Finite Group Databasebeta

← #25009817

Subgroups — #25009817

Order 11008.

396 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 67 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#19145346C211yesmaximal, characteristic
2#19136781C212yesmaximal, complemented
3#19136023C211yesmaximal, characteristic, complemented
4#19132605C212yesmaximal, complemented
5C43×#1314C211yesmaximal, characteristic, complemented
6C2×#13063299—21no—
7#14583213—22no—
8#14583135—21no—
9#14583135C2212yes—
10#14583035—22no—
11C2×#13063259C2211yescharacteristic, complemented
12#14582759—21no—
13#14582727—22no—
14#14582701—22no—
15#14582662—21no—
16#14582662C2211yescharacteristic, complemented
17C2×C22⋊C8×C43C2211yescharacteristic
18C43×C22⋊C16C2212yescomplemented
19C22×D172—21no—
20C22×C22⋊D43—41no—
21C2×D344—21no—
22C2×D344D412yes—
23#13063299—22no—
24#13063299—22no—
25#13063299—41no—
26#13063299—41no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×C22⋊Dic43—41no—
31C2×(C2×D43)⋊C4—41no—
32#13063259—21no—
33#13063259—22no—
34#13063259D412yes—
35#13063247—22no—
36#13063247—22no—
37C43⋊#95—41no—
38C23×C4×C43D411yescharacteristic
39C22×C8×C43D411yescharacteristic
40C22×C8×C43C2311yescharacteristic
41C2×C16×C43—22no—
42C22⋊C8×C43—22no—
43C24×C43D811yescharacteristic
44C23×D43—41no—
45C22×C4×C43—21no—
46C22×C4×C43—21no—
47C22×C4×C43—41no—
48C22×C4×C43—41no—
49C22×C4×C43D811yescharacteristic
50C22×C4×C43C2×D411yescharacteristic
51C2×C22⋊D43—42no—
52C2×C22⋊D43—42no—
53C2×C22⋊D43—82no—
54C2×C22⋊D43—82no—
55C22×Dic43—41no—
56C22×Dic43—41no—
57C22×Dic43—41no—
58C2×D172—22no—
59C2×D172—41no—
60C2×D172—81no—
61C2×D172—81no—
62C2×C8×C43—21no—
63C2×C8×C43—41no—
64C2×C8×C43—41no—
65C2×C8×C43C2×D412yes—
66C22⋊Dic43—82no—
67(C2×D43)⋊C4—42no—
68(C2×D43)⋊C4—42no—
69C4⋊Dic43—22no—
70C4⋊Dic43—41no—
71C4⋊Dic43—41no—
72C4⋊Dic43—41no—
73C4⋊Dic43—41no—
74C4⋊Dic43—41no—
75D344—42no—
76D344—81no—
77C16×C43—42no—
78C23×C43—21no—
79C23×C43—21no—
80C23×C43—41no—
81C23×C43—41no—
82C23×C43SD3212yes—
83C23×C43C2×D811yescharacteristic
84C22×D43—42no—
85C22×D43—82no—
86C22×D43—82no—
87C22×D43—82no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—81no—
95C2×C4×C43#12011yescharacteristic
96C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
97C22⋊D43—84no—
98C22⋊D43—82no—
99C22⋊D43—82no—
100C2×Dic43—42no—
101C2×Dic43—82no—
102C2×Dic43—81no—
103C2×Dic43—81no—
104C2×Dic43—81no—
105C2×Dic43—81no—
106C2×Dic43—81no—
107C2×Dic43—81no—
108D172—42no—
109D172—42no—
110D172—82no—
111C8×C43—22no—
112C8×C43—41no—
113#12281—431nomaximal, Sylow
114C22×C43—21no—
115C22×C43—21no—
116C22×C43—22no—
117C22×C43—42no—
118C22×C43—41no—
119C22×C43—41no—
120C22×C43—81no—
121C22×C43#44711yescharacteristic
122C22×C43C2×SD3211yescharacteristic
123C22×C43#50911yescharacteristic
124C2×D43—82no—
125C2×D43—82no—
126C2×D43—82no—
127C2×D43—164no—
128C4×C43—21no—
129C4×C43—41no—
130C4×C43#45511yescharacteristic
131C4×C43#45811yescharacteristic
132Dic43—82no—
133Dic43—161no—
134Dic43—161no—
135#3186—431no—
136#2233—432no—
137#2076—431no—
138#1347—432no—
139#1314D4311yescharacteristic, complemented
140C2×C43—21no—
141C2×C43—21no—
142C2×C43—42no—
143C2×C43#160711yescharacteristic
