Finite Group Databasebeta

← #24984684

Subgroups — #24984684

Order 11008.

630 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 117 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#391×D43C211yesmaximal, characteristic
2#19134662C212yesmaximal
3#19132421C211yesmaximal, characteristic, complemented
4#19132420C212yesmaximal, complemented
5C43×#1272C211yesmaximal, characteristic, complemented
6C22×Q8×D43C411yescharacteristic
7C2×C4⋊C4×D43C411yescharacteristic
8C2×C42×D43C2211yescharacteristic
9C2×(C2×D43)⋊C8—22no—
10#14582806C411yescharacteristic
11#14582805C2211yescharacteristic
12#14582804C411yescharacteristic
13#14582803—22no—
14#95×D43—22no—
15#14582654C2212yes—
16#14582653—22no—
17C43×#391C2211yescharacteristic
18C43×#336C2212yes—
19C22×Dic86—21no—
20C22×Dic86C2×C411yescharacteristic
21C2×Q8×D43—22no—
22C2×Q8×D43—42no—
23C2×Q8×D43—42no—
24C2×Q8×D43C814yescomplemented
25C22×C4×D43—21no—
26C22×C4×D43—21no—
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D412yes—
29C22×C43⋊C8—22no—
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×Dic43⋊C4—21no—
32C4⋊C4×D43—42no—
33C2×C4×Dic43C2×C411yescharacteristic
34C2×C4×Dic43D412yes—
35C42×D43—42no—
36(C2×D43)⋊C8—44no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C22×Q8×C43C2×C411yescharacteristic
41C22×C8×C43—22no—
42C2×C4⋊C4×C43C2×C411yescharacteristic
43C2×C42×C43C2311yescharacteristic
44#95×C43—22no—
45C23×D43C22⋊C411yescharacteristic
46C2×Q8×C43—21no—
47C2×Q8×C43—41no—
48C2×Q8×C43—41no—
49C2×Q8×C43C2×C812yes—
50C22×C4×C43—21no—
51C22×C4×C43—21no—
52C22×C4×C43C22×C411yescharacteristic
53C22×C4×C43C2×D412yes—
54C22×Dic43—21no—
55C22×Dic43—21no—
56C22×Dic43C22⋊C412yes—
57C22×Dic43C22⋊C411yescharacteristic
58Q8×D43—48no—
59Q8×D43—48no—
60C2×C4×D43—22no—
61C2×C4×D43—22no—
62C2×C4×D43—24no—
63C2×C4×D43—22no—
64C2×C4×D43—24no—
65C2×C4×D43—22no—
66C2×C4×D43—42no—
67C2×C4×D43—44no—
68C2×C4×D43—42no—
69C2×C4×D43—42no—
70C2×C4×D43—42no—
71C2×C4×D43C2×C812yes—
72C2×C4×D43M1612yes—
73C2×Dic86—21no—
74C2×Dic86—24no—
75C2×Dic86—42no—
76C2×Dic86—42no—
77C2×Dic86—41no—
78C2×Dic86—41no—
79C2×Dic86C2×C812yes—
80C2×C8×C43—42no—
81C2×C8×C43—42no—
82C2×C8×C43—42no—
83C4⋊C4×C43—41no—
84C42×C43—41no—
85C4⋊Dic43—41no—
86Dic43⋊C4—42no—
87C4×Dic43—41no—
88C4×Dic43—42no—
89C2×C43⋊C8—42no—
90C2×C43⋊C8—42no—
91C2×C43⋊C8—42no—
92C23×C43C2×C22⋊C411yescharacteristic
93C22×D43—22no—
94C22×D43—22no—
95C22×D43C22⋊C812yes—
96C22×D43#9912yes—
97C22×D43#10012yes—
98Q8×C43—42no—
99Q8×C43—42no—
100C2×C4×C43—22no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—42no—
109C2×C4×C43C22×C811yescharacteristic
110C2×C4×C43C2×M1611yescharacteristic
111C2×C4×C43#13712yes—
112C2×C4×C43#13712yes—
113C2×Dic43—21no—
114C2×Dic43—21no—
115C2×Dic43—22no—
116C2×Dic43—22no—
117C2×Dic43—22no—
118C2×Dic43—22no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—42no—
123C2×Dic43C22⋊C812yes—
124C4×D43—24no—
125C4×D43—24no—
126C4×D43—44no—
127C4×D43—44no—
128C4×D43—48no—
129C4×D43—84no—
130Dic86—48no—
131Dic86—42no—
132Dic86—42no—
133C8×C43—82no—
134C43⋊C8—82no—
135#7595—431nomaximal, Sylow
136C22×C43C2×C22⋊C811yescharacteristic
137C22×C43C2×#9911yescharacteristic
138C22×C43C2×#10011yescharacteristic
139C22×C43#41912yes—
140C22×C43#42112yes—
141C2×D43—22no—
142C2×D43—24no—
143C2×D43—24no—
144C2×D43—22no—
145C2×D43#32314yes—
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—22no—
149C4×C43—22no—
150C4×C43—42no—
151C4×C43—81no—
152Dic43—22no—
153Dic43—42no—
154Dic43—42no—
