Finite Group Databasebeta

← #25005925

Subgroups — #25005925

Order 11008.

356 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 87 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#19143303C211yesmaximal, characteristic
2#19136395C212yesmaximal, complemented
3#19132521C211yesmaximal, characteristic, complemented
4#19132520C212yesmaximal, complemented
5C43×#1315C211yesmaximal, characteristic, complemented
6C2×#13063333C411yescharacteristic
7C2×#13063332C411yescharacteristic
8#14583445C411yescharacteristic
9#14582974—22no—
10(C22⋊D43)⋊C8—22no—
11#14582922C411yescharacteristic
12#14582865C2211yescharacteristic
13C2×C8×Dic43C2211yescharacteristic
14Dic43⋊C16—22no—
15C22⋊(C43⋊C16)C2212yes—
16#14582674—22no—
17C43×#408C2211yescharacteristic
18C43×C22⋊C16C2212yes—
19C2×#10621898C2×C411yescharacteristic
20#13063333—42no—
21#13063332—42no—
22C2×#10621877—21no—
23C2×#10621877C2×C411yescharacteristic
24C2×#10621872—21no—
25C22×C43⋊C8—21no—
26C22×C43⋊C8C2×C411yescharacteristic
27C2×C8×D43—21no—
28#13063323C811yescharacteristic
29#13063321C811yescharacteristic
30#13063314C811yescharacteristic
31#13063312C811yescharacteristic
32#13063297—22no—
33C4×C22⋊D43—22no—
34C2×C4×Dic43C2×C411yescharacteristic
35C2×C43⋊C16—22no—
36Dic43⋊C8—22no—
37(C2×D43)⋊C8—22no—
38C8×Dic43D412yes—
39C8×Dic43D412yes—
40C2×#41×C43C2×C411yescharacteristic
41C2×M16×C43C2×C411yescharacteristic
42C22×C8×C43C2311yescharacteristic
43C2×C16×C43—22no—
44C22⋊C8×C43—22no—
45#41×C43—41no—
46#41×C43—41no—
47C2×Q8×C43C2×C811yescharacteristic
48C2×D4×C43—21no—
49C2×D4×C43C2×C811yescharacteristic
50C22×C4×C43—21no—
51C22×C4×C43C22×C411yescharacteristic
52C2×C22⋊D43—22no—
53C2×C22⋊D43—21no—
54C22×Dic43M1612yes—
55#10621898—41no—
56#10621898—41no—
57C2×D172C2×C811yescharacteristic
58C2×C4×D43—21no—
59C2×Dic86C2×C811yescharacteristic
60M16×C43—41no—
61C2×C8×C43—21no—
62C2×C8×C43—41no—
63C2×C8×C43C2×D412yes—
64C22⋊Dic43—22no—
65(C2×D43)⋊C4—22no—
66Dic43⋊C4—22no—
67C4×Dic43C22⋊C412yes—
68C4×Dic43C2×C811yescharacteristic
69C4×Dic43C2×C811yescharacteristic
70#10621877—42no—
71#10621877—41no—
72C2×C43⋊C8—22no—
73C2×C43⋊C8—21no—
74C2×C43⋊C8—42no—
75C2×C43⋊C8C22⋊C411yescharacteristic
76C2×C43⋊C8C22⋊C411yescharacteristic
77#10621872—42no—
78C8×D43—42no—
79C16×C43—42no—
80C43⋊C16—42no—
81C23×C43—21no—
82C23×C43C2×M1611yescharacteristic
83C22×D43—21no—
84Q8×C43—41no—
85D4×C43—41no—
86D4×C43—42no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—41no—
91C2×C4×C43—41no—
92C2×C4×C43C2×C22⋊C411yescharacteristic
93C2×C4×C43C22×C811yescharacteristic
94C22⋊D43—44no—
95C22⋊D43—42no—
96C2×Dic43—21no—
97C2×Dic43—42no—
98C2×Dic43C22⋊C812yes—
99C2×Dic43C22⋊C812yes—
100D172—41no—
101C4×D43—41no—
102C4×D43—41no—
103Dic86—41no—
104C8×C43—22no—
105C8×C43—41no—
106C43⋊C8—21no—
107C43⋊C8—41no—
108C43⋊C8#10012yes—
109#11491—431nomaximal, Sylow
110C22×C43—22no—
111C22×C43—21no—
112C22×C43—42no—
113C22×C43—41no—
114C22×C43C2×C22⋊C811yescharacteristic
115C2×D43—42no—
116C2×D43—41no—
117C4×C43—21no—
118C4×C43—41no—
119C4×C43#41011yescharacteristic
120C4×C43C2×#10011yescharacteristic
