Finite Group Databasebeta

← #25000108

Subgroups — #25000108

Order 11008.

614 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#19139511C211yesmaximal, characteristic
2#19134592C211yesmaximal, characteristic, complemented
3#19134592C211yesmaximal, characteristic, complemented
4C2×#14582628C211yesmaximal, characteristic, complemented
5C2×#14582628C211yesmaximal, characteristic, complemented
6#19132478C211yesmaximal, characteristic, complemented
7C43×#1834C211yesmaximal, characteristic, complemented
8C2×#13063300—21no—
9C2×#13063300—21no—
10C2×C4×D172C2211yescharacteristic
11C2×C4×D172C2211yescharacteristic
12C2×C4⋊(C43⋊C8)C2211yescharacteristic
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×#13063245—21no—
15C2×#13063245—21no—
16#14582816—22no—
17#14582756—21no—
18#14582756—21no—
19#14582661—21no—
20#14582661—21no—
21#14582628—22no—
22#14582628—22no—
23C2×C4×C8×C43C2211yescharacteristic
24C43×#384C2211yescharacteristic
25C43×#384C2211yescharacteristic
26C43×#340—22no—
27C22×D172—22no—
28C22×D172D411yescharacteristic
29C22×D172D411yescharacteristic
30C22×C4×D43—21no—
31C22×C4×D43—21no—
32C22×C43⋊C8—21no—
33C22×C43⋊C8—21no—
34#13063300—42no—
35#13063300—42no—
36#13063300—42no—
37#13063300—42no—
38C4×D172—21no—
39C4×D172—21no—
40C4×D172—21no—
41C4×D172—21no—
42C4×D172—21no—
43C4×D172—21no—
44C4×D172—21no—
45C4×D172—21no—
46C2×C4⋊Dic43D411yescharacteristic
47C2×C4⋊Dic43D411yescharacteristic
48C2×(C2×D43)⋊C4—22no—
49C2×(C2×D43)⋊C4—22no—
50C2×(C2×D43)⋊C4—21no—
51C2×(C2×D43)⋊C4—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)—21no—
56#13063245—42no—
57#13063245—42no—
58C43⋊#95—22no—
59C22×C8×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43D412yes—
66C2×C42×C43C2311yescharacteristic
67C4×C8×C43—21no—
68C4×C8×C43D412yescomplemented
69C23×D43—21no—
70C23×D43—21no—
71C22×C4×C43—22no—
72C22×C4×C43—41no—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—21no—
77C22×Dic43—21no—
78C2×D172—21no—
79C2×D172—21no—
80C2×D172—21no—
81C2×D172—21no—
82C2×D172—21no—
83C2×D172—21no—
84C2×D172—21no—
85C2×D172—21no—
86C2×D172—21no—
87C2×D172—21no—
88C2×D172—44no—
89C2×D172—44no—
90C2×D172—82no—
91C2×D172D812yes—
92C2×D172SD1612yes—
93C2×C4×D43—41no—
94C2×C4×D43—41no—
95C2×C4×D43—41no—
96C2×C4×D43—41no—
97C2×C4×D43—41no—
98C2×C4×D43—41no—
99C2×C4×D43—41no—
100C2×C4×D43—41no—
101C2×C4×D43—41no—
102C2×C4×D43—41no—
103C2×C4×D43—41no—
104C2×C4×D43—41no—
105C2×C8×C43—22no—
106C2×C8×C43—41no—
107C2×C8×C43—41no—
108C4⋊C4×C43—42no—
109C4⋊C4×C43—42no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43—41no—
116C4⋊C4×C43—41no—
117C4⋊C4×C43—41no—
118C42×C43C2×D411yescharacteristic
119C42×C43#4111yescharacteristic
120C42×C43#4111yescharacteristic
121C42×C43#4111yescharacteristic
122(C2×D43)⋊C4—44no—
123(C2×D43)⋊C4—44no—
124(C2×D43)⋊C4—41no—
125(C2×D43)⋊C4—41no—
126(C2×D43)⋊C4—41no—
127(C2×D43)⋊C4—41no—
128C4⋊Dic43—21no—
129C4⋊Dic43—21no—
130C4⋊Dic43—21no—
131C4⋊Dic43—21no—
132C2×C43⋊C8—41no—
133C2×C43⋊C8—41no—
134C2×C43⋊C8—41no—
135C2×C43⋊C8—41no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8—41no—
138C23×C43#12011yescharacteristic
139C22×D43—22no—
140C22×D43—22no—
141C22×D43—41no—
142C22×D43—41no—
143C22×D43—41no—
144C22×D43—41no—
145C22×D43—41no—
146C22×D43—41no—
147C22×D43—41no—
148C22×D43—41no—
149C22×D43—41no—
150C22×D43—41no—
151C22×D43—41no—
152C22×D43—41no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—81no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43#12111yescharacteristic
164C2×C4×C43#12311yescharacteristic
165C2×C4×C43#12311yescharacteristic
