Finite Group Databasebeta

← #24995948

Subgroups — #24995948

Order 11008.

428 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144918C211yesmaximal, characteristic
2#19133343C211yesmaximal, characteristic, complemented
3#19133093C211yesmaximal, characteristic, complemented
4#19133089C211yesmaximal, characteristic
5#19132997C211yesmaximal, characteristic, complemented
6#19132993C211yesmaximal, characteristic
7C8×C4⋊C4×C43C211yesmaximal, characteristic, complemented
8#14583456C2211yescharacteristic
9#14583449C2211yescharacteristic
10#14583254—21no—
11#14583254—21no—
12#14583250C411yescharacteristic, complemented
13#14583250C411yescharacteristic, complemented
14#14583246C411yescharacteristic, complemented
15#14583246C411yescharacteristic, complemented
16#14582952C2211yescharacteristic
17#14582952C2211yescharacteristic
18#14582896—21no—
19#14582896—21no—
20#14582652—21no—
21#14582650—21no—
22#14582635—22no—
23#14582632—22no—
24#14582629—22no—
25#14582626—22no—
26C2×C4⋊C8×C43C2211yescharacteristic
27C2×C4×C8×C43—21no—
28C2×C4×C8×C43C2211yescharacteristic
29C4×C4⋊C4×C43C2211yescharacteristic
30C43×#336—21no—
31C2×#10621898—21no—
32#13063325C2×C411yescharacteristic
33#13063325C2×C411yescharacteristic
34#13063325C2×C411yescharacteristic
35#13063322C2×C411yescharacteristic
36#13063317—21no—
37#13063313—21no—
38#13063304—21no—
39#13063304—21no—
40#13063299—21no—
41#13063299—21no—
42C4×Dic86—21no—
43C4×Dic86—21no—
44C4×D172—21no—
45C4×D172—21no—
46#13063284—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49#13063250—21no—
50#13063250—21no—
51#13063250—21no—
52#13063250—21no—
53#13063247—21no—
54#13063247—21no—
55#13063247—21no—
56#13063247—21no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)—21no—
59C4×C43⋊C8—21no—
60C4×C43⋊C8—21no—
61C22×C8×C43—21no—
62C22×C8×C43D411yescharacteristic
63C22×C8×C43D411yescharacteristic
64C2×C4⋊C4×C43—21no—
65C2×C42×C43—21no—
66C2×C42×C43C2311yescharacteristic
67C4⋊C8×C43—21no—
68C4⋊C8×C43D412yes—
69C4×C8×C43—42no—
70C4×C8×C43C2×C411yescharacteristic
71C4×C8×C43C2×C411yescharacteristic
72C4×C8×C43D411yescharacteristic
73C4×C8×C43D411yescharacteristic
74#95×C43D412yes—
75C22×C4×C43—22no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C2×C22⋊D43—41no—
80#10621898—41no—
81#10621898—41no—
82#10621898—41no—
83#10621898—41no—
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—21no—
92C2×C8×C43—21no—
93C2×C8×C43—21no—
94C2×C8×C43—21no—
95C2×C8×C43—22no—
96C2×C8×C43—41no—
97C2×C8×C43—41no—
98C2×C8×C43C22⋊C411yescharacteristic
99C2×C8×C43C22⋊C411yescharacteristic
100C2×C8×C43C22⋊C411yescharacteristic
101C2×C8×C43C22⋊C411yescharacteristic
102C4⋊C4×C43—24no—
103C42×C43—41no—
104C42×C43—41no—
105C42×C43C22×C411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43#4111yescharacteristic
109C22⋊Dic43—41no—
110(C2×D43)⋊C4—41no—
111(C2×D43)⋊C4—41no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118Dic43⋊C4—41no—
119Dic43⋊C4—41no—
120C4×Dic43—41no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—41no—
123C23×C43#12111yescharacteristic
124C22×D43—41no—
125C2×C4×C43—22no—
126C2×C4×C43—24no—
127C2×C4×C43—41no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43C2×C22⋊C411yescharacteristic
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12411yescharacteristic
135C2×C4×C43#12711yescharacteristic
136C2×C4×C43#13511yescharacteristic
137C2×C4×C43#13511yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C43#13711yescharacteristic
140C22⋊D43—81no—
141C22⋊D43—81no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145D172—41no—
146D172—41no—
147D172—42no—
148D172—81no—
149C4×D43—81no—
150C4×D43—81no—
151Dic86—41no—
152Dic86—41no—
153Dic86—42no—
154Dic86—81no—
155C8×C43—21no—
156C8×C43—21no—
157C8×C43—21no—
158C8×C43—21no—
159C8×C43—42no—
160C43⋊C8—81no—
161C43⋊C8—81no—
162#9751—431nomaximal, Sylow
163C22×C43—21no—
164C22×C43—21no—
165C22×C43#39011yescharacteristic
166C22×C43#46311yescharacteristic
167C22×C43#46411yescharacteristic
168C2×D43—81no—
169C2×D43—81no—
170C2×D43—81no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—44no—
175C4×C43#41611yescharacteristic
176C4×C43#41711yescharacteristic
177C4×C43#44312yes—
178C4×C43#46311yescharacteristic
179C4×C43#46411yescharacteristic
180Dic43—81no—
181Dic43—81no—
182Dic43—81no—
183#3131—431no—
184C8×C4⋊C4D4311yescharacteristic, complemented
185#1564—431no—
186#1503—431no—
187#1502—431no—
188#1481—431no—
189#1480—431no—
190C2×C43—21no—
191C2×C43—21no—
