Finite Group Databasebeta

← #24989775

Subgroups — #24989775

Order 11008.

432 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143556C211yesmaximal, characteristic
2#19134616C211yesmaximal, characteristic
3#19134612C211yesmaximal, characteristic
4C4×#13063256C211yesmaximal, characteristic, complemented
5#19133353C211yesmaximal, characteristic, complemented
6#19132497C211yesmaximal, characteristic, complemented
7C43×#1303C211yesmaximal, characteristic, complemented
8C4×#10621898C2211yescharacteristic
9#14583026C411yescharacteristic, complemented
10#14583026C411yescharacteristic, complemented
11#14582976C411yescharacteristic, complemented
12#14582976C411yescharacteristic, complemented
13#14582967—21no—
14#14582967—21no—
15#14582950—21no—
16C2×#13063256—21no—
17#14582923C2211yescharacteristic
18C2×#13063253—21no—
19C2×#13063251—21no—
20C4×#10621872—21no—
21C2×C4×C43⋊C8C2211yescharacteristic
22C4×C4⋊Dic43C2211yescharacteristic
23#14582661—21no—
24#14582660—21no—
25#14582659—21no—
26#14582651—21no—
27#14582651—21no—
28C43×#431C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C4×C4⋊C4×C43C2211yescharacteristic
31C2×#10621898D411yescharacteristic
32C2×#10621877—21no—
33C2×#10621872—21no—
34C2×#10621872—21no—
35C22×C43⋊C8D411yescharacteristic
36C22×C43⋊C8D411yescharacteristic
37C4×Dic86C2×C411yescharacteristic
38C4×Dic86Q811yescharacteristic
39C4×D172C2×C411yescharacteristic
40C4×D172Q811yescharacteristic
41C4×C22⋊D43—21no—
42C4×C22⋊D43—21no—
43#13063284D411yescharacteristic
44#13063282—21no—
45C2×C4⋊Dic43—21no—
46C2×C4×Dic43—21no—
47C42×D43—21no—
48#13063256—24no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)—21no—
51Dic43⋊C8—21no—
52Dic43⋊C8—21no—
53#13063253—42no—
54#13063251—42no—
55(C2×D43)⋊C8—21no—
56(C2×D43)⋊C8—21no—
57#13063235—21no—
58#13063235—21no—
59C4×C43⋊C8C2×C411yescharacteristic
60C4×C43⋊C8C2×C411yescharacteristic
61C4×C43⋊C8D411yescharacteristic
62C4×C43⋊C8D411yescharacteristic
63C43⋊#95—21no—
64C2×M16×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C42×C43—21no—
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43—21no—
69C4⋊C8×C43—21no—
70C4⋊C8×C43C2×C411yescharacteristic
71C4⋊C8×C43C2×C411yescharacteristic
72C22⋊C8×C43—21no—
73C4×C8×C43—21no—
74#95×C43—21no—
75C22×C4×C43—41no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C2×C22⋊D43—21no—
80C22×Dic43—41no—
81#10621898—21no—
82#10621898—21no—
83#10621898—21no—
84#10621898—21no—
85C2×D172C4⋊C411yescharacteristic
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×Dic86C4⋊C411yescharacteristic
90M16×C43—41no—
91M16×C43—41no—
92C2×C8×C43—21no—
93C2×C8×C43—21no—
94C2×C8×C43—41no—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—41no—
97C42×C43—41no—
98C42×C43—41no—
99C42×C43C22×C411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43C2×Q811yescharacteristic
102C42×C43#4111yescharacteristic
103C22⋊Dic43—21no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106C4⋊Dic43—22no—
107C4⋊Dic43—41no—
108C4⋊Dic43C4⋊C411yescharacteristic
109C4⋊Dic43C4⋊C411yescharacteristic
110Dic43⋊C4—21no—
111Dic43⋊C4—21no—
112C4×Dic43—21no—
113C4×Dic43—21no—
114C4×Dic43—21no—
115C4×Dic43—41no—
116C4×Dic43—41no—
