Finite Group Databasebeta

← #24991232

Subgroups — #24991232

Order 11008.

540 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143708C211yesmaximal, characteristic, complemented
2C4×#13063351C211yesmaximal, characteristic
3#19135390C211yesmaximal, characteristic, complemented
4#19132975C211yesmaximal, characteristic, complemented
5#19132444C211yesmaximal, characteristic, complemented
6#19132431C211yesmaximal, characteristic, complemented
7C43×#1478C211yesmaximal, characteristic, complemented
8C2×#13063351C411yescharacteristic
9C4×#10621898C2211yescharacteristic
10#14583029—21no—
11#14583009—21no—
12#14582999—21no—
13C4×#10621883—21no—
14C4×#10621882—21no—
15#14582978—21no—
16#14582967—22no—
17#14582955—21no—
18#14582939C411yescharacteristic
19#14582921—21no—
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21#14582904C411yescharacteristic
22#14582898C411yescharacteristic
23C2×C22⋊(C43⋊C8)—22no—
24C4×#10621877C2211yescharacteristic
25C2×C4×C43⋊C8C2211yescharacteristic
26#14582629—21no—
27#14582626—21no—
28C2×C4×D4×C43C2211yescharacteristic
29C43×#431C2211yescharacteristic
30C43×#431C2211yescharacteristic
31C43×D4⋊C8—21no—
32C43×D4⋊C8—21no—
33C2×#10621898C2×C411yescharacteristic
34#13063351—22no—
35#13063351—22no—
36C2×#10621883—21no—
37C2×#10621882—21no—
38C2×#10621877C2×C411yescharacteristic
39C2×#10621877C2×C411yescharacteristic
40C2×#10621872—22no—
41C22×C43⋊C8—21no—
42C22×C43⋊C8D412yes—
43C4×Dic86D411yescharacteristic
44C4×Dic86D411yescharacteristic
45C4×D172D411yescharacteristic
46C4×D172D411yescharacteristic
47C4×C22⋊D43—21no—
48C4×C22⋊D43—21no—
49#13063284C2×C411yescharacteristic
50#13063282—21no—
51C42×D43—21no—
52#13063258—21no—
53#13063256—21no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)—21no—
56Dic43⋊C8—22no—
57#13063248—21no—
58#13063246—21no—
59#13063246—21no—
60#13063245—21no—
61C22⋊(C43⋊C8)—44no—
62(C2×D43)⋊C8—22no—
63#13063236—21no—
64#13063235—22no—
65C4×C43⋊C8—21no—
66C4×C43⋊C8—21no—
67C4×C43⋊C8—21no—
68C22×D4×C43C2×C411yescharacteristic
69C23×C4×C43—21no—
70C4×D4×C43—21no—
71C4×D4×C43—21no—
72C4×D4×C43—21no—
73C4×D4×C43—21no—
74C2×C4⋊C4×C43C2×C411yescharacteristic
75C2×C22⋊C4×C43—21no—
76C2×C42×C43C2311yescharacteristic
77C4⋊C8×C43—21no—
78C4⋊C8×C43D411yescharacteristic
79C4⋊C8×C43D411yescharacteristic
80C22⋊C8×C43—21no—
81C22⋊C8×C43—21no—
82C4×C8×C43—21no—
83C4×C8×C43—21no—
84C24×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—21no—
87C2×D4×C43—21no—
88C2×D4×C43—21no—
89C2×D4×C43—21no—
90C2×D4×C43M1612yescomplemented
91C22×C4×C43—21no—
92C22×C4×C43—42no—
93C22×C4×C43—42no—
94C22×C4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43C22×C411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43#4111yescharacteristic
99C2×C22⋊D43—21no—
100#10621898—21no—
101#10621898—21no—
102#10621898—21no—
103#10621898—21no—
104C2×D172C22⋊C411yescharacteristic
105C2×C4×D43—21no—
106C2×C4×D43—21no—
107C2×C4×D43—21no—
108C2×Dic86C22⋊C411yescharacteristic
109C2×C8×C43—21no—
110C2×C8×C43—21no—
111C2×C8×C43—41no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C22⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C42×C43C2×D411yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43#4111yescharacteristic
120C22⋊Dic43—21no—
121#10621883—24no—
122#10621882—24no—
123(C2×D43)⋊C4—21no—
124(C2×D43)⋊C4—21no—
125C4⋊Dic43C22⋊C411yescharacteristic
126C4⋊Dic43C22⋊C411yescharacteristic
127Dic43⋊C4—21no—
128Dic43⋊C4—21no—
129C4×Dic43—21no—
130C4×Dic43—21no—
131C4×Dic43—21no—
132#10621877—21no—
133#10621877—21no—
