Finite Group Databasebeta

← #25071023

Subgroups — #25071023

Order 11008.

996 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148398C211yesmaximal, characteristic, complemented
2#19145401C212yesmaximal, complemented
3#19133636C212yesmaximal, complemented
4#19133619C212yesmaximal, complemented
5#19133534C212yesmaximal, complemented
6#19133517C212yesmaximal, complemented
7#19133127C212yesmaximal, complemented
8#19132933C211yesmaximal, characteristic, complemented
9C43×#2635C211yesmaximal, characteristic
10#14583608—24no—
11#14583606—22no—
12D4×Dic86—22no—
13#14583530C2212yes—
14#14583525—21no—
15#14583525C2212yes—
16#14583456—21no—
17C2×#13063304—21no—
18C2×#13063304C2212yes—
19#14583374—21no—
20#14583234C2214yes—
21#14583210—22no—
22#14583143—24no—
23#14583050C2214yes—
24#14583037—22no—
25#14582863C2212yes—
26#14582635C2214yes—
27#14582635C2214yes—
28#14582625C2212yes—
29#14582623C2212yes—
30C2×#121×C43C2211yescharacteristic
31C2×C4×D4×C43C2211yescharacteristic
32C43×#400C2211yescharacteristic
33C43×#399C2211yescharacteristic
34C43×#394—21no—
35C43×#394C2211yescharacteristic
36C43×#392—21no—
37C43×#392C2211yescharacteristic
38C43×#388—21no—
39C43×#386—21no—
40C43×#381C2211yescharacteristic
41C22×Dic86—21no—
42C22×Dic86D412yescomplemented
43C2×#10621883—24no—
44C2×#10621877—22no—
45#13063325—21no—
46#13063325—21no—
47#13063324—24no—
48#13063317—22no—
49#13063316—24no—
50#13063304—22no—
51#13063304—22no—
52#13063304—22no—
53#13063304—22no—
54#13063304—22no—
55#13063304—22no—
56#13063304D414yescomplemented
57#13063304C2314yes—
58#13063302—24no—
59#13063302—24no—
60#13063302—24no—
61#13063302—24no—
62C4×Dic86—22no—
63C4×Dic86—22no—
64D4×Dic43—24no—
65D4×Dic43—24no—
66#13063284—22no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43D412yescomplemented
69C2×Dic43⋊C4—22no—
70C2×Dic43⋊C4—22no—
71C2×C22⋊Dic43—22no—
72C2×C22⋊Dic43—22no—
73#13063258—24no—
74#13063248—24no—
75#13063246—24no—
76C22⋊(C43⋊C8)—22no—
77C22⋊(C43⋊C8)C2314yes—
78C22×D4×C43—21no—
79C22×D4×C43—21no—
80C22×D4×C43D411yescharacteristic
81C22×D4×C43C2311yescharacteristic
82C23×C4×C43D411yescharacteristic
83C23×C4×C43C2311yescharacteristic
84#121×C43—22no—
85#121×C43—22no—
86C4×D4×C43—22no—
87C4×D4×C43—22no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C4⋊C4×C43C2311yescharacteristic
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43D411yescharacteristic
98C2×C22⋊C4×C43C2311yescharacteristic
99C2×C42×C43D411yescharacteristic
100#95×C43—21no—
101#95×C43—21no—
102#95×C43—21no—
103#95×C43C2311yescharacteristic
104#95×C43C2311yescharacteristic
105C24×C43—21no—
106C24×C43C2×D411yescharacteristic
107C24×C43C2×D411yescharacteristic
108C2×D4×C43—22no—
109C2×D4×C43—22no—
110C2×D4×C43—22no—
111C2×D4×C43—22no—
112C2×D4×C43—42no—
113C2×D4×C43—42no—
114C2×D4×C43—81no—
115C2×D4×C43—81no—
116C2×D4×C43—81no—
117C2×D4×C43—81no—
118C2×D4×C43—81no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—81no—
125C22×C4×C43—81no—
126C22×C4×C43C2×D412yes—
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C2×Dic86—22no—
138C2×Dic86—22no—
139C2×Dic86—22no—
140C2×Dic86—82no—
141C2×Dic86—82no—
142C2×Dic86C2×D414yes—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—81no—
146C22⋊C4×C43—22no—
147C22⋊C4×C43—22no—
148C22⋊C4×C43—41no—
149C22⋊C4×C43—41no—
150C22⋊C4×C43—42no—
151C22⋊C4×C43—81no—
152C22⋊C4×C43—81no—
153C22⋊C4×C43—81no—
154C22⋊C4×C43—81no—
155C42×C43—21no—
156C42×C43—21no—
157C22⋊Dic43—24no—
