Finite Group Databasebeta

← #25012071

Subgroups — #25012071

Order 11008.

1228 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582689C212yesmaximal, complemented
2C2×#14582686C212yesmaximal, complemented
3#19134516C211yesmaximal, characteristic, complemented
4#19134510C211yesmaximal, characteristic, complemented
5C2×C43×#534C211yesmaximal, characteristic
6C2×#13063242—21no—
7C2×#13063242C2212yes—
8C2×#13063240—21no—
9C2×#13063240C2212yes—
10#14582863—21no—
11#14582755—21no—
12#14582689—24no—
13#14582686—24no—
14C23×D4×C43C411yescharacteristic, complemented
15C23×D4×C43C2211yescharacteristic
16C43×#534—24no—
17C43×#534—24no—
18C2×#123×C43—21no—
19C2×#123×C43C411yescharacteristic, complemented
20C2×#123×C43C2211yescharacteristic
21C2×#121×C43—21no—
22C2×#121×C43—21no—
23C2×#120×C43—21no—
24C2×#120×C43C411yescharacteristic, complemented
25C2×#120×C43C2211yescharacteristic
26C22×C22⋊C4×C43C411yescharacteristic, complemented
27C2×#10621877—22no—
28C2×C22⋊Dic43—22no—
29C2×C22⋊Dic43—42no—
30#13063242—22no—
31#13063242—22no—
32#13063242—42no—
33#13063240—22no—
34#13063240—22no—
35#13063240—42no—
36C22⋊(C43⋊C8)—42no—
37C25×C43C2×C411yescharacteristic
38C25×C43C2×C411yescharacteristic
39C25×C43D411yescharacteristic
40C22×D4×C43—21no—
41C22×D4×C43—21no—
42C22×D4×C43—22no—
43C22×D4×C43—21no—
44C22×D4×C43—21no—
45C22×D4×C43—22no—
46C22×D4×C43—22no—
47C22×D4×C43—22no—
48C22×D4×C43—42no—
49C22×D4×C43—42no—
50C22×D4×C43—42no—
51C22×D4×C43—42no—
52C22×D4×C43C2×C411yescharacteristic
53C22×D4×C43D411yescharacteristic
54C22×D4×C43D411yescharacteristic
55C22×D4×C43C2311yescharacteristic
56C23×C4×C43—21no—
57C23×C4×C43C2×C411yescharacteristic
58C23×C4×C43D411yescharacteristic
59#123×C43—28no—
60#123×C43—22no—
61#123×C43—22no—
62#123×C43—22no—
63#123×C43D414yes—
64#121×C43—28no—
65#121×C43—28no—
66#120×C43—28no—
67#120×C43—22no—
68#120×C43—22no—
69#120×C43—22no—
70#120×C43D414yes—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43—21no—
78C2×C22⋊C4×C43—22no—
79C2×C22⋊C4×C43—22no—
80C2×C22⋊C4×C43C2×C411yescharacteristic
81C2×C22⋊C4×C43C2×C411yescharacteristic
82C24×C43—22no—
83C24×C43—22no—
84C24×C43—21no—
85C24×C43—21no—
86C24×C43—21no—
87C24×C43—22no—
88C24×C43—21no—
89C24×C43—22no—
90C24×C43—41no—
91C24×C43—41no—
92C24×C43—41no—
93C24×C43—82no—
94C24×C43—82no—
95C24×C43—82no—
96C24×C43C22⋊C411yescharacteristic
97C24×C43C22⋊C411yescharacteristic
98C24×C43C22⋊C411yescharacteristic
99C24×C43C22⋊C412yescomplemented
100C24×C43C22×C411yescharacteristic
101C24×C43C2×D411yescharacteristic
102C2×D4×C43—24no—
103C2×D4×C43—24no—
104C2×D4×C43—24no—
105C2×D4×C43—22no—
106C2×D4×C43—22no—
107C2×D4×C43—22no—
108C2×D4×C43—21no—
109C2×D4×C43—21no—
110C2×D4×C43—22no—
111C2×D4×C43—24no—
112C2×D4×C43—41no—
113C2×D4×C43—41no—
114C2×D4×C43—41no—
115C2×D4×C43—41no—
116C2×D4×C43—41no—
117C2×D4×C43—41no—
118C2×D4×C43—48no—
