Finite Group Databasebeta

← #25078496

Subgroups — #25078496

Order 11008.

806 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149090C211yesmaximal, characteristic, complemented
2#19145789C212yesmaximal
3#19133921C214yesmaximal, complemented
4#19133896C214yesmaximal, complemented
5#19133233C211yesmaximal, characteristic, complemented
6#19133209C212yesmaximal, complemented
7C43×#3135C211yesmaximal, characteristic
8C43⋊#564C2214yes—
9#14583628—22no—
10#14583627—22no—
11#14583624—22no—
12#14583511—22no—
13#14583509—24no—
14#14583456C2212yes—
15#14583305C2214yes—
16#14583263C2214yes—
17#14583220—24no—
18#14583189—22no—
19#14583179—22no—
20#14582956C2212yes—
21#14582641C2214yes—
22#14582640C2218yes—
23C43×#533C2211yescharacteristic
24C43×#532C2211yescharacteristic
25C43×#491C2212yes—
26C43×#490C2212yes—
27C43×#489—22no—
28C43×#416—22no—
29C2×#97×C43C2211yescharacteristic
30#13063325—22no—
31#13063325D412yes—
32#13063325D412yes—
33#13063323—24no—
34#13063318—28no—
35#13063317—22no—
36#13063317C2314yes—
37#13063316—24no—
38#13063316—28no—
39#13063315—28no—
40#13063315—28no—
41#13063304—22no—
42#13063304—22no—
43Q8×Dic43—24no—
44C4×Dic86—24no—
45C4×Dic86—22no—
46C4×Dic86—22no—
47#13063290—24no—
48#13063284D414yes—
49#13063258—24no—
50#13063256—24no—
51C4⋊(C43⋊C8)—22no—
52#13063246—24no—
53#13063246—24no—
54C22⋊(C43⋊C8)—22no—
55#13063236C2314yes—
56C2×#41×C43—21no—
57C22×C8×C43—21no—
58C4⋊Q8×C43D412yes—
59C4⋊Q8×C43C2311yescharacteristic
60#127×C43C2311yescharacteristic
61#125×C43C2312yes—
62#124×C43—21no—
63C22⋊Q8×C43—22no—
64#121×C43—22no—
65C4×Q8×C43—22no—
66C4×D4×C43—22no—
67#117×C43D412yes—
68C2×C42×C43C2311yescharacteristic
69#103×C43—24no—
70#102×C43—24no—
71#97×C43—21no—
72#97×C43C2312yes—
73#41×C43—44no—
74C2×Q8×C43—22no—
75C2×Q8×C43—21no—
76C2×D4×C43—21no—
77C2×D4×C43—22no—
78C2×D4×C43—41no—
79C22×C4×C43—41no—
80C22×C4×C43C2×D412yes—
81C22×C4×C43C2×D411yescharacteristic
82C2×Dic86—22no—
83C2×Dic86—22no—
84C2×C8×C43—22no—
85C2×C8×C43—42no—
86C4⋊C4×C43—22no—
87C4⋊C4×C43—24no—
88C4⋊C4×C43—22no—
89C4⋊C4×C43C2×D414yes—
90C22⋊C4×C43—22no—
91C22⋊C4×C43—42no—
92C42×C43—22no—
93C42×C43C2×D412yes—
94C42×C43C2×D411yescharacteristic
95C42×C43C2411yescharacteristic
96C22⋊Dic43—24no—
97C4⋊Dic43—28no—
98C4⋊Dic43—22no—
99C4⋊Dic43—22no—
100C4⋊Dic43C2×D414yes—
101C4⋊Dic43C2×D414yes—
102Dic43⋊C4—28no—
103Dic43⋊C4—28no—
104Dic43⋊C4—24no—
105Dic43⋊C4—24no—
106C4×Dic43—28no—
107C4×Dic43—24no—
108C2×C43⋊C8—24no—
109C23×C43—41no—
110C23×C43#12011yescharacteristic
111Q8×C43—44no—
112Q8×C43—42no—
113D4×C43—44no—
114D4×C43—42no—
115D4×C43—82no—
116C2×C4×C43—22no—
117C2×C4×C43—24no—
118C2×C4×C43—42no—
119C2×C4×C43—41no—
120C2×C4×C43—82no—
121C2×C4×C43#12012yes—
122C2×C4×C43#12011yescharacteristic
123C2×C4×C43C22×D412yes—
124C2×C4×C43C22×D411yescharacteristic
125C2×Dic43—24no—
126C2×Dic43—24no—
127Dic86—44no—
128Dic86—44no—
129C8×C43—42no—
130C43⋊C8—44no—
131#19063—431nomaximal, Sylow
132C22×C43—21no—
133C22×C43—22no—
134C22×C43—81no—
135C22×C43—82no—
136C22×C43C2×#12011yescharacteristic
137C4×C43—21no—
138C4×C43—22no—
139C4×C43—22no—
140C4×C43—44no—
141C4×C43—81no—
142C4×C43#45412yes—
143Dic43—44no—
144Dic43—44no—
145#3556—431no—
146#3235—432no—
147#3135D4311yescharacteristic
148#1663—434no—
149#1658—434no—
