Finite Group Databasebeta

← #25001330

Subgroups — #25001330

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#19135530C211yesmaximal, characteristic
2#19134751C211yesmaximal, characteristic
3#19134601C211yesmaximal, characteristic
4#19134597C211yesmaximal, characteristic
5#19132479C211yesmaximal, characteristic
6#19132429C211yesmaximal, characteristic
7C43×#1296C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9C2×#13063256—21no—
10C2×#13063256—21no—
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×#13063250—21no—
13C2×#13063248—21no—
14C2×C4×C43⋊C8C2211yescharacteristic
15#14582769C2211yescharacteristic
16#14582662—21no—
17#14582661—21no—
18#14582653—21no—
19#14582653—21no—
20C2×C4⋊C8×C43C2211yescharacteristic
21C2×C4⋊C8×C43C2211yescharacteristic
22C43×#384C2211yescharacteristic
23C22×Dic86D411yescharacteristic
24C22×C43⋊C8—21no—
25C22×C43⋊C8D411yescharacteristic
26C22×C43⋊C8D411yescharacteristic
27C4×Dic86—21no—
28C4×Dic86—21no—
29C4×Dic86—21no—
30C4×Dic86—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43D411yescharacteristic
35C2×Dic43⋊C4—21no—
36C2×C4×Dic43—21no—
37#13063256—42no—
38#13063256—42no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41#13063250—42no—
42#13063248—42no—
43C4×C43⋊C8—21no—
44C4×C43⋊C8—21no—
45C22×C8×C43—21no—
46C22×C8×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C42×C43C2311yescharacteristic
51C4⋊C8×C43—21no—
52C4⋊C8×C43—21no—
53C4⋊C8×C43—21no—
54C4⋊C8×C43—21no—
55C22×C4×C43—41no—
56C22×C4×C43C2×D411yescharacteristic
57C22×C4×C43C2×D411yescharacteristic
58C22×C4×C43#4111yescharacteristic
59C22×Dic43—21no—
60C22×Dic43—21no—
61C22×Dic43—41no—
62C2×Dic86—21no—
63C2×Dic86—21no—
64C2×Dic86—21no—
65C2×Dic86—21no—
66C2×Dic86—21no—
67C2×Dic86SD1612yes—
68C2×C8×C43—41no—
69C2×C8×C43—41no—
70C2×C8×C43—41no—
71C2×C8×C43—41no—
72C2×C8×C43—41no—
73C2×C8×C43—41no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—81no—
79C42×C43#4111yescharacteristic
80C42×C43#4111yescharacteristic
81C42×C43#4111yescharacteristic
82C42×C43#4111yescharacteristic
83C4⋊Dic43—21no—
84C4⋊Dic43—21no—
85C4⋊Dic43—41no—
86C4⋊Dic43—41no—
87C4⋊Dic43—41no—
88C4⋊Dic43—41no—
89C4⋊Dic43—81no—
90Dic43⋊C4—41no—
91Dic43⋊C4—41no—
92C4×Dic43—41no—
93C4×Dic43—41no—
94C2×C43⋊C8—21no—
95C2×C43⋊C8—21no—
96C2×C43⋊C8—21no—
97C2×C43⋊C8—21no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8—41no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8SD1612yes—
102C2×C43⋊C8Q1612yes—
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#12311yescharacteristic
110C2×C4×C43#12311yescharacteristic
111C2×C4×C43#12311yescharacteristic
112C2×C4×C43#12411yescharacteristic
113C2×C4×C43#12611yescharacteristic
114C2×C4×C43#12611yescharacteristic
115C2×C4×C43C2×SD1611yescharacteristic
116C2×C4×C43C2×SD1611yescharacteristic
117C2×C4×C43C2×Q1611yescharacteristic
118C2×C4×C43#13511yescharacteristic
119C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C43#13711yescharacteristic
122C2×C4×C43#13711yescharacteristic
123C2×Dic43—22no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—81no—
130C2×Dic43—81no—
131C2×Dic43—81no—
132Dic86—22no—
133Dic86—22no—
134Dic86—41no—
135Dic86—41no—
136C8×C43—81no—
137C8×C43—81no—
138C43⋊C8—22no—
139C43⋊C8—22no—
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#48111yescharacteristic
153C4×C43#48211yescharacteristic
154C4×C43#48311yescharacteristic
155C4×C43#48311yescharacteristic
156C4×C43#48411yescharacteristic
157C4×C43#48511yescharacteristic
158C4×C43#48711yescharacteristic
159C4×C43#48911yescharacteristic
160Dic43—42no—
161Dic43—81no—
162Dic43—161no—
163#1984—431no—
164#1844—431no—
165#1803—431no—
166#1803—431no—
167#1296—431no—
