Finite Group Databasebeta

← #25015075

Subgroups — #25015075

Order 11008.

498 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145019C211yesmaximal, characteristic
2#19136350C211yesmaximal, characteristic, complemented
3C2×#14582710C211yesmaximal, characteristic, complemented
4C2×#14582709C211yesmaximal, characteristic, complemented
5C2×#14582708C211yesmaximal, characteristic, complemented
6#106×Dic43C211yesmaximal, characteristic, complemented
7C2×C43×#360C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9C2×#13063345—21no—
10#14583445—21no—
11C2×#13063265C2211yescharacteristic
12#14583284C411yescharacteristic, complemented
13#14583282C411yescharacteristic, complemented
14#14583280—21no—
15#14583277C411yescharacteristic, complemented
16#14583274C411yescharacteristic, complemented
17#14583270—21no—
18C2×#13063257C2211yescharacteristic
19C2×C8×Dic43C2211yescharacteristic
20C4⋊C4×Dic43—21no—
21Dic43⋊C16—21no—
22Dic43⋊C16—21no—
23#14582710—22no—
24#14582709—22no—
25#14582708—22no—
26#14582661—21no—
27C2×#135×C43C2211yescharacteristic
28C2×M32×C43C2211yescharacteristic
29C2×#106×C43C2211yescharacteristic
30C43×#360—22no—
31C2×#10621898—21no—
32#13063347—21no—
33#13063347—21no—
34#13063347—21no—
35#13063347—21no—
36#13063345—42no—
37#13063345—42no—
38C2×Dic172C2×C411yescharacteristic
39C2×#10621885—21no—
40C2×#10621873—21no—
41C2×#10621883—21no—
42C2×#10621884—21no—
43C2×D344C2×C411yescharacteristic
44C2×#10621882—21no—
45C22×C43⋊C8D411yescharacteristic
46#13063323—21no—
47#13063321—21no—
48#13063314—21no—
49#13063312—21no—
50#13063297—41no—
51#13063297—41no—
52C4×C22⋊D43—41no—
53C4×C22⋊D43—41no—
54C2×C4⋊Dic43—21no—
55C2×C4×Dic43—41no—
56C2×C4×Dic43D411yescharacteristic
57#13063265—21no—
58#13063265—21no—
59C2×C43⋊C16—21no—
60#13063257—21no—
61#13063257D412yescomplemented
62C8×Dic43C2×C411yescharacteristic
63C8×Dic43C2×C411yescharacteristic
64C8×Dic43D411yescharacteristic
65C8×Dic43D411yescharacteristic
66C43⋊#95—41no—
67C2×#41×C43—21no—
68#135×C43—21no—
69#135×C43—21no—
70#135×C43—21no—
71#135×C43—21no—
72C2×Q16×C43C2×C411yescharacteristic
73C2×SD16×C43—21no—
74C2×D8×C43C2×C411yescharacteristic
75C22×C8×C43C2311yescharacteristic
76C2×C4⋊C4×C43—21no—
77M32×C43—21no—
78M32×C43—21no—
79C2×C16×C43—21no—
80#106×C43—21no—
81#106×C43D412yescomplemented
82#41×C43—41no—
83#41×C43—41no—
84#41×C43—41no—
85#41×C43—41no—
86C2×Q8×C43—21no—
87C2×D4×C43—21no—
88C2×D4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43C2×D411yescharacteristic
92C2×C22⋊D43—41no—
93C2×C22⋊D43—41no—
94C2×C22⋊D43—41no—
95C22×Dic43—41no—
96C22×Dic43D811yescharacteristic
97C22×Dic43D811yescharacteristic
98#10621898—41no—
99#10621898—41no—
100#10621898—41no—
101#10621898—41no—
102C2×D172—21no—
103C2×C4×D43—41no—
104C2×Dic86—21no—
105Q16×C43—21no—
106Q16×C43—21no—
107SD16×C43—41no—
108SD16×C43—41no—
109D8×C43—21no—
110D8×C43—21no—
111C2×C8×C43C22×C411yescharacteristic
112C2×C8×C43C2×D411yescharacteristic
113C2×C8×C43C2×D411yescharacteristic
114C2×C8×C43C2×D411yescharacteristic
115C2×C8×C43#4111yescharacteristic
116C2×C8×C43#4111yescharacteristic
117C4⋊C4×C43—22no—
118C4⋊C4×C43—41no—
119C22⋊Dic43—41no—
120C22⋊Dic43—41no—
121#10621885—42no—
122#10621884—42no—
123#10621883—42no—
124#10621882—42no—
125(C2×D43)⋊C4—41no—
126(C2×D43)⋊C4—41no—
127C4⋊Dic43—22no—
128C4⋊Dic43—41no—
129Dic43⋊C4—41no—
130Dic43⋊C4—41no—
131C4×Dic43—82no—
132C4×Dic43C22⋊C411yescharacteristic
133C4×Dic43C22⋊C411yescharacteristic
134C4×Dic43SD1611yescharacteristic
135C4×Dic43SD1611yescharacteristic
136C2×C43⋊C8—21no—
137C2×C43⋊C8—21no—