150#1537—431no—
151#1531—432no—
152C2×C43—41no—
153C2×C43—161no—
154C2×C43C2×#45411yescharacteristic
155C2×C43#302012yes—
156#564—434no—
157#557—862no—
158#557—862no—
159#557—862no—
160#541—864no—
161#541—862no—
162#533—432no—
163#533C2×D4311yescharacteristic
164#532C2×D4311yescharacteristic
165#501—434no—
166#491C2×D4312yes—
167#490—434no—
168#490C2×D4312yes—
169#489—22no—
170#482—864no—
171#476—862no—
172#474—862no—
173#432—432no—
174#416—22no—
175C2×#97C2×D4311yescharacteristic
176#330—434no—
177#330—438no—
178C43#1906311yescharacteristic, complemented, Sylow
179C2×#41—21no—
180C22×C8—21no—
181C4⋊Q8—432no—
182C4⋊Q8—432no—
183C4⋊Q8—862no—
184C4⋊Q8—864no—
185C4⋊Q8C22⋊D4312yes—
186C4⋊Q8C22×D4311yescharacteristic
187#127C22×D4311yescharacteristic
188#126—868no—
189#125—434no—
190#125—862no—
191#125—868no—
192#125—868no—
193#125—864no—
194#125—868no—
195#125C22×D4312yes—
196#124—21no—
197C22⋊Q8—22no—
198C22⋊Q8—862no—
199C22⋊Q8—862no—
200#121—22no—
201C4×Q8—22no—
202C4×Q8—864no—
203C4×Q8—864no—
204C4×Q8—864no—
205C4×Q8—862no—
206C4×Q8—862no—
207C4×D4—22no—
208#117—434no—
209#117C22⋊D4312yes—
210C2×C42C22×D4311yescharacteristic
211#107—864no—
212#106—864no—
213C4⋊C8—862no—
214#103—24no—
215#102—24no—
216#102—864no—
217#102—864no—
218C22⋊C8—862no—
219#97—21no—
220#97—434no—
221#97C22×D4312yes—
222#41—44no—
223C2×Q8—22no—
224C2×Q8—21no—
225C2×Q8—862no—
226C2×Q8—862no—
227C2×D4—22no—
228C2×D4—21no—
229C2×D4—41no—
230C22×C4—41no—
231C22×C4D4×D4312yes—
232C22×C4C2×C22⋊D4311yescharacteristic
233C2×C8—22no—
234C2×C8—42no—
235C2×C8—864no—
236C4⋊C4—22no—
237C4⋊C4—24no—
238C4⋊C4—22no—
239C4⋊C4—434no—
240C4⋊C4—434no—
241C4⋊C4—868no—
242C4⋊C4—868no—
243C4⋊C4—868no—
244C4⋊C4—862no—
245C4⋊C4—862no—
246C4⋊C4—864no—
247C4⋊C4—864no—
248C4⋊C4C2×C22⋊D4314yes—
249C22⋊C4—22no—
250C22⋊C4—42no—
251C22⋊C4—864no—
252C42—22no—
253C42—868no—
254C42—864no—
255C42D4×D4312yes—
256C42C2×C22⋊D4311yescharacteristic
257C42C23×D4311yescharacteristic
258C23—41no—
259C23#1306329311yescharacteristic
260Q8—44no—
261Q8—42no—
262Q8—1724no—
263Q8—1724no—
264D4—42no—
265D4—44no—
266D4—82no—
267C2×C4—22no—
268C2×C4—24no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—82no—
272C2×C4—864no—
273C2×C4—864no—
274C2×C4#1306329312yes—
275C2×C4#1306329311yescharacteristic
276C2×C4C2×D4×D4312yes—
277C2×C4C22×C22⋊D4311yescharacteristic
278C8—42no—
279C8—1724no—
280C22—22no—
281C22—21no—
282C22—82no—
283C22—81no—
284C22C2×#1306329311yescharacteristic
285C4—22no—
286C4—22no—
287C4—21no—
288C4—44no—
289C4—81no—
290C4—1724no—
291C4—1724no—
292C4#1458307112yes—
293C2—41no—
294C2—161no—
295C2C2×#1458307111yescharacteristic
296C2#1914395712yes—
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3135C2
socleC22×C43C2×#120
prime radicalC43×#532C22
hypercenter#3135D43
hypocenterC43#19063
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3135

Complements

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

NH ≅ G/Ntype
1. #19149090C2semidirect
3. #19133921C2semidirect
4. #19133896C2semidirect
5. #19133233C2semidirect
6. #19133209C2semidirect
178. C43#19063semidirect

Maximal subgroups

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

subgroupindex
#191490902
#191457892
#191339212
#191338962
#191332332
#191332092
C43×#31352
#1906343