Finite Group Databasebeta

← #25078498

Subgroups — #25078498

Order 11008.

806 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 171 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#19145793C212yesmaximal
2#19144943C211yesmaximal, characteristic
3#19133923C214yesmaximal, complemented
4#19133897C214yesmaximal, complemented
5#19133233C211yesmaximal, characteristic, complemented
6#19133210C212yesmaximal, complemented
7C43×#3556C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583309C2214yes—
10#14583269C2212yes—
11#14583265C2214yes—
12#14583265C2212yes—
13#14583261—22no—
14#14583223—24no—
15#14583186—22no—
16#14583176—22no—
17#14582956C2212yes—
18#14582893—22no—
19C2×#13063236C2211yescharacteristic
20#14582641C2218yes—
21#14582641C2214yes—
22C43×#564C2214yes—
23C43×#557—22no—
24C43×#557—22no—
25C43×#557—22no—
26C43×#541—22no—
27C43×#541—24no—
28C43×#533C2212yes—
29C43×#533C2211yescharacteristic
30C2×#10621898—21no—
31C22×C43⋊C8—21no—
32#13063325C2311yescharacteristic
33#13063322C2311yescharacteristic
34#13063313—21no—
35#13063299—22no—
36C4×D172—22no—
37#13063258—24no—
38#13063256—24no—
39C4⋊(C43⋊C8)—22no—
40#13063248—24no—
41#13063245—24no—
42#13063245—24no—
43#13063245—24no—
44C22⋊(C43⋊C8)—22no—
45#13063236—21no—
46#13063236C2314yes—
47#13063236C2312yes—
48C4⋊Q8×C43—24no—
49C4⋊Q8×C43—22no—
50C4⋊Q8×C43D412yes—
51C4⋊Q8×C43D412yes—
52C4⋊Q8×C43D412yes—
53#126×C43—28no—
54#125×C43—24no—
55#125×C43—22no—
56#125×C43—28no—
57#125×C43—28no—
58#125×C43—28no—
59#125×C43C2314yes—
60#125×C43C2312yes—
61C22⋊Q8×C43—22no—
62C22⋊Q8×C43—22no—
63C22⋊Q8×C43—22no—
64C4×Q8×C43—24no—
65C4×Q8×C43—24no—
66C4×Q8×C43—24no—
67C4×Q8×C43—22no—
68C4×Q8×C43—22no—
69C4×Q8×C43—22no—
70#117×C43D412yes—
71#117×C43D414yes—
72C2×C42×C43C2311yescharacteristic
73C2×Q8×C43—22no—
74C2×Q8×C43—22no—
75C2×Q8×C43—22no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D412yes—
78C2×C22⋊D43—41no—
79#10621898—44no—
80C2×D172—22no—
81C2×D172—21no—
82C2×C4×D43—41no—
83C2×Dic86—21no—
84C4⋊C4×C43—28no—
85C4⋊C4×C43—28no—
86C4⋊C4×C43—28no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—22no—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—24no—
91C4⋊C4×C43—24no—
92C4⋊C4×C43—24no—
93C4⋊C4×C43C2×D414yes—
94C4⋊C4×C43C2×D414yes—
95C4⋊C4×C43C2×D414yes—
96C22⋊C4×C43—22no—
97C22⋊C4×C43—24no—
98C42×C43—28no—
99C42×C43—24no—
100C42×C43—22no—
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D412yes—
103C42×C43C2411yescharacteristic
104(C2×D43)⋊C4—42no—
105C4⋊Dic43—22no—
106C2×C43⋊C8—22no—
107C2×C43⋊C8—24no—
108C2×C43⋊C8—42no—
109C23×C43#12011yescharacteristic
110C22×D43—41no—
111Q8×C43—44no—
112Q8×C43—44no—
113Q8×C43—44no—
114C2×C4×C43—22no—
115C2×C4×C43—24no—
116C2×C4×C43—24no—
117C2×C4×C43—24no—
118C2×C4×C43—42no—
119C2×C4×C43#12012yes—
120C2×C4×C43#12011yescharacteristic
121C2×C4×C43C22×D412yes—
122C2×C4×C43C22×D411yescharacteristic
123C22⋊D43—82no—
124C2×Dic43—41no—
125D172—44no—
126D172—42no—
127C4×D43—82no—
128Dic86—42no—
129C43⋊C8—44no—
130C43⋊C8—42no—
131#19063—431nomaximal, Sylow
132C22×C43—21no—
133C22×C43—22no—
134C22×C43C2×#12011yescharacteristic
135C2×D43—81no—
136C2×D43—82no—
137C4×C43—21no—
138C4×C43—22no—
139C4×C43—22no—
140C4×C43—44no—
141C4×C43—44no—
142C4×C43—44no—
143C4×C43#45412yes—
144Dic43—81no—
145#3556D4311yescharacteristic, complemented