134#10621877—21no—
135#10621877M1612yescomplemented
136C2×C43⋊C8—21no—
137C2×C43⋊C8—22no—
138C2×C43⋊C8—21no—
139C2×C43⋊C8—22no—
140C2×C43⋊C8—41no—
141C2×C43⋊C8—41no—
142C2×C43⋊C8—42no—
143#10621872—82no—
144C23×C43—22no—
145C23×C43—42no—
146C23×C43—42no—
147C23×C43—41no—
148C23×C43—41no—
149C23×C43C4×D411yescharacteristic
150C22×D43—21no—
151D4×C43—22no—
152D4×C43—22no—
153D4×C43—41no—
154D4×C43—41no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—41no—
158C2×C4×C43—42no—
159C2×C4×C43—41no—
160C2×C4×C43—82no—
161C2×C4×C43—81no—
162C2×C4×C43—81no—
163C2×C4×C43C2×C22⋊C411yescharacteristic
164C2×C4×C43C4×D411yescharacteristic
165C2×C4×C43#12011yescharacteristic
166C2×C4×C43#12111yescharacteristic
167C2×C4×C43#12111yescharacteristic
168C2×C4×C43#12311yescharacteristic
169C2×C4×C43C2×M1611yescharacteristic
170C2×C4×C43C2×M1611yescharacteristic
171C2×C4×C43#13111yescharacteristic
172C2×C4×C43#13111yescharacteristic
173C22⋊D43—41no—
174C22⋊D43—41no—
175C2×Dic43—21no—
176C2×Dic43—21no—
177C2×Dic43—21no—
178D172—21no—
179D172—21no—
180C4×D43—41no—
181C4×D43—41no—
182C4×D43—41no—
183C4×D43—41no—
184C4×D43—81no—
185Dic86—21no—
186Dic86—21no—
187C8×C43—41no—
188C8×C43—41no—
189C8×C43—81no—
190C43⋊C8—22no—
191C43⋊C8—42no—
192C43⋊C8—41no—
193C43⋊C8—42no—
194#8956—431nomaximal, Sylow
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—44no—
198C22×C43—42no—
199C22×C43—82no—
200C22×C43—81no—
201C22×C43—81no—
202C22×C43#38611yescharacteristic
203C22×C43#43511yescharacteristic
204C22×C43#43611yescharacteristic
205C2×D43—41no—
206C2×D43—41no—
207C2×D43—41no—
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—81no—
212C4×C43#40711yescharacteristic
213C4×C43#40811yescharacteristic
214C4×C43#43511yescharacteristic
215C4×C43#43611yescharacteristic
216C4×C43#45311yescharacteristic
217C4×C43#45411yescharacteristic
218Dic43—41no—
219Dic43—41no—
220Dic43—41no—
221#2989—431no—
222C4×AGL(1,ℤ/8)—431no—
223#1954—431no—
224#1478D4311yescharacteristic, complemented
225#1476—431no—
226#1283—431no—
227#1278—431no—
228C2×C43—21no—
229C2×C43—21no—
230C2×C43—82no—
231C2×C43#187011yescharacteristic
232C2×C43#188111yescharacteristic
233C2×C43#188311yescharacteristic
234D43—81no—
235C2×AGL(1,ℤ/8)—431no—
236C4×#41—431no—
237C2×C4×D4C2×D4311yescharacteristic
238#446—861no—
239#442—861no—
240#440—861no—
241C4×SD16—861no—
242C4×D8—861no—
243#436—861no—
244#435—862no—
245#432—861no—
246#431C2×D4311yescharacteristic
247#431C2×D4311yescharacteristic
248#428—431no—
249#423—861no—
250C2×C4⋊C8—431no—
251#418—431no—
252#417—431no—
253C2×C22⋊C8—862no—
254C4×M16—431no—
255C2×C4×C8—431no—
256Q8⋊C8—861no—
257D4⋊C8—21no—
258D4⋊C8—21no—
259D4⋊C8—861no—
260C43#895611yescharacteristic, complemented, Sylow
261C2×#41—431no—
262C22×D4C4×D4311yescharacteristic
263C23×C4—21no—
264AGL(1,ℤ/8)—862no—
265AGL(1,ℤ/8)—862no—
266C2×SD16—861no—
267C2×D8—861no—
268C2×M16—431no—
269C2×M16—431no—
270C2×M16—862no—
271C22×C8—432no—
272C22×C8—861no—
273C4×Q8—431no—
274C4×Q8—431no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—431no—
280C4×D4—431no—
281C4×D4—861no—
282C4×D4—861no—
283#117—431no—
284#117—861no—
285C2×C4⋊C4C4×D4311yescharacteristic
286C2×C22⋊C4—21no—
287C2×C42—861no—
288C2×C42C22×D4311yescharacteristic
289#107—861no—
290#106—861no—
291C4⋊C8—21no—
292C4⋊C8—862no—
293C4⋊C8—861no—
294C4⋊C8—861no—
295C4⋊C8C22⋊D4311yescharacteristic
296C4⋊C8C22⋊D4311yescharacteristic
297#103—861no—
298#102—861no—
299#102—861no—
300#102—861no—
301C22⋊C8—21no—
302C22⋊C8—21no—
303C22⋊C8—862no—
