Finite Group Databasebeta

← #25069141

Subgroups — #25069141

Order 11008.

960 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148000C211yesmaximal, characteristic, complemented
2#19144694C212yesmaximal, complemented
3#19133636C212yesmaximal, complemented
4#19133619C212yesmaximal, complemented
5#19133534C212yesmaximal, complemented
6#19133517C212yesmaximal
7#19133145C212yesmaximal, complemented
8#19132929C211yesmaximal, characteristic, complemented
9C43×#2598C211yesmaximal, characteristic
10#14583530—21no—
11#14583530C2212yes—
12#14583527—22no—
13#14583527—22no—
14#14583525—21no—
15#14583525C2212yes—
16#14583456—21no—
17#14583456C2212yes—
18#14583452—24no—
19C2×#13063284—21no—
20#14583234C2214yes—
21#14583179—22no—
22#14583104—22no—
23#14583050C2214yes—
24#14582999—24no—
25#14582956C2212yes—
26#14582635C2214yes—
27#14582635C2214yes—
28#14582625C2212yes—
29#14582623C2212yes—
30C2×C4×D4×C43C2211yescharacteristic
31C2×#117×C43C2211yescharacteristic
32C43×#400C2211yescharacteristic
33C43×#399C2211yescharacteristic
34C43×#394C2211yescharacteristic
35C43×#392C2211yescharacteristic
36C43×#388—21no—
37C43×#386—21no—
38C43×#386—21no—
39C43×#385—21no—
40C43×#383C2211yescharacteristic
41C2×#10621883—24no—
42#13063325—21no—
43#13063325—21no—
44#13063325D412yescomplemented
45#13063325D412yescomplemented
46#13063324—24no—
47#13063324—24no—
48#13063317—22no—
49#13063317—22no—
50#13063316—24no—
51#13063316—24no—
52#13063304—22no—
53#13063304—22no—
54#13063304—22no—
55#13063304C2314yes—
56#13063302—24no—
57#13063302—24no—
58#13063302—24no—
59#13063302—24no—
60C4×Dic86—22no—
61C4×Dic86—22no—
62C4×Dic86—22no—
63C4×Dic86D414yescomplemented
64#13063284—22no—
65#13063284—22no—
66#13063284—22no—
67#13063284—22no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C22⋊Dic43—22no—
71C2×C4×Dic43—22no—
72#13063258—24no—
73C4⋊(C43⋊C8)—22no—
74#13063248—24no—
75#13063246—24no—
76C22⋊(C43⋊C8)C2314yes—
77#13063236—22no—
78C22×D4×C43—21no—
79C22×D4×C43C2311yescharacteristic
80C23×C4×C43—21no—
81C23×C4×C43D411yescharacteristic
82C4×D4×C43—22no—
83C4×D4×C43—22no—
84#117×C43—22no—
85#117×C43—22no—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43D411yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43D411yescharacteristic
96C2×C22⋊C4×C43C2311yescharacteristic
97C2×C42×C43D411yescharacteristic
98C2×C42×C43C2311yescharacteristic
99#95×C43—21no—
100#95×C43—21no—
101#95×C43—21no—
102#95×C43—21no—
103#95×C43C2311yescharacteristic
104#95×C43C2311yescharacteristic
105C24×C43—21no—
106C24×C43C2×D411yescharacteristic
107C2×D4×C43—22no—
108C2×D4×C43—42no—
109C2×D4×C43—42no—
110C2×D4×C43—42no—
111C2×D4×C43—81no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—42no—
120C22×C4×C43—81no—
121C22×C4×C43—81no—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C22×Dic43—22no—
129C22×Dic43—22no—
130C2×Dic86—22no—
131C2×Dic86—22no—
132C2×Dic86—22no—
133C2×Dic86C2×D414yes—
134C4⋊C4×C43—22no—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—22no—
137C4⋊C4×C43—81no—
138C22⋊C4×C43—22no—
139C22⋊C4×C43—22no—
140C22⋊C4×C43—42no—
141C22⋊C4×C43—41no—
142C22⋊C4×C43—41no—
143C22⋊C4×C43—42no—
144C22⋊C4×C43—81no—
145C22⋊C4×C43—81no—
146C42×C43—21no—
147C42×C43—21no—
148C42×C43C2×D412yes—
149C42×C43C2×D412yes—
150C22⋊Dic43—24no—
151C22⋊Dic43—24no—
152#10621883—48no—
153C4⋊Dic43—22no—
154C4⋊Dic43—22no—
155C4⋊Dic43—22no—
