Finite Group Databasebeta

← #25067066

Subgroups — #25067066

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144599C211yesmaximal, characteristic
2#19143690C211yesmaximal, characteristic, complemented
3#19143635C211yesmaximal, characteristic
4#19133500C212yesmaximal, complemented
5#19133482C212yesmaximal, complemented
6#19133470C212yesmaximal, complemented
7#19133435C212yesmaximal, complemented
8#19133373C211yesmaximal, characteristic, complemented
9#19133039C211yesmaximal, characteristic
10#19132892C211yesmaximal, characteristic, complemented
11C43×#1485C211yesmaximal, characteristic, complemented
12C2×C4×D172C2211yescharacteristic
13#14583227C412yes—
14#14583186C412yes—
15#14583101C412yes—
16#14583049C412yes—
17#14583030—22no—
18#14583030C2212yescomplemented
19Q8×C43⋊C8C2212yescomplemented
20C4×#10621884C2212yes—
21C4×#10621884C2212yes—
22#14582978—22no—
23#14582976C2212yes—
24#14582976C2212yes—
25#14582960—22no—
26#14582956C2211yescharacteristic
27#14582952C2211yescharacteristic
28#14582952C2211yescharacteristic
29#14582861—22no—
30#14582651C2212yescomplemented
31#14582649C2212yescomplemented
32#14582628C2212yes—
33#14582628C2212yes—
34#14582621C2211yescharacteristic, complemented
35#14582621C2211yescharacteristic, complemented
36#14582620C2211yescharacteristic, complemented
37C8×C43⋊C8C2211yescharacteristic, complemented
38C43×#533C2211yescharacteristic
39C43×#431C2211yescharacteristic
40C4×M16×C43C2211yescharacteristic
41C43×Q8⋊C8C2212yescomplemented
42C43×Q8⋊C8C2212yescomplemented
43C22×D172C2×C411yescharacteristic
44C22×C4×D43—21no—
45C2×#10621884C2×C412yes—
46C2×#10621884C2×C412yes—
47C2×#10621872—22no—
48C2×#10621872—22no—
49C4×D172—21no—
50C4×D172—21no—
51C4×D172C2×C412yes—
52C4×D172C2312yes—
53C2×C4⋊Dic43C2×C411yescharacteristic
54C2×(C2×D43)⋊C4—21no—
55#13063256C2×C412yes—
56#13063256C2×C412yes—
57C4⋊(C43⋊C8)—22no—
58C4⋊(C43⋊C8)—22no—
59C4⋊(C43⋊C8)C2×C412yes—
60C4⋊(C43⋊C8)D412yes—
61C4⋊(C43⋊C8)C2312yes—
62#13063249C2×C412yes—
63#13063249C2×C412yes—
64#13063245C2×C412yes—
65#13063245C2×C412yes—
66C22⋊(C43⋊C8)—21no—
67C22⋊(C43⋊C8)C2×C412yes—
68C22⋊(C43⋊C8)D412yes—
69(C2×D43)⋊C8—22no—
70(C2×D43)⋊C8—22no—
71#13063236—21no—
72#13063236—22no—
73C4×C43⋊C8—22no—
74C4×C43⋊C8C2311yescharacteristic
75C4×C43⋊C8C2311yescharacteristic
76C4×C43⋊C8C2311yescharacteristic
77C4×C43⋊C8C2311yescharacteristic
78C2×M16×C43—21no—
79C4⋊Q8×C43C2×C411yescharacteristic
80C4⋊Q8×C43C2×C411yescharacteristic
81#125×C43—21no—
82C22⋊Q8×C43—21no—
83C22⋊Q8×C43C2×C412yes—
84C4×Q8×C43—21no—
85C4×Q8×C43C2312yes—
86#117×C43—21no—
87C2×C42×C43C2311yescharacteristic
88C4⋊C8×C43C2312yes—
89C22⋊C8×C43—21no—
90#97×C43—21no—
91C4×C8×C43—21no—
92C4×C8×C43C2311yescharacteristic
93C4×C8×C43C2311yescharacteristic
94C23×D43—21no—
95C2×Q8×C43—21no—
96C2×Q8×C43C22×C412yes—
97C22×C4×C43C22×C411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C22×Dic43—21no—
101C2×D172—21no—
102C2×D172—42no—
103C2×D172C22×C412yes—
104C2×C4×D43—22no—
105C2×C4×D43—22no—
106C2×C4×D43—82no—
107M16×C43—42no—
108C2×C8×C43—21no—
109C2×C8×C43—22no—
110C2×C8×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—22no—
