Finite Group Databasebeta

← #24984570

Subgroups — #24984570

Order 11008.

684 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 143 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#19134443C212yesmaximal, complemented
3#19132416C211yesmaximal, characteristic, complemented
4#19132415C212yesmaximal, complemented
5C43×#1270C211yesmaximal, characteristic, complemented
6C2×#13063321C411yescharacteristic
7C2×D4×Dic43C411yescharacteristic
8C2×#13063287C411yescharacteristic
9C2×(C22⋊D43)⋊C4—22no—
10C2×Dic43⋊C8—22no—
11C2×C8×Dic43—22no—
12#14582801C2211yescharacteristic
13#14582799—22no—
14#14582768C411yescharacteristic
15C42×Dic43C2211yescharacteristic
16#14582654C2212yes—
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—
39Dic43⋊C8—28no—
40C8×Dic43—44no—
41C22×D4×C43C2×C411yescharacteristic
42C22×C8×C43—22no—
43C2×C4⋊C4×C43C2×C411yescharacteristic
44C2×C22⋊C4×C43—22no—
45C2×C42×C43C2311yescharacteristic
46C24×C43—21no—
47C23×D43—21no—
48C2×D4×C43—21no—
49C2×D4×C43—41no—
50C2×D4×C43—41no—
51C2×D4×C43C2×C812yes—
52C22×C4×C43—21no—
53C22×C4×C43C22×C411yescharacteristic
54C22×C4×C43C2×D412yes—
55C2×C22⋊D43—28no—
56C2×C22⋊D43—44no—
57C2×C22⋊D43—44no—
58C22×Dic43—21no—
59C22×Dic43—42no—
60C22×Dic43—44no—
61C22×Dic43C22⋊C411yescharacteristic
62C22×Dic43C22⋊C412yes—
63C22×Dic43C22⋊C411yescharacteristic
64C2×D172—21no—
65C2×D172—41no—
66C2×D172—41no—
67C2×D172C2×C812yes—
68C2×C4×D43—42no—
69C2×C4×D43—44no—
70C2×C8×C43—24no—
71C2×C8×C43—42no—
72C2×C8×C43—42no—
73C4⋊C4×C43—41no—
74C22⋊C4×C43—42no—
75C22⋊C4×C43—42no—
76C42×C43—41no—
77C22⋊Dic43—42no—
78(C2×D43)⋊C4—42no—
79(C2×D43)⋊C4—42no—
80(C2×D43)⋊C4—42no—
81C4⋊Dic43—41no—
82Dic43⋊C4—44no—
83C4×Dic43—22no—
84C4×Dic43—24no—
85C4×Dic43C2×C812yes—
86C4×Dic43M1612yes—
87C4×Dic43D814yes—
88C4×Dic43SD1614yes—
89C2×C43⋊C8—24no—
90C2×C43⋊C8—42no—
91C2×C43⋊C8—42no—
92C23×C43—22no—
93C23×C43—41no—
94C23×C43—41no—
95C23×C43—42no—
96C23×C43—42no—
97C23×C43C2×C22⋊C411yescharacteristic
98C22×D43—22no—
99C22×D43—41no—
100C22×D43—41no—
101C22×D43—42no—
102C22×D43—42no—
103D4×C43—42no—
104D4×C43—42no—
105C2×C4×C43—22no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—22no—
109C2×C4×C43—41no—
110C2×C4×C43—42no—
111C2×C4×C43C22×C811yescharacteristic
112C2×C4×C43C2×M1611yescharacteristic
113C2×C4×C43C2×D812yes—
114C2×C4×C43C2×SD1612yes—
115C22⋊D43—416no—
116C2×Dic43—21no—
117C2×Dic43—22no—
118C2×Dic43—41no—
119C2×Dic43—42no—
120C2×Dic43—84no—
121C2×Dic43C22⋊C814yes—
122C2×Dic43#10012yes—
123C2×Dic43#10214yes—
124C2×Dic43#10214yes—
125C2×Dic43#10414yes—
126D172—42no—
127D172—42no—
128C4×D43—84no—
129C8×C43—44no—
130C43⋊C8—44no—
131#7569—431nomaximal, Sylow
132C22×C43—42no—
133C22×C43—44no—
134C22×C43—81no—
135C22×C43—82no—
136C22×C43—81no—
137C22×C43C2×C22⋊C811yescharacteristic
138C22×C43#41011yescharacteristic
139C22×C43C2×#10011yescharacteristic
140C22×C43C2×#10212yes—
141C22×C43C2×#10412yes—
142C2×D43—42no—
143C2×D43—44no—
144C2×D43—81no—
145C2×D43—82no—
146C2×D43—81no—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—22no—
150C4×C43—22no—
151C4×C43—81no—
152Dic43—41no—
153Dic43—81no—
154Dic43D4⋊C818yes—
155Dic43#33114yes—
156C4×#127—431no—
157C4×C4⋊C8—432no—
158#1270—431no—
159#1270—432no—
160#1270D4311yescharacteristic, complemented
161C2×C43—82no—
162C2×C43#146011yescharacteristic
163C2×C43C2×D4⋊C812yes—
