Finite Group Databasebeta

← #25012603

Subgroups — #25012603

Order 11008.

480 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 93 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#19137309C211yesmaximal, characteristic
2C2×#14582695C212yesmaximal
3#19134589C212yesmaximal, complemented
4#19132722C211yesmaximal, characteristic, complemented
5C43×#1394C211yesmaximal, characteristic, complemented
6C2×#13063314C2211yescharacteristic
7C2×Q8×Dic43C2211yescharacteristic
8C2×#13063287C411yescharacteristic
9#14582922—22no—
10C2×#13063244C2212yes—
11#14582801C411yescharacteristic
12#14582788—22no—
13#14582773—22no—
14#14582768C411yescharacteristic
15#14582745C411yescharacteristic
16#14582695—24no—
17#14582667—22no—
18C2×#101×C43C2212yes—
19C43×#391C2211yescharacteristic
20C22×D172C2×C411yescharacteristic
21C22×C4×D43—21no—
22C2×#10621877—22no—
23#13063314—22no—
24#13063314D412yes—
25#13063314Q812yes—
26Q8×Dic43—42no—
27#13063287—42no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×C4⋊Dic43D412yes—
30C2×Dic43⋊C4—22no—
31C2×(C2×D43)⋊C4—22no—
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—22no—
34C2×C4×Dic43C2×C411yescharacteristic
35C2×C4×Dic43C2×C411yescharacteristic
36C2×C4×Dic43D412yes—
37Dic43⋊C8—44no—
38#13063244—22no—
39#13063244—22no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C22×Q8×C43C2311yescharacteristic
43C2×M16×C43—22no—
44C2×C4⋊C4×C43C2×C411yescharacteristic
45C2×C42×C43C2×C411yescharacteristic
46#101×C43—22no—
47#101×C43—22no—
48#95×C43—22no—
49C23×D43—21no—
50C2×Q8×C43—41no—
51C2×Q8×C43—41no—
52C2×Q8×C43C2×D411yescharacteristic
53C2×Q8×C43C2×Q811yescharacteristic
54C2×Q8×C43#4112yes—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43C22×C411yescharacteristic
58C22×C4×C43C2×D412yes—
59C22×Dic43—21no—
60C22×Dic43C22⋊C411yescharacteristic
61C22×Dic43C22⋊C412yes—
62C22×Dic43C22⋊C411yescharacteristic
63C2×D172—21no—
64C2×D172—41no—
65C2×D172—41no—
66C2×D172C4⋊C412yes—
67C2×C4×D43—42no—
68C2×C4×D43—82no—
69M16×C43—42no—
70M16×C43—42no—
71C2×C8×C43—42no—
72C4⋊C4×C43—41no—
73C42×C43—41no—
74(C2×D43)⋊C4—24no—
75(C2×D43)⋊C4—24no—
76(C2×D43)⋊C4—42no—
77(C2×D43)⋊C4—82no—
78C4⋊Dic43—41no—
79C4⋊Dic43—42no—
80Dic43⋊C4—82no—
81C4×Dic43—21no—
82C4×Dic43—24no—
83C4×Dic43—22no—
84C4×Dic43C4⋊C412yes—
85#10621877—42no—
86#10621877—42no—
87C2×C43⋊C8—42no—
88C23×C43C2×C22⋊C411yescharacteristic
89C22×D43—22no—
90C22×D43—42no—
91C22×D43—42no—
92C22×D43—41no—
93C22×D43—41no—
94Q8×C43—41no—
95Q8×C43—41no—
96Q8×C43—42no—
97C2×C4×C43—22no—
98C2×C4×C43—21no—
99C2×C4×C43—22no—
100C2×C4×C43—21no—
101C2×C4×C43—42no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43C2×C4⋊C411yescharacteristic
107C2×C4×C43#11711yescharacteristic
108C2×C4×C43#12112yes—
109C2×C4×C43C22⋊Q812yes—
110C2×Dic43—22no—
111C2×Dic43—21no—
112C2×Dic43—22no—
113C2×Dic43—41no—
114C2×Dic43—41no—
115C2×Dic43—41no—
116C2×Dic43—42no—
117C2×Dic43—41no—
118C2×Dic43#9912yes—
119D172—42no—
120D172—42no—
121C4×D43—84no—
122C8×C43—82no—
123C43⋊C8—82no—
124#12803—431nomaximal, Sylow
125C22×C43—21no—
126C22×C43—21no—
127C22×C43#38011yescharacteristic
128C22×C43C2×#9911yescharacteristic
129C22×C43#41011yescharacteristic
130C2×D43—44no—
131C2×D43—42no—
132C2×D43—82no—
133C2×D43—81no—
134C2×D43—81no—
135C4×C43—22no—
136C4×C43—21no—
137C4×C43—21no—
138C4×C43—22no—
139C4×C43—81no—
140C4×C43—81no—
141Dic43—22no—
