Finite Group Databasebeta

← #25146378

Subgroups — #25146378

Order 11008.

712 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144975C211yesmaximal, characteristic, complemented
2#19144394C211yesmaximal, characteristic
3C2×#14583101C211yesmaximal, characteristic
4#19143542C211yesmaximal, characteristic, complemented
5#19135958C212yesmaximal, complemented
6#19135854C212yesmaximal
7#19135499C212yesmaximal
8#19135368C211yesmaximal, characteristic, complemented
9#19135252C212yesmaximal, complemented
10C4×#13063241C211yesmaximal, characteristic
11C43×#1966C211yesmaximal, characteristic, complemented
12C22×#10621884C2212yes—
13#14583456C2211yescharacteristic
14C2×C4×D172C2211yescharacteristic
15#14583267—22no—
16#14583249—21no—
17#14583249—21no—
18#14583200—22no—
19#14583190—21no—
20#14583180—21no—
21#14583101—21no—
22#14583101—22no—
23#14583101—21no—
24#14583029—21no—
25#14583027—22no—
26C8×Dic86—21no—
27C2×#13063260C2212yes—
28#14582941C2212yes—
29#14582927C2212yes—
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31#14582908C2212yes—
32#14582908C2212yes—
33#14582905C2212yes—
34C2×#13063249C2212yes—
35C2×#13063241C2211yescharacteristic
36C2×#13063241C2211yescharacteristic
37#14582857C2212yes—
38C4×#10621877C2211yescharacteristic
39#14582667C2211yescharacteristic
40#14582667C2211yescharacteristic
41#14582663C2212yes—
42C2×C4⋊Q8×C43C2211yescharacteristic
43C43×#423C2211yescharacteristic
44C2×#101×C43C2212yes—
45C2×#101×C43C2212yes—
46C4×M16×C43C2211yescharacteristic
47C22×D172C2311yescharacteristic
48C22×C4×D43—21no—
49C2×#10621884—24no—
50C2×#10621884—22no—
51C2×#10621884—22no—
52C2×#10621884—42no—
53C2×#10621877C2311yescharacteristic
54C2×#10621877C2311yescharacteristic
55C22×C43⋊C8C2312yes—
56#13063325D411yescharacteristic
57#13063325D411yescharacteristic
58#13063317D412yes—
59#13063304—21no—
60#13063304—21no—
61C4×Dic86—21no—
62C4×Dic86—21no—
63C4×D172—21no—
64C4×D172—21no—
65C4×D172—21no—
66C4×D172—21no—
67#13063284C2312yes—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×(C2×D43)⋊C4—21no—
70#13063260—42no—
71#13063259—22no—
72#13063257—22no—
73C4⋊(C43⋊C8)D411yescharacteristic
74C4⋊(C43⋊C8)D412yes—
75C4⋊(C43⋊C8)D411yescharacteristic
76Dic43⋊C8—22no—
77Dic43⋊C8—22no—
78#13063249—22no—
79#13063249—22no—
80#13063249—22no—
81#13063249—22no—
82#13063249—22no—
83#13063249—22no—
84#13063247—22no—
85#13063247—22no—
86#13063241—22no—
87#13063241—22no—
88#13063236—21no—
89#13063235—22no—
90C4×C43⋊C8—21no—
91C8×Dic43—22no—
92C22×Q8×C43C2312yes—
93C2×M16×C43C2311yescharacteristic
94C2×M16×C43C2312yes—
95C2×M16×C43C2311yescharacteristic
96C4⋊Q8×C43—21no—
97C4⋊Q8×C43—21no—
98C4⋊Q8×C43—21no—
99C4⋊Q8×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C42×C43C2311yescharacteristic
103C4⋊C8×C43—21no—
104C4⋊C8×C43—21no—
105#101×C43—24no—
106#101×C43—42no—
107#97×C43—21no—
108C4×C8×C43—21no—
109C23×D43—21no—
110C2×Q8×C43—22no—
111C2×Q8×C43—22no—
112C2×Q8×C43—22no—
113C2×Q8×C43—22no—
114C2×Q8×C43—22no—
115C2×Q8×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43#4111yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C22×C4×C43C2411yescharacteristic
120C22×Dic43—21no—
121C2×D172—21no—
122C2×D172—21no—
123C2×D172—21no—
124C2×D172—21no—
125C2×D172—21no—
126C2×D172#4112yes—
127C2×C4×D43—41no—
128C2×C4×D43—41no—
129C2×C4×D43—82no—
130C2×Dic86—21no—
131C2×Dic86—21no—
132M16×C43—21no—
133M16×C43—22no—
134M16×C43—21no—
135M16×C43—21no—
136M16×C43—22no—
137M16×C43#4112yes—
138C2×C8×C43—21no—
139C2×C8×C43—21no—
140C2×C8×C43—22no—
141C4⋊C4×C43—41no—
142C4⋊C4×C43—41no—
143C4⋊C4×C43—41no—
144C4⋊C4×C43—41no—
145C42×C43C2×D411yescharacteristic
146C42×C43C2×D411yescharacteristic
