Finite Group Databasebeta

← #24996346

Subgroups — #24996346

Order 11008.

578 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583245C211yesmaximal, characteristic
2#19135556C211yesmaximal, characteristic, complemented
3#19135402C211yesmaximal, characteristic
4#19135396C211yesmaximal, characteristic, complemented
5#19134722C211yesmaximal, characteristic, complemented
6C2×C8×C43⋊C8C211yesmaximal, characteristic, complemented
7C43×#1957C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9#14583245—22no—
10#14583245C414yescomplemented
11C2×#13063248—22no—
12C2×#13063246—22no—
13C2×#13063246—22no—
14C2×C4×C43⋊C8C2211yescharacteristic
15C2×C4×C43⋊C8C2211yescharacteristic
16#14582769C2211yescharacteristic
17#14582662—22no—
18#14582661—22no—
19C8×C43⋊C8—22no—
20C2×#127×C43C2211yescharacteristic
21C2×#102×C43—22no—
22C2×C4×C8×C43C2211yescharacteristic
23C43×#384C2211yescharacteristic
24C22×Dic86—21no—
25C22×C43⋊C8D412yes—
26C22×C43⋊C8D412yes—
27#13063325—21no—
28#13063325—21no—
29#13063325—21no—
30#13063325C2×C412yes—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—21no—
36#13063248—44no—
37#13063246—28no—
38#13063246—44no—
39C4×C43⋊C8—21no—
40C4×C43⋊C8—21no—
41C4×C43⋊C8C2×C412yes—
42C4×C43⋊C8D412yes—
43C22×D4×C43—21no—
44C22×D4×C43—21no—
45C22×D4×C43—21no—
46C22×C8×C43D412yes—
47#127×C43—21no—
48#127×C43—21no—
49#127×C43—21no—
50#127×C43C2×C412yes—
51C2×C4⋊C4×C43—21no—
52C2×C4⋊C4×C43—21no—
53C2×C4⋊C4×C43—21no—
54C2×C42×C43C2311yescharacteristic
55#102×C43—44no—
56C4×C8×C43—21no—
57C4×C8×C43—21no—
58C24×C43—41no—
59C2×D4×C43—22no—
60C2×D4×C43—22no—
61C2×D4×C43—22no—
62C2×D4×C43—41no—
63C2×D4×C43—41no—
64C2×D4×C43—41no—
65C2×D4×C43—42no—
66C2×D4×C43—42no—
67C2×D4×C43—42no—
68C2×D4×C43—42no—
69C2×D4×C43—42no—
70C2×D4×C43—42no—
71C22×C4×C43—41no—
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—41no—
76C22×Dic43—41no—
77C2×Dic86—22no—
78C2×Dic86—42no—
79C2×Dic86—42no—
80C2×Dic86—41no—
81C2×C8×C43—22no—
82C2×C8×C43—22no—
83C2×C8×C43SD1614yes—
84C4⋊C4×C43—42no—
85C4⋊C4×C43—42no—
86C4⋊C4×C43—42no—
87C42×C43C22×C411yescharacteristic
88C42×C43C2×D411yescharacteristic
89C42×C43#4111yescharacteristic
90C42×C43#4111yescharacteristic
91C4⋊Dic43—22no—
92C4⋊Dic43—22no—
93C4⋊Dic43—41no—
94C4⋊Dic43—41no—
95C4⋊Dic43—42no—
96C4⋊Dic43—42no—
97C4⋊Dic43—42no—
98C2×C43⋊C8—22no—
99C2×C43⋊C8—22no—
100C2×C43⋊C8—22no—
101C2×C43⋊C8—22no—
102C2×C43⋊C8C22⋊C414yes—
103C2×C43⋊C8D814yes—
104C23×C43—42no—
105C23×C43—81no—
106C23×C43—81no—
107C23×C43—81no—
108C23×C43—81no—
109C23×C43—81no—
110C23×C43—81no—
111C23×C43#12711yescharacteristic
112D4×C43—44no—
113D4×C43—44no—
114D4×C43—44no—
115D4×C43—82no—
116D4×C43—82no—
117D4×C43—82no—
118C2×C4×C43—81no—
119C2×C4×C43—81no—
120C2×C4×C43—81no—
121C2×C4×C43C2×C22⋊C411yescharacteristic
122C2×C4×C43C4×D411yescharacteristic
123C2×C4×C43C4×D411yescharacteristic
124C2×C4×C43#12111yescharacteristic
125C2×C4×C43#12111yescharacteristic
126C2×C4×C43#12411yescharacteristic
127C2×C4×C43C2×D812yes—
128C2×C4×C43C2×SD1612yes—
129C2×C4×C43#13512yes—
130C2×C4×C43#13512yes—
131C2×C4×C43#13512yes—
132C2×C4×C43#13512yes—
133C2×Dic43—42no—
134C2×Dic43—81no—
135C2×Dic43—81no—
136C2×Dic43—81no—
137C2×Dic43—81no—
138C2×Dic43—81no—
139Dic86—44no—
140Dic86—82no—
141C8×C43—24no—
142C43⋊C8—24no—
143C43⋊C8—24no—
144#9822—431nomaximal, Sylow
145C22×C43—82no—
146C22×C43—82no—
147C22×C43—82no—
148C22×C43—161no—
149C22×C43—161no—
150C22×C43—161no—
151C22×C43—161no—
152C22×C43#39011yescharacteristic
153C22×C43#49211yescharacteristic
154C22×C43#49311yescharacteristic
155C22×C43#49511yescharacteristic
156C22×C43#49511yescharacteristic
157C22×C43#49511yescharacteristic
158C22×C43#49511yescharacteristic
159C4×C43—161no—
160C4×C43#41612yes—
161C4×C43C4×D812yes—
162C4×C43C4×SD1612yes—
163C4×C43#46512yes—
164C4×C43#46612yes—
165C4×C43#48812yes—
166Dic43—82no—
167Dic43—161no—
168C2×#486—431no—
169#1990—431no—
170#1957—431no—
171#1957D4311yescharacteristic
172#1956—431no—
173#1834—431no—
174C2×C82—431no—
175C2×C43—162no—
176C2×C43#170611yescharacteristic
