Finite Group Databasebeta

← #24997921

Subgroups — #24997921

Order 11008.

600 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#14583258C212yesmaximal, complemented
2#19135414C211yesmaximal, characteristic, complemented
3C2×#14582639C212yesmaximal, complemented
4#19132476C211yesmaximal, characteristic, complemented
5C43×#2819C211yesmaximal, characteristic
6C2×#13063325C2211yescharacteristic
7#14583258—24no—
8#14583258—24no—
9C2×#13063249—22no—
10C2×#13063248—22no—
11C2×#13063246—22no—
12C2×#13063236C2211yescharacteristic
13C2×#13063236C2212yes—
14#14582639—24no—
15C2×#124×C43C2212yes—
16C43×#394—22no—
17C43×#393—22no—
18C43×#392—22no—
19C43×#382C2211yescharacteristic
20C22×Dic86—21no—
21C22×C43⋊C8—22no—
22C22×C43⋊C8—21no—
23#13063325—22no—
24#13063325—21no—
25#13063325D412yescomplemented
26C2×C4⋊Dic43—22no—
27#13063249—28no—
28#13063248—44no—
29#13063246—28no—
30#13063236—22no—
31#13063236—22no—
32#13063236D414yescomplemented
33C22×Q8×C43D412yes—
34C22×D4×C43—22no—
35C22×D4×C43D412yes—
36#124×C43—22no—
37#124×C43—22no—
38#124×C43—22no—
39#124×C43—22no—
40C2×C4⋊C4×C43D412yes—
41C2×C22⋊C4×C43—22no—
42C2×C22⋊C4×C43—22no—
43C2×C22⋊C4×C43—24no—
44C2×C42×C43C2311yescharacteristic
45#95×C43—22no—
46#95×C43—22no—
47C24×C43—22no—
48C2×Q8×C43—22no—
49C2×Q8×C43—22no—
50C2×Q8×C43—44no—
51C2×D4×C43—22no—
52C2×D4×C43—22no—
53C2×D4×C43—44no—
54C2×D4×C43—82no—
55C2×D4×C43—84no—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43C2×D412yes—
59C22×C4×C43C2×D411yescharacteristic
60C22×Dic43—41no—
61C2×Dic86—22no—
62C2×Dic86—42no—
63C2×Dic86—42no—
64C2×Dic86—41no—
65C4⋊C4×C43—42no—
66C22⋊C4×C43—42no—
67C22⋊C4×C43—42no—
68C22⋊C4×C43—42no—
69C22⋊C4×C43—42no—
70C22⋊C4×C43—84no—
71C42×C43C2×D411yescharacteristic
72C42×C43C2×D412yes—
73C42×C43#4111yescharacteristic
74C4⋊Dic43—24no—
75C4⋊Dic43—42no—
76C2×C43⋊C8—22no—
77C2×C43⋊C8—24no—
78C2×C43⋊C8—41no—
79C2×C43⋊C8—44no—
80C2×C43⋊C8—41no—
81C23×C43—42no—
82C23×C43—42no—
83C23×C43—42no—
84C23×C43—44no—
85C23×C43—44no—
86C23×C43#12011yescharacteristic
87Q8×C43—44no—
88Q8×C43—82no—
89D4×C43—44no—
90D4×C43—82no—
91D4×C43—88no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—24no—
95C2×C4×C43—42no—
96C2×C4×C43—42no—
97C2×C4×C43—44no—
98C2×C4×C43—44no—
99C2×C4×C43#12012yes—
100C2×C4×C43#12111yescharacteristic
101C2×C4×C43#12112yes—
102C2×C4×C43#12711yescharacteristic
103C2×Dic43—42no—
104C2×Dic43—81no—
105C2×Dic43—81no—
106Dic86—44no—
107Dic86—82no—
108C43⋊C8—44no—
109C43⋊C8—42no—
110#10085—431nomaximal, Sylow
111C22×C43—84no—
112C22×C43—84no—
113C22×C43—82no—
114C22×C43—82no—
115C22×C43—82no—
116C22×C43#39211yescharacteristic
117C22×C43#45311yescharacteristic
118C22×C43#45411yescharacteristic
119C22×C43#45514yes—
120C4×C43—22no—
121C4×C43—22no—
122C4×C43—21no—
123C4×C43—21no—
124C4×C43—82no—
125C4×C43—82no—
126Dic43—82no—
127C2×#489—432no—
128#2819D4311yescharacteristic
129#1960—431no—
130C2×#329—432no—
131#1295—431no—
132C2×C43—162no—
133C2×C43#165912yes—
134C2×C43#166212yes—