192C2×C43#197411yescharacteristic
193C2×C43#197611yescharacteristic
194C2×C43#198311yescharacteristic
195D43—161no—
196#533—431no—
197#532—431no—
198#488—861no—
199#488—861no—
200#487—431no—
201#487—431no—
202#486—431no—
203#486—431no—
204#431—431no—
205#431—431no—
206C2×C4⋊C8C2×D4311yescharacteristic
207#416—861no—
208#416—861no—
209C2×C4×C8—21no—
210C2×C4×C8C2×D4311yescharacteristic
211C4×C4⋊C4C2×D4311yescharacteristic
212#336—21no—
213#335—861no—
214#334—861no—
215#328—862no—
216#327—862no—
217Q8⋊C8—862no—
218D4⋊C8—862no—
219C43#975111yescharacteristic, complemented, Sylow
220C2×#41—861no—
221C22×C8—21no—
222C22×C8C22⋊D4311yescharacteristic
223C22×C8C22⋊D4311yescharacteristic
224C4⋊Q8—431no—
225C4⋊Q8—431no—
226C4⋊Q8—431no—
227#127—431no—
228#125—861no—
229#124—861no—
230C22⋊Q8—861no—
231C22⋊Q8—861no—
232#121—861no—
233#121—861no—
234C4×Q8—861no—
235C4×Q8—861no—
236C4×D4—861no—
237C4×D4—861no—
238#117—861no—
239C2×C4⋊C4—21no—
240C2×C42—21no—
241C2×C42C22×D4311yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—861no—
244C4⋊C8—861no—
245C4⋊C8D17212yes—
246#103—861no—
247#103—861no—
248#103—861no—
249#103—861no—
250#102—861no—
251#102—861no—
252#102—861no—
253#102—861no—
254C22⋊C8—861no—
255C22⋊C8—861no—
256C4×C8—42no—
257C4×C8—861no—
258C4×C8—861no—
259C4×C8C4×D4311yescharacteristic
260C4×C8C4×D4311yescharacteristic
261C4×C8D17211yescharacteristic
262C4×C8D17211yescharacteristic
263#95D17212yes—
264#41—1721no—
265#41—1721no—
266#41—1721no—
267#41—1721no—
268C2×Q8—861no—
269C2×Q8—861no—
270C2×Q8—861no—
271C2×D4—861no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—1721no—
275C22×C4—22no—
276C22×C4—1721no—
277C22×C4C2×D17211yescharacteristic
278C22×C4#1062189811yescharacteristic
279C22×C4C2×C22⋊D4311yescharacteristic
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—22no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—1721no—
288C2×C8—1721no—
289C2×C8(C2×D43)⋊C411yescharacteristic
290C2×C8(C2×D43)⋊C411yescharacteristic
291C2×C8(C2×D43)⋊C411yescharacteristic
292C2×C8(C2×D43)⋊C411yescharacteristic
293C4⋊C4—24no—
294C4⋊C4—861no—
295C4⋊C4—861no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4—861no—
299C4⋊C4—861no—
300C4⋊C4—1721no—
301C4⋊C4—1721no—
302C22⋊C4—1721no—
303C22⋊C4—1721no—
304C22⋊C4—1721no—
305C42—41no—
306C42—41no—
307C42—1721no—
308C42C2×C4×D4311yescharacteristic
309C42C2×D17211yescharacteristic
310C42C2×D17211yescharacteristic
311C42#1062189811yescharacteristic
312C23—1721no—
313C23#1306329911yescharacteristic
314Q8—3441no—
315Q8—1721no—
316Q8—1721no—
317Q8—1722no—
318D4—3441no—
319D4—3441no—
320D4—3441no—
321D4—1721no—
322D4—1721no—
323D4—1722no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—3441no—
330C2×C4—3441no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4C2×(C2×D43)⋊C411yescharacteristic
335C2×C4C4×D17211yescharacteristic
336C2×C4C4×D17211yescharacteristic
337C2×C4#1306329911yescharacteristic
338C2×C4#1306331311yescharacteristic
339C2×C4#1306332211yescharacteristic
340C2×C4#1306334511yescharacteristic
341C2×C4#1306334511yescharacteristic
342C2×C4#1306335111yescharacteristic
343C2×C4#1306335611yescharacteristic
344C8—21no—
345C8—21no—
346C8—21no—
347C8—21no—
348C8—42no—
349C8—3441no—
350C8—3441no—
351C22—21no—
352C22—21no—
353C22—3441no—
354C22—3441no—
355C22—3441no—
356C22#1458280111yescharacteristic
357C22#1458311411yescharacteristic
358C22#1458312111yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—44no—
363C4—3441no—
364C4—3441no—
365C4—3441no—
366C4#1458289311yescharacteristic
367C4#1458289811yescharacteristic
368C4#1458301712yes—
369C4#1458311411yescharacteristic
370C4#1458312111yescharacteristic
371C2—21no—
372C2—21no—
373C2—6881no—
374C2#1913548311yescharacteristic
375C2#1913549311yescharacteristic
376C2#1913552711yescharacteristic
subgroupG/H
centerC2×C4#13063299
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC8×C4⋊C4×C43C2
socleC22×C43#390
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenterC8×C4⋊C4D43
hypocenterC43#9751
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #19133343C2semidirect
3. #19133093C2semidirect
5. #19132997C2semidirect
7. C8×C4⋊C4×C43C2semidirect
12. #14583250C4semidirect
13. #14583250C4semidirect
14. #14583246C4semidirect
15. #14583246C4semidirect
184. C8×C4⋊C4D43semidirect
219. C43#9751semidirect

Maximal subgroups

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

subgroupindex
#191449182
#191333432
#191330932
#191330892
#191329972
#191329932
C8×C4⋊C4×C432
#975143