Finite Group Databasebeta

← #25254173

Subgroups — #25254173

Order 11008.

476 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146992C211yesmaximal, characteristic
2#19146966C211yesmaximal, characteristic, complemented
3#19136872C211yesmaximal, characteristic, complemented
4#19136800C211yesmaximal, characteristic, complemented
5#19136791C211yesmaximal, characteristic, complemented
6#19136784C211yesmaximal, characteristic, complemented
7#19136778C211yesmaximal, characteristic, complemented
8#19136761C211yesmaximal, characteristic, complemented
9#19136754C211yesmaximal, characteristic, complemented
10#19136705C211yesmaximal, characteristic, complemented
11SD32×Dic43C211yesmaximal, characteristic, complemented
12#19136425C211yesmaximal, characteristic, complemented
13#19136383C211yesmaximal, characteristic, complemented
14#19136380C211yesmaximal, characteristic, complemented
15C43×#2220C211yesmaximal, characteristic, complemented
16#14583596—21no—
17#14583591—21no—
18C2×#13063264C2211yescharacteristic
19#14583300C2211yescharacteristic
20#14583300C2211yescharacteristic
21#14583239—21no—
22#14583227—21no—
23#14583220—21no—
24#14583216—21no—
25#14583208—21no—
26#14583201—21no—
27#14583137C2211yescharacteristic
28#14583132C2211yescharacteristic
29Q16×Dic43C2211yescharacteristic
30D8×Dic43C2211yescharacteristic
31C8×C22⋊D43C2211yescharacteristic
32#14582937C2211yescharacteristic
33#14582936C2211yescharacteristic
34C2×#13063259C2211yescharacteristic
35#107×D43C2211yescharacteristic
36#14582727C2211yescharacteristic
37#14582727C2211yescharacteristic
38#14582726C2211yescharacteristic
39#14582726C2211yescharacteristic
40#14582726C2211yescharacteristic
41#14582725C2211yescharacteristic
42#14582725C2211yescharacteristic
43#14582724C2211yescharacteristic
44Dic43⋊C16C2211yescharacteristic
45#14582703C2211yescharacteristic
46#14582703C2211yescharacteristic
47#14582700C2211yescharacteristic
48#14582700C2211yescharacteristic
49C22⋊(C43⋊C16)C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C2×SD32×C43C2211yescharacteristic
53C2×M32×C43C2211yescharacteristic
54C43×#467C2211yescharacteristic
55C43×#466C2211yescharacteristic
56C43×#366C2211yescharacteristic
57C43×#358C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×C8×D43C2311yescharacteristic
60#13063320—41no—
61#13063318—41no—
62#13063316—21no—
63#13063316—21no—
64#13063316—41no—
65#13063309—41no—
66#13063306—41no—
67#13063301—21no—
68#13063296—21no—
69#13063296—41no—
70Q8×Dic43—21no—
71D4×Dic43—21no—
72C4×C22⋊D43D411yescharacteristic
73(C22⋊D43)⋊C4—41no—
74#13063284—21no—
75#13063283—21no—
76#13063281—41no—
77C2×C4⋊Dic43—21no—
78C4⋊C4×D43—21no—
79#13063264—22no—
80C2×C43⋊C16C2311yescharacteristic
81C2×C43⋊C16C2311yescharacteristic
82#13063259—21no—
83#13063259C2311yescharacteristic
84#13063259C2311yescharacteristic
85#13063259C2311yescharacteristic
86#13063259C2311yescharacteristic
87#13063258—21no—
88#13063257—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92Dic43⋊C8D411yescharacteristic
93#13063249—21no—
94#13063249—21no—
95#13063246—21no—
96#13063246—21no—
97C22⋊(C43⋊C8)D411yescharacteristic
98(C2×D43)⋊C8D411yescharacteristic
99C8×Dic43C2311yescharacteristic
100C2×Q16×C43C2311yescharacteristic
101C2×D8×C43C2311yescharacteristic
102C22×C8×C43C2311yescharacteristic
103C22⋊Q8×C43—21no—
104#121×C43—21no—
105SD32×C43—22no—
106M32×C43—22no—
107C2×C16×C43C2311yescharacteristic
108C2×C16×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#107×C43C2311yescharacteristic
111#103×C43—21no—
112#102×C43—21no—
113C2×Q8×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—41no—
116C22×C4×C43C2×D411yescharacteristic
117C2×C22⋊D43—41no—
118C2×C22⋊D43D811yescharacteristic
119C22×Dic43—41no—