135C2×C43#200412yes—
136C2×C43#200611yescharacteristic
137C2×C4⋊Q8—431no—
138C2×#124C2×D4312yes—
139#489—864no—
140#489—864no—
141C2×#103—862no—
142C2×#103—862no—
143C2×#102—862no—
144C2×#97—432no—
145C2×#97—431no—
146#394—22no—
147#393—22no—
148#392—22no—
149#382C2×D4311yescharacteristic
150#329—864no—
151C43#1008511yescharacteristic, complemented, Sylow
152C22×Q8—861no—
153C22×Q8C22⋊D4312yes—
154C22×D4—22no—
155C22×D4C22⋊D4312yes—
156C22×C8—862no—
157C22×C8—861no—
158C4⋊Q8—432no—
159C4⋊Q8—862no—
160C4⋊Q8—861no—
161#124—22no—
162#124—22no—
163#124—22no—
164#124—22no—
165C2×C4⋊C4—862no—
166C2×C4⋊C4C22⋊D4312yes—
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—24no—
170C2×C42C22×D4311yescharacteristic
171#103—868no—
172#103—1724no—
173#102—868no—
174#97—434no—
175#97—862no—
176#97—862no—
177#95—22no—
178#95—22no—
179C24—22no—
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—44no—
183C2×Q8—862no—
184C2×Q8—1722no—
185C2×Q8—1722no—
186C2×Q8—1721no—
187C2×D4—22no—
188C2×D4—22no—
189C2×D4—44no—
190C2×D4—82no—
191C2×D4—84no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—1721no—
195C22×C4C2×C22⋊D4312yes—
196C22×C4C2×C22⋊D4311yescharacteristic
197C2×C8—862no—
198C2×C8—864no—
199C2×C8—1721no—
200C2×C8—1724no—
201C2×C8—1721no—
202C4⋊C4—42no—
203C4⋊C4—864no—
204C4⋊C4—1722no—
205C22⋊C4—42no—
206C22⋊C4—42no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C22⋊C4—84no—
210C42D4×D4311yescharacteristic
211C42D4×D4312yes—
212C42#1062190011yescharacteristic
213C23—42no—
214C23—42no—
215C23—42no—
216C23—44no—
217C23—44no—
218C23#1306329411yescharacteristic
219Q8—44no—
220Q8—82no—
221Q8—3442no—
222Q8—1724no—
223D4—44no—
224D4—82no—
225D4—88no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—24no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—44no—
232C2×C4—44no—
233C2×C4—3441no—
234C2×C4—3441no—
235C2×C4—1722no—
236C2×C4#1306329312yes—
237C2×C4#1306329611yescharacteristic
238C2×C4#1306329712yes—
239C2×C4#1306332111yescharacteristic
240C8—1724no—
241C8—1722no—
242C22—82no—
243C22—82no—
244C22—82no—
245C22—84no—
246C22—84no—
247C22#1458280711yescharacteristic
248C22#1458306711yescharacteristic
249C22#1458307211yescharacteristic
250C22#1458307714yes—
251C4—22no—
252C4—22no—
253C4—21no—
254C4—21no—
255C4—82no—
256C4—82no—
257C4—3442no—
258C2—162no—
259C2#1913390112yes—
260C2#1913391812yes—
261C2#1913562212yes—
262C2#1913563711yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#2819C2
socleC23×C43#120
hypercenter#2819D43
hypocenterC43#10085
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2819

Complements

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

NH ≅ G/Ntype
1. C2×#14583258C2semidirect
2. #19135414C2semidirect
3. C2×#14582639C2semidirect
4. #19132476C2semidirect
25. #13063325D4semidirect
32. #13063236D4semidirect
151. C43#10085semidirect

Maximal subgroups

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

subgroupindex
C2×#145832582
#191354142
C2×#145826392
#191324762
C43×#28192
#1008543