Finite Group Databasebeta

← #25133285

Subgroups — #25133285

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#19140410C212yesmaximal, complemented
2#19137260C211yesmaximal, characteristic
3#19135947C212yesmaximal, complemented
4#19135761C212yesmaximal, complemented
5#19135581C212yesmaximal, complemented
6#19135008C212yesmaximal
7#19134876C212yesmaximal
8#19134583C211yesmaximal, characteristic
9C43×#3501C211yesmaximal, characteristic
10C2×#13063306C2211yescharacteristic
11C22×Dic43⋊C4C2211yescharacteristic
12C2×#13063240C2212yes—
13#14582837—22no—
14#14582832—24no—
15#14582818—22no—
16#14582794—21no—
17#14582793—21no—
18#14582783—21no—
19#14582779C2211yescharacteristic
20#14582772—21no—
21#14582771C2214yes—
22#14582771C2211yescharacteristic
23#14582760C2211yescharacteristic
24#14582760C2214yes—
25#14582759C2212yes—
26C4×C22⋊Dic43C2211yescharacteristic
27#14582666C2214yes—
28#14582666C2212yes—
29#14582666C2214yes—
30C43×#554—24no—
31C43×#554—22no—
32D4×Q8×C43—22no—
33C43×#544—21no—
34C43×#543—21no—
35C43×#543C2212yes—
36C43×#533—21no—
37C2×C22⋊Q8×C43—21no—
38C2×C22⋊Q8×C43C2212yes—
39C43×#518C2212yes—
40C2×C4×D4×C43C2211yescharacteristic
41C23×Dic43C2311yescharacteristic
42C23×Dic43C2311yescharacteristic
43#13063306—22no—
44#13063306Q814yescomplemented
45C2×C4⋊Dic43—22no—
46C2×Dic43⋊C4—21no—
47C2×Dic43⋊C4—21no—
48C2×Dic43⋊C4—22no—
49C2×Dic43⋊C4—22no—
50C2×Dic43⋊C4—21no—
51C2×Dic43⋊C4—21no—
52C2×Dic43⋊C4—24no—
53C2×C22⋊Dic43—21no—
54C2×C22⋊Dic43—21no—
55C2×C22⋊Dic43C2314yes—
56C2×C22⋊Dic43C2311yescharacteristic
57C2×C22⋊Dic43C2311yescharacteristic
58C2×C4×Dic43—21no—
59#13063240—24no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95—24no—
65C43⋊#95—22no—
66C43⋊#95—24no—
67C43⋊#95—24no—
68C43⋊#95—21no—
69C22×Q8×C43—21no—
70C22×Q8×C43D412yes—
71C22×D4×C43C2311yescharacteristic
72C23×C4×C43D411yescharacteristic
73C23×C4×C43C2311yescharacteristic
74C4⋊Q8×C43—21no—
75C4⋊Q8×C43—21no—
76C4⋊Q8×C43—24no—
77#125×C43—22no—
78#125×C43—24no—
79C22⋊Q8×C43—22no—
80C22⋊Q8×C43—22no—
81C22⋊Q8×C43—24no—
82C22⋊Q8×C43—24no—
83C22⋊Q8×C43—22no—
84C22⋊Q8×C43—22no—
85C22⋊Q8×C43—22no—
86C22⋊Q8×C43—22no—
87C22⋊Q8×C43—22no—
88C22⋊Q8×C43—22no—
89C22⋊Q8×C43—24no—
90C22⋊Q8×C43—24no—
91C4×Q8×C43—22no—
92C4×Q8×C43—22no—
93C4×D4×C43—22no—
94C4×D4×C43—22no—
95C4×D4×C43—24no—
96C4×D4×C43—24no—
97#117×C43—22no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—22no—
100C2×C4⋊C4×C43D411yescharacteristic
101C2×C4⋊C4×C43D414yes—
102C2×C4⋊C4×C43D412yes—
103C2×C22⋊C4×C43—22no—
104C2×C22⋊C4×C43D411yescharacteristic
105C2×C22⋊C4×C43C2311yescharacteristic
106C2×C22⋊C4×C43C2314yes—
107C2×C42×C43D411yescharacteristic
108C24×C43C2×D411yescharacteristic
109C24×C43C2411yescharacteristic
110C2×Q8×C43—22no—
111C2×Q8×C43—22no—
112C2×Q8×C43—22no—
113C2×Q8×C43—22no—
114C2×Q8×C43—82no—
115C2×Q8×C43—82no—
116C2×D4×C43—22no—
117C2×D4×C43—22no—
118C2×D4×C43C2×Q812yes—
119C2×D4×C43#4112yes—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—81no—
125C22×C4×C43—81no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D414yes—
129C22×C4×C43C2×D414yes—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D412yes—
134C22×C4×C43C2×D412yes—
135C22×Dic43—22no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—24no—
140C22×Dic43—21no—
141C22×Dic43—22no—
142C22×Dic43—21no—
143C22×Dic43—22no—
144C22×Dic43—81no—
145C22×Dic43C2×Q812yescomplemented
146C4⋊C4×C43—22no—
147C4⋊C4×C43—24no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—24no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—24no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—24no—
157C22⋊C4×C43—24no—
158C22⋊C4×C43—22no—
159C22⋊C4×C43—24no—
160C22⋊C4×C43—22no—
161C22⋊C4×C43—24no—