120C22×Dic43—41no—
121C2×C4×D43—41no—
122C2×C4×D43C2×D411yescharacteristic
123Q16×C43—21no—
124Q16×C43—21no—
125D8×C43—21no—
126D8×C43—21no—
127C2×C8×C43—21no—
128C2×C8×C43—21no—
129C2×C8×C43C2×D411yescharacteristic
130C2×C8×C43C2411yescharacteristic
131C4⋊C4×C43—21no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—41no—
134C22⋊C4×C43—41no—
135C22⋊C4×C43—41no—
136C22⋊Dic43—41no—
137C22⋊Dic43—41no—
138C22⋊Dic43—41no—
139C22⋊Dic43D811yescharacteristic
140(C2×D43)⋊C4—41no—
141(C2×D43)⋊C4—41no—
142(C2×D43)⋊C4D811yescharacteristic
143C4⋊Dic43—21no—
144C4⋊Dic43—21no—
145C4⋊Dic43—21no—
146C4⋊Dic43—21no—
147C4⋊Dic43—41no—
148C4⋊Dic43—41no—
149C4⋊Dic43—41no—
150C4⋊Dic43—41no—
151Dic43⋊C4—41no—
152Dic43⋊C4—41no—
153Dic43⋊C4—41no—
154Dic43⋊C4—41no—
155Dic43⋊C4D811yescharacteristic
156C4×Dic43—41no—
157C4×Dic43—41no—
158C4×Dic43—41no—
159C4×Dic43C2×D411yescharacteristic
160C2×C43⋊C8C2×D411yescharacteristic
161C2×C43⋊C8C2×D411yescharacteristic
162C8×D43—21no—
163C8×D43—21no—
164C16×C43—21no—
165C16×C43#4112yes—
166C43⋊C16—21no—
167C43⋊C16—21no—
168C23×C43—41no—
169C23×C43C2×D811yescharacteristic
170C22×D43C2×D811yescharacteristic
171Q8×C43—41no—
172Q8×C43—41no—
173D4×C43—41no—
174D4×C43—41no—
175D4×C43—161no—
176C2×C4×C43—21no—
177C2×C4×C43—21no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43C2×D811yescharacteristic
182C2×C4×C43C22×D411yescharacteristic
183C22⋊D43—41no—
184C22⋊D43—82no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—82no—
190C2×Dic43—161no—
191C2×Dic43C2×D811yescharacteristic
192C2×Dic43C2×D811yescharacteristic
193C2×Dic43C2×D811yescharacteristic
194C4×D43—21no—
195C4×D43—21no—
196C4×D43—161no—
197C8×C43—21no—
198C8×C43C2×#4111yescharacteristic
199C8×C432−1+411yescharacteristic
200C43⋊C8—21no—
201C43⋊C8—21no—
202#33918—431nomaximal, Sylow
203C22×C43—21no—
204C22×C43—21no—
205C22×C43—21no—
206C22×C43—81no—
207C22×C43—81no—
208C22×C43—81no—
209C22×C43C22×D811yescharacteristic
210C2×D43—21no—
211C2×D43—21no—
212C2×D43—21no—
213C4×C43—21no—
214C4×C43—81no—
215C4×C43—81no—
216C4×C43—81no—
217C4×C43#54711yescharacteristic
218C4×C43#57811yescharacteristic
219Dic43—21no—
220Dic43—21no—
221Dic43—21no—
222Dic43—81no—
223Dic43—81no—
224Dic43—81no—
225Dic43—81no—
226#3339—431no—
227#3336—431no—
228#2253—431no—
229#2237—431no—
230#2235—431no—
231#2234—431no—
232#2233—431no—
233#2229—431no—
234#2228—431no—
235#2220—431no—
236#2220D4311yescharacteristic, complemented
237C4×SD32—431no—
238#2169—431no—
239#2159—431no—
240#2159—431no—
241C2×C43—41no—
242C2×C43—161no—
243C2×C43#333411yescharacteristic
244C2×C43#341411yescharacteristic
245C2×C43#341611yescharacteristic
246D43—41no—
247#553—861no—
248#552—861no—
249C2×SD32C2×D4311yescharacteristic
250C2×M32—431no—
251C2×M32C2×D4311yescharacteristic
252#499—431no—
253#499—431no—
254#485—861no—
255#483—861no—
256#482—861no—
257#481—861no—
258#479—861no—
259#478—861no—
260#467—431no—
261#467C2×D4311yescharacteristic
262#466—431no—
263#466C2×D4311yescharacteristic
264C4×Q16—431no—
265C4×D8—431no—
266C8×D4—431no—
267#427—431no—
268#427—431no—
269C2×#107—431no—
270C2×#107—431no—
271#367—431no—
272#367—431no—
273#367—431no—
274#367—431no—
275#367—431no—
276#366—431no—
277#366—431no—
278#366—431no—
279#366C2×D4311yescharacteristic
280C4⋊C16—431no—
281#358—431no—
282#358—431no—
283#358C2×D4311yescharacteristic
284#357—431no—
285#357—431no—
286#357C2×D4311yescharacteristic
287C22⋊C16—431no—
288C22⋊C16—431no—
289C4×C16—431no—
290C43#3391811yescharacteristic, complemented, Sylow
291C2×Q16C22×D4311yescharacteristic
292C2×D8C22×D4311yescharacteristic
293C22×C8—431no—
294C22×C8C22×D4311yescharacteristic
295#126—1721no—
296#126—1721no—
297#125—861no—
298#125—861no—
299#125—1721no—
300#123—1721no—
