Finite Group Databasebeta

← #25000950

Subgroups — #25000950

Order 11008.

448 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 79 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#19135063C212yesmaximal
3#19133114C212yesmaximal
4#19132472C211yesmaximal, characteristic
5C43×#1851C211yesmaximal, characteristic
6C2×#13063304C2212yes—
7#14583235—22no—
8#14583140—21no—
9#14583140—21no—
10#14583057—22no—
11C2×#13063243—22no—
12#14582863C2212yes—
13#14582667—22no—
14#14582635—22no—
15#14582635—22no—
16C22×M16×C43C2211yescharacteristic
17C2×C4⋊C8×C43—21no—
18C2×C22⋊C8×C43C2211yescharacteristic
19C4×C22⋊C4×C43C2211yescharacteristic
20C43×#336—21no—
21C22×Dic86D412yes—
22C2×Dic172—21no—
23C2×Dic172—21no—
24C2×#10621877—22no—
25#13063304—22no—
26#13063304—22no—
27#13063304—22no—
28#13063304—22no—
29C2×C4⋊Dic43D412yes—
30C2×Dic43⋊C4—22no—
31C2×C22⋊Dic43—22no—
32#13063259—21no—
33#13063259—21no—
34#13063250—22no—
35#13063250—22no—
36#13063243—44no—
37C22⋊(C43⋊C8)—22no—
38C22⋊(C43⋊C8)—22no—
39C23×C4×C43C2311yescharacteristic
40C2×M16×C43—22no—
41C2×M16×C43—42no—
42C22×C8×C43—21no—
43C22×C8×C43D411yescharacteristic
44C22×C8×C43D411yescharacteristic
45C2×C22⋊C4×C43—21no—
46C2×C42×C43—21no—
47C4⋊C8×C43—42no—
48C22⋊C8×C43—22no—
49#95×C43D411yescharacteristic
50#95×C43D411yescharacteristic
51C24×C43#4111yescharacteristic
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—41no—
55C22×C4×C43—41no—
56C22×C4×C43C2×D411yescharacteristic
57C22×C4×C43C2×D411yescharacteristic
58C22×C4×C43C2×D412yes—
59C22×C4×C43#4112yes—
60C22×Dic43—22no—
61C22×Dic43—22no—
62C2×Dic86—22no—
63C2×Dic86—22no—
64C2×Dic86—42no—
65C2×Dic86—42no—
66M16×C43—24no—
67M16×C43—42no—
68C2×C8×C43—22no—
69C2×C8×C43—21no—
70C2×C8×C43—21no—
71C2×C8×C43—41no—
72C2×C8×C43—41no—
73C2×C8×C43—41no—
74C2×C8×C43—41no—
75C22⋊C4×C43—42no—
76C42×C43—41no—
77C42×C43—41no—
78C22⋊Dic43—42no—
79C22⋊Dic43—42no—
80C4⋊Dic43—22no—
81C4⋊Dic43—22no—
82Dic43⋊C4—42no—
83Dic43⋊C4—42no—
84#10621877—42no—
85#10621877—42no—
86C2×C43⋊C8—42no—
87Dic172—81no—
88Dic172—81no—
89C23×C43—21no—
90C23×C43—21no—
91C23×C43—41no—
92C23×C43—41no—
93C23×C43#12111yescharacteristic
94C23×C43#12312yes—
95C2×C4×C43—22no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43—21no—
99C2×C4×C43—22no—
100C2×C4×C43—41no—
101C2×C4×C43—42no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43#12011yescharacteristic
108C2×C4×C43#12112yes—
109C2×C4×C43#12411yescharacteristic
110C2×Dic43—44no—
111C2×Dic43—42no—
112C2×Dic43—42no—
113C2×Dic43—82no—
114Dic86—42no—
115Dic86—42no—
116Dic86—82no—
117C8×C43—41no—
118C8×C43—42no—
119C8×C43—41no—
120C43⋊C8—82no—
121#10559—431nomaximal, Sylow
122C22×C43—21no—
123C22×C43—21no—
124C22×C43—22no—
125C22×C43—22no—
126C22×C43—22no—
127C22×C43—81no—
128C22×C43—81no—
129C22×C43#39411yescharacteristic
130C22×C43#47311yescharacteristic
131C22×C43#47311yescharacteristic
132C4×C43—22no—
133C4×C43—21no—
134C4×C43—42no—
135C4×C43—81no—
136C4×C43B(4,𝔽2)11yescharacteristic
137C4×C43#45811yescharacteristic
138Dic43—82no—
139Dic43—82no—
140#3189—431no—
141#1901—432no—
142#1851D4311yescharacteristic
