Finite Group Databasebeta

← #25009038

Subgroups — #25009038

Order 11008.

434 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 71 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#19136506C212yesmaximal, complemented
2#19135906C211yesmaximal, characteristic, complemented
3#19132604C212yesmaximal, complemented
4#19132535C211yesmaximal, characteristic, complemented
5C43×#3245C211yesmaximal, characteristic, complemented
6C22×D344C2211yescharacteristic
7C2×#13063266—22no—
8C2×#13063247—21no—
9#14582801—21no—
10#14582699—22no—
11C22⋊(C43⋊C16)C2212yes—
12#14582662C2211yescharacteristic
13C43×#532—21no—
14C43×#474—22no—
15C43×#466—21no—
16C43×#466C2212yes—
17C43×#459—22no—
18C2×C4⋊C8×C43C2211yescharacteristic
19C22×D172—21no—
20C2×D344—22no—
21C2×D344—42no—
22C2×C4⋊Dic43—21no—
23C2×(C2×D43)⋊C4—41no—
24C2×(C2×D43)⋊C4—41no—
25#13063266—44no—
26C2×C43⋊C16—22no—
27#13063247—42no—
28C2×#41×C43—41no—
29C2×D8×C43—21no—
30C2×D8×C43D412yes—
31C22×C8×C43D411yescharacteristic
32C22×C8×C43C2311yescharacteristic
33C4⋊Q8×C43—21no—
34#127×C43—21no—
35#124×C43—41no—
36#121×C43—22no—
37#121×C43—41no—
38C4×D4×C43—22no—
39C4×D4×C43—41no—
40C2×C42×C43D411yescharacteristic
41#107×C43—21no—
42#107×C43D412yes—
43C4⋊C8×C43—22no—
44#102×C43—22no—
45#102×C43—22no—
46C23×D43—41no—
47#41×C43—82no—
48#41×C43—82no—
49C2×Q8×C43—41no—
50C2×D4×C43—22no—
51C2×D4×C43—41no—
52C2×D4×C43—41no—
53C2×D4×C43—42no—
54C22×C4×C43—42no—
55C22×C4×C43D811yescharacteristic
56C22×C4×C43D811yescharacteristic
57C22×C4×C43C2×D411yescharacteristic
58C22×Dic43—41no—
59C2×D172—22no—
60C2×D172—41no—
61C2×D172—41no—
62C2×D172—41no—
63C2×D172—41no—
64C2×D172—41no—
65D8×C43—42no—
66D8×C43—81no—
67C2×C8×C43—21no—
68C2×C8×C43—41no—
69C2×C8×C43—41no—
70C2×C8×C43C2×D412yes—
71C4⋊C4×C43—22no—
72C4⋊C4×C43—41no—
73C22⋊C4×C43—42no—
74C22⋊C4×C43—42no—
75C42×C43—21no—
76C42×C43—21no—
77(C2×D43)⋊C4—82no—
78(C2×D43)⋊C4—82no—
79C4⋊Dic43—41no—
80C4⋊Dic43—41no—
81D344—24no—
82D344—42no—
83C43⋊C16—42no—
84C23×C43—42no—
85C23×C43C2×D811yescharacteristic
86C22×D43—42no—
87C22×D43—81no—
88C22×D43—81no—
89C22×D43—81no—
90C22×D43—81no—
91C22×D43—81no—
92C22×D43—81no—
93Q8×C43—82no—
94D4×C43—42no—
95D4×C43—42no—
96D4×C43—82no—
97D4×C43—82no—
98D4×C43—82no—
99D4×C43—82no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—41no—
106C2×C4×C43—42no—
107C2×C4×C43—84no—
108C2×C4×C43D1612yescomplemented
109C2×C4×C43#12011yescharacteristic
110C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
111C2×Dic43—81no—
112C2×Dic43—81no—
113C2×Dic43—81no—
114D172—42no—
115D172—42no—
116D172—81no—
117D172—81no—
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#44711yescharacteristic
127C22×C43C2×D1611yescharacteristic
128C22×C43#50911yescharacteristic
129C2×D43—82no—
130C2×D43—82no—
131C2×D43—82no—
132C2×D43—161no—
133C2×D43—161no—
134C2×D43—161no—
135C2×D43—161no—
136C4×C43—21no—
137C4×C43—22no—
138C4×C43—41no—
139C4×C43—82no—
140C4×C43#45411yescharacteristic
141C4×C43B(4,𝔽2)11yescharacteristic
142Dic43—161no—
143#3245D4311yescharacteristic, complemented
144#2184—432no—
145#2054—431no—