166C2×C4×C43#12411yescharacteristic
167C2×C4×C43C2×D811yescharacteristic
168C2×C4×C43C2×SD1611yescharacteristic
169C2×C4×C43#13511yescharacteristic
170C2×C4×C43#13511yescharacteristic
171C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C43#13711yescharacteristic
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180C2×Dic43—41no—
181D172—22no—
182D172—22no—
183D172—22no—
184D172—22no—
185D172—41no—
186D172—41no—
187D172—41no—
188D172—41no—
189D172—88no—
190C4×D43—81no—
191C4×D43—81no—
192C4×D43—81no—
193C4×D43—81no—
194C4×D43—81no—
195C4×D43—81no—
196C4×D43—81no—
197C4×D43—81no—
198C8×C43—42no—
199C43⋊C8—81no—
200C43⋊C8—81no—
201#10431—431nomaximal, Sylow
202C22×C43#39411yescharacteristic
203C22×C43#44711yescharacteristic
204C22×C43#44911yescharacteristic
205C22×C43#45011yescharacteristic
206C22×C43#45211yescharacteristic
207C22×C43#45411yescharacteristic
208C22×C43#45511yescharacteristic
209C2×D43—42no—
210C2×D43—42no—
211C2×D43—42no—
212C2×D43—42no—
213C2×D43—42no—
214C2×D43—42no—
215C2×D43—81no—
216C2×D43—81no—
217C2×D43—81no—
218C2×D43—81no—
219C2×D43—81no—
220C2×D43—81no—
221C2×D43—81no—
222C2×D43—81no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—82no—
226C4×C43—161no—
227C4×C43#46511yescharacteristic
228C4×C43#46611yescharacteristic
229C4×C43#46811yescharacteristic
230C4×C43#46911yescharacteristic
231C4×C43#48011yescharacteristic
232C4×C43#48111yescharacteristic
233C4×C43#48211yescharacteristic
234C4×C43#48211yescharacteristic
235Dic43—81no—
236Dic43—81no—
237#2537—431no—
238#1834D4311yescharacteristic, complemented
239#1802—431no—
240#1802—431no—
241C2×D4⋊C8—431no—
242C2×D4⋊C8—431no—
243#1296—431no—
244C2×C43#162511yescharacteristic
245C2×C43#163511yescharacteristic
246C2×C43#163911yescharacteristic
247C2×C43#164611yescharacteristic
248C2×C43#203311yescharacteristic
249C2×C43#203411yescharacteristic
250C2×C43#204011yescharacteristic
251D43—82no—
252D43—82no—
253C2×#121—861no—
254C2×#121—861no—
255C2×C4×D4—431no—
256C2×C4×D4—431no—
257C2×C4⋊C8—431no—
258C2×C4⋊C8—431no—
259C2×#102—861no—
260C2×#102—861no—
261C2×C4×C8C2×D4311yescharacteristic
262#394—862no—
263#384C2×D4311yescharacteristic
264#384C2×D4311yescharacteristic
265#380—861no—
266#380—861no—
267#340—22no—
268#340—861no—
269#340—861no—
270D4⋊C8—862no—
271D4⋊C8—862no—
272C43#1043111yescharacteristic, complemented, Sylow
273C22×D4—431no—
274C22×D4—431no—
275C22×D4—862no—
276C23×C4—861no—
277C23×C4—861no—
278C22×C8—21no—
279C22×C8—861no—
280C22×C8—861no—
281#121—1722no—
282#121—1722no—
283#121—1722no—
284#121—1722no—
285C4×D4—861no—
286C4×D4—861no—
287C4×D4—861no—
288C4×D4—861no—
289C4×D4—861no—
290C4×D4—861no—
291C4×D4—861no—
292C4×D4—861no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—431no—
299C2×C4⋊C4—431no—
300C2×C4⋊C4C22⋊D4312yes—
301C2×C22⋊C4—862no—
302C2×C22⋊C4—862no—
303C2×C22⋊C4—861no—
304C2×C22⋊C4—861no—
305C2×C42C22×D4311yescharacteristic
306C4⋊C8—861no—
307C4⋊C8—861no—
308C4⋊C8—861no—
309C4⋊C8—861no—
310#102—1722no—
311#102—1722no—
312C4×C8—21no—
313C4×C8D17212yescomplemented
314#95—862no—
315C24—861no—
316C24—861no—
317C2×D4—432no—
318C2×D4—432no—
319C2×D4—861no—
320C2×D4—861no—
321C2×D4—861no—
322C2×D4—861no—
323C2×D4—861no—
324C2×D4—861no—
325C2×D4—861no—
326C2×D4—861no—
327C2×D4—861no—
328C2×D4—861no—
329C2×D4—3442no—
330C2×D4—1724no—
331C2×D4—1724no—
332C22×C4—22no—
333C22×C4—41no—
334C22×C4—861no—
335C22×C4—861no—
336C22×C4—1721no—
337C22×C4—1721no—
338C22×C4—1721no—
339C22×C4—1721no—
340C22×C4—1721no—
341C22×C4—1721no—
342C22×C4—1721no—
343C22×C4—1721no—
344C22×C4—1721no—
