Finite Group Databasebeta

← #25016962

Subgroups — #25016962

Order 11008.

318 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 71 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#19144995C211yesmaximal, characteristic
2#19136280C211yesmaximal, characteristic
3#19132767C214yesmaximal, complemented
4C43×#2132C211yesmaximal, characteristic
5C2×#13063317C411yescharacteristic
6#14583267C2212yes—
7#14583263C412yes—
8#14583253—21no—
9#14583253—21no—
10#14582900—21no—
11#14582900—21no—
12#14582883—21no—
13C4×#10621877C411yescharacteristic
14#14582698C2212yes—
15#14582696—21no—
16C43×#532C2211yescharacteristic
17C43×#413—21no—
18C43×#356C2212yes—
19C43×#355—21no—
20C2×#10621877—21no—
21C2×#10621877—41no—
22#13063317—21no—
23#13063317—41no—
24#13063317C2×C412yes—
25C2×C4⋊Dic43—21no—
26C2×Dic43⋊C4—41no—
27#13063249—22no—
28#13063249—22no—
29#13063246—22no—
30#13063246—22no—
31#13063244—22no—
32#13063242—41no—
33#13063236C2×C412yes—
34C4×C43⋊C8—21no—
35C2×#41×C43D411yescharacteristic
36C2×#41×C43D411yescharacteristic
37C2×M16×C43—41no—
38C4⋊Q8×C43C2311yescharacteristic
39#127×C43C2×C411yescharacteristic
40#124×C43D411yescharacteristic
41#124×C43D411yescharacteristic
42#121×C43—41no—
43C4×D4×C43—41no—
44C2×C42×C43C2×C411yescharacteristic
45#101×C43—22no—
46#100×C43—41no—
47#41×C43—41no—
48#41×C43—41no—
49#41×C43—41no—
50#41×C43—41no—
51C2×Q8×C43C2×D411yescharacteristic
52C2×Q8×C43C2×D411yescharacteristic
53C2×D4×C43—21no—
54C2×D4×C43—21no—
55C2×D4×C43—41no—
56C2×D4×C43C22⋊C411yescharacteristic
57C2×D4×C43C22⋊C411yescharacteristic
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43C22⋊C411yescharacteristic
62C22×Dic43—41no—
63M16×C43—42no—
64M16×C43—81no—
65C2×C8×C43—81no—
66C4⋊C4×C43—41no—
67C22⋊C4×C43—41no—
68C22⋊C4×C43—41no—
69C42×C43—21no—
70C42×C43C22⋊C411yescharacteristic
71C42×C43C22×C411yescharacteristic
72C4⋊Dic43—22no—
73C4⋊Dic43—41no—
74Dic43⋊C4—42no—
75Dic43⋊C4—42no—
76#10621877—41no—
77#10621877—41no—
78#10621877—42no—
79#10621877—81no—
80C2×C43⋊C8—22no—
81C2×C43⋊C8—81no—
82C23×C43—21no—
83C23×C43—21no—
84C23×C43#9911yescharacteristic
85Q8×C43—41no—
86Q8×C43—41no—
87D4×C43—41no—
88D4×C43—41no—
89D4×C43—81no—
90D4×C43—81no—
91D4×C43—82no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—21no—
98C2×C4×C43—41no—
99C2×C4×C43—41no—
100C2×C4×C43—41no—
101C2×C4×C43—41no—
102C2×C4×C43—81no—
103C2×C4×C43#9911yescharacteristic
104C2×C4×C43C2×C22⋊C411yescharacteristic
105C2×Dic43—42no—
106C2×Dic43—82no—
107C8×C43—82no—
108C43⋊C8—42no—
109C43⋊C8—82no—
110#13600—431nomaximal, Sylow
111C22×C43—21no—
112C22×C43—41no—
113C22×C43—41no—
114C22×C43—41no—
115C22×C43—81no—
116C22×C43—81no—
117C22×C43C2×#9911yescharacteristic
118C4×C43—21no—
119C4×C43—41no—
120C4×C43—41no—
121C4×C43—41no—
122C4×C43—41no—
123C4×C43#35411yescharacteristic
124C4×C43#35411yescharacteristic
125Dic43—82no—
126#3142—431no—
127#2132—431no—
128#2132D4311yescharacteristic
129#1413—434no—
