Finite Group Databasebeta

← #25009399

Subgroups — #25009399

Order 11008.

484 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135759C211yesmaximal, characteristic
2#19133551C212yesmaximal, complemented
3#19132616C212yesmaximal, complemented
4#19132523C211yesmaximal, characteristic
5C43×#2840C211yesmaximal, characteristic
6#14583525C2211yescharacteristic
7#14583055—22no—
8#14582755—21no—
9#14582666C2211yescharacteristic
10#14582665—21no—
11#14582635—22no—
12#14582623C2212yes—
13C43×#393—22no—
14C43×#393—21no—
15C43×#393—22no—
16C43×#393C2212yes—
17C43×#379—21no—
18C43×#379C2211yescharacteristic
19C2×#10621885—42no—
20#13063304—22no—
21#13063302—42no—
22C2×C22⋊Dic43—21no—
23C2×C22⋊Dic43—21no—
24C2×C22⋊Dic43—42no—
25#13063249—42no—
26C22⋊(C43⋊C8)—22no—
27C25×C43D411yescharacteristic
28C22×Q8×C43—21no—
29C22×Q8×C43D412yes—
30C2×C22⋊C4×C43—21no—
31C2×C22⋊C4×C43—22no—
32C2×C22⋊C4×C43—21no—
33C2×C22⋊C4×C43—22no—
34C2×C22⋊C4×C43—22no—
35C2×C22⋊C4×C43D411yescharacteristic
36C2×C22⋊C4×C43C2311yescharacteristic
37#95×C43—21no—
38#95×C43—22no—
39#95×C43—22no—
40#95×C43D412yes—
41C24×C43—21no—
42C24×C43—21no—
43C24×C43—41no—
44C24×C43—41no—
45C24×C43—82no—
46C24×C43Q1612yescomplemented
47C24×C43C2×D411yescharacteristic
48C2×Q8×C43—42no—
49C2×Q8×C43—82no—
50C2×Q8×C43—82no—
51C2×Q8×C43—81no—
52C22×C4×C43—22no—
53C22×C4×C43—21no—
54C22×C4×C43—22no—
55C22×C4×C43C2×D412yes—
56C22×Dic43—22no—
57C22×Dic43—41no—
58C2×Dic86—22no—
59C22⋊C4×C43—41no—
60C22⋊C4×C43—41no—
61C22⋊C4×C43—82no—
62C22⋊C4×C43—82no—
63C22⋊C4×C43—82no—
64C22⋊C4×C43—81no—
65C22⋊C4×C43—81no—
66C22⋊Dic43—41no—
67C22⋊Dic43—41no—
68C22⋊Dic43—41no—
69C22⋊Dic43—41no—
70C22⋊Dic43—84no—
71#10621885—84no—
72C4⋊Dic43—22no—
73Dic43⋊C4—42no—
74C2×C43⋊C8—42no—
75C23×C43—21no—
76C23×C43—21no—
77C23×C43—22no—
78C23×C43—42no—
79C23×C43—42no—
80C23×C43—42no—
81C23×C43—42no—
82C23×C43—44no—
83C23×C43—41no—
84C23×C43—41no—
85C23×C43—81no—
86C23×C43—82no—
87C23×C43—82no—
88C23×C43—82no—
89C23×C43—84no—
90C23×C43#12011yescharacteristic
91C23×C43C2×Q1611yescharacteristic
92C23×C43#13711yescharacteristic
93Q8×C43—44no—
94Q8×C43—82no—
95Q8×C43—84no—
96C2×C4×C43—22no—
97C2×C4×C43—42no—
98C2×C4×C43—42no—
99C2×C4×C43—42no—
100C2×C4×C43—42no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43—41no—
104C2×C4×C43—42no—
105C2×C4×C43—42no—
106C2×Dic43—42no—
107C2×Dic43—82no—
108C2×Dic43—81no—
109C2×Dic43—82no—
110Dic86—82no—
111C43⋊C8—82no—
112#12217—431nomaximal, Sylow
113C22×C43—22no—
114C22×C43—21no—
115C22×C43—21no—
116C22×C43—41no—
117C22×C43—41no—
118C22×C43—42no—
119C22×C43—42no—
120C22×C43—42no—
121C22×C43—44no—
122C22×C43—42no—
123C22×C43—81no—
124C22×C43—82no—
125C22×C43—82no—
126C22×C43—84no—
127C22×C43—82no—
128C22×C43#45111yescharacteristic
129C22×C43#45511yescharacteristic
130C22×C43B(4,𝔽2)11yescharacteristic
131C4×C43—42no—
132C4×C43—81no—
133C4×C43—82no—
134C4×C43—82no—
135Dic43—82no—
136Dic43—161no—
137#2840D4311yescharacteristic
138#2029—431no—
139#1602—432no—
140#1351—432no—
141#1316—431no—