156C4⋊Dic43—22no—
157C4⋊Dic43—22no—
158C4⋊Dic43—22no—
159C4⋊Dic43—22no—
160C4⋊Dic43C2×D414yes—
161Dic43⋊C4—24no—
162Dic43⋊C4—24no—
163Dic43⋊C4—24no—
164Dic43⋊C4—24no—
165C4×Dic43—24no—
166C4×Dic43—24no—
167C2×C43⋊C8—24no—
168C23×C43—21no—
169C23×C43—21no—
170C23×C43—22no—
171C23×C43—41no—
172C23×C43—41no—
173C23×C43—41no—
174C23×C43—41no—
175C23×C43—41no—
176C23×C43—41no—
177C23×C43—41no—
178C23×C43—41no—
179C23×C43#13712yes—
180C23×C43C22×D411yescharacteristic
181D4×C43—24no—
182D4×C43—42no—
183D4×C43—84no—
184C2×C4×C43—24no—
185C2×C4×C43—24no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—21no—
191C2×C4×C43—21no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—84no—
206C2×C4×C43#12011yescharacteristic
207C2×C4×C43#12012yes—
208C2×C4×C43#12011yescharacteristic
209C2×C4×C43#13712yes—
210C2×C4×C43C22×D412yes—
211C2×Dic43—24no—
212C2×Dic43—24no—
213C2×Dic43—82no—
214C2×Dic43—82no—
215Dic86—44no—
216Dic86—82no—
217Dic86—82no—
218Dic86—82no—
219C43⋊C8—44no—
220#18154—431nomaximal, Sylow
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—22no—
224C22×C43—42no—
225C22×C43—42no—
226C22×C43—42no—
227C22×C43—41no—
228C22×C43—41no—
229C22×C43—42no—
230C22×C43—81no—
231C22×C43—81no—
232C22×C43—81no—
233C22×C43—81no—
234C22×C43—81no—
235C22×C43C2×#12011yescharacteristic
236C22×C43C2×#13711yescharacteristic
237C22×C43C2×#13711yescharacteristic
238C4×C43—21no—
239C4×C43—21no—
240C4×C43—22no—
241C4×C43—22no—
242C4×C43—22no—
243C4×C43—41no—
244C4×C43—41no—
245C4×C43—81no—
246C4×C43—81no—
247C4×C43—81no—
248Dic43—44no—
249Dic43—44no—
250#3458—431no—
251#3110—432no—
252#2598D4311yescharacteristic
253#1617—432no—
254#1614—432no—
255#1599—432no—
256#1596—432no—
257#1515—432no—
258#1464—431no—
259C2×C43—21no—
260C2×C43—21no—
261C2×C43—42no—
262C2×C43—82no—
263C2×C43#300411yescharacteristic
264C2×C43#302111yescharacteristic
265C2×C43#302511yescharacteristic
266#544—432no—
267#544—862no—
268#544—862no—
269#544—861no—
270#543—432no—
271#543—861no—
272#533—432no—
273#533—864no—
274#533—861no—
275C2×C4×D4C2×D4311yescharacteristic
276C2×#117—861no—
277C2×#117C2×D4311yescharacteristic
278#484—434no—
279#474—862no—
280#461—862no—
281#450—434no—
282#440—864no—
283#432—432no—
284#400C2×D4311yescharacteristic
285#399C2×D4311yescharacteristic
286#394C2×D4311yescharacteristic
287#392C2×D4311yescharacteristic
288#388—21no—
289#386—21no—
290#386—21no—
291#385—21no—
292#383C2×D4311yescharacteristic
293#328—434no—
294#328—434no—
295#324—432no—
296#323—432no—
297C43#1815411yescharacteristic, complemented, Sylow
298C22×D4—21no—
299C22×D4C22×D4311yescharacteristic
300C23×C4—21no—
301C23×C4C22⋊D4311yescharacteristic
302C2×SD16—864no—
303C4⋊Q8—432no—
304C4⋊Q8—432no—
305C4⋊Q8—861no—
306C4⋊Q8—861no—
307C4⋊Q8—864no—
308C4⋊Q8—864no—
309#125—862no—
310#125—864no—
311#125—864no—
312#125—862no—
313C22⋊Q8—434no—
314C22⋊Q8—864no—
315C22⋊Q8—864no—
316C22⋊Q8—864no—
317C22⋊Q8—864no—
318C22⋊Q8—862no—
319C22⋊Q8—862no—
320C22⋊Q8—862no—
321C4×Q8—434no—
322C4×Q8—862no—
323C4×Q8—862no—
324C4×Q8—862no—
325C4×D4—22no—
326C4×D4—22no—
327#117—22no—
328#117—22no—
329#117—862no—
330#117—862no—
331#117—862no—
332#117—862no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—861no—
335C2×C4⋊C4—861no—
336C2×C4⋊C4C22⋊D4311yescharacteristic
337C2×C4⋊C4C22×D4311yescharacteristic
338C2×C4⋊C4C22×D4311yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—862no—
