Finite Group Databasebeta

← #25001325

Subgroups — #25001325

Order 11008.

366 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135531C211yesmaximal, characteristic
2#19134597C211yesmaximal, characteristic
3#19134597C211yesmaximal, characteristic
4#19132478C211yesmaximal, characteristic
5#19132478C211yesmaximal, characteristic
6#19132430C211yesmaximal, characteristic
7C43×#1844C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×#13063248—21no—
13C2×#13063248—21no—
14#14582661—21no—
15#14582661—21no—
16#14582653—21no—
17#14582653—21no—
18C2×#106×C43—21no—
19C2×#106×C43—21no—
20C2×C4×C8×C43C2211yescharacteristic
21C43×#384C2211yescharacteristic
22C43×#384C2211yescharacteristic
23C22×Dic86D411yescharacteristic
24C22×C43⋊C8—21no—
25C22×C43⋊C8—21no—
26C22×C43⋊C8—21no—
27C4×Dic86—21no—
28C4×Dic86—21no—
29C4×Dic86—21no—
30C4×Dic86—21no—
31C2×C4⋊Dic43D411yescharacteristic
32C2×Dic43⋊C4—21no—
33C2×C4×Dic43—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40#13063248—42no—
41#13063248—42no—
42C22×C8×C43D411yescharacteristic
43C22×C8×C43D411yescharacteristic
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C42×C43C2311yescharacteristic
51#106×C43—42no—
52#106×C43—42no—
53C4×C8×C43—21no—
54C4×C8×C43—21no—
55C22×C4×C43—41no—
56C22×C4×C43—41no—
57C22×C4×C43C2×D411yescharacteristic
58C22×C4×C43C2×D411yescharacteristic
59C22×C4×C43#4111yescharacteristic
60C22×Dic43—21no—
61C22×Dic43—21no—
62C2×Dic86—21no—
63C2×Dic86—21no—
64C2×Dic86—21no—
65C2×Dic86—21no—
66C2×Dic86—21no—
67C2×Dic86SD1612yes—
68C2×C8×C43—21no—
69C2×C8×C43—21no—
70C2×C8×C43—21no—
71C2×C8×C43—21no—
72C2×C8×C43SD1612yes—
73C2×C8×C43Q1612yes—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—81no—
83C4⋊C4×C43—81no—
84C42×C43#4111yescharacteristic
85C42×C43#4111yescharacteristic
86C42×C43#4111yescharacteristic
87C42×C43#4111yescharacteristic
88C4⋊Dic43—21no—
89C4⋊Dic43—21no—
90Dic43⋊C4—41no—
91Dic43⋊C4—41no—
92C4×Dic43—41no—
93C4×Dic43—41no—
94C2×C43⋊C8—41no—
95C2×C43⋊C8—41no—
96C2×C43⋊C8—41no—
97C2×C43⋊C8—41no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8—41no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—41no—
103C23×C43#12111yescharacteristic
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—81no—
107C2×C4×C43—81no—
108C2×C4×C43—81no—
109C2×C4×C43—81no—
110C2×C4×C43—81no—
111C2×C4×C43—81no—
112C2×C4×C43#12311yescharacteristic
113C2×C4×C43#12311yescharacteristic
114C2×C4×C43#12311yescharacteristic
115C2×C4×C43#12411yescharacteristic
116C2×C4×C43#12611yescharacteristic
117C2×C4×C43#12611yescharacteristic
118C2×C4×C43C2×SD1611yescharacteristic
119C2×C4×C43C2×SD1611yescharacteristic
120C2×C4×C43C2×Q1611yescharacteristic
121C2×C4×C43#13511yescharacteristic
122C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C43#13711yescharacteristic
125C2×C4×C43#13711yescharacteristic
126C2×Dic43—22no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132Dic86—22no—
133Dic86—22no—
134Dic86—41no—
135Dic86—41no—
136C8×C43—22no—
137C8×C43—22no—
138C43⋊C8—81no—
139C43⋊C8—81no—
140C43⋊C8—81no—
141#10620—431nomaximal, Sylow
142C22×C43#39711yescharacteristic
143C22×C43#46011yescharacteristic
144C22×C43#46211yescharacteristic
145C22×C43#46511yescharacteristic
146C22×C43#46811yescharacteristic
147C22×C43#47111yescharacteristic
148C22×C43#47111yescharacteristic
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—161no—
152C4×C43—161no—
153C4×C43#48111yescharacteristic
154C4×C43#48211yescharacteristic
155C4×C43#48311yescharacteristic
156C4×C43#48311yescharacteristic
157C4×C43#48411yescharacteristic
158C4×C43#48511yescharacteristic
159C4×C43#48711yescharacteristic
160C4×C43#48911yescharacteristic
161Dic43—42no—
162Dic43—81no—
163#1984—431no—
164#1844D4311yescharacteristic
165#1803—431no—
166#1803—431no—
167#1296—431no—
168#1296—431no—
169#1277—431no—
170C2×C43#166611yescharacteristic
171C2×C43#167211yescharacteristic
172C2×C43#168611yescharacteristic
173C2×C43#169211yescharacteristic
