Finite Group Databasebeta

← #24997277

Subgroups — #24997277

Order 11008.

750 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 750 conjugacy classes of subgroups — too many to draw. Only its 87 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#19145395C211yesmaximal, characteristic
2C2×#14583038C212yesmaximal, complemented
3#19132956C212yesmaximal, complemented
4#19132482C211yesmaximal, characteristic, complemented
5C43×#1784C211yesmaximal, characteristic, complemented
6C22×#10621884—22no—
7C2×#13063299C2212yes—
8#14583218—22no—
9#14583152—22no—
10#14583038—24no—
11#14583038—24no—
12#14583035—22no—
13C2×#13063249—22no—
14C2×C22⋊(C43⋊C8)C2212yes—
15#14582622—24no—
16C23×Q8×C43C2211yescharacteristic
17C2×#101×C43—22no—
18C43×#407C2211yescharacteristic
19C43×#407C2211yescharacteristic
20C22×D172D412yes—
21C22×C22⋊D43—22no—
22C2×#10621884—28no—
23C2×#10621884—48no—
24C2×D344—22no—
25C22×C43⋊C8—22no—
26#13063299—22no—
27#13063299—22no—
28#13063299—22no—
29#13063299—22no—
30C2×C4⋊Dic43D412yes—
31C2×(C2×D43)⋊C4—22no—
32#13063257—22no—
33#13063249—28no—
34#13063247—24no—
35C22⋊(C43⋊C8)—22no—
36C22⋊(C43⋊C8)D414yes—
37C22×Q8×C43—21no—
38C22×Q8×C43—22no—
39C22×Q8×C43—22no—
40C22×Q8×C43—44no—
41C22×Q8×C43D412yes—
42C23×C4×C43—21no—
43C23×C4×C43C2311yescharacteristic
44C2×M16×C43—21no—
45C2×M16×C43D412yes—
46#101×C43—44no—
47C22⋊C8×C43—22no—
48C22⋊C8×C43—22no—
49C24×C43#4111yescharacteristic
50C23×D43—22no—
51C2×Q8×C43—24no—
52C2×Q8×C43—28no—
53C2×Q8×C43—24no—
54C2×Q8×C43—44no—
55C2×Q8×C43—44no—
56C2×Q8×C43—42no—
57C2×Q8×C43—48no—
58C2×Q8×C43—41no—
59C2×Q8×C43—41no—
60C22×C4×C43—22no—
61C22×C4×C43—42no—
62C22×C4×C43—44no—
63C22×C4×C43—42no—
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D412yes—
66C22×C4×C43C2×D412yes—
67C22×C4×C43C2×D411yescharacteristic
68C2×C22⋊D43—42no—
69C2×C22⋊D43—42no—
70C2×C22⋊D43—84no—
71C22×Dic43—22no—
72C2×D172—22no—
73C2×D172—22no—
74C2×D172—44no—
75M16×C43—42no—
76M16×C43—42no—
77C2×C8×C43—22no—
78C2×C8×C43—41no—
79#10621884—416no—
80(C2×D43)⋊C4—42no—
81(C2×D43)⋊C4—42no—
82C4⋊Dic43—22no—
83C4⋊Dic43—22no—
84C2×C43⋊C8—24no—
85C2×C43⋊C8—44no—
86D344—82no—
87C23×C43—24no—
88C23×C43—41no—
89C23×C43#12112yes—
90C23×C43#12111yescharacteristic
91C22×D43—42no—
92C22×D43—44no—
93C22×D43—82no—
94C22×D43—82no—
95Q8×C43—28no—
96Q8×C43—44no—
97Q8×C43—44no—
98Q8×C43—44no—
99C2×C4×C43—24no—
100C2×C4×C43—22no—
101C2×C4×C43—24no—
102C2×C4×C43—41no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—48no—
106C2×C4×C43—42no—
107C2×C4×C43#12011yescharacteristic
108C2×C4×C43#12012yes—
109C2×C4×C43#12711yescharacteristic
110C22⋊D43—84no—
111C22⋊D43—84no—
112C2×Dic43—42no—
113C2×Dic43—82no—
114D172—44no—
115D172—44no—
116C8×C43—42no—
117C8×C43—81no—
118C43⋊C8—44no—
119#9988—431nomaximal, Sylow
120C22×C43—22no—
121C22×C43—22no—
122C22×C43—22no—
123C22×C43—21no—
124C22×C43—44no—
125C22×C43#39211yescharacteristic
126C22×C43#47114yes—
127C2×D43—82no—
128C2×D43—82no—
129C2×D43—82no—
130C2×D43—164no—
131C4×C43—22no—
132C4×C43—21no—
133C4×C43—44no—
134C4×C43B(4,𝔽2)12yes—
135Dic43—82no—
136#3192—431no—
137C2×#448—432no—
138#1784D4311yescharacteristic, complemented
