Finite Group Databasebeta

← #25148710

Subgroups — #25148710

Order 11008.

664 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145137C211yesmaximal, characteristic, complemented
2#19144394C211yesmaximal, characteristic
3C2×#14583176C211yesmaximal, characteristic
4#19143542C211yesmaximal, characteristic, complemented
5#19136104C212yesmaximal, complemented
6#19135956C212yesmaximal
7#19135379C212yesmaximal, complemented
8#19135368C211yesmaximal, characteristic, complemented
9#19135255C212yesmaximal
10C4×#13063241C211yesmaximal, characteristic
11C43×#1997C211yesmaximal, characteristic, complemented
12#14583456C2211yescharacteristic
13C2×C4×D172C2211yescharacteristic
14#14583305—22no—
15#14583302—21no—
16#14583295—21no—
17#14583200—22no—
18#14583190—21no—
19#14583180—21no—
20#14583176—21no—
21#14583176—22no—
22#14583176—21no—
23#14583029—21no—
24#14583027—22no—
25C8×Dic86—21no—
26C2×#13063260C2212yes—
27#14582941C2212yes—
28#14582939C2212yes—
29#14582939C2212yes—
30C2×#13063258C2212yes—
31#14582927C2212yes—
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33#14582905C2212yes—
34C2×#13063245C2212yes—
35C2×#13063241C2211yescharacteristic
36C2×#13063241C2211yescharacteristic
37#14582857C2212yes—
38C4×#10621877C2211yescharacteristic
39#14582667C2211yescharacteristic
40#14582667C2211yescharacteristic
41#14582663C2212yes—
42C2×C4⋊Q8×C43C2211yescharacteristic
43C43×#423C2211yescharacteristic
44C4×M16×C43C2211yescharacteristic
45C43×#343C2212yes—
46C43×#343C2212yes—
47C22×D172C2311yescharacteristic
48C22×C4×D43—21no—
49C2×#10621877C2311yescharacteristic
50C2×#10621877C2311yescharacteristic
51C22×C43⋊C8C2312yes—
52#13063325D411yescharacteristic
53#13063325D411yescharacteristic
54#13063317D412yes—
55#13063304—21no—
56#13063304—21no—
57C4×Dic86—21no—
58C4×Dic86—21no—
59C4×D172—21no—
60C4×D172—21no—
61C4×D172—21no—
62C4×D172—21no—
63#13063284C2312yes—
64C2×C4⋊Dic43C2311yescharacteristic
65C2×(C2×D43)⋊C4—21no—
66#13063260—24no—
67#13063259—22no—
68#13063258—22no—
69#13063258—22no—
70#13063258—22no—
71#13063258—22no—
72#13063257—22no—
73#13063256—22no—
74#13063256—22no—
75C4⋊(C43⋊C8)D411yescharacteristic
76C4⋊(C43⋊C8)D412yes—
77C4⋊(C43⋊C8)D411yescharacteristic
78Dic43⋊C8—22no—
79Dic43⋊C8—22no—
80#13063247—22no—
81#13063247—22no—
82#13063245—22no—
83#13063245—22no—
84#13063241—22no—
85#13063241Q814yescomplemented
86#13063236—21no—
87#13063235—22no—
88C4×C43⋊C8—21no—
89C8×Dic43—22no—
90C22×Q8×C43—21no—
91C2×M16×C43C2311yescharacteristic
92C2×M16×C43C2312yes—
93C2×M16×C43C2311yescharacteristic
94C4⋊Q8×C43—21no—
95C4⋊Q8×C43—21no—
96C4⋊Q8×C43—21no—
97C4⋊Q8×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43C2312yes—
100C2×C42×C43C2311yescharacteristic
101C4⋊C8×C43—21no—
102C4⋊C8×C43—21no—
103#97×C43—21no—
104C4×C8×C43—21no—
105C23×D43—21no—
106C2×Q8×C43—41no—
107C2×Q8×C43—41no—
108C2×Q8×C43—82no—
109C22×C4×C43—22no—
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43C2411yescharacteristic
113C22×Dic43—21no—
114C2×D172—21no—
115C2×D172—21no—
116C2×D172—21no—
117C2×D172—21no—
118C2×D172—21no—
119C2×D172C2×Q812yes—
120C2×C4×D43—41no—
121C2×C4×D43—41no—
122C2×C4×D43—82no—
123C2×Dic86—21no—
124C2×Dic86—21no—
125M16×C43—21no—
126M16×C43—21no—
127M16×C43—22no—
128M16×C43—22no—
129M16×C43—21no—
130M16×C43C2×Q812yes—
131C2×C8×C43—21no—
132C2×C8×C43—21no—
133C2×C8×C43—22no—
134C4⋊C4×C43—22no—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—41no—
137C4⋊C4×C43—41no—
138C42×C43C2×D411yescharacteristic
139C42×C43C2×D411yescharacteristic
140C42×C43C2×D411yescharacteristic