155Dic43—81no—
156C2×#391—431no—
157#1817—432no—
158#1272—431no—
159#1272—432no—
160#1272D4311yescharacteristic, complemented
161C2×C43C2×#32311yescharacteristic
162C2×C43#147912yes—
163C2×C43#151112yes—
164C2×C43#153311yescharacteristic
165C2×C43#155811yescharacteristic
166D43—24no—
167C23×Q8—431no—
168C22×C4⋊C4—431no—
169C22×C42—431no—
170C2×C22⋊C8—862no—
171#391—431no—
172#391—431no—
173#391—431no—
174#391—862no—
175#391C2×D4311yescharacteristic
176C2×#95—862no—
177#336—432no—
178#336—862no—
179#336C2×D4312yes—
180C43#759511yescharacteristic, complemented, Sylow
181C22×Q8—434no—
182C22×Q8—431no—
183C22×Q8—861no—
184C22×Q8—862no—
185C22×Q8—1722no—
186C22×Q8—1722no—
187C22×Q8C4×D4311yescharacteristic
188C23×C4—431no—
189C23×C4—432no—
190C23×C4—861no—
191C23×C4—861no—
192C22×C8—22no—
193C22×C8—862no—
194C2×C4⋊C4—431no—
195C2×C4⋊C4—861no—
196C2×C4⋊C4—1722no—
197C2×C4⋊C4C4×D4311yescharacteristic
198C2×C42—431no—
199C2×C42—432no—
200C2×C42—1722no—
201C2×C42C22×D4311yescharacteristic
202C22⋊C8—1724no—
203#95—22no—
204#95—862no—
205#95—862no—
206#95—862no—
207C24—431no—
208C2×Q8—21no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8—432no—
212C2×Q8—864no—
213C2×Q8—861no—
214C2×Q8—1721no—
215C2×Q8—1721no—
216C2×Q8—1722no—
217C2×Q8—1722no—
218C2×Q8—1728no—
219C2×Q8—1728no—
220C2×Q8C8×D4312yes—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—431no—
224C22×C4—432no—
225C22×C4—432no—
226C22×C4—432no—
227C22×C4—862no—
228C22×C4—862no—
229C22×C4—864no—
230C22×C4—864no—
231C22×C4—861no—
232C22×C4—862no—
233C22×C4—862no—
234C22×C4—861no—
235C22×C4—1722no—
236C22×C4—1722no—
237C22×C4—1724no—
238C22×C4—1722no—
239C22×C4—1722no—
240C22×C4C2×C4×D4311yescharacteristic
241C22×C4D4×D4312yes—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—1722no—
246C2×C8—1722no—
247C2×C8—1722no—
248C4⋊C4—41no—
249C4⋊C4—1721no—
250C4⋊C4—1722no—
251C42—41no—
252C42—1722no—
253C42—1721no—
254C23—432no—
255C23—432no—
256C23—432no—
257C23—862no—
258C23—862no—
259C23C22⋊C4×D4311yescharacteristic
260Q8—42no—
261Q8—42no—
262Q8—1722no—
263Q8—1722no—
264Q8—1728no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—432no—
275C2×C4—864no—
276C2×C4—864no—
277C2×C4—861no—
278C2×C4—861no—
279C2×C4—862no—
280C2×C4—862no—
281C2×C4—862no—
282C2×C4—862no—
283C2×C4—3444no—
284C2×C4—1724no—
285C2×C4—1724no—
286C2×C4—1728no—
287C2×C4—1721no—
288C2×C4—1722no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4C2×C8×D4311yescharacteristic
292C2×C4M16×D4311yescharacteristic
293C2×C4#1306335412yes—
294C2×C4#1306335712yes—
295C8—82no—
296C8—3442no—
297C22—434no—
298C22—862no—
299C22—864no—
300C22—862no—
301C22—864no—
302C22C22⋊C8×D4311yescharacteristic
303C22#99×D4311yescharacteristic
304C22#100×D4311yescharacteristic
305C22#1458290612yes—
306C22#1458291412yes—
307C4—22no—
308C4—22no—
309C4—21no—
310C4—21no—
311C4—42no—
312C4—81no—
313C4—862no—
314C4—3441no—
315C4—1722no—
316C4—1722no—
317C2—864no—
318C2#323×D4311yescharacteristic
319C2#1913298812yes—
320C2#1913312612yes—
321C2#1913321711yescharacteristic
322C2#1913331911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1272D43
hypocenterC43#7595
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
3. #19132421C2semidirect
4. #19132420C2semidirect
5. C43×#1272C2semidirect
24. C2×Q8×D43C8semidirect
160. #1272D43semidirect
180. C43#7595semidirect

Maximal subgroups

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

subgroupindex
#391×D432
#191346622
#191324212
#191324202
C43×#12722
#759543