Finite Group Databasebeta

← #24984548

Subgroups — #24984548

Order 11008.

690 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 121 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#19137084C211yesmaximal, characteristic
2#19134352C212yesmaximal, complemented
3#19132421C211yesmaximal, characteristic, complemented
4#19132415C212yesmaximal, complemented
5C43×#1272C211yesmaximal, characteristic, complemented
6C22×#10621902C411yescharacteristic
7C2×#13063283C411yescharacteristic
8C2×C42×D43C2211yescharacteristic
9C2×(C2×D43)⋊C8—22no—
10C2×C8×Dic43—22no—
11#14582806C411yescharacteristic
12#14582801C2211yescharacteristic
13#14582800C411yescharacteristic
14#14582777—22no—
15#14582746—22no—
16#14582654C2212yes—
17C43×#391C2211yescharacteristic
18C43×#336C2212yes—
19C2×#10621902—22no—
20C2×#10621902—42no—
21C2×#10621902—42no—
22C2×#10621902C814yescomplemented
23C22×D172—21no—
24C22×D172C2×C411yescharacteristic
25C22×C4×D43—21no—
26C22×C4×D43C2×C411yescharacteristic
27C22×C4×D43D412yes—
28C22×C43⋊C8—22no—
29#13063283—42no—
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×(C2×D43)⋊C4—21no—
32C2×(C2×D43)⋊C4—22no—
33C2×(C2×D43)⋊C4—22no—
34C2×C4×Dic43—21no—
35C2×C4×Dic43C2×C411yescharacteristic
36C2×C4×Dic43D412yes—
37C42×D43—42no—
38(C2×D43)⋊C8—28no—
39C8×Dic43—44no—
40C43⋊#95—22no—
41C22×Q8×C43C2×C411yescharacteristic
42C22×C8×C43—22no—
43C2×C4⋊C4×C43C2×C411yescharacteristic
44C2×C42×C43C2311yescharacteristic
45#95×C43—22no—
46C23×D43—21no—
47C23×D43C22⋊C411yescharacteristic
48C2×Q8×C43—21no—
49C2×Q8×C43—41no—
50C2×Q8×C43—41no—
51C2×Q8×C43C2×C812yes—
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43C22×C411yescharacteristic
55C22×C4×C43C2×D412yes—
56C22×Dic43—21no—
57C22×Dic43C22⋊C412yes—
58C22×Dic43C22⋊C411yescharacteristic
59#10621902—48no—
60#10621902—48no—
61C2×D172—21no—
62C2×D172—24no—
63C2×D172—42no—
64C2×D172—42no—
65C2×D172—41no—
66C2×D172—41no—
67C2×D172C2×C812yes—
68C2×C4×D43—22no—
69C2×C4×D43—22no—
70C2×C4×D43—22no—
71C2×C4×D43—22no—
72C2×C4×D43—24no—
73C2×C4×D43—24no—
74C2×C4×D43—42no—
75C2×C4×D43—42no—
76C2×C4×D43—42no—
77C2×C4×D43C2×C812yes—
78C2×C4×D43M1612yes—
79C2×C8×C43—24no—
80C2×C8×C43—42no—
81C2×C8×C43—42no—
82C4⋊C4×C43—41no—
83C42×C43—41no—
84(C2×D43)⋊C4—42no—
85(C2×D43)⋊C4—42no—
86(C2×D43)⋊C4—42no—
87(C2×D43)⋊C4—44no—
88C4⋊Dic43—41no—
89C4×Dic43—24no—
90C4×Dic43—41no—
91C4×Dic43—42no—
92C2×C43⋊C8—24no—
93C2×C43⋊C8—42no—
94C2×C43⋊C8—42no—
95C23×C43C2×C22⋊C411yescharacteristic
96C22×D43—21no—
97C22×D43—21no—
98C22×D43—22no—
99C22×D43—22no—
100C22×D43—22no—
101C22×D43—41no—
102C22×D43—41no—
103C22×D43—42no—
104C22×D43—42no—
105C22×D43C22⋊C812yes—
106Q8×C43—42no—
107Q8×C43—42no—
108C2×C4×C43—22no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—22no—
112C2×C4×C43—22no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—42no—
117C2×C4×C43C22×C811yescharacteristic
118C2×C4×C43C2×M1611yescharacteristic
119C2×C4×C43#13512yes—
120C2×C4×C43#13512yes—
121C2×Dic43—22no—
122C2×Dic43—22no—
123C2×Dic43—41no—
124C2×Dic43—42no—
125C2×Dic43C22⋊C812yes—
126C2×Dic43#9912yes—
127C2×Dic43#10012yes—
128C2×Dic43#10414yes—
129D172—42no—
130D172—42no—
131D172—48no—
132C4×D43—24no—
133C4×D43—24no—
134C4×D43—44no—
135C4×D43—44no—
136C4×D43—48no—
137C8×C43—44no—
138C43⋊C8—44no—
139#7563—431nomaximal, Sylow
140C22×C43C2×C22⋊C811yescharacteristic
141C22×C43C2×#9911yescharacteristic
142C22×C43C2×#10011yescharacteristic
143C22×C43#41612yes—
144C22×C43C2×#10412yes—
145C2×D43—22no—
146C2×D43—24no—
147C2×D43—41no—
148C2×D43—42no—
149C2×D43—41no—
150C2×D43—42no—
151C2×D43—44no—
152C2×D43—81no—
153C2×D43—82no—
154C2×D43—81no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—22no—
158C4×C43—22no—
159C4×C43—42no—
160C4×C43—81no—
161Dic43—24no—
162Dic43—81no—