301#123—1721no—
302C22⋊Q8—21no—
303C22⋊Q8—861no—
304#121—21no—
305#121—861no—
306#121—1721no—
307C4×Q8—861no—
308C4×D4—431no—
309C4×D4—861no—
310C4×D4—1721no—
311#117—861no—
312#117—861no—
313#117—1721no—
314C2×C4⋊C4—861no—
315C2×C4⋊C4—861no—
316SD32—22no—
317M32—22no—
318M32—862no—
319C2×C16—431no—
320C2×C16—431no—
321C2×C16C22×D4311yescharacteristic
322C2×C16C22×D4311yescharacteristic
323#107—431no—
324#107—431no—
325#107—431no—
326#107—431no—
327#107—861no—
328#107—861no—
329#107C22×D4311yescharacteristic
330#107C22×D4311yescharacteristic
331#106—861no—
332#106—861no—
333#106—861no—
334#106—861no—
335C4⋊C8—431no—
336#103—21no—
337#103—861no—
338#103—861no—
339#102—21no—
340#102—861no—
341#102—861no—
342C22⋊C8—431no—
343C22⋊C8—431no—
344C4×C8—431no—
345C2×Q8—21no—
346C2×D4—21no—
347C2×D4—41no—
348C2×D4—431no—
349C2×D4—1721no—
350C22×C4—431no—
351C22×C4—1721no—
352C22×C4—1721no—
353C22×C4—1721no—
354C22×C4D4×D4311yescharacteristic
355Q16—21no—
356Q16—21no—
357D8—21no—
358D8—21no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—431no—
362C2×C8—431no—
363C2×C8—861no—
364C2×C8—861no—
365C2×C8D4×D4311yescharacteristic
366C2×C8C23×D4311yescharacteristic
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—431no—
371C4⋊C4—861no—
372C4⋊C4—861no—
373C4⋊C4—861no—
374C4⋊C4—861no—
375C4⋊C4—1721no—
376C4⋊C4—1721no—
377C4⋊C4—1721no—
378C4⋊C4—1721no—
379C4⋊C4—1721no—
380C4⋊C4—1721no—
381C4⋊C4—1721no—
382C4⋊C4—1721no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—431no—
386C22⋊C4—431no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C42—431no—
393C42—1721no—
394C42—1721no—
395C42—1721no—
396C16—21no—
397C16—861no—
398C16—861no—
399C16#1062190012yes—
400C23—41no—
401C23—431no—
402C23D8×D4311yescharacteristic
403Q8—41no—
404Q8—41no—
405D4—41no—
406D4—41no—
407D4—161no—
408D4—3442no—
409D4—1721no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—431no—
416C2×C4—431no—
417C2×C4—431no—
418C2×C4—861no—
419C2×C4—861no—
420C2×C4—3442no—
421C2×C4—1721no—
422C2×C4—1721no—
423C2×C4—1721no—
424C2×C4—1721no—
425C2×C4—6881no—
426C2×C4—6881no—
427C2×C4D8×D4311yescharacteristic
428C2×C4C2×D4×D4311yescharacteristic
429C8—21no—
430C8—861no—
431C8—861no—
432C8C2×#1062190011yescharacteristic
433C8#1306337211yescharacteristic
434C22—21no—
435C22—21no—
436C22—21no—
437C22—81no—
438C22—81no—
439C22—81no—
440C22—861no—
441C22—861no—
442C22—861no—
443C22C2×D8×D4311yescharacteristic
444C4—21no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—861no—
449C4—861no—
450C4—861no—
451C4—3441no—
452C4—3441no—
453C4—3441no—
454C4—3441no—
455C4#1458354911yescharacteristic
456C4#1458371311yescharacteristic
457C2—41no—
458C2—161no—
459C2—1721no—
460C2#1914693911yescharacteristic
461C2#1914773011yescharacteristic
462C2#1914774111yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2220C2
socleC22×C43C22×D8
prime radical#19146992C2
hypercenter#2220D43
hypocenterC43#33918
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2220

Complements

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

NH ≅ G/Ntype
2. #19146966C2semidirect
3. #19136872C2semidirect
4. #19136800C2semidirect
5. #19136791C2semidirect
6. #19136784C2semidirect
7. #19136778C2semidirect
8. #19136761C2semidirect
9. #19136754C2semidirect
10. #19136705C2semidirect
11. SD32×Dic43C2semidirect
12. #19136425C2semidirect
13. #19136383C2semidirect
14. #19136380C2semidirect
15. C43×#2220C2semidirect
236. #2220D43semidirect
290. C43#33918semidirect

Maximal subgroups

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

subgroupindex
#191469922
#191469662
#191368722
#191368002
#191367912
#191367842
#191367782
#191367612
#191367542
#191367052
SD32×Dic432
#191364252
#191363832
#191363802
C43×#22202
#3391843