Finite Group Databasebeta

← #25001175

Subgroups — #25001175

Order 11008.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135548C211yesmaximal, characteristic
2#19135356C211yesmaximal, characteristic
3#19135313C211yesmaximal, characteristic
4C2×#14582650C211yesmaximal, characteristic
5C2×#14582645C211yesmaximal, characteristic
6#19132478C211yesmaximal, characteristic
7C43×#1956C211yesmaximal, characteristic
8C2×#13063256—21no—
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×Dic43⋊C8—21no—
13C4×C4⋊Dic43C2211yescharacteristic
14#14582661—21no—
15#14582661—21no—
16#14582661—21no—
17#14582653—21no—
18#14582650—22no—
19#14582645—22no—
20C2×C4⋊Q8×C43C2211yescharacteristic
21C2×#103×C43—21no—
22C2×#103×C43—21no—
23C2×C4×C8×C43C2211yescharacteristic
24C43×#384C2211yescharacteristic
25C22×C43⋊C8—21no—
26C22×C43⋊C8—21no—
27C22×C43⋊C8—21no—
28C2×C4⋊Dic43D411yescharacteristic
29C2×C4⋊Dic43D411yescharacteristic
30C2×C4×Dic43—21no—
31#13063256—42no—
32C4⋊(C43⋊C8)—21no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)D412yes—
38Dic43⋊C8—42no—
39C43⋊#95—21no—
40C22×Q8×C43—21no—
41C22×C8×C43D411yescharacteristic
42C22×C8×C43D411yescharacteristic
43C4⋊Q8×C43—21no—
44C4⋊Q8×C43—21no—
45C4⋊Q8×C43—21no—
46C4⋊Q8×C43Q812yes—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43—21no—
52C2×C42×C43C2311yescharacteristic
53#103×C43—42no—
54#103×C43—42no—
55C4×C8×C43—21no—
56C4×C8×C43—21no—
57C2×Q8×C43—22no—
58C2×Q8×C43—41no—
59C2×Q8×C43—41no—
60C2×Q8×C43—41no—
61C2×Q8×C43—41no—
62C2×Q8×C43—41no—
63C22×C4×C43—41no—
64C22×C4×C43—41no—
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43#4111yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C2×C8×C43—21no—
71C2×C8×C43—21no—
72C2×C8×C43—21no—
73C2×C8×C43—21no—
74C2×C8×C43—21no—
75C2×C8×C43SD1612yes—
76C4⋊C4×C43—22no—
77C4⋊C4×C43—22no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—81no—
85C42×C43C2×D411yescharacteristic
86C42×C43C2×Q811yescharacteristic
87C42×C43#4111yescharacteristic
88C42×C43#4111yescharacteristic
89C4⋊Dic43—21no—
90C4⋊Dic43—21no—
91C4⋊Dic43—21no—
92C4⋊Dic43SD1612yes—
93C4×Dic43—41no—
94C4×Dic43—41no—
95C2×C43⋊C8—22no—
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—
103C2×C43⋊C8—41no—
104C23×C43#12111yescharacteristic
105Q8×C43—42no—
106Q8×C43—42no—
107Q8×C43—81no—
108Q8×C43—81no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—42no—
112C2×C4×C43—81no—
113C2×C4×C43—81no—
114C2×C4×C43—81no—
115C2×C4×C43—81no—
116C2×C4×C43—81no—
117C2×C4×C43#12111yescharacteristic
118C2×C4×C43#12111yescharacteristic
119C2×C4×C43C22⋊Q811yescharacteristic
120C2×C4×C43C22⋊Q811yescharacteristic
121C2×C4×C43C22⋊Q811yescharacteristic
122C2×C4×C43#12611yescharacteristic
123C2×C4×C43C2×SD1611yescharacteristic
124C2×C4×C43C2×SD1611yescharacteristic
125C2×C4×C43#13511yescharacteristic
126C2×C4×C43#13511yescharacteristic
127C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C43#13711yescharacteristic
130C2×C4×C43#13711yescharacteristic
131C2×Dic43—22no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C8×C43—22no—
138C8×C43—41no—
139C43⋊C8—42no—
140C43⋊C8—81no—
141C43⋊C8—81no—
142#10596—431nomaximal, Sylow
143C22×C43#39611yescharacteristic
144C22×C43#46011yescharacteristic
145C22×C43#46311yescharacteristic
146C22×C43#46511yescharacteristic
147C22×C43#47011yescharacteristic
148C22×C43#47111yescharacteristic
149C22×C43#47311yescharacteristic
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—82no—
153C4×C43—161no—
154C4×C43#46111yescharacteristic
155C4×C43#46411yescharacteristic
156C4×C43#46511yescharacteristic
157C4×C43#46911yescharacteristic
158C4×C43#47511yescharacteristic
159C4×C43#47611yescharacteristic
160C4×C43#47811yescharacteristic
161C4×C43#47911yescharacteristic
162Dic43—42no—
163Dic43—81no—
164#1988—431no—
165#1956D4311yescharacteristic
166#1948—431no—
167#1939—431no—
168C2×#334—431no—
169C2×#332—431no—
170#1296—431no—
171C2×C43#166611yescharacteristic
