Finite Group Databasebeta

← #24996199

Subgroups — #24996199

Order 11008.

426 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C2×#14583249C211yesmaximal, characteristic
2#19135585C211yesmaximal, characteristic
3#19135438C211yesmaximal, characteristic
4#19133350C211yesmaximal, characteristic
5#19133266C211yesmaximal, characteristic
6#19132876C211yesmaximal, characteristic
7C43×#1548C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9#14583249—21no—
10#14583249—21no—
11#14583249—22no—
12#14582923C2211yescharacteristic
13C2×#13063249C414yes—
14C2×#13063243—22no—
15C4×#10621877C2211yescharacteristic
16C2×C4×C43⋊C8C2211yescharacteristic
17#14582668—22no—
18#14582649—22no—
19#14582644—22no—
20#14582621—21no—
21C8×C43⋊C8—21no—
22C2×C4⋊Q8×C43C2211yescharacteristic
23C43×#431C2211yescharacteristic
24C43×#423C2211yescharacteristic
25C43×#333—22no—
26C22×Dic86—21no—
27C2×#10621877—21no—
28C2×#10621877D412yes—
29C22×C43⋊C8C2×C412yes—
30#13063325—21no—
31#13063325—21no—
32#13063325—21no—
33#13063325—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43C2×C412yes—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38#13063249—24no—
39#13063249—24no—
40#13063243—44no—
41#13063236—21no—
42C4×C43⋊C8—21no—
43C4×C43⋊C8D411yescharacteristic
44C4×C43⋊C8D411yescharacteristic
45C4×C43⋊C8D412yes—
46C22×Q8×C43C2×C412yes—
47C2×M16×C43—21no—
48C4⋊Q8×C43—21no—
49C4⋊Q8×C43—21no—
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43—21no—
52C2×C4⋊C4×C43—21no—
53C2×C4⋊C4×C43—21no—
54C2×C42×C43C2311yescharacteristic
55C4⋊C8×C43—21no—
56C4⋊C8×C43—21no—
57C4⋊C8×C43D412yes—
58C22⋊C8×C43—21no—
59C4×C8×C43—21no—
60C2×Q8×C43—22no—
61C2×Q8×C43—22no—
62C2×Q8×C43—44no—
63C22×C4×C43—22no—
64C22×C4×C43C22×C411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43#4111yescharacteristic
67C22×Dic43—22no—
68C2×Dic86—41no—
69C2×Dic86—41no—
70C2×Dic86—42no—
71C2×Dic86—42no—
72M16×C43—42no—
73C2×C8×C43—22no—
74C2×C8×C43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C42×C43C2×D411yescharacteristic
80C42×C43C2×D411yescharacteristic
81C42×C43C2×D411yescharacteristic
82C42×C43#4111yescharacteristic
83C4⋊Dic43—22no—
84C4⋊Dic43—22no—
85C4⋊Dic43—41no—
86C4⋊Dic43—41no—
87#10621877—22no—
88#10621877—42no—
89#10621877SD1614yes—
90C2×C43⋊C8—22no—
91C2×C43⋊C8—42no—
92C2×C43⋊C8—41no—
93C2×C43⋊C8C22⋊C412yes—
94C2×C43⋊C8C22⋊C412yes—
95C23×C43C4×D411yescharacteristic
96Q8×C43—44no—
97Q8×C43—82no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—42no—
101C2×C4×C43—82no—
102C2×C4×C43C2×C22⋊C411yescharacteristic
103C2×C4×C43C4×D411yescharacteristic
104C2×C4×C43#12111yescharacteristic
105C2×C4×C43#12111yescharacteristic
106C2×C4×C43#12411yescharacteristic
107C2×C4×C43#12711yescharacteristic
108C2×C4×C43C2×SD1612yes—
109C2×C4×C43#13512yes—
110C2×Dic43—42no—
111C2×Dic43—44no—
112Dic86—82no—
113Dic86—81no—
114Dic86—81no—
115C8×C43—42no—
116C8×C43—81no—
117C43⋊C8—22no—
118C43⋊C8—22no—
119C43⋊C8—24no—
120C43⋊C8—81no—
121#9797—431nomaximal, Sylow
122C22×C43—21no—
123C22×C43—21no—
124C22×C43#39011yescharacteristic
125C22×C43C4×SD1612yes—
126C4×C43—21no—
127C4×C43—21no—
128C4×C43—82no—
129C4×C43#41312yes—
130C4×C43#46512yes—
131C4×C43#47312yes—
132C4×C43#49211yescharacteristic
133C4×C43#49511yescharacteristic
134Dic43—82no—
135C2×#487—431no—
136#1997—431no—
