Finite Group Databasebeta

← #25133274

Subgroups — #25133274

Order 11008.

1122 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148398C211yesmaximal, characteristic
2#19142935C212yesmaximal, complemented
3C4×#13063306C211yesmaximal, characteristic
4#19135949C212yesmaximal, complemented
5#19135763C212yesmaximal, complemented
6#19135579C212yesmaximal, complemented
7#19135006C212yesmaximal
8#19134878C212yesmaximal
9C43×#1799C211yesmaximal, characteristic
10#14583608—24no—
11#14583606—22no—
12D4×Dic86—22no—
13#14583530—21no—
14#14583525—21no—
15#14583525C2212yes—
16#14583456—21no—
17C2×#13063306C2211yescharacteristic
18C2×#13063304—21no—
19C2×#13063304C2212yes—
20#14583374C2212yes—
21C22×C4×Dic43C2211yescharacteristic
22#14582804—22no—
23#14582798—22no—
24#14582787—21no—
25#14582784—24no—
26#14582780—21no—
27#14582779C2211yescharacteristic
28#14582774C2214yes—
29#14582771C2211yescharacteristic
30#14582760C2211yescharacteristic
31#14582760C2214yes—
32C4×Dic43⋊C4—21no—
33C4×C22⋊Dic43—21no—
34C4×C22⋊Dic43C2211yescharacteristic
35#14582665C2214yes—
36#14582665C2214yes—
37C2×C4×D4×C43C2211yescharacteristic
38C2×#99×C43C2212yes—
39C43×#380C2212yes—
40C43×#342C2212yes—
41C22×Dic86—21no—
42C22×Dic86D412yes—
43C23×Dic43C2311yescharacteristic
44C23×Dic43C2311yescharacteristic
45#13063325—21no—
46#13063325—21no—
47#13063324—24no—
48#13063317—22no—
49#13063316—24no—
50#13063306—22no—
51#13063306Q814yescomplemented
52#13063304—22no—
53#13063304—22no—
54#13063304—22no—
55#13063304—22no—
56#13063304—22no—
57#13063304—22no—
58#13063304—22no—
59#13063304—22no—
60#13063302—24no—
61#13063302—24no—
62#13063302—24no—
63#13063302—24no—
64C4×Dic86—22no—
65C4×Dic86—22no—
66D4×Dic43—24no—
67D4×Dic43—24no—
68#13063284—22no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—24no—
71C2×C4⋊Dic43D412yes—
72C2×Dic43⋊C4—22no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4D414yes—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—22no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43C2311yescharacteristic
80C2×C22⋊Dic43C2314yes—
81C2×C22⋊Dic43C2311yescharacteristic
82C2×C4×Dic43—22no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—22no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—24no—
93C43⋊#95—24no—
94C43⋊#95—24no—
95C22×D4×C43C2311yescharacteristic
96C23×C4×C43D411yescharacteristic
97C23×C4×C43C2311yescharacteristic
98C4×D4×C43—22no—
99C4×D4×C43—22no—
100C2×C4⋊C4×C43—22no—
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C22⋊C4×C43D411yescharacteristic
103C2×C22⋊C4×C43C2314yes—
104C2×C22⋊C4×C43C2311yescharacteristic
105C2×C42×C43D411yescharacteristic
106#99×C43—24no—
107#95×C43—22no—
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—24no—
117C22×C4×C43—42no—
118C22×C4×C43—42no—
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D412yes—
125C22×C4×C43C2×D412yes—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—22no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—22no—
136C22×Dic43—42no—
137C22×Dic43C2×D414yes—
138C22×Dic43C2×D414yes—
139C22×Dic43C2×Q812yescomplemented
140C2×Dic86—22no—
141C2×Dic86—22no—
142C2×Dic86—22no—
143C2×Dic86—22no—
144C2×Dic86—44no—
145C2×Dic86—82no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—44no—
148C22⋊C4×C43—22no—
149C22⋊C4×C43—22no—
150C22⋊C4×C43—24no—
151C22⋊C4×C43—24no—
152C42×C43—21no—
153C42×C43—21no—
154C22⋊Dic43—24no—
155C22⋊Dic43—24no—
156C22⋊Dic43—24no—
157C22⋊Dic43—24no—
158C22⋊Dic43—21no—
159C22⋊Dic43—22no—
160C22⋊Dic43—42no—
161C22⋊Dic43C2×Q812yescomplemented
162C4⋊Dic43—22no—
163C4⋊Dic43—22no—
164C4⋊Dic43—22no—
165C4⋊Dic43—22no—
166C4⋊Dic43—22no—
167C4⋊Dic43—22no—
168C4⋊Dic43—48no—
169Dic43⋊C4—24no—
170Dic43⋊C4—24no—
