Finite Group Databasebeta

← #24995771

Subgroups — #24995771

Order 11008.

460 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#19145154C211yesmaximal, characteristic
2#19135538C211yesmaximal, characteristic, complemented
3#19135513C211yesmaximal, characteristic
4#19133093C211yesmaximal, characteristic, complemented
5#19133089C211yesmaximal, characteristic
6#19132884C211yesmaximal, characteristic, complemented
7C4×#107×C43C211yesmaximal, characteristic, complemented
8#14583456C2211yescharacteristic
9#14583449C2211yescharacteristic
10#14583297C411yescharacteristic, complemented
11#14583272C411yescharacteristic, complemented
12#14583250C411yescharacteristic, complemented
13#14583246C411yescharacteristic, complemented
14#14583128—21no—
15#14583128—21no—
16C4×#10621873—21no—
17C4×#10621873—21no—
18#14582952C2211yescharacteristic
19C2×#13063253—22no—
20C4×#10621877C2211yescharacteristic
21#14582659—22no—
22#14582635—22no—
23#14582632—22no—
24#14582621—21no—
25#14582620—21no—
26C2×#107×C43—21no—
27C2×C4×C8×C43C2211yescharacteristic
28C4×C4⋊C4×C43C2211yescharacteristic
29C4×C4⋊C4×C43C2211yescharacteristic
30C43×#340—21no—
31C2×#10621898—21no—
32C2×#10621873—21no—
33C2×#10621873—21no—
34C2×#10621877D412yes—
35#13063325C2×C411yescharacteristic
36#13063325C2×C411yescharacteristic
37#13063325C2×C411yescharacteristic
38#13063322C2×C411yescharacteristic
39#13063317—21no—
40#13063313—21no—
41#13063304—21no—
42#13063304—21no—
43#13063299—21no—
44#13063299—21no—
45C4×Dic86—21no—
46C4×Dic86—21no—
47C4×D172—21no—
48C4×D172—21no—
49#13063284—21no—
50#13063257—21no—
51#13063257—21no—
52C4⋊(C43⋊C8)—21no—
53#13063253—44no—
54#13063250—21no—
55#13063250—21no—
56#13063247—21no—
57#13063247—21no—
58C22⋊(C43⋊C8)D412yes—
59#13063236—21no—
60C4×C43⋊C8—21no—
61C4×C43⋊C8—21no—
62C22×C8×C43D411yescharacteristic
63C22×C8×C43D411yescharacteristic
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C42×C43—21no—
67C2×C42×C43—21no—
68C2×C42×C43C2311yescharacteristic
69#107×C43—24no—
70C4×C8×C43C2×C411yescharacteristic
71C4×C8×C43C2×C411yescharacteristic
72C4×C8×C43D411yescharacteristic
73C4×C8×C43D411yescharacteristic
74#95×C43—21no—
75#95×C43—21no—
76C22×C4×C43—41no—
77C22×C4×C43—41no—
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C2×C22⋊D43—41no—
82#10621898—42no—
83#10621898—42no—
84C2×D172—21no—
85C2×D172—21no—
86C2×D172—21no—
87C2×C4×D43—41no—
88C2×Dic86—21no—
89C2×Dic86—21no—
90C2×Dic86—21no—
91C2×C8×C43—22no—
92C2×C8×C43—41no—
93C2×C8×C43C22⋊C411yescharacteristic
94C2×C8×C43C22⋊C411yescharacteristic
95C2×C8×C43C22⋊C411yescharacteristic
96C2×C8×C43C22⋊C411yescharacteristic
97C4⋊C4×C43—22no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C42×C43—42no—
102C42×C43—42no—
103C42×C43C22×C411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43#4111yescharacteristic
106C42×C43#4111yescharacteristic
107C22⋊Dic43—41no—
108(C2×D43)⋊C4—41no—
109(C2×D43)⋊C4—41no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116Dic43⋊C4—41no—
117Dic43⋊C4—41no—
118C4×Dic43—41no—
119#10621877—22no—
120#10621877—22no—
121C2×C43⋊C8—22no—
122C2×C43⋊C8—22no—
123#10621873—42no—
124#10621873—42no—
125C23×C43#12711yescharacteristic
126C22×D43—41no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—41no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43—81no—
133C2×C4×C43—81no—
134C2×C4×C43—81no—
135C2×C4×C43—81no—
136C2×C4×C43C2×C22⋊C411yescharacteristic
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43#12111yescharacteristic
140C2×C4×C43#12111yescharacteristic
141C2×C4×C43#12411yescharacteristic
142C2×C4×C43AGL(1,ℤ/8)12yes—
143C2×C4×C43#13712yes—
144C22⋊D43—81no—
145C22⋊D43—81no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149D172—41no—
150D172—41no—
151D172—42no—
152D172—81no—
153C4×D43—82no—
154Dic86—41no—
155Dic86—41no—
156Dic86—42no—
157Dic86—81no—
158C8×C43—21no—
159C8×C43—21no—
160C8×C43—21no—
161C8×C43#10412yescomplemented
162C43⋊C8—42no—
163C43⋊C8—42no—
164#9722—431nomaximal, Sylow
165C22×C43—21no—
166C22×C43—21no—
167C22×C43#39011yescharacteristic
168C22×C43#49611yescharacteristic
169C22×C43#49711yescharacteristic
170C2×D43—81no—
171C2×D43—81no—
172C2×D43—81no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—82no—
177C4×C43—82no—
178C4×C43C2×#10411yescharacteristic
179C4×C43#42111yescharacteristic
180C4×C43#44012yes—
181C4×C43#46812yes—
182Dic43—81no—
183Dic43—81no—
184Dic43—81no—