158C22⋊Dic43—24no—
159C22⋊Dic43—24no—
160#10621883—84no—
161C4⋊Dic43—22no—
162C4⋊Dic43—22no—
163C4⋊Dic43—22no—
164C4⋊Dic43—22no—
165C4⋊Dic43—22no—
166C4⋊Dic43C2×D414yes—
167Dic43⋊C4—24no—
168Dic43⋊C4—24no—
169Dic43⋊C4—24no—
170Dic43⋊C4—24no—
171C4×Dic43—24no—
172#10621877—82no—
173C2×C43⋊C8—24no—
174C23×C43—21no—
175C23×C43—21no—
176C23×C43—21no—
177C23×C43—21no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43—41no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—41no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43#12012yes—
190C23×C43#13712yes—
191C23×C43C22×D411yescharacteristic
192D4×C43—28no—
193D4×C43—44no—
194D4×C43—84no—
195D4×C43—84no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—42no—
201C2×C4×C43—42no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—42no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—81no—
217C2×C4×C43#12011yescharacteristic
218C2×C4×C43#12011yescharacteristic
219C2×C4×C43#13712yes—
220C2×C4×C43C22×D412yes—
221C2×Dic43—24no—
222C2×Dic43—24no—
223C2×Dic43—82no—
224C2×Dic43—82no—
225C2×Dic43—82no—
226C2×Dic43—82no—
227Dic86—44no—
228Dic86—44no—
229Dic86—82no—
230Dic86—82no—
231C43⋊C8—44no—
232#18352—431nomaximal, Sylow
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—22no—
236C22×C43—22no—
237C22×C43—22no—
238C22×C43—22no—
239C22×C43—42no—
240C22×C43—41no—
241C22×C43—41no—
242C22×C43—81no—
243C22×C43—81no—
244C22×C43—81no—
245C22×C43—81no—
246C22×C43—81no—
247C22×C43—81no—
248C22×C43—81no—
249C22×C43—81no—
250C22×C43—81no—
251C22×C43—81no—
252C22×C43C2×#12011yescharacteristic
253C22×C43C2×#13711yescharacteristic
254C22×C43C2×#13711yescharacteristic
255C4×C43—22no—
256C4×C43—22no—
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—81no—
262C4×C43—81no—
263C4×C43—81no—
264Dic43—44no—
265Dic43—44no—
266#3501—431no—
267#3193—432no—
268#2635D4311yescharacteristic
269#1617—432no—
270#1614—432no—
271#1599—432no—
272#1596—432no—
273#1511—432no—
274#1465—431no—
275C2×C43—21no—
276C2×C43—21no—
277C2×C43—42no—
278C2×C43—42no—
279C2×C43—161no—
280C2×C43#300411yescharacteristic
281C2×C43#302111yescharacteristic
282C2×C43#302611yescharacteristic
283#554—862no—
284#554—864no—
285D4×Q8—862no—
286#544—432no—
287#543—432no—
288#543—861no—
289#533—861no—
290C2×C22⋊Q8—432no—
291C2×C22⋊Q8—861no—
292C2×#121C2×D4311yescharacteristic
293#518—861no—
294C2×C4×D4C2×D4311yescharacteristic
295#484—434no—
296#480—862no—
297#468—864no—
298#450—434no—
299#448—862no—
300#407—432no—
301#400C2×D4311yescharacteristic
302#399C2×D4311yescharacteristic
303#394—21no—
304#394C2×D4311yescharacteristic
305#392—21no—
306#392C2×D4311yescharacteristic
307#388—21no—
308#386—21no—
309#381C2×D4311yescharacteristic
310#328—434no—
311#328—434no—
312#324—432no—
313#323—432no—
314C43#1835211yescharacteristic, complemented, Sylow
315C22×Q8—432no—
316C22×Q8—861no—
317C22×D4—21no—
318C22×D4—21no—
319C22×D4C22⋊D4311yescharacteristic
320C22×D4C22×D4311yescharacteristic
321C23×C4C22⋊D4311yescharacteristic
322C23×C4C22×D4311yescharacteristic
323C2×SD16—864no—
324C2×M16—862no—
325C4⋊Q8—861no—
326C4⋊Q8—861no—
327C4⋊Q8—864no—
328#125—862no—
329#125—864no—
330C22⋊Q8—434no—
331C22⋊Q8—434no—
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—
342#121—22no—
343#121—22no—
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—432no—
353C2×C4⋊C4—862no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—862no—
356C2×C4⋊C4C22×D4311yescharacteristic