115C4⋊C4×C43—22no—
116C4⋊C4×C43C22×C412yes—
117C22⋊C4×C43—22no—
118C42×C43—22no—
119C42×C43C22×C411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122C42×C43C2411yescharacteristic
123#10621884—42no—
124#10621884—42no—
125(C2×D43)⋊C4—22no—
126(C2×D43)⋊C4—22no—
127C4⋊Dic43—21no—
128C4⋊Dic43C22×C412yes—
129C2×C43⋊C8—22no—
130C2×C43⋊C8C22×C412yes—
131C2×C43⋊C8C22×C412yes—
132C2×C43⋊C8C2×D412yes—
133C2×C43⋊C8C2×D412yes—
134#10621872—82no—
135#10621872—82no—
136C23×C43C4×D411yescharacteristic
137C22×D43—22no—
138C22×D43—42no—
139C22×D43—81no—
140C22×D43—81no—
141Q8×C43—22no—
142Q8×C43—22no—
143Q8×C43—81no—
144C2×C4×C43—22no—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—41no—
149C2×C4×C43C4×D411yescharacteristic
150C2×C4×C43C4×D411yescharacteristic
151C2×C4×C43C4×D411yescharacteristic
152C2×C4×C43C23×C411yescharacteristic
153C2×C4×C43C22×D411yescharacteristic
154C2×C4×C43C2×#4111yescharacteristic
155C2×Dic43—22no—
156C2×Dic43—81no—
157D172—22no—
158D172—22no—
159D172—42no—
160C4×D43—42no—
161C4×D43—42no—
162C4×D43—82no—
163C8×C43—22no—
164C8×C43—41no—
165C8×C43—42no—
166C43⋊C8—22no—
167C43⋊C8—22no—
168C43⋊C8—22no—
169C43⋊C8—22no—
170C43⋊C8—42no—
171#17952—431nomaximal, Sylow
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43C2×C4×D411yescharacteristic
176C2×D43—42no—
177C2×D43—42no—
178C2×D43—42no—
179C2×D43—84no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—42no—
185C4×C43—42no—
186C4×C43#56812yes—
187C4×C43#57712yes—
188Dic43—42no—
189#3101—431no—
190#2985—431no—
191#2975—431no—
192#1592—432no—
193#1590—432no—
194#1588—432no—
195#1583—432no—
196#1572—431no—
197#1490—431no—
198#1485D4311yescharacteristic, complemented
199#1453—431no—
200C2×C43—41no—
201C2×C43#293011yescharacteristic
202C2×C43#294911yescharacteristic
203C2×C43#295611yescharacteristic
204D43—82no—
205#533C2×D4311yescharacteristic
206C2×C4×D4—431no—
207#483—432no—
208#476—432no—
209#461—432no—
210#450—432no—
211#446—432no—
212#446—862no—
213C8×Q8—432no—
214C4×SD16—432no—
215C4×SD16—432no—
216#436—432no—
217#436—432no—
218#436—862no—
219#433—862no—
220#432—431no—
221#431—431no—
222#431—431no—
223#431C2×D4311yescharacteristic
224#407—862no—
225C4×M16C2×D4311yescharacteristic
226#335—432no—
227#334—432no—
228Q8⋊C8C2×D4312yescomplemented
229Q8⋊C8C2×D4312yescomplemented
230D4⋊C8—432no—
231D4⋊C8—432no—
232#322—431no—
233#322—431no—
234#322—431no—
235C82—431no—
236C43#1795211yescharacteristic, complemented, Sylow
237C22×D4—431no—
238C23×C4—861no—
239C2×SD16—432no—
240C2×SD16—432no—
241C2×M16—21no—
242C2×M16—862no—
243C2×M16—862no—
244C4⋊Q8C4×D4311yescharacteristic
245C4⋊Q8C4×D4311yescharacteristic
246#125—21no—
247C22⋊Q8—21no—
248C22⋊Q8C4×D4312yes—
249C4×Q8—21no—
250C4×Q8C22×D4312yes—
251C4×D4—432no—
252C4×D4—432no—
253C4×D4—861no—
254C4×D4—861no—
255#117—21no—
256C2×C4⋊C4—431no—
257C2×C22⋊C4—861no—
258C2×C42C22×D4311yescharacteristic
259#106—432no—
260#106—432no—
261C4⋊C8—432no—
262C4⋊C8—432no—
263C4⋊C8—432no—
264C4⋊C8—862no—
265C4⋊C8—862no—
266C4⋊C8C22×D4312yes—
267#103—432no—
268#103—432no—
269#102—432no—
270#102—432no—
