Finite Group Databasebeta

← #24995749

Subgroups — #24995749

Order 11008.

468 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145155C211yesmaximal, characteristic
2#19135514C211yesmaximal, characteristic
3C4×#13063256C211yesmaximal, characteristic, complemented
4#19133094C211yesmaximal, characteristic, complemented
5#19133089C211yesmaximal, characteristic
6M16×C43⋊C8C211yesmaximal, characteristic, complemented
7C43×#1986C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583295C411yescharacteristic, complemented
10#14583273C411yescharacteristic, complemented
11#14583249C411yescharacteristic, complemented
12#14583247C411yescharacteristic, complemented
13#14583130—21no—
14#14583130—21no—
15C4×#10621884—21no—
16C4×#10621884—21no—
17#14582952C2211yescharacteristic
18C2×#13063256—21no—
19C2×#13063251—22no—
20C2×C4×C43⋊C8C2211yescharacteristic
21C4×C4⋊Dic43C2211yescharacteristic
22#14582661—21no—
23#14582636—22no—
24#14582632—22no—
25#14582620—21no—
26C8×C43⋊C8—21no—
27C43×#533C2211yescharacteristic
28C4×M16×C43C2211yescharacteristic
29C4×C4⋊C4×C43C2211yescharacteristic
30C43×#339—22no—
31C2×#10621898—21no—
32C2×#10621884—21no—
33C2×#10621884—21no—
34C22×C43⋊C8D411yescharacteristic
35C22×C43⋊C8D411yescharacteristic
36#13063325C2×C411yescharacteristic
37#13063322C2×C411yescharacteristic
38#13063313—21no—
39#13063299—21no—
40#13063299—21no—
41C4×D172—21no—
42C4×D172—21no—
43C2×C4⋊Dic43—21no—
44C2×C4×Dic43—21no—
45#13063256—24no—
46#13063256—21no—
47#13063256—21no—
48C4⋊(C43⋊C8)—21no—
49#13063251—44no—
50#13063249—21no—
51#13063249—21no—
52#13063245—21no—
53#13063245—21no—
54C22⋊(C43⋊C8)D412yes—
55C4×C43⋊C8—21no—
56C4×C43⋊C8C2×C411yescharacteristic
57C4×C43⋊C8C2×C411yescharacteristic
58C4×C43⋊C8D411yescharacteristic
59C4×C43⋊C8D411yescharacteristic
60C43⋊#95—21no—
61C2×M16×C43D412yes—
62C4⋊Q8×C43C2×C411yescharacteristic
63C4⋊Q8×C43C2×C411yescharacteristic
64#125×C43—21no—
65C22⋊Q8×C43—21no—
66C22⋊Q8×C43—21no—
67C4×Q8×C43—21no—
68C4×Q8×C43—21no—
69#117×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C42×C43—21no—
72C2×C42×C43C2311yescharacteristic
73#97×C43—21no—
74C4×C8×C43—21no—
75#95×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43—21no—
78C22×C4×C43—41no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C2×C22⋊D43—41no—
83C22×Dic43—41no—
84#10621898—42no—
85#10621898—42no—
86C2×D172—21no—
87C2×D172—21no—
88C2×D172—21no—
89C2×C4×D43—41no—
90C2×Dic86—21no—
91M16×C43—22no—
92M16×C43SD1614yescomplemented
93C2×C8×C43—22no—
94C4⋊C4×C43—22no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C22⋊C4×C43—41no—
103C42×C43—41no—
104C42×C43—42no—
105C42×C43C22×C411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43#4111yescharacteristic
108C42×C43#4111yescharacteristic
109#10621884—42no—
110#10621884—42no—
111(C2×D43)⋊C4—41no—
112(C2×D43)⋊C4—41no—
113C4⋊Dic43—22no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116C4⋊Dic43—41no—
117C4×Dic43—42no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8C22⋊C411yescharacteristic
122C2×C43⋊C8C22⋊C411yescharacteristic
123C2×C43⋊C8C22⋊C411yescharacteristic
124C2×C43⋊C8C22⋊C411yescharacteristic
125C23×C43#12711yescharacteristic
126C22×D43—41no—
127Q8×C43—41no—
128Q8×C43—41no—
129Q8×C43—81no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—41no—
133C2×C4×C43—42no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—81no—
137C2×C4×C43—81no—
138C2×C4×C43C2×C22⋊C411yescharacteristic
139C2×C4×C43C4×D411yescharacteristic
140C2×C4×C43C4×D411yescharacteristic
141C2×C4×C43#12111yescharacteristic
142C2×C4×C43#12111yescharacteristic
143C2×C4×C43#12411yescharacteristic
144C2×C4×C43C2×SD1612yes—
145C2×C4×C43#13512yes—
146C22⋊D43—81no—
147C22⋊D43—81no—
148C2×Dic43—42no—
149C2×Dic43—41no—
150C2×Dic43—81no—
151C2×Dic43—81no—
152D172—41no—
153D172—41no—
154D172—42no—
155D172—81no—
156C4×D43—82no—
157Dic86—42no—
158C8×C43—24no—
159C43⋊C8—21no—
160C43⋊C8—21no—
161C43⋊C8—21no—
162C43⋊C8—42no—
163C43⋊C8#10412yescomplemented
164#9717—431nomaximal, Sylow
165C22×C43—21no—
166C22×C43—21no—
167C22×C43#39011yescharacteristic
168C22×C43#49211yescharacteristic
169C22×C43#49511yescharacteristic
170C2×D43—81no—
171C2×D43—81no—
172C2×D43—81no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—82no—
177C4×C43—81no—
178C4×C43—81no—
179C4×C43C2×#10411yescharacteristic
180C4×C43#42111yescharacteristic
181C4×C43C4×SD1612yes—
182C4×C43#46512yes—