177C2×C43#170811yescharacteristic
178C2×C43#170911yescharacteristic
179C2×C43#171111yescharacteristic
180C2×C43#195811yescharacteristic
181C2×C43#196811yescharacteristic
182C2×C43#197011yescharacteristic
183C2×C4⋊Q8—431no—
184C2×#127C2×D4311yescharacteristic
185#486—434no—
186#486—862no—
187C2×#103—862no—
188C2×#102—22no—
189C2×#102—862no—
190C2×#102—862no—
191C2×C4×C8—431no—
192C2×C4×C8—431no—
193C2×C4×C8C2×D4311yescharacteristic
194#384—431no—
195#384C2×D4311yescharacteristic
196#340—862no—
197#340—862no—
198C82—862no—
199C43#982211yescharacteristic, complemented, Sylow
200C22×Q8—861no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×C8—432no—
205C22×C8—432no—
206C22×C8C22⋊D4312yes—
207C4⋊Q8—432no—
208C4⋊Q8—861no—
209C4⋊Q8—861no—
210C4⋊Q8—861no—
211#127—21no—
212#127—21no—
213#127—21no—
214#127C4×D4312yes—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4—861no—
222C2×C4⋊C4—861no—
223C2×C42C22×D4311yescharacteristic
224#103—1724no—
225#102—44no—
226#102—868no—
227#102—1724no—
228C4×C8—21no—
229C4×C8—21no—
230C4×C8—432no—
231C4×C8—432no—
232C4×C8—861no—
233C4×C8—861no—
234C24—41no—
235C2×Q8—862no—
236C2×Q8—1722no—
237C2×Q8—1722no—
238C2×Q8—1721no—
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—42no—
250C2×D4—42no—
251C22×C4—41no—
252C22×C4—1721no—
253C22×C4—1721no—
254C22×C4D4×D4311yescharacteristic
255C22×C4D4×D4311yescharacteristic
256C22×C4C2×C22⋊D4311yescharacteristic
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—434no—
260C2×C8—434no—
261C2×C8—862no—
262C2×C8—862no—
263C2×C8—862no—
264C2×C8—862no—
265C2×C8#1062188314yes—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—862no—
270C4⋊C4—862no—
271C4⋊C4—1722no—
272C4⋊C4—1722no—
273C4⋊C4—1722no—
274C4⋊C4—1721no—
275C4⋊C4—1721no—
276C42C2×C4×D4311yescharacteristic
277C42#1062189811yescharacteristic
278C42D4×D4311yescharacteristic
279C42#1062190011yescharacteristic
280C23—42no—
281C23—81no—
282C23—81no—
283C23—81no—
284C23—81no—
285C23—81no—
286C23—81no—
287C23#1306332111yescharacteristic
288Q8—3442no—
289Q8—1724no—
290D4—44no—
291D4—44no—
292D4—44no—
293D4—82no—
294D4—82no—
295D4—82no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—3441no—
300C2×C4—3441no—
301C2×C4—3441no—
302C2×C4—3441no—
303C2×C4—3441no—
304C2×C4—1722no—
305C2×C4C22⋊C4×D4311yescharacteristic
306C2×C4(C22⋊D43)⋊C411yescharacteristic
307C2×C4C4×C22⋊D4311yescharacteristic
308C2×C4#1306329711yescharacteristic
309C2×C4#1306329811yescharacteristic
310C2×C4#1306331111yescharacteristic
311C2×C4D8×D4312yes—
312C2×C4C2×#1062188312yes—
313C2×C4#1306334412yes—
314C2×C4#1306334512yes—
315C2×C4#1306334612yes—
316C2×C4#1306334612yes—
317C8—24no—
318C8—864no—
319C8—864no—
320C22—82no—
321C22—82no—
322C22—82no—
323C22—161no—
324C22—161no—
325C22—161no—
326C22—161no—
327C22#1458279911yescharacteristic
328C22#1458327111yescharacteristic
329C22#1458327411yescharacteristic
330C22#1458328011yescharacteristic
331C22#1458328011yescharacteristic
332C22#1458328111yescharacteristic
333C22#1458328211yescharacteristic
334C4—161no—
335C4—3442no—
336C4—6881no—
337C4#1458289212yes—
338C4#1458297912yes—
339C4C4×#1062188312yes—
340C4#1458312612yes—
341C4#1458313412yes—
342C4#1458325212yes—
343C2—162no—
344C2#1913418411yescharacteristic
345C2#1913419411yescharacteristic
346C2#1913419911yescharacteristic
347C2#1913420611yescharacteristic
348C2#1913540511yescharacteristic
349C2#1913544811yescharacteristic
350C2#1913545811yescharacteristic
subgroupG/H
centerC23#13063321
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1957C2
socleC23×C43#127
prime radicalC2×#127×C43C22
cosocleC2×C42×C43C23
hypercenter#1957D43
hypocenterC43#9822
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #19135556C2semidirect
4. #19135396C2semidirect
5. #19134722C2semidirect
6. C2×C8×C43⋊C8C2semidirect
10. #14583245C4semidirect
199. C43#9822semidirect

Maximal subgroups

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

subgroupindex
C2×#145832452
#191355562
#191354022
#191353962
#191347222
C2×C8×C43⋊C82
C43×#19572
#982243