139#1471—432no—
140#1298—431no—
141C2×C43—24no—
142C2×C43—41no—
143C2×C43#201912yes—
144C2×C43#202111yescharacteristic
145D43—162no—
146C23×Q8C2×D4311yescharacteristic
147C22×SD16—862no—
148C2×#121—432no—
149#481—862no—
150#469—862no—
151#448—864no—
152#448—864no—
153#447—862no—
154C2×#103—862no—
155C2×#101—22no—
156#407C2×D4311yescharacteristic
157#407C2×D4311yescharacteristic
158C2×C22⋊C8—432no—
159#323—864no—
160C43#998811yescharacteristic, complemented, Sylow
161C22×Q8—21no—
162C22×Q8—22no—
163C22×Q8—22no—
164C22×Q8—44no—
165C22×Q8D17212yes—
166C22×D4—432no—
167C22×D4—862no—
168C23×C4—21no—
169C23×C4C22×D4311yescharacteristic
170C2×SD16—868no—
171C2×SD16—1728no—
172C2×D8—862no—
173C2×M16—21no—
174C2×M16C22⋊D4312yes—
175C22×C8—862no—
176#121—862no—
177#121—862no—
178#121—862no—
179#121—862no—
180C2×C4⋊C4—432no—
181C2×C22⋊C4—862no—
182#106—862no—
183#103—868no—
184#102—864no—
185#101—44no—
186C22⋊C8—22no—
187C22⋊C8—22no—
188C22⋊C8—434no—
189C22⋊C8—862no—
190C24—862no—
191C24#1062189811yescharacteristic
192C2×Q8—24no—
193C2×Q8—28no—
194C2×Q8—24no—
195C2×Q8—44no—
196C2×Q8—44no—
197C2×Q8—42no—
198C2×Q8—48no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×D4—862no—
202C2×D4—862no—
203C2×D4—3444no—
204C2×D4—1724no—
205C2×D4—1722no—
206C2×D4—1722no—
207C22×C4—22no—
208C22×C4—42no—
209C22×C4—44no—
210C22×C4—42no—
211C22×C4—862no—
212C22×C4C2×D17211yescharacteristic
213C22×C4D4×D4312yes—
214C22×C4D4×D4312yes—
215C22×C4C2×C22⋊D4311yescharacteristic
216SD16—17216no—
217D8—3442no—
218M16—42no—
219M16—42no—
220C2×C8—22no—
221C2×C8—41no—
222C2×C8—864no—
223C2×C8—1724no—
224C4⋊C4—862no—
225C4⋊C4—862no—
226C22⋊C4—1722no—
227C22⋊C4—1722no—
228C23—24no—
229C23—41no—
230C23—3442no—
231C23—3442no—
232C23—1722no—
233C23—1724no—
234C23#1306329812yes—
235C23#1306329911yescharacteristic
236Q8—28no—
237Q8—44no—
238Q8—44no—
239Q8—44no—
240D4—3444no—
241D4—3444no—
242D4—1724no—
243D4—1724no—
244C2×C4—24no—
245C2×C4—22no—
246C2×C4—24no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—48no—
251C2×C4—42no—
252C2×C4—3442no—
253C2×C4—1722no—
254C2×C4#1306329311yescharacteristic
255C2×C4#1306329512yes—
256C2×C4#1306332111yescharacteristic
257C8—42no—
258C8—81no—
259C8—1724no—
260C22—22no—
261C22—22no—
262C22—22no—
263C22—21no—
264C22—44no—
265C22—3442no—
266C22—3442no—
267C22—3442no—
268C22—6884no—
269C22#1458280811yescharacteristic
270C22#1458316514yes—
271C4—21no—
272C4—22no—
273C4—44no—
274C4—3442no—
275C4#1458308512yes—
276C2—24no—
277C2—41no—
278C2—6882no—
279C2#1913570812yes—
280C2#1913572111yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1784C2
socleC22×C43#392
prime radical#19145395C2
hypercenter#1784D43
hypocenterC43#9988
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1784

Complements

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

NH ≅ G/Ntype
2. C2×#14583038C2semidirect
3. #19132956C2semidirect
4. #19132482C2semidirect
5. C43×#1784C2semidirect
138. #1784D43semidirect
160. C43#9988semidirect

Maximal subgroups

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

subgroupindex
#191453952
C2×#145830382
#191329562
#191324822
C43×#17842
#998843