164C2×C43#150212yes—
165C2×C43#152511yescharacteristic
166C2×C43C2×#33111yescharacteristic
167D43—82no—
168C2×#127—431no—
169C2×C4×D4—431no—
170C2×C4×D4—431no—
171C2×C4×D4—862no—
172C2×C4⋊C8—862no—
173C2×C4×C8—862no—
174#390—431no—
175#390—862no—
176#390C2×D4311yescharacteristic
177#384—431no—
178C43—431no—
179#336—432no—
180#336C2×D4312yes—
181C43#756911yescharacteristic, complemented, Sylow
182C22×D4—431no—
183C22×D4—862no—
184C22×D4C4×D4311yescharacteristic
185C23×C4—861no—
186C23×C4—861no—
187C22×C8—22no—
188C22×C8—862no—
189#127—434no—
190#127—862no—
191C4×D4—1724no—
192C4×D4—1724no—
193C4×D4—1722no—
194C4×D4—1722no—
195C2×C4⋊C4—431no—
196C2×C4⋊C4—862no—
197C2×C4⋊C4C4×D4311yescharacteristic
198C2×C22⋊C4—22no—
199C2×C22⋊C4—861no—
200C2×C22⋊C4—861no—
201C2×C22⋊C4—862no—
202C2×C42—431no—
203C2×C42—432no—
204C2×C42—431no—
205C2×C42—432no—
206C2×C42C22×D4311yescharacteristic
207C4⋊C8—868no—
208C4×C8—1724no—
209C24—21no—
210C24—861no—
211C2×D4—21no—
212C2×D4—41no—
213C2×D4—41no—
214C2×D4—432no—
215C2×D4—868no—
216C2×D4—861no—
217C2×D4—1721no—
218C2×D4—1721no—
219C2×D4—1724no—
220C2×D4—1724no—
221C2×D4C8×D4312yes—
222C22×C4—21no—
223C22×C4—432no—
224C22×C4—431no—
225C22×C4—431no—
226C22×C4—861no—
227C22×C4—1724no—
228C22×C4—1722no—
229C22×C4—1724no—
230C22×C4—1722no—
231C22×C4C2×C4×D4311yescharacteristic
232C22×C4D4×D4312yes—
233C2×C8—24no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—864no—
237C2×C8—1722no—
238C2×C8—1722no—
239C4⋊C4—41no—
240C4⋊C4—1721no—
241C4⋊C4—1724no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—1722no—
245C22⋊C4—1722no—
246C22⋊C4—1722no—
247C22⋊C4—1722no—
248C42—41no—
249C42—432no—
250C42—432no—
251C42—434no—
252C42—434no—
253C42—864no—
254C42—862no—
255C23—22no—
256C23—41no—
257C23—41no—
258C23—42no—
259C23—42no—
260C23—862no—
261C23—1721no—
262C23—1721no—
263C23—1722no—
264C23—1722no—
265C23C22⋊C4×D4311yescharacteristic
266D4—42no—
267D4—42no—
268D4—1722no—
269D4—1722no—
270D4—17216no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—434no—
278C2×C4—432no—
279C2×C4—434no—
280C2×C4—434no—
281C2×C4—434no—
282C2×C4—861no—
283C2×C4—862no—
284C2×C4—3444no—
285C2×C4—3444no—
286C2×C4—1721no—
287C2×C4—1722no—
288C2×C4C2×C8×D4311yescharacteristic
289C2×C4M16×D4311yescharacteristic
290C2×C4D8×D4312yes—
291C2×C4SD16×D4312yes—
292C8—44no—
293C8—1724no—
294C22—44no—
295C22—42no—
296C22—81no—
297C22—81no—
298C22—82no—
299C22—3441no—
300C22—3441no—
301C22—3442no—
302C22—1724no—
303C22—1722no—
304C22C22⋊C8×D4311yescharacteristic
305C22#1458287111yescharacteristic
306C22#100×D4311yescharacteristic
307C22#102×D4312yes—
308C22#104×D4312yes—
309C4—22no—
310C4—22no—
311C4—21no—
312C4—21no—
313C4—81no—
314C4—438no—
315C4—434no—
316C4—3441no—
317C4—1721no—
318C2—82no—
319C2—3442no—
320C2#1913291411yescharacteristic
321C2D4⋊C8×D4312yes—
322C2#1913308812yes—
323C2#1913318511yescharacteristic
324C2#331×D4311yescharacteristic
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#7569
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. #19134443C2semidirect
3. #19132416C2semidirect
4. #19132415C2semidirect
5. C43×#1270C2semidirect
25. #13063321C8semidirect
160. #1270D43semidirect
181. C43#7569semidirect

Maximal subgroups

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

subgroupindex
#191371592
#191344432
#191324162
#191324152
C43×#12702
#756943