Finite Group Databasebeta

← #24986967

Subgroups — #24986967

Order 11008.

942 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 155 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#407×D43C212yesmaximal
2#381×D43C211yesmaximal, characteristic
3#19132504C212yesmaximal, complemented
4#19132503C211yesmaximal, characteristic, complemented
5C43×#1306C211yesmaximal, characteristic, complemented
6C23×C4×D43C2211yescharacteristic
7C2×M16×D43—22no—
8C2×C22⋊C4×D43C412yes—
9#14582863C2212yes—
10#14582862—22no—
11#14582861—22no—
12#14582861C414yescomplemented
13C22⋊C8×D43—22no—
14C22⋊C8×D43C414yescomplemented
15#14582762C2211yescharacteristic
16#14582761—22no—
17#14582760C412yes—
18#95×D43—22no—
19C43×#407C2212yes—
20C43×#381C2211yescharacteristic
21C24×D43C2×C411yescharacteristic
22C23×Dic43C2×C411yescharacteristic
23C22×C4×D43—22no—
24C22×C4×D43—44no—
25C22×C4×D43C2×C412yes—
26C22×C4×D43C2×C412yes—
27C22×C4×D43D412yes—
28C22×C4×D43D412yes—
29C22×C4×D43D412yes—
30C22×C4×D43Q812yes—
31C2×#10621877—22no—
32C2×#10621872—24no—
33M16×D43—48no—
34C2×C8×D43—24no—
35C2×C22⋊Dic43C2×C412yes—
36C2×(C2×D43)⋊C4—22no—
37C22⋊C4×D43—44no—
38C22⋊(C43⋊C8)—22no—
39C22⋊(C43⋊C8)C2×C414yescomplemented
40(C2×D43)⋊C8—24no—
41(C2×D43)⋊C8—24no—
42C43⋊#95—22no—
43C43⋊#95—24no—
44C23×C4×C43C2311yescharacteristic
45C2×M16×C43—22no—
46C2×C22⋊C4×C43C2×C412yes—
47C22⋊C8×C43—22no—
48C22⋊C8×C43C2×C414yescomplemented
49#95×C43—22no—
50C24×C43C22×C411yescharacteristic
51C23×D43—24no—
52C23×D43—44no—
53C23×D43C4212yes—
54C23×D43C22⋊C411yescharacteristic
55C23×D43C22⋊C411yescharacteristic
56C23×D43C4⋊C412yes—
57C22×C4×C43—22no—
58C22×C4×C43—42no—
59C22×C4×C43C22×C412yes—
60C22×C4×C43C2×D412yes—
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43C2×Q811yescharacteristic
63C22×Dic43—22no—
64C22×Dic43—42no—
65C22×Dic43C4211yescharacteristic
66C22×Dic43C4211yescharacteristic
67C22×Dic43C22⋊C412yes—
68C22×Dic43C4⋊C412yes—
69C2×C4×D43—28no—
70C2×C4×D43—44no—
71C2×C4×D43—44no—
72C2×C4×D43—44no—
73C2×C4×D43—44no—
74C2×C4×D43—44no—
75C2×C4×D43—44no—
76C2×C4×D43—48no—
77C2×C4×D43C22⋊C412yes—
78C2×C4×D43C22⋊C412yes—
79C2×C4×D43C22⋊C412yes—
80C2×C4×D43C22⋊C412yes—
81C2×C4×D43C4⋊C412yes—
82C2×C4×D43C4⋊C412yes—
83C2×C4×D43C4⋊C412yes—
84C2×C4×D43C4⋊C412yes—
85M16×C43—44no—
86C2×C8×C43—24no—
87C22⋊C4×C43—42no—
88C22⋊Dic43—42no—
89(C2×D43)⋊C4—44no—
90#10621877—44no—
91C2×C43⋊C8—24no—
92#10621872—48no—
93C8×D43—48no—
94C23×C43—22no—
95C23×C43—42no—
96C23×C43C2×C4211yescharacteristic
97C23×C43C2×C22⋊C411yescharacteristic
98C23×C43C2×C4⋊C411yescharacteristic
99C22×D43—22no—
100C22×D43—24no—
101C22×D43—24no—
102C22×D43—24no—
103C22×D43—24no—
104C22×D43—24no—
105C22×D43—42no—
106C22×D43—42no—
107C22×D43—42no—
108C22×D43—416no—
109C22×D43#9512yes—
110C22×D43#9512yes—
111C22×D43#9914yes—
112C2×C4×C43—24no—
113C2×C4×C43—42no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—44no—
117C2×C4×C43—42no—
118C2×C4×C43C2×C22⋊C412yes—
119C2×C4×C43C2×C4⋊C412yes—
120C2×Dic43—24no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—42no—
124C2×Dic43—44no—
125C2×Dic43—42no—
126C2×Dic43#9512yes—
127C2×Dic43#9512yes—
128C4×D43—24no—
129C4×D43—24no—
130C4×D43—24no—
131C4×D43—24no—
132C4×D43—42no—
133C4×D43—42no—
134C4×D43—42no—
135C4×D43—42no—
136C4×D43—88no—
137C8×C43—44no—
138C43⋊C8—44no—
139#8114—431nomaximal, Sylow
140C22×C43—22no—
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—22no—
144C22×C43—22no—
145C22×C43—44no—
146C22×C43C2×#9511yescharacteristic
147C22×C43C2×#9912yes—
148C2×D43—28no—
149C2×D43—22no—
150C2×D43—22no—
151C2×D43—22no—
152C2×D43—22no—
153C2×D43—44no—
154C2×D43—48no—
155C2×D43—48no—
156C2×D43#34214yes—
157C2×D43#34414yes—
158C4×C43—22no—
159C4×C43—22no—
160C4×C43—82no—
161Dic43—22no—
162Dic43—22no—
163Dic43—82no—
