Finite Group Databasebeta

← #24991649

Subgroups — #24991649

Order 11008.

616 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 127 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×#14582829C211yesmaximal, characteristic
2#19137198C211yesmaximal, characteristic
3#19134682C212yesmaximal
4#19132475C212yesmaximal
5C2×C43×#324C211yesmaximal, characteristic
6C22×C4⋊Dic43C2211yescharacteristic
7C22×Dic43⋊C4—21no—
8#14582829—22no—
9#14582829C414yescomplemented
10#14582785—24no—
11#14582762—21no—
12#14582759C2212yes—
13C4×C22⋊Dic43—21no—
14C2×C43⋊#95—21no—
15C2×C43⋊#95C2211yescharacteristic
16#14582662—24no—
17C22×C4⋊C4×C43C2211yescharacteristic
18C2×C22⋊C8×C43C2212yes—
19C43×#324—22no—
20C23×Dic43—21no—
21C23×Dic43—21no—
22C2×C4⋊Dic43—22no—
23C2×C4⋊Dic43—22no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43C2×C412yes—
26C2×C4⋊Dic43D414yes—
27C2×Dic43⋊C4—24no—
28C2×Dic43⋊C4—44no—
29C2×C22⋊Dic43—22no—
30C2×C4×Dic43—22no—
31C43⋊#95—22no—
32C43⋊#95—24no—
33C43⋊#95—24no—
34C43⋊#95—22no—
35C43⋊#95—21no—
36C43⋊#95C2×C412yes—
37C23×C4×C43D411yescharacteristic
38C23×C4×C43D411yescharacteristic
39C23×C4×C43C2311yescharacteristic
40C22×C8×C43—22no—
41C2×C4⋊C4×C43—22no—
42C2×C4⋊C4×C43—22no—
43C2×C4⋊C4×C43C2×C412yes—
44C2×C4⋊C4×C43D412yes—
45C22⋊C8×C43—22no—
46C22⋊C8×C43—22no—
47C24×C43C2×D411yescharacteristic
48C22×C4×C43—21no—
49C22×C4×C43—21no—
50C22×C4×C43—21no—
51C22×C4×C43—21no—
52C22×C4×C43—22no—
53C22×C4×C43—22no—
54C22×C4×C43—42no—
55C22×C4×C43—42no—
56C22×C4×C43C22⋊C412yes—
57C22×C4×C43C22⋊C412yes—
58C22×C4×C43C22×C411yescharacteristic
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D412yes—
61C22×C4×C43#4112yes—
62C22×Dic43—24no—
63C22×Dic43—22no—
64C22×Dic43—22no—
65C22×Dic43—24no—
66C22×Dic43—42no—
67C22×Dic43—41no—
68C22×Dic43—41no—
69C22×Dic43—42no—
70C22×Dic43—42no—
71C22×Dic43—42no—
72C2×C8×C43—44no—
73C2×C8×C43—42no—
74C4⋊C4×C43—24no—
75C4⋊C4×C43—24no—
76C22⋊Dic43—42no—
77C22⋊Dic43—42no—
78C4⋊Dic43—24no—
79C4⋊Dic43—42no—
80C4⋊Dic43—44no—
81Dic43⋊C4—48no—
82C4×Dic43—82no—
83C23×C43—22no—
84C23×C43—22no—
85C23×C43C2×C22⋊C411yescharacteristic
86C23×C43#12011yescharacteristic
87C23×C43#12311yescharacteristic
88C23×C43#13512yes—
89C23×C43AGL(1,ℤ/8)12yes—
90C2×C4×C43—24no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—41no—
96C2×C4×C43—41no—
97C2×C4×C43—42no—
98C2×C4×C43—42no—
99C2×C4×C43—42no—
100C2×C4×C43—42no—
101C2×C4×C43—42no—
102C2×C4×C43—81no—
103C2×C4×C43C4×D412yes—
104C2×C4×C43#12112yes—
105C2×Dic43—24no—
106C2×Dic43—48no—
107C2×Dic43—42no—
108C2×Dic43—42no—
109C2×Dic43—42no—
110C2×Dic43—42no—
111C2×Dic43—42no—
112C2×Dic43—44no—
113C2×Dic43—44no—
114C2×Dic43—44no—
115C2×Dic43—82no—
116C2×Dic43—82no—
117C8×C43—82no—
118#9026—431nomaximal, Sylow
119C22×C43—24no—
120C22×C43—24no—
121C22×C43—21no—
122C22×C43—21no—
123C22×C43—21no—
124C22×C43—21no—
125C22×C43#38611yescharacteristic
126C22×C43#41611yescharacteristic
127C22×C43#41811yescharacteristic
128C22×C43#44912yes—
129C22×C43#45612yes—
130C22×C43#45812yes—
131C22×C43#48212yes—
132C4×C43—22no—
133C4×C43—22no—
134C4×C43—42no—
135C4×C43—42no—
136Dic43—44no—
137Dic43—84no—
138Dic43—82no—
139C2×#398—431no—
140#2313—431no—
141#1823—432no—
142C2×#324D4311yescharacteristic
