Finite Group Databasebeta

← #24997539

Subgroups — #24997539

Order 11008.

512 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 85 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#19144713C212yesmaximal, complemented
2#19135534C211yesmaximal, characteristic, complemented
3#19133206C212yesmaximal, complemented
4#19132465C211yesmaximal, characteristic, complemented
5C43×#3245C211yesmaximal, characteristic
6C2×C4×Dic86C2211yescharacteristic
7#14583210—22no—
8#14583191—22no—
9#14583096—22no—
10#14583037—22no—
11#14582999—24no—
12#14582956C2212yes—
13C2×#13063236C2211yescharacteristic
14#14582653—22no—
15#14582639—24no—
16C43×#532C2212yes—
17C43×#474—22no—
18C43×#466—22no—
19C43×#459—22no—
20C2×C4⋊C8×C43C2211yescharacteristic
21C22×Dic86D411yescharacteristic
22C2×#10621883—24no—
23C22×C43⋊C8—21no—
24C4×Dic86—22no—
25C4×Dic86—22no—
26C2×C4⋊Dic43D411yescharacteristic
27C2×Dic43⋊C4—21no—
28C2×C4×Dic43—21no—
29#13063258—24no—
30C4⋊(C43⋊C8)—22no—
31#13063248—24no—
32#13063246—24no—
33C22⋊(C43⋊C8)—22no—
34#13063236—22no—
35#13063236D414yes—
36C2×#41×C43—22no—
37C2×D8×C43—22no—
38C22×C8×C43D412yes—
39C4⋊Q8×C43D412yes—
40#127×C43D412yes—
41#124×C43—22no—
42#121×C43—22no—
43#121×C43—22no—
44C4×D4×C43—22no—
45C4×D4×C43—22no—
46C2×C42×C43C2311yescharacteristic
47#107×C43—22no—
48C4⋊C8×C43—22no—
49#102×C43—24no—
50#41×C43—84no—
51C2×Q8×C43—22no—
52C2×D4×C43—22no—
53C2×D4×C43—22no—
54C2×D4×C43—22no—
55C2×D4×C43—42no—
56C22×C4×C43—42no—
57C22×C4×C43C2×D411yescharacteristic
58C22×C4×C43C2×D411yescharacteristic
59C22×C4×C43#4111yescharacteristic
60C22×Dic43—21no—
61C22×Dic43—21no—
62C2×Dic86—22no—
63C2×Dic86—42no—
64D8×C43—82no—
65C2×C8×C43—22no—
66C2×C8×C43—42no—
67C4⋊C4×C43—22no—
68C4⋊C4×C43—22no—
69C22⋊C4×C43—42no—
70C22⋊C4×C43—42no—
71C42×C43C2×D412yes—
72C42×C43C2×D412yes—
73#10621883—48no—
74C4⋊Dic43—22no—
75Dic43⋊C4—42no—
76C4×Dic43—41no—
77C4×Dic43—41no—
78C2×C43⋊C8—22no—
79C2×C43⋊C8—24no—
80C2×C43⋊C8—41no—
81C2×C43⋊C8—41no—
82C23×C43—42no—
83C23×C43#12111yescharacteristic
84Q8×C43—82no—
85D4×C43—44no—
86D4×C43—42no—
87D4×C43—42no—
88D4×C43—82no—
89D4×C43—84no—
90C2×C4×C43—22no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—41no—
94C2×C4×C43—42no—
95C2×C4×C43—84no—
96C2×C4×C43#12012yes—
97C2×C4×C43#12011yescharacteristic
98C2×C4×C43#12112yes—
99C2×C4×C43#12711yescharacteristic
100C2×Dic43—22no—
101C2×Dic43—41no—
102C2×Dic43—41no—
103C2×Dic43—41no—
104C2×Dic43—42no—
105Dic86—24no—
106Dic86—42no—
107C8×C43—42no—
108C43⋊C8—42no—
109C43⋊C8—44no—
110#10028—431nomaximal, Sylow
111C22×C43—21no—
112C22×C43—21no—
113C22×C43—82no—
114C22×C43—82no—
115C22×C43—82no—
116C22×C43#39211yescharacteristic
117C22×C43#47212yes—
118C4×C43—21no—
119C4×C43—22no—
120C4×C43—22no—
121C4×C43—82no—
122C4×C43#45511yescharacteristic
123C4×C43#45611yescharacteristic
124Dic43—42no—
125Dic43—81no—
126#3245D4311yescharacteristic
127#3112—432no—