138C2×C43⋊C8C22⋊C411yescharacteristic
139C2×C43⋊C8C22⋊C411yescharacteristic
140Dic172—21no—
141Dic172—21no—
142D344—21no—
143D344—21no—
144#10621873—41no—
145#10621873—41no—
146C16×C43—41no—
147C43⋊C16—41no—
148C23×C43—41no—
149C23×C43C2×D811yescharacteristic
150C22×D43—41no—
151Q8×C43—41no—
152Q8×C43—41no—
153D4×C43—41no—
154D4×C43—41no—
155D4×C43—81no—
156D4×C43—81no—
157C2×C4×C43—41no—
158C2×C4×C43—42no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×C4×C43—81no—
162C2×C4×C43—81no—
163C2×C4×C43C2×C22⋊C411yescharacteristic
164C2×C4×C43#12111yescharacteristic
165C2×C4×C43#12111yescharacteristic
166C2×C4×C43C2×SD1611yescharacteristic
167C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
169C22⋊D43—82no—
170C22⋊D43—81no—
171C22⋊D43—81no—
172C22⋊D43—82no—
173C2×Dic43—22no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—42no—
177C2×Dic43—81no—
178C2×Dic43—81no—
179C2×Dic43#10211yescharacteristic
180C2×Dic43#10211yescharacteristic
181C2×Dic43#10211yescharacteristic
182C2×Dic43#10211yescharacteristic
183D172—41no—
184D172—41no—
185C4×D43—81no—
186C4×D43—81no—
187Dic86—41no—
188Dic86—41no—
189C8×C43C4×D411yescharacteristic
190C8×C43C4×D411yescharacteristic
191C8×C43#12411yescharacteristic
192C8×C43#12711yescharacteristic
193C43⋊C8—21no—
194C43⋊C8—21no—
195#13255—431nomaximal, Sylow
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—81no—
199C22×C43—81no—
200C22×C43—81no—
201C22×C43C2×#10211yescharacteristic
202C22×C43#45911yescharacteristic
203C22×C43#45911yescharacteristic
204C2×D43—81no—
205C2×D43—81no—
206C2×D43—81no—
207C4×C43—82no—
208C4×C43—81no—
209C4×C43#39011yescharacteristic
210C4×C43#41811yescharacteristic
211C4×C43#46011yescharacteristic
212C4×C43#46011yescharacteristic
213Dic43—21no—
214Dic43—21no—
215Dic43—21no—
216Dic43—82no—
217Dic43—81no—
218Dic43#36012yescomplemented
219#3147—431no—
220#2150—431no—
221C2×#360—431no—
222C2×#360—431no—
223C2×#360—431no—
224C2×#360D4311yescharacteristic, complemented
225C4×#106—431no—
226C2×C43—21no—
227C2×C43—21no—
228C2×C43—161no—
229C2×C43#198211yescharacteristic
230C2×C43C2×#36011yescharacteristic
231C2×C43#214511yescharacteristic
232D43—161no—
233C2×#135—431no—
234C2×#135—861no—
235C2×#135C2×D4311yescharacteristic
236#532—861no—
237C2×M32—431no—
238C2×M32C2×D4311yescharacteristic
239#495—431no—
240#495—431no—
241#495—861no—
242#494—431no—
243#493—431no—
244#492—861no—
245C2×#106—431no—
246C2×#106C2×D4311yescharacteristic
247C2×C4×C8—431no—
248C4×C4⋊C4—861no—
249C4⋊C16—861no—
250C4⋊C16—861no—
251#360—22no—
252#360—862no—
253#360—862no—
254#360—862no—
255#340—861no—
256C43#1325511yescharacteristic, complemented, Sylow
257C2×#41—21no—
258C2×#41—861no—
259#135—21no—
260#135—21no—
261#135—21no—
262#135—21no—
263#135—861no—
264#135—861no—
265#135—861no—
266#135—861no—
267#135—1722no—
268#135—1722no—
269C2×Q16—431no—
270C2×Q16—861no—
271C2×Q16C4×D4311yescharacteristic
272C2×SD16—21no—
273C2×SD16—861no—
274C2×SD16—861no—
275C2×SD16—861no—
276C2×D8—431no—
277C2×D8—861no—
278C2×D8C4×D4311yescharacteristic
279C22×C8—431no—
280C22×C8C22×D4311yescharacteristic
281C4⋊Q8—861no—
282#127—861no—
283#124—861no—
284#124—861no—
285#121—1721no—
286#121—1721no—
287C4×D4—1721no—
288C4×D4—1721no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—861no—
291C2×C42—431no—
292C2×C42—1721no—
293M32—21no—
294M32—21no—
295M32—861no—
296M32—861no—
297C2×C16—21no—
298C2×C16—861no—
299#106—21no—
300#106—432no—
301#106—861no—
302#106C22⋊D4312yescomplemented
303C4×C8—431no—
304C4×C8—431no—
305C4×C8—431no—
306C4×C8—431no—
307#95—1721no—
