Finite Group Databasebeta

← #24985012

Subgroups — #24985012

Order 11008.

438 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#19142962C211yesmaximal, characteristic
2C4×C4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
3#19132417C212yesmaximal, complemented
4#19132415C212yesmaximal
5C43×#1839C211yesmaximal, characteristic, complemented
6C2×#13063319—21no—
7C2×C4⋊(C43⋊C8)—21no—
8C2×C4×C43⋊C8—21no—
9#14582801C411yescharacteristic
10#14582801C411yescharacteristic
11#14582801C2211yescharacteristic
12#14582797C411yescharacteristic
13#14582797C411yescharacteristic
14#14582797C2211yescharacteristic
15#14582790—21no—
16#14582790—21no—
17#14582790—21no—
18#14582654C2212yes—
19C43×C43C2211yescharacteristic
20C43×#336—21no—
21C43×#336—21no—
22C43×#336C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C43⋊C8—22no—
25#13063319—42no—
26#13063319—42no—
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C4⋊(C43⋊C8)—24no—
40C4×C43⋊C8—42no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C22×C8×C43—22no—
45C2×C42×C43C2×C411yescharacteristic
46C2×C42×C43C2×C411yescharacteristic
47C2×C42×C43D411yescharacteristic
48C2×C42×C43D411yescharacteristic
49C2×C42×C43D411yescharacteristic
50C2×C42×C43D411yescharacteristic
51C2×C42×C43C2311yescharacteristic
52C23×D43—21no—
53C22×C4×C43C22⋊C411yescharacteristic
54C22×C4×C43C22⋊C411yescharacteristic
55C22×C4×C43C22⋊C411yescharacteristic
56C22×C4×C43C22⋊C411yescharacteristic
57C22×C4×C43C22×C411yescharacteristic
58C22×C4×C43C2×D411yescharacteristic
59C22×C4×C43C2×D411yescharacteristic
60C22×Dic43—21no—
61C22×Dic43—21no—
62C22×Dic43—21no—
63C2×D172—22no—
64C2×D172—41no—
65C2×D172—41no—
66C2×C8×C43—42no—
67C2×C8×C43—42no—
68C2×C8×C43—42no—
69C42×C43—22no—
70C42×C43—22no—
71C42×C43—22no—
72C42×C43—41no—
73C42×C43—41no—
74C42×C43—41no—
75C42×C43D812yes—
76C42×C43SD1612yes—
77(C2×D43)⋊C4—42no—
78(C2×D43)⋊C4—42no—
79(C2×D43)⋊C4—42no—
80(C2×D43)⋊C4—42no—
81(C2×D43)⋊C4—41no—
82(C2×D43)⋊C4—41no—
83(C2×D43)⋊C4—42no—
84C4⋊Dic43—22no—
85C4⋊Dic43—41no—
86C4⋊Dic43—41no—
87Dic43⋊C4—42no—
88Dic43⋊C4—42no—
89Dic43⋊C4—41no—
90Dic43⋊C4—41no—
91C2×C43⋊C8—24no—
92C2×C43⋊C8—42no—
93C2×C43⋊C8—42no—
94C23×C43C2×C22⋊C411yescharacteristic
95C22×D43—41no—
96C22×D43—41no—
97C22×D43—41no—
98C22×D43—41no—
99C22×D43—41no—
100C22×D43—41no—
101C22×D43—41no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43#10212yes—
118C2×C4×C43#10212yes—
119C2×C4×C43#10412yes—
120C2×C4×C43#13112yes—
121C2×C4×C43C2×D811yescharacteristic
122C2×C4×C43C2×SD1611yescharacteristic
123C2×C4×C43#13512yes—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133D172—82no—
134C8×C43—82no—
135C43⋊C8—44no—
136#7672—431nomaximal, Sylow
137C22×C43#40811yescharacteristic
138C22×C43#41011yescharacteristic
139C22×C43#41311yescharacteristic
140C22×C43C2×#10211yescharacteristic
141C22×C43#41611yescharacteristic
142C22×C43C2×#10411yescharacteristic
143C22×C43#42111yescharacteristic
144C2×D43—81no—
145C2×D43—81no—
146C2×D43—81no—
147C2×D43—81no—
148C2×D43—81no—
149C2×D43—81no—
150C2×D43—81no—
151C4×C43—22no—
152C4×C43—22no—
153C4×C43—22no—
154C4×C43—22no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—22no—
158C4×C43—41no—
159Dic43—81no—
160Dic43—81no—
161Dic43—81no—
162#2860—431no—
163#1839D4311yescharacteristic, complemented
164C4×C4⋊C8—431no—
165#1271—432no—
166#1270—432no—
167C2×C43#147311yescharacteristic
168C2×C43#148011yescharacteristic
169C2×C43#149411yescharacteristic
170C2×C43#150211yescharacteristic
171C2×C43#152111yescharacteristic
172C2×C43#152911yescharacteristic
173C2×C43#154011yescharacteristic
