Finite Group Databasebeta

← #25012633

Subgroups — #25012633

Order 11008.

412 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 89 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#19143310C211yesmaximal, characteristic
2#19136278C212yesmaximal
3#19134643C212yesmaximal, complemented
4#19132718C211yesmaximal, characteristic, complemented
5C43×#1392C211yesmaximal, characteristic, complemented
6C2×#13063333C411yescharacteristic
7C2×#13063332C2211yescharacteristic
8#14583445C2211yescharacteristic
9#14582973—22no—
10#14582967—22no—
11C2×#13063260—22no—
12#14582922C411yescharacteristic
13#14582883C2212yes—
14#14582865C411yescharacteristic
15C2×#13063235C411yescharacteristic
16#14582697—22no—
17#14582695—22no—
18C43⋊#338—22no—
19C43×#413C2212yes—
20C43×#408C2211yescharacteristic
21C2×#10621898C2×C411yescharacteristic
22#13063333—42no—
23#13063332—42no—
24C2×#10621877—22no—
25C2×#10621877C2×C411yescharacteristic
26C2×#10621877D412yes—
27C2×#10621872—21no—
28C22×C43⋊C8C2×C411yescharacteristic
29C22×C43⋊C8D412yes—
30C2×C8×D43—21no—
31#13063323D411yescharacteristic
32#13063321Q811yescharacteristic
33#13063314D411yescharacteristic
34#13063312Q811yescharacteristic
35#13063297—22no—
36C4×C22⋊D43—22no—
37C2×C4×Dic43C2×C411yescharacteristic
38#13063260—44no—
39Dic43⋊C8—22no—
40#13063244—22no—
41#13063242—22no—
42(C2×D43)⋊C8—22no—
43#13063235—21no—
44#13063235—21no—
45C2×#41×C43C2311yescharacteristic
46C2×M16×C43—22no—
47C2×M16×C43C2×C411yescharacteristic
48C22×C8×C43C2×C411yescharacteristic
49#101×C43—22no—
50#100×C43—22no—
51C22⋊C8×C43—22no—
52#41×C43—41no—
53#41×C43—41no—
54C2×Q8×C43C2×D411yescharacteristic
55C2×D4×C43C2×Q811yescharacteristic
56C2×D4×C43#4112yes—
57C22×C4×C43C22×C411yescharacteristic
58C22×C4×C43C2×D412yes—
59C2×C22⋊D43—21no—
60C2×C22⋊D43—22no—
61C22×Dic43—21no—
62#10621898—41no—
63#10621898—41no—
64C2×D172C4⋊C411yescharacteristic
65C2×C4×D43—21no—
66C2×Dic86C4⋊C411yescharacteristic
67M16×C43—41no—
68M16×C43—42no—
69M16×C43—42no—
70C2×C8×C43—21no—
71C2×C8×C43—21no—
72C2×C8×C43—41no—
73C2×C8×C43—42no—
74C22⋊Dic43—22no—
75(C2×D43)⋊C4—22no—
76Dic43⋊C4—22no—
77C4×Dic43—21no—
78C4×Dic43C4⋊C411yescharacteristic
79C4×Dic43C4⋊C411yescharacteristic
80#10621877—41no—
81#10621877—42no—
82#10621877—42no—
83#10621877—42no—
84C2×C43⋊C8—24no—
85C2×C43⋊C8—22no—
86C2×C43⋊C8—42no—
87C2×C43⋊C8C22⋊C411yescharacteristic
88C2×C43⋊C8C22⋊C412yes—
89C2×C43⋊C8C22⋊C411yescharacteristic
90#10621872—42no—
91C8×D43—42no—
92C23×C43#11711yescharacteristic
93C23×C43C22⋊Q812yes—
94C22×D43—21no—
95Q8×C43—41no—
96D4×C43—41no—
97D4×C43—42no—
98C2×C4×C43—22no—
99C2×C4×C43—21no—
100C2×C4×C43—22no—
101C2×C4×C43—21no—
102C2×C4×C43C2×C22⋊C411yescharacteristic
103C2×C4×C43C2×C4⋊C411yescharacteristic
104C2×C4×C43#12112yes—
105C22⋊D43—42no—
106C22⋊D43—82no—
107C2×Dic43—21no—
108C2×Dic43—21no—
109C2×Dic43—21no—
110C2×Dic43—81no—
111D172—41no—
112C4×D43—41no—
113C4×D43—41no—
114Dic86—41no—
115C8×C43—41no—
116C8×C43—41no—
117C8×C43—82no—
118C43⋊C8—21no—
119C43⋊C8—22no—
120C43⋊C8—82no—
121C43⋊C8#9912yes—
122#12810—431nomaximal, Sylow
123C22×C43—21no—
124C22×C43—22no—
125C22×C43—41no—
126C22×C43—42no—
127C22×C43#38011yescharacteristic
128C2×D43—42no—
129C2×D43—41no—
130C4×C43—22no—
131C4×C43—21no—
132C4×C43C2×#9911yescharacteristic
