Finite Group Databasebeta

← #24991698

Subgroups — #24991698

Order 11008.

566 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143232C211yesmaximal, characteristic, complemented
2#19137833C211yesmaximal, characteristic
3#19133020C211yesmaximal, characteristic, complemented
4#19132907C211yesmaximal, characteristic, complemented
5#19132497C211yesmaximal, characteristic, complemented
6#19132496C211yesmaximal, characteristic, complemented
7C43×#1486C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D43—21no—
9C2×#13063282C2211yescharacteristic
10#14582959—22no—
11#14582959—22no—
12#14582952C2211yescharacteristic
13#14582923C2211yescharacteristic
14#14582862—21no—
15M16×Dic43—21no—
16#14582830C411yescharacteristic
17#14582825C411yescharacteristic
18#14582822—21no—
19#14582815—21no—
20#14582813C411yescharacteristic
21#14582807C411yescharacteristic
22C4×C4⋊Dic43C2211yescharacteristic
23C4×C22⋊Dic43—21no—
24D4⋊(C43⋊C8)—22no—
25#14582624—21no—
26#14582622—21no—
27C2×C4×D4×C43C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C43×D4⋊C8—22no—
31C22×C22⋊D43—21no—
32C22×C4×D43D411yescharacteristic
33C2×#10621877—21no—
34C4×C22⋊D43—42no—
35C4×C22⋊D43—42no—
36#13063282—21no—
37#13063282—21no—
38#13063282—21no—
39#13063282—21no—
40C2×C4⋊Dic43—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4C2×C411yescharacteristic
43C2×Dic43⋊C4D411yescharacteristic
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4C2×C411yescharacteristic
49C2×(C2×D43)⋊C4D411yescharacteristic
50C2×C4×Dic43—21no—
51C2×C4×Dic43D411yescharacteristic
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)D412yescomplemented
55C22⋊(C43⋊C8)—21no—
56(C2×D43)⋊C8—24no—
57#13063235—22no—
58C4×C43⋊C8—21no—
59C8×Dic43—22no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95C2×C411yescharacteristic
63C43⋊#95C2×C411yescharacteristic
64C22×D4×C43C2×C411yescharacteristic
65C23×C4×C43—21no—
66C2×M16×C43—21no—
67C4×D4×C43—21no—
68C4×D4×C43—21no—
69C4×D4×C43—21no—
70C4×D4×C43—21no—
71C2×C4⋊C4×C43C2×C411yescharacteristic
72C2×C22⋊C4×C43—21no—
73C2×C42×C43C2311yescharacteristic
74C4⋊C8×C43—21no—
75C4⋊C8×C43—21no—
76C4⋊C8×C43D412yescomplemented
77C22⋊C8×C43—21no—
78C4×C8×C43—21no—
79C24×C43—21no—
80C23×D43C22⋊C411yescharacteristic
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—42no—
84C22×C4×C43—21no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43C22×C411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C2×C22⋊D43—42no—
95C2×C22⋊D43—42no—
96C2×C22⋊D43—42no—
97C22×Dic43—21no—
98C22×Dic43—21no—
99C22×Dic43C22⋊C411yescharacteristic
100C22×Dic43C22⋊C411yescharacteristic
101C22×Dic43C22⋊C411yescharacteristic
102C2×C4×D43—21no—
103C2×C4×D43—21no—
104C2×C4×D43—21no—
105C2×C4×D43—21no—
106C2×C4×D43—21no—
107C2×C4×D43—21no—
108M16×C43—41no—
109M16×C43—41no—
110C2×C8×C43—22no—
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×C43#4111yescharacteristic
119C42×C43#4111yescharacteristic
120C22⋊Dic43—42no—
121C22⋊Dic43—42no—
122C22⋊Dic43—42no—
123(C2×D43)⋊C4—21no—
124(C2×D43)⋊C4—21no—
125(C2×D43)⋊C4—21no—
126(C2×D43)⋊C4—21no—
127(C2×D43)⋊C4—42no—
128C4⋊Dic43—42no—
129Dic43⋊C4—21no—
130Dic43⋊C4—21no—
131Dic43⋊C4—21no—
132Dic43⋊C4—21no—
133Dic43⋊C4—42no—
134C4×Dic43—21no—
135C4×Dic43—21no—
136C4×Dic43—41no—
137C4×Dic43—41no—
138#10621877—41no—
139#10621877—41no—
140C2×C43⋊C8—22no—
141C2×C43⋊C8—41no—
142C23×C43—22no—
143C23×C43—41no—
144C23×C43—41no—
