Finite Group Databasebeta

← #25001152

Subgroups — #25001152

Order 11008.

370 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135557C211yesmaximal, characteristic
2#19135544C211yesmaximal, characteristic
3#19135354C211yesmaximal, characteristic
4#19135311C211yesmaximal, characteristic
5C2×#14582651C211yesmaximal, characteristic
6#19132479C211yesmaximal, characteristic
7C2×C43×#333C211yesmaximal, characteristic
8C2×#13063259—21no—
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×Dic43⋊C8—21no—
11C2×C4×C43⋊C8C2211yescharacteristic
12#14582769C2211yescharacteristic
13C4×C4⋊Dic43C2211yescharacteristic
14#14582662—21no—
15#14582661—21no—
16#14582661—21no—
17#14582661—21no—
18#14582661—21no—
19#14582653—21no—
20#14582651—22no—
21C2×C4⋊Q8×C43C2211yescharacteristic
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C43×#333—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#13063259—42no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37Dic43⋊C8—42no—
38C4×C43⋊C8—21no—
39C4×C43⋊C8—21no—
40C43⋊#95—21no—
41C22×Q8×C43—21no—
42C22×C8×C43—21no—
43C22×C8×C43—21no—
44C4⋊Q8×C43—21no—
45C4⋊Q8×C43—21no—
46C4⋊Q8×C43—21no—
47C4⋊Q8×C43Q812yes—
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×C43D412yes—
55C2×Q8×C43—22no—
56C2×Q8×C43—41no—
57C2×Q8×C43—81no—
58C2×Q8×C43—81no—
59C22×C4×C43—41no—
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43#4111yescharacteristic
63C22×Dic43—21no—
64C22×Dic43—21no—
65C22×Dic43—41no—
66C2×C8×C43—22no—
67C2×C8×C43—41no—
68C2×C8×C43—41no—
69C2×C8×C43—41no—
70C2×C8×C43—41no—
71C2×C8×C43—41no—
72C4⋊C4×C43—22no—
73C4⋊C4×C43—22no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C42×C43C2×D411yescharacteristic
77C42×C43C2×Q811yescharacteristic
78C42×C43#4111yescharacteristic
79C42×C43#4111yescharacteristic
80C4⋊Dic43—21no—
81C4⋊Dic43—21no—
82C4⋊Dic43—21no—
83C4⋊Dic43—41no—
84C4⋊Dic43—41no—
85C4⋊Dic43—41no—
86C4⋊Dic43—41no—
87C4⋊Dic43—81no—
88C4⋊Dic43Q1612yes—
89C4×Dic43—41no—
90C4×Dic43—41no—
91C2×C43⋊C8—21no—
92C2×C43⋊C8—21no—
93C2×C43⋊C8—21no—
94C2×C43⋊C8—21no—
95C2×C43⋊C8—21no—
96C2×C43⋊C8—41no—
97C2×C43⋊C8—41no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8Q1612yes—
100C23×C43#12111yescharacteristic
101Q8×C43—82no—
102Q8×C43—82no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—42no—
106C2×C4×C43—81no—
107C2×C4×C43—81no—
108C2×C4×C43#12111yescharacteristic
109C2×C4×C43#12111yescharacteristic
110C2×C4×C43C22⋊Q811yescharacteristic
111C2×C4×C43C22⋊Q811yescharacteristic
112C2×C4×C43C22⋊Q811yescharacteristic
113C2×C4×C43#12611yescharacteristic
114C2×C4×C43C2×Q1611yescharacteristic
115C2×C4×C43C2×Q1611yescharacteristic
116C2×C4×C43#13511yescharacteristic
117C2×C4×C43#13511yescharacteristic
118C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C43#13711yescharacteristic
121C2×C4×C43#13711yescharacteristic
122C2×Dic43—22no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—81no—
129C2×Dic43—81no—
130C2×Dic43—81no—
131C8×C43—42no—
132C8×C43—81no—
133C43⋊C8—22no—
134C43⋊C8—41no—
135C43⋊C8—81no—
136#10593—431nomaximal, Sylow
137C22×C43#39611yescharacteristic
138C22×C43#46211yescharacteristic
139C22×C43#46311yescharacteristic
140C22×C43#46711yescharacteristic
141C22×C43#46811yescharacteristic
142C22×C43#47111yescharacteristic
143C22×C43#47211yescharacteristic
144C4×C43—21no—
145C4×C43—21no—
146C4×C43—82no—
147C4×C43#46211yescharacteristic
148C4×C43#46311yescharacteristic
149C4×C43#46711yescharacteristic
150C4×C43#46811yescharacteristic
151C4×C43#47711yescharacteristic
152C4×C43#47711yescharacteristic
153C4×C43#47911yescharacteristic
154C4×C43#47911yescharacteristic
155Dic43—42no—
156Dic43—81no—
157Dic43—161no—
158#1990—431no—
159#1987—431no—
160#1947—431no—
161#1939—431no—
162C2×#335—431no—
163C2×#333D4311yescharacteristic
164#1296—431no—
165C2×C43#167611yescharacteristic
166C2×C43#168311yescharacteristic
167C2×C43#169211yescharacteristic
168C2×C43#169711yescharacteristic
169C2×C43#206311yescharacteristic