147C42×C43C2×D411yescharacteristic
148C42×C43C2×D411yescharacteristic
149C22⋊Dic43—22no—
150#10621884—44no—
151#10621884—44no—
152(C2×D43)⋊C4—41no—
153(C2×D43)⋊C4—41no—
154C4⋊Dic43—21no—
155C4⋊Dic43—21no—
156C4⋊Dic43—21no—
157C4⋊Dic43—21no—
158C4⋊Dic43C2×D412yes—
159C4⋊Dic43C2×D412yes—
160Dic43⋊C4—22no—
161Dic43⋊C4—22no—
162C4×Dic43—22no—
163#10621877—21no—
164#10621877—21no—
165#10621877—21no—
166#10621877—21no—
167C2×C43⋊C8—22no—
168C2×C43⋊C8—22no—
169C2×C43⋊C8—21no—
170C2×C43⋊C8—21no—
171C2×C43⋊C8C2×D412yes—
172C2×C43⋊C8C2×D412yes—
173C23×C43C2×#4111yescharacteristic
174C22×D43—22no—
175C22×D43—41no—
176C22×D43—41no—
177C22×D43—81no—
178C22×D43—81no—
179Q8×C43—42no—
180Q8×C43—42no—
181Q8×C43—42no—
182Q8×C43—42no—
183C2×C4×C43—22no—
184C2×C4×C43—41no—
185C2×C4×C43—42no—
186C2×C4×C43—42no—
187C2×C4×C43—42no—
188C2×C4×C43#12111yescharacteristic
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43#12111yescharacteristic
191C2×C4×C43#12111yescharacteristic
192C2×C4×C43C22×D411yescharacteristic
193C2×C4×C43C22×D411yescharacteristic
194C2×C4×C43C2×#4111yescharacteristic
195C2×C4×C43C2×#4111yescharacteristic
196C2×C4×C43H(5,𝔽2)11yescharacteristic
197C2×C4×C432−1+411yescharacteristic
198C2×Dic43—22no—
199C2×Dic43—22no—
200C2×Dic43—41no—
201C2×Dic43—81no—
202D172—22no—
203D172—22no—
204D172—41no—
205D172—41no—
206C4×D43—82no—
207C4×D43—82no—
208Dic86—42no—
209Dic86—81no—
210C8×C43—22no—
211C8×C43—41no—
212C8×C43—42no—
213C43⋊C8—22no—
214C43⋊C8—22no—
215C43⋊C8—41no—
216C43⋊C8—41no—
217#25313—431nomaximal, Sylow
218C22×C43—21no—
219C22×C43—21no—
220C22×C43C2×#12111yescharacteristic
221C22×C43#52911yescharacteristic
222C22×C43#54211yescharacteristic
223C2×D43—42no—
224C2×D43—82no—
225C2×D43—81no—
226C2×D43—81no—
227C2×D43—82no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—82no—
232C4×C43#47112yes—
233C4×C43#54611yescharacteristic
234C4×C43#54811yescharacteristic
235C4×C43#54811yescharacteristic
236C4×C43#55011yescharacteristic
237Dic43—42no—
238Dic43—42no—
239Dic43—81no—
240#3139—431no—
241#3077—431no—
242C2×#461—431no—
243#2962—431no—
244#2064—432no—
245#2046—432no—
246#1977—432no—
247#1966D4311yescharacteristic, complemented
248#1950—431no—
249#1930—432no—
250C4×#100—431no—
251C2×C43—21no—
252C2×C43—21no—
253C2×C43#242611yescharacteristic
254C2×C43C2×#47111yescharacteristic
255C2×C43#306911yescharacteristic
256D43—82no—
257C22×SD16—432no—
258#533—431no—
259C2×C4⋊Q8C2×D4311yescharacteristic
260C2×C4×D4—431no—
261#491—862no—
262#487—861no—
263#487—861no—
264#478—862no—
265#476—861no—
266#474—861no—
267#461—861no—
268#461—862no—
269#461—861no—
270#446—861no—
271#446—862no—
272C8×Q8—861no—
273C2×#108—432no—
274#428—432no—
275#424—432no—
276#423C2×D4311yescharacteristic
277C2×C4⋊C8—431no—
278#419—432no—
279#419—432no—
280#418—432no—
281C2×#103—432no—
282C2×#101C2×D4312yes—
283C2×#101C2×D4312yes—
284C2×#100—431no—
285C2×#100—431no—
286#405—432no—
287C4×M16—431no—
288C4×M16C2×D4311yescharacteristic
289#343—431no—
290#343—431no—
291#341—432no—
292C43#2531311yescharacteristic, complemented, Sylow
293C22×Q8C22×D4312yes—
294C22×D4—431no—
295C23×C4—861no—
296C2×SD16—862no—
297C2×SD16—862no—
298C2×SD16—864no—
299C2×SD16—1722no—
300C2×M16—431no—
301C2×M16—431no—
302C2×M16C22×D4312yes—
303C2×M16C22×D4311yescharacteristic
304C2×M16C22×D4311yescharacteristic
305C22×C8—432no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—431no—
311C4⋊Q8—431no—
312#125—432no—
313C22⋊Q8—861no—
314C22⋊Q8—861no—
315C4×Q8—861no—
316C4×Q8—861no—
317C4×D4—861no—
318C4×D4—861no—
319C4×D4—861no—
320C4×D4—861no—
321#117—432no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—431no—
325C2×C22⋊C4—861no—
326C2×C42C22×D4311yescharacteristic