142C2×C43—21no—
143C2×C43—21no—
144C2×C43—41no—
145C2×C43—41no—
146C2×C43—82no—
147C2×C43#160211yescharacteristic
148C2×C43#219912yes—
149#543—431no—
150#451—862no—
151#393—22no—
152#393—21no—
153#393—22no—
154#393C2×D4312yes—
155#379—21no—
156#379—861no—
157#379C2×D4311yescharacteristic
158#342—431no—
159#342—861no—
160#328—862no—
161#323—432no—
162C43#1221711yescharacteristic, complemented, Sylow
163C25C22⋊D4311yescharacteristic
164C22×Q8—21no—
165C22×Q8C22⋊D4312yes—
166C2×Q16—1722no—
167C22⋊Q8—862no—
168C22⋊Q8—1722no—
169C2×C22⋊C4—21no—
170C2×C22⋊C4—22no—
171C2×C22⋊C4—21no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—861no—
175C2×C22⋊C4—861no—
176C2×C22⋊C4—1722no—
177C2×C22⋊C4C22⋊D4311yescharacteristic
178C2×C22⋊C4C22×D4311yescharacteristic
179#103—1722no—
180C22⋊C8—862no—
181#95—21no—
182#95—22no—
183#95—22no—
184#95C22⋊D4312yes—
185C24—21no—
186C24—21no—
187C24—41no—
188C24—41no—
189C24—82no—
190C24#1062188512yescomplemented
191C24C2×C22⋊D4311yescharacteristic
192C2×Q8—42no—
193C2×Q8—82no—
194C2×Q8—82no—
195C2×Q8—81no—
196C2×Q8—862no—
197C22×C4—22no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4—862no—
201C22×C4—1721no—
202C22×C4C2×C22⋊D4312yes—
203Q16—3444no—
204C2×C8—1722no—
205C4⋊C4—862no—
206C4⋊C4—1722no—
207C22⋊C4—41no—
208C22⋊C4—41no—
209C22⋊C4—82no—
210C22⋊C4—82no—
211C22⋊C4—82no—
212C22⋊C4—81no—
213C22⋊C4—81no—
214C22⋊C4—3444no—
215C22⋊C4—1721no—
216C22⋊C4—1721no—
217C22⋊C4—1721no—
218C22⋊C4—1721no—
219C23—21no—
220C23—21no—
221C23—22no—
222C23—42no—
223C23—42no—
224C23—42no—
225C23—42no—
226C23—44no—
227C23—41no—
228C23—41no—
229C23—81no—
230C23—82no—
231C23—82no—
232C23—82no—
233C23—84no—
234C23#1306329411yescharacteristic
235C23C2×#1062188511yescharacteristic
236C23#1306335611yescharacteristic
237Q8—44no—
238Q8—82no—
239Q8—84no—
240Q8—3442no—
241C2×C4—22no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—3442no—
252C2×C4—3441no—
253C2×C4—3442no—
254C2×C4—1722no—
255C8—3442no—
256C22—22no—
257C22—21no—
258C22—21no—
259C22—41no—
260C22—41no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—44no—
265C22—42no—
266C22—81no—
267C22—82no—
268C22—82no—
269C22—84no—
270C22—82no—
271C22#1458305511yescharacteristic
272C22#1458307711yescharacteristic
273C22#1458308611yescharacteristic
274C4—42no—
275C4—81no—
276C4—82no—
277C4—82no—
278C4—3442no—
279C4—6881no—
280C2—21no—
281C2—21no—
282C2—41no—
283C2—41no—
284C2—82no—
285C2#1913355211yescharacteristic
286C2#1913659612yes—
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2840C2
socleC22×C43B(4,𝔽2)
prime radicalC25×C43D4
hypercenter#2840D43
hypocenterC43#12217
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2840

Complements

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

NH ≅ G/Ntype
2. #19133551C2semidirect
3. #19132616C2semidirect
46. C24×C43Q16semidirect
162. C43#12217semidirect
190. C24#10621885semidirect

Maximal subgroups

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

subgroupindex
#191357592
#191335512
#191326162
#191325232
C43×#28402
#1221743