⋊C4—862no—
369C2×C22⋊C4C22⋊D4311yescharacteristic
370C2×C22⋊C4C22×D4311yescharacteristic
371C2×C22⋊C4C22×D4311yescharacteristic
372C2×C22⋊C4C22×D4311yescharacteristic
373C2×C42—21no—
374C2×C42C22⋊D4311yescharacteristic
375#99—864no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—864no—
382#95—864no—
383#95—864no—
384#95—862no—
385C24C2×C22⋊D4311yescharacteristic
386C24C23×D4311yescharacteristic
387C2×Q8—862no—
388C2×Q8—862no—
389C2×Q8—862no—
390C2×Q8—862no—
391C2×Q8—3442no—
392C2×Q8—3442no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4C2×Dic8612yes—
396C2×D4#1062189812yes—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—81no—
408C22×C4—81no—
409C22×C4—81no—
410C22×C4—434no—
411C22×C4—434no—
412C22×C4—862no—
413C22×C4—862no—
414C22×C4—864no—
415C22×C4C2×Dic8612yescomplemented
416C22×C4D4×D4312yes—
417C22×C4D4×D4312yes—
418C22×C4C2×C22⋊D4311yescharacteristic
419C22×C4C2×C22⋊D4311yescharacteristic
420C22×C4C2×C22⋊D4311yescharacteristic
421C22×C4C2×C22⋊D4311yescharacteristic
422C22×C4C2×C22⋊D4311yescharacteristic
423C4⋊C4—22no—
424C4⋊C4—24no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4—42no—
428C4⋊C4—81no—
429C4⋊C4—862no—
430C4⋊C4—864no—
431C4⋊C4—862no—
432C4⋊C4—862no—
433C4⋊C4—864no—
434C4⋊C4—862no—
435C4⋊C4—864no—
436C4⋊C4—862no—
437C4⋊C4—862no—
438C4⋊C4—864no—
439C4⋊C4—3444no—
440C4⋊C4—3442no—
441C22⋊C4—24no—
442C22⋊C4—22no—
443C22⋊C4—21no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—81no—
447C22⋊C4—864no—
448C22⋊C4—864no—
449C22⋊C4—864no—
450C22⋊C4—864no—
451C22⋊C4—864no—
452C22⋊C4C2×Dic8612yescomplemented
453C42—21no—
454C42—21no—
455C42—81no—
456C42—864no—
457C23—21no—
458C23—21no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23#1306330412yes—
464C23C2×D4×D4312yes—
465C23C22×C22⋊D4311yescharacteristic
466C23C22×Dic8611yescharacteristic
467C23C2×#1062189811yescharacteristic
468C23#1306337212yes—
469Q8—3442no—
470Q8—3442no—
471Q8—3442no—
472Q8—1724no—
473D4—24no—
474D4—24no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—24no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—44no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—81no—
502C2×C4—864no—
503C2×C4—864no—
504C2×C4—3442no—
505C2×C4—3442no—
506C2×C4—1724no—
507C2×C4—1724no—
508C2×C4—1724no—
509C2×C4—1724no—
510C2×C4—1724no—
511C2×C4#1306329311yescharacteristic
512C2×C4#1306329311yescharacteristic
513C2×C4#1306329312yes—
514C2×C4#1306330412yes—
515C22—21no—
516C22—22no—
517C22—21no—
518C22—22no—
519C22—22no—
520C22—41no—
521C22—41no—
522C22—42no—
523C22—42no—
524C22—41no—
525C22—41no—
526C22—81no—
527C22C2×#1306329311yescharacteristic
528C22C2×#1306330411yescharacteristic
529C22#1458347011yescharacteristic
530C22#1458355812yes—
531C22D4×Dic8612yes—
532C4—21no—
533C4—21no—
534C4—22no—
535C4—22no—
536C4—42no—
537C4—41no—
538C4—41no—
539C4—42no—
540C4—81no—
541C4—81no—
542C4—3444no—
543C4—1724no—
544C4—1724no—
545C2—21no—
546C2—21no—
547C2—22no—
548C2—22no—
549C2—42no—
550C2#1913796011yescharacteristic
551C2#1914399111yescharacteristic
552C2#1914400011yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC24×C43C24
FrattiniC24C23×D43
FittingC43×#2322C2
socleC22×C43C2×#120
prime radicalC22×D4×C43C23
hypercenter#2322D43
hypocenterC43#24353
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2322

Complements

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

NH ≅ G/Ntype
2. #19140408C2semidirect
3. #19135948C2semidirect
4. #19135762C2semidirect
5. #19135580C2semidirect
85. #123×C43Q8semidirect
134. C22×C4×C43C2×Q8semidirect
158. C22⋊C4×C43C2×Q8semidirect
317. C43#24353semidirect
331. #123Dic86semidirect
415. C22×C4C2×Dic86semidirect
452. C22⋊C4C2×Dic86semidirect

Maximal subgroups

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

subgroupindex
#191483982
#191404082
#191359482
#191357622
#191355802
#191350092
#191348752
#191345832
C43×#23222
#2435343