171Dic43⋊C4—24no—
172Dic43⋊C4—24no—
173Dic43⋊C4—24no—
174Dic43⋊C4—42no—
175C4×Dic43—24no—
176C4×Dic43—42no—
177C4×Dic43—41no—
178C4×Dic43—42no—
179C4×Dic43—41no—
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—22no—
197C2×C4×C43—24no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—41no—
201C2×C4×C43—42no—
202C2×C4×C43—42no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—44no—
206C2×C4×C43—44no—
207C2×C4×C43—44no—
208C2×C4×C43—81no—
209C2×C4×C43#12011yescharacteristic
210C2×C4×C43#12012yes—
211C2×C4×C43#12011yescharacteristic
212C2×C4×C43C22⋊Q812yes—
213C2×Dic43—22no—
214C2×Dic43—24no—
215C2×Dic43—24no—
216C2×Dic43—24no—
217C2×Dic43—22no—
218C2×Dic43—22no—
219C2×Dic43—24no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—42no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—42no—
228C2×Dic43—44no—
229C2×Dic43—44no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—82no—
234C2×Dic43—82no—
235Dic86—44no—
236Dic86—82no—
237Dic86—82no—
238Dic86—82no—
239#24351—431nomaximal, Sylow
240C22×C43—21no—
241C22×C43—22no—
242C22×C43—21no—
243C22×C43—22no—
244C22×C43—22no—
245C22×C43—41no—
246C22×C43—41no—
247C22×C43—42no—
248C22×C43—42no—
249C22×C43—41no—
250C22×C43—41no—
251C22×C43—81no—
252C22×C43C2×#12011yescharacteristic
253C22×C43C2×C22⋊Q811yescharacteristic
254C22×C43#53611yescharacteristic
255C22×C43#54812yes—
256C22×C43D4×Q812yes—
257C4×C43—22no—
258C4×C43—22no—
259C4×C43—21no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—84no—
263C4×C43#45812yes—
264Dic43—42no—
265Dic43—42no—
266Dic43—44no—
267Dic43—44no—
268Dic43—42no—
269Dic43—81no—
270#3501—431no—
271#2855—432no—
272C4×#123—431no—
273#2062—432no—
274#2030—432no—
275#1996—432no—
276#1890—432no—
277#1867—432no—
278#1799D4311yescharacteristic
279C2×C43—21no—
280C2×C43—21no—
281C2×C43—22no—
282C2×C43—22no—
283C2×C43—42no—
284C2×C43#240911yescharacteristic
285C2×C43C2×#45811yescharacteristic
286C2×C43#302511yescharacteristic
287#554—862no—
288#554—864no—
289D4×Q8—862no—
290#544—861no—
291#543—432no—
292#543—861no—
293#533—861no—
294C2×#123—431no—
295C2×C22⋊Q8—432no—
296C2×C22⋊Q8—861no—
297#518—432no—
298C2×C4×D4C2×D4311yescharacteristic
299C22×C42—431no—
300C2×#99C2×D4312yes—
301#391—862no—
302#389—862no—
303#388—861no—
304#387—864no—
305#387—861no—
306#386—431no—
307#385—431no—
308#385—434no—
309#381—434no—
310#381—431no—
311#380C2×D4312yes—
312C4×C4⋊C4—861no—
313C4×C22⋊C4—431no—
314C4×C22⋊C4—861no—
315#342—434no—
316#342—434no—
317#342C2×D4312yes—
318C43#2435111yescharacteristic, complemented, Sylow
319C22×Q8—432no—
320C22×Q8—861no—
321C22×D4C22×D4311yescharacteristic
322C23×C4—431no—
323C23×C4—431no—
324C23×C4D17211yescharacteristic
325C23×C4C22×D4311yescharacteristic
326C4⋊Q8—861no—
327C4⋊Q8—861no—
328C4⋊Q8—864no—
329#125—862no—
330#125—864no—
331#123—434no—
332#123—862no—
333C22⋊Q8—864no—
334C22⋊Q8—864no—
335C22⋊Q8—864no—
336C22⋊Q8—864no—
337C22⋊Q8—862no—
338C22⋊Q8—862no—
339C22⋊Q8—862no—
340C22⋊Q8—862no—
341C22⋊Q8—862no—
342C22⋊Q8—862no—
343C22⋊Q8—862no—
344C22⋊Q8—862no—
345C4×Q8—862no—
346C4×Q8—862no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—864no—
350C4×D4—864no—
351#117—862no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—434no—
354C2×C4⋊C4—432no—
355C2×C4⋊C4—862no—
356C2×C4⋊C4—861no—
357C2×C4⋊C4—861no—
358C2×C4⋊C4—864no—
359C2×C4⋊C4—861no—
360C2×C4⋊C4D17211yescharacteristic
361C2×C22⋊C4—431no—
362C2×C22⋊C4—434no—
363C2×C22⋊C4—431no—
364C2×C22⋊C4—862no—
365C2×C22⋊C4—861no—
366C2×C22⋊C4—861no—
367C2×C22⋊C4D17211yescharacteristic
368C2×C22⋊C4C22×D4314yes—
369C2×C22⋊C4C22×D4311yescharacteristic
370C2×C42—861no—
371C2×C42—861no—
372C2×C42—861no—
373C2×C42—862no—
374C2×C42—862no—
375C2×C42D17211yescharacteristic