357C2×C4⋊C4C22×D4311yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—862no—
365C2×C22⋊C4—862no—
366C2×C22⋊C4C22⋊D4311yescharacteristic
367C2×C22⋊C4C22×D4311yescharacteristic
368C2×C42C22⋊D4311yescharacteristic
369#107—864no—
370#103—864no—
371#102—864no—
372C22⋊C8—434no—
373C22⋊C8—862no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95C22×D4311yescharacteristic
378#95C22×D4311yescharacteristic
379C24—21no—
380C24C2×C22⋊D4311yescharacteristic
381C24C2×C22⋊D4311yescharacteristic
382C2×Q8—434no—
383C2×Q8—862no—
384C2×Q8—862no—
385C2×Q8—862no—
386C2×Q8—3442no—
387C2×Q8—3442no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4—81no—
395C2×D4—81no—
396C2×D4—81no—
397C2×D4—81no—
398C2×D4—81no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—81no—
405C22×C4—81no—
406C22×C4—862no—
407C22×C4—862no—
408C22×C4—862no—
409C22×C4—862no—
410C22×C4D4×D4312yes—
411C22×C4D4×D4312yes—
412C22×C4C2×C22⋊D4311yescharacteristic
413C22×C4C2×C22⋊D4311yescharacteristic
414C22×C4C2×C22⋊D4311yescharacteristic
415C22×C4C2×C22⋊D4311yescharacteristic
416C22×C4C23×D4311yescharacteristic
417SD16—3444no—
418M16—3442no—
419C2×C8—864no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—81no—
423C4⋊C4—434no—
424C4⋊C4—862no—
425C4⋊C4—864no—
426C4⋊C4—862no—
427C4⋊C4—862no—
428C4⋊C4—864no—
429C4⋊C4—862no—
430C4⋊C4—862no—
431C4⋊C4—864no—
432C4⋊C4—864no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—42no—
438C22⋊C4—81no—
439C22⋊C4—81no—
440C22⋊C4—81no—
441C22⋊C4—81no—
442C22⋊C4—864no—
443C22⋊C4—864no—
444C22⋊C4—864no—
445C42—21no—
446C42—21no—
447C42—864no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23#1306329312yes—
464C23#1306335512yes—
465C23C22×C22⋊D4311yescharacteristic
466Q8—3442no—
467Q8—3442no—
468Q8—1724no—
469Q8—1724no—
470D4—28no—
471D4—44no—
472D4—84no—
473D4—84no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—81no—
495C2×C4—864no—
496C2×C4—864no—
497C2×C4—3442no—
498C2×C4—3442no—
499C2×C4—3442no—
500C2×C4—3442no—
501C2×C4#1306329311yescharacteristic
502C2×C4#1306329311yescharacteristic
503C2×C4#1306335512yes—
504C2×C4C2×D4×D4312yes—
505C8—1724no—
506C22—21no—
507C22—21no—
508C22—22no—
509C22—22no—
510C22—22no—
511C22—22no—
512C22—42no—
513C22—41no—
514C22—41no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22C2×#1306329311yescharacteristic
526C22C2×#1306335511yescharacteristic
527C22C2×#1306335511yescharacteristic
528C4—22no—
529C4—21no—
530C4—21no—
531C4—22no—
532C4—41no—
533C4—41no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4—1724no—
538C4—1724no—
539C2—21no—
540C2—21no—
541C2—42no—
542C2—42no—
543C2—161no—
544C2#1914382811yescharacteristic
545C2#1914396611yescharacteristic
546C2#1914399111yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2635C2
socleC22×C43C2×#120
hypercenter#2635D43
hypocenterC43#18352
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2635

Complements

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

NH ≅ G/Ntype
1. #19148398C2semidirect
2. #19145401C2semidirect
3. #19133636C2semidirect
4. #19133619C2semidirect
5. #19133534C2semidirect
6. #19133517C2semidirect
7. #19133127C2semidirect
8. #19132933C2semidirect
42. C22×Dic86D4semidirect
56. #13063304D4semidirect
68. C2×C4⋊Dic43D4semidirect
314. C43#18352semidirect

Maximal subgroups

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

subgroupindex
#191483982
#191454012
#191336362
#191336192
#191335342
#191335172
#191331272
#191329332
C43×#26352
#1835243