304C22⋊C8—1724no—
305#97—862no—
306#97—861no—
307C4×C8—21no—
308C4×C8—21no—
309C4×C8—861no—
310C4×C8—861no—
311C4×C8—861no—
312C24—21no—
313#41—861no—
314#41—861no—
315#41—861no—
316#41—861no—
317C2×Q8—431no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—431no—
324C2×D4—861no—
325C2×D4#1062187212yescomplemented
326C22×C4—21no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—861no—
332C22×C4—861no—
333C22×C4—861no—
334C22×C4C2×C4×D4311yescharacteristic
335C22×C4D4×D4311yescharacteristic
336C22×C4#1062190011yescharacteristic
337SD16—864no—
338D8—864no—
339M16—432no—
340M16—861no—
341M16—861no—
342M16—861no—
343M16—3442no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—41no—
347C2×C8—861no—
348C2×C8—862no—
349C2×C8—861no—
350C2×C8—862no—
351C2×C8—1721no—
352C2×C8—1721no—
353C2×C8—1722no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—431no—
357C4⋊C4—431no—
358C4⋊C4—861no—
359C4⋊C4—861no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—861no—
363C22⋊C4—861no—
364C22⋊C4—861no—
365C42—861no—
366C42—861no—
367C42—861no—
368C42#1062189811yescharacteristic
369C42D4×D4311yescharacteristic
370C42D4×D4311yescharacteristic
371C42C2×C22⋊D4311yescharacteristic
372C23—22no—
373C23—42no—
374C23—42no—
375C23—41no—
376C23—41no—
377C23—861no—
378C23(C22⋊D43)⋊C411yescharacteristic
379Q8—861no—
380Q8—861no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385D4—861no—
386D4—861no—
387D4—1721no—
388D4—1721no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—82no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—861no—
398C2×C4—861no—
399C2×C4—861no—
400C2×C4—3441no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4—1721no—
404C2×C4—1721no—
405C2×C4C22⋊C4×D4311yescharacteristic
406C2×C4C4×C22⋊D4311yescharacteristic
407C2×C4#1306329311yescharacteristic
408C2×C4#1306329611yescharacteristic
409C2×C4#1306329811yescharacteristic
410C2×C4#1306330711yescharacteristic
411C2×C4M16×D4311yescharacteristic
412C2×C4C2×#1062187211yescharacteristic
413C2×C4#1306333111yescharacteristic
414C2×C4#1306333311yescharacteristic
415C8—41no—
416C8—41no—
417C8—81no—
418C8—862no—
419C8—1722no—
420C8—1722no—
421C8—1721no—
422C22—21no—
423C22—21no—
424C22—44no—
425C22—42no—
426C22—82no—
427C22—81no—
428C22—81no—
429C22—1721no—
430C22—1721no—
431C22—1721no—
432C22#1458277511yescharacteristic
433C22#1458296711yescharacteristic
434C22#1458297411yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—81no—
439C4—1721no—
440C4—1721no—
441C4—1721no—
442C4#1458286111yescharacteristic
443C4#1458286411yescharacteristic
444C4#1458297011yescharacteristic
445C4#1458297511yescharacteristic
446C4#1458306511yescharacteristic
447C4#1458307011yescharacteristic
448C2—21no—
449C2—21no—
450C2—82no—
451C2—3441no—
452C2#1913488911yescharacteristic
453C2#1913495411yescharacteristic
454C2#1913496811yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1478C2
socleC22×C43#386
prime radicalC2×#13063351C4
cosocleC2×C42×C43C23
hypercenter#1478D43
hypocenterC43#8956
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
1. #19143708C2semidirect
3. #19135390C2semidirect
4. #19132975C2semidirect
5. #19132444C2semidirect
6. #19132431C2semidirect
7. C43×#1478C2semidirect
90. C2×D4×C43M16semidirect
135. #10621877M16semidirect
224. #1478D43semidirect
260. C43#8956semidirect
325. C2×D4#10621872semidirect

Maximal subgroups

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

subgroupindex
#191437082
C4×#130633512
#191353902
#191329752
#191324442
#191324312
C43×#14782
#895643