Finite Group Databasebeta

← #24989134

Subgroups — #24989134

Order 11008.

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

normal subgroups only

This group has 784 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×#14583503C211yesmaximal, characteristic
2#19133309C211yesmaximal, characteristic, complemented
3#19133221C212yesmaximal, complemented
4#19132927C212yesmaximal, complemented
5C43×#1555C211yesmaximal, characteristic, complemented
6#14583503—24no—
7#14583503—22no—
8#14583503—22no—
9C2×#13063317C2211yescharacteristic
10C2×#13063306—22no—
11C2×#13063297—22no—
12C2×#13063296C412yes—
13C2×D4×Dic43C412yes—
14C2×#13063282C2211yescharacteristic
15#14582956C2212yes—
16#14582643—22no—
17#14582640—24no—
18#14582624—22no—
19#14582622—22no—
20C2×#127×C43C2211yescharacteristic
21C43×#432C2212yes—
22C43×#331—22no—
23C22×C22⋊D43—22no—
24C23×Dic43—22no—
25C22×C4×D43C2×C411yescharacteristic
26#13063317—21no—
27#13063317—21no—
28#13063317D414yes—
29#13063306—28no—
30#13063306—28no—
31#13063297—28no—
32#13063297—28no—
33#13063296—24no—
34#13063296—24no—
35D4×Dic43—24no—
36D4×Dic43—24no—
37#13063282—21no—
38#13063282—22no—
39#13063282—21no—
40C2×C4⋊Dic43C2×C412yes—
41C2×Dic43⋊C4—22no—
42C2×Dic43⋊C4D412yes—
43C2×C22⋊Dic43—22no—
44C2×C22⋊Dic43—22no—
45C2×(C2×D43)⋊C4D412yes—
46C2×C4×Dic43C2×C411yescharacteristic
47C4⋊(C43⋊C8)—22no—
48C22⋊(C43⋊C8)—22no—
49#13063236—22no—
50C22×D4×C43—22no—
51C22×D4×C43C2×C412yes—
52#127×C43—22no—
53#127×C43D412yes—
54#127×C43D412yes—
55C2×C42×C43C2311yescharacteristic
56C4⋊C8×C43—22no—
57C22⋊C8×C43—22no—
58#97×C43—22no—
59C24×C43—22no—
60C23×D43C22⋊C411yescharacteristic
61C2×D4×C43—22no—
62C2×D4×C43—24no—
63C2×D4×C43—24no—
64C2×D4×C43—44no—
65C2×D4×C43—84no—
66C2×D4×C43C22⋊C414yes—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D412yes—
69C2×C22⋊D43—28no—
70C2×C22⋊D43—84no—
71C22×Dic43—28no—
72C22×Dic43—22no—
73C22×Dic43—84no—
74C22×Dic43C22⋊C411yescharacteristic
75C22×Dic43C22⋊C412yes—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—42no—
79C2×C8×C43—42no—
80C42×C43C2×D411yescharacteristic
81C42×C43C2×D412yes—
82C42×C43C2×D411yescharacteristic
83C22⋊Dic43—28no—
84C22⋊Dic43—28no—
85(C2×D43)⋊C4—22no—
86(C2×D43)⋊C4—22no—
87C4⋊Dic43—22no—
88C4⋊Dic43C22⋊C414yes—
89Dic43⋊C4—24no—
90Dic43⋊C4—24no—
91Dic43⋊C4—22no—
92Dic43⋊C4—22no—
93C4×Dic43—21no—
94C4×Dic43—21no—
95C2×C43⋊C8—42no—
96C23×C43—24no—
97C23×C43—44no—
98C23×C43—44no—
99C23×C43—44no—
100C23×C43C2×C22⋊C411yescharacteristic
101C22×D43—21no—
102C22×D43—22no—
103C22×D43—42no—
104D4×C43—44no—
105D4×C43—44no—
106D4×C43—84no—
107D4×C43—84no—
108C2×C4×C43—22no—
109C2×C4×C43—42no—
110C2×C4×C43C2×C22⋊C411yescharacteristic
111C2×C4×C43C2×C22⋊C411yescharacteristic
112C2×C4×C43#12012yes—
113C2×C4×C43#12012yes—
114C22⋊D43—88no—
115C2×Dic43—22no—
116C2×Dic43—24no—
117C2×Dic43—21no—
118C2×Dic43—22no—
119C2×Dic43—44no—
120C2×Dic43—42no—
121C2×Dic43—88no—
122C4×D43—42no—
123C4×D43—42no—
124C8×C43—82no—
125C43⋊C8—82no—
126#8526—431nomaximal, Sylow
127C22×C43—22no—
128C22×C43—44no—
129C22×C43—44no—
130C22×C43—44no—
131C22×C43—88no—
132C22×C43#37911yescharacteristic
133C22×C43#41312yes—
134C2×D43—42no—
135C2×D43—41no—
136C2×D43—82no—
137C4×C43—22no—
138C4×C43—22no—
139C4×C43—21no—
140C4×C43—21no—
141Dic43—44no—
142Dic43—42no—
143Dic43—41no—
144C2×#540—431no—
145#1555—431no—
