Finite Group Databasebeta

← #24993584

Subgroups — #24993584

Order 11008.

360 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 85 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#19145803C211yesmaximal, characteristic
2#19143700C211yesmaximal, characteristic
3#19133303C211yesmaximal, characteristic
4#19133221C211yesmaximal, characteristic
5#19132950C211yesmaximal, characteristic
6C43⋊#1308C211yesmaximal, characteristic
7C43×#1287C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×#13063317C2211yescharacteristic
10#14583308—21no—
11#14583268—21no—
12#14583235C412yes—
13#14583230C412yes—
14#14583207—22no—
15#14583028—22no—
16#14583027—22no—
17#14582957—22no—
18#14582956C2211yescharacteristic
19#14582956C2211yescharacteristic
20#14582647—21no—
21#14582644—21no—
22#14582640—22no—
23#14582624—22no—
24C43×#432C2211yescharacteristic
25C43×#432C2211yescharacteristic
26C43×#431C2211yescharacteristic
27#13063325D411yescharacteristic
28#13063325D411yescharacteristic
29#13063317—21no—
30#13063317—21no—
31#13063317—21no—
32#13063317—21no—
33#13063317—21no—
34#13063304—21no—
35#13063304C2×C412yes—
36C4×Dic86—21no—
37C4×Dic86D412yes—
38#13063284—21no—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×C4⋊Dic43C2×C411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43#13063259—22no—
44#13063257—22no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47Dic43⋊C8—24no—
48#13063250—22no—
49#13063250—22no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)D412yes—
52#13063236—21no—
53#13063236—21no—
54#13063235—22no—
55C8×Dic43—22no—
56C2×C42×C43C2311yescharacteristic
57C4⋊C8×C43—21no—
58C4⋊C8×C43—21no—
59C4⋊C8×C43—21no—
60C22⋊C8×C43—21no—
61C22⋊C8×C43—21no—
62C22⋊C8×C43C2×C412yes—
63#97×C43—21no—
64#97×C43D412yes—
65C4×C8×C43—21no—
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43#4111yescharacteristic
69C22×Dic43—21no—
70C22×Dic43—21no—
71C2×Dic86—21no—
72C2×Dic86C22⋊C412yes—
73C2×C8×C43—22no—
74C2×C8×C43—22no—
75C2×C8×C43—41no—
76C42×C43C2×D411yescharacteristic
77C42×C43C2×D411yescharacteristic
78C42×C43C2×D411yescharacteristic
79C42×C43#4111yescharacteristic
80C22⋊Dic43—22no—
81C4⋊Dic43—21no—
82C4⋊Dic43—21no—
83C4⋊Dic43—21no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43—21no—
88C4⋊Dic43C22⋊C412yes—
89Dic43⋊C4—22no—
90Dic43⋊C4—22no—
91Dic43⋊C4—41no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94Dic43⋊C4—41no—
95C4×Dic43—22no—
96C2×C43⋊C8—22no—
97C2×C43⋊C8—41no—
98C23×C43C4×D411yescharacteristic
99C2×C4×C43—41no—
100C2×C4×C43—41no—
101C2×C4×C43—41no—
102C2×C4×C43C2×C22⋊C411yescharacteristic
103C2×C4×C43C4×D411yescharacteristic
104C2×C4×C43#12011yescharacteristic
105C2×C4×C43#12111yescharacteristic
106C2×C4×C43#12111yescharacteristic
107C2×C4×C43#12311yescharacteristic
108C2×Dic43—22no—
109C2×Dic43—22no—
110C2×Dic43—42no—
111C2×Dic43—41no—
112C2×Dic43—41no—
113C2×Dic43—81no—
114Dic86—42no—
115Dic86—81no—
116C8×C43—42no—
117C8×C43—42no—
118C8×C43—81no—
119C43⋊C8—42no—
120C43⋊C8—81no—
121#9336—431nomaximal, Sylow
122C22×C43—21no—
123C22×C43—21no—
124C22×C43—21no—
125C22×C43#38611yescharacteristic
126C4×C43—21no—
127C4×C43—21no—
128C4×C43—21no—
129C4×C43—21no—
130C4×C43—21no—
131C4×C43—21no—
132Dic43—42no—
133Dic43—42no—
134Dic43—81no—
