Finite Group Databasebeta

← #25009442

Subgroups — #25009442

Order 11008.

380 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 59 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#19142588C211yesmaximal, characteristic
2#19135756C211yesmaximal, characteristic
3#19133571C212yesmaximal
4#19132626C212yesmaximal
5C43×#1319C211yesmaximal, characteristic
6#14583530C2211yescharacteristic
7#14583057—22no—
8#14582908—21no—
9#14582820—22no—
10#14582819C2212yes—
11#14582806—21no—
12#14582805—21no—
13#14582803—22no—
14#14582668C2211yescharacteristic
15#14582659—21no—
16#14582637—22no—
17C43×#391C2211yescharacteristic
18C43×#324C2212yes—
19C22×Dic86—21no—
20C22×Dic86D412yes—
21C2×Dic172—42no—
22C2×#10621877—21no—
23#13063324—41no—
24#13063316—41no—
25#13063304—22no—
26#13063284—21no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×Dic43⋊C4—22no—
30C2×C4×Dic43—21no—
31#13063250—42no—
32#13063249—41no—
33#13063249—41no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C43⋊#95—22no—
37C43⋊#95D412yes—
38C22×Q8×C43D411yescharacteristic
39C2×C4⋊C4×C43C2311yescharacteristic
40C2×C42×C43D411yescharacteristic
41C22⋊C8×C43—22no—
42#95×C43—22no—
43C2×Q8×C43—21no—
44C2×Q8×C43—41no—
45C2×Q8×C43—41no—
46C2×Q8×C43Q1612yescomplemented
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43C2×D411yescharacteristic
50C22×C4×C43C2×D412yes—
51C22×Dic43—22no—
52C22×Dic43—22no—
53C2×Dic86—24no—
54C2×Dic86—22no—
55C2×Dic86—42no—
56C2×Dic86—82no—
57C2×Dic86—81no—
58C2×Dic86—81no—
59C2×C8×C43—42no—
60C4⋊C4×C43—41no—
61C42×C43—41no—
62C22⋊Dic43—41no—
63C4⋊Dic43—21no—
64C4⋊Dic43—21no—
65C4⋊Dic43—22no—
66C4⋊Dic43—81no—
67C4⋊Dic43—81no—
68Dic43⋊C4—42no—
69Dic43⋊C4—82no—
70C4×Dic43—41no—
71C4×Dic43—81no—
72#10621877—41no—
73#10621877—41no—
74C2×C43⋊C8—41no—
75Dic172—84no—
76C23×C43#12011yescharacteristic
77Q8×C43—42no—
78Q8×C43—81no—
79C2×C4×C43—21no—
80C2×C4×C43—21no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—41no—
85C2×C4×C43—41no—
86C2×C4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—42no—
89C2×C4×C43C2×Q1611yescharacteristic
90C2×C4×C43#13711yescharacteristic
91C2×Dic43—24no—
92C2×Dic43—42no—
93C2×Dic43—42no—
94C2×Dic43—42no—
95C2×Dic43—42no—
96C2×Dic43—41no—
97C2×Dic43—41no—
98C2×Dic43—42no—
99Dic86—44no—
100Dic86—84no—
101Dic86—82no—
102Dic86—82no—
103C8×C43—82no—
104C43⋊C8—81no—
105#12224—431nomaximal, Sylow
106C22×C43—21no—
107C22×C43—21no—
108C22×C43#45111yescharacteristic
109C22×C43#45511yescharacteristic
110C22×C43B(4,𝔽2)11yescharacteristic
111C4×C43—21no—
112C4×C43—21no—
113C4×C43—42no—
114C4×C43—42no—
115C4×C43—42no—
116Dic43—44no—
117Dic43—82no—
118Dic43—81no—
119Dic43—81no—
120#2811—431no—
121#2028—431no—
122#1605—432no—
123#1354—432no—
124#1319D4311yescharacteristic
125C2×C43—21no—
126C2×C43—21no—
127C2×C43#160211yescharacteristic
128C2×C43#219911yescharacteristic
129C2×C43#220511yescharacteristic
130#544—431no—
131#451—862no—
132#419—861no—
133#395—432no—
134#395—862no—
135#391—862no—
136#391—861no—
137#391—861no—
138#391C2×D4311yescharacteristic
139#343—431no—
140#339—861no—
141#328—862no—
142#324C2×D4312yes—
143C43#1222411yescharacteristic, complemented, Sylow
144C22×Q8—432no—
145C22×Q8—861no—
146C22×Q8D17211yescharacteristic
147C2×Q16—1722no—
148C2×M16—861no—
149C4⋊Q8—1721no—
150#125—1721no—
151C22⋊Q8—862no—
152#117—861no—
153C2×C4⋊C4—861no—
154C2×C4⋊C4—861no—
155C2×C4⋊C4—862no—
156C2×C4⋊C4C22×D4311yescharacteristic
157C2×C42—861no—
158C2×C42D17211yescharacteristic
159#103—1722no—
160#103—1721no—
161#103—1721no—
162C22⋊C8—22no—
163#95—22no—
164#95—432no—
165#95—862no—
166#95—862no—
167#95—862no—
168C2×Q8—21no—
169C2×Q8—41no—
170C2×Q8—41no—
171C2×Q8—864no—
172C2×Q8—862no—
173C2×Q8—3441no—
174C2×Q8—3441no—
175C2×Q8—3442no—
176C2×Q8—1722no—
177C2×Q8Dic17212yescomplemented
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—862no—
181C22×C4—862no—
182C22×C4C2×D17211yescharacteristic
183C22×C4D4×D4312yes—
184Q16—3444no—
185M16—1721no—
186M16—1721no—
187C2×C8—42no—
188C2×C8—1721no—
189C4⋊C4—41no—
190C4⋊C4—861no—
191C4⋊C4—861no—
192C4⋊C4—862no—
193C4⋊C4—3442no—
194C4⋊C4—3441no—
195C4⋊C4—3441no—
196C4⋊C4—1722no—
197C22⋊C4—1721no—
198C42—41no—
199C42—3441no—
200C42—1721no—
201C23#1306329511yescharacteristic
202Q8—42no—
203Q8—81no—
204Q8—3442no—
205Q8—3442no—
206Q8—3444no—
207Q8—1724no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—864no—
219C2×C4—1722no—
220C2×C4—1722no—
221C2×C4—1721no—
222C2×C4—1721no—
223C2×C4—1722no—
224C2×C4—1722no—
225C2×C4—1722no—
226C2×C4C2×Dic17211yescharacteristic
227C2×C4#1306335811yescharacteristic
228C8—82no—
229C8—3441no—
230C22—21no—
231C22—21no—
232C22#1458305711yescharacteristic
233C22#1458307911yescharacteristic
234C22#1458308711yescharacteristic
235C4—21no—
236C4—21no—
237C4—42no—
238C4—42no—
239C4—42no—
240C4—3442no—
241C4—3441no—
242C4—3441no—
243C4—1724no—
244C2—21no—
245C2—21no—
246C2#1913355411yescharacteristic
247C2#1913659811yescharacteristic
248C2#1913662611yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1319C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1319D43
hypocenterC43#12224
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
46. C2×Q8×C43Q16semidirect
143. C43#12224semidirect
177. C2×Q8Dic172semidirect

Maximal subgroups

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

subgroupindex
#191425882
#191357562
#191335712
#191326262
C43×#13192
#1222443