130C2×C43—21no—
131C2×C43—41no—
132C2×C43—81no—
133C2×C43—81no—
134C2×C43C2×#35411yescharacteristic
135#532C2×D4311yescharacteristic
136C2×#125—431no—
137#491—432no—
138#490—432no—
139#488—861no—
140#488—861no—
141#417—861no—
142#417—861no—
143#413—21no—
144#413—861no—
145C4×M16—431no—
146#356—432no—
147#356C2×D4312yes—
148#355—21no—
149#355—861no—
150C43#1360011yescharacteristic, complemented, Sylow
151C2×#41D17211yescharacteristic
152C2×#41C22⋊D4311yescharacteristic
153C2×M16—41no—
154C2×M16—861no—
155C2×M16—1721no—
156C4⋊Q8C22×D4311yescharacteristic
157#127C4×D4311yescharacteristic
158#125—432no—
159#125—861no—
160#125—1721no—
161#124D17211yescharacteristic
162#124C22⋊D4311yescharacteristic
163#121—41no—
164C4×D4—41no—
165C2×C4⋊C4—861no—
166C2×C4⋊C4—1721no—
167C2×C42C4×D4311yescharacteristic
168#103—862no—
169#103—862no—
170#102—862no—
171#102—862no—
172#101—22no—
173#101—862no—
174#100—41no—
175#100—1721no—
176#97—432no—
177C4×C8—861no—
178#41—41no—
179#41—41no—
180#41—41no—
181#41—41no—
182C2×Q8C2×D17211yescharacteristic
183C2×Q8C2×C22⋊D4311yescharacteristic
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—41no—
187C2×D4(C2×D43)⋊C411yescharacteristic
188C2×D4(C2×D43)⋊C411yescharacteristic
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—1721no—
193C22×C4(C2×D43)⋊C411yescharacteristic
194M16—42no—
195M16—81no—
196M16—3441no—
197M16—1722no—
198M16—1721no—
199M16—1721no—
200C2×C8—81no—
201C2×C8—862no—
202C2×C8—3441no—
203C4⋊C4—41no—
204C4⋊C4—862no—
205C4⋊C4—1722no—
206C4⋊C4—1722no—
207C4⋊C4—1721no—
208C22⋊C4—41no—
209C22⋊C4—41no—
210C42—21no—
211C42(C2×D43)⋊C411yescharacteristic
212C42C2×C4×D4311yescharacteristic
213C23—21no—
214C23—21no—
215C23#1306323911yescharacteristic
216Q8—41no—
217Q8—41no—
218D4—41no—
219D4—41no—
220D4—81no—
221D4—81no—
222D4—82no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—81no—
234C2×C4—3442no—
235C2×C4—1722no—
236C2×C4#1306323911yescharacteristic
237C2×C4C2×(C2×D43)⋊C411yescharacteristic
238C8—82no—
239C8—3442no—
240C8—1722no—
241C22—21no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—81no—
246C22—81no—
247C22C2×#1306323911yescharacteristic
248C4—21no—
249C4—41no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—3442no—
254C4#1458269311yescharacteristic
255C4#1458269311yescharacteristic
256C2—21no—
257C2—41no—
258C2—81no—
259C2—81no—
260C2C2×#1458269311yescharacteristic
subgroupG/H
centerC2C2×#14582693
commutatorC42×C43C22×C4
FrattiniC4⋊Q8C22×D43
FittingC43×#2132C2
socleC2×C43C2×#354
prime radicalC43×#532C22
cosocleC4⋊Q8×C43C23
hypercenter#2132D43
hypocenterC43#13600
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #2132

Complements

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

NH ≅ G/Ntype
3. #19132767C2semidirect
150. C43#13600semidirect

Maximal subgroups

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

subgroupindex
#191449952
#191362802
#191327672
C43×#21322
#1360043