Finite Group Databasebeta

← #24995016

Subgroups — #24995016

Order 11008.

370 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135556C211yesmaximal, characteristic
2#19135542C211yesmaximal, characteristic
3#19135354C211yesmaximal, characteristic
4#19134462C211yesmaximal, characteristic
5C2×#14582647C211yesmaximal, characteristic
6#19132479C211yesmaximal, characteristic
7C43×#1277C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9C2×#13063259—21no—
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×#13063235—21no—
12#14582769C2211yescharacteristic
13C4×C4⋊Dic43C2211yescharacteristic
14#14582662—21no—
15#14582662—21no—
16#14582662—21no—
17#14582662—21no—
18#14582662—21no—
19#14582653—21no—
20#14582647C414yescomplemented
21C2×C4⋊C8×C43C2211yescharacteristic
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×C4×C8×C43C2211yescharacteristic
24C22×Dic86—21no—
25C22×C43⋊C8—21no—
26#13063325—21no—
27#13063325—21no—
28#13063325—21no—
29#13063325C2×C412yes—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43D411yescharacteristic
36C2×C4⋊Dic43D411yescharacteristic
37C2×C4×Dic43—21no—
38#13063259—42no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)C2×C412yes—
41#13063235—42no—
42C43⋊#95—21no—
43C22×C8×C43—21no—
44C22×C8×C43—21no—
45C22×C8×C43D411yescharacteristic
46C22×C8×C43D411yescharacteristic
47C2×C42×C43C2311yescharacteristic
48C4⋊C8×C43—21no—
49C4⋊C8×C43—21no—
50C4⋊C8×C43—21no—
51C4⋊C8×C43C2×C412yes—
52C4×C8×C43—21no—
53C4×C8×C43—21no—
54C22×C4×C43C2×D411yescharacteristic
55C22×C4×C43C2×D411yescharacteristic
56C22×C4×C43#4111yescharacteristic
57C22×Dic43—21no—
58C22×Dic43—21no—
59C22×Dic43—41no—
60C22×Dic43—41no—
61C2×Dic86—22no—
62C2×Dic86—41no—
63C2×Dic86—81no—
64C2×Dic86—81no—
65C2×C8×C43—21no—
66C2×C8×C43—21no—
67C2×C8×C43—22no—
68C2×C8×C43—21no—
69C2×C8×C43—21no—
70C2×C8×C43—21no—
71C2×C8×C43—41no—
72C2×C8×C43—41no—
73C2×C8×C43—41no—
74C2×C8×C43—41no—
75C2×C8×C43—41no—
76C2×C8×C43Q1612yes—
77C42×C43C22×C411yescharacteristic
78C42×C43#4111yescharacteristic
79C42×C43#4111yescharacteristic
80C42×C43#4111yescharacteristic
81C4⋊Dic43—22no—
82C4⋊Dic43—22no—
83C4⋊Dic43—21no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43—41no—
88C4⋊Dic43—41no—
89C4⋊Dic43—41no—
90C4⋊Dic43—41no—
91C4⋊Dic43—41no—
92C4⋊Dic43—41no—
93C4⋊Dic43—81no—
94C4×Dic43—41no—
95C4×Dic43—41no—
96C2×C43⋊C8—22no—
97C2×C43⋊C8—41no—
98C2×C43⋊C8—41no—
99C23×C43#12111yescharacteristic
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43#11711yescharacteristic
103C2×C4×C43C4×D411yescharacteristic
104C2×C4×C43C4×D411yescharacteristic
105C2×C4×C43#12311yescharacteristic
106C2×C4×C43#12411yescharacteristic
107C2×C4×C43#12611yescharacteristic
108C2×C4×C43C2×Q1611yescharacteristic
109C2×C4×C43#13511yescharacteristic
110C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
111C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C43#13711yescharacteristic
113C2×C4×C43#13711yescharacteristic
114C2×C4×C43#13711yescharacteristic
115C2×C4×C43#13711yescharacteristic
116C2×Dic43—42no—
117C2×Dic43—41no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—81no—
124C2×Dic43—81no—
125C2×Dic43—81no—
126C2×Dic43—81no—
127C2×Dic43—81no—
128Dic86—82no—
129Dic86—82no—
130C8×C43—22no—
131C8×C43—42no—
132C8×C43—41no—
133C8×C43—81no—
134C43⋊C8—42no—
135#9576—431nomaximal, Sylow
136C22×C43#38811yescharacteristic
137C22×C43#46211yescharacteristic
138C22×C43#46311yescharacteristic
139C22×C43#46811yescharacteristic
140C22×C43#47011yescharacteristic
141C22×C43#47111yescharacteristic
142C22×C43#47211yescharacteristic
143C4×C43—21no—
144C4×C43—21no—
145C4×C43C4×Q1611yescharacteristic
146C4×C43#44011yescharacteristic
147C4×C43#44011yescharacteristic
148C4×C43#44111yescharacteristic
149C4×C43#48411yescharacteristic
150C4×C43#48511yescharacteristic
151C4×C43#48911yescharacteristic
152C4×C43#49111yescharacteristic
153Dic43—82no—
154Dic43—81no—
155Dic43—81no—
156Dic43—161no—
157#1990—431no—
158#1987—431no—
159#1947—431no—
160#1770—431no—
161C2×#333—431no—
162#1296—431no—
163#1277D4311yescharacteristic
164C2×C43#169211yescharacteristic
165C2×C43#169611yescharacteristic