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×D8—431no—
156#532—21no—
157C2×D16—862no—
158#474—22no—
159#466—21no—
160#466C2×D4312yes—
161#459—22no—
162C2×C4⋊C8C2×D4311yescharacteristic
163C2×#102—861no—
164#390—861no—
165#357—862no—
166C22⋊C16—432no—
167#340—431no—
168C43#1215811yescharacteristic, complemented, Sylow
169C2×#41—41no—
170C22×D4—861no—
171C2×D8—21no—
172C2×D8—862no—
173C2×D8—1722no—
174C2×D8C22⋊D4312yes—
175C22×C8C22⋊D4311yescharacteristic
176C22×C8C22×D4311yescharacteristic
177C4⋊Q8—21no—
178#127—21no—
179#124—41no—
180#121—22no—
181#121—41no—
182C4×D4—22no—
183C4×D4—41no—
184C2×C4⋊C4—861no—
185C2×C22⋊C4—1721no—
186C2×C22⋊C4—1721no—
187C2×C42C22⋊D4311yescharacteristic
188D16—1724no—
189C2×C16—862no—
190#107—21no—
191#107C22⋊D4312yes—
192C4⋊C8—22no—
193#102—22no—
194#102—22no—
195#102—1722no—
196C24—1721no—
197#41—82no—
198#41—82no—
199C2×Q8—41no—
200C2×D4—22no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4—42no—
204C2×D4—862no—
205C2×D4—1721no—
206C2×D4—1721no—
207C2×D4—1721no—
208C2×D4—1721no—
209C2×D4—1721no—
210C22×C4—42no—
211C22×C4—1721no—
212C22×C4#1062188211yescharacteristic
213C22×C4#1062188211yescharacteristic
214C22×C4C2×C22⋊D4311yescharacteristic
215D8—42no—
216D8—81no—
217D8—864no—
218D8—1722no—
219C2×C8—21no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8C2×C22⋊D4312yes—
223C4⋊C4—22no—
224C4⋊C4—41no—
225C4⋊C4—1721no—
226C4⋊C4—1721no—
227C22⋊C4—42no—
228C22⋊C4—42no—
229C22⋊C4—3442no—
230C22⋊C4—3442no—
231C42—21no—
232C42—21no—
233C16—1722no—
234C23—42no—
235C23—3441no—
236C23—3441no—
237C23—3441no—
238C23—3441no—
239C23—3441no—
240C23—3441no—
241C23—1722no—
242C23C2×#1062188211yescharacteristic
243Q8—82no—
244D4—42no—
245D4—42no—
246D4—82no—
247D4—82no—
248D4—82no—
249D4—82no—
250D4—3441no—
251D4—3441no—
252D4—1722no—
253D4—1722no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—84no—
262C2×C4—3441no—
263C2×C4—3441no—
264C2×C4—3441no—
265C2×C4#1306326612yescomplemented
266C2×C4#1306329411yescharacteristic
267C2×C4#1306335111yescharacteristic
268C8—22no—
269C8—41no—
270C22—21no—
271C22—21no—
272C22—82no—
273C22—82no—
274C22—82no—
275C22—3442no—
276C22—3442no—
277C22—3442no—
278C22—6881no—
279C22—6881no—
280C22—6881no—
281C22—6881no—
282C22#1458303311yescharacteristic
283C22C2×#1306326611yescharacteristic
284C22#1458333511yescharacteristic
285C4—21no—
286C4—22no—
287C4—41no—
288C4—82no—
289C4—6881no—
290C4#1458307211yescharacteristic
291C4#1458308611yescharacteristic
292C2—21no—
293C2—21no—
294C2—162no—
295C2—6882no—
296C2#1913353011yescharacteristic
297C2#1913650711yescharacteristic
298C2#1913654111yescharacteristic
subgroupG/H
centerC22#14583033
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#3245C2
socleC22×C43#447
hypercenter#3245D43
hypocenterC43#12158
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #19136506C2semidirect
2. #19135906C2semidirect
3. #19132604C2semidirect
4. #19132535C2semidirect
5. C43×#3245C2semidirect
108. C2×C4×C43D16semidirect
143. #3245D43semidirect
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
#191365062
#191359062
#191326042
#191325352
C43×#32452
#1215843