Finite Group Databasebeta

← #24994436

Subgroups — #24994436

Order 11008.

542 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 131 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#19139949C211yesmaximal, characteristic
2#19134587C211yesmaximal, characteristic
3#19133025C212yesmaximal, complemented
4#19132454C212yesmaximal, complemented
5C43×#2972C211yesmaximal, characteristic
6C2×C4×Dic86C2211yescharacteristic
7#14582923C2212yes—
8C2×#13063242—21no—
9#14582835C412yes—
10#14582811C412yes—
11#14582802—21no—
12#14582795—21no—
13#14582772—22no—
14#14582765C2211yescharacteristic
15#14582668—21no—
16#14582631—24no—
17C2×C4×D4×C43C2211yescharacteristic
18C8×D4×C43—24no—
19C43×#431C2212yes—
20C2×C22⋊C8×C43—22no—
21C22×Dic86C2×C411yescharacteristic
22C2×#10621877—22no—
23C4×Dic86—22no—
24C4×Dic86—22no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×Dic43⋊C4—21no—
28C2×Dic43⋊C4—22no—
29C2×C22⋊Dic43—22no—
30C2×C22⋊Dic43—22no—
31C2×C4×Dic43—21no—
32C4⋊(C43⋊C8)—22no—
33C4⋊(C43⋊C8)—22no—
34#13063242—42no—
35C43⋊#95—22no—
36C43⋊#95—21no—
37C43⋊#95C2×C412yes—
38C22×D4×C43D411yescharacteristic
39C23×C4×C43D412yes—
40C22×C8×C43—24no—
41C4×D4×C43—22no—
42C4×D4×C43—22no—
43C2×C4⋊C4×C43D411yescharacteristic
44C2×C22⋊C4×C43C2×C412yes—
45C2×C42×C43C2311yescharacteristic
46C4⋊C8×C43—22no—
47C22⋊C8×C43—24no—
48C22⋊C8×C43—22no—
49C4×C8×C43D414yes—
50C24×C43C22⋊C412yes—
51C2×D4×C43—22no—
52C2×D4×C43—22no—
53C2×D4×C43SD1612yes—
54C2×D4×C43Q1612yes—
55C22×C4×C43—22no—
56C22×C4×C43—22no—
57C22×C4×C43—82no—
58C22×C4×C43C22⋊C412yes—
59C22×C4×C43C22×C411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43C2×D411yescharacteristic
62C22×Dic43—21no—
63C22×Dic43—22no—
64C22×Dic43—21no—
65C2×Dic86—22no—
66C2×Dic86—42no—
67C2×C8×C43—24no—
68C2×C8×C43—84no—
69C4⋊C4×C43—22no—
70C22⋊C4×C43—24no—
71C42×C43C2×D412yes—
72C42×C43#4112yes—
73C22⋊Dic43—44no—
74C22⋊Dic43—82no—
75C4⋊Dic43—22no—
76C4⋊Dic43—42no—
77Dic43⋊C4—41no—
78Dic43⋊C4—41no—
79Dic43⋊C4—82no—
80C4×Dic43—42no—
81#10621877—42no—
82#10621877—42no—
83C2×C43⋊C8—42no—
84C23×C43—22no—
85C23×C43—22no—
86C23×C43—42no—
87C23×C43—42no—
88C23×C43#10314yes—
89C23×C43C2×C22⋊C411yescharacteristic
90D4×C43—24no—
91D4×C43—24no—
92C2×C4×C43—22no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43—44no—
96C2×C4×C43—42no—
97C2×C4×C43—82no—
98C2×C4×C43C4×D412yes—
99C2×C4×C43#12011yescharacteristic
100C2×C4×C43#12112yes—
101C2×C4×C43#12311yescharacteristic
102C2×C4×C43C2×SD1611yescharacteristic
103C2×C4×C43C2×Q1611yescharacteristic
104C2×C4×C43#13512yes—
105C2×Dic43—22no—
106C2×Dic43—41no—
107C2×Dic43—41no—
108C2×Dic43—41no—
109C2×Dic43—42no—
110C2×Dic43—42no—
111C2×Dic43—41no—
112C2×Dic43—41no—
113C2×Dic43—42no—
114Dic86—24no—
115Dic86—42no—
116C8×C43—44no—
117C43⋊C8—82no—
118#9483—431nomaximal, Sylow
119C22×C43—21no—
120C22×C43—21no—
121C22×C43—24no—
122C22×C43—44no—
123C22×C43—42no—
124C22×C43—42no—
125C22×C43—82no—
126C22×C43#38611yescharacteristic
127C22×C43C2×#10311yescharacteristic
128C22×C43#41611yescharacteristic
129C4×C43—22no—
130C4×C43—21no—
131C4×C43—21no—
132C4×C43—42no—
133C4×C43#46512yes—
134C4×C43#46712yes—
135Dic43—42no—
136Dic43—82no—
137Dic43—81no—
138#2972D4311yescharacteristic
139#2580—431no—
140#1800—431no—
141#1487—432no—
142#1286—432no—
143C2×C43—21no—
144C2×C43—21no—
145C2×C43—44no—
