Finite Group Databasebeta

← #24984716

Subgroups — #24984716

Order 11008.

608 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 111 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#19137159C211yesmaximal, characteristic
2#19134737C212yesmaximal, complemented
3#19132416C211yesmaximal, characteristic, complemented
4#19132415C212yesmaximal, complemented
5C43×#1270C211yesmaximal, characteristic, complemented
6C2×#13063321C411yescharacteristic
7C2×D4×Dic43C411yescharacteristic
8C2×#13063287C411yescharacteristic
9C2×(C22⋊D43)⋊C4—22no—
10#14582801C2211yescharacteristic
11#14582799—22no—
12#14582768C411yescharacteristic
13C42×Dic43C2211yescharacteristic
14#14582654C2212yes—
15#14582653—22no—
16#14582653—22no—
17C43×#390C2211yescharacteristic
18C43×#336C2212yes—
19C22×D172C2×C411yescharacteristic
20C22×C22⋊D43—22no—
21C23×Dic43—21no—
22C22×C4×D43—21no—
23C22×C43⋊C8—22no—
24#13063321—22no—
25#13063321C814yescomplemented
26D4×Dic43—42no—
27#13063287—42no—
28(C22⋊D43)⋊C4—44no—
29(C22⋊D43)⋊C4—44no—
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×Dic43⋊C4—22no—
32C2×C22⋊Dic43—21no—
33C2×(C2×D43)⋊C4—22no—
34C2×(C2×D43)⋊C4—21no—
35C2×C4×Dic43C2×C411yescharacteristic
36C2×C4×Dic43C2×C411yescharacteristic
37C2×C4×Dic43D412yes—
38C2×C4×Dic43D412yes—
39C22×D4×C43C2×C411yescharacteristic
40C22×C8×C43—22no—
41C2×C4⋊C4×C43C2×C411yescharacteristic
42C2×C22⋊C4×C43—22no—
43C2×C42×C43C2311yescharacteristic
44C24×C43—21no—
45C23×D43—21no—
46C2×D4×C43—21no—
47C2×D4×C43—41no—
48C2×D4×C43—41no—
49C2×D4×C43C2×C812yes—
50C22×C4×C43—21no—
51C22×C4×C43C22×C411yescharacteristic
52C22×C4×C43C2×D412yes—
53C2×C22⋊D43—28no—
54C2×C22⋊D43—44no—
55C2×C22⋊D43—44no—
56C22×Dic43—21no—
57C22×Dic43—44no—
58C22×Dic43—42no—
59C22×Dic43C22⋊C411yescharacteristic
60C22×Dic43C22⋊C412yes—
61C22×Dic43C22⋊C411yescharacteristic
62C2×D172—21no—
63C2×D172—41no—
64C2×D172—41no—
65C2×D172C2×C812yes—
66C2×C4×D43—44no—
67C2×C4×D43—42no—
68C2×C8×C43—42no—
69C2×C8×C43—42no—
70C2×C8×C43—42no—
71C4⋊C4×C43—41no—
72C22⋊C4×C43—42no—
73C22⋊C4×C43—42no—
74C42×C43—41no—
75C22⋊Dic43—42no—
76(C2×D43)⋊C4—42no—
77(C2×D43)⋊C4—42no—
78(C2×D43)⋊C4—42no—
79C4⋊Dic43—41no—
80Dic43⋊C4—44no—
81C4×Dic43—22no—
82C4×Dic43—22no—
83C4×Dic43—22no—
84C4×Dic43—42no—
85C4×Dic43C2×C812yes—
86C4×Dic43M1612yes—
87C2×C43⋊C8—42no—
88C2×C43⋊C8—42no—
89C2×C43⋊C8—42no—
90C23×C43—22no—
91C23×C43—41no—
92C23×C43—41no—
93C23×C43—42no—
94C23×C43—42no—
95C23×C43C2×C22⋊C411yescharacteristic
96C22×D43—22no—
97C22×D43—41no—
98C22×D43—41no—
99C22×D43—42no—
100C22×D43—42no—
101D4×C43—42no—
102D4×C43—42no—
103C2×C4×C43—22no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—22no—
107C2×C4×C43—41no—
108C2×C4×C43—42no—
109C2×C4×C43C22×C811yescharacteristic
110C2×C4×C43C2×M1611yescharacteristic
111C2×C4×C43AGL(1,ℤ/8)12yes—
112C2×C4×C43AGL(1,ℤ/8)12yes—
113C22⋊D43—416no—
114C2×Dic43—22no—
115C2×Dic43—22no—
116C2×Dic43—22no—
117C2×Dic43—21no—
118C2×Dic43—22no—
119C2×Dic43—41no—
120C2×Dic43—42no—
121C2×Dic43—84no—
122C2×Dic43C22⋊C814yes—
123C2×Dic43#10012yes—
124D172—42no—
125D172—42no—
126C4×D43—84no—
127C8×C43—82no—
128C43⋊C8—82no—
129#7603—431nomaximal, Sylow
130C22×C43—42no—
131C22×C43—44no—
132C22×C43—81no—
133C22×C43—81no—
134C22×C43—82no—
135C22×C43C2×C22⋊C811yescharacteristic
136C22×C43#41011yescharacteristic
137C22×C43C2×#10011yescharacteristic
138C22×C43#41812yes—
139C22×C43#42112yes—
140C2×D43—42no—
141C2×D43—44no—
142C2×D43—81no—
143C2×D43—81no—
144C2×D43—82no—
145C4×C43—21no—
146C4×C43—21no—
147C4×C43—22no—
148C4×C43—22no—
149C4×C43—81no—
150Dic43—22no—
151Dic43—24no—
152Dic43—41no—
153Dic43—81no—