119C2×D4×C43—48no—
120C2×D4×C43—48no—
121C2×D4×C43—48no—
122C2×D4×C43—42no—
123C2×D4×C43—42no—
124C2×D4×C43—42no—
125C2×D4×C43—42no—
126C2×D4×C43—82no—
127C2×D4×C43—82no—
128C2×D4×C43C2×D412yes—
129C2×D4×C43C2×D412yes—
130C22×C4×C43—24no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—41no—
138C22×C4×C43—41no—
139C22×C4×C43—41no—
140C22×C4×C43—82no—
141C22×C4×C43C22⋊C411yescharacteristic
142C22×C4×C43C22⋊C412yescomplemented
143C22×C4×C43C2×D411yescharacteristic
144C22×Dic43—42no—
145C4⋊C4×C43—24no—
146C4⋊C4×C43—24no—
147C22⋊C4×C43—24no—
148C22⋊C4×C43—24no—
149C22⋊C4×C43—24no—
150C22⋊C4×C43—24no—
151C22⋊C4×C43—21no—
152C22⋊C4×C43—21no—
153C22⋊C4×C43—24no—
154C22⋊C4×C43C22⋊C412yescomplemented
155C22⋊C4×C43C22⋊C412yescomplemented
156C22⋊Dic43—42no—
157C22⋊Dic43—42no—
158C22⋊Dic43—84no—
159#10621877—42no—
160#10621877—42no—
161C2×C43⋊C8—42no—
162C23×C43—24no—
163C23×C43—24no—
164C23×C43—21no—
165C23×C43—21no—
166C23×C43—21no—
167C23×C43—21no—
168C23×C43—21no—
169C23×C43—21no—
170C23×C43—21no—
171C23×C43—21no—
172C23×C43—21no—
173C23×C43—22no—
174C23×C43—21no—
175C23×C43—21no—
176C23×C43—42no—
177C23×C43—44no—
178C23×C43—42no—
179C23×C43—42no—
180C23×C43—42no—
181C23×C43—42no—
182C23×C43—44no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—42no—
186C23×C43—42no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—82no—
190C23×C43—82no—
191C23×C43—82no—
192C23×C43—82no—
193C23×C43—82no—
194C23×C43—82no—
195C23×C43—82no—
196C23×C43—84no—
197C23×C43—84no—
198C23×C43—84no—
199C23×C43—84no—
200C23×C43—84no—
201C23×C43#9912yes—
202C23×C43#9912yes—
203C23×C43C2×C22⋊C411yescharacteristic
204C23×C43C2×C22⋊C411yescharacteristic
205C23×C43C2×C22⋊C411yescharacteristic
206C23×C43#12012yes—
207D4×C43—42no—
208D4×C43—42no—
209D4×C43—44no—
210D4×C43—44no—
211D4×C43—42no—
212D4×C43—42no—
213D4×C43—48no—
214D4×C43—48no—
215D4×C43—84no—
216D4×C43—84no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—22no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—44no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—42no—
232C2×C4×C43—84no—
233C2×C4×C43#12012yes—
234C2×Dic43—82no—
235C2×Dic43—84no—
236C43⋊C8—82no—
237#12690—431nomaximal, Sylow
238C22×C43—22no—
239C22×C43—22no—
240C22×C43—22no—
241C22×C43—22no—
242C22×C43—21no—
243C22×C43—21no—
244C22×C43—22no—
245C22×C43—22no—
246C22×C43—41no—
247C22×C43—41no—
248C22×C43—42no—
249C22×C43—42no—
250C22×C43—42no—
251C22×C43—42no—
252C22×C43—42no—
253C22×C43—42no—
254C22×C43—42no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43—42no—
261C22×C43—41no—
262C22×C43—42no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43—82no—
266C22×C43—84no—
267C22×C43—84no—
268C22×C43—88no—
269C22×C43—84no—
270C22×C43—84no—
271C22×C43—82no—
272C22×C43#37911yescharacteristic
273C22×C43C2×#9911yescharacteristic
274C22×C43C2×#9911yescharacteristic
275C4×C43—22no—
276C4×C43—42no—
