Finite Group Databasebeta

← #24986960

Subgroups — #24986960

Order 11008.

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

normal subgroups only

This group has 914 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#19136975C211yesmaximal, characteristic
3#19132504C212yesmaximal, complemented
4#19132503C211yesmaximal, characteristic, complemented
5C43×#1306C211yesmaximal, characteristic, complemented
6C23×C4×D43C2211yescharacteristic
7C2×M16×D43—22no—
8C2×#13063281C412yes—
9#14582863C2212yes—
10#14582862—22no—
11#14582861—22no—
12#14582861C414yescomplemented
13C22⋊C8×D43—22no—
14C22⋊C8×D43C414yescomplemented
15#14582762C2211yescharacteristic
16#14582758—22no—
17#14582754C412yes—
18#14582746—22no—
19C43×#407C2212yes—
20C43×#381C2211yescharacteristic
21C24×D43C2×C411yescharacteristic
22C23×Dic43C2×C411yescharacteristic
23C22×C4×D43—44no—
24C22×C4×D43C2×C412yes—
25C22×C4×D43C2×C412yes—
26C22×C4×D43D412yes—
27C22×C4×D43D411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D412yes—
30C22×C4×D43Q811yescharacteristic
31C22×C4×D43Q811yescharacteristic
32C2×#10621877—22no—
33C2×#10621872—24no—
34M16×D43—48no—
35C2×C8×D43—24no—
36#13063281—44no—
37C2×Dic43⋊C4—22no—
38C2×C22⋊Dic43C2×C412yes—
39C2×(C2×D43)⋊C4—24no—
40C2×C4×Dic43—22no—
41C22⋊(C43⋊C8)—22no—
42C22⋊(C43⋊C8)C2×C414yes—
43(C2×D43)⋊C8—24no—
44(C2×D43)⋊C8—24no—
45C43⋊#95—22no—
46C23×C4×C43C2311yescharacteristic
47C2×M16×C43—22no—
48C2×C22⋊C4×C43C2×C412yes—
49C22⋊C8×C43—22no—
50C22⋊C8×C43C2×C414yes—
51#95×C43—22no—
52C24×C43C22×C411yescharacteristic
53C23×D43—44no—
54C23×D43—42no—
55C23×D43C4212yes—
56C23×D43C22⋊C412yes—
57C23×D43C4⋊C411yescharacteristic
58C23×D43C4⋊C411yescharacteristic
59C22×C4×C43—22no—
60C22×C4×C43—42no—
61C22×C4×C43C22×C412yes—
62C22×C4×C43C2×D412yes—
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×Q811yescharacteristic
65C22×Dic43—24no—
66C22×Dic43—22no—
67C22×Dic43C4211yescharacteristic
68C22×Dic43C4211yescharacteristic
69C22×Dic43C22⋊C411yescharacteristic
70C22×Dic43C22⋊C411yescharacteristic
71C22×Dic43C4⋊C411yescharacteristic
72C22×Dic43C4⋊C411yescharacteristic
73C2×C4×D43—28no—
74C2×C4×D43—44no—
75C2×C4×D43—44no—
76C2×C4×D43—44no—
77C2×C4×D43—42no—
78C2×C4×D43—42no—
79C2×C4×D43—42no—
80C2×C4×D43—42no—
81C2×C4×D43C22⋊C412yes—
82C2×C4×D43C22⋊C412yes—
83C2×C4×D43C22⋊C412yes—
84C2×C4×D43C22⋊C412yes—
85C2×C4×D43C4⋊C412yes—
86C2×C4×D43C4⋊C412yes—
87C2×C4×D43C4⋊C412yes—
88C2×C4×D43C4⋊C412yes—
89M16×C43—44no—
90C2×C8×C43—24no—
91C22⋊C4×C43—42no—
92C22⋊Dic43—42no—
93(C2×D43)⋊C4—48no—
94Dic43⋊C4—44no—
95C4×Dic43—44no—