145C23×C43—41no—
146C23×C43—41no—
147C23×C43—41no—
148C23×C43—41no—
149C23×C43C2×C22⋊C411yescharacteristic
150C22×D43—21no—
151C22×D43—21no—
152C22×D43—21no—
153C22×D43—41no—
154C22×D43—41no—
155D4×C43—22no—
156D4×C43—22no—
157D4×C43—41no—
158D4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—81no—
165C2×C4×C43—81no—
166C2×C4×C43—81no—
167C2×C4×C43—81no—
168C2×C4×C43C4×D411yescharacteristic
169C2×C4×C43C4×D411yescharacteristic
170C2×C4×C43#12011yescharacteristic
171C2×C4×C43#12111yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×C4×C43#12311yescharacteristic
174C2×C4×C43#13511yescharacteristic
175C2×C4×C43#13511yescharacteristic
176C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
178C22⋊D43—48no—
179C2×Dic43—22no—
180C2×Dic43—21no—
181C2×Dic43—21no—
182C2×Dic43—21no—
183C2×Dic43—21no—
184C2×Dic43—21no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—41no—
190C2×Dic43—41no—
191C2×Dic43—41no—
192C4×D43—41no—
193C4×D43—41no—
194C4×D43—41no—
195C4×D43—41no—
196C8×C43—42no—
197C8×C43—81no—
198C43⋊C8—42no—
199C43⋊C8—81no—
200#9036—431nomaximal, Sylow
201C22×C43—21no—
202C22×C43—21no—
203C22×C43—42no—
204C22×C43—42no—
205C22×C43—42no—
206C22×C43—81no—
207C22×C43—81no—
208C22×C43—81no—
209C22×C43—81no—
210C22×C43#38611yescharacteristic
211C22×C43#41611yescharacteristic
212C22×C43#41811yescharacteristic
213C2×D43—42no—
214C2×D43—41no—
215C2×D43—41no—
216C2×D43—41no—
217C2×D43—81no—
218C4×C43—21no—
219C4×C43—21no—
220C4×C43—21no—
221C4×C43—21no—
222C4×C43—81no—
223C4×C43#44911yescharacteristic
224C4×C43#44911yescharacteristic
225C4×C43#48211yescharacteristic
226C4×C43#48211yescharacteristic
227Dic43—42no—
228Dic43—41no—
229Dic43—41no—
230Dic43—41no—
231Dic43—81no—
232#2921—431no—
233#2392—431no—
234#1486—431no—
235#1486D4311yescharacteristic, complemented
236#1458—431no—
237#1303—431no—
238#1303—431no—
239C2×C43—21no—
240C2×C43—21no—
241C2×C43—82no—
242C2×C43#187511yescharacteristic
243C2×C43#188411yescharacteristic
244C2×C43#189111yescharacteristic
245D43—81no—
246C2×C4×D4—861no—
247C2×C4×D4C2×D4311yescharacteristic
248C2×#117—431no—
249#433—862no—
250#433—862no—
251#431—431no—
252#431C2×D4311yescharacteristic
253#423—431no—
254#423C2×D4311yescharacteristic
255#407—861no—
256C4×M16—861no—
257#398—431no—
258#397—431no—
259#396—861no—
260#394—431no—
261#394—861no—
262#392—431no—
263C4×C4⋊C4—431no—
264C4×C22⋊C4—861no—
265D4⋊C8—22no—
266D4⋊C8—862no—
267#324—861no—
268#323—861no—
269C43#903611yescharacteristic, complemented, Sylow
270C22×D4—861no—
271C22×D4C4×D4311yescharacteristic
272C23×C4—21no—
273C23×C4—431no—
274C2×M16—21no—
275C2×M16—861no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—1722no—
281C4×D4—1722no—
282#117—861no—
283#117—861no—
284#117—861no—
285#117—861no—
286C2×C4⋊C4—431no—
287C2×C4⋊C4—431no—
288C2×C4⋊C4—861no—
289C2×C4⋊C4—861no—
290C2×C4⋊C4C4×D4311yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—431no—
293C2×C22⋊C4—431no—
294C2×C22⋊C4—861no—
295C2×C22⋊C4—861no—
296C2×C22⋊C4—861no—
297C2×C22⋊C4—861no—
298C2×C42—431no—
299C2×C42—861no—
300C2×C42C22×D4311yescharacteristic
301C4⋊C8—21no—
302C4⋊C8—21no—
303C4⋊C8—432no—
304C4⋊C8—861no—
305C4⋊C8—861no—
306C4⋊C8C22⋊D4312yescomplemented
307C22⋊C8—21no—
308C22⋊C8—864no—
309C22⋊C8—861no—
310#97—862no—
311C4×C8—21no—
312C4×C8—862no—
313C4×C8—861no—
314#95—431no—
315#95—431no—
316#95—861no—
317#95—861no—
318C24—21no—