135Dic43—81no—
136#3236—431no—
137#2987—431no—
138#1554—431no—
139#1534—431no—
140#1470—431no—
141#1308—431no—
142#1287D4311yescharacteristic
143C2×C43—41no—
144C2×C43#188111yescharacteristic
145C2×C43#190511yescharacteristic
146C2×C43#191511yescharacteristic
147#533—431no—
148C2×#125—431no—
149#501—861no—
150#491—861no—
151#484—432no—
152#483—432no—
153#479—862no—
154#446—862no—
155#446—862no—
156#433—862no—
157#432—431no—
158#432—431no—
159#432C2×D4311yescharacteristic
160#432C2×D4311yescharacteristic
161#431C2×D4311yescharacteristic
162#333—861no—
163#332—861no—
164#330—862no—
165#324—862no—
166C43#933611yescharacteristic, complemented, Sylow
167C4⋊Q8—431no—
168C4⋊Q8—431no—
169#125—861no—
170#125—861no—
171#125—861no—
172#125—861no—
173#125—861no—
174C22⋊Q8—432no—
175C22⋊Q8—861no—
176C4×Q8—432no—
177C4×Q8—861no—
178#117—861no—
179C2×C4⋊C4—431no—
180C2×C4⋊C4—431no—
181C2×C4⋊C4—861no—
182C2×C4⋊C4—861no—
183C2×C42C22×D4311yescharacteristic
184#107—862no—
185#106—862no—
186C4⋊C8—21no—
187C4⋊C8—21no—
188C4⋊C8—21no—
189C4⋊C8—864no—
190C4⋊C8—861no—
191C4⋊C8—861no—
192#103—862no—
193#103—862no—
194C22⋊C8—21no—
195C22⋊C8—21no—
196C22⋊C8—432no—
197C22⋊C8—861no—
198C22⋊C8C4×D4312yes—
199#97—21no—
200#97—862no—
201#97—861no—
202#97—861no—
203#97D17212yes—
204C4×C8—21no—
205C4×C8—862no—
206C2×Q8—432no—
207C2×Q8—861no—
208C22×C4—861no—
209C22×C4—861no—
210C22×C4C2×C4×D4311yescharacteristic
211C22×C4D4×D4311yescharacteristic
212C22×C4#1062190211yescharacteristic
213C2×C8—22no—
214C2×C8—22no—
215C2×C8—41no—
216C2×C8—862no—
217C2×C8—1721no—
218C4⋊C4—432no—
219C4⋊C4—862no—
220C4⋊C4—861no—
221C4⋊C4—861no—
222C4⋊C4—861no—
223C4⋊C4—862no—
224C4⋊C4—861no—
225C4⋊C4—861no—
226C4⋊C4—861no—
227C4⋊C4—861no—
228C4⋊C4—1721no—
229C4⋊C4—1721no—
230C4⋊C4—1721no—
231C4⋊C4—1721no—
232C22⋊C4—862no—
233C42—862no—
234C42C2×D17211yescharacteristic
235C42#1062189811yescharacteristic
236C42D4×D4311yescharacteristic
237C42D4×D4311yescharacteristic
238C23#1306328711yescharacteristic
239Q8—3441no—
240Q8—1722no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—862no—
245C2×C4—862no—
246C2×C4—3441no—
247C2×C4—1722no—
248C2×C4—1721no—
249C2×C4—1721no—
250C2×C4C22⋊C4×D4311yescharacteristic
251C2×C4C4×D17211yescharacteristic
252C2×C4#1306329511yescharacteristic
253C2×C4#1306329811yescharacteristic
254C2×C4#1306330011yescharacteristic
255C2×C4#1306331011yescharacteristic
256C8—42no—
257C8—42no—
258C8—81no—
259C8—3441no—
260C8—1722no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22#1458277711yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—21no—
271C4—3441no—
272C4—3441no—
273C4—1722no—
274C4—1722no—
275C2—41no—
276C2#1913495811yescharacteristic
277C2#1913509011yescharacteristic
278C2#1913514611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1287C2
socleC22×C43#386
prime radicalC23×C43C4×D4
cosocleC2×C42×C43C23
hypercenter#1287D43
hypocenterC43#9336
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1287

Complements

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

NH ≅ G/Ntype
166. C43#9336semidirect

Maximal subgroups

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

subgroupindex
#191458032
#191437002
#191333032
#191332212
#191329502
C43⋊#13082
C43×#12872
#933643