117#10621877—41no—
118#10621877—41no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8C22⋊C411yescharacteristic
123C2×C43⋊C8C22⋊C411yescharacteristic
124C2×C43⋊C8C22⋊C411yescharacteristic
125C2×C43⋊C8C22⋊C411yescharacteristic
126#10621872—42no—
127#10621872—42no—
128C23×C43#12111yescharacteristic
129C22×D43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—41no—
133C2×C4×C43—42no—
134C2×C4×C43—81no—
135C2×C4×C43—81no—
136C2×C4×C43C2×C22⋊C411yescharacteristic
137C2×C4×C43C2×C4⋊C411yescharacteristic
138C2×C4×C43#11711yescharacteristic
139C2×C4×C43#12111yescharacteristic
140C2×C4×C43C22⋊Q811yescharacteristic
141C2×C4×C43C22⋊Q811yescharacteristic
142C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C43#13711yescharacteristic
145C2×C4×C43#13711yescharacteristic
146C22⋊D43—41no—
147C22⋊D43—41no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—42no—
152C2×Dic43—81no—
153C2×Dic43—81no—
154D172—21no—
155D172—21no—
156C4×D43—42no—
157C4×D43—41no—
158C4×D43—41no—
159C4×D43—41no—
160C4×D43—41no—
161Dic86—21no—
162Dic86—21no—
163C8×C43—41no—
164C8×C43—41no—
165C8×C43—81no—
166C43⋊C8—21no—
167C43⋊C8—21no—
168C43⋊C8—21no—
169C43⋊C8—81no—
170C43⋊C8#10412yescomplemented
171#8669—431nomaximal, Sylow
172C22×C43—21no—
173C22×C43—21no—
174C22×C43#38011yescharacteristic
175C22×C43#46811yescharacteristic
176C22×C43#46811yescharacteristic
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—41no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—82no—
184C4×C43C2×#10411yescharacteristic
185C4×C43#42111yescharacteristic
186C4×C43#42811yescharacteristic
187C4×C43#42811yescharacteristic
188C4×C43#46911yescharacteristic
189C4×C43#47011yescharacteristic
190Dic43—41no—
191Dic43—41no—
192Dic43—41no—
193Dic43—82no—
194#2965—431no—
195#1806—431no—
196#1806—431no—
197C4×#106—431no—
198#1567—431no—
199#1303—431no—
200#1303D4311yescharacteristic, complemented
201C2×C43—21no—
202C2×C43—21no—
203C2×C43#180611yescharacteristic
204C2×C43#180911yescharacteristic
205C2×C43#181411yescharacteristic
206D43—81no—
207C4×#41—431no—
208#446—431no—
209#446—431no—
210#436—431no—
211#436—431no—
212#435—861no—
213#435—861no—
214#431—861no—
215#431C2×D4311yescharacteristic
216C2×#106—861no—
217#423—431no—
218#423C2×D4311yescharacteristic
219C2×#104—861no—
220C2×#104—861no—
221C4×M16—861no—
222C2×C4×C8—431no—
223C4×C4⋊C4—431no—
224C4×C4⋊C4C2×D4311yescharacteristic
225#340—861no—
226#339—861no—
227#339—861no—
228#335—861no—
229#335—861no—
230C43#866911yescharacteristic, complemented, Sylow
231C2×#41—431no—
232C2×M16—21no—
233C2×M16—861no—
234C2×M16—861no—
235C2×M16—861no—
236C22×C8—431no—
237C22×C8—431no—
238C4×Q8—431no—
239C4×Q8—431no—
240C4×D4—431no—
241C4×D4—431no—
242C4×D4—861no—
243C4×D4—861no—
244#117—431no—
245#117—861no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—861no—
248C2×C42—21no—
249C2×C42—861no—
250C2×C42—861no—
251C2×C42C22×D4311yescharacteristic
252#106—864no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—861no—
256C4⋊C8—861no—
257C4⋊C8—861no—
258C4⋊C8—861no—
259C4⋊C8C4×D4311yescharacteristic
260C4⋊C8C4×D4311yescharacteristic
261#104—1722no—
262#104—1722no—
263C22⋊C8—21no—
264C22⋊C8—861no—
