Finite Group Databasebeta

← #24988844

Subgroups — #24988844

Order 11008.

682 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 115 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#19148482C211yesmaximal, characteristic
2#19135583C212yesmaximal, complemented
3#19133190C211yesmaximal, characteristic, complemented
4#19133032C212yesmaximal
5C43×#1561C211yesmaximal, characteristic, complemented
6#14583628—22no—
7#14583622—22no—
8#14583591—24no—
9#14583512—22no—
10#14583475C412yes—
11#14583454—22no—
12C2×#13063325C2211yescharacteristic
13#14583376C412yes—
14C4×#10621898C2211yescharacteristic
15C4×#10621877C2212yes—
16#14582667—24no—
17#14582641—22no—
18#14582629—22no—
19#14582626—22no—
20C43×#533C2211yescharacteristic
21C43×#423C2212yes—
22C43×#332—22no—
23C2×#10621898C2×C411yescharacteristic
24C22×Dic86C2×C412yes—
25C2×#10621877—22no—
26#13063325—22no—
27#13063325—22no—
28#13063325—21no—
29#13063325—21no—
30#13063320—28no—
31#13063316—24no—
32#13063316—28no—
33#13063313—22no—
34#13063309—24no—
35#13063305—24no—
36#13063301—24no—
37Q8×Dic43—24no—
38C4×Dic86—24no—
39C4×Dic86D412yes—
40#13063290—24no—
41C4×D172D412yes—
42C4×C22⋊D43—22no—
43#13063284C2×C411yescharacteristic
44#13063283—24no—
45#13063282—21no—
46#13063281—24no—
47C2×C4⋊Dic43D414yes—
48C42×D43—21no—
49#13063236—22no—
50C4×C43⋊C8—22no—
51C2×M16×C43—22no—
52C4⋊Q8×C43D412yes—
53#125×C43D412yes—
54C22⋊Q8×C43—22no—
55C4×Q8×C43—22no—
56#117×C43C2×C412yes—
57C2×C42×C43C2311yescharacteristic
58C4⋊C8×C43—22no—
59C4⋊C8×C43—22no—
60C2×Q8×C43—22no—
61C22×C4×C43C22×C411yescharacteristic
62C22×C4×C43C2×D412yes—
63C2×C22⋊D43—21no—
64C22×Dic43C22⋊C414yes—
65#10621898—42no—
66C2×D172C22⋊C411yescharacteristic
67C2×C4×D43—21no—
68C2×C4×D43—22no—
69C2×Dic86—22no—
70C2×Dic86—22no—
71C2×Dic86—44no—
72C2×Dic86C22⋊C411yescharacteristic
73M16×C43—44no—
74C2×C8×C43—42no—
75C4⋊C4×C43—24no—
76C4⋊C4×C43—22no—
77C4⋊C4×C43C22⋊C414yes—
78C22⋊C4×C43—22no—
79C42×C43—22no—
80C42×C43C2×D411yescharacteristic
81C42×C43C2×D412yes—
82C42×C43C2×D411yescharacteristic
83C22⋊Dic43—21no—
84(C2×D43)⋊C4—28no—
85(C2×D43)⋊C4—22no—
86C4⋊Dic43—28no—
87C4⋊Dic43—24no—
88C4⋊Dic43—24no—
89C4⋊Dic43C22⋊C412yes—
90Dic43⋊C4—28no—
91Dic43⋊C4—22no—
92C4×Dic43—28no—
93C4×Dic43—21no—
94C4×Dic43—22no—
95#10621877—24no—
96#10621877—42no—
97C2×C43⋊C8—42no—
98C23×C43C2×C22⋊C411yescharacteristic
99C22×D43—21no—
100Q8×C43—42no—
101Q8×C43—42no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—24no—
106C2×C4×C43C2×C22⋊C411yescharacteristic
107C2×C4×C43C2×C22⋊C411yescharacteristic
108C2×C4×C43#12012yes—
109C2×C4×C43#12012yes—
110C22⋊D43—42no—
111C2×Dic43—22no—
112C2×Dic43—21no—
113C2×Dic43—24no—
114C2×Dic43—44no—
115D172—22no—
116C4×D43—42no—
117C4×D43—42no—
118C4×D43—42no—
119Dic86—22no—
120Dic86—44no—
121Dic86—44no—
122C8×C43—82no—
123C43⋊C8—44no—
124#8474—431nomaximal, Sylow
125C22×C43—22no—
126C22×C43—21no—
127C22×C43#37911yescharacteristic
128C2×D43—42no—
129C2×D43—41no—
130C4×C43—22no—
131C4×C43—21no—
132C4×C43—44no—
133C4×C43#41312yes—
134C4×C43#45412yes—
135C4×C43#45612yes—
136Dic43—42no—
137Dic43—41no—
138Dic43—44no—
139#3509—431no—
140#1997—432no—