141C42×C43C2×D411yescharacteristic
142C22⋊Dic43—22no—
143(C2×D43)⋊C4—41no—
144(C2×D43)⋊C4—41no—
145C4⋊Dic43—21no—
146C4⋊Dic43—21no—
147C4⋊Dic43—21no—
148C4⋊Dic43—21no—
149C4⋊Dic43C2×D412yes—
150C4⋊Dic43C2×D412yes—
151Dic43⋊C4—22no—
152Dic43⋊C4—22no—
153C4×Dic43—22no—
154#10621877—21no—
155#10621877—21no—
156#10621877C2×Q812yes—
157#10621877#4112yes—
158C2×C43⋊C8—21no—
159C2×C43⋊C8—21no—
160C2×C43⋊C8—22no—
161C2×C43⋊C8—22no—
162C2×C43⋊C8C2×D412yes—
163C2×C43⋊C8C2×D412yes—
164C23×C43C2×#4111yescharacteristic
165C22×D43—22no—
166C22×D43—41no—
167C22×D43—41no—
168C22×D43—81no—
169C22×D43—81no—
170Q8×C43—82no—
171Q8×C43—82no—
172C2×C4×C43—22no—
173C2×C4×C43—41no—
174C2×C4×C43—42no—
175C2×C4×C43—82no—
176C2×C4×C43#12111yescharacteristic
177C2×C4×C43#12111yescharacteristic
178C2×C4×C43#12111yescharacteristic
179C2×C4×C43#12111yescharacteristic
180C2×C4×C43C22×D411yescharacteristic
181C2×C4×C43C22×D411yescharacteristic
182C2×C4×C43C22×Q811yescharacteristic
183C2×C4×C43C2×#4111yescharacteristic
184C2×C4×C432−1+411yescharacteristic
185C2×C4×C432−1+411yescharacteristic
186C2×Dic43—22no—
187C2×Dic43—22no—
188C2×Dic43—41no—
189C2×Dic43—81no—
190D172—22no—
191D172—22no—
192D172—41no—
193D172—41no—
194C4×D43—82no—
195C4×D43—82no—
196Dic86—42no—
197Dic86—81no—
198C8×C43—22no—
199C8×C43—41no—
200C8×C43—42no—
201C43⋊C8—22no—
202C43⋊C8—22no—
203C43⋊C8—22no—
204C43⋊C8—22no—
205#25489—431nomaximal, Sylow
206C22×C43—21no—
207C22×C43—21no—
208C22×C43C2×#12111yescharacteristic
209C22×C43#53311yescharacteristic
210C22×C43#54111yescharacteristic
211C2×D43—42no—
212C2×D43—82no—
213C2×D43—81no—
214C2×D43—81no—
215C2×D43—82no—
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—21no—
219C4×C43—82no—
220C4×C43#47212yes—
221C4×C43#54711yescharacteristic
222C4×C43#54811yescharacteristic
223C4×C43D4×Q811yescharacteristic
224C4×C43D4×Q811yescharacteristic
225Dic43—42no—
226Dic43—42no—
227Dic43—81no—
228#3165—431no—
229#3077—431no—
230C2×#474—431no—
231#2962—431no—
232#2089—432no—
233#2063—432no—
234#1997D4311yescharacteristic, complemented
235#1952—432no—
236#1950—431no—
237#1931—432no—
238C4×#100—431no—
239C2×C43—21no—
240C2×C43—21no—
241C2×C43#242911yescharacteristic
242C2×C43C2×#47211yescharacteristic
243C2×C43#306911yescharacteristic
244D43—82no—
245#533—431no—
246C2×C4⋊Q8C2×D4311yescharacteristic
247C2×C4×D4—431no—
248#501—862no—
249#500—861no—
250#498—861no—
251#478—862no—
252#476—861no—
253#474—861no—
254#474—861no—
255#474—862no—
256#474—861no—
257#446—861no—
258#446—862no—
259C8×Q8—861no—
260C2×#108—432no—
261#428—432no—
262#428—432no—
263#428—432no—
264C2×#107—432no—
265#424—432no—
266#423C2×D4311yescharacteristic
267C2×C4⋊C8—431no—
268#418—432no—
269C2×#102—432no—
270C2×#100—431no—
271C2×#100—431no—
272#405—432no—
273C4×M16—431no—
274C4×M16C2×D4311yescharacteristic
275#343—431no—
276#343—431no—
277#343C2×D4312yes—
278#343C2×D4312yes—
279#341—432no—
280C43#2548911yescharacteristic, complemented, Sylow
281C22×Q8—21no—
282C22×D4—431no—
283C23×C4—861no—
284C2×M16—431no—
285C2×M16—431no—
286C2×M16C22×D4312yes—
287C2×M16C22×D4311yescharacteristic
288C2×M16C22×D4311yescharacteristic
289C22×C8—432no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—431no—
295C4⋊Q8—431no—
296#125—432no—
297C22⋊Q8—861no—
298C22⋊Q8—861no—
299C4×Q8—861no—
300C4×Q8—861no—
301C4×D4—861no—
302C4×D4—861no—
303C4×D4—861no—
304C4×D4—861no—
305#117—432no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—431no—
308C2×C4⋊C4C22×D4312yes—
309C2×C22⋊C4—861no—
310C2×C42C22×D4311yescharacteristic
311#108—864no—
312#107—862no—
