Finite Group Databasebeta

← #25016084

Subgroups — #25016084

Order 11008.

402 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 73 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#19136290C212yesmaximal
2#19135148C212yesmaximal
3#19134814C211yesmaximal, characteristic
4#19132718C211yesmaximal, characteristic
5C43×#3202C211yesmaximal, characteristic
6#14583666C2211yescharacteristic
7#14582947—21no—
8#14582883C2212yes—
9#14582883C2211yescharacteristic
10C2×#13063244—22no—
11#14582698—24no—
12#14582669—22no—
13#14582664—21no—
14C43×#536C2212yes—
15C43×#485—22no—
16C43×#470—21no—
17C43×#467—21no—
18C43×#451—22no—
19C43×#408C2211yescharacteristic
20#13063332—42no—
21C2×#10621877—22no—
22C2×#10621877—21no—
23C2×#10621877—21no—
24C2×#10621877—22no—
25#13063260—42no—
26#13063244—22no—
27#13063244—44no—
28#13063244D412yes—
29#13063242—21no—
30#13063242—22no—
31C2×#41×C43C2311yescharacteristic
32C22×Q8×C43D412yes—
33C2×Q16×C43—21no—
34C2×Q16×C43—21no—
35C2×M16×C43D411yescharacteristic
36C22×C8×C43D411yescharacteristic
37C4⋊Q8×C43—22no—
38#124×C43—22no—
39#123×C43—22no—
40#123×C43—22no—
41C22⋊Q8×C43—22no—
42C22⋊Q8×C43—22no—
43#117×C43D412yes—
44#107×C43—21no—
45#106×C43—21no—
46#103×C43—22no—
47#103×C43—22no—
48C22⋊C8×C43—22no—
49#41×C43—41no—
50#41×C43—41no—
51C2×Q8×C43—22no—
52C2×Q8×C43—22no—
53C2×Q8×C43—42no—
54C2×Q8×C43—42no—
55C2×Q8×C43C2×D411yescharacteristic
56C2×D4×C43#4111yescharacteristic
57C2×D4×C43#4112yes—
58C22×C4×C43—22no—
59C22×C4×C43C2×D412yes—
60C22×C4×C43C2×D411yescharacteristic
61Q16×C43—81no—
62Q16×C43—81no—
63M16×C43—41no—
64C2×C8×C43—21no—
65C2×C8×C43—21no—
66C2×C8×C43—41no—
67C4⋊C4×C43—22no—
68C4⋊C4×C43—42no—
69C4⋊C4×C43—42no—
70C22⋊C4×C43—22no—
71C22⋊C4×C43—42no—
72C22⋊C4×C43—42no—
73C42×C43—22no—
74#10621877—24no—
75#10621877—22no—
76#10621877—22no—
77#10621877—41no—
78#10621877—41no—
79#10621877—42no—
80#10621877—42no—
81C2×C43⋊C8—41no—
82C2×C43⋊C8—41no—
83C2×C43⋊C8—42no—
84C2×C43⋊C8—42no—
85C23×C43#12312yes—
86C23×C43#12411yescharacteristic
87Q8×C43—41no—
88Q8×C43—42no—
89Q8×C43—42no—
90Q8×C43—82no—
91D4×C43—41no—
92D4×C43—42no—
93C2×C4×C43—21no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—21no—
97C2×C4×C43—44no—
98C2×C4×C43—42no—
99C2×C4×C43—42no—
100C2×C4×C43#12011yescharacteristic
101C2×C4×C43#12111yescharacteristic
102C2×C4×C43#12112yes—
103C8×C43—41no—
104C8×C43—41no—
105C43⋊C8—42no—
106C43⋊C8—42no—
107C43⋊C8—82no—
108#13431—431nomaximal, Sylow
109C22×C43—22no—
110C22×C43—21no—
111C22×C43—42no—
112C22×C43—41no—
113C22×C43#39411yescharacteristic
114C4×C43—21no—
115C4×C43—22no—
116C4×C43—82no—
117C4×C43—82no—
118C4×C43B(4,𝔽2)11yescharacteristic
119C4×C43#45811yescharacteristic
120#3202D4311yescharacteristic
121#2135—432no—
122#1915—432no—
123#1858—431no—
