Finite Group Databasebeta

← #24990900

Subgroups — #24990900

Order 11008.

438 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143160C211yesmaximal, characteristic
2#19134616C211yesmaximal, characteristic
3#19133369C211yesmaximal, characteristic, complemented
4#19133354C211yesmaximal, characteristic, complemented
5#19132978C211yesmaximal, characteristic
6#19132498C211yesmaximal, characteristic, complemented
7C43×#1279C211yesmaximal, characteristic, complemented
8C2×#13063331—21no—
9C4×#10621898C2211yescharacteristic
10#14582952C2211yescharacteristic
11#14582925—21no—
12#14582924—22no—
13#14582923C2211yescharacteristic
14#14582923C2211yescharacteristic
15#14582921—21no—
16C4⋊C8×D43—21no—
17C2×#13063253—21no—
18#14582659—21no—
19#14582652—22no—
20#14582651—21no—
21#14582651—21no—
22#14582631C411yescharacteristic, complemented
23#14582631C411yescharacteristic, complemented
24#14582628C411yescharacteristic, complemented
25#14582628C411yescharacteristic, complemented
26C2×C4⋊C8×C43C2211yescharacteristic
27C2×C4×C8×C43C2211yescharacteristic
28C4×C4⋊C4×C43C2211yescharacteristic
29C2×#10621898D411yescharacteristic
30#13063331—42no—
31#13063331—42no—
32C2×#10621877—21no—
33C2×#10621877—21no—
34C2×#10621872—22no—
35C2×C8×D43—22no—
36C4×Dic86C2×C411yescharacteristic
37C4×Dic86Q811yescharacteristic
38C4×D172C2×C411yescharacteristic
39C4×D172Q811yescharacteristic
40C4×C22⋊D43—21no—
41C4×C22⋊D43—21no—
42#13063284D411yescharacteristic
43#13063282—21no—
44C42×D43—21no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)C2×C411yescharacteristic
49C4⋊(C43⋊C8)C2×C411yescharacteristic
50C4⋊(C43⋊C8)D412yes—
51Dic43⋊C8—22no—
52Dic43⋊C8—22no—
53#13063253—42no—
54C22⋊(C43⋊C8)—21no—
55C4×C43⋊C8—21no—
56C22×C8×C43—21no—
57C22×C8×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C42×C43—21no—
60C2×C42×C43C2311yescharacteristic
61C4⋊C8×C43—21no—
62C4⋊C8×C43D411yescharacteristic
63C4⋊C8×C43D411yescharacteristic
64C4×C8×C43—21no—
65C4×C8×C43C2×C411yescharacteristic
66C4×C8×C43C2×C411yescharacteristic
67#95×C43—21no—
68C22×C4×C43—41no—
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43#4111yescharacteristic
71C22×C4×C43#4111yescharacteristic
72C2×C22⋊D43—21no—
73#10621898—21no—
74#10621898—21no—
75#10621898D812yes—
76#10621898Q1612yes—
77C2×D172C4⋊C411yescharacteristic
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×Dic86C4⋊C411yescharacteristic
82C2×C8×C43—21no—
83C2×C8×C43—21no—
84C2×C8×C43—21no—
85C2×C8×C43—21no—
86C2×C8×C43—42no—
87C2×C8×C43—41no—
88C2×C8×C43—41no—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—41no—
91C42×C43—41no—
92C42×C43—41no—
93C42×C43C22×C411yescharacteristic
94C42×C43C2×D411yescharacteristic
95C42×C43C2×D411yescharacteristic
96C42×C43C2×Q811yescharacteristic
97C22⋊Dic43—21no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100C4⋊Dic43C4⋊C411yescharacteristic
101C4⋊Dic43C4⋊C411yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107#10621877—41no—
108#10621877—41no—
109#10621877—41no—
110#10621877—41no—
111C2×C43⋊C8—21no—
112C2×C43⋊C8—21no—
113C2×C43⋊C8—22no—
114C2×C43⋊C8—41no—
115#10621872—44no—
116C8×D43—44no—
117C23×C43#12311yescharacteristic
118C22×D43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—41no—
122C2×C4×C43—42no—
123C2×C4×C43—81no—
124C2×C4×C43—81no—
125C2×C4×C43C2×C4⋊C411yescharacteristic
126C2×C4×C43C4×D411yescharacteristic
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43#12011yescharacteristic
129C2×C4×C43C22⋊Q811yescharacteristic
130C2×C4×C43C22⋊Q811yescharacteristic
131C2×C4×C43C2×D811yescharacteristic
132C2×C4×C43C2×Q1611yescharacteristic
133C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C43#13711yescharacteristic
135C22⋊D43—22no—
136C22⋊D43—22no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140D172—21no—
141D172#10712yes—
142C4×D43—22no—
143C4×D43—22no—
144C4×D43—41no—
145C4×D43—41no—
146C4×D43—81no—
147Dic86—21no—
148Dic86#10712yes—
149C8×C43—22no—
150C8×C43—41no—
151C8×C43—41no—
152C8×C43—41no—
153C43⋊C8—41no—
154C43⋊C8—41no—
155C43⋊C8—42no—
156C43⋊C8—81no—
157#8902—431nomaximal, Sylow
158C22×C43—21no—
159C22×C43—21no—
160C22×C43#38511yescharacteristic
161C22×C43#48011yescharacteristic
162C22×C43#48411yescharacteristic
163C2×D43—22no—
164C2×D43—41no—
165C2×D43—41no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—82no—
170C4×C43C2×#10711yescharacteristic
171C4×C43#42811yescharacteristic
172C4×C43#44311yescharacteristic
173C4×C43#44411yescharacteristic
174C4×C43#44711yescharacteristic
