Finite Group Databasebeta

← #24984855

Subgroups — #24984855

Order 11008.

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

normal subgroups only

This group has 520 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
1#19137142C211yesmaximal, characteristic
2#19134447C212yesmaximal, complemented
3#19132420C212yesmaximal, complemented
4#19132416C211yesmaximal, characteristic
5C43×#1270C211yesmaximal, characteristic
6C2×#13063312C411yescharacteristic
7C2×#13063290C411yescharacteristic
8C2×D4×Dic43C411yescharacteristic
9C2×Dic43⋊C8—22no—
10C2×#13063235—22no—
11#14582805C2211yescharacteristic
12#14582787—22no—
13#14582764C411yescharacteristic
14C22⋊C4×Dic43—22no—
15C42×Dic43C2211yescharacteristic
16#14582654C2212yes—
17C43×#390C2211yescharacteristic
18C43×#336C2212yes—
19C22×Dic86C2×C411yescharacteristic
20C23×Dic43—21no—
21C22×C43⋊C8—22no—
22#13063312—22no—
23#13063312—22no—
24#13063290—42no—
25D4×Dic43—42no—
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×Dic43⋊C4—21no—
28C2×C22⋊Dic43—22no—
29C2×C22⋊Dic43—21no—
30C2×C4×Dic43—21no—
31C2×C4×Dic43C2×C411yescharacteristic
32C2×C4×Dic43C2×C411yescharacteristic
33C2×C4×Dic43D412yes—
34C2×C4×Dic43D412yes—
35Dic43⋊C8—28no—
36#13063235—44no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C22×D4×C43C2×C411yescharacteristic
40C22×C8×C43—22no—
41C2×C4⋊C4×C43C2×C411yescharacteristic
42C2×C22⋊C4×C43—22no—
43C2×C42×C43C2311yescharacteristic
44C24×C43—21no—
45C2×D4×C43—21no—
46C2×D4×C43—41no—
47C2×D4×C43—41no—
48C2×D4×C43M1612yes—
49C22×C4×C43—21no—
50C22×C4×C43C22×C411yescharacteristic
51C22×C4×C43C2×D412yes—
52C22×Dic43—21no—
53C22×Dic43—21no—
54C22×Dic43—42no—
55C22×Dic43—44no—
56C22×Dic43C22⋊C412yes—
57C22×Dic43C22⋊C411yescharacteristic
58C22×Dic43C22⋊C411yescharacteristic
59C2×Dic86—21no—
60C2×Dic86—41no—
61C2×Dic86—41no—
62C2×Dic86M1612yes—
63C2×C8×C43—24no—
64C2×C8×C43—42no—
65C2×C8×C43—42no—
66C4⋊C4×C43—41no—
67C22⋊C4×C43—42no—
68C22⋊C4×C43—42no—
69C42×C43—41no—
70C22⋊Dic43—28no—
71C22⋊Dic43—42no—
72C4⋊Dic43—41no—
73Dic43⋊C4—42no—
74C4×Dic43—21no—
75C4×Dic43—21no—
76C4×Dic43—22no—
77C4×Dic43—22no—
78C4×Dic43—22no—
79C4×Dic43—24no—
80C4×Dic43—42no—
81C2×C43⋊C8—24no—
82C2×C43⋊C8—42no—
83C2×C43⋊C8—42no—
84C23×C43—22no—
85C23×C43—41no—
86C23×C43—41no—
87C23×C43—42no—
88C23×C43—42no—
89C23×C43C2×C22⋊C411yescharacteristic
90D4×C43—42no—
91D4×C43—42no—
92C2×C4×C43—22no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43—22no—
96C2×C4×C43—41no—
97C2×C4×C43—42no—
98C2×C4×C43C2×M1611yescharacteristic
99C2×C4×C43C2×M1611yescharacteristic
100C2×C4×C43AGL(1,ℤ/8)12yes—
101C2×C4×C43#13712yes—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—21no—
105C2×Dic43—22no—
106C2×Dic43—22no—
107C2×Dic43—22no—
108C2×Dic43—41no—
109C2×Dic43—41no—
110C2×Dic43—41no—
111C2×Dic43—42no—
112C2×Dic43—84no—
113C2×Dic43#10012yes—
114C2×Dic43#10414yes—
115Dic86—42no—
116Dic86—42no—
117C8×C43—44no—
118C43⋊C8—44no—
119#7635—431nomaximal, Sylow
120C22×C43—42no—
121C22×C43—44no—
122C22×C43—81no—
123C22×C43—82no—
124C22×C43—81no—
125C22×C43#40711yescharacteristic
126C22×C43#41011yescharacteristic
127C22×C43C2×#10011yescharacteristic
128C22×C43#41712yes—
129C22×C43C2×#10412yes—
130C4×C43—21no—
131C4×C43—21no—
132C4×C43—22no—
133C4×C43—22no—
134C4×C43—81no—
135Dic43—41no—