143#1508—432no—
144#1293—431no—
145C2×C43—21no—
146C2×C43—21no—
147C2×C43—42no—
148C2×C43#204411yescharacteristic
149C2×C43#204711yescharacteristic
150C2×C43#205011yescharacteristic
151C22×M16C2×D4311yescharacteristic
152C2×C22⋊Q8—432no—
153#484—862no—
154#467—861no—
155#467—861no—
156#451—862no—
157C2×C4⋊C8—21no—
158C2×#101—862no—
159#407—432no—
160C2×C22⋊C8C2×D4311yescharacteristic
161C4×C22⋊C4C2×D4311yescharacteristic
162#343—862no—
163#336—21no—
164#328—862no—
165#328—862no—
166C43#1055911yescharacteristic, complemented, Sylow
167C22×Q8—432no—
168C23×C4C22×D4311yescharacteristic
169C2×Q16—861no—
170C2×Q16—861no—
171C2×M16—22no—
172C2×M16—42no—
173C2×M16—862no—
174C22×C8—21no—
175C22×C8C22⋊D4311yescharacteristic
176C22×C8C22⋊D4311yescharacteristic
177C22⋊Q8—862no—
178C22⋊Q8—862no—
179C22⋊Q8—862no—
180C22⋊Q8—862no—
181C2×C4⋊C4—432no—
182C2×C4⋊C4—862no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—862no—
185C2×C42—21no—
186#107—861no—
187#107—861no—
188C4⋊C8—42no—
189#103—862no—
190#103—862no—
191#101—1724no—
192C22⋊C8—22no—
193C22⋊C8—862no—
194C22⋊C8—862no—
195#95D17211yescharacteristic
196#95D17211yescharacteristic
197C24#1062189811yescharacteristic
198C2×Q8—862no—
199C2×Q8—862no—
200C2×Q8—1722no—
201C2×Q8—1722no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—862no—
207C22×C4—862no—
208C22×C4C2×D17211yescharacteristic
209C22×C4D4×D4312yes—
210C22×C4#1062190212yes—
211C22×C4C2×C22⋊D4311yescharacteristic
212Q16—3441no—
213Q16—3441no—
214M16—24no—
215M16—42no—
216M16—1722no—
217M16—1722no—
218C2×C8—22no—
219C2×C8—21no—
220C2×C8—21no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—1722no—
226C4⋊C4—862no—
227C4⋊C4—862no—
228C4⋊C4—1722no—
229C4⋊C4—1722no—
230C22⋊C4—42no—
231C22⋊C4—1722no—
232C22⋊C4—1722no—
233C42—41no—
234C42—41no—
235C23—21no—
236C23—21no—
237C23—41no—
238C23—41no—
239C23#1306329911yescharacteristic
240C23#1306331012yes—
241Q8—3442no—
242Q8—1722no—
243Q8—1722no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—3442no—
257C2×C4—1724no—
258C2×C4—1722no—
259C2×C4—1722no—
260C2×C4#1306329311yescharacteristic
261C2×C4#1306330012yes—
262C2×C4#1306331411yescharacteristic
263C8—42no—
264C8—41no—
265C8—41no—
266C8—3442no—
267C22—21no—
268C22—21no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—81no—
273C22—81no—
274C22#1458281611yescharacteristic
275C22#1458317411yescharacteristic
276C22#1458317411yescharacteristic
277C4—22no—
278C4—21no—
279C4—42no—
280C4—81no—
281C4—3442no—
282C4—3442no—
283C4#1458308511yescharacteristic
284C4#1458308811yescharacteristic
285C2—21no—
286C2—21no—
287C2—42no—
288C2#1913584611yescharacteristic
289C2#1913586311yescharacteristic
290C2#1913588211yescharacteristic
subgroupG/H
centerC22#14582816
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1851C2
socleC22×C43#394
prime radicalC24×C43#41
hypercenter#1851D43
hypocenterC43#10559
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
166. C43#10559semidirect

Maximal subgroups

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

subgroupindex
#191453702
#191350632
#191331142
#191324722
C43×#18512
#1055943