142Dic43—42no—
143Dic43—41no—
144Dic43—42no—
145#2326—431no—
146C2×#355—432no—
147#1801—432no—
148#1394—431no—
149#1394D4311yescharacteristic, complemented
150C2×C43—21no—
151C2×C43—21no—
152C2×C43#179911yescharacteristic
153C2×C43#213311yescharacteristic
154C2×C43#213411yescharacteristic
155D43—82no—
156C2×#124—431no—
157C2×C4×Q8—431no—
158C2×C4×D4—431no—
159#423—862no—
160C2×#101—432no—
161C2×#101C2×D4312yes—
162#391C2×D4311yescharacteristic
163#390—431no—
164#388—862no—
165#385—862no—
166#384—431no—
167#376—431no—
168#355—864no—
169#343—862no—
170C43#1280311yescharacteristic, complemented, Sylow
171C22×Q8C22×D4311yescharacteristic
172C22×D4—431no—
173C23×C4—861no—
174C2×M16—22no—
175C2×M16—862no—
176#124—432no—
177#124—432no—
178#124—862no—
179C4×Q8—1722no—
180C4×D4—1722no—
181C2×C4⋊C4—431no—
182C2×C4⋊C4—432no—
183C2×C4⋊C4—862no—
184C2×C4⋊C4C4×D4311yescharacteristic
185C2×C22⋊C4—862no—
186C2×C22⋊C4—862no—
187C2×C22⋊C4—861no—
188C2×C42—431no—
189C2×C42—431no—
190C2×C42—432no—
191C2×C42C4×D4311yescharacteristic
192C4⋊C8—1724no—
193#101—22no—
194#101—22no—
195#101—862no—
196#101—862no—
197#95—22no—
198#95—861no—
199#95—861no—
200C24—861no—
201C2×Q8—41no—
202C2×Q8—41no—
203C2×Q8#1062189812yes—
204C2×Q8D4×D4311yescharacteristic
205C2×Q8Q8×D4311yescharacteristic
206C2×D4—432no—
207C2×D4—861no—
208C2×D4—1721no—
209C2×D4—1721no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—431no—
213C22×C4—431no—
214C22×C4—432no—
215C22×C4—861no—
216C22×C4—3442no—
217C22×C4—1722no—
218C22×C4C2×C4×D4311yescharacteristic
219C22×C4D4×D4312yes—
220M16—42no—
221M16—42no—
222M16—1722no—
223M16—1722no—
224C2×C8—42no—
225C2×C8—1722no—
226C4⋊C4—41no—
227C4⋊C4—3442no—
228C4⋊C4—1721no—
229C4⋊C4—1722no—
230C22⋊C4—864no—
231C22⋊C4—864no—
232C22⋊C4—3442no—
233C22⋊C4—1722no—
234C42—41no—
235C42—432no—
236C42—864no—
237C42—862no—
238C42—861no—
239C23—862no—
240C23—1722no—
241C23—1722no—
242C23—1721no—
243C23—1721no—
244C23C22⋊C4×D4311yescharacteristic
245Q8—42no—
246Q8—41no—
247Q8—41no—
248D4—1722no—
249D4—1722no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—432no—
260C2×C4—861no—
261C2×C4—862no—
262C2×C4—862no—
263C2×C4—3444no—
264C2×C4—1721no—
265C2×C4—1721no—
266C2×C4—1721no—
267C2×C4—1722no—
268C2×C4—1721no—
269C2×C4C4⋊C4×D4311yescharacteristic
270C2×C4#1306328211yescharacteristic
271C2×C4#1306329812yes—
272C2×C4#1306330312yes—
273C8—82no—
274C8—3442no—
275C22—21no—
276C22—21no—
277C22—3442no—
278C22—3441no—
279C22—3441no—
280C22—1724no—
281C22—1722no—
282C22#1458275811yescharacteristic
283C22#99×D4311yescharacteristic
284C22#1458287111yescharacteristic
285C4—22no—
286C4—21no—
287C4—21no—
288C4—22no—
289C4—81no—
290C4—81no—
291C4—862no—
292C4—1722no—
293C4—1721no—
294C4—1722no—
295C2—21no—
296C2—21no—
297C2—3442no—
298C2#1913458211yescharacteristic
299C2#1913628311yescharacteristic
300C2#1913628511yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC43×#1394C2
socleC22×C43C2×#99
prime radicalC22×D172C2×C4
cosocleC22×Q8×C43C23
hypercenter#1394D43
hypocenterC43#12803
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
3. #19134589C2semidirect
4. #19132722C2semidirect
5. C43×#1394C2semidirect
149. #1394D43semidirect
170. C43#12803semidirect

Maximal subgroups

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

subgroupindex
#191373092
C2×#145826952
#191345892
#191327222
C43×#13942
#1280343