174D43—161no—
175C2×#126—861no—
176C2×C4⋊C8—861no—
177C2×C4×C8—861no—
178#390—431no—
179#390—431no—
180#390—431no—
181#389—431no—
182#389—431no—
183#389—431no—
184#388—861no—
185#388—861no—
186#388—861no—
187C43C2×D4311yescharacteristic
188#336—21no—
189#336—21no—
190#336—432no—
191#336C2×D4312yes—
192C43#767211yescharacteristic, complemented, Sylow
193C22×D4—431no—
194C22×C8—22no—
195C22×C8—862no—
196#126—1722no—
197#126—1722no—
198C2×C4⋊C4—431no—
199C2×C4⋊C4—431no—
200C2×C4⋊C4—431no—
201C2×C4⋊C4—861no—
202C2×C4⋊C4—861no—
203C2×C4⋊C4—861no—
204C2×C22⋊C4—861no—
205C2×C22⋊C4—861no—
206C2×C22⋊C4—861no—
207C2×C22⋊C4—861no—
208C2×C22⋊C4—861no—
209C2×C22⋊C4—861no—
210C2×C42C4×D4311yescharacteristic
211C2×C42C4×D4311yescharacteristic
212C2×C42D17211yescharacteristic
213C2×C42D17211yescharacteristic
214C2×C42C22⋊D4311yescharacteristic
215C2×C42C22⋊D4311yescharacteristic
216C2×C42C22×D4311yescharacteristic
217C4⋊C8—864no—
218C4×C8—1722no—
219#95—861no—
220#95—861no—
221#95—861no—
222C24—861no—
223C2×D4—862no—
224C2×D4—1721no—
225C2×D4—1721no—
226C22×C4—861no—
227C22×C4—861no—
228C22×C4—861no—
229C22×C4(C2×D43)⋊C411yescharacteristic
230C22×C4(C2×D43)⋊C411yescharacteristic
231C22×C4(C2×D43)⋊C411yescharacteristic
232C22×C4(C2×D43)⋊C411yescharacteristic
233C22×C4C2×C4×D4311yescharacteristic
234C22×C4C2×D17211yescharacteristic
235C22×C4C2×C22⋊D4311yescharacteristic
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—864no—
240C2×C8—1722no—
241C2×C8—1722no—
242C4⋊C4—862no—
243C4⋊C4—1721no—
244C4⋊C4—1721no—
245C4⋊C4—1722no—
246C4⋊C4—1722no—
247C4⋊C4—1721no—
248C4⋊C4—1721no—
249C22⋊C4—1722no—
250C22⋊C4—1722no—
251C22⋊C4—1722no—
252C22⋊C4—1722no—
253C22⋊C4—1721no—
254C22⋊C4—1721no—
255C22⋊C4—1722no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—41no—
260C42—41no—
261C42—41no—
262C42#1062187312yes—
263C42D34412yes—
264C23—1721no—
265C23—1721no—
266C23—1721no—
267C23—1721no—
268C23—1721no—
269C23—1721no—
270C23—1721no—
271C23C2×(C2×D43)⋊C411yescharacteristic
272D4—3442no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4#1306324712yes—
298C2×C4#1306324712yes—
299C2×C4#1306325112yes—
300C2×C4#1306333312yes—
301C2×C4C2×D34411yescharacteristic
302C2×C4C2×#1062187311yescharacteristic
303C2×C4#1306334512yes—
304C8—82no—
305C8—1724no—
306C22—3441no—
307C22—3441no—
308C22—3441no—
309C22—3441no—
310C22—3441no—
311C22—3441no—
312C22—3441no—
313C22#1458286711yescharacteristic
314C22#1458287211yescharacteristic
315C22#1458288111yescharacteristic
316C22C2×#1306324711yescharacteristic
317C22#1458289311yescharacteristic
318C22C2×#1306325111yescharacteristic
319C22#1458291711yescharacteristic
320C4—22no—
321C4—22no—
322C4—22no—
323C4—22no—
324C4—21no—
325C4—21no—
326C4—22no—
327C4—41no—
328C4—3441no—
329C4—3441no—
330C4—3441no—
331C2—6881no—
332C2#1913296511yescharacteristic
333C2#1913299511yescharacteristic
334C2#1913305311yescharacteristic
335C2#1913309111yescharacteristic
336C2#1913317011yescharacteristic
337C2#1913320311yescharacteristic
338C2#1913324211yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1839C2
socleC23×C43C2×C22⋊C4
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1839D43
hypocenterC43#7672
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C43 ◁ #1839

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊(C43⋊C8)C2semidirect
3. #19132417C2semidirect
5. C43×#1839C2semidirect
163. #1839D43semidirect
192. C43#7672semidirect

Maximal subgroups

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

subgroupindex
#191429622
C4×C4⋊(C43⋊C8)2
#191324172
#191324152
C43×#18392
#767243