Finite Group Databasebeta

← #24993099

Subgroups — #24993099

Order 11008.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145522C211yesmaximal, characteristic
2#19143341C211yesmaximal, characteristic
3#19135584C211yesmaximal, characteristic, complemented
4#19133270C211yesmaximal, characteristic
5C2×#14582647C211yesmaximal, characteristic, complemented
6#19132491C211yesmaximal, characteristic, complemented
7C43×#1283C211yesmaximal, characteristic, complemented
8C2×#13063333—21no—
9#14583449C2211yescharacteristic
10C2×#13063325C2211yescharacteristic
11#14583272—21no—
12#14583250—21no—
13#14583105—22no—
14#14583040C414yes—
15#14582978—21no—
16#14582972—22no—
17C8×D172—21no—
18#14582923C2211yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20#14582867—21no—
21#14582667—21no—
22#14582667—21no—
23#14582647—21no—
24#14582647—21no—
25#14582644—21no—
26#14582642—21no—
27C43×#431C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C4×M16×C43C2211yescharacteristic
30C2×#10621898—21no—
31C22×Dic86C2×C412yes—
32C2×#10621873—24no—
33#13063333—42no—
34#13063333—42no—
35C2×#10621877—21no—
36C2×#10621872—22no—
37C22×C43⋊C8—21no—
38C2×C8×D43—22no—
39#13063325—21no—
40#13063325—21no—
41#13063325—21no—
42#13063325—21no—
43#13063325D411yescharacteristic
44#13063322D411yescharacteristic
45#13063313—21no—
46#13063299—21no—
47#13063299C2×C412yes—
48C4×D172—21no—
49C4×D172D412yes—
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)D411yescharacteristic
56C4⋊(C43⋊C8)D411yescharacteristic
57#13063250—24no—
58(C2×D43)⋊C8—22no—
59(C2×D43)⋊C8—22no—
60C2×M16×C43D411yescharacteristic
61C2×M16×C43D411yescharacteristic
62C22×C8×C43—21no—
63C2×C42×C43C2311yescharacteristic
64C4⋊C8×C43—21no—
65C4⋊C8×C43—21no—
66C4⋊C8×C43—21no—
67C22⋊C8×C43C2×C412yes—
68#97×C43—21no—
69C4×C8×C43—21no—
70C4×C8×C43—21no—
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43#4111yescharacteristic
74C2×C22⋊D43—22no—
75C22×Dic43—22no—
76#10621898—41no—
77#10621898—41no—
78#10621898—41no—
79#10621898—41no—
80C2×D172—21no—
81C2×D172—21no—
82C2×D172C22⋊C412yes—
83C2×C4×D43—22no—
84C2×Dic86—21no—
85C2×Dic86—22no—
86C2×Dic86—22no—
87C2×Dic86—82no—
88M16×C43—21no—
89M16×C43—21no—
90M16×C43—21no—
91M16×C43SD1612yescomplemented
92C2×C8×C43—21no—
93C2×C8×C43—22no—
94C2×C8×C43—21no—
95C2×C8×C43—41no—
96C2×C8×C43—81no—
97C42×C43C2×D411yescharacteristic
98C42×C43C2×D411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43#4111yescharacteristic
101(C2×D43)⋊C4—22no—
102(C2×D43)⋊C4—22no—
103C4⋊Dic43—21no—
104C4⋊Dic43—41no—
105C4⋊Dic43—41no—
106C4⋊Dic43—41no—
107C4⋊Dic43—41no—
108C4⋊Dic43C22⋊C412yes—
109#10621877—41no—
110#10621877—41no—
111C2×C43⋊C8—21no—
112C2×C43⋊C8—21no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116#10621873—84no—
117#10621872—44no—
118C8×D43—44no—
119C23×C43C4×D411yescharacteristic
120C22×D43—22no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—41no—
124C2×C4×C43C2×C22⋊C411yescharacteristic
125C2×C4×C43C4×D411yescharacteristic
126C2×C4×C43#12011yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43#12111yescharacteristic
129C2×C4×C43#12311yescharacteristic
130C2×C4×C43C2×SD1611yescharacteristic
131C2×C4×C43#13511yescharacteristic
132C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C43#13711yescharacteristic
134C22⋊D43—42no—
135C22⋊D43—42no—
136C2×Dic43—22no—
137C2×Dic43—42no—
138C2×Dic43—82no—
139D172—42no—
140D172—41no—
141D172—41no—
142D172—41no—
143D172—41no—
144C4×D43—42no—
145C4×D43—42no—
146Dic86—41no—
147Dic86—41no—
148Dic86—44no—
149Dic86—82no—
150C8×C43—22no—
151C8×C43—42no—
152C8×C43—41no—
153C8×C43—81no—
154C43⋊C8—41no—
155C43⋊C8—41no—
156C43⋊C8—81no—
157#9267—431nomaximal, Sylow
158C22×C43—21no—
159C22×C43—21no—
160C22×C43#38611yescharacteristic
161C22×C43C4×SD1611yescharacteristic
162C22×C43#44011yescharacteristic
163C2×D43—42no—
164C2×D43—42no—
165C2×D43—42no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43#45011yescharacteristic
170C4×C43#45211yescharacteristic
171C4×C43#46111yescharacteristic
172C4×C43#46311yescharacteristic
173C4×C43#47111yescharacteristic
174C4×C43#47311yescharacteristic
175Dic43—42no—
176Dic43—82no—
177#3206—431no—
178#2935—431no—
179#1997—431no—
180#1547—431no—
181C2×#333—431no—
182#1301—431no—
