Finite Group Databasebeta

← #25008655

Subgroups — #25008655

Order 11008.

458 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135726C211yesmaximal, characteristic
2#19133580C212yesmaximal
3#19132595C212yesmaximal, complemented
4#19132525C211yesmaximal, characteristic, complemented
5C43×#2817C211yesmaximal, characteristic, complemented
6#14583461C2211yescharacteristic
7C2×#13063308—21no—
8#14583212—22no—
9C2×#13063239—21no—
10#14582666C2211yescharacteristic
11#14582632—22no—
12#14582623C2212yes—
13C2×C22⋊Q8×C43—21no—
14C43×#400—22no—
15C43×#397—21no—
16C43×#397C2212yes—
17C43×#395—22no—
18C43×#381C2211yescharacteristic
19C22×C22⋊D43—21no—
20#13063309—41no—
21#13063308—42no—
22#13063308—42no—
23#13063299—22no—
24#13063295—41no—
25C2×Dic43⋊C4—41no—
26C2×C22⋊Dic43—21no—
27C2×(C2×D43)⋊C4—41no—
28#13063258—42no—
29#13063245—42no—
30#13063239—42no—
31C22⋊(C43⋊C8)—22no—
32C22×Q8×C43—21no—
33C23×C4×C43D411yescharacteristic
34C22⋊Q8×C43—42no—
35C22⋊Q8×C43—42no—
36C2×C4⋊C4×C43—22no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43D412yes—
40C2×C22⋊C4×C43—22no—
41C2×C22⋊C4×C43D411yescharacteristic
42C2×C22⋊C4×C43C2311yescharacteristic
43#95×C43—22no—
44#95×C43—21no—
45#95×C43—22no—
46#95×C43—22no—
47#95×C43D412yes—
48C24×C43C2×D411yescharacteristic
49C23×D43—21no—
50C2×Q8×C43—42no—
51C2×Q8×C43—81no—
52C2×Q8×C43—81no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—22no—
56C22×C4×C43—22no—
57C22×C4×C43—21no—
58C22×C4×C43—41no—
59C22×C4×C43—41no—
60C22×C4×C43D812yes—
61C22×C4×C43C2×D412yes—
62C2×C22⋊D43—41no—
63C2×C22⋊D43—41no—
64C2×C22⋊D43—41no—
65C2×C22⋊D43—41no—
66C2×C22⋊D43—41no—
67C2×C22⋊D43—41no—
68C22×Dic43—21no—
69C22×Dic43—41no—
70C2×D172—22no—
71C4⋊C4×C43—42no—
72C4⋊C4×C43—42no—
73C4⋊C4×C43—44no—
74C4⋊C4×C43—81no—
75C22⋊C4×C43—41no—
76C22⋊C4×C43—41no—
77C22⋊C4×C43—42no—
78C22⋊C4×C43—42no—
79C22⋊Dic43—22no—
80C22⋊Dic43—41no—
81(C2×D43)⋊C4—42no—
82(C2×D43)⋊C4—44no—
83C4⋊Dic43—22no—
84Dic43⋊C4—44no—
85C2×C43⋊C8—42no—
86C23×C43—21no—
87C23×C43—21no—
88C23×C43—42no—
89C23×C43#12011yescharacteristic
90C23×C43C2×D811yescharacteristic
91C23×C43AGL(1,ℤ/8)11yescharacteristic
92C22×D43—41no—
93C22×D43—41no—
94C22×D43—41no—
95C22×D43—82no—
96Q8×C43—84no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—41no—
100C2×C4×C43—41no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43—42no—
104C2×C4×C43—44no—
105C2×C4×C43—42no—
106C2×C4×C43—42no—
107C2×C4×C43—41no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43—81no—
111C22⋊D43—81no—
112C22⋊D43—81no—
113C22⋊D43—81no—
114C22⋊D43—81no—
115C2×Dic43—41no—
116C2×Dic43—42no—
117C2×Dic43—41no—
118C2×Dic43—41no—
119C2×Dic43—82no—
120D172—82no—
121C43⋊C8—82no—
122#12095—431nomaximal, Sylow
123C22×C43—22no—
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—41no—
127C22×C43—41no—
128C22×C43—42no—
129C22×C43—81no—
130C22×C43#44711yescharacteristic
131C22×C43#45311yescharacteristic
132C22×C43B(4,𝔽2)11yescharacteristic
133C2×D43—82no—
134C2×D43—81no—
135C2×D43—82no—
136C2×D43—161no—
137C4×C43—42no—
138C4×C43—42no—
139C4×C43—82no—
140C4×C43—81no—
141C4×C43—82no—
142Dic43—82no—
143Dic43—81no—
144#2817D4311yescharacteristic, complemented
145#2022—431no—