327#108—1722no—
328#107—862no—
329#106—862no—
330C4⋊C8—21no—
331C4⋊C8—21no—
332C4⋊C8—431no—
333C4⋊C8—431no—
334C4⋊C8—432no—
335C4⋊C8—862no—
336C4⋊C8—862no—
337#103—862no—
338#103—862no—
339#103—862no—
340#103—862no—
341#103—862no—
342#103—862no—
343#102—862no—
344#102—862no—
345#101—24no—
346#101—42no—
347#100—862no—
348#100—862no—
349#97—21no—
350#97—862no—
351#97—861no—
352C4×C8—21no—
353C4×C8—862no—
354C4×C8—861no—
355C24—861no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—861no—
363C2×Q8—861no—
364C2×D4—432no—
365C2×D4—861no—
366C2×D4—861no—
367C2×D4—861no—
368C2×D4—861no—
369C2×D4—861no—
370C22×C4—22no—
371C22×C4—861no—
372C22×C4—3442no—
373C22×C4—1721no—
374C22×C4—1721no—
375C22×C4#1062189811yescharacteristic
376C22×C4#1062189811yescharacteristic
377C22×C4C23×D4311yescharacteristic
378SD16—1724no—
379SD16—1724no—
380M16—21no—
381M16—21no—
382M16—22no—
383M16—21no—
384M16—22no—
385M16—861no—
386M16—861no—
387M16—861no—
388M16—861no—
389M16#1062190012yes—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—22no—
393C2×C8—432no—
394C2×C8—432no—
395C2×C8—862no—
396C2×C8—862no—
397C2×C8—861no—
398C2×C8—861no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4—432no—
404C4⋊C4—432no—
405C4⋊C4—862no—
406C4⋊C4—862no—
407C4⋊C4—861no—
408C4⋊C4—861no—
409C4⋊C4—861no—
410C4⋊C4—861no—
411C22⋊C4—862no—
412C22⋊C4—1721no—
413C22⋊C4—1721no—
414C42—862no—
415C42D4×D4311yescharacteristic
416C42D4×D4311yescharacteristic
417C42D4×D4311yescharacteristic
418C42D4×D4311yescharacteristic
419C23—862no—
420C23—3441no—
421C23—3441no—
422C23—1721no—
423C23—1721no—
424C23C2×#1062189811yescharacteristic
425Q8—42no—
426Q8—42no—
427Q8—42no—
428Q8—42no—
429Q8—3441no—
430Q8—1722no—
431D4—862no—
432D4—862no—
433D4—1721no—
434D4—1721no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—862no—
441C2×C4—862no—
442C2×C4—3442no—
443C2×C4—3442no—
444C2×C4—3441no—
445C2×C4—1721no—
446C2×C4#1306329811yescharacteristic
447C2×C4#1306329811yescharacteristic
448C2×C4#1306329811yescharacteristic
449C2×C4#1306329811yescharacteristic
450C2×C4C2×D4×D4311yescharacteristic
451C2×C4C2×D4×D4311yescharacteristic
452C2×C4#41×D4311yescharacteristic
453C2×C4C2×#1062190011yescharacteristic
454C2×C4#1306337011yescharacteristic
455C2×C4#1306337211yescharacteristic
456C8—22no—
457C8—42no—
458C8—41no—
459C8—862no—
460C8—862no—
461C8—1721no—
462C8—1721no—
463C22—21no—
464C22—21no—
465C22—3442no—
466C22—3442no—
467C22—3441no—
468C22—3441no—
469C22—1722no—
470C22C2×#1306329811yescharacteristic
471C22#1458343111yescharacteristic
472C22#1458351411yescharacteristic
473C4—21no—
474C4—21no—
475C4—21no—
476C4—82no—
477C4—3441no—
478C4—1722no—
479C4—1722no—
480C4#1458316512yes—
481C4#1458354611yescharacteristic
482C4#1458355511yescharacteristic
483C4#1458355711yescharacteristic
484C4#1458356911yescharacteristic
485C2—21no—
486C2—21no—
487C2—3442no—
488C2#1913816211yescharacteristic
489C2C2×#1458316511yescharacteristic
490C2#1914433111yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1966C2
socleC22×C43C2×#121
prime radicalC22×D172C23
hypercenter#1966D43
hypocenterC43#25313
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1966

Complements

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

NH ≅ G/Ntype
1. #19144975C2semidirect
4. #19143542C2semidirect
5. #19135958C2semidirect
8. #19135368C2semidirect
9. #19135252C2semidirect
11. C43×#1966C2semidirect
247. #1966D43semidirect
292. C43#25313semidirect

Maximal subgroups

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

subgroupindex
#191449752
#191443942
C2×#145831012
#191435422
#191359582
#191358542
#191354992
#191353682
#191352522
C4×#130632412
C43×#19662
#2531343