Finite Group Databasebeta

← #24995950

Subgroups — #24995950

Order 11008.

428 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×C4⋊Dic43C211yesmaximal, characteristic, complemented
2#19133343C211yesmaximal, characteristic, complemented
3#19133094C211yesmaximal, characteristic, complemented
4#19133090C211yesmaximal, characteristic
5#19132998C211yesmaximal, characteristic, complemented
6#19132994C211yesmaximal, characteristic
7C43×#3131C211yesmaximal, characteristic
8#14582952C2211yescharacteristic
9#14582952C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×C8×Dic43—21no—
12C4×C4⋊Dic43C2211yescharacteristic
13#14582653—21no—
14#14582652—21no—
15#14582650—21no—
16#14582636—22no—
17#14582633—22no—
18Q8⋊(C43⋊C8)—22no—
19D4⋊(C43⋊C8)—22no—
20C43×#533C2211yescharacteristic
21C43×#532C2211yescharacteristic
22C43×#488—21no—
23C43×#488—21no—
24C43×#487C411yescharacteristic, complemented
25C43×#487C411yescharacteristic, complemented
26C43×#486C411yescharacteristic, complemented
27C43×#486C411yescharacteristic, complemented
28C43×#416—21no—
29C43×#416—21no—
30C2×C4×C8×C43C2211yescharacteristic
31C22×C43⋊C8—21no—
32C2×C4⋊Dic43—21no—
33C2×C4×Dic43—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)D412yes—
38C22⋊(C43⋊C8)—21no—
39C22⋊(C43⋊C8)—21no—
40C4×C43⋊C8—21no—
41C4×C43⋊C8—21no—
42C8×Dic43—42no—
43C43⋊#95D412yes—
44C2×#41×C43—21no—
45C22×C8×C43D411yescharacteristic
46C22×C8×C43D411yescharacteristic
47C4⋊Q8×C43C2×C411yescharacteristic
48C4⋊Q8×C43C2×C411yescharacteristic
49C4⋊Q8×C43C2×C411yescharacteristic
50#127×C43C2×C411yescharacteristic
51#125×C43—21no—
52#124×C43—21no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43—21no—
55#121×C43—21no—
56#121×C43—21no—
57C4×Q8×C43—21no—
58C4×Q8×C43—21no—
59C4×D4×C43—21no—
60C4×D4×C43—21no—
61#117×C43—21no—
62C2×C42×C43C2311yescharacteristic
63#103×C43—21no—
64#103×C43—21no—
65#103×C43—21no—
66#103×C43—21no—
67#102×C43—21no—
68#102×C43—21no—
69#102×C43—21no—
70#102×C43—21no—
71C4×C8×C43C2×C411yescharacteristic
72C4×C8×C43C2×C411yescharacteristic
73C4×C8×C43D411yescharacteristic
74C4×C8×C43D411yescharacteristic
75#41×C43—41no—
76#41×C43—41no—
77#41×C43—41no—
78#41×C43—41no—
79C2×Q8×C43—21no—
80C2×Q8×C43—21no—
81C2×Q8×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C22×Dic43—22no—
91C2×C8×C43—21no—
92C2×C8×C43—21no—
93C2×C8×C43—21no—
94C2×C8×C43—21no—
95C2×C8×C43C22⋊C411yescharacteristic
96C2×C8×C43C22⋊C411yescharacteristic
97C2×C8×C43C22⋊C411yescharacteristic
98C2×C8×C43C22⋊C411yescharacteristic
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—41no—
110C42×C43—41no—
111C42×C43C22×C411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43#4111yescharacteristic
115C4⋊Dic43—24no—
116C4×Dic43—41no—
117C4×Dic43—41no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8—41no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—41no—
123C23×C43—41no—
124C23×C43#12111yescharacteristic
125Q8×C43—41no—
126Q8×C43—41no—
127Q8×C43—42no—
128Q8×C43—81no—
129D4×C43—41no—
130D4×C43—41no—
131D4×C43—42no—
132D4×C43—81no—
133D4×C43—81no—
134D4×C43—81no—
135C2×C4×C43—22no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—81no—
141C2×C4×C43—81no—
142C2×C4×C43C2×C22⋊C411yescharacteristic
143C2×C4×C43C4×D411yescharacteristic
144C2×C4×C43C4×D411yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43#12411yescharacteristic
147C2×C4×C43#12711yescharacteristic
148C2×C4×C43#13511yescharacteristic
149C2×C4×C43#13511yescharacteristic
150C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C43#13711yescharacteristic
152C2×Dic43—24no—
153C2×Dic43—42no—
154C2×Dic43—42no—
155C8×C43—21no—
156C8×C43—21no—
157C8×C43—21no—
158C8×C43—21no—
159C43⋊C8—42no—
160C43⋊C8—81no—
161C43⋊C8—81no—
162#9751—431nomaximal, Sylow
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—81no—
166C22×C43—81no—
167C22×C43—81no—
168C22×C43#39011yescharacteristic
169C22×C43#46311yescharacteristic
170C22×C43#46411yescharacteristic
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—81no—
175C4×C43—81no—
176C4×C43—81no—
177C4×C43#41611yescharacteristic
178C4×C43#41711yescharacteristic
179C4×C43#44312yes—
180C4×C43#46311yescharacteristic
181C4×C43#46411yescharacteristic
182Dic43—44no—
183#3131D4311yescharacteristic
184C8×C4⋊C4—431no—
185#1564—431no—
186#1503—431no—
187#1502—431no—
188#1481—431no—
189#1480—431no—
190C2×C43—21no—
191C2×C43—21no—
192C2×C43—161no—