313#107—862no—
314#107—862no—
315#107—862no—
316#107—862no—
317#106—862no—
318#106—862no—
319#106—862no—
320C4⋊C8—21no—
321C4⋊C8—21no—
322C4⋊C8—431no—
323C4⋊C8—431no—
324C4⋊C8—432no—
325C4⋊C8—862no—
326C4⋊C8—862no—
327#102—862no—
328#102—862no—
329#102—862no—
330#102—862no—
331#100—434no—
332#100—862no—
333#97—21no—
334#97—862no—
335#97—861no—
336C4×C8—21no—
337C4×C8—862no—
338C4×C8—861no—
339C24—861no—
340C2×Q8—41no—
341C2×Q8—41no—
342C2×Q8—82no—
343C2×Q8—861no—
344C2×Q8—861no—
345C2×D4—432no—
346C2×D4—861no—
347C2×D4—861no—
348C2×D4—861no—
349C2×D4—861no—
350C2×D4—861no—
351C22×C4—22no—
352C22×C4—861no—
353C22×C4—3442no—
354C22×C4—1721no—
355C22×C4—1721no—
356C22×C4#1062189811yescharacteristic
357C22×C4#1062189811yescharacteristic
358C22×C4C23×D4311yescharacteristic
359M16—21no—
360M16—21no—
361M16—22no—
362M16—22no—
363M16—21no—
364M16—432no—
365M16—432no—
366M16—861no—
367M16—861no—
368M16Q8×D4312yes—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—22no—
372C2×C8—432no—
373C2×C8—432no—
374C2×C8—861no—
375C2×C8—861no—
376C2×C8—862no—
377C2×C8—862no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—432no—
383C4⋊C4—432no—
384C4⋊C4—862no—
385C4⋊C4—862no—
386C4⋊C4—861no—
387C4⋊C4—861no—
388C4⋊C4—861no—
389C4⋊C4—861no—
390C22⋊C4—862no—
391C22⋊C4—1721no—
392C22⋊C4—1721no—
393C42—862no—
394C42D4×D4311yescharacteristic
395C42D4×D4311yescharacteristic
396C42D4×D4311yescharacteristic
397C42D4×D4311yescharacteristic
398C23—862no—
399C23—3441no—
400C23—3441no—
401C23—1721no—
402C23—1721no—
403C23C2×#1062189811yescharacteristic
404Q8—82no—
405Q8—82no—
406Q8—3441no—
407Q8—1722no—
408D4—862no—
409D4—862no—
410D4—1721no—
411D4—1721no—
412C2×C4—22no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—82no—
416C2×C4—862no—
417C2×C4—862no—
418C2×C4—3442no—
419C2×C4—3442no—
420C2×C4—3441no—
421C2×C4—1721no—
422C2×C4#1306329811yescharacteristic
423C2×C4#1306329811yescharacteristic
424C2×C4#1306329811yescharacteristic
425C2×C4#1306329811yescharacteristic
426C2×C4C2×D4×D4311yescharacteristic
427C2×C4C2×D4×D4311yescharacteristic
428C2×C4C2×Q8×D4311yescharacteristic
429C2×C4#41×D4311yescharacteristic
430C2×C4#1306337211yescharacteristic
431C2×C4#1306337311yescharacteristic
432C8—22no—
433C8—42no—
434C8—41no—
435C8—862no—
436C8—862no—
437C8—862no—
438C8—862no—
439C22—21no—
440C22—21no—
441C22—3442no—
442C22—3442no—
443C22—3441no—
444C22—3441no—
445C22—1722no—
446C22C2×#1306329811yescharacteristic
447C22#1458345311yescharacteristic
448C22#1458350711yescharacteristic
449C4—21no—
450C4—21no—
451C4—21no—
452C4—82no—
453C4—3441no—
454C4—1722no—
455C4—1722no—
456C4#1458316812yes—
457C4#1458355111yescharacteristic
458C4#1458355711yescharacteristic
459C4#1458356211yescharacteristic
460C4#1458356411yescharacteristic
461C2—21no—
462C2—21no—
463C2—3442no—
464C2#1913819511yescharacteristic
465C2C2×#1458316811yescharacteristic
466C2#1914433111yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1997C2
socleC22×C43C2×#121
prime radicalC22×D172C23
hypercenter#1997D43
hypocenterC43#25489
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
1. #19145137C2semidirect
4. #19143542C2semidirect
5. #19136104C2semidirect
7. #19135379C2semidirect
8. #19135368C2semidirect
11. C43×#1997C2semidirect
85. #13063241Q8semidirect
234. #1997D43semidirect
280. C43#25489semidirect

Maximal subgroups

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

subgroupindex
#191451372
#191443942
C2×#145831762
#191435422
#191361042
#191359562
#191353792
#191353682
#191352552
C4×#130632412
C43×#19972
#2548943