166C2×C43#169711yescharacteristic
167C2×C43#170311yescharacteristic
168C2×C43#192811yescharacteristic
169C2×C43#193111yescharacteristic
170C2×C43#193511yescharacteristic
171C2×C4⋊Q8—431no—
172C2×#107—861no—
173C2×C4⋊C8—431no—
174C2×C4⋊C8C2×D4311yescharacteristic
175C2×C4⋊C8C2×D4311yescharacteristic
176C2×#97—861no—
177C2×C4×C8C2×D4311yescharacteristic
178#384—431no—
179C4×C4⋊C4—431no—
180#340—861no—
181#340—861no—
182#340—861no—
183#340—861no—
184#340—861no—
185#336—861no—
186#333—434no—
187C43#957611yescharacteristic, complemented, Sylow
188C22×Q8—861no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—861no—
192C22×C8D17211yescharacteristic
193C22×C8D17211yescharacteristic
194C4⋊Q8—432no—
195C4⋊Q8—861no—
196C4⋊Q8—861no—
197C4⋊Q8—861no—
198C2×C4⋊C4—431no—
199C2×C4⋊C4—431no—
200C2×C4⋊C4—861no—
201C2×C4⋊C4—861no—
202C2×C4⋊C4—861no—
203C2×C4⋊C4—861no—
204C2×C4⋊C4—861no—
205C2×C42—861no—
206C2×C42C22×D4311yescharacteristic
207#107—1722no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—432no—
212C4⋊C8—861no—
213C4⋊C8C4×D4312yes—
214#97—1722no—
215C4×C8—21no—
216C4×C8—21no—
217#95—861no—
218C2×Q8—862no—
219C2×Q8—3441no—
220C2×Q8—3441no—
221C2×Q8—1721no—
222C22×C4—861no—
223C22×C4—861no—
224C22×C4—1721no—
225C22×C4—1721no—
226C22×C4C2×D17211yescharacteristic
227C22×C4D4×D4311yescharacteristic
228C22×C4#1062190211yescharacteristic
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—22no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—862no—
241C2×C8—1721no—
242C2×C8—1721no—
243C2×C8Dic17212yes—
244C4⋊C4—862no—
245C4⋊C4—862no—
246C4⋊C4—861no—
247C4⋊C4—861no—
248C4⋊C4—861no—
249C4⋊C4—861no—
250C4⋊C4—3441no—
251C4⋊C4—1721no—
252C4⋊C4—1721no—
253C4⋊C4—1721no—
254C4⋊C4—1721no—
255C4⋊C4—1721no—
256C4⋊C4—1721no—
257C42—1721no—
258C42—1721no—
259C42C2×C4×D4311yescharacteristic
260C42#1062189811yescharacteristic
261C42#1062190011yescharacteristic
262C42#1062190011yescharacteristic
263C23#1306330011yescharacteristic
264Q8—3442no—
265Q8—3442no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—3441no—
269C2×C4—3441no—
270C2×C4—3441no—
271C2×C4—3441no—
272C2×C4—3441no—
273C2×C4—1722no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4—1721no—
279C2×C4—1721no—
280C2×C4#1306328311yescharacteristic
281C2×C4(C22⋊D43)⋊C411yescharacteristic
282C2×C4C4×D17211yescharacteristic
283C2×C4#1306330911yescharacteristic
284C2×C4#1306331111yescharacteristic
285C2×C4#1306332011yescharacteristic
286C2×C4C2×Dic17211yescharacteristic
287C2×C4#1306334711yescharacteristic
288C2×C4#1306334911yescharacteristic
289C2×C4#1306335311yescharacteristic
290C2×C4#1306335411yescharacteristic
291C2×C4#1306335411yescharacteristic
292C2×C4#1306335711yescharacteristic
293C2×C4#1306335811yescharacteristic
294C8—22no—
295C8—41no—
296C8—42no—
297C8—81no—
298C8—1722no—
299C22#1458279111yescharacteristic
300C22#1458311011yescharacteristic
301C22#1458311511yescharacteristic
302C22#1458314611yescharacteristic
303C22#1458315811yescharacteristic
304C22#1458316311yescharacteristic
305C22#1458317011yescharacteristic
306C4—21no—
307C4—21no—
308C4—3442no—
309C4—3441no—
310C4—3441no—
311C4—6881no—
312C4C4×Dic17211yescharacteristic
313C4#1458299611yescharacteristic
314C4#1458300111yescharacteristic
315C4#1458300311yescharacteristic
316C4#1458323511yescharacteristic
317C4#1458324111yescharacteristic
318C4#1458325711yescharacteristic
319C4#1458326611yescharacteristic
320C2#1913410211yescharacteristic
321C2#1913412411yescharacteristic
322C2#1913412911yescharacteristic
323C2#1913417111yescharacteristic
324C2#1913523711yescharacteristic
325C2#1913525811yescharacteristic
326C2#1913528611yescharacteristic
subgroupG/H
centerC23#13063300
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1277C2
socle, prime radicalC23×C43#121
cosocleC2×C42×C43C23
hypercenter#1277D43
hypocenterC43#9576
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
20. #14582647C4semidirect
187. C43#9576semidirect

Maximal subgroups

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

subgroupindex
#191355562
#191355422
#191353542
#191344622
C2×#145826472
#191324792
C43×#12772
#957643