146C2×C43#189111yescharacteristic
147C2×C43#189211yescharacteristic
148C2×C43#191111yescharacteristic
149C2×C4×Q8—431no—
150C2×C4×D4C2×D4311yescharacteristic
151C8×D4—24no—
152#431C2×D4312yes—
153#423—432no—
154C2×#100—861no—
155C2×C22⋊C8—22no—
156#399—432no—
157#393—432no—
158#390—861no—
159#389—861no—
160#385—862no—
161#382—431no—
162#343—861no—
163Q8⋊C8—864no—
164C43#948311yescharacteristic, complemented, Sylow
165C22×Q8—431no—
166C22×D4D17211yescharacteristic
167C23×C4C22⋊D4312yes—
168C2×M16—862no—
169C22×C8—24no—
170C4×Q8—862no—
171C4×Q8—862no—
172C4×D4—22no—
173C4×D4—22no—
174C2×C4⋊C4—431no—
175C2×C4⋊C4—862no—
176C2×C4⋊C4—861no—
177C2×C4⋊C4—861no—
178C2×C4⋊C4D17211yescharacteristic
179C2×C22⋊C4—862no—
180C2×C22⋊C4—862no—
181C2×C22⋊C4C4×D4312yes—
182C2×C42—861no—
183C2×C42C22×D4311yescharacteristic
184C4⋊C8—22no—
185C4⋊C8—862no—
186C4⋊C8—862no—
187#100—1722no—
188C22⋊C8—24no—
189C22⋊C8—22no—
190C4×C8C22⋊D4314yes—
191#95—432no—
192#95—862no—
193#95—861no—
194C24(C2×D43)⋊C412yes—
195C2×Q8—862no—
196C2×Q8—1722no—
197C2×D4—22no—
198C2×D4—22no—
199C2×D4#1062187312yes—
200C2×D4Dic17212yes—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—82no—
204C22×C4—861no—
205C22×C4—862no—
206C22×C4—861no—
207C22×C4(C2×D43)⋊C412yes—
208C22×C4C2×C4×D4311yescharacteristic
209C22×C4C2×D17211yescharacteristic
210C22×C4C2×C22⋊D4311yescharacteristic
211M16—1722no—
212M16—1722no—
213C2×C8—24no—
214C2×C8—84no—
215C2×C8—1722no—
216C4⋊C4—22no—
217C4⋊C4—862no—
218C4⋊C4—3442no—
219C4⋊C4—1721no—
220C4⋊C4—1721no—
221C4⋊C4—1722no—
222C22⋊C4—24no—
223C22⋊C4—3442no—
224C22⋊C4—1724no—
225C42—1722no—
226C42#1062189812yes—
227C42C2×C22⋊D4312yes—
228C23—22no—
229C23—22no—
230C23—42no—
231C23—42no—
232C23#1306325014yes—
233C23C2×(C2×D43)⋊C411yescharacteristic
234Q8—864no—
235Q8—1722no—
236D4—24no—
237D4—24no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—44no—
242C2×C4—42no—
243C2×C4—82no—
244C2×C4—862no—
245C2×C4—1721no—
246C2×C4—1722no—
247C2×C4—1722no—
248C2×C4—1721no—
249C2×C4—1722no—
250C2×C4—1721no—
251C2×C4—1721no—
252C2×C4—1721no—
253C2×C4C4×C22⋊D4312yes—
254C2×C4#1306329411yescharacteristic
255C2×C4#1306329912yes—
256C2×C4#1306330811yescharacteristic
257C2×C4C2×#1062187311yescharacteristic
258C2×C4C2×Dic17211yescharacteristic
259C2×C4#1306334712yes—
260C8—44no—
261C8—3442no—
262C22—21no—
263C22—21no—
264C22—24no—
265C22—44no—
266C22—42no—
267C22—42no—
268C22—82no—
269C22#1458277811yescharacteristic
270C22C2×#1306325011yescharacteristic
271C22#1458289611yescharacteristic
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—3442no—
277C4—3441no—
278C4—1722no—
279C4#1458312812yes—
280C4#1458314012yes—
281C2—21no—
282C2—21no—
283C2—44no—
284C2#1913501311yescharacteristic
285C2#1913501811yescharacteristic
286C2#1913512711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2972C2
socleC22×C43#386
prime radicalC22×D4×C43D4
cosocleC2×C42×C43C23
hypercenter#2972D43
hypocenterC43#9483
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2972

Complements

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

NH ≅ G/Ntype
3. #19133025C2semidirect
4. #19132454C2semidirect
164. C43#9483semidirect

Maximal subgroups

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

subgroupindex
#191399492
#191345872
#191330252
#191324542
C43×#29722
#948343