Finite Group Databasebeta

← #24994728

Subgroups — #24994728

Order 11008.

372 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135313C211yesmaximal, characteristic
2C4×#13063256C211yesmaximal, characteristic
3#19132436C211yesmaximal, characteristic
4#19132434C211yesmaximal, characteristic
5#19132429C211yesmaximal, characteristic
6C43⋊#1273C211yesmaximal, characteristic
7C8×C4⋊C4×C43C211yesmaximal, characteristic
8C2×#13063256C411yescharacteristic
9C2×#13063256C411yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×Dic43⋊C8—21no—
12C2×C4×C43⋊C8C2211yescharacteristic
13C2×C4×C43⋊C8C2211yescharacteristic
14C4×C4⋊Dic43C2211yescharacteristic
15#14582661C411yescharacteristic
16#14582661C411yescharacteristic
17#14582653—21no—
18C2×C4⋊C8×C43C2211yescharacteristic
19C2×C4×C8×C43—21no—
20C2×C4×C8×C43C2211yescharacteristic
21C4×C4⋊C4×C43C2211yescharacteristic
22C43×#336—21no—
23C22×C43⋊C8—21no—
24C22×C43⋊C8—21no—
25C22×C43⋊C8C2×C411yescharacteristic
26C22×C43⋊C8C2×C411yescharacteristic
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×C4×Dic43—21no—
30#13063256—22no—
31#13063256C814yescomplemented
32C4⋊(C43⋊C8)—21no—
33C4⋊(C43⋊C8)—21no—
34Dic43⋊C8—42no—
35C4×C43⋊C8—21no—
36C4×C43⋊C8—21no—
37C4×C43⋊C8—21no—
38C4×C43⋊C8—21no—
39C43⋊#95—21no—
40C22×C8×C43—21no—
41C22×C8×C43D411yescharacteristic
42C22×C8×C43D411yescharacteristic
43C2×C4⋊C4×C43C2×C411yescharacteristic
44C2×C4⋊C4×C43C2×C411yescharacteristic
45C2×C42×C43—21no—
46C2×C42×C43C2311yescharacteristic
47C4⋊C8×C43—21no—
48C4⋊C8×C43Q812yes—
49C4×C8×C43—21no—
50C4×C8×C43—21no—
51C4×C8×C43—42no—
52#95×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43C22×C411yescharacteristic
56C22×C4×C43C2×D411yescharacteristic
57C22×C4×C43#4111yescharacteristic
58C22×Dic43—21no—
59C22×Dic43—21no—
60C2×C8×C43—21no—
61C2×C8×C43—21no—
62C2×C8×C43—22no—
63C2×C8×C43—21no—
64C2×C8×C43—21no—
65C2×C8×C43—21no—
66C2×C8×C43—41no—
67C2×C8×C43—41no—
68C2×C8×C43SD1612yes—
69C4⋊C4×C43—21no—
70C4⋊C4×C43—21no—
71C4⋊C4×C43C2×C812yes—
72C4⋊C4×C43M1612yes—
73C42×C43—41no—
74C42×C43—41no—
75C42×C43C2×Q811yescharacteristic
76C42×C43#4111yescharacteristic
77C42×C43#4111yescharacteristic
78C42×C43#4111yescharacteristic
79C4⋊Dic43—21no—
80C4⋊Dic43—21no—
81C4⋊Dic43—21no—
82C4⋊Dic43C2×C812yes—
83C4×Dic43—41no—
84C4×Dic43—41no—
85C2×C43⋊C8—21no—
86C2×C43⋊C8—21no—
87C2×C43⋊C8—22no—
88C2×C43⋊C8—21no—
89C2×C43⋊C8—21no—
90C2×C43⋊C8—21no—
91C2×C43⋊C8—41no—
92C2×C43⋊C8—41no—
93C2×C43⋊C8—41no—
94C2×C43⋊C8—41no—
95C2×C43⋊C8—41no—
96C2×C43⋊C8C2×C812yes—
97C23×C43C4×D411yescharacteristic
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—22no—
101C2×C4×C43—22no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43#11711yescharacteristic
107C2×C4×C43C4×Q811yescharacteristic
108C2×C4×C43C22⋊Q811yescharacteristic
109C2×C4×C43#12311yescharacteristic
110C2×C4×C43#12511yescharacteristic
111C2×C4×C43#12611yescharacteristic
112C2×C4×C43C22×C811yescharacteristic
113C2×C4×C43C2×M1611yescharacteristic
114C2×C4×C43#13111yescharacteristic
115C2×C4×C43#13111yescharacteristic
116C2×C4×C43C2×SD1611yescharacteristic
117C2×C4×C43#13511yescharacteristic
118C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C43#13711yescharacteristic
120C2×Dic43—22no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C8×C43—22no—
127C8×C43—42no—
128C8×C43—41no—
129C43⋊C8—22no—
130C43⋊C8—42no—
131C43⋊C8—41no—
132C43⋊C8—81no—
133#9535—431nomaximal, Sylow
134C22×C43#38711yescharacteristic
135C22×C43C8×D411yescharacteristic
136C22×C43#43511yescharacteristic
137C22×C43C4×SD1611yescharacteristic
138C22×C43#44011yescharacteristic
139C22×C43#44311yescharacteristic
140C22×C43#44411yescharacteristic
141C4×C43—21no—
142C4×C43—21no—
143C4×C43—42no—
144C4×C43—42no—
145C4×C43#43111yescharacteristic
146C4×C43#43311yescharacteristic
147C4×C43C8×Q811yescharacteristic
148C4×C43#44611yescharacteristic
149C4×C43#47611yescharacteristic
150C4×C43#47911yescharacteristic
151C4×C43#48211yescharacteristic
152C4×C43#48311yescharacteristic
153Dic43—42no—
154Dic43—81no—
155#1939—431no—
156C4×#106—431no—
157C8×C4⋊C4D4311yescharacteristic
158#1279—431no—
159#1279—431no—
160#1277—431no—