146#1607—432no—
147#1344—432no—
148#1317—431no—
149C2×C43—21no—
150C2×C43—21no—
151C2×C43—41no—
152C2×C43—41no—
153C2×C43#159511yescharacteristic
154C2×C43#220112yes—
155D43—161no—
156#534—431no—
157C2×#123—861no—
158C2×C22⋊Q8—21no—
159#480—862no—
160C2×#99—861no—
161#400—22no—
162#397—21no—
163#397C2×D4312yes—
164#395—22no—
165#381C2×D4311yescharacteristic
166#342—431no—
167#327—862no—
168#323—432no—
169C43#1209511yescharacteristic, complemented, Sylow
170C22×Q8—21no—
171C22×D4—861no—
172C23×C4C22⋊D4311yescharacteristic
173#123—1721no—
174#123—1722no—
175#123—1722no—
176C22⋊Q8—42no—
177C22⋊Q8—42no—
178#121—862no—
179#120—1721no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—1721no—
184C2×C4⋊C4C22⋊D4312yes—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—861no—
187C2×C22⋊C4—1721no—
188C2×C22⋊C4C22⋊D4311yescharacteristic
189C2×C22⋊C4C22×D4311yescharacteristic
190#107—1722no—
191#102—1722no—
192#99—1722no—
193C22⋊C8—862no—
194#95—22no—
195#95—21no—
196#95—22no—
197#95—22no—
198#95C22⋊D4312yes—
199C24—861no—
200C24C2×C22⋊D4311yescharacteristic
201C2×Q8—42no—
202C2×Q8—81no—
203C2×Q8—81no—
204C2×D4—862no—
205C2×D4—1721no—
206C2×D4—1721no—
207C2×D4—1721no—
208C2×D4—1721no—
209C2×D4—1721no—
210C2×D4—1721no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—861no—
219C22×C4—1721no—
220C22×C4#1062188212yes—
221C22×C4C2×C22⋊D4312yes—
222C2×C8—1722no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—44no—
226C4⋊C4—81no—
227C4⋊C4—862no—
228C4⋊C4—1724no—
229C22⋊C4—41no—
230C22⋊C4—42no—
231C22⋊C4—42no—
232C22⋊C4—41no—
233C22⋊C4—862no—
234C22⋊C4—1722no—
235C22⋊C4—1724no—
236C22⋊C4—1721no—
237C23—21no—
238C23—21no—
239C23—42no—
240C23—3442no—
241C23—1721no—
242C23—1721no—
243C23—1721no—
244C23#1306329411yescharacteristic
245C23C2×#1062188211yescharacteristic
246C23#1306335111yescharacteristic
247Q8—84no—
248D4—3442no—
249D4—3441no—
250D4—3441no—
251D4—3441no—
252D4—3441no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—44no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—81no—
267C2×C4—3442no—
268C2×C4—1722no—
269C2×C4—1721no—
270C2×C4—1721no—
271C2×C4—1721no—
272C8—3442no—
273C22—22no—
274C22—21no—
275C22—21no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—81no—
280C22—3442no—
281C22—3441no—
282C22—3442no—
283C22—6881no—
284C22#1458303311yescharacteristic
285C22#1458306711yescharacteristic
286C22#1458308611yescharacteristic
287C4—42no—
288C4—42no—
289C4—82no—
290C4—81no—
291C4—82no—
292C4—3442no—
293C4—3441no—
294C2—21no—
295C2—21no—
296C2—41no—
297C2—41no—
298C2—6881no—
299C2#1913351311yescharacteristic
300C2#1913660812yes—
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2817C2
socleC22×C43B(4,𝔽2)
prime radical#14583461C22
hypercenter#2817D43
hypocenterC43#12095
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2817

Complements

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

NH ≅ G/Ntype
3. #19132595C2semidirect
4. #19132525C2semidirect
5. C43×#2817C2semidirect
144. #2817D43semidirect
169. C43#12095semidirect

Maximal subgroups

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

subgroupindex
#191357262
#191335802
#191325952
#191325252
C43×#28172
#1209543