Finite Group Databasebeta

← #25000995

Subgroups — #25000995

Order 11008.

490 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 99 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#19135580C212yesmaximal
3#19135018C212yesmaximal
4#19132463C211yesmaximal, characteristic
5C43×#1850C211yesmaximal, characteristic
6C2×#13063304C2212yes—
7#14583235—22no—
8#14583140—21no—
9#14583140—21no—
10#14583057—22no—
11C2×#13063250—22no—
12#14582759C2212yes—
13#14582665—22no—
14#14582665—22no—
15#14582662—22no—
16C23×C8×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—
24#13063304—22no—
25#13063304—22no—
26#13063304—22no—
27#13063304—22no—
28C2×C4⋊Dic43—22no—
29C2×C4⋊Dic43D412yes—
30C2×Dic43⋊C4—22no—
31C2×C22⋊Dic43—22no—
32C2×C22⋊Dic43—22no—
33#13063259—21no—
34#13063259—21no—
35#13063250—22no—
36#13063250—22no—
37#13063250—44no—
38C43⋊#95—22no—
39C23×C4×C43C2311yescharacteristic
40C22×C8×C43—21no—
41C22×C8×C43—22no—
42C22×C8×C43—42no—
43C22×C8×C43D411yescharacteristic
44C22×C8×C43D411yescharacteristic
45C2×C22⋊C4×C43D411yescharacteristic
46C2×C22⋊C4×C43D411yescharacteristic
47C2×C42×C43—21no—
48C4⋊C8×C43—42no—
49C22⋊C8×C43—22no—
50#95×C43—21no—
51C24×C43C2×D411yescharacteristic
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—41no—
55C22×C4×C43—41no—
56C22×C4×C43C2×D412yes—
57C22×C4×C43C2×D411yescharacteristic
58C22×C4×C43#4111yescharacteristic
59C22×C4×C43#4112yes—
60C22×Dic43—22no—
61C22×Dic43—22no—
62C22×Dic43—42no—
63C2×Dic86—22no—
64C2×Dic86—22no—
65C2×Dic86—42no—
66C2×Dic86—42no—
67C2×C8×C43—22no—
68C2×C8×C43—24no—
69C2×C8×C43—21no—
70C2×C8×C43—21no—
71C2×C8×C43—42no—
72C2×C8×C43—41no—
73C2×C8×C43—41no—
74C2×C8×C43—41no—
75C2×C8×C43—41no—
76C22⋊C4×C43—21no—
77C22⋊C4×C43—22no—
78C22⋊C4×C43Q1612yescomplemented
79C42×C43—41no—
80C42×C43—41no—
81C22⋊Dic43—42no—
82C22⋊Dic43—42no—
83C22⋊Dic43—42no—
84C22⋊Dic43—42no—
85C4⋊Dic43—22no—
86C4⋊Dic43—22no—
87C4⋊Dic43—42no—
88C4⋊Dic43—42no—
89Dic43⋊C4—42no—
90Dic43⋊C4—42no—
91Dic172—81no—
92Dic172—81no—
93C23×C43—41no—
94C23×C43—41no—
95C23×C43#12111yescharacteristic
96C23×C43#12112yes—
97C23×C43C2×Q1611yescharacteristic
98C23×C43#13511yescharacteristic
99C23×C43#13712yes—
100C2×C4×C43—22no—
101C2×C4×C43—21no—
102C2×C4×C43—22no—
103C2×C4×C43—21no—
104C2×C4×C43—22no—
105C2×C4×C43—41no—
106C2×C4×C43—42no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43#12011yescharacteristic
113C2×C4×C43#12312yes—
114C2×C4×C43#12411yescharacteristic
115C2×Dic43—42no—
116C2×Dic43—42no—
117C2×Dic43—82no—
118C2×Dic43—82no—
119C2×Dic43—82no—
120C2×Dic43—82no—
121C2×Dic43—82no—
122Dic86—44no—
123Dic86—42no—
124Dic86—42no—
125C8×C43—41no—
126C8×C43—42no—
127C8×C43—41no—
128#10566—431nomaximal, Sylow
129C22×C43—22no—
130C22×C43—21no—
131C22×C43—22no—
132C22×C43—21no—
133C22×C43—41no—
134C22×C43—41no—
135C22×C43—42no—
136C22×C43#39411yescharacteristic
137C22×C43#46212yes—
138C22×C43#46412yes—
139C22×C43#46711yescharacteristic
140C22×C43#47011yescharacteristic
141C4×C43—22no—
142C4×C43—21no—
143C4×C43—42no—
144C4×C43—81no—
145C4×C43B(4,𝔽2)11yescharacteristic
146C4×C43#45811yescharacteristic
147Dic43—82no—
148Dic43—82no—
149Dic43—162no—
150#3189—431no—
151#1996—432no—
152#1892—432no—
153#1850D4311yescharacteristic
154#1289—431no—
155C2×C43—22no—
156C2×C43—21no—
157C2×C43—21no—
158C2×C43—22no—
159C2×C43#204411yescharacteristic