154C4×#127—431no—
155#1839—432no—
156#1270—431no—
157#1270—432no—
158#1270D4311yescharacteristic, complemented
159C2×C43—82no—
160C2×C43#146011yescharacteristic
161C2×C43#147812yes—
162C2×C43#151412yes—
163C2×C43#153611yescharacteristic
164C2×C43#155511yescharacteristic
165D43—82no—
166C2×#127—431no—
167C2×C4×D4—431no—
168C2×C4×D4—431no—
169C2×C4×D4—862no—
170#390—431no—
171#390—862no—
172#390C2×D4311yescharacteristic
173#384—431no—
174C43—431no—
175#336—432no—
176#336—862no—
177#336—862no—
178#336C2×D4312yes—
179C43#760311yescharacteristic, complemented, Sylow
180C22×D4—431no—
181C22×D4—862no—
182C22×D4C4×D4311yescharacteristic
183C23×C4—861no—
184C23×C4—861no—
185C22×C8—22no—
186C22×C8—862no—
187#127—434no—
188#127—862no—
189C4×D4—1724no—
190C4×D4—1724no—
191C4×D4—1722no—
192C4×D4—1722no—
193C2×C4⋊C4—431no—
194C2×C4⋊C4—862no—
195C2×C4⋊C4C4×D4311yescharacteristic
196C2×C22⋊C4—22no—
197C2×C22⋊C4—861no—
198C2×C22⋊C4—861no—
199C2×C22⋊C4—862no—
200C2×C42—431no—
201C2×C42—431no—
202C2×C42—432no—
203C2×C42—432no—
204C2×C42C22×D4311yescharacteristic
205C24—21no—
206C24—861no—
207C2×D4—21no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—432no—
211C2×D4—868no—
212C2×D4—861no—
213C2×D4—1721no—
214C2×D4—1721no—
215C2×D4—1724no—
216C2×D4—1724no—
217C2×D4C8×D4312yes—
218C22×C4—21no—
219C22×C4—432no—
220C22×C4—431no—
221C22×C4—431no—
222C22×C4—861no—
223C22×C4—1722no—
224C22×C4—1724no—
225C22×C4—1722no—
226C22×C4—1724no—
227C22×C4C2×C4×D4311yescharacteristic
228C22×C4D4×D4312yes—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—1722no—
233C2×C8—1722no—
234C2×C8—1722no—
235C4⋊C4—41no—
236C4⋊C4—1721no—
237C4⋊C4—1724no—
238C22⋊C4—42no—
239C22⋊C4—42no—
240C22⋊C4—1722no—
241C22⋊C4—1722no—
242C22⋊C4—1722no—
243C22⋊C4—1722no—
244C42—41no—
245C42—432no—
246C42—432no—
247C42—862no—
248C42—862no—
249C42—862no—
250C42—1722no—
251C23—22no—
252C23—41no—
253C23—41no—
254C23—42no—
255C23—42no—
256C23—862no—
257C23—1721no—
258C23—1721no—
259C23—1722no—
260C23—1722no—
261C23C22⋊C4×D4311yescharacteristic
262D4—42no—
263D4—42no—
264D4—1722no—
265D4—1722no—
266D4—17216no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—434no—
274C2×C4—432no—
275C2×C4—862no—
276C2×C4—862no—
277C2×C4—862no—
278C2×C4—861no—
279C2×C4—862no—
280C2×C4—3444no—
281C2×C4—3444no—
282C2×C4—1721no—
283C2×C4—1722no—
284C2×C4C2×C8×D4311yescharacteristic
285C2×C4M16×D4311yescharacteristic
286C2×C4#1306334912yes—
287C2×C4#1306335212yes—
288C8—82no—
289C8—3442no—
290C22—44no—
291C22—42no—
292C22—81no—
293C22—81no—
294C22—82no—
295C22—3441no—
296C22—3441no—
297C22—3442no—
298C22—1724no—
299C22—1722no—
300C22C22⋊C8×D4311yescharacteristic
301C22#1458287111yescharacteristic
302C22#100×D4311yescharacteristic
303C22#1458290212yes—
304C22#1458291412yes—
305C4—22no—
306C4—22no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—864no—
311C4—862no—
312C4—3441no—
313C4—1721no—
314C2—82no—
315C2—3442no—
316C2#1913291411yescharacteristic
317C2#1913298412yes—
318C2#1913314012yes—
319C2#1913322811yescharacteristic
320C2#1913330711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1270C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063321C4
cosocleC2×C42×C43C23
hypercenter#1270D43
hypocenterC43#7603
LCSG ▷ C2×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. #19134737C2semidirect
3. #19132416C2semidirect
4. #19132415C2semidirect
5. C43×#1270C2semidirect
25. #13063321C8semidirect
158. #1270D43semidirect
179. C43#7603semidirect

Maximal subgroups

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

subgroupindex
#191371592
#191347372
#191324162
#191324152
C43×#12702
#760343