164C2×#407—432no—
165C2×#381—431no—
166#1306—432no—
167#1306—431no—
168#1306D4311yescharacteristic, complemented
169C2×C43—22no—
170C2×C43—41no—
171C2×C43—41no—
172C2×C43C2×#34211yescharacteristic
173C2×C43C2×#34412yes—
174D43—24no—
175D43—24no—
176C24×C4—431no—
177C22×M16—862no—
178C22×C22⋊C4—432no—
179#407—432no—
180#407—434no—
181#407—862no—
182#407—862no—
183#407C2×D4312yes—
184C2×C22⋊C8—434no—
185C2×C22⋊C8—862no—
186#381—431no—
187#381—432no—
188#381—862no—
189#381C2×D4311yescharacteristic
190C2×#95—862no—
191C43#811411yescharacteristic, complemented, Sylow
192C25—431no—
193C23×C4—431no—
194C23×C4—432no—
195C23×C4—432no—
196C23×C4—432no—
197C23×C4—432no—
198C23×C4—432no—
199C23×C4—432no—
200C23×C4—862no—
201C23×C4—1724no—
202C23×C4C22×D4311yescharacteristic
203C2×M16—22no—
204C2×M16—864no—
205C2×M16—862no—
206C2×M16—1728no—
207C22×C8—864no—
208C2×C22⋊C4—432no—
209C2×C22⋊C4—862no—
210C2×C22⋊C4—1724no—
211C2×C22⋊C4C4×D4312yes—
212C22⋊C8—22no—
213C22⋊C8—434no—
214C22⋊C8—864no—
215C22⋊C8—864no—
216C22⋊C8—862no—
217C22⋊C8C4×D4314yescomplemented
218#95—22no—
219#95—864no—
220#95—862no—
221C24—431no—
222C24—431no—
223C24—432no—
224C24—432no—
225C24—864no—
226C24—1724no—
227C24C2×C4×D4311yescharacteristic
228C22×C4—22no—
229C22×C4—42no—
230C22×C4—432no—
231C22×C4—431no—
232C22×C4—431no—
233C22×C4—432no—
234C22×C4—432no—
235C22×C4—432no—
236C22×C4—432no—
237C22×C4—432no—
238C22×C4—432no—
239C22×C4—432no—
240C22×C4—432no—
241C22×C4—432no—
242C22×C4—868no—
243C22×C4—862no—
244C22×C4—1724no—
245C22×C4—1724no—
246C22×C4—1724no—
247C22×C4—1724no—
248C22×C4—1724no—
249C22×C4—1724no—
250C22×C4—1728no—
251C22×C4—1722no—
252C22×C4C2×C4×D4312yes—
253C22×C4D4×D4312yes—
254C22×C4D4×D4311yescharacteristic
255C22×C4Q8×D4311yescharacteristic
256M16—44no—
257M16—1728no—
258M16—1724no—
259C2×C8—24no—
260C2×C8—864no—
261C2×C8—1728no—
262C22⋊C4—42no—
263C22⋊C4—1724no—
264C22⋊C4—1722no—
265C23—22no—
266C23—42no—
267C23—432no—
268C23—432no—
269C23—434no—
270C23—864no—
271C23—864no—
272C23—864no—
273C23—864no—
274C23—864no—
275C23—862no—
276C23—1722no—
277C23—1722no—
278C23—1722no—
279C23—17216no—
280C23C42×D4311yescharacteristic
281C23C22⋊C4×D4311yescharacteristic
282C23C4⋊C4×D4311yescharacteristic
283C2×C4—24no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—44no—
288C2×C4—42no—
289C2×C4—432no—
290C2×C4—432no—
291C2×C4—864no—
292C2×C4—864no—
293C2×C4—864no—
294C2×C4—864no—
295C2×C4—864no—
296C2×C4—3448no—
297C2×C4—1722no—
298C2×C4—1722no—
299C2×C4—1722no—
300C2×C4—1722no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1722no—
304C2×C4—1724no—
305C2×C4—1722no—
306C2×C4C22⋊C4×D4312yes—
307C2×C4C4⋊C4×D4312yes—
308C8—44no—
309C8—1724no—
310C22—22no—
311C22—21no—
312C22—21no—
313C22—22no—
314C22—22no—
315C22—44no—
316C22—434no—
317C22—434no—
318C22—868no—
319C22—862no—
320C22—862no—
321C22—862no—
322C22—862no—
323C22—1724no—
324C22—1728no—
325C22—1728no—
326C22#95×D4311yescharacteristic
327C22#99×D4312yes—
328C4—22no—
329C4—22no—
330C4—82no—
331C4—862no—
332C4—862no—
333C4—3442no—
334C2—22no—
335C2—41no—
336C2—41no—
337C2—864no—
338C2—864no—
339C2#342×D4311yescharacteristic
340C2#344×D4312yes—
subgroupG/H
centerC22#95×D43
commutatorC23×C43C2×C42
FrattiniC23×C4C22×D43
FittingC43×#1306C2
socleC22×C43C2×#95
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenter#1306D43
hypocenterC43#8114
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
3. #19132504C2semidirect
4. #19132503C2semidirect
5. C43×#1306C2semidirect
12. #14582861C4semidirect
14. C22⋊C8×D43C4semidirect
39. C22⋊(C43⋊C8)C2×C4semidirect
48. C22⋊C8×C43C2×C4semidirect
168. #1306D43semidirect
191. C43#8114semidirect
217. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
#407×D432
#381×D432
#191325042
#191325032
C43×#13062
#811443