137#1966—431no—
138#1566—431no—
139#1548D4311yescharacteristic
140#1546—431no—
141C8×M16—431no—
142C2×C43—22no—
143C2×C43#196711yescharacteristic
144C2×C43#196811yescharacteristic
145C2×C43#197911yescharacteristic
146C2×C4⋊Q8—431no—
147C2×C4⋊Q8C2×D4311yescharacteristic
148#487—861no—
149#487—861no—
150#487—862no—
151#431C2×D4311yescharacteristic
152#423—431no—
153#423C2×D4311yescharacteristic
154C2×#103—434no—
155C2×#101—862no—
156C4×M16—431no—
157C2×C4×C8—431no—
158#343—862no—
159#334—862no—
160#333—22no—
161#332—862no—
162#322—861no—
163C82—861no—
164C43#979711yescharacteristic, complemented, Sylow
165C22×Q8—861no—
166C22×Q8C4×D4312yes—
167C2×M16—21no—
168C2×M16—432no—
169C2×M16—861no—
170C22×C8—432no—
171C4⋊Q8—21no—
172C4⋊Q8—21no—
173C4⋊Q8—21no—
174C4⋊Q8—21no—
175C4⋊Q8—861no—
176C4⋊Q8—861no—
177C4⋊Q8—861no—
178C4⋊Q8—861no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—432no—
182C2×C4⋊C4—861no—
183C2×C42C22×D4311yescharacteristic
184C4⋊C8—21no—
185C4⋊C8—21no—
186C4⋊C8—861no—
187C4⋊C8—861no—
188C4⋊C8C22⋊D4312yes—
189#103—864no—
190#103—864no—
191#101—1724no—
192C22⋊C8—21no—
193#97—861no—
194C4×C8—21no—
195C4×C8—431no—
196C4×C8—431no—
197C4×C8—432no—
198C4×C8—861no—
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—44no—
202C2×Q8—1721no—
203C2×Q8—1721no—
204C2×Q8—1722no—
205C2×Q8—1722no—
206C22×C4—22no—
207C22×C4—862no—
208C22×C4C2×C4×D4311yescharacteristic
209C22×C4D4×D4311yescharacteristic
210C22×C4#1062190011yescharacteristic
211M16—42no—
212M16—434no—
213M16—862no—
214M16—1722no—
215C2×C8—22no—
216C2×C8—41no—
217C2×C8—432no—
218C2×C8—432no—
219C2×C8—862no—
220C2×C8—1722no—
221C2×C8—1721no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—862no—
227C4⋊C4—862no—
228C4⋊C4—1721no—
229C4⋊C4—1721no—
230C42#1062189811yescharacteristic
231C42D4×D4311yescharacteristic
232C42D4×D4311yescharacteristic
233C42C2×C22⋊D4311yescharacteristic
234C23(C22⋊D43)⋊C411yescharacteristic
235Q8—44no—
236Q8—82no—
237Q8—3442no—
238Q8—3441no—
239Q8—3441no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—42no—
243C2×C4—82no—
244C2×C4—1722no—
245C2×C4—1724no—
246C2×C4C22⋊C4×D4311yescharacteristic
247C2×C4C4×C22⋊D4311yescharacteristic
248C2×C4#1306329711yescharacteristic
249C2×C4#1306329811yescharacteristic
250C2×C4#1306331111yescharacteristic
251C2×C4#1306332111yescharacteristic
252C2×C4SD16×D4312yes—
253C2×C4#1306334812yes—
254C8—42no—
255C8—81no—
256C8—864no—
257C8—862no—
258C8—862no—
259C8—3441no—
260C22—21no—
261C22—21no—
262C22#1458279911yescharacteristic
263C22#1458298412yes—
264C4—21no—
265C4—21no—
266C4—82no—
267C4—3442no—
268C4#1458288012yes—
269C4#1458313112yes—
270C4#1458317212yes—
271C4#1458327011yescharacteristic
272C4#1458328411yescharacteristic
273C2—22no—
274C2#1913544111yescharacteristic
275C2#1913544611yescharacteristic
276C2#1913550911yescharacteristic
subgroupG/H
centerC22#14582799
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1548C2
socleC22×C43#390
prime radicalC23×C43C4×D4
cosocleC2×C42×C43C23
hypercenter#1548D43
hypocenterC43#9797
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
164. C43#9797semidirect

Maximal subgroups

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

subgroupindex
C2×#145832492
#191355852
#191354382
#191333502
#191332662
#191328762
C43×#15482
#979743