Finite Group Databasebeta

← #25009037

Subgroups — #25009037

Order 11008.

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

normal subgroups only

This group has 434 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#19145905C211yesmaximal, characteristic, complemented
2#19136507C212yesmaximal, complemented
3#19132603C212yesmaximal, complemented
4#19132535C211yesmaximal, characteristic, complemented
5C43×#2054C211yesmaximal, characteristic, complemented
6#14583449—21no—
7C2×#13063266—22no—
8#14583180—22no—
9#14583135—21no—
10#14583135C2212yes—
11#14583095—22no—
12#14582700—22no—
13C22⋊(C43⋊C16)C2212yes—
14C22×D8×C43C2211yescharacteristic
15C2×C4⋊C8×C43C2211yescharacteristic
16C2×#102×C43—21no—
17C43×#390—21no—
18C43×#340C2211yescharacteristic
19C2×#10621898—41no—
20C2×D344—21no—
21C2×D344D412yes—
22#13063325—21no—
23#13063322—21no—
24#13063313—41no—
25#13063299—22no—
26#13063299—41no—
27C4×D172—22no—
28C4×D172—41no—
29#13063266—44no—
30C2×C43⋊C16—22no—
31#13063259—21no—
32#13063259D412yes—
33#13063247—22no—
34#13063247—22no—
35C22×D4×C43—21no—
36C2×D8×C43—22no—
37C2×D8×C43—42no—
38C22×C8×C43D411yescharacteristic
39C22×C8×C43C2311yescharacteristic
40C2×C4⋊C4×C43—21no—
41C2×C22⋊C4×C43—41no—
42C2×C22⋊C4×C43—41no—
43C2×C42×C43D411yescharacteristic
44C4⋊C8×C43—22no—
45#102×C43—42no—
46C24×C43—41no—
47C2×D4×C43—22no—
48C2×D4×C43—41no—
49C2×D4×C43—41no—
50C2×D4×C43—41no—
51C2×D4×C43—41no—
52C2×D4×C43—41no—
53C22×C4×C43—41no—
54C22×C4×C43D811yescharacteristic
55C22×C4×C43D811yescharacteristic
56C22×C4×C43C2×D411yescharacteristic
57C2×C22⋊D43—42no—
58#10621898—82no—
59#10621898—82no—
60C2×D172—22no—
61C2×D172—41no—
62C2×D172—41no—
63C2×C4×D43—42no—
64C2×Dic86—41no—
65D8×C43—24no—
66D8×C43—42no—
67C2×C8×C43—21no—
68C2×C8×C43—41no—
69C2×C8×C43—41no—
70C2×C8×C43C2×D412yes—
71C4⋊C4×C43—41no—
72C4⋊C4×C43—41no—
73C22⋊C4×C43—82no—
74C22⋊C4×C43—82no—
75C42×C43—21no—
76C42×C43—21no—
77(C2×D43)⋊C4—42no—
78(C2×D43)⋊C4—42no—
79C4⋊Dic43—22no—
80C4⋊Dic43—41no—
81D344—42no—
82D344—81no—
83C43⋊C16—42no—
84C23×C43—42no—
85C23×C43—81no—
86C23×C43—81no—
87C23×C43—81no—
88C23×C43—81no—
89C23×C43—81no—
90C23×C43—81no—
91C23×C43C2×D811yescharacteristic
92C22×D43—42no—
93D4×C43—42no—
94D4×C43—42no—
95D4×C43—81no—
96D4×C43—81no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—41no—
103C2×C4×C43—81no—
104C2×C4×C43—81no—
105C2×C4×C43—81no—
106C2×C4×C43D1612yescomplemented
107C2×C4×C43#12011yescharacteristic
108C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
109C22⋊D43—82no—
110C22⋊D43—82no—
111C2×Dic43—42no—
112D172—42no—
113D172—42no—
114D172—82no—
115D172—82no—
116C4×D43—84no—
117Dic86—82no—
118C8×C43—22no—
119C8×C43—41no—
120#12158—431nomaximal, Sylow
121C22×C43—21no—
122C22×C43—21no—
123C22×C43—82no—
124C22×C43—82no—
125C22×C43—82no—
126C22×C43—161no—
127C22×C43—161no—
128C22×C43—161no—
129C22×C43—161no—
130C22×C43#44711yescharacteristic
131C22×C43C2×D1611yescharacteristic
132C22×C43#50911yescharacteristic
133C2×D43—82no—
134C2×D43—82no—
135C2×D43—82no—
136C4×C43—21no—
137C4×C43—22no—
138C4×C43—41no—
139C4×C43—161no—
140C4×C43#45411yescharacteristic
141C4×C43B(4,𝔽2)11yescharacteristic
142Dic43—82no—
143#3245—431no—
144#2184—432no—
145#2054D4311yescharacteristic, complemented
146#1347—432no—
147#1322—431no—
148C2×C43—21no—
149C2×C43—21no—
150C2×C43—162no—