160C2×C43#205311yescharacteristic
161C2×C43#205611yescharacteristic
162C23×C8C2×D4311yescharacteristic
163C2×C22⋊Q8—432no—
164#484—862no—
165#467—861no—
166#467—861no—
167#451—862no—
168C2×C4⋊C8—21no—
169C2×#103—862no—
170C2×C22⋊C8C2×D4311yescharacteristic
171#380—432no—
172C4×C22⋊C4C2×D4311yescharacteristic
173#342—862no—
174#342—862no—
175#340—862no—
176#336—21no—
177C43#1056611yescharacteristic, complemented, Sylow
178C22×Q8—432no—
179C23×C4C22×D4311yescharacteristic
180C2×Q16—861no—
181C2×Q16—861no—
182C22×C8—22no—
183C22×C8—21no—
184C22×C8—42no—
185C22×C8C22⋊D4311yescharacteristic
186C22×C8C22⋊D4311yescharacteristic
187C22⋊Q8—862no—
188C22⋊Q8—862no—
189C22⋊Q8—862no—
190C22⋊Q8—862no—
191C2×C4⋊C4—432no—
192C2×C4⋊C4—862no—
193C2×C4⋊C4—862no—
194C2×C22⋊C4—862no—
195C2×C22⋊C4—862no—
196C2×C22⋊C4D17211yescharacteristic
197C2×C22⋊C4D17211yescharacteristic
198C2×C42—21no—
199#107—861no—
200#107—861no—
201C4⋊C8—42no—
202#103—862no—
203#103—862no—
204#103—1724no—
205C22⋊C8—22no—
206#95—21no—
207#95—862no—
208C24C2×D17211yescharacteristic
209C2×Q8—862no—
210C2×Q8—862no—
211C2×Q8—1722no—
212C2×Q8—1722no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—862no—
218C22×C4—862no—
219C22×C4—1722no—
220C22×C4#1062189811yescharacteristic
221C22×C4D4×D4312yes—
222C22×C4#1062190212yes—
223C22×C4C2×C22⋊D4311yescharacteristic
224Q16—3441no—
225Q16—3441no—
226C2×C8—24no—
227C2×C8—22no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—41no—
231C2×C8—42no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C4⋊C4—862no—
236C4⋊C4—862no—
237C4⋊C4—1722no—
238C4⋊C4—1722no—
239C4⋊C4—1722no—
240C4⋊C4—1722no—
241C22⋊C4—21no—
242C22⋊C4—22no—
243C22⋊C4—1722no—
244C22⋊C4—1722no—
245C22⋊C4—1722no—
246C22⋊C4—1722no—
247C22⋊C4Dic17212yescomplemented
248C42—41no—
249C42—41no—
250C23—41no—
251C23—41no—
252C23#1306329911yescharacteristic
253C23#1306330012yes—
254C23C2×Dic17211yescharacteristic
255C23#1306334711yescharacteristic
256C23#1306335812yes—
257Q8—1724no—
258Q8—1722no—
259Q8—1722no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—3442no—
273C2×C4—3442no—
274C2×C4—3442no—
275C2×C4—3442no—
276C2×C4—3442no—
277C2×C4—1722no—
278C2×C4—1722no—
279C2×C4#1306329311yescharacteristic
280C2×C4#1306331012yes—
281C2×C4#1306331411yescharacteristic
282C8—42no—
283C8—41no—
284C8—41no—
285C22—21no—
286C22—22no—
287C22—21no—
288C22—22no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22#1458281611yescharacteristic
293C22#1458311012yes—
294C22#1458312212yes—
295C22#1458314011yescharacteristic
296C22#1458315711yescharacteristic
297C4—22no—
298C4—21no—
299C4—42no—
300C4—81no—
301C4—3442no—
302C4—3442no—
303C4—6882no—
304C4#1458308511yescharacteristic
305C4#1458308811yescharacteristic
306C2—21no—
307C2—21no—
308C2—22no—
309C2—22no—
310C2#1913584611yescharacteristic
311C2#1913590111yescharacteristic
312C2#1913591811yescharacteristic
subgroupG/H
centerC22#14582816
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1850C2
socleC22×C43#394
prime radicalC24×C43C2×D4
hypercenter#1850D43
hypocenterC43#10566
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
78. C22⋊C4×C43Q16semidirect
177. C43#10566semidirect
247. C22⋊C4Dic172semidirect

Maximal subgroups

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

subgroupindex
#191453702
#191355802
#191350182
#191324632
C43×#18502
#1056643