265C22⋊C8—861no—
266#97—861no—
267#97—861no—
268C4×C8—21no—
269C4×C8—431no—
270C4×C8—431no—
271C4×C8—431no—
272C4×C8—431no—
273#95—21no—
274#95—861no—
275#41—861no—
276#41—861no—
277#41—861no—
278#41—861no—
279C2×Q8—431no—
280C2×D4—431no—
281C2×D4—861no—
282C22×C4—41no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—1721no—
287C22×C4#1062189811yescharacteristic
288C22×C4D4×D4311yescharacteristic
289C22×C4D4×D4311yescharacteristic
290M16—41no—
291M16—41no—
292M16—1722no—
293M16—1722no—
294M16—1721no—
295M16—1721no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—41no—
299C2×C8—431no—
300C2×C8—431no—
301C2×C8—431no—
302C2×C8—431no—
303C2×C8—862no—
304C2×C8—1721no—
305C2×C8—1721no—
306C4⋊C4—22no—
307C4⋊C4—41no—
308C4⋊C4—431no—
309C4⋊C4—431no—
310C4⋊C4—862no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4—1721no—
314C22⋊C4—861no—
315C22⋊C4—861no—
316C22⋊C4—861no—
317C42—41no—
318C42—41no—
319C42—861no—
320C42—861no—
321C42—861no—
322C42—1721no—
323C42—1721no—
324C42C2×C4×D4311yescharacteristic
325C42#1062189811yescharacteristic
326C42D4×D4311yescharacteristic
327C42Q8×D4311yescharacteristic
328C23—861no—
329C23#1306329811yescharacteristic
330Q8—861no—
331Q8—861no—
332D4—861no—
333D4—861no—
334D4—1721no—
335D4—1721no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—3441no—
346C2×C4—3441no—
347C2×C4—1722no—
348C2×C4—1722no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4C22⋊C4×D4311yescharacteristic
354C2×C4C4⋊C4×D4311yescharacteristic
355C2×C4#1306328211yescharacteristic
356C2×C4#1306329811yescharacteristic
357C2×C4#1306330311yescharacteristic
358C2×C4#1306330311yescharacteristic
359C2×C4#1306334911yescharacteristic
360C2×C4#1306335211yescharacteristic
361C2×C4#1306335411yescharacteristic
362C2×C4#1306335711yescharacteristic
363C8—41no—
364C8—41no—
365C8—81no—
366C8—432no—
367C8—861no—
368C8—861no—
369C8—861no—
370C8—3441no—
371C22—21no—
372C22—21no—
373C22—1721no—
374C22—1721no—
375C22—1721no—
376C22#1458275811yescharacteristic
377C22#1458314411yescharacteristic
378C22#1458314811yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—3442no—
384C4—1721no—
385C4—1721no—
386C4—1721no—
387C4#104×D4311yescharacteristic
388C4#1458291411yescharacteristic
389C4#1458293811yescharacteristic
390C4#1458294011yescharacteristic
391C4#1458315111yescharacteristic
392C4#1458315611yescharacteristic
393C2—21no—
394C2—21no—
395C2—3441no—
396C2#1913461411yescharacteristic
397C2#1913462711yescharacteristic
398C2#1913464811yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1303C2
socleC22×C43#380
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1303D43
hypocenterC43#8669
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
4. C4×#13063256C2semidirect
5. #19133353C2semidirect
6. #19132497C2semidirect
7. C43×#1303C2semidirect
9. #14583026C4semidirect
10. #14583026C4semidirect
11. #14582976C4semidirect
12. #14582976C4semidirect
170. C43⋊C8#104semidirect
200. #1303D43semidirect
230. C43#8669semidirect

Maximal subgroups

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

subgroupindex
#191435562
#191346162
#191346122
C4×#130632562
#191333532
#191324972
C43×#13032
#866943