162C42×C43—24no—
163C42×C43—21no—
164C42×C43—21no—
165C22⋊Dic43—24no—
166C22⋊Dic43—21no—
167C22⋊Dic43—24no—
168C22⋊Dic43—22no—
169C22⋊Dic43—24no—
170C22⋊Dic43—81no—
171C22⋊Dic43C2×Q812yescomplemented
172C4⋊Dic43—82no—
173Dic43⋊C4—24no—
174Dic43⋊C4—41no—
175Dic43⋊C4—41no—
176Dic43⋊C4—42no—
177Dic43⋊C4—81no—
178Dic43⋊C4—84no—
179C4×Dic43—81no—
180C23×C43—21no—
181C23×C43—21no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—41no—
185C23×C43—41no—
186C23×C43C22⋊Q812yes—
187C23×C43C22×D411yescharacteristic
188C23×C43C22×D412yes—
189C23×C43C22×Q811yescharacteristic
190C23×C43C2×#4111yescharacteristic
191C23×C432−1+412yes—
192Q8×C43—44no—
193Q8×C43—82no—
194Q8×C43—82no—
195Q8×C43—82no—
196D4×C43—24no—
197D4×C43—24no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—24no—
202C2×C4×C43—24no—
203C2×C4×C43—21no—
204C2×C4×C43—41no—
205C2×C4×C43—42no—
206C2×C4×C43—41no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—41no—
210C2×C4×C43—44no—
211C2×C4×C43—44no—
212C2×C4×C43—41no—
213C2×C4×C43—81no—
214C2×C4×C43—82no—
215C2×C4×C43—82no—
216C2×C4×C43#12011yescharacteristic
217C2×C4×C43#12011yescharacteristic
218C2×C4×C43#12012yes—
219C2×C4×C43C22⋊Q812yes—
220C2×Dic43—22no—
221C2×Dic43—22no—
222C2×Dic43—24no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—42no—
228C2×Dic43—41no—
229C2×Dic43—44no—
230C2×Dic43—41no—
231C2×Dic43—44no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—44no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—44no—
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—21no—
259C4×C43—22no—
260C4×C43—41no—
261C4×C43—44no—
262C4×C43—44no—
263C4×C43—41no—
264Dic43—42no—
265Dic43—42no—
266Dic43—84no—
267Dic43—81no—
268Dic43—81no—
269#3501D4311yescharacteristic
270#2627—432no—
271#2322—431no—
272#2062—432no—
273#2030—432no—
274#1996—432no—
275#1890—432no—
276#1867—432no—
277#1799—431no—
278C2×C43—21no—
279C2×C43—22no—
280C2×C43—21no—
281C2×C43—22no—
282C2×C43—42no—
283C2×C43#240911yescharacteristic
284C2×C43#302611yescharacteristic
285C2×C43#302811yescharacteristic
286#554—24no—
287#554—22no—
288D4×Q8—22no—
289#544—21no—
290#543—21no—
291#543C2×D4312yes—
292#533—21no—
293C2×#123—431no—
294C2×C22⋊Q8—21no—
295C2×C22⋊Q8C2×D4312yes—
296#518C2×D4312yes—
297C2×C4×D4C2×D4311yescharacteristic
298C22×C4⋊C4—431no—
299C2×#99—432no—
300#400—862no—
301#398—864no—
302#395—862no—
303#389—861no—
304#388—861no—
305#387—861no—
306#386—431no—
307#385—431no—
308#385—434no—
309#385—861no—
310#381—431no—
311#381—434no—
312#380—432no—
313C4×C22⋊C4—431no—
314#342—432no—
315#342—434no—
316#342—434no—
317C43#2435311yescharacteristic, complemented, Sylow
318C22×Q8—21no—
319C22×Q8C22⋊D4312yes—
320C22×D4C22×D4311yescharacteristic
321C23×C4—431no—
322C23×C4—431no—
323C23×C4C22⋊D4311yescharacteristic
324C23×C4C22×D4311yescharacteristic
325C4⋊Q8—21no—
326C4⋊Q8—21no—
327C4⋊Q8—24no—
328#125—22no—
329#125—24no—
330#123—434no—
331#123—862no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8—24no—
343C22⋊Q8—24no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—24no—
349C4×D4—24no—
350#117—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—861no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—864no—
356C2×C4⋊C4—862no—
357C2×C4⋊C4—861no—
358C2×C4⋊C4—861no—
359C2×C4⋊C4—862no—
360C2×C4⋊C4—862no—
361C2×C4⋊C4C22⋊D4311yescharacteristic
362C2×C4⋊C4C22⋊D4314yes—
363C2×C4⋊C4C22⋊D4312yes—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—431no—
366C2×C22⋊C4—431no—
367C2×C22⋊C4—434no—
368C2×C22⋊C4—861no—
369C2×C22⋊C4—861no—
370C2×C22⋊C4C22⋊D4311yescharacteristic
371C2×C22⋊C4C22×D4311yescharacteristic
372C2×C22⋊C4C22×D4314yes—
373C2×C42—861no—
374C2×C42C22⋊D4311yescharacteristic
375#99—864no—
