Finite Group Databasebeta

← #25001173

Subgroups — #25001173

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#19135398C211yesmaximal, characteristic
3#19135359C211yesmaximal, characteristic
4#19135311C211yesmaximal, characteristic
5C2×#14582649C211yesmaximal, characteristic
6#19132479C211yesmaximal, characteristic
7C2×C43×#332C211yesmaximal, characteristic
8C2×#13063257—21no—
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×Dic43⋊C8—21no—
11C2×#13063249—21no—
12C2×#13063249—21no—
13C2×C4×C43⋊C8C2211yescharacteristic
14#14582769C2211yescharacteristic
15C4×C4⋊Dic43C2211yescharacteristic
16#14582662—21no—
17#14582661—21no—
18#14582661—21no—
19#14582653—21no—
20#14582649—22no—
21C2×C4⋊Q8×C43C2211yescharacteristic
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C43×#332—22no—
25C22×C43⋊C8—21no—
26C22×C43⋊C8D411yescharacteristic
27C22×C43⋊C8D411yescharacteristic
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43D411yescharacteristic
32C2×C4⋊Dic43D411yescharacteristic
33C2×C4×Dic43—21no—
34#13063257—42no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37Dic43⋊C8—42no—
38#13063249—42no—
39#13063249—42no—
40C4×C43⋊C8—21no—
41C4×C43⋊C8—21no—
42C43⋊#95—21no—
43C22×Q8×C43—21no—
44C22×C8×C43—21no—
45C22×C8×C43—21no—
46C4⋊Q8×C43—21no—
47C4⋊Q8×C43—21no—
48C4⋊Q8×C43—21no—
49C4⋊Q8×C43Q812yes—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43—21no—
52C2×C42×C43C2311yescharacteristic
53C4⋊C8×C43—21no—
54C4⋊C8×C43—21no—
55C4⋊C8×C43—21no—
56C4⋊C8×C43D412yes—
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×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43#4111yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—41no—
70C2×C8×C43—22no—
71C2×C8×C43—41no—
72C2×C8×C43—41no—
73C2×C8×C43—41no—
74C2×C8×C43—41no—
75C2×C8×C43—41no—
76C4⋊C4×C43—22no—
77C4⋊C4×C43—22no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C42×C43C2×D411yescharacteristic
81C42×C43C2×Q811yescharacteristic
82C42×C43#4111yescharacteristic
83C42×C43#4111yescharacteristic
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43—41no—
88C4⋊Dic43—41no—
89C4⋊Dic43—41no—
90C4⋊Dic43—41no—
91C4⋊Dic43—81no—
92C4⋊Dic43SD1612yes—
93C4×Dic43—41no—
94C4×Dic43—41no—
95C2×C43⋊C8—21no—
96C2×C43⋊C8—21no—
97C2×C43⋊C8—21no—
98C2×C43⋊C8—21no—
99C2×C43⋊C8—21no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8SD1612yes—
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#12111yescharacteristic
115C2×C4×C43#12111yescharacteristic
116C2×C4×C43C22⋊Q811yescharacteristic
117C2×C4×C43C22⋊Q811yescharacteristic
118C2×C4×C43C22⋊Q811yescharacteristic
119C2×C4×C43#12611yescharacteristic
120C2×C4×C43C2×SD1611yescharacteristic
121C2×C4×C43C2×SD1611yescharacteristic
122C2×C4×C43#13511yescharacteristic
123C2×C4×C43#13511yescharacteristic
124C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C43#13711yescharacteristic
127C2×C4×C43#13711yescharacteristic
128C2×Dic43—22no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—81no—
135C2×Dic43—81no—
136C2×Dic43—81no—
137C8×C43—42no—
138C8×C43—81no—
139C43⋊C8—22no—
140C43⋊C8—41no—
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#46111yescharacteristic
154C4×C43#46411yescharacteristic
155C4×C43#46511yescharacteristic
156C4×C43#46911yescharacteristic
157C4×C43#47511yescharacteristic
158C4×C43#47611yescharacteristic
159C4×C43#47811yescharacteristic
160C4×C43#47911yescharacteristic
161Dic43—42no—
162Dic43—81no—
163Dic43—161no—
164#1988—431no—
165#1956—431no—
166#1948—431no—
167#1939—431no—
168C2×#334—431no—
169C2×#332D4311yescharacteristic
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—861no—