376#99—24no—
377#95—22no—
378#95—864no—
379#95—864no—
380#95—864no—
381#95—861no—
382#95—861no—
383#95—861no—
384#95—861no—
385#95—861no—
386C24C2×D17211yescharacteristic
387C24C23×D4311yescharacteristic
388C2×Q8—862no—
389C2×Q8—862no—
390C2×Q8—862no—
391C2×Q8—862no—
392C2×Q8—3442no—
393C2×Q8—1724no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4#1062190012yes—
397C2×D4Q8×D4312yes—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—24no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—432no—
404C22×C4—434no—
405C22×C4—434no—
406C22×C4—862no—
407C22×C4—862no—
408C22×C4—862no—
409C22×C4—862no—
410C22×C4—861no—
411C22×C4—861no—
412C22×C4—861no—
413C22×C4—861no—
414C22×C4—862no—
415C22×C4—861no—
416C22×C4—1722no—
417C22×C4C2×D17211yescharacteristic
418C22×C4C2×D17211yescharacteristic
419C22×C4C2×D17211yescharacteristic
420C22×C4C2×D17211yescharacteristic
421C22×C4C2×D17211yescharacteristic
422C22×C4D4×D4312yes—
423C22×C4D4×D4312yes—
424C4⋊C4—22no—
425C4⋊C4—44no—
426C4⋊C4—862no—
427C4⋊C4—864no—
428C4⋊C4—862no—
429C4⋊C4—862no—
430C4⋊C4—864no—
431C4⋊C4—862no—
432C4⋊C4—864no—
433C4⋊C4—862no—
434C4⋊C4—862no—
435C4⋊C4—864no—
436C4⋊C4—864no—
437C4⋊C4—1722no—
438C4⋊C4—1728no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—432no—
444C22⋊C4—864no—
445C22⋊C4—864no—
446C22⋊C4—864no—
447C22⋊C4—864no—
448C22⋊C4—861no—
449C22⋊C4—862no—
450C22⋊C4—1722no—
451C42—21no—
452C42—21no—
453C42—864no—
454C42—1722no—
455C42—1721no—
456C42—1722no—
457C42—1721no—
458C23—21no—
459C23—21no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23#1306330512yes—
465C23C2×D4×D4312yes—
466C23C22×D17211yescharacteristic
467C23C2×Q8×D4311yescharacteristic
468C23C2×#1062190011yescharacteristic
469C23#1306337212yes—
470Q8—3442no—
471Q8—3442no—
472Q8—3442no—
473Q8—1724no—
474D4—24no—
475D4—24no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—44no—
490C2×C4—81no—
491C2×C4—862no—
492C2×C4—864no—
493C2×C4—864no—
494C2×C4—864no—
495C2×C4—864no—
496C2×C4—862no—
497C2×C4—862no—
498C2×C4—3442no—
499C2×C4—3442no—
500C2×C4—1721no—
501C2×C4—1721no—
502C2×C4—1721no—
503C2×C4—1721no—
504C2×C4—1721no—
505C2×C4—1722no—
506C2×C4—1721no—
507C2×C4—1722no—
508C2×C4—1721no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4—1724no—
512C2×C4—1724no—
513C2×C4#1306329511yescharacteristic
514C2×C4#1306329512yes—
515C2×C4#1306329511yescharacteristic
516C2×C4#1306330512yes—
517C22—22no—
518C22—21no—
519C22—22no—
520C22—21no—
521C22—22no—
522C22—41no—
523C22—41no—
524C22—42no—
525C22—42no—
526C22—41no—
527C22—41no—
528C22—81no—
529C22C2×#1306329511yescharacteristic
530C22C2×#1306330511yescharacteristic
531C22#1458347511yescharacteristic
532C22#1458355512yes—
533C22#1458356212yes—
534C4—21no—
535C4—22no—
536C4—22no—
537C4—41no—
538C4—41no—
539C4—84no—
540C4—3441no—
541C4—1722no—
542C4—1724no—
543C4—1722no—
544C4—1724no—
545C4—1722no—
546C4#1458309012yes—
547C2—22no—
548C2—21no—
549C2—21no—
550C2—22no—
551C2—42no—
552C2#1913796111yescharacteristic
553C2C2×#1458309011yescharacteristic
554C2#1914398911yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC24×C43C24
FrattiniC24C23×D43
FittingC43×#1799C2
socleC22×C43C2×#120
prime radicalC22×D4×C43C23
hypercenter#1799D43
hypocenterC43#24351
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #19142935C2semidirect
4. #19135949C2semidirect
5. #19135763C2semidirect
6. #19135579C2semidirect
51. #13063306Q8semidirect
139. C22×Dic43C2×Q8semidirect
161. C22⋊Dic43C2×Q8semidirect
318. C43#24351semidirect

Maximal subgroups

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

subgroupindex
#191483982
#191429352
C4×#130633062
#191359492
#191357632
#191355792
#191350062
#191348782
C43×#17992
#2435143