345C2×C22⋊C4C22⋊D4311yescharacteristic
346C2×C22⋊C4C22×D4311yescharacteristic
347C2×C42—862no—
348C2×C42C22⋊D4311yescharacteristic
349C2×C42C22×D4311yescharacteristic
350#107—864no—
351C4⋊C8—862no—
352#103—864no—
353#102—864no—
354C22⋊C8—434no—
355#97—862no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95C22×D4311yescharacteristic
361#95C22×D4311yescharacteristic
362C24—21no—
363C24C2×C22⋊D4311yescharacteristic
364C2×Q8—434no—
365C2×Q8—862no—
366C2×Q8—862no—
367C2×Q8—862no—
368C2×D4—22no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—81no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—42no—
381C22×C4—81no—
382C22×C4—81no—
383C22×C4—862no—
384C22×C4—862no—
385C22×C4C2×C22⋊D4311yescharacteristic
386C22×C4C2×C22⋊D4311yescharacteristic
387C22×C4C2×C22⋊D4311yescharacteristic
388C22×C4C2×C22⋊D4311yescharacteristic
389C22×C4C2×C22⋊D4311yescharacteristic
390C22×C4C23×D4311yescharacteristic
391SD16—1728no—
392C2×C8—864no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—81no—
397C4⋊C4—434no—
398C4⋊C4—862no—
399C4⋊C4—862no—
400C4⋊C4—864no—
401C4⋊C4—864no—
402C4⋊C4—862no—
403C4⋊C4—862no—
404C4⋊C4—862no—
405C4⋊C4—862no—
406C4⋊C4—864no—
407C4⋊C4—862no—
408C4⋊C4—864no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—42no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—42no—
415C22⋊C4—81no—
416C22⋊C4—81no—
417C22⋊C4—864no—
418C22⋊C4—864no—
419C42—21no—
420C42—21no—
421C42—864no—
422C42—864no—
423C42D4×D4312yes—
424C42D4×D4312yes—
425C23—21no—
426C23—21no—
427C23—22no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23#1306335512yes—
437C23C22×C22⋊D4311yescharacteristic
438Q8—3442no—
439Q8—3442no—
440Q8—3442no—
441Q8—1724no—
442D4—24no—
443D4—42no—
444D4—84no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—84no—
467C2×C4—864no—
468C2×C4—864no—
469C2×C4—3442no—
470C2×C4—3442no—
471C2×C4#1306329311yescharacteristic
472C2×C4#1306329311yescharacteristic
473C2×C4#1306329312yes—
474C2×C4#1306335512yes—
475C2×C4C2×D4×D4312yes—
476C8—1724no—
477C22—21no—
478C22—21no—
479C22—22no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—41no—
484C22—41no—
485C22—42no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C2×#1306329311yescharacteristic
492C22C2×#1306335511yescharacteristic
493C22C2×#1306335511yescharacteristic
494C4—22no—
495C4—22no—
496C4—21no—
497C4—21no—
498C4—22no—
499C4—41no—
500C4—41no—
501C4—81no—
502C4—81no—
503C4—81no—
504C4—1724no—
505C4—1724no—
506C2—21no—
507C2—21no—
508C2—42no—
509C2—82no—
510C2#1914382811yescharacteristic
511C2#1914396611yescharacteristic
512C2#1914398611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2598C2
socleC22×C43C2×#120
prime radicalC43×#392C22
hypercenter#2598D43
hypocenterC43#18154
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2598

Complements

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

NH ≅ G/Ntype
1. #19148000C2semidirect
2. #19144694C2semidirect
3. #19133636C2semidirect
4. #19133619C2semidirect
5. #19133534C2semidirect
7. #19133145C2semidirect
8. #19132929C2semidirect
44. #13063325D4semidirect
45. #13063325D4semidirect
63. C4×Dic86D4semidirect
297. C43#18154semidirect

Maximal subgroups

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

subgroupindex
#191480002
#191446942
#191336362
#191336192
#191335342
#191335172
#191331452
#191329292
C43×#25982
#1815443