121Dic43—22no—
122Dic43—22no—
123Dic43—41no—
124#2931—431no—
125#2163—432no—
126#1315—431no—
127#1315—432no—
128#1315D4311yescharacteristic, complemented
129C2×C43—41no—
130C2×C43—81no—
131C2×C43#146011yescharacteristic
132C2×C43#211712yes—
133D43—81no—
134C2×#131—431no—
135C2×#131—431no—
136#532—431no—
137#436—862no—
138C8×D4—862no—
139#423—431no—
140#408—431no—
141#408C2×D4311yescharacteristic
142C2×C4×C8—431no—
143C4⋊C16—862no—
144C22⋊C16—432no—
145C22⋊C16C2×D4312yes—
146#346—862no—
147C43#1149111yescharacteristic, complemented, Sylow
148C2×#41—431no—
149C2×#41C4×D4311yescharacteristic
150#131—1722no—
151#131—1722no—
152C2×M16—431no—
153C2×M16—861no—
154C2×M16—861no—
155C2×M16C4×D4311yescharacteristic
156C22×C8—431no—
157C22×C8—861no—
158C22×C8—861no—
159C22×C8C22×D4311yescharacteristic
160C4⋊Q8—431no—
161#127—431no—
162#124—431no—
163#124—431no—
164#121—862no—
165C4×D4—862no—
166C2×C42—431no—
167C2×C16—22no—
168C2×C16—862no—
169C4⋊C8—862no—
170C22⋊C8—22no—
171C22⋊C8—862no—
172C4×C8—432no—
173C4×C8—432no—
174#41—41no—
175#41—41no—
176#41—1721no—
177#41—1721no—
178C2×Q8—431no—
179C2×Q8C8×D4311yescharacteristic
180C2×D4—21no—
181C2×D4—431no—
182C2×D4—862no—
183C2×D4—861no—
184C2×D4C8×D4311yescharacteristic
185C22×C4—21no—
186C22×C4—432no—
187C22×C4—861no—
188C22×C4C2×C4×D4311yescharacteristic
189M16—41no—
190M16—1722no—
191M16—1722no—
192M16—1721no—
193C2×C8—21no—
194C2×C8—41no—
195C2×C8—431no—
196C2×C8—431no—
197C2×C8—862no—
198C2×C8—861no—
199C2×C8—1722no—
200C2×C8—1722no—
201C2×C8D4×D4312yes—
202C4⋊C4—862no—
203C22⋊C4—862no—
204C22⋊C4—862no—
205C42—432no—
206C42—431no—
207C42—431no—
208C16—42no—
209C16—1722no—
210C23—21no—
211C23—861no—
212C23M16×D4311yescharacteristic
213Q8—41no—
214Q8—1721no—
215D4—41no—
216D4—42no—
217D4—1721no—
218D4—1724no—
219D4—1722no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—432no—
226C2×C4—432no—
227C2×C4—861no—
228C2×C4—1722no—
229C2×C4—1721no—
230C2×C4—1721no—
231C2×C4C22⋊C4×D4311yescharacteristic
232C2×C4C2×C8×D4311yescharacteristic
233C8—22no—
234C8—41no—
235C8—432no—
236C8—861no—
237C8—1721no—
238C22—22no—
239C22—21no—
240C22—42no—
241C22—41no—
242C22—1722no—
243C22—1721no—
244C22C22⋊C8×D4311yescharacteristic
245C4—21no—
246C4—41no—
247C4—862no—
248C4—862no—
249C4—1721no—
250C4#1458287111yescharacteristic
251C4#100×D4311yescharacteristic
252C2—41no—
253C2—81no—
254C2—3441no—
255C2#1913291411yescharacteristic
256C2#1913622112yes—
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC22×C8C22×D43
FittingC43×#1315C2
socleC22×C43C2×C22⋊C8
prime radical#14583445C4
cosocleC22×C8×C43C23
hypercenter#1315D43
hypocenterC43#11491
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1315

Complements

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

NH ≅ G/Ntype
2. #19136395C2semidirect
3. #19132521C2semidirect
4. #19132520C2semidirect
5. C43×#1315C2semidirect
128. #1315D43semidirect
147. C43#11491semidirect

Maximal subgroups

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

subgroupindex
#191433032
#191363952
#191325212
#191325202
C43×#13152
#1149143