183#1283D4311yescharacteristic, complemented
184C2×C43—21no—
185C2×C43—21no—
186C2×C43#187711yescharacteristic
187C2×C43#190811yescharacteristic
188C2×C43#191411yescharacteristic
189D43—82no—
190C2×#131—861no—
191#532—431no—
192C2×C4⋊Q8—431no—
193#492—861no—
194#487—861no—
195#461—862no—
196#448—434no—
197#436—861no—
198#435—862no—
199C8×D4—861no—
200#431C2×D4311yescharacteristic
201#423—431no—
202C2×C4⋊C8—431no—
203C2×C4⋊C8C2×D4311yescharacteristic
204#408—861no—
205C4×M16C2×D4311yescharacteristic
206#343—861no—
207#343—861no—
208#333—861no—
209#333—861no—
210#332—861no—
211#331—861no—
212C43#926711yescharacteristic, complemented, Sylow
213C2×#41—861no—
214C22×Q8—432no—
215C2×SD16—864no—
216#131—1722no—
217#131—1722no—
218C2×M16—862no—
219C2×M16—861no—
220C2×M16D17211yescharacteristic
221C2×M16D17211yescharacteristic
222C22×C8—21no—
223C22×C8—862no—
224C22×C8—861no—
225C4⋊Q8—431no—
226C4⋊Q8—861no—
227C4⋊Q8—861no—
228C4⋊Q8—861no—
229C4⋊Q8—861no—
230#127—431no—
231#124—861no—
232#121—432no—
233#121—861no—
234C4×D4—432no—
235C4×D4—861no—
236C2×C4⋊C4—861no—
237C2×C4⋊C4—861no—
238C2×C42C22×D4311yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—431no—
243C4⋊C8—431no—
244C4⋊C8—861no—
245C4⋊C8—861no—
246C4⋊C8—861no—
247#103—864no—
248C22⋊C8—862no—
249C22⋊C8—862no—
250C22⋊C8C4×D4312yes—
251#97—21no—
252C4×C8—21no—
253C4×C8—21no—
254#41—1721no—
255#41—1721no—
256#41—1721no—
257#41—1721no—
258C2×Q8—861no—
259C2×Q8—862no—
260C2×Q8—862no—
261C2×Q8—3442no—
262C2×D4—432no—
263C2×D4—862no—
264C2×D4—861no—
265C2×D4—861no—
266C22×C4—862no—
267C22×C4—862no—
268C22×C4C2×C4×D4311yescharacteristic
269C22×C4C2×D17211yescharacteristic
270C22×C4#1062189811yescharacteristic
271SD16—3444no—
272M16—21no—
273M16—21no—
274M16—21no—
275M16—1724no—
276M16—1721no—
277M16—1721no—
278M16#1062187312yescomplemented
279C2×C8—21no—
280C2×C8—22no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—81no—
284C2×C8—861no—
285C2×C8—861no—
286C2×C8—1724no—
287C2×C8—1721no—
288C2×C8—1721no—
289C2×C8—1721no—
290C4⋊C4—432no—
291C4⋊C4—861no—
292C4⋊C4—1721no—
293C4⋊C4—1721no—
294C4⋊C4—1721no—
295C4⋊C4—1721no—
296C22⋊C4—862no—
297C22⋊C4—862no—
298C42D4×D4311yescharacteristic
299C42D4×D4311yescharacteristic
300C42D4×D4311yescharacteristic
301C42#1062190211yescharacteristic
302C23—862no—
303C23C4×D17211yescharacteristic
304Q8—3442no—
305Q8—1724no—
306Q8—1721no—
307Q8—1721no—
308D4—1722no—
309D4—1722no—
310D4—1722no—
311D4—1721no—
312D4—1721no—
313D4—1721no—
314D4—1721no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—862no—
319C2×C4—3442no—
320C2×C4—1722no—
321C2×C4—1722no—
322C2×C4—1722no—
323C2×C4C22⋊C4×D4311yescharacteristic
324C2×C4#1306328711yescharacteristic
325C2×C4#1306329511yescharacteristic
326C2×C4#1306329811yescharacteristic
327C2×C4#1306330011yescharacteristic
328C2×C4#1306331011yescharacteristic
329C2×C4C2×#1062187311yescharacteristic
330C2×C4#1306334711yescharacteristic
331C2×C4#1306335311yescharacteristic
332C2×C4#1306335811yescharacteristic
333C8—22no—
334C8—42no—
335C8—41no—
336C8—81no—
337C8—3441no—
338C8—1721no—
339C8—1721no—
340C22—21no—
341C22—21no—
342C22—1722no—
343C22—1722no—
344C22—1722no—
345C22#1458277711yescharacteristic
346C22C4×#1062187311yescharacteristic
347C22#1458300111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—3442no—
352C4—1722no—
353C4#1458305211yescharacteristic
354C4#1458306311yescharacteristic
355C4#1458310511yescharacteristic
356C4#1458311511yescharacteristic
357C4#1458316111yescharacteristic
358C4#1458317311yescharacteristic
359C2—21no—
360C2—21no—
361C2—3442no—
362C2#1913492811yescharacteristic
363C2#1913511111yescharacteristic
364C2#1913514111yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1283C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1283D43
hypocenterC43#9267
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
3. #19135584C2semidirect
5. C2×#14582647C2semidirect
6. #19132491C2semidirect
7. C43×#1283C2semidirect
91. M16×C43SD16semidirect
183. #1283D43semidirect
212. C43#9267semidirect
278. M16#10621873semidirect

Maximal subgroups

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

subgroupindex
#191455222
#191433412
#191355842
#191332702
C2×#145826472
#191324912
C43×#12832
#926743