319C24—431no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—42no—
323C2×D4—1722no—
324C2×D4—1722no—
325C2×D4—1722no—
326C22×C4—21no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—431no—
334C22×C4—431no—
335C22×C4—431no—
336C22×C4—861no—
337C22×C4—861no—
338C22×C4—861no—
339C22×C4—861no—
340C22×C4—861no—
341C22×C4—861no—
342C22×C4—861no—
343C22×C4—861no—
344C22×C4C2×C4×D4311yescharacteristic
345C22×C4D4×D4311yescharacteristic
346C22×C4D4×D4311yescharacteristic
347M16—41no—
348M16—41no—
349M16—1721no—
350M16—1721no—
351C2×C8—22no—
352C2×C8—41no—
353C2×C8—862no—
354C2×C8—1721no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—861no—
358C4⋊C4—861no—
359C4⋊C4—861no—
360C4⋊C4—861no—
361C4⋊C4—1722no—
362C4⋊C4—1722no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—861no—
366C22⋊C4—861no—
367C22⋊C4—861no—
368C22⋊C4—861no—
369C22⋊C4—1722no—
370C22⋊C4—1722no—
371C22⋊C4—1722no—
372C22⋊C4—1722no—
373C42—861no—
374C42—861no—
375C42—1721no—
376C42—1721no—
377C42#1062189811yescharacteristic
378C42D4×D4311yescharacteristic
379C42#1062190011yescharacteristic
380C42C2×C22⋊D4311yescharacteristic
381C23—22no—
382C23—41no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—861no—
389C23—861no—
390C23—861no—
391C23—1721no—
392C23—1721no—
393C23C22⋊C4×D4311yescharacteristic
394D4—22no—
395D4—22no—
396D4—41no—
397D4—41no—
398D4—1728no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—862no—
409C2×C4—861no—
410C2×C4—861no—
411C2×C4—861no—
412C2×C4—861no—
413C2×C4—861no—
414C2×C4—1721no—
415C2×C4—1721no—
416C2×C4—1721no—
417C2×C4—1721no—
418C2×C4—1721no—
419C2×C4—1721no—
420C2×C4—1721no—
421C2×C4—1721no—
422C2×C4—1721no—
423C2×C4—1721no—
424C2×C4—1721no—
425C2×C4(C22⋊D43)⋊C411yescharacteristic
426C2×C4C4×C22⋊D4311yescharacteristic
427C2×C4#1306329311yescharacteristic
428C2×C4#1306329611yescharacteristic
429C2×C4#1306329811yescharacteristic
430C2×C4#1306330711yescharacteristic
431C2×C4#1306334411yescharacteristic
432C2×C4#1306334611yescharacteristic
433C2×C4#1306334911yescharacteristic
434C2×C4#1306335211yescharacteristic
435C8—42no—
436C8—81no—
437C8—3441no—
438C8—1722no—
439C22—21no—
440C22—21no—
441C22—42no—
442C22—42no—
443C22—42no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22—3441no—
449C22—1722no—
450C22—1721no—
451C22—1721no—
452C22—1721no—
453C22#1458277511yescharacteristic
454C22#1458289211yescharacteristic
455C22#1458290211yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—81no—
461C4—3441no—
462C4—1722no—
463C4—1721no—
464C4—1721no—
465C4—1721no—
466C4#1458304111yescharacteristic
467C4#1458304311yescharacteristic
468C4#1458322111yescharacteristic
469C4#1458322211yescharacteristic
470C2—21no—
471C2—21no—
472C2—82no—
473C2—3441no—
474C2#1913491411yescharacteristic
475C2#1913497511yescharacteristic
476C2#1913501011yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1486C2
socleC22×C43#386
prime radical#14582807C4
cosocleC2×C42×C43C23
hypercenter#1486D43
hypocenterC43#9036
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
1. #19143232C2semidirect
3. #19133020C2semidirect
4. #19132907C2semidirect
5. #19132497C2semidirect
6. #19132496C2semidirect
7. C43×#1486C2semidirect
54. C4⋊(C43⋊C8)D4semidirect
76. C4⋊C8×C43D4semidirect
235. #1486D43semidirect
269. C43#9036semidirect
306. C4⋊C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191432322
#191378332
#191330202
#191329072
#191324972
#191324962
C43×#14862
#903643