308#41—41no—
309#41—41no—
310#41—41no—
311#41—41no—
312#41—1721no—
313#41—1721no—
314#41—1721no—
315#41—1721no—
316C2×Q8—21no—
317C2×Q8—861no—
318C2×D4—21no—
319C2×D4—41no—
320C2×D4—861no—
321C2×D4—1721no—
322C2×D4—1721no—
323C2×D4—1721no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—431no—
327C22×C4—431no—
328C22×C4—1721no—
329C22×C4—1721no—
330C22×C4D4×D4311yescharacteristic
331Q16—21no—
332Q16—21no—
333Q16—861no—
334Q16—861no—
335Q16—1722no—
336SD16—41no—
337SD16—41no—
338SD16—1722no—
339SD16—1722no—
340SD16—1721no—
341SD16—1721no—
342D8—21no—
343D8—21no—
344D8—861no—
345D8—861no—
346D8—1722no—
347C2×C8—431no—
348C2×C8—431no—
349C2×C8—861no—
350C2×C8—861no—
351C2×C8C2×C4×D4311yescharacteristic
352C2×C8#1062189811yescharacteristic
353C2×C8D4×D4311yescharacteristic
354C2×C8D4×D4311yescharacteristic
355C2×C8#1062190011yescharacteristic
356C2×C8C2×C22⋊D4311yescharacteristic
357C4⋊C4—22no—
358C4⋊C4—41no—
359C4⋊C4—862no—
360C4⋊C4—1721no—
361C4⋊C4—1721no—
362C4⋊C4—1721no—
363C22⋊C4—1721no—
364C22⋊C4—1721no—
365C22⋊C4—1721no—
366C22⋊C4—1721no—
367C42—431no—
368C42—431no—
369C42—431no—
370C42—431no—
371C42—3442no—
372C16—41no—
373C16—1721no—
374C23—41no—
375C23—1721no—
376C23D8×D4311yescharacteristic
377Q8—41no—
378Q8—41no—
379Q8—1721no—
380Q8—1721no—
381D4—41no—
382D4—41no—
383D4—81no—
384D4—81no—
385D4—3442no—
386D4—3442no—
387D4—3441no—
388D4—3441no—
389D4—1721no—
390D4—1721no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—431no—
398C2×C4—431no—
399C2×C4—431no—
400C2×C4—431no—
401C2×C4—862no—
402C2×C4—3441no—
403C2×C4—3441no—
404C2×C4—3441no—
405C2×C4—3441no—
406C2×C4—1721no—
407C2×C4—1722no—
408C2×C4—1721no—
409C2×C4C22⋊C4×D4311yescharacteristic
410C2×C4#1306329711yescharacteristic
411C2×C4#1306329811yescharacteristic
412C2×C4SD16×D4311yescharacteristic
413C2×C4#1306334911yescharacteristic
414C2×C4#1306335211yescharacteristic
415C8—861no—
416C8—861no—
417C8(C22⋊D43)⋊C411yescharacteristic
418C8C4×C22⋊D4311yescharacteristic
419C8#1306331111yescharacteristic
420C8#1306332111yescharacteristic
421C22—21no—
422C22—21no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—3441no—
427C22—3441no—
428C22—3441no—
429C22#102×D4311yescharacteristic
430C22#1458309211yescharacteristic
431C22#1458309311yescharacteristic
432C4—82no—
433C4—81no—
434C4—432no—
435C4—861no—
436C4—861no—
437C4—861no—
438C4—3442no—
439C4—3441no—
440C4#1458279911yescharacteristic
441C4#1458290211yescharacteristic
442C4#1458309711yescharacteristic
443C4#1458309811yescharacteristic
444C2—21no—
445C2—21no—
446C2—161no—
447C2—6881no—
448C2#1913552011yescharacteristic
449C2#360×D4311yescharacteristic
450C2#1913632911yescharacteristic
subgroupG/H
centerC22#102×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#360C2
socleC22×C43C2×#102
prime radical#19145019C2
cosocleC22×C8×C43C23
hypercenterC2×#360D43
hypocenterC43#13255
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

Complements

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

NH ≅ G/Ntype
2. #19136350C2semidirect
3. C2×#14582710C2semidirect
4. C2×#14582709C2semidirect
5. C2×#14582708C2semidirect
6. #106×Dic43C2semidirect
7. C2×C43×#360C2semidirect
12. #14583284C4semidirect
13. #14583282C4semidirect
15. #14583277C4semidirect
16. #14583274C4semidirect
61. #13063257D4semidirect
81. #106×C43D4semidirect
218. Dic43#360semidirect
224. C2×#360D43semidirect
256. C43#13255semidirect
302. #106C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191450192
#191363502
C2×#145827102
C2×#145827092
C2×#145827082
#106×Dic432
C2×C43×#3602
#1325543