271C22⋊C8—21no—
272C22⋊C8—432no—
273C22⋊C8—432no—
274C22⋊C8—862no—
275C22⋊C8—862no—
276C22⋊C8—861no—
277#97—21no—
278#97—862no—
279#97—861no—
280C4×C8—21no—
281C4×C8—431no—
282C4×C8—431no—
283C4×C8—431no—
284C4×C8—431no—
285C4×C8—862no—
286C4×C8C22×D4311yescharacteristic
287C4×C8C22×D4311yescharacteristic
288C24—861no—
289C2×Q8—21no—
290C2×Q8C2×C4×D4312yes—
291C2×D4—432no—
292C2×D4—861no—
293C2×D4—1722no—
294C22×C4—861no—
295C22×C4—862no—
296C22×C4—862no—
297C22×C4—3442no—
298C22×C4C2×C4×D4311yescharacteristic
299C22×C4D4×D4311yescharacteristic
300C22×C4#1062190011yescharacteristic
301SD16—1722no—
302SD16—1722no—
303M16—42no—
304M16—3442no—
305M16—3442no—
306C2×C8—21no—
307C2×C8—22no—
308C2×C8—21no—
309C2×C8—432no—
310C2×C8—432no—
311C2×C8—432no—
312C2×C8—432no—
313C2×C8—862no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—432no—
320C4⋊C4—861no—
321C4⋊C4C2×C4×D4312yes—
322C22⋊C4—22no—
323C22⋊C4—862no—
324C22⋊C4—862no—
325C42—22no—
326C42C2×C4×D4311yescharacteristic
327C42D4×D4311yescharacteristic
328C42#1062190011yescharacteristic
329C42C23×D4311yescharacteristic
330C23—862no—
331C23—3441no—
332C23—3441no—
333C23—1722no—
334C23(C22⋊D43)⋊C411yescharacteristic
335Q8—22no—
336Q8—22no—
337Q8—81no—
338D4—862no—
339D4—862no—
340D4—1722no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—862no—
347C2×C4—3442no—
348C2×C4—3441no—
349C2×C4—1722no—
350C2×C4—1722no—
351C2×C4(C22⋊D43)⋊C411yescharacteristic
352C2×C4(C22⋊D43)⋊C411yescharacteristic
353C2×C4(C22⋊D43)⋊C411yescharacteristic
354C2×C4C22×C4×D4311yescharacteristic
355C2×C4C2×D4×D4311yescharacteristic
356C2×C4C2×#1062190011yescharacteristic
357C8—22no—
358C8—41no—
359C8—42no—
360C8—862no—
361C8—862no—
362C8—862no—
363C8—862no—
364C8—1722no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—3444no—
369C22—1722no—
370C22—1722no—
371C22—1722no—
372C22C2×(C22⋊D43)⋊C411yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—1722no—
380C4#1458366412yes—
381C4#1458370812yes—
382C2—41no—
383C2—3442no—
384C2#1914330111yescharacteristic
385C2#1914345011yescharacteristic
386C2#1914350111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1485C2
socleC22×C43C2×C4×D4
prime radicalC22×D172C2×C4
cosocleC42×C43C24
hypercenter#1485D43
hypocenterC43#17952
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
2. #19143690C2semidirect
4. #19133500C2semidirect
5. #19133482C2semidirect
6. #19133470C2semidirect
7. #19133435C2semidirect
8. #19133373C2semidirect
10. #19132892C2semidirect
11. C43×#1485C2semidirect
18. #14583030C22semidirect
19. Q8×C43⋊C8C22semidirect
30. #14582651C22semidirect
31. #14582649C22semidirect
34. #14582621C22semidirect
35. #14582621C22semidirect
36. #14582620C22semidirect
37. C8×C43⋊C8C22semidirect
41. C43×Q8⋊C8C22semidirect
42. C43×Q8⋊C8C22semidirect
198. #1485D43semidirect
228. Q8⋊C8C2×D43semidirect
229. Q8⋊C8C2×D43semidirect
236. C43#17952semidirect

Maximal subgroups

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

subgroupindex
#191445992
#191436902
#191436352
#191335002
#191334822
#191334702
#191334352
#191333732
#191330392
#191328922
C43×#14852
#1795243