Finite Group Databasebeta

← #24989136

Subgroups — #24989136

Order 11008.

656 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 107 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×#14583512C211yesmaximal, characteristic
2#19133320C212yesmaximal, complemented
3#19133222C211yesmaximal, characteristic, complemented
4#19132927C212yesmaximal
5C43×#1534C211yesmaximal, characteristic, complemented
6#14583512—24no—
7#14583512—22no—
8#14583512—22no—
9C2×#13063325C2211yescharacteristic
10C2×#13063320—22no—
11C2×#13063316—22no—
12C2×#13063305C412yes—
13C2×#13063290C412yes—
14C2×#13063282C2211yescharacteristic
15#14582956C2212yes—
16#14582647—24no—
17#14582641—22no—
18#14582624—22no—
19#14582622—22no—
20C2×#125×C43C2211yescharacteristic
21C43×#432C2212yes—
22C43×#330—22no—
23C22×Dic86C2×C412yes—
24C22×C4×D43C2×C411yescharacteristic
25#13063325—21no—
26#13063325—21no—
27#13063325D414yes—
28#13063320—28no—
29#13063320—28no—
30#13063316—28no—
31#13063316—28no—
32#13063305—24no—
33#13063305—24no—
34#13063290—24no—
35#13063290—24no—
36#13063282—21no—
37#13063282—22no—
38#13063282—21no—
39C2×C4⋊Dic43—22no—
40C2×C4⋊Dic43—22no—
41C2×Dic43⋊C4—22no—
42C2×Dic43⋊C4D412yes—
43C2×(C2×D43)⋊C4—22no—
44C2×(C2×D43)⋊C4D412yes—
45C2×C4×Dic43—22no—
46C2×C4×Dic43C2×C411yescharacteristic
47C4⋊(C43⋊C8)—22no—
48C22⋊(C43⋊C8)—22no—
49#13063236—22no—
50#125×C43—22no—
51#125×C43D412yes—
52#125×C43D412yes—
53C2×C4⋊C4×C43—22no—
54C2×C4⋊C4×C43C2×C412yes—
55C2×C42×C43C2311yescharacteristic
56C4⋊C8×C43—22no—
57C22⋊C8×C43—22no—
58#97×C43—22no—
59C23×D43C22⋊C411yescharacteristic
60C22×C4×C43—22no—
61C22×C4×C43C22×C411yescharacteristic
62C22×C4×C43C2×D412yes—
63C22×Dic43—22no—
64C22×Dic43C22⋊C411yescharacteristic
65C22×Dic43C22⋊C412yes—
66C2×C4×D43—21no—
67C2×C4×D43—21no—
68C2×C4×D43—42no—
69C2×Dic86—22no—
70C2×Dic86—44no—
71C2×Dic86C22⋊C414yes—
72C2×C8×C43—42no—
73C4⋊C4×C43—22no—
74C4⋊C4×C43—24no—
75C4⋊C4×C43—24no—
76C4⋊C4×C43C22⋊C414yes—
77C42×C43C2×D411yescharacteristic
78C42×C43C2×D412yes—
79C42×C43C2×D411yescharacteristic
80(C2×D43)⋊C4—28no—
81(C2×D43)⋊C4—22no—
82(C2×D43)⋊C4—22no—
83C4⋊Dic43—28no—
84C4⋊Dic43—24no—
85C4⋊Dic43—24no—
86Dic43⋊C4—28no—
87Dic43⋊C4—22no—
88Dic43⋊C4—22no—
89C4×Dic43—28no—
90C4×Dic43—21no—
91C4×Dic43—21no—
92C2×C43⋊C8—42no—
93C23×C43C2×C22⋊C411yescharacteristic
94C22×D43—21no—
95C22×D43—22no—
96C22×D43—42no—
97C2×C4×C43—22no—
98C2×C4×C43—24no—
99C2×C4×C43—42no—
100C2×C4×C43—44no—
101C2×C4×C43C2×C22⋊C411yescharacteristic
102C2×C4×C43C2×C22⋊C411yescharacteristic
103C2×C4×C43#12012yes—
104C2×C4×C43#12012yes—
105C2×Dic43—22no—
106C2×Dic43—24no—
107C2×Dic43—21no—
108C2×Dic43—22no—
109C2×Dic43—44no—
110C2×Dic43—42no—
111C4×D43—42no—
112C4×D43—42no—
113Dic86—44no—
114Dic86—44no—
115C8×C43—82no—
116C43⋊C8—82no—
117#8527—431nomaximal, Sylow
118C22×C43—22no—
119C22×C43#37911yescharacteristic
120C22×C43#41312yes—
121C2×D43—42no—
122C2×D43—41no—
123C2×D43—82no—
124C4×C43—22no—
125C4×C43—22no—
126C4×C43—21no—
127C4×C43—21no—
128C4×C43—44no—
129Dic43—42no—
130Dic43—44no—
131Dic43—41no—
132C2×#541—431no—
133#1558—432no—
134#1534—431no—
