Finite Group Databasebeta

← #24985917

Subgroups — #24985917

Order 11008.

438 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 83 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#19142541C211yesmaximal, characteristic
2#19136132C212yesmaximal, complemented
3#19136128C211yesmaximal, characteristic
4#19132420C212yesmaximal, complemented
5C43×#1270C211yesmaximal, characteristic
6C2×#13063259—22no—
7C2×#13063256—21no—
8C2×#13063250—22no—
9C2×#13063246—21no—
10#14582838—21no—
11#14582811—22no—
12#14582805C2212yes—
13#14582779—21no—
14#14582774—22no—
15#14582769C2211yescharacteristic
16#14582654C2211yescharacteristic
17C43×#390C2211yescharacteristic
18C43×#336C2212yes—
19C22×Dic86D412yes—
20C23×Dic43—21no—
21C22×C43⋊C8—21no—
22C2×C4⋊Dic43—21no—
23C2×C4⋊Dic43—22no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43D412yes—
26C2×C22⋊Dic43—21no—
27C2×C22⋊Dic43—22no—
28#13063259—44no—
29#13063256—42no—
30#13063250—44no—
31#13063246—42no—
32C43⋊#95—21no—
33C43⋊#95—22no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C22×D4×C43D411yescharacteristic
37C22×C8×C43—22no—
38C2×C4⋊C4×C43D411yescharacteristic
39C2×C22⋊C4×C43—22no—
40C2×C42×C43C2311yescharacteristic
41C24×C43—21no—
42C2×D4×C43—21no—
43C2×D4×C43—41no—
44C2×D4×C43—41no—
45C2×D4×C43Q1612yes—
46C22×C4×C43—21no—
47C22×C4×C43C2×D411yescharacteristic
48C22×C4×C43C2×D412yes—
49C22×Dic43—22no—
50C22×Dic43—22no—
51C22×Dic43—41no—
52C22×Dic43—82no—
53C22×Dic43—81no—
54C2×Dic86—22no—
55C2×Dic86—22no—
56C2×Dic86—42no—
57C2×Dic86—42no—
58C2×C8×C43—24no—
59C2×C8×C43—42no—
60C2×C8×C43—42no—
61C4⋊C4×C43—41no—
62C22⋊C4×C43—42no—
63C22⋊C4×C43—42no—
64C42×C43—41no—
65C22⋊Dic43—82no—
66C22⋊Dic43—81no—
67C4⋊Dic43—42no—
68C4⋊Dic43—41no—
69C4⋊Dic43—42no—
70C4⋊Dic43—41no—
71C4⋊Dic43—42no—
72C4⋊Dic43—81no—
73C2×C43⋊C8—22no—
74C2×C43⋊C8—41no—
75C2×C43⋊C8—41no—
76C23×C43—22no—
77C23×C43—42no—
78C23×C43—42no—
79C23×C43—41no—
80C23×C43—41no—
81C23×C43#12011yescharacteristic
82D4×C43—42no—
83D4×C43—81no—
84C2×C4×C43—21no—
85C2×C4×C43—22no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—42no—
89C2×C4×C43—41no—
90C2×C4×C43C2×Q1611yescharacteristic
91C2×C4×C43#13512yes—
92C2×C4×C43#13712yes—
93C2×C4×C43#13711yescharacteristic
94C2×Dic43—42no—
95C2×Dic43—42no—
96C2×Dic43—42no—
97C2×Dic43—42no—
98C2×Dic43—42no—
99C2×Dic43—42no—
100C2×Dic43—84no—
101C2×Dic43—82no—
102C2×Dic43—81no—
103Dic86—44no—
104Dic86—82no—
105C8×C43—44no—
106C43⋊C8—42no—
107#7833—431nomaximal, Sylow
108C22×C43—42no—
109C22×C43—44no—
110C22×C43—82no—
111C22×C43—81no—
112C22×C43—81no—
113C22×C43#45111yescharacteristic
114C22×C43#45212yes—
115C22×C43#45312yes—
116C22×C43#45311yescharacteristic
117C22×C43#45811yescharacteristic
118C4×C43—21no—
119C4×C43—21no—
120C4×C43—22no—
121C4×C43—22no—
122C4×C43—81no—
123Dic43—82no—
124Dic43—82no—
125Dic43—161no—
126#2804—431no—
127#2095—432no—
128#2094—431no—
129#1272—432no—