133C4×C43#41011yescharacteristic
134Dic43—41no—
135Dic43—41no—
136Dic43—41no—
137#2932—431no—
138#2132—432no—
139#1813—432no—
140#1392—431no—
141#1392D4311yescharacteristic, complemented
142C2×C43—21no—
143C2×C43—41no—
144C2×C43—42no—
145C2×C43#179911yescharacteristic
146D43—81no—
147C2×#131—431no—
148C2×#131—431no—
149#532—431no—
150#435—862no—
151#435—862no—
152C2×#108—862no—
153#423—431no—
154#413—432no—
155#413C2×D4312yes—
156#408—431no—
157#408C2×D4311yescharacteristic
158C2×#97—431no—
159#356—862no—
160#355—862no—
161#338—862no—
162C43#1281011yescharacteristic, complemented, Sylow
163C2×#41—431no—
164C2×#41C22×D4311yescharacteristic
165#131—1722no—
166#131—1722no—
167C2×M16—22no—
168C2×M16—431no—
169C2×M16—432no—
170C2×M16—861no—
171C2×M16—862no—
172C2×M16C4×D4311yescharacteristic
173C22×C8—431no—
174C22×C8—432no—
175C22×C8—861no—
176C22×C8C4×D4311yescharacteristic
177C4⋊Q8—431no—
178#127—431no—
179#124—431no—
180#124—431no—
181#121—862no—
182C4×D4—862no—
183C2×C42—431no—
184#108—1724no—
185C4⋊C8—862no—
186#101—22no—
187#101—862no—
188#100—22no—
189#100—862no—
190C22⋊C8—22no—
191C22⋊C8—862no—
192#97—861no—
193#97—861no—
194#41—41no—
195#41—41no—
196#41—1721no—
197#41—1721no—
198C2×Q8—431no—
199C2×Q8D4×D4311yescharacteristic
200C2×D4—431no—
201C2×D4—862no—
202C2×D4—861no—
203C2×D4#1062189812yes—
204C2×D4Q8×D4311yescharacteristic
205C22×C4—861no—
206C22×C4—861no—
207C22×C4C2×C4×D4311yescharacteristic
208C22×C4D4×D4312yes—
209M16—41no—
210M16—42no—
211M16—42no—
212M16—1722no—
213M16—1722no—
214M16—1721no—
215M16—1722no—
216M16—1722no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—41no—
220C2×C8—42no—
221C2×C8—431no—
222C2×C8—431no—
223C2×C8—432no—
224C2×C8—864no—
225C2×C8—862no—
226C2×C8—1722no—
227C2×C8—1722no—
228C4⋊C4—862no—
229C22⋊C4—862no—
230C22⋊C4—862no—
231C42—431no—
232C42—431no—
233C42—861no—
234C23—861no—
235C23#1306328211yescharacteristic
236C23#1306330312yes—
237Q8—41no—
238Q8—1721no—
239D4—42no—
240D4—41no—
241D4—3442no—
242D4—1721no—
243D4—1722no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—861no—
249C2×C4—861no—
250C2×C4—861no—
251C2×C4—3441no—
252C2×C4—1721no—
253C2×C4—1721no—
254C2×C4C22⋊C4×D4311yescharacteristic
255C2×C4C4⋊C4×D4311yescharacteristic
256C2×C4#1306329812yes—
257C8—41no—
258C8—41no—
259C8—82no—
260C8—432no—
261C8—861no—
262C8—862no—
263C8—3442no—
264C22—21no—
265C22—22no—
266C22—41no—
267C22—42no—
268C22—1722no—
269C22—1721no—
270C22#1458275811yescharacteristic
271C4—22no—
272C4—21no—
273C4—1721no—
274C4—1721no—
275C4—1721no—
276C4#99×D4311yescharacteristic
277C4#1458287111yescharacteristic
278C2—21no—
279C2—41no—
280C2—42no—
281C2—3441no—
282C2#1913458211yescharacteristic
subgroupG/H
centerC4#14582871
commutatorC22×C4×C43C22×C4
FrattiniC2×#41C22×D43
FittingC43×#1392C2
socleC2×C43#1799
prime radical#14583445C22
cosocleC2×#41×C43C23
hypercenter#1392D43
hypocenterC43#12810
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1392

Complements

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

NH ≅ G/Ntype
3. #19134643C2semidirect
4. #19132718C2semidirect
5. C43×#1392C2semidirect
141. #1392D43semidirect
162. C43#12810semidirect

Maximal subgroups

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

subgroupindex
#191433102
#191362782
#191346432
#191327182
C43×#13922
#1281043