Finite Group Databasebeta

← #24992603

Subgroups — #24992603

Order 11008.

458 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 111 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#19143233C211yesmaximal, characteristic
2#19140416C211yesmaximal, characteristic
3#19133275C212yesmaximal, complemented
4#19132454C212yesmaximal, complemented
5C43×#1458C211yesmaximal, characteristic
6C2×#13063325C2211yescharacteristic
7#14582960—24no—
8#14582923C2212yes—
9#14582863—21no—
10C4×#10621877—21no—
11#14582838—21no—
12#14582835—21no—
13#14582819C412yes—
14#14582811C412yes—
15#14582797—21no—
16#14582765C2211yescharacteristic
17#14582759—21no—
18#14582647—24no—
19C2×#117×C43C2211yescharacteristic
20C43×#431C2212yes—
21C43×#324—21no—
22C43×#323—21no—
23C22×Dic86C2×C412yes—
24C2×#10621877—22no—
25#13063325—22no—
26#13063325—22no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×Dic43⋊C4—22no—
31C2×C22⋊Dic43—22no—
32C4⋊(C43⋊C8)—22no—
33C4⋊(C43⋊C8)D414yes—
34C22⋊(C43⋊C8)—24no—
35#13063236—22no—
36C4×C43⋊C8—22no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95—21no—
40C43⋊#95C2×C412yes—
41C23×C4×C43D411yescharacteristic
42#117×C43—22no—
43#117×C43—22no—
44C2×C4⋊C4×C43C2×C411yescharacteristic
45C2×C4⋊C4×C43D411yescharacteristic
46C2×C22⋊C4×C43C2×C411yescharacteristic
47C2×C22⋊C4×C43D411yescharacteristic
48C2×C42×C43D411yescharacteristic
49C2×C42×C43C2311yescharacteristic
50C4⋊C8×C43—22no—
51C22⋊C8×C43—22no—
52C4×C8×C43—22no—
53C24×C43C22⋊C411yescharacteristic
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43C22⋊C411yescharacteristic
59C22×C4×C43C22⋊C411yescharacteristic
60C22×C4×C43C22⋊C411yescharacteristic
61C22×C4×C43C22×C411yescharacteristic
62C22×C4×C43C2×D411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×Dic43—22no—
65C22×Dic43—22no—
66C2×Dic86—24no—
67C2×Dic86—82no—
68C2×C8×C43—42no—
69C4⋊C4×C43—22no—
70C4⋊C4×C43—22no—
71C22⋊C4×C43—22no—
72C22⋊C4×C43—22no—
73C42×C43—21no—
74C42×C43—21no—
75C42×C43C2×D412yes—
76C42×C43#4112yes—
77C22⋊Dic43—82no—
78C4⋊Dic43—41no—
79C4⋊Dic43—42no—
80C4⋊Dic43—41no—
81C4⋊Dic43—42no—
82Dic43⋊C4—82no—
83#10621877—42no—
84#10621877—42no—
85C2×C43⋊C8—24no—
86C23×C43—21no—
87C23×C43—21no—
88C23×C43—21no—
89C23×C43—41no—
90C23×C43—41no—
91C23×C43C2×C22⋊C411yescharacteristic
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—41no—
98C2×C4×C43—41no—
99C2×C4×C43—42no—
100C2×C4×C43—42no—
101C2×C4×C43—41no—
102C2×C4×C43—41no—
103C2×C4×C43C4×D412yes—
104C2×C4×C43#12011yescharacteristic
105C2×C4×C43#12112yes—
106C2×C4×C43#12311yescharacteristic
107C2×C4×C43#13512yes—
108C2×C4×C43#13712yes—
109C2×Dic43—42no—
110C2×Dic43—42no—
111C2×Dic43—42no—
112C2×Dic43—42no—
113C2×Dic43—42no—
114C2×Dic43—42no—
115Dic86—84no—
116C8×C43—82no—
117C43⋊C8—44no—
118#9192—431nomaximal, Sylow
119C22×C43—21no—
120C22×C43—21no—
121C22×C43—42no—
122C22×C43—41no—
123C22×C43—41no—
124C22×C43—41no—
125C22×C43—81no—
126C22×C43#38611yescharacteristic
127C22×C43#41611yescharacteristic
128C22×C43#41911yescharacteristic
129C4×C43—22no—
130C4×C43—22no—
131C4×C43—41no—
132C4×C43—41no—
133C4×C43—41no—
134C4×C43#45212yes—
135C4×C43#48512yes—
136Dic43—82no—
137Dic43—82no—
138#2921—431no—
139#2628—431no—
140#1548—432no—