183Dic43—82no—
184Dic43—81no—
185#3167—431no—
186#1986D4311yescharacteristic, complemented
187#1980—431no—
188C4×#106—431no—
189#1503—431no—
190#1502—431no—
191C8×M16—431no—
192C2×C43—21no—
193C2×C43—21no—
194C2×C43#196811yescharacteristic
195C2×C43#197611yescharacteristic
196C2×C43#198011yescharacteristic
197D43—161no—
198#533C2×D4311yescharacteristic
199#532—431no—
200#498—431no—
201#492—431no—
202#487—431no—
203#486—431no—
204#465—861no—
205#465—861no—
206C4×SD16—861no—
207C4×SD16—861no—
208#431—431no—
209C2×#106—861no—
210C2×#104—862no—
211C4×M16C2×D4311yescharacteristic
212C2×C4×C8—431no—
213C4×C4⋊C4—431no—
214C4×C4⋊C4C2×D4311yescharacteristic
215#340—861no—
216#339—22no—
217#328—862no—
218#327—862no—
219#322—861no—
220C82—861no—
221C43#971711yescharacteristic, complemented, Sylow
222C2×#41—861no—
223C2×SD16—861no—
224C2×SD16—861no—
225C2×M16C22⋊D4312yes—
226C22×C8—431no—
227C22×C8—431no—
228C4⋊Q8—431no—
229C4⋊Q8C4×D4311yescharacteristic
230C4⋊Q8C4×D4311yescharacteristic
231#127—431no—
232#125—21no—
233#124—861no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236#121—861no—
237#121—861no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×D4—861no—
241C4×D4—861no—
242#117—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—861no—
245C2×C42—21no—
246C2×C42—861no—
247C2×C42C22×D4311yescharacteristic
248#106—861no—
249#106—861no—
250#106—864no—
251C4⋊C8—861no—
252#104—1724no—
253#103—861no—
254#103—861no—
255#102—861no—
256#102—861no—
257C22⋊C8—432no—
258#97—21no—
259C4×C8—21no—
260C4×C8—431no—
261C4×C8—431no—
262C4×C8—431no—
263C4×C8—431no—
264C4×C8—861no—
265#95—21no—
266#95—861no—
267#41—1722no—
268#41—1722no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—861no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4—1721no—
276C22×C4—41no—
277C22×C4—1721no—
278C22×C4—1721no—
279C22×C4D4×D4311yescharacteristic
280C22×C4D4×D4311yescharacteristic
281C22×C4C2×C22⋊D4311yescharacteristic
282SD16—1722no—
283SD16—1722no—
284M16—22no—
285M16#1062188414yescomplemented
286C2×C8—22no—
287C2×C8—431no—
288C2×C8—431no—
289C2×C8—431no—
290C2×C8—431no—
291C2×C8—862no—
292C2×C8—862no—
293C2×C8—1721no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—862no—
303C4⋊C4—861no—
304C4⋊C4—861no—
305C4⋊C4—1721no—
306C22⋊C4—41no—
307C22⋊C4—1721no—
308C22⋊C4—1721no—
309C42—41no—
310C42—42no—
311C42—1722no—
312C42C2×C4×D4311yescharacteristic
313C42#1062189811yescharacteristic
314C42D4×D4311yescharacteristic
315C42#1062190011yescharacteristic
316C23—1721no—
317C23#1306332111yescharacteristic
318Q8—41no—
319Q8—41no—
320Q8—81no—
321Q8—1722no—
322D4—3441no—
323D4—3441no—
324D4—3441no—
325D4—1721no—
326D4—1721no—
327D4—1722no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—3441no—
337C2×C4—3441no—
338C2×C4—3442no—
339C2×C4—1722no—
340C2×C4—1721no—
341C2×C4C22⋊C4×D4311yescharacteristic
342C2×C4(C22⋊D43)⋊C411yescharacteristic
343C2×C4C4×C22⋊D4311yescharacteristic
344C2×C4#1306329711yescharacteristic
345C2×C4#1306329811yescharacteristic
346C2×C4#1306331111yescharacteristic
347C2×C4C2×#1062188412yes—
348C2×C4#1306334512yes—
349C8—24no—
350C8—432no—
351C8—861no—
352C8—861no—
353C8—861no—
354C8—1722no—
355C22—21no—
356C22—21no—
357C22—3441no—
358C22—3441no—
359C22—3441no—
360C22#1458279911yescharacteristic
361C22#1458327311yescharacteristic
362C22#1458328111yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—81no—
368C4—81no—
369C4—3442no—
370C4—3441no—
371C4#104×D4311yescharacteristic
372C4#1458291411yescharacteristic
373C4C4×#1062188412yes—
374C4#1458313012yes—
375C2—21no—
376C2—21no—
377C2—6881no—
378C2#1913545211yescharacteristic
379C2#1913549211yescharacteristic
380C2#1913551211yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1986C2
socleC22×C43#390
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1986D43
hypocenterC43#9717
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
3. C4×#13063256C2semidirect
4. #19133094C2semidirect
6. M16×C43⋊C8C2semidirect
7. C43×#1986C2semidirect
9. #14583295C4semidirect
10. #14583273C4semidirect
11. #14583249C4semidirect
12. #14583247C4semidirect
92. M16×C43SD16semidirect
163. C43⋊C8#104semidirect
186. #1986D43semidirect
221. C43#9717semidirect
285. M16#10621884semidirect

Maximal subgroups

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

subgroupindex
#191451552
#191355142
C4×#130632562
#191330942
#191330892
M16×C43⋊C82
C43×#19862
#971743