Finite Group Databasebeta

← #24990978

Subgroups — #24990978

Order 11008.

468 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 119 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#19137769C211yesmaximal, characteristic
2#19135412C211yesmaximal, characteristic
3#19134729C212yesmaximal, complemented
4#19132477C212yesmaximal, complemented
5C2×C43×#329C211yesmaximal, characteristic
6C2×#13063249—21no—
7C2×#13063246—21no—
8C2×#13063236C2211yescharacteristic
9#14582806—21no—
10#14582792—22no—
11#14582779—21no—
12#14582774—22no—
13#14582769C2211yescharacteristic
14#14582765C2212yes—
15#14582662—22no—
16#14582662—22no—
17C2×#124×C43C2211yescharacteristic
18C2×#97×C43C2212yes—
19C43×#329C414yescomplemented
20C23×Dic43—21no—
21C22×C43⋊C8—21no—
22C2×C4⋊Dic43—21no—
23C2×C4⋊Dic43—22no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43D412yes—
26C2×C4⋊Dic43D412yes—
27C2×C22⋊Dic43—21no—
28C2×C22⋊Dic43—22no—
29C2×C4×Dic43—21no—
30#13063249—42no—
31#13063246—42no—
32#13063236—22no—
33C43⋊#95—22no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C22×Q8×C43D411yescharacteristic
37C22×D4×C43D411yescharacteristic
38C22×C8×C43—22no—
39#124×C43—22no—
40#124×C43C2×C412yes—
41#124×C43Q812yes—
42C2×C22⋊C4×C43—22no—
43C2×C42×C43C2311yescharacteristic
44#97×C43—22no—
45#97×C43C2×C414yescomplemented
46C24×C43—21no—
47C2×Q8×C43—21no—
48C2×Q8×C43—41no—
49C2×Q8×C43—41no—
50C2×Q8×C43C4⋊C412yes—
51C2×D4×C43—21no—
52C2×D4×C43—41no—
53C2×D4×C43—41no—
54C2×D4×C43C4⋊C412yes—
55C22×C4×C43—21no—
56C22×C4×C43C2×D411yescharacteristic
57C22×C4×C43C2×D412yes—
58C22×Dic43—22no—
59C22×Dic43—22no—
60C22×Dic43—41no—
61C22×Dic43—81no—
62C22×Dic43—82no—
63C2×C8×C43—24no—
64C2×C8×C43—42no—
65C2×C8×C43—42no—
66C22⋊C4×C43—24no—
67C22⋊C4×C43—24no—
68C42×C43C22×C411yescharacteristic
69C42×C43C2×Q811yescharacteristic
70C42×C43#4112yes—
71C22⋊Dic43—82no—
72C22⋊Dic43—81no—
73C4⋊Dic43—42no—
74C4⋊Dic43—42no—
75C4⋊Dic43—41no—
76C4⋊Dic43—41no—
77C4⋊Dic43—44no—
78C4⋊Dic43—81no—
79C4×Dic43—81no—
80C2×C43⋊C8—22no—
81C2×C43⋊C8—41no—
82C2×C43⋊C8—41no—
83C23×C43—22no—
84C23×C43—41no—
85C23×C43—42no—
86C23×C43—42no—
87C23×C43—41no—
88C23×C43#12011yescharacteristic
89Q8×C43—42no—
90Q8×C43—81no—
91D4×C43—42no—
92D4×C43—81no—
93C2×C4×C43—21no—
94C2×C4×C43—22no—
95C2×C4×C43—21no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—41no—
99C2×C4×C43—41no—
100C2×C4×C43C2×C4⋊C411yescharacteristic
101C2×C4×C43C4×D412yes—
102C2×C4×C43C22⋊Q812yes—
103C2×C4×C43#12311yescharacteristic
104C2×Dic43—42no—
105C2×Dic43—42no—
106C2×Dic43—42no—
107C2×Dic43—42no—
108C2×Dic43—42no—
109C2×Dic43—42no—
110C2×Dic43—84no—
111C2×Dic43—81no—
112C2×Dic43—82no—
113C8×C43—44no—
114C43⋊C8—42no—
115#8914—431nomaximal, Sylow
116C22×C43—42no—
117C22×C43—44no—
118C22×C43—81no—
119C22×C43—81no—
120C22×C43—82no—
121C22×C43#38511yescharacteristic
122C22×C43#45311yescharacteristic
123C22×C43#45412yes—
124C22×C43#45512yes—
125C22×C43#45511yescharacteristic
126C4×C43—21no—
127C4×C43—21no—
128C4×C43—22no—
129C4×C43—22no—
130C4×C43—42no—
131Dic43—82no—
132Dic43—82no—
133Dic43—161no—
134#2379—431no—
135#1959—431no—
136#1836—432no—
137C2×#329D4311yescharacteristic
138#1295—432no—
139C2×C43—82no—