345C22×C4—1721no—
346C22×C4—1721no—
347C22×C4—1721no—
348C22×C4D4×D4311yescharacteristic
349C22×C4D4×D4311yescharacteristic
350C22×C4C2×C22⋊D4311yescharacteristic
351C2×C8—22no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—1721no—
355C2×C8—1721no—
356C2×C8—1721no—
357C2×C8—1721no—
358C2×C8—1721no—
359C2×C8—1721no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—861no—
371C4⋊C4—861no—
372C4⋊C4—861no—
373C4⋊C4—861no—
374C22⋊C4—1724no—
375C22⋊C4—1724no—
376C22⋊C4—1721no—
377C22⋊C4—1721no—
378C22⋊C4—1721no—
379C22⋊C4—1721no—
380C42C2×D17211yescharacteristic
381C42#1062189811yescharacteristic
382C42#1062190211yescharacteristic
383C42#1062190211yescharacteristic
384C23—862no—
385C23—862no—
386C23—1721no—
387C23—1721no—
388C23—1721no—
389C23—1721no—
390C23—1721no—
391C23—1721no—
392C23—1721no—
393C23—1721no—
394C23—1721no—
395C23—1721no—
396C23—1721no—
397C23—1721no—
398C23#1306329311yescharacteristic
399D4—862no—
400D4—862no—
401D4—862no—
402D4—862no—
403D4—3448no—
404D4—1721no—
405D4—1721no—
406D4—1721no—
407D4—1721no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—3441no—
417C2×C4—3441no—
418C2×C4—3441no—
419C2×C4—3441no—
420C2×C4—3441no—
421C2×C4—3441no—
422C2×C4—3441no—
423C2×C4—3441no—
424C2×C4—1721no—
425C2×C4—1721no—
426C2×C4—1721no—
427C2×C4—1721no—
428C2×C4—1721no—
429C2×C4—1721no—
430C2×C4#1306329911yescharacteristic
431C2×C4#1306330011yescharacteristic
432C2×C4#1306330011yescharacteristic
433C2×C4#1306331011yescharacteristic
434C2×C4#1306331011yescharacteristic
435C2×C4#1306331411yescharacteristic
436C2×C4D8×D4311yescharacteristic
437C2×C4SD16×D4311yescharacteristic
438C2×C4#1306334611yescharacteristic
439C2×C4#1306334811yescharacteristic
440C2×C4#1306334911yescharacteristic
441C2×C4#1306335211yescharacteristic
442C2×C4#1306335211yescharacteristic
443C2×C4#1306335711yescharacteristic
444C8—42no—
445C8—3441no—
446C8—3441no—
447C22—3441no—
448C22—3441no—
449C22—3441no—
450C22—3441no—
451C22—3441no—
452C22—3441no—
453C22—3441no—
454C22—3441no—
455C22—1722no—
456C22—1722no—
457C22—1722no—
458C22—1722no—
459C22—1722no—
460C22—1722no—
461C22#1458281611yescharacteristic
462C22#1458303111yescharacteristic
463C22#1458304311yescharacteristic
464C22#1458304811yescharacteristic
465C22#1458306011yescharacteristic
466C22#1458307111yescharacteristic
467C22#1458307611yescharacteristic
468C4—21no—
469C4—21no—
470C4—82no—
471C4—161no—
472C4—3441no—
473C4—3441no—
474C4#1458312911yescharacteristic
475C4#1458313611yescharacteristic
476C4#1458314611yescharacteristic
477C4#1458315311yescharacteristic
478C4#1458321411yescharacteristic
479C4#1458321911yescharacteristic
480C4#1458322511yescharacteristic
481C4#1458322611yescharacteristic
482C2—3442no—
483C2—3442no—
484C2#1913368111yescharacteristic
485C2#1913374311yescharacteristic
486C2#1913377111yescharacteristic
487C2#1913382011yescharacteristic
488C2#1913577911yescharacteristic
489C2#1913578611yescharacteristic
490C2#1913582411yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1834C2
socleC23×C43#120
prime radical#19139511C2
hypercenter#1834D43
hypocenterC43#10431
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
2. #19134592C2semidirect
3. #19134592C2semidirect
4. C2×#14582628C2semidirect
5. C2×#14582628C2semidirect
6. #19132478C2semidirect
7. C43×#1834C2semidirect
68. C4×C8×C43D4semidirect
238. #1834D43semidirect
272. C43#10431semidirect
313. C4×C8D172semidirect

Maximal subgroups

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

subgroupindex
#191395112
#191345922
C2×#145826282
#191324782
C43×#18342
#1043143