124#1392—431no—
125C2×C43—21no—
126C2×C43—42no—
127C2×C43—41no—
128C2×C43#204411yescharacteristic
129#568—431no—
130#536C2×D4312yes—
131#485—22no—
132#470—21no—
133#467—21no—
134#451—22no—
135#430—861no—
136#413—431no—
137#413—432no—
138C2×#101—862no—
139#408C2×D4311yescharacteristic
140#356—864no—
141#344—862no—
142#341—861no—
143C43#1343111yescharacteristic, complemented, Sylow
144C2×#41C22×D4311yescharacteristic
145C22×Q8C22⋊D4312yes—
146C2×Q16—21no—
147C2×Q16—21no—
148#131—1722no—
149C2×M16—861no—
150C2×M16—862no—
151C2×M16—861no—
152C2×M16—862no—
153C2×M16C22⋊D4311yescharacteristic
154C22×C8C22⋊D4311yescharacteristic
155C4⋊Q8—22no—
156#124—22no—
157#123—22no—
158#123—22no—
159C22⋊Q8—22no—
160C22⋊Q8—22no—
161#117C22⋊D4312yes—
162#108—1722no—
163#107—21no—
164#106—21no—
165#103—22no—
166#103—22no—
167#101—432no—
168#101—862no—
169#101—1724no—
170#100—861no—
171#100—862no—
172C22⋊C8—22no—
173#41—41no—
174#41—41no—
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—42no—
178C2×Q8—42no—
179C2×Q8D4×D4311yescharacteristic
180C2×D4#1062190011yescharacteristic
181C2×D4#1062190012yes—
182C22×C4—22no—
183C22×C4C2×C22⋊D4311yescharacteristic
184C22×C4C2×C22⋊D4312yes—
185Q16—81no—
186Q16—81no—
187M16—41no—
188M16—864no—
189M16—862no—
190M16—862no—
191M16—1722no—
192M16—1722no—
193M16—1721no—
194M16—1721no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—41no—
198C2×C8—1722no—
199C2×C8—1721no—
200C2×C8—1721no—
201C2×C8—1722no—
202C4⋊C4—22no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C22⋊C4—22no—
206C22⋊C4—42no—
207C22⋊C4—42no—
208C42—22no—
209C23#1306330612yes—
210C23#1306331211yescharacteristic
211Q8—41no—
212Q8—42no—
213Q8—42no—
214Q8—82no—
215D4—42no—
216D4—41no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—44no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4#1306329411yescharacteristic
225C2×C4#1306329611yescharacteristic
226C2×C4#1306329712yes—
227C8—41no—
228C8—41no—
229C8—3442no—
230C8—1722no—
231C8—1722no—
232C22—22no—
233C22—21no—
234C22—42no—
235C22—41no—
236C22#1458281311yescharacteristic
237C4—22no—
238C4—21no—
239C4—82no—
240C4—82no—
241C4#1458308611yescharacteristic
242C4#1458308911yescharacteristic
243C2—21no—
244C2—42no—
245C2—41no—
246C2#1913584311yescharacteristic
subgroupG/H
centerC2#19135843
commutator, prime radical, cosocleC2×#41×C43C23
FrattiniC2×#41C22×D43
FittingC43×#3202C2
socleC2×C43#2044
hypercenter#3202D43
hypocenterC43#13431
LCSG ▷ C2×#41×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #3202

Complements

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

NH ≅ G/Ntype
143. C43#13431semidirect

Maximal subgroups

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

subgroupindex
#191362902
#191351482
#191348142
#191327182
C43×#32022
#1343143