146#1555D4311yescharacteristic, complemented
147#1534—432no—
148#1464—432no—
149C2×C43—22no—
150C2×C43—84no—
151C2×C43#178511yescharacteristic
152C2×C43#179512yes—
153D43—81no—
154#540—864no—
155#540—862no—
156#540—862no—
157C2×#127C2×D4311yescharacteristic
158C2×#125—431no—
159C2×#123—862no—
160C2×#121—432no—
161C2×#121—862no—
162C2×C4×D4—432no—
163C2×#117—431no—
164#432—432no—
165#432C2×D4312yes—
166#331—22no—
167#331—862no—
168#330—864no—
169#324—862no—
170#323—862no—
171C43#852611yescharacteristic, complemented, Sylow
172C22×D4—22no—
173C22×D4—862no—
174C22×D4C4×D4312yes—
175C23×C4—431no—
176C23×C4—862no—
177#127—22no—
178#127D17212yes—
179#127C22⋊D4312yes—
180#125—434no—
181#125—861no—
182#125—861no—
183#123—868no—
184#123—868no—
185#121—864no—
186#121—868no—
187#121—868no—
188#121—864no—
189C4×D4—864no—
190C4×D4—864no—
191#117—861no—
192#117—862no—
193#117—861no—
194C2×C4⋊C4—432no—
195C2×C4⋊C4—432no—
196C2×C4⋊C4—862no—
197C2×C22⋊C4—432no—
198C2×C22⋊C4—862no—
199C2×C22⋊C4—862no—
200C2×C42—431no—
201C2×C42C22×D4311yescharacteristic
202C4⋊C8—22no—
203C4⋊C8—862no—
204C22⋊C8—22no—
205C22⋊C8—862no—
206#97—22no—
207#97—862no—
208C24—22no—
209C24—431no—
210C2×D4—22no—
211C2×D4—24no—
212C2×D4—24no—
213C2×D4—44no—
214C2×D4—84no—
215C2×D4—868no—
216C2×D4—3444no—
217C2×D4(C2×D43)⋊C414yes—
218C22×C4—431no—
219C22×C4—432no—
220C22×C4—868no—
221C22×C4—862no—
222C22×C4—861no—
223C22×C4—861no—
224C22×C4—3444no—
225C22×C4—1722no—
226C22×C4C2×C4×D4311yescharacteristic
227C22×C4D4×D4312yes—
228C2×C8—42no—
229C2×C8—1722no—
230C4⋊C4—434no—
231C4⋊C4—862no—
232C4⋊C4—862no—
233C4⋊C4—864no—
234C4⋊C4—862no—
235C4⋊C4—864no—
236C22⋊C4—868no—
237C22⋊C4—868no—
238C22⋊C4—862no—
239C22⋊C4—862no—
240C42—861no—
241C42—861no—
242C42C2×D17211yescharacteristic
243C42D4×D4312yes—
244C42C2×C22⋊D4311yescharacteristic
245C23—24no—
246C23—44no—
247C23—44no—
248C23—44no—
249C23—862no—
250C23—861no—
251C23—1722no—
252C23C22⋊C4×D4311yescharacteristic
253D4—44no—
254D4—44no—
255D4—84no—
256D4—84no—
257D4—3448no—
258C2×C4—22no—
259C2×C4—42no—
260C2×C4—862no—
261C2×C4—862no—
262C2×C4—861no—
263C2×C4—864no—
264C2×C4—3448no—
265C2×C4—1722no—
266C2×C4—1722no—
267C2×C4—1724no—
268C2×C4—1722no—
269C2×C4C22⋊C4×D4311yescharacteristic
270C2×C4C2×(C2×D43)⋊C411yescharacteristic
271C2×C4#1306329312yes—
272C2×C4#1306329512yes—
273C8—82no—
274C8—3442no—
275C22—22no—
276C22—44no—
277C22—44no—
278C22—44no—
279C22—88no—
280C22—3442no—
281C22—1721no—
282C22—1722no—
283C22#1458275411yescharacteristic
284C22#1458288012yes—
285C4—21no—
286C4—21no—
287C4—22no—
288C4—22no—
289C4—1721no—
290C4—1722no—
291C4—1724no—
292C2—22no—
293C2—84no—
294C2—3441no—
295C2#1913452011yescharacteristic
296C2#1913456212yes—
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1555C2
socleC22×C43#379
prime radicalC2×#14583503C2
cosocleC2×C42×C43C23
hypercenter#1555D43
hypocenterC43#8526
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1555

Complements

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

NH ≅ G/Ntype
2. #19133309C2semidirect
3. #19133221C2semidirect
4. #19132927C2semidirect
5. C43×#1555C2semidirect
146. #1555D43semidirect
171. C43#8526semidirect

Maximal subgroups

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

subgroupindex
C2×#145835032
#191333092
#191332212
#191329272
C43×#15552
#852643