277C4×C43—42no—
278C4×C43—41no—
279C4×C43—42no—
280Dic43—162no—
281C2×#534D4311yescharacteristic
282C2×#352—432no—
283C2×AΣL(1,𝔽16)—432no—
284#1783—431no—
285#1781—431no—
286C2×C43—21no—
287C2×C43—21no—
288C2×C43—42no—
289C2×C43—42no—
290C2×C43—42no—
291C2×C43—41no—
292C2×C43—41no—
293C2×C43—81no—
294C2×C43—82no—
295C2×C43#178111yescharacteristic
296C2×C43#212112yes—
297C23×D4Dic4311yescharacteristic, complemented
298C23×D4C2×D4311yescharacteristic
299#534—24no—
300#534—24no—
301C2×#123—21no—
302C2×#123Dic4311yescharacteristic, complemented
303C2×#123C2×D4311yescharacteristic
304C2×#121—21no—
305C2×#121—21no—
306C2×#120—21no—
307C2×#120Dic4311yescharacteristic, complemented
308C2×#120C2×D4311yescharacteristic
309C22×C22⋊C4Dic4311yescharacteristic, complemented
310C2×#100—432no—
311C2×#100—861no—
312C2×#99—432no—
313C2×#99—861no—
314#407—861no—
315#379—861no—
316#352—864no—
317AΣL(1,𝔽16)—864no—
318C43#1269011yescharacteristic, complemented, Sylow
319C25C2×Dic4311yescharacteristic
320C25C2×Dic4311yescharacteristic
321C25C22⋊D4311yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—22no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—42no—
331C22×D4—42no—
332C22×D4—42no—
333C22×D4—42no—
334C22×D4C2×Dic4311yescharacteristic
335C22×D4C22⋊D4311yescharacteristic
336C22×D4C22⋊D4311yescharacteristic
337C22×D4C22×D4311yescharacteristic
338C23×C4—21no—
339C23×C4C2×Dic4311yescharacteristic
340C23×C4C22⋊D4311yescharacteristic
341C2×M16—862no—
342#123—28no—
343#123—22no—
344#123—22no—
345#123—22no—
346#123C22⋊D4314yes—
347#121—28no—
348#121—28no—
349#120—28no—
350#120—22no—
351#120—22no—
352#120—22no—
353#120C22⋊D4314yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—862no—
364C2×C22⋊C4—1722no—
365C2×C22⋊C4C2×Dic4311yescharacteristic
366C2×C22⋊C4C2×Dic4311yescharacteristic
367#100—862no—
368#100—862no—
369#100—1722no—
370#99—862no—
371#99—862no—
372#99—1722no—
373C22⋊C8—1722no—
374C24—22no—
375C24—22no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—22no—
380C24—21no—
381C24—22no—
382C24—41no—
383C24—41no—
384C24—41no—
385C24—82no—
386C24—82no—
387C24—82no—
388C24C22⋊Dic4311yescharacteristic
389C24C22⋊Dic4311yescharacteristic
390C24C22⋊Dic4311yescharacteristic
391C24C22⋊Dic4312yescomplemented
392C24C22×Dic4311yescharacteristic
393C24C2×C22⋊D4311yescharacteristic
394C2×D4—24no—
395C2×D4—24no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—22no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—48no—
411C2×D4—48no—
412C2×D4—48no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4—48no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—82no—
419C2×D4—82no—
420C2×D4C2×C22⋊D4312yes—
421C2×D4C2×C22⋊D4312yes—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—82no—
433C22×C4—1722no—
434C22×C4C22⋊Dic4311yescharacteristic
435C22×C4C22⋊Dic4312yescomplemented
436C22×C4C2×C22⋊D4311yescharacteristic