172C2×C43#167911yescharacteristic
173C2×C43#169011yescharacteristic
174C2×C43#170311yescharacteristic
175C2×C43#206411yescharacteristic
176C2×C43#206511yescharacteristic
177C2×C43#206611yescharacteristic
178C2×C4⋊Q8C2×D4311yescharacteristic
179C2×#106—861no—
180C2×C4⋊C8—431no—
181C2×C4⋊C8—431no—
182C2×C4⋊C8—431no—
183C2×C4⋊C8—861no—
184C2×#103—21no—
185C2×#103—21no—
186C2×C4×C8C2×D4311yescharacteristic
187#384C2×D4311yescharacteristic
188C4×C4⋊C4—431no—
189#340—861no—
190#340—861no—
191#340—861no—
192#336—861no—
193#334—862no—
194#332—862no—
195C43#1059611yescharacteristic, complemented, Sylow
196C22×Q8—21no—
197C22×C8—861no—
198C22×C8—861no—
199C22×C8—861no—
200C22×C8C22⋊D4311yescharacteristic
201C22×C8C22⋊D4311yescharacteristic
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8Dic8612yes—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—431no—
212C2×C4⋊C4—431no—
213C2×C42—861no—
214C2×C42C22×D4311yescharacteristic
215#106—1722no—
216C4⋊C8—432no—
217C4⋊C8—861no—
218C4⋊C8—861no—
219C4⋊C8—861no—
220C4⋊C8—861no—
221C4⋊C8—861no—
222C4⋊C8—1722no—
223#103—42no—
224#103—42no—
225C4×C8—21no—
226C4×C8—21no—
227#95—861no—
228C2×Q8—22no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—861no—
237C22×C4—861no—
238C22×C4D4×D4311yescharacteristic
239C22×C4#1062190011yescharacteristic
240C22×C4C2×C22⋊D4311yescharacteristic
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—862no—
247C2×C8—1721no—
248C2×C8—1721no—
249C2×C8—1721no—
250C2×C8—1721no—
251C2×C8—1721no—
252C2×C8—1721no—
253C2×C8—1721no—
254C2×C8—1721no—
255C2×C8#1062188312yes—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—81no—
265C4⋊C4—432no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C42—1721no—
270C42—1721no—
271C42C2×Dic8611yescharacteristic
272C42#1062189811yescharacteristic
273C42D4×D4311yescharacteristic
274C42#1062190011yescharacteristic
275C23#1306329611yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—81no—
279Q8—81no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—862no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4#1306329711yescharacteristic
295C2×C4#1306329811yescharacteristic
296C2×C4#1306330211yescharacteristic
297C2×C4#1306330211yescharacteristic
298C2×C4#1306330411yescharacteristic
299C2×C4#1306331811yescharacteristic
300C2×C4SD16×D4311yescharacteristic
301C2×C4C2×#1062188311yescharacteristic
302C2×C4#1306334511yescharacteristic
303C2×C4#1306334611yescharacteristic
304C2×C4#1306335011yescharacteristic
305C2×C4#1306335111yescharacteristic
306C2×C4#1306335711yescharacteristic
307C2×C4#1306335711yescharacteristic
308C8—22no—
309C8—41no—
310C8—3441no—
311C8—3441no—
312C8—1722no—
313C22#1458282211yescharacteristic
314C22#1458309611yescharacteristic
315C22#1458311111yescharacteristic
316C22#1458312511yescharacteristic
317C22#1458315411yescharacteristic
318C22#1458315911yescharacteristic
319C22#1458317111yescharacteristic
320C4—21no—
321C4—21no—
322C4—82no—
323C4—161no—
324C4—3441no—
325C4—1722no—
326C4#1458310311yescharacteristic
327C4#1458312411yescharacteristic
328C4#1458312611yescharacteristic
329C4#1458315011yescharacteristic
330C4#1458318211yescharacteristic
331C4#1458318911yescharacteristic
332C4#1458319911yescharacteristic
333C4#1458320411yescharacteristic
334C2#1913394011yescharacteristic
335C2#1913401511yescharacteristic
336C2#1913408611yescharacteristic
337C2#1913416711yescharacteristic
338C2#1913596011yescharacteristic
339C2#1913596911yescharacteristic
340C2#1913597411yescharacteristic
subgroupG/H
centerC23#13063296
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1956C2
socle, prime radicalC23×C43#121
hypercenter#1956D43
hypocenterC43#10596
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
195. C43#10596semidirect

Maximal subgroups

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

subgroupindex
#191355482
#191353562
#191353132
C2×#145826502
C2×#145826452
#191324782
C43×#19562
#1059643