96#10621877—44no—
97C2×C43⋊C8—24no—
98#10621872—48no—
99C8×D43—48no—
100C23×C43—22no—
101C23×C43—42no—
102C23×C43C2×C4211yescharacteristic
103C23×C43C2×C22⋊C411yescharacteristic
104C23×C43C2×C4⋊C411yescharacteristic
105C22×D43—24no—
106C22×D43—24no—
107C22×D43—24no—
108C22×D43—24no—
109C22×D43—42no—
110C22×D43—41no—
111C22×D43—41no—
112C22×D43—42no—
113C22×D43—42no—
114C22×D43—42no—
115C22×D43—416no—
116C22×D43#9512yes—
117C22×D43#9512yes—
118C2×C4×C43—24no—
119C2×C4×C43—42no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—44no—
123C2×C4×C43—42no—
124C2×C4×C43C2×C22⋊C412yes—
125C2×C4×C43C2×C4⋊C412yes—
126C2×Dic43—22no—
127C2×Dic43—22no—
128C2×Dic43—22no—
129C2×Dic43—22no—
130C2×Dic43—22no—
131C2×Dic43—44no—
132C2×Dic43—42no—
133C2×Dic43#9511yescharacteristic
134C2×Dic43#9511yescharacteristic
135C2×Dic43#9511yescharacteristic
136C2×Dic43#9511yescharacteristic
137C2×Dic43#9914yes—
138C4×D43—24no—
139C4×D43—24no—
140C4×D43—24no—
141C4×D43—24no—
142C4×D43—42no—
143C4×D43—42no—
144C4×D43—42no—
145C4×D43—42no—
146C8×C43—44no—
147C43⋊C8—44no—
148#8112—431nomaximal, Sylow
149C22×C43—22no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—22no—
153C22×C43—22no—
154C22×C43—44no—
155C22×C43C2×#9511yescharacteristic
156C22×C43C2×#9912yes—
157C2×D43—22no—
158C2×D43—22no—
159C2×D43—22no—
160C2×D43—22no—
161C2×D43—22no—
162C2×D43—44no—
163C2×D43—48no—
164C2×D43—48no—
165C2×D43—44no—
166C2×D43#34414yes—
167C4×C43—22no—
168C4×C43—22no—
169C4×C43—82no—
170Dic43—21no—
171Dic43—21no—
172Dic43—82no—
173Dic43#34212yes—
174Dic43#34212yes—
175C2×#407—432no—
176#2280—431no—
177#1306—432no—
178#1306—431no—
179#1306D4311yescharacteristic, complemented
180C2×C43—22no—
181C2×C43—41no—
182C2×C43—41no—
183C2×C43C2×#34211yescharacteristic
184C2×C43C2×#34412yes—
185D43—24no—
186D43—42no—
187C24×C4—431no—
188C22×M16—862no—
189C2×#117—432no—
190#407—432no—
191#407—434no—
192#407—862no—
193#407—862no—
194#407C2×D4312yes—
195C2×C22⋊C8—434no—
196C2×C22⋊C8—862no—
197#381—431no—
198#381C2×D4311yescharacteristic
199#380—862no—
200#379—432no—
201C4×C22⋊C4—862no—
202C43#811211yescharacteristic, complemented, Sylow
203C25—431no—
204C23×C4—431no—
205C23×C4—432no—
206C23×C4—432no—
207C23×C4—432no—
208C23×C4—432no—
209C23×C4—431no—
210C23×C4—431no—
211C23×C4—431no—
212C23×C4—431no—
213C23×C4—1724no—
214C23×C4C22×D4311yescharacteristic
215C2×M16—22no—
216C2×M16—864no—
217C2×M16—862no—
218C2×M16—1728no—
219C22×C8—864no—
220#117—1724no—
221C2×C4⋊C4—862no—
222C2×C22⋊C4—432no—
223C2×C22⋊C4—864no—
224C2×C22⋊C4C4×D4312yes—
225C2×C42—862no—
226C22⋊C8—22no—