168#1296D4311yescharacteristic
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—861no—
179C2×#106—861no—
180C2×C4⋊C8—431no—
181C2×C4⋊C8C2×D4311yescharacteristic
182C2×C4⋊C8C2×D4311yescharacteristic
183C2×#103—861no—
184C2×#103—861no—
185C2×C4×C8—431no—
186#384—431no—
187#384C2×D4311yescharacteristic
188#340—861no—
189#340—861no—
190#336—861no—
191#336—861no—
192C43#1062011yescharacteristic, complemented, Sylow
193C22×Q8—431no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—431no—
197C22×C8—431no—
198C22×C8—861no—
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—431no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4—861no—
211C2×C42—861no—
212C2×C42C22×D4311yescharacteristic
213#106—1722no—
214#106—1722no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—861no—
220C4⋊C8—861no—
221#103—1722no—
222#103—1722no—
223C4×C8—861no—
224C4×C8—861no—
225C2×Q8—432no—
226C2×Q8—861no—
227C2×Q8—861no—
228C2×Q8—861no—
229C2×Q8—861no—
230C2×Q8—861no—
231C22×C4—41no—
232C22×C4—861no—
233C22×C4—861no—
234C22×C4—1721no—
235C22×C4#1062189811yescharacteristic
236C22×C4D4×D4311yescharacteristic
237C22×C4D4×D4311yescharacteristic
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—432no—
245C2×C8—432no—
246C2×C8—861no—
247C2×C8—861no—
248C2×C8—861no—
249C2×C8—861no—
250C2×C8—1721no—
251C2×C8—1721no—
252C2×C8—1721no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—81no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—3441no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C42—1721no—
268C42—1721no—
269C42#1062189811yescharacteristic
270C42#1062189811yescharacteristic
271C42#1062190011yescharacteristic
272C42#1062190211yescharacteristic
273C23#1306329811yescharacteristic
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—862no—
284C2×C4—3441no—
285C2×C4—3441no—
286C2×C4—3441no—
287C2×C4—1721no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4#1306330711yescharacteristic
293C2×C4#1306331011yescharacteristic
294C2×C4#1306331011yescharacteristic
295C2×C4#1306331111yescharacteristic
296C2×C4#1306331911yescharacteristic
297C2×C4#1306332011yescharacteristic
298C2×C4SD16×D4311yescharacteristic
299C2×C4SD16×D4311yescharacteristic
300C2×C4Q16×D4311yescharacteristic
301C2×C4#1306334811yescharacteristic
302C2×C4#1306334911yescharacteristic
303C2×C4#1306334911yescharacteristic
304C2×C4#1306335411yescharacteristic
305C2×C4#1306335411yescharacteristic
306C8—81no—
307C8—81no—
308C8—862no—
309C8—862no—
310C8—3441no—
311C22#1458282811yescharacteristic
312C22#1458309811yescharacteristic
313C22#1458310811yescharacteristic
314C22#1458313111yescharacteristic
315C22#1458314411yescharacteristic
316C22#1458316111yescharacteristic
317C22#1458316511yescharacteristic
318C4—21no—
319C4—21no—
320C4—161no—
321C4—3441no—
322C4—1722no—
323C4—6881no—
324C4#1458321611yescharacteristic
325C4#1458322611yescharacteristic
326C4#1458323111yescharacteristic
327C4#1458323111yescharacteristic
328C4#1458323611yescharacteristic
329C4#1458323911yescharacteristic
330C4#1458324811yescharacteristic
331C4#1458325711yescharacteristic
332C2#1913394611yescharacteristic
333C2#1913398011yescharacteristic
334C2#1913406611yescharacteristic
335C2#1913410011yescharacteristic
336C2#1913600711yescharacteristic
337C2#1913603411yescharacteristic
338C2#1913604411yescharacteristic
subgroupG/H
centerC23#13063298
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1296C2
socle, prime radicalC23×C43#121
hypercenter#1296D43
hypocenterC43#10620
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

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
#191355302
#191347512
#191346012
#191345972
#191324792
#191324292
C43×#12962
#1062043