193C2×C43#197411yescharacteristic
194C2×C43#197611yescharacteristic
195C2×C43#198311yescharacteristic
196#533C2×D4311yescharacteristic
197#532C2×D4311yescharacteristic
198#488—21no—
199#488—21no—
200#487Dic4311yescharacteristic, complemented
201#487Dic4311yescharacteristic, complemented
202#486Dic4311yescharacteristic, complemented
203#486Dic4311yescharacteristic, complemented
204#431—431no—
205#431—431no—
206C2×C4⋊C8—431no—
207#416—21no—
208#416—21no—
209C2×C4×C8—861no—
210C2×C4×C8C2×D4311yescharacteristic
211C4×C4⋊C4—431no—
212#336—861no—
213#335—861no—
214#334—861no—
215#328—862no—
216#327—862no—
217Q8⋊C8—862no—
218D4⋊C8—862no—
219C43#975111yescharacteristic, complemented, Sylow
220C2×#41—21no—
221C22×C8—861no—
222C22×C8C22⋊D4311yescharacteristic
223C22×C8C22⋊D4311yescharacteristic
224C4⋊Q8C2×Dic4311yescharacteristic
225C4⋊Q8C2×Dic4311yescharacteristic
226C4⋊Q8C2×Dic4311yescharacteristic
227#127C2×Dic4311yescharacteristic
228#125—21no—
229#124—21no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232#121—21no—
233#121—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×D4—21no—
237C4×D4—21no—
238#117—21no—
239C2×C4⋊C4—861no—
240C2×C42—861no—
241C2×C42C22×D4311yescharacteristic
242C4⋊C8—432no—
243C4⋊C8—861no—
244C4⋊C8—861no—
245C4⋊C8—861no—
246#103—21no—
247#103—21no—
248#103—21no—
249#103—21no—
250#102—21no—
251#102—21no—
252#102—21no—
253#102—21no—
254C22⋊C8—861no—
255C22⋊C8—861no—
256C4×C8—861no—
257C4×C8—861no—
258C4×C8—1722no—
259C4×C8C2×Dic4311yescharacteristic
260C4×C8C2×Dic4311yescharacteristic
261C4×C8C22⋊D4311yescharacteristic
262C4×C8C22⋊D4311yescharacteristic
263#95—432no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C22×C4—41no—
276C22×C4—862no—
277C22×C4D4×D4311yescharacteristic
278C22×C4#1062190011yescharacteristic
279C22×C4C2×C22⋊D4311yescharacteristic
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—862no—
285C2×C8—1721no—
286C2×C8—1721no—
287C2×C8—1721no—
288C2×C8—1721no—
289C2×C8C22⋊Dic4311yescharacteristic
290C2×C8C22⋊Dic4311yescharacteristic
291C2×C8C22⋊Dic4311yescharacteristic
292C2×C8C22⋊Dic4311yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—864no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C42—41no—
306C42—1721no—
307C42—1721no—
308C42D4×D4311yescharacteristic
309C42#1062190011yescharacteristic
310C42C22×Dic4311yescharacteristic
311C42C2×C22⋊D4311yescharacteristic
312C23—41no—
313C23#1306329611yescharacteristic
314Q8—41no—
315Q8—41no—
316Q8—42no—
317Q8—81no—
318D4—41no—
319D4—41no—
320D4—42no—
321D4—81no—
322D4—81no—
323D4—81no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—864no—
332C2×C4—1722no—
333C2×C4—1722no—
334C2×C4C2×C22⋊Dic4311yescharacteristic
335C2×C4D4×Dic4311yescharacteristic
336C2×C4D4×Dic4311yescharacteristic
337C2×C4#1306329611yescharacteristic
338C2×C4#1306331211yescharacteristic
339C2×C4#1306332111yescharacteristic
340C2×C4#1306334511yescharacteristic
341C2×C4#1306334511yescharacteristic
342C2×C4#1306335011yescharacteristic
343C2×C4#1306335511yescharacteristic
344C8—21no—
345C8—21no—
346C8—21no—
347C8—21no—
348C8—3441no—
349C8—3441no—
350C8—1722no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#1458280211yescharacteristic
357C22#1458311111yescharacteristic
358C22#1458311811yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—81no—
364C4—81no—
365C4—1724no—
366C4#1458289511yescharacteristic
367C4#1458290011yescharacteristic
368C4#1458301612yes—
369C4#1458311111yescharacteristic
370C4#1458311811yescharacteristic
371C2—21no—
372C2—21no—
373C2—161no—
374C2#1913548411yescharacteristic
375C2#1913549411yescharacteristic
376C2#1913552811yescharacteristic
subgroupG/H
centerC2×C4#13063296
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#3131C2
socleC22×C43#390
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#3131D43
hypocenterC43#9751
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. C8×C4⋊Dic43C2semidirect
2. #19133343C2semidirect
3. #19133094C2semidirect
5. #19132998C2semidirect
24. C43×#487C4semidirect
25. C43×#487C4semidirect
26. C43×#486C4semidirect
27. C43×#486C4semidirect
200. #487Dic43semidirect
201. #487Dic43semidirect
202. #486Dic43semidirect
203. #486Dic43semidirect
219. C43#9751semidirect

Maximal subgroups

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

subgroupindex
C8×C4⋊Dic432
#191333432
#191330942
#191330902
#191329982
#191329942
C43×#31312
#975143