174C2×C43#207211yescharacteristic
175C2×C43#207711yescharacteristic
176C2×C43#207911yescharacteristic
177C2×C4×Q8—431no—
178C2×#106—21no—
179C2×#106—21no—
180C2×C4⋊C8—431no—
181C2×C4⋊C8—431no—
182C2×C4⋊C8—431no—
183C2×#103—861no—
184C2×#103—861no—
185C2×C4×C8C2×D4311yescharacteristic
186#384C2×D4311yescharacteristic
187#384C2×D4311yescharacteristic
188#340—861no—
189#340—861no—
190#336—861no—
191#336—861no—
192C43#1062011yescharacteristic, complemented, Sylow
193C22×Q8—431no—
194C22×C8—861no—
195C22×C8—861no—
196C22×C8—861no—
197C22×C8C22⋊D4311yescharacteristic
198C22×C8C22⋊D4311yescharacteristic
199C4×Q8—861no—
200C4×Q8—861no—
201C4×Q8—861no—
202C4×Q8—861no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—431no—
210C2×C4⋊C4—861no—
211C2×C42—861no—
212C2×C42C22×D4311yescharacteristic
213#106—42no—
214#106—42no—
215C4⋊C8—861no—
216C4⋊C8—861no—
217C4⋊C8—861no—
218C4⋊C8—861no—
219C4⋊C8—861no—
220C4⋊C8—861no—
221#103—1722no—
222#103—1722no—
223C4×C8—21no—
224C4×C8—21no—
225C2×Q8—432no—
226C2×Q8—861no—
227C2×Q8—861no—
228C2×Q8—861no—
229C2×Q8—861no—
230C2×Q8—861no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—861no—
234C22×C4—861no—
235C22×C4D4×D4311yescharacteristic
236C22×C4#1062190011yescharacteristic
237C22×C4C2×C22⋊D4311yescharacteristic
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—1721no—
243C2×C8—1721no—
244C2×C8—1721no—
245C2×C8—1721no—
246C2×C8—1721no—
247C2×C8—1721no—
248C2×C8—1721no—
249C2×C8—1721no—
250C2×C8—1721no—
251C2×C8#1062188312yes—
252C2×C8#1062188512yes—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—81no—
262C4⋊C4—81no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C42—1721no—
268C42—1721no—
269C42#1062189811yescharacteristic
270C42#1062189811yescharacteristic
271C42#1062190211yescharacteristic
272C42#1062190211yescharacteristic
273C23#1306329611yescharacteristic
274Q8—862no—
275Q8—862no—
276Q8—1721no—
277Q8—1721no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—862no—
287C2×C4—1721no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4#1306330811yescharacteristic
293C2×C4#1306331011yescharacteristic
294C2×C4#1306331011yescharacteristic
295C2×C4#1306331411yescharacteristic
296C2×C4#1306332011yescharacteristic
297C2×C4#1306332011yescharacteristic
298C2×C4SD16×D4311yescharacteristic
299C2×C4C2×#1062188311yescharacteristic
300C2×C4C2×#1062188511yescharacteristic
301C2×C4#1306334611yescharacteristic
302C2×C4#1306335111yescharacteristic
303C2×C4#1306335211yescharacteristic
304C2×C4#1306335411yescharacteristic
305C2×C4#1306335611yescharacteristic
306C8—22no—
307C8—22no—
308C8—3441no—
309C8—3441no—
310C8—3441no—
311C22#1458282511yescharacteristic
312C22#1458309611yescharacteristic
313C22#1458310611yescharacteristic
314C22#1458312511yescharacteristic
315C22#1458314211yescharacteristic
316C22#1458315911yescharacteristic
317C22#1458315911yescharacteristic
318C4—21no—
319C4—21no—
320C4—161no—
321C4—161no—
322C4—3441no—
323C4—1722no—
324C4#1458321911yescharacteristic
325C4#1458322511yescharacteristic
326C4#1458322911yescharacteristic
327C4#1458323111yescharacteristic
328C4#1458323411yescharacteristic
329C4#1458324311yescharacteristic
330C4#1458325111yescharacteristic
331C4#1458326111yescharacteristic
332C2#1913394011yescharacteristic
333C2#1913397411yescharacteristic
334C2#1913406411yescharacteristic
335C2#1913409811yescharacteristic
336C2#1913600411yescharacteristic
337C2#1913602911yescharacteristic
338C2#1913604111yescharacteristic
subgroupG/H
centerC23#13063296
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1844C2
socle, prime radicalC23×C43#121
hypercenter#1844D43
hypocenterC43#10620
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1844

Complements

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

NH ≅ G/Ntype
192. C43#10620semidirect

Maximal subgroups

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

subgroupindex
#191355312
#191345972
#191324782
#191324302
C43×#18442
#1062043