Finite Group Databasebeta

← #24990907

Subgroups — #24990907

Order 11008.

392 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143260C211yesmaximal, characteristic
2#19134616C211yesmaximal, characteristic
3#19133365C211yesmaximal, characteristic, complemented
4#19133354C211yesmaximal, characteristic, complemented
5#19132978C211yesmaximal, characteristic
6#19132498C211yesmaximal, characteristic, complemented
7C43×#1279C211yesmaximal, characteristic, complemented
8C4×#10621898C2211yescharacteristic
9#14582959—22no—
10#14582955—21no—
11#14582952C2211yescharacteristic
12#14582951—21no—
13#14582923C2211yescharacteristic
14#14582923C2211yescharacteristic
15C2×#13063253—21no—
16#14582865—21no—
17#14582854—21no—
18#14582659—21no—
19#14582652—22no—
20#14582649—21no—
21#14582649—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
30C2×#10621877—21no—
31C2×#10621877—21no—
32C4×Dic86C2×C411yescharacteristic
33C4×Dic86Q811yescharacteristic
34C4×D172C2×C411yescharacteristic
35C4×D172Q811yescharacteristic
36C4×C22⋊D43—21no—
37C4×C22⋊D43—21no—
38#13063284D411yescharacteristic
39#13063282—21no—
40C42×D43—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)C2×C411yescharacteristic
45C4⋊(C43⋊C8)C2×C411yescharacteristic
46C4⋊(C43⋊C8)D412yes—
47#13063253—42no—
48C22⋊(C43⋊C8)—21no—
49(C2×D43)⋊C8—22no—
50(C2×D43)⋊C8—22no—
51#13063235—22no—
52C4×C43⋊C8—21no—
53C8×Dic43—22no—
54C22×C8×C43—21no—
55C22×C8×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C42×C43—21no—
58C2×C42×C43C2311yescharacteristic
59C4⋊C8×C43—21no—
60C4⋊C8×C43D411yescharacteristic
61C4⋊C8×C43D411yescharacteristic
62C4×C8×C43—21no—
63C4×C8×C43C2×C411yescharacteristic
64C4×C8×C43C2×C411yescharacteristic
65#95×C43—21no—
66C22×C4×C43—41no—
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43#4111yescharacteristic
69C22×C4×C43#4111yescharacteristic
70C2×C22⋊D43—21no—
71#10621898—21no—
72#10621898—21no—
73#10621898—21no—
74#10621898—21no—
75C2×D172C4⋊C411yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×Dic86C4⋊C411yescharacteristic
80C2×C8×C43—21no—
81C2×C8×C43—21no—
82C2×C8×C43—21no—
83C2×C8×C43—21no—
84C2×C8×C43—42no—
85C2×C8×C43—41no—
86C2×C8×C43—41no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—41no—
89C42×C43—41no—
90C42×C43—41no—
91C42×C43C22×C411yescharacteristic
92C42×C43C2×D411yescharacteristic
93C42×C43C2×D411yescharacteristic
94C42×C43C2×Q811yescharacteristic
95C22⋊Dic43—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98C4⋊Dic43C4⋊C411yescharacteristic
99C4⋊Dic43C4⋊C411yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105#10621877—41no—
106#10621877—41no—
107#10621877—41no—
108#10621877—41no—
109C2×C43⋊C8—21no—
110C2×C43⋊C8—21no—
111C2×C43⋊C8—22no—
112C2×C43⋊C8—41no—
113C23×C43#12311yescharacteristic
114C22×D43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—41no—
118C2×C4×C43—42no—
119C2×C4×C43—81no—
120C2×C4×C43—81no—
121C2×C4×C43C2×C4⋊C411yescharacteristic
122C2×C4×C43C4×D411yescharacteristic
123C2×C4×C43C4×D411yescharacteristic
124C2×C4×C43#12011yescharacteristic
125C2×C4×C43C22⋊Q811yescharacteristic
126C2×C4×C43C22⋊Q811yescharacteristic
127C2×C4×C43#13511yescharacteristic
128C2×C4×C43#13511yescharacteristic
129C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C43#13711yescharacteristic
131C22⋊D43—41no—
132C22⋊D43—41no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136D172—21no—
137D172—21no—
138C4×D43—41no—
139C4×D43—41no—
140C4×D43—41no—
141C4×D43—41no—
142C4×D43—81no—
143Dic86—21no—
144Dic86—21no—
145C8×C43—22no—
146C8×C43—41no—
147C8×C43—41no—
148C8×C43—41no—
149C43⋊C8—41no—
150C43⋊C8—41no—
151C43⋊C8—42no—
152C43⋊C8—81no—
153#8903—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43#38511yescharacteristic
157C22×C43#48211yescharacteristic
158C22×C43#48511yescharacteristic
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—41no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—82no—
166C4×C43#42711yescharacteristic
167C4×C43#42811yescharacteristic
168C4×C43#44311yescharacteristic
169C4×C43#44411yescharacteristic
170C4×C43#44911yescharacteristic
171C4×C43#45211yescharacteristic
172Dic43—41no—
173Dic43—41no—
174Dic43—41no—