175C4×C43#45111yescharacteristic
176Dic43—22no—
177Dic43—41no—
178Dic43—41no—
179#2906—431no—
180#1806—431no—
181#1571—431no—
182#1567—431no—
183#1476—431no—
184#1303—431no—
185#1279D4311yescharacteristic, complemented
186C2×C43—21no—
187C2×C43—21no—
188C2×C43#185211yescharacteristic
189C2×C43#186111yescharacteristic
190C2×C43#186611yescharacteristic
191D43—42no—
192C2×#131—861no—
193C4×#41—431no—
194#431—431no—
195#424—862no—
196#424—861no—
197#423—431no—
198#423—431no—
199#423—861no—
200C2×C4⋊C8—861no—
201C2×C4⋊C8C2×D4311yescharacteristic
202C2×#104—861no—
203C2×C4×C8C2×D4311yescharacteristic
204C4×C4⋊C4C2×D4311yescharacteristic
205#339—861no—
206#335—862no—
207#335—861no—
208#335—861no—
209Q8⋊C8—431no—
210Q8⋊C8—431no—
211D4⋊C8—431no—
212D4⋊C8—431no—
213C43#890211yescharacteristic, complemented, Sylow
214C2×#41—431no—
215#131—1722no—
216#131—1722no—
217C2×M16—862no—
218C2×M16—861no—
219C2×M16—861no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—862no—
223C4×Q8—431no—
224C4×Q8—431no—
225C4×D4—431no—
226C4×D4—431no—
227C4×D4—861no—
228C4×D4—861no—
229#117—431no—
230#117—861no—
231C2×C4⋊C4—21no—
232C2×C42—21no—
233C2×C42—861no—
234C2×C42C22×D4311yescharacteristic
235C4⋊C8—21no—
236C4⋊C8—431no—
237C4⋊C8—431no—
238C4⋊C8—432no—
239C4⋊C8—862no—
240C4⋊C8—862no—
241C4⋊C8—861no—
242C4⋊C8—861no—
243C4⋊C8—861no—
244C4⋊C8D17211yescharacteristic
245C4⋊C8D17211yescharacteristic
246#104—1722no—
247C22⋊C8—861no—
248C4×C8—21no—
249C4×C8—861no—
250C4×C8C4×D4311yescharacteristic
251C4×C8C4×D4311yescharacteristic
252#95—21no—
253#41—432no—
254#41—432no—
255#41—861no—
256#41—861no—
257C2×Q8—431no—
258C2×D4—431no—
259C2×D4—861no—
260C22×C4—41no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4#1062189811yescharacteristic
265C22×C4D4×D4311yescharacteristic
266C22×C4#1062190011yescharacteristic
267M16—1724no—
268M16—1721no—
269M16—1721no—
270M16—1721no—
271M16—1721no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—42no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—861no—
280C2×C8—861no—
281C2×C8—862no—
282C2×C8—1724no—
283C2×C8—1721no—
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—431no—
287C4⋊C4—431no—
288C4⋊C4—861no—
289C4⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C42—41no—
294C42—41no—
295C42—861no—
296C42—861no—
297C42—861no—
298C42C2×C4×D4311yescharacteristic
299C42C2×D17211yescharacteristic
300C42D4×D4311yescharacteristic
301C42Q8×D4311yescharacteristic
302C23—861no—
303C23#1306330711yescharacteristic
304Q8—432no—
305Q8—861no—
306D4—432no—
307D4—862no—
308D4—862no—
309D4—861no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—861no—
317C2×C4—862no—
318C2×C4—862no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—3441no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4C4⋊C4×D4311yescharacteristic
325C2×C4(C22⋊D43)⋊C411yescharacteristic
326C2×C4C4×D17211yescharacteristic
327C2×C4#1306329511yescharacteristic
328C2×C4#1306330311yescharacteristic
329C2×C4#1306330511yescharacteristic
330C2×C4D8×D4311yescharacteristic
331C2×C4Q16×D4311yescharacteristic
332C2×C4#1306335211yescharacteristic
333C2×C4#1306335411yescharacteristic
334C8—22no—
335C8—41no—
336C8—41no—
337C8—41no—
338C8—3441no—
339C8—1721no—
340C8—1721no—
341C8—1722no—
342C22—21no—
343C22—21no—
344C22—862no—
345C22—1721no—
346C22—1721no—
347C22#1458277311yescharacteristic
348C22#1458321111yescharacteristic
349C22#1458323311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—82no—
354C4—862no—
355C4—1721no—
356C4—1721no—
357C4#107×D4311yescharacteristic
358C4#1458293811yescharacteristic
359C4#1458301711yescharacteristic
360C4#1458302211yescharacteristic
361C4#1458303411yescharacteristic
362C4#1458305611yescharacteristic
363C2—21no—
364C2—21no—
365C2—1722no—
366C2#1913478411yescharacteristic
367C2#1913483611yescharacteristic
368C2#1913487311yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1279C2
socleC22×C43#385
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1279D43
hypocenterC43#8902
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
3. #19133369C2semidirect
4. #19133354C2semidirect
6. #19132498C2semidirect
7. C43×#1279C2semidirect
22. #14582631C4semidirect
23. #14582631C4semidirect
24. #14582628C4semidirect
25. #14582628C4semidirect
185. #1279D43semidirect
213. C43#8902semidirect

Maximal subgroups

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

subgroupindex
#191431602
#191346162
#191333692
#191333542
#191329782
#191324982
C43×#12792
#890243