182C2×C4⋊C8C2×D4311yescharacteristic
183C2×C4⋊C8C2×D4311yescharacteristic
184C2×#103—861no—
185C2×#103—861no—
186C2×C4×C8—431no—
187#384—431no—
188C4×C4⋊C4—431no—
189#340—861no—
190#340—861no—
191#340—861no—
192#336—861no—
193#334—862no—
194#332—22no—
195C43#1059611yescharacteristic, complemented, Sylow
196C22×Q8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—431no—
200C22×C8—431no—
201C22×C8—861no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8Dic8612yes—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4—431no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4—861no—
213C2×C42—861no—
214C2×C42C22×D4311yescharacteristic
215#106—1722no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—861no—
220C4⋊C8—861no—
221C4⋊C8—1722no—
222C4⋊C8C22⋊D4312yes—
223#103—1722no—
224#103—1722no—
225C4×C8—861no—
226C4×C8—861no—
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—861no—
236C22×C4—861no—
237C22×C4—1721no—
238C22×C4#1062189811yescharacteristic
239C22×C4D4×D4311yescharacteristic
240C22×C4D4×D4311yescharacteristic
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—432no—
248C2×C8—861no—
249C2×C8—861no—
250C2×C8—861no—
251C2×C8—861no—
252C2×C8—861no—
253C2×C8—1721no—
254C2×C8—1721no—
255C2×C8—1721no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—432no—
261C4⋊C4—861no—
262C4⋊C4—861no—
263C4⋊C4—861no—
264C4⋊C4—3441no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C4⋊C4—1721no—
269C42—1721no—
270C42—1721no—
271C42C2×Dic8611yescharacteristic
272C42#1062190011yescharacteristic
273C42#1062190011yescharacteristic
274C42C2×C22⋊D4311yescharacteristic
275C23#1306329811yescharacteristic
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—862no—
286C2×C4—3441no—
287C2×C4—3441no—
288C2×C4—3441no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4#1306329611yescharacteristic
295C2×C4#1306329711yescharacteristic
296C2×C4#1306330211yescharacteristic
297C2×C4#1306330211yescharacteristic
298C2×C4#1306330411yescharacteristic
299C2×C4#1306331811yescharacteristic
300C2×C4SD16×D4311yescharacteristic
301C2×C4SD16×D4311yescharacteristic
302C2×C4#1306334611yescharacteristic
303C2×C4#1306334811yescharacteristic
304C2×C4#1306334911yescharacteristic
305C2×C4#1306334911yescharacteristic
306C2×C4#1306335411yescharacteristic
307C2×C4#1306335711yescharacteristic
308C8—42no—
309C8—81no—
310C8—862no—
311C8—3441no—
312C8—1721no—
313C22#1458282211yescharacteristic
314C22#1458309811yescharacteristic
315C22#1458311311yescharacteristic
316C22#1458313111yescharacteristic
317C22#1458315611yescharacteristic
318C22#1458316511yescharacteristic
319C22#1458317311yescharacteristic
320C4—21no—
321C4—21no—
322C4—82no—
323C4—3441no—
324C4—1722no—
325C4—6881no—
326C4#1458310211yescharacteristic
327C4#1458312311yescharacteristic
328C4#1458312511yescharacteristic
329C4#1458314911yescharacteristic
330C4#1458318211yescharacteristic
331C4#1458318711yescharacteristic
332C4#1458320111yescharacteristic
333C4#1458320811yescharacteristic
334C2#1913394611yescharacteristic
335C2#1913401711yescharacteristic
336C2#1913408811yescharacteristic
337C2#1913416911yescharacteristic
338C2#1913595811yescharacteristic
339C2#1913596711yescharacteristic
340C2#1913597211yescharacteristic
subgroupG/H
centerC23#13063298
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×#332C2
socle, prime radicalC23×C43#121
hypercenterC2×#332D43
hypocenterC43#10596
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

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
#191353982
#191353592
#191353112
C2×#145826492
#191324792
C2×C43×#3322
#1059643