143#1294—432no—
144C2×C43—21no—
145C2×C43—21no—
146C2×C43—22no—
147C2×C43#160914yes—
148C2×C43#187511yescharacteristic
149C2×C43#188611yescharacteristic
150C2×C43#189011yescharacteristic
151C22×C4⋊C4—431no—
152C22×C4⋊C4—861no—
153C22×C4⋊C4C2×D4311yescharacteristic
154C2×C22⋊C8C2×D4312yes—
155#398—434no—
156#398—862no—
157#387—864no—
158#381—861no—
159#380—432no—
160C4×C22⋊C4—861no—
161C2×#95—431no—
162C2×#95—861no—
163#340—864no—
164#324—22no—
165C43#902611yescharacteristic, complemented, Sylow
166C23×C4—861no—
167C23×C4—861no—
168C23×C4D17211yescharacteristic
169C23×C4D17211yescharacteristic
170C23×C4C22×D4311yescharacteristic
171C22×C8—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—432no—
175C2×C4⋊C4—434no—
176C2×C4⋊C4—862no—
177C2×C4⋊C4—862no—
178C2×C4⋊C4—864no—
179C2×C4⋊C4—861no—
180C2×C4⋊C4—1724no—
181C2×C4⋊C4C4×D4312yes—
182C2×C4⋊C4C22⋊D4312yes—
183C2×C22⋊C4—862no—
184C2×C42—862no—
185C22⋊C8—22no—
186C22⋊C8—22no—
187#95—432no—
188#95—862no—
189#95—864no—
190#95—864no—
191#95—862no—
192#95—861no—
193C24C2×D17211yescharacteristic
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—21no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—864no—
203C22×C4—862no—
204C22×C4—862no—
205C22×C4—864no—
206C22×C4—1721no—
207C22×C4—1721no—
208C22×C4—1722no—
209C22×C4—1722no—
210C22×C4—1722no—
211C22×C4—1722no—
212C22×C4(C2×D43)⋊C412yes—
213C22×C4(C2×D43)⋊C412yes—
214C22×C4C2×C4×D4311yescharacteristic
215C22×C4D4×D4312yes—
216C22×C4#1062190012yes—
217C22×C4C2×C22⋊D4311yescharacteristic
218C2×C8—44no—
219C2×C8—42no—
220C4⋊C4—24no—
221C4⋊C4—24no—
222C4⋊C4—864no—
223C4⋊C4—1724no—
224C4⋊C4—1728no—
225C4⋊C4—1722no—
226C22⋊C4—1722no—
227C22⋊C4—1722no—
228C42—3442no—
229C23—22no—
230C23—22no—
231C23C2×(C2×D43)⋊C411yescharacteristic
232C23#1306329511yescharacteristic
233C23#1306330911yescharacteristic
234C23#1306334712yes—
235C23#1306335312yes—
236C2×C4—24no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—81no—
249C2×C4—864no—
250C2×C4—3442no—
251C2×C4—3442no—
252C2×C4—1724no—
253C2×C4—1724no—
254C2×C4—1724no—
255C2×C4—1722no—
256C2×C4—1722no—
257C2×C4—1722no—
258C2×C4—1722no—
259C2×C4—1728no—
260C2×C4—1722no—
261C2×C4(C22⋊D43)⋊C412yes—
262C2×C4#1306329712yes—
263C8—82no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—24no—
269C22—24no—
270C22#1458277611yescharacteristic
271C22#1458289611yescharacteristic
272C22#1458290511yescharacteristic
273C22#1458304612yes—
274C22#1458308412yes—
275C22#1458309012yes—
276C22#1458322412yes—
277C4—22no—
278C4—22no—
279C4—42no—
280C4—42no—
281C4—3444no—
282C4—3442no—
283C4—1724no—
284C2—21no—
285C2—21no—
286C2—22no—
287C2#1913359414yes—
288C2#1913491511yescharacteristic
289C2#1913498611yescharacteristic
290C2#1913500611yescharacteristic
subgroupG/H
centerC23#13063295
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#324C2
socleC23×C43#120
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenterC2×#324D43
hypocenterC43#9026
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
9. #14582829C4semidirect
165. C43#9026semidirect

Maximal subgroups

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

subgroupindex
C2×#145828292
#191371982
#191346822
#191324752
C2×C43×#3242
#902643