Finite Group Databasebeta

← #25008718

Subgroups — #25008718

Order 11008.

424 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 67 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#19145370C211yesmaximal, characteristic
2#19136531C212yesmaximal, complemented
3#19135605C211yesmaximal, characteristic
4#19132608C212yesmaximal, complemented
5C43×#1314C211yesmaximal, characteristic
6C22×Dic172C2211yescharacteristic
7C2×#13063304—21no—
8C2×#13063304—21no—
9C2×Dic344—22no—
10#14583235—22no—
11#14583140—21no—
12#14583140C2212yes—
13#14583057—22no—
14C2×#13063250—21no—
15#14582704—22no—
16#14582662C2211yescharacteristic
17C2×C22⋊C8×C43C2211yescharacteristic
18C43×C22⋊C16C2212yes—
19C22×Dic86—21no—
20C22×Dic86—21no—
21C2×Dic172—22no—
22C2×Dic172—21no—
23C2×Dic172—42no—
24C2×Dic172D412yes—
25#13063304—22no—
26#13063304—22no—
27#13063304—42no—
28#13063304—42no—
29#13063304—41no—
30#13063304—41no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—21no—
33C2×Dic43⋊C4—41no—
34C2×Dic43⋊C4—41no—
35C2×C22⋊Dic43—41no—
36C2×C22⋊Dic43—41no—
37Dic344—44no—
38#13063259—21no—
39#13063259D412yes—
40#13063250—22no—
41#13063250—22no—
42#13063250—42no—
43C23×C4×C43D411yescharacteristic
44C22×C8×C43D411yescharacteristic
45C22×C8×C43C2311yescharacteristic
46C2×C16×C43—22no—
47C22⋊C8×C43—22no—
48C24×C43D811yescharacteristic
49C22×C4×C43—21no—
50C22×C4×C43—21no—
51C22×C4×C43—41no—
52C22×C4×C43—41no—
53C22×C4×C43D811yescharacteristic
54C22×C4×C43C2×D411yescharacteristic
55C22×Dic43—41no—
56C22×Dic43—41no—
57C22×Dic43—41no—
58C22×Dic43—41no—
59C2×Dic86—22no—
60C2×Dic86—22no—
61C2×Dic86—41no—
62C2×Dic86—41no—
63C2×Dic86—41no—
64C2×Dic86—41no—
65C2×Dic86—41no—
66C2×Dic86—41no—
67C2×Dic86—81no—
68C2×Dic86—81no—
69C2×C8×C43—21no—
70C2×C8×C43—41no—
71C2×C8×C43—41no—
72C2×C8×C43C2×D412yes—
73C22⋊Dic43—42no—
74C22⋊Dic43—44no—
75C22⋊Dic43—42no—
76C4⋊Dic43—22no—
77C4⋊Dic43—22no—
78C4⋊Dic43—41no—
79C4⋊Dic43—41no—
80Dic43⋊C4—42no—
81Dic43⋊C4—44no—
82Dic43⋊C4—42no—
83Dic172—24no—
84Dic172—42no—
85Dic172—42no—
86Dic172—81no—
87C16×C43—42no—
88C23×C43—21no—
89C23×C43—21no—
90C23×C43—41no—
91C23×C43—41no—
92C23×C43Q3212yescomplemented
93C23×C43C2×D811yescharacteristic
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—41no—
98C2×C4×C43—41no—
99C2×C4×C43—41no—
100C2×C4×C43—81no—
101C2×C4×C43#12011yescharacteristic
102C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
103C2×Dic43—42no—
104C2×Dic43—42no—
105C2×Dic43—42no—
106C2×Dic43—42no—
107C2×Dic43—81no—
108C2×Dic43—81no—
109C2×Dic43—82no—
110C2×Dic43—82no—
111C2×Dic43—81no—
112C2×Dic43—81no—
113Dic86—42no—
114Dic86—42no—
115Dic86—42no—
116Dic86—42no—
117Dic86—81no—
118Dic86—82no—
119Dic86—81no—
120C8×C43—22no—
121C8×C43—41no—
122#12106—431nomaximal, Sylow
123C22×C43—21no—
124C22×C43—21no—
125C22×C43—22no—
126C22×C43—42no—
127C22×C43—41no—
128C22×C43—41no—
129C22×C43—81no—
130C22×C43#44711yescharacteristic
131C22×C43C2×Q3211yescharacteristic
132C22×C43#51011yescharacteristic
133C4×C43—21no—
134C4×C43—41no—
135C4×C43#45311yescharacteristic
136C4×C43B(4,𝔽2)11yescharacteristic
137Dic43—82no—
138Dic43—82no—
139Dic43—82no—
140Dic43—82no—
141#3189—431no—
142#2188—432no—
143#2001—431no—
144#1348—432no—
145#1314D4311yescharacteristic
146C2×C43—21no—