141#1458D4311yescharacteristic
142#1286—432no—
143C2×C43—21no—
144C2×C43—21no—
145C2×C43—81no—
146C2×C43#187311yescharacteristic
147C2×C43#190911yescharacteristic
148C2×C43#191411yescharacteristic
149C2×C4⋊Q8—431no—
150C2×#117C2×D4311yescharacteristic
151#433—864no—
152#431C2×D4312yes—
153#423—432no—
154#407—861no—
155C4×M16—861no—
156#400—861no—
157#399—861no—
158#395—432no—
159#393—432no—
160#389—861no—
161#382—431no—
162#380—861no—
163#333—864no—
164#324—21no—
165#323—21no—
166C43#919211yescharacteristic, complemented, Sylow
167C22×Q8—432no—
168C23×C4D17211yescharacteristic
169C2×M16—862no—
170C4⋊Q8—862no—
171C4⋊Q8—862no—
172#117—22no—
173#117—22no—
174C2×C4⋊C4—862no—
175C2×C4⋊C4—861no—
176C2×C4⋊C4—861no—
177C2×C4⋊C4—861no—
178C2×C4⋊C4C4×D4311yescharacteristic
179C2×C4⋊C4C22⋊D4311yescharacteristic
180C2×C22⋊C4—862no—
181C2×C22⋊C4C4×D4311yescharacteristic
182C2×C22⋊C4C22⋊D4311yescharacteristic
183C2×C42D17211yescharacteristic
184C2×C42C22×D4311yescharacteristic
185C4⋊C8—22no—
186C4⋊C8—434no—
187C4⋊C8—862no—
188C22⋊C8—22no—
189C22⋊C8—864no—
190#97—862no—
191C4×C8—22no—
192C4×C8—862no—
193#95—432no—
194#95—862no—
195#95—862no—
196#95—861no—
197C24(C2×D43)⋊C411yescharacteristic
198C2×Q8—864no—
199C2×Q8—3442no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—862no—
205C22×C4—862no—
206C22×C4(C2×D43)⋊C411yescharacteristic
207C22×C4(C2×D43)⋊C411yescharacteristic
208C22×C4(C2×D43)⋊C411yescharacteristic
209C22×C4C2×C4×D4311yescharacteristic
210C22×C4C2×D17211yescharacteristic
211C22×C4C2×C22⋊D4311yescharacteristic
212M16—1722no—
213M16—1722no—
214C2×C8—42no—
215C2×C8—864no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—3442no—
219C4⋊C4—1721no—
220C4⋊C4—1722no—
221C4⋊C4—1721no—
222C4⋊C4—1722no—
223C22⋊C4—22no—
224C22⋊C4—22no—
225C22⋊C4—3442no—
226C42—21no—
227C42—21no—
228C42D4×D4312yes—
229C42#1062190012yes—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—41no—
234C23—41no—
235C23C2×(C2×D43)⋊C411yescharacteristic
236Q8—3444no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—1722no—
249C2×C4—1722no—
250C2×C4—1722no—
251C2×C4—1722no—
252C2×C4—1722no—
253C2×C4—1722no—
254C2×C4(C22⋊D43)⋊C412yes—
255C2×C4#1306329511yescharacteristic
256C2×C4#1306329712yes—
257C2×C4#1306330911yescharacteristic
258C2×C4#1306334712yes—
259C2×C4#1306335812yes—
260C8—82no—
261C8—1724no—
262C22—21no—
263C22—21no—
264C22—42no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22#1458277611yescharacteristic
270C22#1458289611yescharacteristic
271C22#1458290911yescharacteristic
272C4—22no—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—3442no—
278C4—3442no—
279C4#1458306312yes—
280C4#1458324112yes—
281C2—21no—
282C2—21no—
283C2—81no—
284C2#1913490511yescharacteristic
285C2#1913511511yescharacteristic
286C2#1913514011yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1458C2
socleC22×C43#386
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1458D43
hypocenterC43#9192
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #19133275C2semidirect
4. #19132454C2semidirect
166. C43#9192semidirect

Maximal subgroups

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

subgroupindex
#191432332
#191404162
#191332752
#191324542
C43×#14582
#919243