437M16—1722no—
438M16—1722no—
439C2×C8—1722no—
440C4⋊C4—24no—
441C4⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—21no—
446C22⋊C4—21no—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—3444no—
450C22⋊C4—1722no—
451C22⋊C4—1722no—
452C22⋊C4C22⋊Dic4312yescomplemented
453C22⋊C4C22⋊Dic4312yescomplemented
454C23—24no—
455C23—24no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—22no—
467C23—21no—
468C23—42no—
469C23—44no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23—44no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—41no—
480C23—41no—
481C23—82no—
482C23—82no—
483C23—82no—
484C23—82no—
485C23—84no—
486C23—82no—
487C23—82no—
488C23—82no—
489C23—84no—
490C23—84no—
491C23—84no—
492C23—84no—
493C23#1306324012yes—
494C23#1306324012yes—
495C23C2×C22⋊Dic4311yescharacteristic
496C23C2×C22⋊Dic4311yescharacteristic
497C23C2×C22⋊Dic4311yescharacteristic
498C23#1306329412yes—
499D4—42no—
500D4—42no—
501D4—44no—
502D4—44no—
503D4—42no—
504D4—42no—
505D4—48no—
506D4—48no—
507D4—84no—
508D4—84no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—44no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—84no—
525C2×C4—3442no—
526C2×C4—3444no—
527C2×C4#1306329412yes—
528C8—3442no—
529C22—22no—
530C22—22no—
531C22—21no—
532C22—21no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—42no—
538C22—41no—
539C22—41no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—41no—
552C22—42no—
553C22—42no—
554C22—81no—
555C22—81no—
556C22—82no—
557C22—84no—
558C22—84no—
559C22—88no—
560C22—84no—
561C22—84no—
562C22—82no—
563C22#1458275511yescharacteristic
564C22C2×#1306324011yescharacteristic
565C22C2×#1306324011yescharacteristic
566C4—22no—
567C4—42no—
568C4—42no—
569C4—41no—
570C4—42no—
571C4—6882no—
572C2—21no—
573C2—21no—
574C2—42no—
575C2—42no—
576C2—41no—
577C2—41no—
578C2—42no—
579C2—81no—
580C2—82no—
581C2#1913451011yescharacteristic
582C2#1913624112yes—
subgroupG/H
centerC22C2×#13063240
commutatorC24×C43C22×C4
FrattiniC22×D4C22×D43
Fitting, prime radicalC2×C43×#534C2
socleC22×C43C2×#99
cosocleC22×D4×C43C23
hypercenterC2×#534D43
hypocenterC43#12690
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. C2×#14582689C2semidirect
2. C2×#14582686C2semidirect
3. #19134516C2semidirect
4. #19134510C2semidirect
14. C23×D4×C43C4semidirect
19. C2×#123×C43C4semidirect
24. C2×#120×C43C4semidirect
26. C22×C22⋊C4×C43C4semidirect
99. C24×C43C22⋊C4semidirect
142. C22×C4×C43C22⋊C4semidirect
154. C22⋊C4×C43C22⋊C4semidirect
155. C22⋊C4×C43C22⋊C4semidirect
297. C23×D4Dic43semidirect
302. C2×#123Dic43semidirect
307. C2×#120Dic43semidirect
309. C22×C22⋊C4Dic43semidirect
318. C43#12690semidirect
391. C24C22⋊Dic43semidirect
435. C22×C4C22⋊Dic43semidirect
452. C22⋊C4C22⋊Dic43semidirect
453. C22⋊C4C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145826892
C2×#145826862
#191345162
#191345102
C2×C43×#5342
#1269043