147C2×C43—21no—
148C2×C43—42no—
149C2×C43#159511yescharacteristic
150C2×C43#218811yescharacteristic
151C2×C43#219111yescharacteristic
152C22×Q16—431no—
153C2×C22⋊Q8—861no—
154C2×C22⋊Q8—861no—
155C2×Q32—862no—
156#484—862no—
157#467—432no—
158#467—861no—
159#451—862no—
160C2×#103—861no—
161C2×C22⋊C8C2×D4311yescharacteristic
162#358—862no—
163C22⋊C16C2×D4312yes—
164#340—431no—
165C43#1210611yescharacteristic, complemented, Sylow
166C22×Q8—861no—
167C22×Q8—861no—
168C23×C4D17211yescharacteristic
169C2×Q16—432no—
170C2×Q16—861no—
171C2×Q16—862no—
172C2×Q16—1722no—
173C22×C8D17211yescharacteristic
174C22×C8C22×D4311yescharacteristic
175C22⋊Q8—862no—
176C22⋊Q8—862no—
177C22⋊Q8—1722no—
178C22⋊Q8—1721no—
179C22⋊Q8—1722no—
180C22⋊Q8—1721no—
181C2×C4⋊C4—861no—
182C2×C4⋊C4—861no—
183C2×C4⋊C4—1721no—
184C2×C4⋊C4—1721no—
185C2×C22⋊C4—1721no—
186C2×C22⋊C4—1721no—
187Q32—1724no—
188C2×C16—22no—
189#107—432no—
190#107—861no—
191#103—862no—
192#103—862no—
193#103—1722no—
194C22⋊C8—22no—
195C24D34411yescharacteristic
196C2×Q8—862no—
197C2×Q8—862no—
198C2×Q8—3441no—
199C2×Q8—3441no—
200C2×Q8—1721no—
201C2×Q8—1721no—
202C2×Q8—1721no—
203C2×Q8—1721no—
204C2×Q8—1721no—
205C2×Q8—1721no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—1721no—
211C22×C4—1721no—
212C22×C4—1721no—
213C22×C4—1721no—
214C22×C4D34411yescharacteristic
215C22×C4C2×D17211yescharacteristic
216Q16—864no—
217Q16—3441no—
218Q16—1722no—
219Q16—1722no—
220C2×C8—21no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8D4×D4312yes—
224C4⋊C4—862no—
225C4⋊C4—862no—
226C4⋊C4—1721no—
227C4⋊C4—1721no—
228C4⋊C4—1722no—
229C4⋊C4—1724no—
230C4⋊C4—1722no—
231C22⋊C4—1722no—
232C22⋊C4—1724no—
233C22⋊C4—1722no—
234C16—42no—
235C23—21no—
236C23—21no—
237C23—41no—
238C23—41no—
239C23Dic34412yescomplemented
240C23C2×D34411yescharacteristic
241Q8—3441no—
242Q8—3442no—
243Q8—3441no—
244Q8—1722no—
245Q8—1722no—
246Q8—1722no—
247Q8—1722no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—81no—
255C2×C4—3441no—
256C2×C4—3441no—
257C2×C4—3442no—
258C2×C4—3442no—
259C2×C4—3441no—
260C2×C4—3441no—
261C2×C4—1722no—
262C2×C4—1722no—
263C2×C4—1722no—
264C2×C4—1722no—
265C2×C4#1306329511yescharacteristic
266C2×C4#1306335311yescharacteristic
267C8—22no—
268C8—41no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—42no—
273C22—41no—
274C22—41no—
275C22—81no—
276C22#1458303511yescharacteristic
277C22C2×Dic34411yescharacteristic
278C22#1458334211yescharacteristic
279C4—21no—
280C4—41no—
281C4—3442no—
282C4—3442no—
283C4—3442no—
284C4—3442no—
285C4#1458306911yescharacteristic
286C4#1458308711yescharacteristic
287C2—21no—
288C2—21no—
289C2—42no—
290C2#1913351511yescharacteristic
291C2#1913653111yescharacteristic
292C2#1913654811yescharacteristic
subgroupG/H
centerC22#14583035
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#1314C2
socleC22×C43#447
prime radicalC24×C43D8
hypercenter#1314D43
hypocenterC43#12106
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. #19136531C2semidirect
4. #19132608C2semidirect
92. C23×C43Q32semidirect
165. C43#12106semidirect
239. C23Dic344semidirect

Maximal subgroups

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

subgroupindex
#191453702
#191365312
#191356052
#191326082
C43×#13142
#1210643