Finite Group Databasebeta

← #24992625

Subgroups — #24992625

Order 11008.

478 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 115 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#19140361C211yesmaximal, characteristic
2#19133268C212yesmaximal, complemented
3#19132909C211yesmaximal, characteristic
4#19132455C212yesmaximal, complemented
5C43×#2921C211yesmaximal, characteristic
6C2×#13063325C2211yescharacteristic
7C2×#13063304—21no—
8#14582952C2212yes—
9#14582829—21no—
10#14582829C412yes—
11#14582824—21no—
12#14582824C412yes—
13#14582805—21no—
14#14582765C2211yescharacteristic
15#14582646—24no—
16#14582625—21no—
17#14582623—21no—
18C2×#117×C43C2211yescharacteristic
19C43×#433—24no—
20C43×#423C2212yes—
21C43×#407—21no—
22C4×M16×C43—21no—
23C22×Dic86—21no—
24#13063325—22no—
25#13063325—22no—
26#13063304—44no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43C2×C412yes—
30C2×Dic43⋊C4—22no—
31C2×C22⋊Dic43—22no—
32C4⋊(C43⋊C8)—22no—
33C22⋊(C43⋊C8)—22no—
34C4×C43⋊C8—22no—
35C43⋊#95—22no—
36C43⋊#95—22no—
37C43⋊#95—21no—
38C43⋊#95C2×C412yes—
39C23×C4×C43D411yescharacteristic
40C2×M16×C43—22no—
41#117×C43—22no—
42#117×C43—22no—
43C2×C4⋊C4×C43C2×C411yescharacteristic
44C2×C4⋊C4×C43D411yescharacteristic
45C2×C22⋊C4×C43C2×C411yescharacteristic
46C2×C22⋊C4×C43D411yescharacteristic
47C2×C42×C43D411yescharacteristic
48C2×C42×C43C2311yescharacteristic
49C4⋊C8×C43—22no—
50C4⋊C8×C43D414yes—
51C22⋊C8×C43—24no—
52#97×C43—22no—
53C4×C8×C43—22no—
54C24×C43C22⋊C411yescharacteristic
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—22no—
58C22×C4×C43—22no—
59C22×C4×C43C22⋊C411yescharacteristic
60C22×C4×C43C22⋊C411yescharacteristic
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×Dic43—22no—
66C22×Dic43—22no—
67C2×Dic86—41no—
68C2×Dic86—41no—
69C2×Dic86—42no—
70C2×Dic86—42no—
71M16×C43—42no—
72M16×C43—42no—
73C2×C8×C43—24no—
74C4⋊C4×C43—22no—
75C4⋊C4×C43—22no—
76C22⋊C4×C43—22no—
77C22⋊C4×C43—22no—
78C42×C43—21no—
79C42×C43—21no—
80C42×C43C2×D412yes—
81C42×C43#4112yes—
82C22⋊Dic43—44no—
83C4⋊Dic43—24no—
84C4⋊Dic43—42no—
85C4⋊Dic43—42no—
86Dic43⋊C4—44no—
87C2×C43⋊C8—42no—
88C23×C43—21no—
89C23×C43—21no—
90C23×C43—21no—
91C23×C43—41no—
92C23×C43—41no—
93C23×C43C2×C22⋊C411yescharacteristic
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—41no—
100C2×C4×C43—41no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43C4×D412yes—
106C2×C4×C43#12011yescharacteristic
107C2×C4×C43#12112yes—
108C2×C4×C43#12311yescharacteristic
109C2×C4×C43#13512yes—
110C2×C4×C43AGL(1,ℤ/8)12yes—
111C2×Dic43—42no—
112C2×Dic43—42no—
113C2×Dic43—42no—
114C2×Dic43—42no—
115C2×Dic43—42no—
116C2×Dic43—42no—
117Dic86—82no—
118Dic86—82no—
119C8×C43—44no—
120C43⋊C8—82no—
121#9196—431nomaximal, Sylow
122C22×C43—21no—
123C22×C43—21no—
124C22×C43—42no—
125C22×C43—41no—
126C22×C43—41no—
127C22×C43—41no—
128C22×C43—81no—
129C22×C43#38611yescharacteristic
130C22×C43#41611yescharacteristic
131C22×C43#41811yescharacteristic
132C4×C43—22no—
133C4×C43—22no—
134C4×C43—41no—
135C4×C43—41no—
136C4×C43—41no—
137C4×C43#44912yes—
138C4×C43#48212yes—
139Dic43—82no—
140Dic43—82no—
141#2921D4311yescharacteristic
142#2621—431no—
143#1546—432no—
144#1458—431no—
145#1286—432no—
146C2×C43—21no—
147C2×C43—21no—
148C2×C43—81no—