144C2×C43#218711yescharacteristic
145C2×C43#219011yescharacteristic
146D43—162no—
147C2×#121—861no—
148#480—862no—
149#466—432no—
150#466—861no—
151#447—862no—
152C2×#107—431no—
153C2×C22⋊C8C2×D4311yescharacteristic
154#380—861no—
155#367—862no—
156#357—862no—
157C22⋊C16C2×D4312yescomplemented
158#340—431no—
159#340—861no—
160C43#1228111yescharacteristic, complemented, Sylow
161C22×D4—861no—
162C22×D4—1721no—
163C23×C4D17211yescharacteristic
164C2×D8—432no—
165C2×D8—861no—
166C22×C8D17211yescharacteristic
167C22×C8C22×D4311yescharacteristic
168#121—862no—
169#121—862no—
170#121—1721no—
171#121—1721no—
172C2×C4⋊C4—861no—
173C2×C4⋊C4—861no—
174C2×C4⋊C4—861no—
175C2×C22⋊C4—1721no—
176C2×C22⋊C4—1721no—
177C2×C16—22no—
178#107—432no—
179#107—861no—
180#107—862no—
181#102—862no—
182#102—862no—
183C22⋊C8—22no—
184#95—1721no—
185C24—1721no—
186C24D34411yescharacteristic
187C2×D4—862no—
188C2×D4—3441no—
189C2×D4—3441no—
190C2×D4—3442no—
191C2×D4—3442no—
192C2×D4—1721no—
193C2×D4—1722no—
194C2×D4—1722no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—1721no—
200C22×C4—1721no—
201C22×C4—1721no—
202C22×C4D34411yescharacteristic
203C22×C4C2×D17211yescharacteristic
204D8—3441no—
205D8—1722no—
206C2×C8—21no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8D4×D4312yes—
210C4⋊C4—862no—
211C4⋊C4—1721no—
212C4⋊C4—1721no—
213C4⋊C4—1721no—
214C4⋊C4—1721no—
215C4⋊C4—1721no—
216C22⋊C4—3442no—
217C22⋊C4—1722no—
218C22⋊C4—1722no—
219C16—42no—
220C23—21no—
221C23—21no—
222C23—41no—
223C23—41no—
224C23—3442no—
225C23—3442no—
226C23—3442no—
227C23—1722no—
228C23#1306327012yes—
229C23C2×D34411yescharacteristic
230D4—3442no—
231D4—3444no—
232D4—3442no—
233D4—3442no—
234D4—1722no—
235D4—1722no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—81no—
243C2×C4—3442no—
244C2×C4—3441no—
245C2×C4—3441no—
246C2×C4—3441no—
247C2×C4—3441no—
248C2×C4—3441no—
249C2×C4—3441no—
250C2×C4—1722no—
251C2×C4#1306329511yescharacteristic
252C2×C4#1306335311yescharacteristic
253C8—22no—
254C8—41no—
255C22—21no—
256C22—21no—
257C22—22no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—81no—
262C22—3442no—
263C22—3442no—
264C22—3442no—
265C22—6884no—
266C22#1458303511yescharacteristic
267C22C2×#1306327011yescharacteristic
268C22#1458333711yescharacteristic
269C4—21no—
270C4—41no—
271C4—3442no—
272C4—6881no—
273C4—6881no—
274C4#1458307911yescharacteristic
275C4#1458309011yescharacteristic
276C2—21no—
277C2—21no—
278C2—42no—
279C2—6882no—
280C2#1913358311yescharacteristic
281C2#1913652611yescharacteristic
282C2#1913654311yescharacteristic
subgroupG/H
centerC22#14583035
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#1314C2
socleC22×C43#447
prime radical#19145346C2
hypercenter#1314D43
hypocenterC43#12281
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. #19136781C2semidirect
3. #19136023C2semidirect
4. #19132605C2semidirect
5. C43×#1314C2semidirect
11. C2×#13063259C22semidirect
16. #14582662C22semidirect
18. C43×C22⋊C16C22semidirect
139. #1314D43semidirect
157. C22⋊C16C2×D43semidirect
160. C43#12281semidirect

Maximal subgroups

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

subgroupindex
#191453462
#191367812
#191360232
#191326052
C43×#13142
#1228143