227C22⋊C8—434no—
228C22⋊C8—864no—
229C22⋊C8—864no—
230C22⋊C8—862no—
231C22⋊C8C4×D4314yes—
232#95—22no—
233#95—862no—
234C24—432no—
235C24—431no—
236C24—432no—
237C24—431no—
238C24—1722no—
239C24—1724no—
240C24C2×C4×D4311yescharacteristic
241C22×C4—22no—
242C22×C4—42no—
243C22×C4—431no—
244C22×C4—431no—
245C22×C4—431no—
246C22×C4—431no—
247C22×C4—431no—
248C22×C4—431no—
249C22×C4—432no—
250C22×C4—432no—
251C22×C4—432no—
252C22×C4—432no—
253C22×C4—432no—
254C22×C4—432no—
255C22×C4—432no—
256C22×C4—432no—
257C22×C4—868no—
258C22×C4—864no—
259C22×C4—862no—
260C22×C4—1724no—
261C22×C4—1724no—
262C22×C4—1724no—
263C22×C4—1722no—
264C22×C4—1722no—
265C22×C4—1722no—
266C22×C4—1722no—
267C22×C4C2×C4×D4312yes—
268C22×C4D4×D4312yes—
269C22×C4D4×D4311yescharacteristic
270C22×C4Q8×D4311yescharacteristic
271M16—44no—
272M16—1728no—
273M16—1724no—
274C2×C8—24no—
275C2×C8—864no—
276C2×C8—1728no—
277C4⋊C4—1724no—
278C22⋊C4—42no—
279C22⋊C4—1728no—
280C22⋊C4—1722no—
281C42—1724no—
282C23—22no—
283C23—42no—
284C23—432no—
285C23—432no—
286C23—864no—
287C23—864no—
288C23—864no—
289C23—864no—
290C23—1722no—
291C23—1721no—
292C23—1721no—
293C23—1722no—
294C23—1722no—
295C23—1722no—
296C23—17216no—
297C23C42×D4311yescharacteristic
298C23C22⋊C4×D4311yescharacteristic
299C23C4⋊C4×D4311yescharacteristic
300C2×C4—24no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—44no—
305C2×C4—42no—
306C2×C4—434no—
307C2×C4—431no—
308C2×C4—431no—
309C2×C4—431no—
310C2×C4—431no—
311C2×C4—864no—
312C2×C4—864no—
313C2×C4—864no—
314C2×C4—864no—
315C2×C4—862no—
316C2×C4—862no—
317C2×C4—862no—
318C2×C4—862no—
319C2×C4—862no—
320C2×C4—1722no—
321C2×C4—1722no—
322C2×C4—1722no—
323C2×C4—1722no—
324C2×C4—1724no—
325C2×C4—1722no—
326C2×C4C22⋊C4×D4312yes—
327C2×C4C4⋊C4×D4312yes—
328C8—44no—
329C8—1724no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22—44no—
336C22—434no—
337C22—862no—
338C22—862no—
339C22—862no—
340C22—862no—
341C22—862no—
342C22—1728no—
343C22—1724no—
344C22—1728no—
345C22—1724no—
346C22#95×D4311yescharacteristic
347C22#99×D4312yes—
348C4—22no—
349C4—22no—
350C4—82no—
351C4—432no—
352C4—432no—
353C4—861no—
354C4—861no—
355C4—3442no—
356C2—22no—
357C2—41no—
358C2—41no—
359C2—864no—
360C2—1722no—
361C2#342×D4311yescharacteristic
362C2#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#8112
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
179. #1306D43semidirect
202. C43#8112semidirect

Maximal subgroups

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

subgroupindex
#407×D432
#191369752
#191325042
#191325032
C43×#13062
#811243