130#1270D4311yescharacteristic
131C2×C43—82no—
132C2×C43#161411yescharacteristic
133C2×C43#161812yes—
134C2×C43#163011yescharacteristic
135C2×C43#163212yes—
136C2×C43#165511yescharacteristic
137C2×#107—862no—
138C2×#106—861no—
139C2×#103—862no—
140C2×#102—861no—
141#400—861no—
142#393—862no—
143#391—432no—
144#390C2×D4311yescharacteristic
145#386—861no—
146#385—862no—
147#384—431no—
148#336—431no—
149#336C2×D4312yes—
150C43#783311yescharacteristic, complemented, Sylow
151C22×Q8—432no—
152C22×D4D17211yescharacteristic
153C23×C4—861no—
154C22×C8—22no—
155C22×C8—861no—
156C2×C4⋊C4—432no—
157C2×C4⋊C4—861no—
158C2×C4⋊C4—861no—
159C2×C4⋊C4—862no—
160C2×C4⋊C4D17211yescharacteristic
161C2×C22⋊C4—22no—
162C2×C22⋊C4—862no—
163C2×C22⋊C4—861no—
164C2×C42C22×D4311yescharacteristic
165#107—1724no—
166#106—1722no—
167#103—1724no—
168#102—1722no—
169#95—862no—
170#95—861no—
171#95—862no—
172#95—862no—
173C24—21no—
174C2×Q8—862no—
175C2×Q8—862no—
176C2×Q8—1722no—
177C2×Q8—1722no—
178C2×D4—21no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4Dic17212yes—
182C22×C4—21no—
183C22×C4—862no—
184C22×C4—862no—
185C22×C4—3442no—
186C22×C4—3441no—
187C22×C4—1721no—
188C22×C4C2×D17211yescharacteristic
189C22×C4D4×D4312yes—
190C2×C8—24no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—862no—
194C2×C8—1721no—
195C2×C8—1721no—
196C4⋊C4—41no—
197C4⋊C4—3441no—
198C4⋊C4—1721no—
199C4⋊C4—1722no—
200C4⋊C4—1721no—
201C4⋊C4—1722no—
202C4⋊C4—1722no—
203C22⋊C4—42no—
204C22⋊C4—42no—
205C22⋊C4—3442no—
206C22⋊C4—3441no—
207C42—41no—
208C23—22no—
209C23—42no—
210C23—42no—
211C23—41no—
212C23—41no—
213C23#1306329511yescharacteristic
214Q8—3442no—
215Q8—1724no—
216D4—42no—
217D4—81no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—3444no—
225C2×C4—3442no—
226C2×C4—3441no—
227C2×C4—1722no—
228C2×C4—1722no—
229C2×C4—1722no—
230C2×C4—1722no—
231C2×C4—1722no—
232C2×C4—1722no—
233C2×C4C2×Dic17211yescharacteristic
234C2×C4#1306334412yes—
235C2×C4#1306335412yes—
236C2×C4#1306335811yescharacteristic
237C8—44no—
238C8—1722no—
239C22—44no—
240C22—42no—
241C22—81no—
242C22—81no—
243C22—82no—
244C22#1458305711yescharacteristic
245C22#1458306212yes—
246C22#1458306812yes—
247C22#1458306911yescharacteristic
248C22#1458309011yescharacteristic
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—81no—
254C4—3442no—
255C4—3442no—
256C4—6881no—
257C2—82no—
258C2#1913362211yescharacteristic
259C2#1913364412yes—
260C2#1913371711yescharacteristic
261C2#1913373112yes—
262C2#1913388511yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1270C2
socleC23×C43#120
prime radicalC22×D4×C43D4
hypercenter#1270D43
hypocenterC43#7833
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #19136132C2semidirect
4. #19132420C2semidirect
150. C43#7833semidirect

Maximal subgroups

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

subgroupindex
#191425412
#191361322
#191361282
#191324202
C43×#12702
#783343