149C2×C43#187511yescharacteristic
150C2×C43#190911yescharacteristic
151C2×C43#191511yescharacteristic
152C2×C4⋊Q8—431no—
153C2×C22⋊Q8—861no—
154C2×#117C2×D4311yescharacteristic
155#433—24no—
156#431—432no—
157#423C2×D4312yes—
158#407—21no—
159C4×M16—21no—
160#398—432no—
161#398—861no—
162#397—432no—
163#397—861no—
164#391—861no—
165#382—431no—
166#332—864no—
167#324—861no—
168#323—861no—
169C43#919611yescharacteristic, complemented, Sylow
170C22×Q8—861no—
171C23×C4C22⋊D4311yescharacteristic
172C2×M16—22no—
173C4⋊Q8—862no—
174C4⋊Q8—862no—
175C22⋊Q8—1724no—
176#117—22no—
177#117—22no—
178C2×C4⋊C4—432no—
179C2×C4⋊C4—862no—
180C2×C4⋊C4—861no—
181C2×C4⋊C4—861no—
182C2×C4⋊C4C4×D4311yescharacteristic
183C2×C4⋊C4D17211yescharacteristic
184C2×C22⋊C4—862no—
185C2×C22⋊C4C4×D4311yescharacteristic
186C2×C22⋊C4D17211yescharacteristic
187C2×C42C22⋊D4311yescharacteristic
188C2×C42C22×D4311yescharacteristic
189C4⋊C8—22no—
190C4⋊C8—862no—
191C4⋊C8C22⋊D4314yes—
192C22⋊C8—24no—
193C22⋊C8—862no—
194#97—22no—
195C4×C8—22no—
196C4×C8—862no—
197#95—432no—
198#95—862no—
199#95—862no—
200#95—861no—
201C24(C2×D43)⋊C411yescharacteristic
202C2×Q8—1721no—
203C2×Q8—1721no—
204C2×Q8—1722no—
205C2×Q8—1722no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—862no—
211C22×C4—862no—
212C22×C4(C2×D43)⋊C411yescharacteristic
213C22×C4(C2×D43)⋊C411yescharacteristic
214C22×C4(C2×D43)⋊C411yescharacteristic
215C22×C4C2×C4×D4311yescharacteristic
216C22×C4C2×D17211yescharacteristic
217C22×C4C2×C22⋊D4311yescharacteristic
218M16—42no—
219M16—42no—
220C2×C8—24no—
221C2×C8—1722no—
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—864no—
225C4⋊C4—1724no—
226C4⋊C4—1722no—
227C4⋊C4—1722no—
228C22⋊C4—22no—
229C22⋊C4—22no—
230C22⋊C4—1724no—
231C42—21no—
232C42—21no—
233C42#1062189812yes—
234C42C2×C22⋊D4312yes—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—41no—
239C23—41no—
240C23C2×(C2×D43)⋊C411yescharacteristic
241Q8—3442no—
242Q8—3442no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—1722no—
255C2×C4—1722no—
256C2×C4—1722no—
257C2×C4—1722no—
258C2×C4—1722no—
259C2×C4—1722no—
260C2×C4C4×C22⋊D4312yes—
261C2×C4#1306329411yescharacteristic
262C2×C4#1306329912yes—
263C2×C4#1306330811yescharacteristic
264C2×C4#1306334512yes—
265C2×C4#1306335012yes—
266C8—44no—
267C8—3442no—
268C22—21no—
269C22—21no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—81no—
275C22#1458277811yescharacteristic
276C22#1458289311yescharacteristic
277C22#1458290311yescharacteristic
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—3442no—
284C4—3442no—
285C4#1458304412yes—
286C4#1458322312yes—
287C2—21no—
288C2—21no—
289C2—81no—
290C2#1913491711yescharacteristic
291C2#1913511711yescharacteristic
292C2#1913514711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2921C2
socleC22×C43#386
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#2921D43
hypocenterC43#9196
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2921

Complements

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

NH ≅ G/Ntype
2. #19133268C2semidirect
4. #19132455C2semidirect
169. C43#9196semidirect

Maximal subgroups

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

subgroupindex
#191403612
#191332682
#191329092
#191324552
C43×#29212
#919643