185#3167—431no—
186#1986—431no—
187#1980—431no—
188C4×#107D4311yescharacteristic, complemented
189#1503—431no—
190#1502—431no—
191#1451—431no—
192C2×C43—21no—
193C2×C43—21no—
194C2×C43#197311yescharacteristic
195C2×C43#197611yescharacteristic
196C2×C43#198011yescharacteristic
197D43—161no—
198#533—431no—
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×#107—21no—
210C2×#104—862no—
211C4×M16—431no—
212C2×C4×C8C2×D4311yescharacteristic
213C4×C4⋊C4C2×D4311yescharacteristic
214C4×C4⋊C4C2×D4311yescharacteristic
215#340—21no—
216#339—862no—
217#328—862no—
218#327—862no—
219#322—861no—
220#322—861no—
221C43#972211yescharacteristic, complemented, Sylow
222C2×#41—861no—
223C2×SD16—861no—
224C2×SD16—861no—
225C2×M16—432no—
226C22×C8C22⋊D4311yescharacteristic
227C22×C8C22⋊D4311yescharacteristic
228C4⋊Q8—431no—
229C4⋊Q8—431no—
230C4⋊Q8—431no—
231#127—431no—
232#125—861no—
233#124—861no—
234C22⋊Q8—861no—
235C22⋊Q8—861no—
236#121—861no—
237#121—861no—
238C4×Q8—861no—
239C4×Q8—861no—
240C4×D4—861no—
241C4×D4—861no—
242#117—861no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42C22×D4311yescharacteristic
248#107—24no—
249#106—861no—
250#106—861no—
251C4⋊C8—861no—
252#104—1724no—
253#103—861no—
254#103—861no—
255#102—861no—
256#102—861no—
257C22⋊C8—432no—
258#97—861no—
259C4×C8—861no—
260C4×C8—861no—
261C4×C8C4×D4311yescharacteristic
262C4×C8C4×D4311yescharacteristic
263C4×C8D17211yescharacteristic
264C4×C8D17211yescharacteristic
265#95—21no—
266#95—21no—
267#41—1722no—
268#41—1722no—
269C2×Q8—861no—
270C2×Q8—861no—
271C2×Q8—861no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4—1721no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—1721no—
279C22×C4D4×D4311yescharacteristic
280C22×C4D4×D4311yescharacteristic
281C22×C4C2×C22⋊D4311yescharacteristic
282SD16—1722no—
283SD16—1722no—
284M16—862no—
285M16—862no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—862no—
289C2×C8—862no—
290C2×C8(C2×D43)⋊C411yescharacteristic
291C2×C8(C2×D43)⋊C411yescharacteristic
292C2×C8(C2×D43)⋊C411yescharacteristic
293C2×C8(C2×D43)⋊C411yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—861no—
299C4⋊C4—861no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C4⋊C4—861no—
303C4⋊C4—861no—
304C4⋊C4—1721no—
305C4⋊C4—1721no—
306C22⋊C4—1721no—
307C22⋊C4—1721no—
308C22⋊C4—1721no—
309C42—42no—
310C42—42no—
311C42—1721no—
312C42C2×C4×D4311yescharacteristic
313C42C2×D17211yescharacteristic
314C42#1062190211yescharacteristic
315C42#1062190211yescharacteristic
316C23—1721no—
317C23#1306332111yescharacteristic
318Q8—3441no—
319Q8—1721no—
320Q8—1721no—
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—42no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—3442no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4C2×(C2×D43)⋊C411yescharacteristic
342C2×C4#1306328711yescharacteristic
343C2×C4#1306328711yescharacteristic
344C2×C4#1306330011yescharacteristic
345C2×C4#1306330011yescharacteristic
346C2×C4#1306331411yescharacteristic
347C2×C4#1306334912yes—
348C2×C4#1306335712yes—
349C8—21no—
350C8—21no—
351C8—21no—
352C8—1722no—
353C8—1722no—
354C8#1306325312yescomplemented
355C22—21no—
356C22—21no—
357C22—3441no—
358C22—3441no—
359C22—3441no—
360C22#1458280011yescharacteristic
361C22#1458328711yescharacteristic
362C22#1458329211yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—82no—
368C4—3441no—
369C4—3441no—
370C4—3441no—
371C4C2×#1306325311yescharacteristic
372C4#1458291711yescharacteristic
373C4#1458299812yes—
374C4#1458314612yes—
375C2—21no—
376C2—21no—
377C2—6881no—
378C2#1913547411yescharacteristic
379C2#1913549111yescharacteristic
380C2#1913551311yescharacteristic
subgroupG/H
centerC2×C4#13063300
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC4×#107×C43C2
socleC22×C43#390
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenterC4×#107D43
hypocenterC43#9722
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
2. #19135538C2semidirect
4. #19133093C2semidirect
6. #19132884C2semidirect
7. C4×#107×C43C2semidirect
10. #14583297C4semidirect
11. #14583272C4semidirect
12. #14583250C4semidirect
13. #14583246C4semidirect
161. C8×C43#104semidirect
188. C4×#107D43semidirect
221. C43#9722semidirect
354. C8#13063253semidirect

Maximal subgroups

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

subgroupindex
#191451542
#191355382
#191355132
#191330932
#191330892
#191328842
C4×#107×C432
#972243