151C2×C43#159811yescharacteristic
152C2×C43#218411yescharacteristic
153C2×C43#219011yescharacteristic
154D43—162no—
155C22×D8C2×D4311yescharacteristic
156#532—861no—
157C2×D16—862no—
158#474—862no—
159#466—432no—
160#466—861no—
161#459—862no—
162C2×C4⋊C8C2×D4311yescharacteristic
163C2×#102—21no—
164#390—21no—
165#357—862no—
166C22⋊C16—432no—
167#340C2×D4311yescharacteristic
168C43#1215811yescharacteristic, complemented, Sylow
169C2×#41—1721no—
170C22×D4—21no—
171C2×D8—22no—
172C2×D8—42no—
173C2×D8—432no—
174C2×D8—861no—
175C22×C8C22⋊D4311yescharacteristic
176C22×C8C22×D4311yescharacteristic
177C4⋊Q8—861no—
178#127—861no—
179#124—1721no—
180#121—862no—
181#121—1721no—
182C4×D4—862no—
183C4×D4—1721no—
184C2×C4⋊C4—21no—
185C2×C22⋊C4—41no—
186C2×C22⋊C4—41no—
187C2×C42C22⋊D4311yescharacteristic
188D16—1724no—
189C2×C16—862no—
190#107—432no—
191#107—861no—
192C4⋊C8—22no—
193#102—42no—
194#102—862no—
195#102—862no—
196C24—41no—
197#41—3442no—
198#41—3442no—
199C2×Q8—1721no—
200C2×D4—22no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4—41no—
205C2×D4—41no—
206C2×D4—862no—
207C2×D4—1721no—
208C2×D4—1721no—
209C2×D4—1722no—
210C22×C4—41no—
211C22×C4—1722no—
212C22×C4#1062188211yescharacteristic
213C22×C4#1062188211yescharacteristic
214C22×C4C2×C22⋊D4311yescharacteristic
215D8—24no—
216D8—42no—
217D8—3441no—
218D8—1722no—
219C2×C8—21no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8D4×D4312yes—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—862no—
226C4⋊C4—1721no—
227C22⋊C4—82no—
228C22⋊C4—82no—
229C22⋊C4—1722no—
230C22⋊C4—1722no—
231C42—21no—
232C42—21no—
233C16—1722no—
234C23—42no—
235C23—81no—
236C23—81no—
237C23—81no—
238C23—81no—
239C23—81no—
240C23—81no—
241C23—1722no—
242C23C2×#1062188211yescharacteristic
243Q8—3442no—
244D4—42no—
245D4—42no—
246D4—81no—
247D4—81no—
248D4—3442no—
249D4—3442no—
250D4—3442no—
251D4—3442no—
252D4—1722no—
253D4—1722no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—3444no—
264C2×C4—1722no—
265C2×C4#1306326612yescomplemented
266C2×C4#1306329311yescharacteristic
267C2×C4#1306335011yescharacteristic
268C8—22no—
269C8—41no—
270C22—21no—
271C22—21no—
272C22—82no—
273C22—82no—
274C22—82no—
275C22—161no—
276C22—161no—
277C22—161no—
278C22—161no—
279C22—3442no—
280C22—3442no—
281C22—3442no—
282C22#1458303211yescharacteristic
283C22C2×#1306326611yescharacteristic
284C22#1458333411yescharacteristic
285C4—21no—
286C4—22no—
287C4—41no—
288C4—161no—
289C4—3442no—
290C4#1458307111yescharacteristic
291C4#1458308511yescharacteristic
292C2—21no—
293C2—21no—
294C2—162no—
295C2—6882no—
296C2#1913352911yescharacteristic
297C2#1913650611yescharacteristic
298C2#1913654011yescharacteristic
subgroupG/H
centerC22#14583032
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#2054C2
socleC22×C43#447
hypercenter#2054D43
hypocenterC43#12158
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2054

Complements

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

NH ≅ G/Ntype
1. #19145905C2semidirect
2. #19136507C2semidirect
3. #19132603C2semidirect
4. #19132535C2semidirect
5. C43×#2054C2semidirect
106. C2×C4×C43D16semidirect
145. #2054D43semidirect
168. C43#12158semidirect
265. C2×C4#13063266semidirect

Maximal subgroups

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

subgroupindex
#191459052
#191365072
#191326032
#191325352
C43×#20542
#1215843