175#2925—431no—
176#1806—431no—
177#1570—431no—
178#1567—431no—
179#1476—431no—
180#1303—431no—
181#1279D4311yescharacteristic, complemented
182C2×C43—21no—
183C2×C43—21no—
184C2×C43#185411yescharacteristic
185C2×C43#186111yescharacteristic
186C2×C43#186611yescharacteristic
187D43—81no—
188C4×#41—431no—
189#433—862no—
190#432—861no—
191#431—431no—
192#431—861no—
193#423—431no—
194#423—431no—
195C2×C4⋊C8C2×D4311yescharacteristic
196C2×#104—861no—
197#408—861no—
198#405—861no—
199C2×C4×C8C2×D4311yescharacteristic
200C4×C4⋊C4C2×D4311yescharacteristic
201#339—861no—
202#335—862no—
203#334—861no—
204#334—861no—
205Q8⋊C8—431no—
206Q8⋊C8—431no—
207D4⋊C8—431no—
208D4⋊C8—431no—
209C43#890311yescharacteristic, complemented, Sylow
210C2×#41—431no—
211C2×M16—861no—
212C2×M16—861no—
213C22×C8—21no—
214C22×C8—21no—
215C4×Q8—431no—
216C4×Q8—431no—
217C4×D4—431no—
218C4×D4—431no—
219C4×D4—861no—
220C4×D4—861no—
221#117—431no—
222#117—861no—
223C2×C4⋊C4—21no—
224C2×C42—21no—
225C2×C42—861no—
226C2×C42C22×D4311yescharacteristic
227C4⋊C8—21no—
228C4⋊C8—431no—
229C4⋊C8—431no—
230C4⋊C8—432no—
231C4⋊C8—861no—
232C4⋊C8—861no—
233C4⋊C8—861no—
234C4⋊C8D17211yescharacteristic
235C4⋊C8D17211yescharacteristic
236#104—1722no—
237C22⋊C8—862no—
238C22⋊C8—862no—
239C22⋊C8—861no—
240#97—862no—
241C4×C8—21no—
242C4×C8—862no—
243C4×C8—861no—
244C4×C8C4×D4311yescharacteristic
245C4×C8C4×D4311yescharacteristic
246#95—21no—
247#41—861no—
248#41—861no—
249#41—861no—
250#41—861no—
251C2×Q8—431no—
252C2×D4—431no—
253C2×D4—861no—
254C22×C4—41no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4#1062189811yescharacteristic
259C22×C4D4×D4311yescharacteristic
260C22×C4#1062190011yescharacteristic
261M16—1721no—
262M16—1721no—
263M16—1721no—
264M16—1721no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—42no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—861no—
273C2×C8—861no—
274C2×C8—862no—
275C2×C8—1721no—
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—431no—
279C4⋊C4—431no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C42—41no—
286C42—41no—
287C42—861no—
288C42—861no—
289C42—861no—
290C42C2×C4×D4311yescharacteristic
291C42C2×D17211yescharacteristic
292C42D4×D4311yescharacteristic
293C42Q8×D4311yescharacteristic
294C23—861no—
295C23#1306330711yescharacteristic
296Q8—861no—
297Q8—861no—
298D4—861no—
299D4—861no—
300D4—1721no—
301D4—1721no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—861no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—3441no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4C4⋊C4×D4311yescharacteristic
317C2×C4(C22⋊D43)⋊C411yescharacteristic
318C2×C4C4×D17211yescharacteristic
319C2×C4#1306329511yescharacteristic
320C2×C4#1306330311yescharacteristic
321C2×C4#1306330511yescharacteristic
322C2×C4#1306334411yescharacteristic
323C2×C4#1306334811yescharacteristic
324C2×C4#1306335211yescharacteristic
325C2×C4#1306335411yescharacteristic
326C8—22no—
327C8—41no—
328C8—41no—
329C8—41no—
330C8—3441no—
331C8—1722no—
332C8—1721no—
333C8—1721no—
334C22—21no—
335C22—21no—
336C22—1721no—
337C22—1721no—
338C22—1721no—
339C22#1458277311yescharacteristic
340C22#1458322111yescharacteristic
341C22#1458323911yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—82no—
346C4—1721no—
347C4—1721no—
348C4—1721no—
349C4#1458293611yescharacteristic
350C4#1458293811yescharacteristic
351C4#1458301711yescharacteristic
352C4#1458302211yescharacteristic
353C4#1458304711yescharacteristic
354C4#1458306211yescharacteristic
355C2—21no—
356C2—21no—
357C2—3441no—
358C2#1913479711yescharacteristic
359C2#1913483611yescharacteristic
360C2#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#8903
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. #19133365C2semidirect
4. #19133354C2semidirect
6. #19132498C2semidirect
7. C43×#1279C2semidirect
22. #14582631C4semidirect
23. #14582631C4semidirect
24. #14582628C4semidirect
25. #14582628C4semidirect
181. #1279D43semidirect
209. C43#8903semidirect

Maximal subgroups

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

subgroupindex
#191432602
#191346162
#191333652
#191333542
#191329782
#191324982
C43×#12792
#890343