140C2×C43#165711yescharacteristic
141C2×C43#165911yescharacteristic
142C2×C43#166212yes—
143C2×C43#185611yescharacteristic
144C2×C43#186012yes—
145C2×#124C2×D4311yescharacteristic
146C2×#103—861no—
147C2×#102—861no—
148C2×#97—431no—
149C2×#97C2×D4312yes—
150#391—861no—
151#388—862no—
152#386—861no—
153#385—862no—
154#384—431no—
155#382—432no—
156#340—862no—
157#340—862no—
158#329Dic4314yescomplemented
159C43#891411yescharacteristic, complemented, Sylow
160C22×Q8D17211yescharacteristic
161C22×D4D17211yescharacteristic
162C23×C4—861no—
163C22×C8—22no—
164C22×C8—861no—
165#124—22no—
166#124Dic8612yes—
167#124C2×Dic4312yes—
168C2×C4⋊C4—432no—
169C2×C4⋊C4—432no—
170C2×C4⋊C4—861no—
171C2×C4⋊C4—861no—
172C2×C4⋊C4—862no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—862no—
175C2×C22⋊C4—861no—
176C2×C42—861no—
177C2×C42C22×D4311yescharacteristic
178#103—1722no—
179#102—1722no—
180#97—22no—
181#97—862no—
182#97C2×Dic4314yescomplemented
183#95—862no—
184#95—862no—
185#95—862no—
186C24—21no—
187C2×Q8—21no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8C4⋊Dic4312yes—
191C2×D4—21no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4C4⋊Dic4312yes—
195C22×C4—21no—
196C22×C4—862no—
197C22×C4—862no—
198C22×C4—3441no—
199C22×C4—3442no—
200C22×C4—1721no—
201C22×C4C2×D17211yescharacteristic
202C22×C4D4×D4312yes—
203C2×C8—24no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—862no—
207C2×C8—1721no—
208C2×C8—1721no—
209C4⋊C4—3441no—
210C4⋊C4—1721no—
211C4⋊C4—1721no—
212C4⋊C4—1724no—
213C4⋊C4—1722no—
214C4⋊C4—1722no—
215C22⋊C4—24no—
216C22⋊C4—24no—
217C22⋊C4—3442no—
218C22⋊C4—3441no—
219C42—3441no—
220C42C2×Dic8611yescharacteristic
221C42#1062190012yes—
222C42C22×Dic4311yescharacteristic
223C23—22no—
224C23—41no—
225C23—42no—
226C23—42no—
227C23—41no—
228C23#1306329511yescharacteristic
229Q8—42no—
230Q8—81no—
231D4—42no—
232D4—81no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—3444no—
241C2×C4—3441no—
242C2×C4—3442no—
243C2×C4—1722no—
244C2×C4—1722no—
245C2×C4—1722no—
246C2×C4—1722no—
247C2×C4—1722no—
248C2×C4—1722no—
249C2×C4C2×C4⋊Dic4311yescharacteristic
250C2×C4D4×Dic4312yes—
251C2×C4#1306330212yes—
252C2×C4#1306330911yescharacteristic
253C8—44no—
254C8—1722no—
255C22—42no—
256C22—44no—
257C22—81no—
258C22—81no—
259C22—82no—
260C22#1458277411yescharacteristic
261C22#1458306911yescharacteristic
262C22#1458307312yes—
263C22#1458307812yes—
264C22#1458307911yescharacteristic
265C4—21no—
266C4—21no—
267C4—22no—
268C4—22no—
269C4—42no—
270C4—3442no—
271C4—3442no—
272C4—6881no—
273C2—82no—
274C2#1913389411yescharacteristic
275C2#1913390211yescharacteristic
276C2#1913392012yes—
277C2#1913480711yescharacteristic
278C2#1913483012yes—
subgroupG/H
centerC23#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#329C2
socleC23×C43#120
prime radicalC22×D4×C43D4
cosocleC2×C42×C43C23
hypercenterC2×#329D43
hypocenterC43#8914
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
3. #19134729C2semidirect
4. #19132477C2semidirect
19. C43×#329C4semidirect
45. #97×C43C2×C4semidirect
158. #329Dic43semidirect
159. C43#8914semidirect
182. #97C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191377692
#191354122
#191347292
#191324772
C2×C43×#3292
#891443