376#95—861no—
377#95—862no—
378#95—861no—
379#95—861no—
380#95—864no—
381#95—864no—
382#95—861no—
383#95—864no—
384#95—861no—
385C24C2×C22⋊D4311yescharacteristic
386C24C23×D4311yescharacteristic
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—82no—
392C2×Q8—82no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4Q8×D4312yes—
396C2×D4#1062190212yes—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—81no—
402C22×C4—81no—
403C22×C4—432no—
404C22×C4—862no—
405C22×C4—861no—
406C22×C4—861no—
407C22×C4—861no—
408C22×C4—862no—
409C22×C4—861no—
410C22×C4—864no—
411C22×C4—861no—
412C22×C4—862no—
413C22×C4—3441no—
414C22×C4C2×C22⋊D4311yescharacteristic
415C22×C4C2×C22⋊D4311yescharacteristic
416C22×C4C2×C22⋊D4314yes—
417C22×C4C2×C22⋊D4314yes—
418C22×C4C2×C22⋊D4311yescharacteristic
419C22×C4C2×C22⋊D4311yescharacteristic
420C22×C4C2×C22⋊D4312yes—
421C22×C4C2×C22⋊D4311yescharacteristic
422C22×C4C2×C22⋊D4312yes—
423C4⋊C4—22no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—24no—
428C4⋊C4—22no—
429C4⋊C4—24no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—24no—
434C4⋊C4—864no—
435C4⋊C4—3441no—
436C4⋊C4—3444no—
437C4⋊C4—3442no—
438C4⋊C4—1721no—
439C4⋊C4—1721no—
440C4⋊C4—1722no—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—22no—
444C22⋊C4—24no—
445C22⋊C4—22no—
446C22⋊C4—432no—
447C22⋊C4—864no—
448C22⋊C4—861no—
449C22⋊C4—864no—
450C22⋊C4—864no—
451C22⋊C4—862no—
452C22⋊C4—3441no—
453C42—24no—
454C42—21no—
455C42—21no—
456C42—3441no—
457C23—21no—
458C23—21no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23#1306330112yes—
464C23C22×C22⋊D4312yes—
465C23C22×C22⋊D4311yescharacteristic
466C23C2×Q8×D4311yescharacteristic
467C23C2×#1062190211yescharacteristic
468C23#1306337312yes—
469Q8—44no—
470Q8—82no—
471Q8—82no—
472Q8—82no—
473D4—24no—
474D4—24no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—21no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—41no—
490C2×C4—81no—
491C2×C4—82no—
492C2×C4—82no—
493C2×C4—864no—
494C2×C4—862no—
495C2×C4—862no—
496C2×C4—1721no—
497C2×C4—1721no—
498C2×C4—1724no—
499C2×C4—1724no—
500C2×C4—1721no—
501C2×C4—1724no—
502C2×C4—1721no—
503C2×C4—1724no—
504C2×C4—1721no—
505C2×C4—1721no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—1722no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4#1306329411yescharacteristic
512C2×C4#1306329411yescharacteristic
513C2×C4#1306329412yes—
514C2×C4#1306330112yes—
515C22—22no—
516C22—21no—
517C22—22no—
518C22—21no—
519C22—22no—
520C22—41no—
521C22—41no—
522C22—42no—
523C22—42no—
524C22—41no—
525C22—41no—
526C22—81no—
527C22C2×#1306329411yescharacteristic
528C22C2×#1306330111yescharacteristic
529C22#1458347311yescharacteristic
530C22#1458356012yes—
531C22Q8×C22⋊D4312yes—
532C4—21no—
533C4—21no—
534C4—22no—
535C4—22no—
536C4—41no—
537C4—44no—
538C4—44no—
539C4—41no—
540C4—3444no—
541C4—3441no—
542C4—3441no—
543C4—1722no—
544C4—1722no—
545C2—22no—
546C2—21no—
547C2—21no—
548C2—22no—
549C2—42no—
550C2#1913795411yescharacteristic
551C2#1914399211yescharacteristic
552C2#1914400111yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC24×C43C24
FrattiniC24C23×D43
FittingC43×#3501C2
socleC22×C43C2×#120
prime radicalC22×D4×C43C23
hypercenter#3501D43
hypocenterC43#24353
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #19140410C2semidirect
3. #19135947C2semidirect
4. #19135761C2semidirect
5. #19135581C2semidirect
44. #13063306Q8semidirect
145. C22×Dic43C2×Q8semidirect
171. C22⋊Dic43C2×Q8semidirect
317. C43#24353semidirect

Maximal subgroups

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

subgroupindex
#191404102
#191372602
#191359472
#191357612
#191355812
#191350082
#191348762
#191345832
C43×#35012
#2435343