161#1273—431no—
162C2×C43C8×SD1611yescharacteristic
163C2×C43SD16⋊C811yescharacteristic
164C2×C43#158211yescharacteristic
165C2×C43#158811yescharacteristic
166C2×C43#191611yescharacteristic
167C2×C43#192011yescharacteristic
168C2×C43#192211yescharacteristic
169C2×#106—431no—
170C2×#106—431no—
171C2×C4⋊C8—431no—
172C2×C4⋊C8—861no—
173C2×C4⋊C8C2×D4311yescharacteristic
174C2×C4×C8—21no—
175C2×C4×C8—431no—
176C2×C4×C8—431no—
177C2×C4×C8C2×D4311yescharacteristic
178C4×C4⋊C4—431no—
179C4×C4⋊C4C2×D4311yescharacteristic
180#340—431no—
181#340—431no—
182#336—21no—
183#336—861no—
184C43#953511yescharacteristic, complemented, Sylow
185C22×C8—21no—
186C22×C8—431no—
187C22×C8—431no—
188C22×C8—861no—
189C22×C8—861no—
190C22×C8C22⋊D4311yescharacteristic
191C22×C8C22⋊D4311yescharacteristic
192C2×C4⋊C4—431no—
193C2×C4⋊C4—431no—
194C2×C4⋊C4C4×D4311yescharacteristic
195C2×C4⋊C4C4×D4311yescharacteristic
196C2×C42—21no—
197C2×C42—861no—
198C2×C42C22×D4311yescharacteristic
199#106—434no—
200#106—862no—
201C4⋊C8—21no—
202C4⋊C8—861no—
203C4⋊C8—861no—
204C4⋊C8—1722no—
205C4⋊C8Dic8612yes—
206C4×C8—21no—
207C4×C8—21no—
208C4×C8—42no—
209C4×C8—861no—
210C4×C8—861no—
211C4×C8—861no—
212C4×C8—861no—
213#95—21no—
214#95—861no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—861no—
218C22×C4—861no—
219C22×C4C2×C4×D4311yescharacteristic
220C22×C4#1062189811yescharacteristic
221C22×C4C2×C22⋊D4311yescharacteristic
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—22no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—432no—
231C2×C8—861no—
232C2×C8—861no—
233C2×C8—862no—
234C2×C8—861no—
235C2×C8—861no—
236C2×C8—861no—
237C2×C8—1721no—
238C2×C8—1721no—
239C2×C8—1721no—
240C2×C8—1721no—
241C2×C8—1721no—
242C2×C8#1062188312yes—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—432no—
246C4⋊C4—861no—
247C4⋊C4—861no—
248C4⋊C4—861no—
249C4⋊C4C8×D4312yes—
250C4⋊C4#1062187212yes—
251C42—41no—
252C42—41no—
253C42—1721no—
254C42—1721no—
255C42C2×Dic8611yescharacteristic
256C42#1062189811yescharacteristic
257C42#1062189811yescharacteristic
258C42#1062189811yescharacteristic
259C23C4×C22⋊D4311yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—862no—
269C2×C4—1721no—
270C2×C4—1721no—
271C2×C4—1721no—
272C2×C4—1721no—
273C2×C4—1721no—
274C2×C4#1306328211yescharacteristic
275C2×C4C4×Dic8611yescharacteristic
276C2×C4#1306330411yescharacteristic
277C2×C4#1306330811yescharacteristic
278C2×C4#1306331711yescharacteristic
279C2×C4#1306331911yescharacteristic
280C2×C4C2×C8×D4311yescharacteristic
281C2×C4C2×#1062187211yescharacteristic
282C2×C4#1306333111yescharacteristic
283C2×C4#1306333111yescharacteristic
284C2×C4C2×#1062188311yescharacteristic
285C2×C4#1306334511yescharacteristic
286C2×C4#1306335011yescharacteristic
287C2×C4#1306335611yescharacteristic
288C8—22no—
289C8—42no—
290C8—41no—
291C8—862no—
292C8—3441no—
293C8—1722no—
294C8—1721no—
295C22#1458278311yescharacteristic
296C22C8×C22⋊D4311yescharacteristic
297C22#1458297011yescharacteristic
298C22C4×#1062188311yescharacteristic
299C22#1458299711yescharacteristic
300C22#1458301411yescharacteristic
301C22#1458301911yescharacteristic
302C4—21no—
303C4—21no—
304C4—42no—
305C4—42no—
306C4—3441no—
307C4—1722no—
308C4#1458295011yescharacteristic
309C4#1458295811yescharacteristic
310C4C8×Dic8611yescharacteristic
311C4#1458302911yescharacteristic
312C4#1458318911yescharacteristic
313C4#1458320611yescharacteristic
314C4#1458322311yescharacteristic
315C4#1458322911yescharacteristic
316C2C8×#1062188311yescharacteristic
317C2#1913340511yescharacteristic
318C2#1913343111yescharacteristic
319C2#1913347311yescharacteristic
320C2#1913515211yescharacteristic
321C2#1913518011yescharacteristic
322C2#1913519411yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC8×C4⋊C4×C43C2
socle, prime radicalC23×C43C4×D4
cosocleC2×C42×C43C23
hypercenterC8×C4⋊C4D43
hypocenterC43#9535
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
31. #13063256C8semidirect
184. C43#9535semidirect

Maximal subgroups

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

subgroupindex
#191353132
C4×#130632562
#191324362
#191324342
#191324292
C43⋊#12732
C8×C4⋊C4×C432
#953543