170C2×C43#206811yescharacteristic
171C2×C43#206811yescharacteristic
172C2×C4⋊Q8C2×D4311yescharacteristic
173C2×#107—861no—
174C2×C4⋊C8—431no—
175C2×C4⋊C8—861no—
176C2×C4⋊C8C2×D4311yescharacteristic
177C2×C4⋊C8C2×D4311yescharacteristic
178C2×C4×C8—431no—
179#384—431no—
180C4×C4⋊C4—431no—
181#340—861no—
182#340—861no—
183#340—861no—
184#340—861no—
185#340—861no—
186#336—861no—
187#335—862no—
188#333—22no—
189C43#1059311yescharacteristic, complemented, Sylow
190C22×Q8—21no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—431no—
194C22×C8—431no—
195C22×C8—861no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8Dic8612yes—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—431no—
203C2×C4⋊C4—431no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4—861no—
206C2×C4⋊C4—861no—
207C2×C42—861no—
208C2×C42C22×D4311yescharacteristic
209#107—1722no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—861no—
214C4⋊C8—861no—
215C4⋊C8—1722no—
216C4⋊C8C22⋊D4312yes—
217C4×C8—861no—
218C4×C8—861no—
219#95—861no—
220C2×Q8—22no—
221C2×Q8—41no—
222C2×Q8—81no—
223C2×Q8—81no—
224C22×C4—41no—
225C22×C4—861no—
226C22×C4—861no—
227C22×C4—1721no—
228C22×C4#1062189811yescharacteristic
229C22×C4D4×D4311yescharacteristic
230C22×C4D4×D4311yescharacteristic
231C2×C8—22no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—432no—
238C2×C8—861no—
239C2×C8—861no—
240C2×C8—861no—
241C2×C8—861no—
242C2×C8—861no—
243C2×C8—1721no—
244C2×C8—1721no—
245C2×C8—1721no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—432no—
251C4⋊C4—861no—
252C4⋊C4—861no—
253C4⋊C4—861no—
254C4⋊C4—3441no—
255C4⋊C4—1721no—
256C4⋊C4—1721no—
257C4⋊C4—1721no—
258C4⋊C4—1721no—
259C42—1721no—
260C42—1721no—
261C42C2×Dic8611yescharacteristic
262C42#1062190011yescharacteristic
263C42#1062190011yescharacteristic
264C42C2×C22⋊D4311yescharacteristic
265C23#1306329811yescharacteristic
266Q8—82no—
267Q8—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—862no—
274C2×C4—3441no—
275C2×C4—3441no—
276C2×C4—3441no—
277C2×C4—1721no—
278C2×C4—1721no—
279C2×C4—1721no—
280C2×C4—1721no—
281C2×C4—1721no—
282C2×C4#1306329611yescharacteristic
283C2×C4#1306329711yescharacteristic
284C2×C4#1306330211yescharacteristic
285C2×C4#1306330211yescharacteristic
286C2×C4#1306330411yescharacteristic
287C2×C4#1306331811yescharacteristic
288C2×C4Q16×D4311yescharacteristic
289C2×C4Q16×D4311yescharacteristic
290C2×C4#1306334611yescharacteristic
291C2×C4#1306334811yescharacteristic
292C2×C4#1306335211yescharacteristic
293C2×C4#1306335211yescharacteristic
294C2×C4#1306335411yescharacteristic
295C2×C4#1306335711yescharacteristic
296C8—42no—
297C8—81no—
298C8—862no—
299C8—3441no—
300C8—1721no—
301C22#1458282211yescharacteristic
302C22#1458310811yescharacteristic
303C22#1458311711yescharacteristic
304C22#1458313911yescharacteristic
305C22#1458314811yescharacteristic
306C22#1458316111yescharacteristic
307C22#1458316811yescharacteristic
308C4—21no—
309C4—21no—
310C4—82no—
311C4—3441no—
312C4—1722no—
313C4—6881no—
314C4#1458310711yescharacteristic
315C4#1458311611yescharacteristic
316C4#1458313711yescharacteristic
317C4#1458314211yescharacteristic
318C4#1458319211yescharacteristic
319C4#1458319211yescharacteristic
320C4#1458320411yescharacteristic
321C4#1458320811yescharacteristic
322C2#1913399811yescharacteristic
323C2#1913404911yescharacteristic
324C2#1913410411yescharacteristic
325C2#1913413111yescharacteristic
326C2#1913595111yescharacteristic
327C2#1913598611yescharacteristic
328C2#1913598811yescharacteristic
subgroupG/H
centerC23#13063298
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×#333C2
socle, prime radicalC23×C43#121
hypercenterC2×#333D43
hypocenterC43#10593
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
189. C43#10593semidirect

Maximal subgroups

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

subgroupindex
#191355572
#191355442
#191353542
#191353112
C2×#145826512
#191324792
C2×C43×#3332
#1059343