128#1985—431no—
129#1530—432no—
130#1290—431no—
131C2×C43—22no—
132C2×C43—162no—
133C2×C43#200711yescharacteristic
134C2×C43#201011yescharacteristic
135C2×C43#201811yescharacteristic
136#532C2×D4312yes—
137C2×C4×Q8—431no—
138#480—862no—
139#477—862no—
140#474—22no—
141#466—22no—
142#460—862no—
143#459—22no—
144#448—862no—
145#440—864no—
146#432—432no—
147C2×C4⋊C8C2×D4311yescharacteristic
148C2×#97—431no—
149#336—862no—
150#329—864no—
151C43#1002811yescharacteristic, complemented, Sylow
152C2×#41—22no—
153C22×Q8—431no—
154C2×SD16—864no—
155C2×D8—22no—
156C22×C8—861no—
157C22×C8C22⋊D4312yes—
158C4⋊Q8C22⋊D4312yes—
159#127C22⋊D4312yes—
160#124—22no—
161#121—22no—
162#121—22no—
163C4×Q8—862no—
164C4×Q8—862no—
165C4×D4—22no—
166C4×D4—22no—
167C2×C4⋊C4—431no—
168C2×C4⋊C4—861no—
169C2×C42—861no—
170C2×C42C22×D4311yescharacteristic
171#107—22no—
172#107—864no—
173C4⋊C8—22no—
174C4⋊C8—862no—
175#103—864no—
176#102—24no—
177#102—864no—
178C22⋊C8—862no—
179#97—434no—
180#97—862no—
181#41—84no—
182C2×Q8—22no—
183C2×Q8—862no—
184C2×Q8—1722no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—22no—
188C2×D4—42no—
189C22×C4—42no—
190C22×C4—861no—
191C22×C4—861no—
192C22×C4D4×D4311yescharacteristic
193C22×C4#1062190011yescharacteristic
194C22×C4C2×C22⋊D4311yescharacteristic
195SD16—1728no—
196D8—82no—
197C2×C8—22no—
198C2×C8—42no—
199C2×C8—862no—
200C2×C8—864no—
201C2×C8—1721no—
202C2×C8—1721no—
203C4⋊C4—22no—
204C4⋊C4—22no—
205C4⋊C4—862no—
206C4⋊C4—1722no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C42—1721no—
210C42—1721no—
211C42D4×D4312yes—
212C42C2×C22⋊D4312yes—
213C23—42no—
214C23#1306329611yescharacteristic
215Q8—82no—
216Q8—864no—
217Q8—1722no—
218D4—44no—
219D4—42no—
220D4—42no—
221D4—82no—
222D4—84no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—84no—
229C2×C4—862no—
230C2×C4—1721no—
231C2×C4—1722no—
232C2×C4—1721no—
233C2×C4—1721no—
234C2×C4#1306329312yes—
235C2×C4#1306329411yescharacteristic
236C2×C4#1306329712yes—
237C2×C4#1306332111yescharacteristic
238C8—42no—
239C8—1722no—
240C8—1724no—
241C22—21no—
242C22—21no—
243C22—82no—
244C22—82no—
245C22—82no—
246C22#1458280711yescharacteristic
247C22#1458316612yes—
248C4—21no—
249C4—22no—
250C4—22no—
251C4—82no—
252C4—3441no—
253C4—1722no—
254C4#1458307711yescharacteristic
255C4#1458308211yescharacteristic
256C2—22no—
257C2—162no—
258C2#1913564211yescharacteristic
259C2#1913565911yescharacteristic
260C2#1913570211yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3245C2
socleC22×C43#392
hypercenter#3245D43
hypocenterC43#10028
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #19144713C2semidirect
2. #19135534C2semidirect
3. #19133206C2semidirect
4. #19132465C2semidirect
151. C43#10028semidirect

Maximal subgroups

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

subgroupindex
#191447132
#191355342
#191332062
#191324652
C43×#32452
#1002843