146#3235—432no—
147#3135—431no—
148#1663—434no—
149#1658—434no—
150#1537—431no—
151#1531—432no—
152C2×C43—41no—
153C2×C43C2×#45411yescharacteristic
154C2×C43#302012yes—
155D43—161no—
156#564C2×D4314yes—
157#557—22no—
158#557—22no—
159#557—22no—
160#541—22no—
161#541—24no—
162#533C2×D4311yescharacteristic
163#533C2×D4312yes—
164#532—431no—
165#501—434no—
166#491—432no—
167#490—432no—
168#490—434no—
169#489—862no—
170#482—864no—
171#476—862no—
172#474—862no—
173#432—432no—
174#416—862no—
175C2×#97—431no—
176#330—434no—
177#330—438no—
178C43#1906311yescharacteristic, complemented, Sylow
179C2×#41—861no—
180C22×C8—861no—
181C4⋊Q8—24no—
182C4⋊Q8—22no—
183C4⋊Q8—431no—
184C4⋊Q8C22⋊D4312yes—
185C4⋊Q8C22⋊D4312yes—
186C4⋊Q8C22⋊D4312yes—
187#127—431no—
188#126—28no—
189#125—24no—
190#125—22no—
191#125—28no—
192#125—28no—
193#125—28no—
194#125C22×D4312yes—
195#125C22×D4314yes—
196#124—861no—
197C22⋊Q8—22no—
198C22⋊Q8—22no—
199C22⋊Q8—22no—
200#121—862no—
201C4×Q8—24no—
202C4×Q8—24no—
203C4×Q8—24no—
204C4×Q8—22no—
205C4×Q8—22no—
206C4×Q8—22no—
207C4×D4—862no—
208#117C22⋊D4312yes—
209#117C22⋊D4314yes—
210C2×C42C22×D4311yescharacteristic
211#107—864no—
212#106—864no—
213C4⋊C8—862no—
214#103—864no—
215#102—864no—
216#102—864no—
217#102—864no—
218C22⋊C8—862no—
219#97—432no—
220#97—434no—
221#97—861no—
222#41—1724no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—861no—
227C2×D4—862no—
228C2×D4—861no—
229C2×D4—1721no—
230C22×C4—1721no—
231C22×C4C2×C22⋊D4311yescharacteristic
232C22×C4C2×C22⋊D4312yes—
233C2×C8—862no—
234C2×C8—864no—
235C2×C8—1722no—
236C4⋊C4—28no—
237C4⋊C4—28no—
238C4⋊C4—28no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—24no—
243C4⋊C4—24no—
244C4⋊C4—24no—
245C4⋊C4—862no—
246C4⋊C4C2×C22⋊D4314yes—
247C4⋊C4C2×C22⋊D4314yes—
248C4⋊C4C2×C22⋊D4314yes—
249C22⋊C4—22no—
250C22⋊C4—24no—
251C22⋊C4—1722no—
252C42—28no—
253C42—24no—
254C42—22no—
255C42C2×C22⋊D4311yescharacteristic
256C42C2×C22⋊D4312yes—
257C42C23×D4311yescharacteristic
258C23—1721no—
259C23#1306329411yescharacteristic
260Q8—44no—
261Q8—44no—
262Q8—44no—
263Q8—1722no—
264D4—3442no—
265D4—1722no—
266D4—1724no—
267C2×C4—22no—
268C2×C4—24no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—42no—
272C2×C4—3442no—
273C2×C4—1721no—
274C2×C4#1306329412yes—
275C2×C4#1306329411yescharacteristic
276C2×C4C22×C22⋊D4312yes—
277C2×C4C22×C22⋊D4311yescharacteristic
278C8—1722no—
279C8—1724no—
280C22—22no—
281C22—21no—
282C22—3442no—
283C22—3441no—
284C22C2×#1306329411yescharacteristic
285C4—22no—
286C4—22no—
287C4—21no—
288C4—44no—
289C4—44no—
290C4—44no—
291C4—3441no—
292C4#1458307212yes—
293C2—41no—
294C2—6881no—
295C2C2×#1458307211yescharacteristic
296C2#1914395912yes—
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3556C2
socleC22×C43C2×#120
prime radical#14583449C22
hypercenter#3556D43
hypocenterC43#19063
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3556

Complements

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

NH ≅ G/Ntype
3. #19133923C2semidirect
4. #19133897C2semidirect
5. #19133233C2semidirect
6. #19133210C2semidirect
7. C43×#3556C2semidirect
145. #3556D43semidirect
178. C43#19063semidirect

Maximal subgroups

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

subgroupindex
#191457932
#191449432
#191339232
#191338972
#191332332
#191332102
C43×#35562
#1906343