141#1561D4311yescharacteristic, complemented
142#1526—431no—
143#1489—432no—
144C2×C43—41no—
145C2×C43#178511yescharacteristic
146C2×C43#179312yes—
147D43—81no—
148#557—862no—
149#556—862no—
150#552—864no—
151#541—862no—
152#536—432no—
153#533—862no—
154#533C2×D4311yescharacteristic
155C2×C4⋊Q8—431no—
156#519—432no—
157C4×#41—431no—
158#423C2×D4312yes—
159C4×M16—432no—
160#343—864no—
161#332—22no—
162#330—862no—
163Q8⋊C8—862no—
164D4⋊C8—862no—
165C43#847411yescharacteristic, complemented, Sylow
166C2×#41—431no—
167C22×Q8—432no—
168C2×M16—22no—
169C2×M16—862no—
170C4⋊Q8—862no—
171C4⋊Q8—861no—
172C4⋊Q8—862no—
173C4⋊Q8—861no—
174C4⋊Q8C22⋊D4312yes—
175#126—868no—
176#125—864no—
177#125—868no—
178#125D17212yes—
179#124—862no—
180#123—864no—
181C22⋊Q8—22no—
182C22⋊Q8—864no—
183C22⋊Q8—864no—
184C4×Q8—22no—
185C4×Q8—432no—
186C4×Q8—864no—
187C4×Q8—864no—
188C4×Q8—864no—
189C4×D4—432no—
190C4×D4—862no—
191#117—431no—
192#117—864no—
193#117—864no—
194#117—861no—
195#117C4×D4312yes—
196C2×C4⋊C4—434no—
197C2×C42—861no—
198C2×C42C22×D4311yescharacteristic
199C4⋊C8—22no—
200C4⋊C8—22no—
201#97—862no—
202C4×C8—862no—
203#41—1722no—
204C2×Q8—22no—
205C2×Q8—431no—
206C2×Q8—862no—
207C2×Q8—862no—
208C2×Q8—1724no—
209C2×D4—431no—
210C2×D4—861no—
211C22×C4—434no—
212C22×C4—861no—
213C22×C4—862no—
214C22×C4C2×C4×D4311yescharacteristic
215C22×C4D4×D4312yes—
216M16—44no—
217M16—864no—
218M16—1722no—
219C2×C8—42no—
220C2×C8—1722no—
221C4⋊C4—22no—
222C4⋊C4—24no—
223C4⋊C4—432no—
224C4⋊C4—868no—
225C4⋊C4—868no—
226C4⋊C4—864no—
227C4⋊C4—864no—
228C4⋊C4—862no—
229C4⋊C4(C2×D43)⋊C414yes—
230C22⋊C4—22no—
231C22⋊C4—868no—
232C22⋊C4—861no—
233C22⋊C4—862no—
234C42—22no—
235C42—868no—
236C42—861no—
237C42—862no—
238C42C2×D17211yescharacteristic
239C42D4×D4312yes—
240C42C2×C22⋊D4311yescharacteristic
241C23—861no—
242C23C22⋊C4×D4311yescharacteristic
243Q8—42no—
244Q8—42no—
245Q8—862no—
246Q8—1724no—
247Q8—1724no—
248D4—862no—
249D4—1722no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—862no—
255C2×C4—864no—
256C2×C4—861no—
257C2×C4—1722no—
258C2×C4—1722no—
259C2×C4—1722no—
260C2×C4—1724no—
261C2×C4C22⋊C4×D4311yescharacteristic
262C2×C4C2×(C2×D43)⋊C411yescharacteristic
263C2×C4#1306329312yes—
264C2×C4#1306329512yes—
265C8—82no—
266C8—1724no—
267C22—21no—
268C22—22no—
269C22—1721no—
270C22—1722no—
271C22#1458275411yescharacteristic
272C4—21no—
273C4—22no—
274C4—44no—
275C4—1721no—
276C4—1724no—
277C4—1722no—
278C4#1458288212yes—
279C4#1458307012yes—
280C4#1458308012yes—
281C2—41no—
282C2—3441no—
283C2#1913452211yescharacteristic
284C2#1913455212yes—
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1561C2
socleC22×C43#379
prime radicalC2×#10621898C2×C4
cosocleC2×C42×C43C23
hypercenter#1561D43
hypocenterC43#8474
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1561

Complements

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

NH ≅ G/Ntype
2. #19135583C2semidirect
3. #19133190C2semidirect
5. C43×#1561C2semidirect
141. #1561D43semidirect
165. C43#8474semidirect

Maximal subgroups

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

subgroupindex
#191484822
#191355832
#191331902
#191330322
C43×#15612
#847443