136Dic43—42no—
137Dic43—42no—
138Dic43—81no—
139Dic43#32914yes—
140C4×#124—431no—
141#1767—432no—
142#1272—432no—
143#1270—431no—
144#1270D4311yescharacteristic
145C2×C43—82no—
146C2×C43#146611yescharacteristic
147C2×C43#148912yes—
148C2×C43#150912yes—
149C2×C43C2×#32911yescharacteristic
150C2×C43#156011yescharacteristic
151C2×#124—431no—
152C2×C4×Q8—431no—
153C2×C4×D4—431no—
154C2×C4⋊C8—862no—
155C2×#97—862no—
156#391—431no—
157#390C2×D4311yescharacteristic
158#388—862no—
159#382—431no—
160C4×C22⋊C4—862no—
161C43—431no—
162#336—432no—
163#336C2×D4312yes—
164C43#763511yescharacteristic, complemented, Sylow
165C22×Q8—431no—
166C22×D4C4×D4311yescharacteristic
167C23×C4—861no—
168C22×C8—22no—
169C22×C8—862no—
170#124—862no—
171#124—862no—
172C4×Q8—1722no—
173C4×D4—1722no—
174C2×C4⋊C4—431no—
175C2×C4⋊C4—861no—
176C2×C4⋊C4C4×D4311yescharacteristic
177C2×C22⋊C4—22no—
178C2×C22⋊C4—862no—
179C2×C22⋊C4—861no—
180C2×C42—431no—
181C2×C42—431no—
182C2×C42—432no—
183C2×C42—432no—
184C2×C42—861no—
185C2×C42C22×D4311yescharacteristic
186C4⋊C8—868no—
187#97—1724no—
188#95—862no—
189#95—862no—
190C24—21no—
191C2×Q8—432no—
192C2×Q8—861no—
193C2×Q8—1721no—
194C2×Q8—1721no—
195C2×D4—21no—
196C2×D4—41no—
197C2×D4—41no—
198C2×D4#1062187212yes—
199C22×C4—21no—
200C22×C4—431no—
201C22×C4—432no—
202C22×C4—431no—
203C22×C4—861no—
204C22×C4—861no—
205C22×C4—1722no—
206C22×C4—1724no—
207C22×C4C2×C4×D4311yescharacteristic
208C22×C4D4×D4312yes—
209C2×C8—24no—
210C2×C8—42no—
211C2×C8—42no—
212C2×C8—864no—
213C2×C8—1722no—
214C2×C8—1722no—
215C4⋊C4—41no—
216C4⋊C4—1721no—
217C4⋊C4—1722no—
218C22⋊C4—42no—
219C22⋊C4—42no—
220C22⋊C4—868no—
221C22⋊C4—1722no—
222C42—41no—
223C42—864no—
224C42—862no—
225C42—861no—
226C42—861no—
227C42—862no—
228C42—862no—
229C42—1722no—
230C23—22no—
231C23—41no—
232C23—41no—
233C23—42no—
234C23—42no—
235C23C22⋊C4×D4311yescharacteristic
236Q8—1722no—
237Q8—1722no—
238D4—42no—
239D4—42no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—432no—
247C2×C4—434no—
248C2×C4—862no—
249C2×C4—862no—
250C2×C4—861no—
251C2×C4—862no—
252C2×C4—862no—
253C2×C4—862no—
254C2×C4—3444no—
255C2×C4—1721no—
256C2×C4—1722no—
257C2×C4—1721no—
258C2×C4—1721no—
259C2×C4M16×D4311yescharacteristic
260C2×C4C2×#1062187211yescharacteristic
261C2×C4#1306334912yes—
262C2×C4#1306335412yes—
263C8—44no—
264C8—1724no—
265C22—42no—
266C22—44no—
267C22—81no—
268C22—82no—
269C22—81no—
270C22#1458286111yescharacteristic
271C22#1458287111yescharacteristic
272C22#100×D4311yescharacteristic
273C22#1458289712yes—
274C22#104×D4312yes—
275C4—21no—
276C4—21no—
277C4—22no—
278C4—22no—
279C4—81no—
280C4—434no—
281C4—3441no—
282C4—1722no—
283C4—1722no—
284C4—1721no—
285C2—82no—
286C2#1913293411yescharacteristic
287C2#1913303112yes—
288C2#1913311712yes—
289C2#329×D4311yescharacteristic
290C2#1913332711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1270C2
socleC23×C43C2×C22⋊C4
prime radicalC22×D4×C43C2×C4
cosocleC2×C42×C43C23
hypercenter#1270D43
hypocenterC43#7635
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #19134447C2semidirect
3. #19132420C2semidirect
164. C43#7635semidirect

Maximal subgroups

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

subgroupindex
#191371422
#191344472
#191324202
#191324162
C43×#12702
#763543