135#1534D4311yescharacteristic, complemented
136#1464—432no—
137C2×C43—22no—
138C2×C43#178511yescharacteristic
139C2×C43#179612yes—
140D43—81no—
141#541—864no—
142#541—862no—
143#541—862no—
144C2×C4⋊Q8—431no—
145C2×#126—862no—
146C2×#125—862no—
147C2×#125C2×D4311yescharacteristic
148C2×C22⋊Q8—432no—
149C2×C4×Q8—432no—
150C2×#117—431no—
151#432—432no—
152#432C2×D4312yes—
153#333—864no—
154#330—22no—
155#330—862no—
156#324—862no—
157#323—862no—
158C43#852711yescharacteristic, complemented, Sylow
159C22×Q8—432no—
160C23×C4—431no—
161C4⋊Q8—434no—
162C4⋊Q8—861no—
163C4⋊Q8—861no—
164#126—868no—
165#126—868no—
166#125—22no—
167#125—868no—
168#125—868no—
169#125D17212yes—
170#125C22⋊D4312yes—
171C22⋊Q8—864no—
172C22⋊Q8—864no—
173C4×Q8—864no—
174C4×Q8—864no—
175#117—861no—
176#117—862no—
177#117—861no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—432no—
180C2×C4⋊C4—862no—
181C2×C4⋊C4—862no—
182C2×C4⋊C4—862no—
183C2×C4⋊C4C4×D4312yes—
184C2×C22⋊C4—432no—
185C2×C22⋊C4—862no—
186C2×C42—431no—
187C2×C42—862no—
188C2×C42C22×D4311yescharacteristic
189C4⋊C8—22no—
190C4⋊C8—862no—
191C22⋊C8—22no—
192C22⋊C8—862no—
193#97—22no—
194#97—862no—
195C24—431no—
196C2×Q8—434no—
197C2×Q8—862no—
198C2×Q8—1724no—
199C22×C4—22no—
200C22×C4—431no—
201C22×C4—432no—
202C22×C4—862no—
203C22×C4—861no—
204C22×C4—861no—
205C22×C4—1722no—
206C22×C4C2×C4×D4311yescharacteristic
207C22×C4D4×D4312yes—
208C2×C8—42no—
209C2×C8—1722no—
210C4⋊C4—22no—
211C4⋊C4—24no—
212C4⋊C4—24no—
213C4⋊C4—868no—
214C4⋊C4—868no—
215C4⋊C4—862no—
216C4⋊C4—864no—
217C4⋊C4—862no—
218C4⋊C4—864no—
219C4⋊C4(C2×D43)⋊C414yes—
220C22⋊C4—868no—
221C22⋊C4—862no—
222C22⋊C4—862no—
223C42—868no—
224C42—861no—
225C42—861no—
226C42C2×D17211yescharacteristic
227C42D4×D4312yes—
228C42C2×C22⋊D4311yescharacteristic
229C23—862no—
230C23—861no—
231C23—1722no—
232C23C22⋊C4×D4311yescharacteristic
233Q8—1724no—
234Q8—1724no—
235C2×C4—22no—
236C2×C4—24no—
237C2×C4—42no—
238C2×C4—44no—
239C2×C4—862no—
240C2×C4—862no—
241C2×C4—864no—
242C2×C4—861no—
243C2×C4—1722no—
244C2×C4—1722no—
245C2×C4—1724no—
246C2×C4—1722no—
247C2×C4C22⋊C4×D4311yescharacteristic
248C2×C4C2×(C2×D43)⋊C411yescharacteristic
249C2×C4#1306329312yes—
250C2×C4#1306329512yes—
251C8—82no—
252C8—3442no—
253C22—22no—
254C22—3442no—
255C22—1721no—
256C22—1722no—
257C22#1458275411yescharacteristic
258C22#1458288212yes—
259C4—21no—
260C4—21no—
261C4—22no—
262C4—22no—
263C4—44no—
264C4—1721no—
265C4—1724no—
266C4—1722no—
267C2—22no—
268C2—3441no—
269C2#1913452211yescharacteristic
270C2#1913456912yes—
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1534C2
socleC22×C43#379
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1534D43
hypocenterC43#8527
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1534

Complements

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

NH ≅ G/Ntype
2. #19133320C2semidirect
3. #19133222C2semidirect
5. C43×#1534C2semidirect
135. #1534D43semidirect
158. C43#8527semidirect

Maximal subgroups

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

subgroupindex
C2×#145835122
#191333202
#191332222
#191329272
C43×#15342
#852743