163Dic43#32314yes—
164#2297—431no—
165C4×C22⋊C8—432no—
166#1272—431no—
167#1272D4311yescharacteristic, complemented
168#1270—432no—
169C2×C43C2×#32311yescharacteristic
170C2×C43#147612yes—
171C2×C43#150112yes—
172C2×C43#152511yescharacteristic
173C2×C43#154311yescharacteristic
174D43—42no—
175D43—82no—
176C22×#41—431no—
177C2×#117—431no—
178C22×C42—431no—
179C2×C22⋊C8—862no—
180C2×C4×C8—862no—
181#391—431no—
182#391C2×D4311yescharacteristic
183#390—431no—
184#390—431no—
185#386—862no—
186C4×C22⋊C4—862no—
187#336—432no—
188#336C2×D4312yes—
189C43#756311yescharacteristic, complemented, Sylow
190C2×#41—434no—
191C2×#41—862no—
192C2×#41—1722no—
193C2×#41—1722no—
194C22×Q8C4×D4311yescharacteristic
195C22×D4—431no—
196C22×D4—861no—
197C23×C4—431no—
198C23×C4—432no—
199C23×C4—861no—
200C22×C8—22no—
201C22×C8—862no—
202#117—1722no—
203C2×C4⋊C4—431no—
204C2×C4⋊C4C4×D4311yescharacteristic
205C2×C22⋊C4—862no—
206C2×C22⋊C4—861no—
207C2×C22⋊C4—862no—
208C2×C42—432no—
209C2×C42—431no—
210C2×C42—861no—
211C2×C42—1722no—
212C2×C42C22×D4311yescharacteristic
213C22⋊C8—868no—
214C4×C8—1724no—
215#95—22no—
216#95—862no—
217C24—431no—
218C24—861no—
219#41—1728no—
220#41—1728no—
221C2×Q8—21no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8C8×D4312yes—
225C2×D4—432no—
226C2×D4—864no—
227C2×D4—861no—
228C2×D4—1721no—
229C2×D4—1721no—
230C2×D4—1722no—
231C2×D4—1722no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—431no—
235C22×C4—432no—
236C22×C4—432no—
237C22×C4—432no—
238C22×C4—862no—
239C22×C4—862no—
240C22×C4—864no—
241C22×C4—864no—
242C22×C4—862no—
243C22×C4—862no—
244C22×C4—861no—
245C22×C4—1722no—
246C22×C4—1722no—
247C22×C4—1722no—
248C22×C4C2×C4×D4311yescharacteristic
249C22×C4D4×D4312yes—
250C2×C8—24no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—864no—
254C2×C8—1722no—
255C2×C8—1722no—
256C4⋊C4—41no—
257C4⋊C4—1721no—
258C22⋊C4—1724no—
259C22⋊C4—1722no—
260C22⋊C4—1722no—
261C22⋊C4—1722no—
262C42—41no—
263C42—864no—
264C42—1721no—
265C42—1722no—
266C23—432no—
267C23—861no—
268C23—861no—
269C23—862no—
270C23—862no—
271C23—862no—
272C23—1721no—
273C23—1721no—
274C23—1722no—
275C23—1722no—
276C23C22⋊C4×D4311yescharacteristic
277Q8—42no—
278Q8—42no—
279D4—1722no—
280D4—1722no—
281D4—1728no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—432no—
292C2×C4—432no—
293C2×C4—432no—
294C2×C4—434no—
295C2×C4—864no—
296C2×C4—864no—
297C2×C4—862no—
298C2×C4—862no—
299C2×C4—1724no—
300C2×C4—1724no—
301C2×C4—1728no—
302C2×C4—1721no—
303C2×C4—1722no—
304C2×C4C2×C8×D4311yescharacteristic
305C2×C4M16×D4311yescharacteristic
306C2×C4#1306334612yes—
307C2×C4#1306334812yes—
308C8—44no—
309C8—1724no—
310C22—864no—
311C22—862no—
312C22—3441no—
313C22—3441no—
314C22—3442no—
315C22—1724no—
316C22—1722no—
317C22—1721no—
318C22—1721no—
319C22—1722no—
320C22C22⋊C8×D4311yescharacteristic
321C22#99×D4311yescharacteristic
322C22#100×D4311yescharacteristic
323C22#1458289412yes—
324C22#104×D4312yes—
325C4—22no—
326C4—22no—
327C4—21no—
328C4—21no—
329C4—42no—
330C4—81no—
331C4—434no—
332C4—864no—
333C4—3441no—
334C2—3442no—
335C2—1722no—
336C2#323×D4311yescharacteristic
337C2#1913297612yes—
338C2#1913308512yes—
339C2#1913318511yescharacteristic
340C2#1913325611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socleC23×C43C2×C22⋊C4
prime radicalC22×#10621902C4
cosocleC2×C42×C43C23
hypercenter#1272D43
hypocenterC43#7563
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
2. #19134352C2semidirect
3. #19132421C2semidirect
4. #19132415C2semidirect
5. C43×#1272C2semidirect
22. C2×#10621902C8semidirect
167. #1272D43semidirect
189. C43#7563semidirect

Maximal subgroups

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

subgroupindex
#191370842
#191343522
#191324212
#191324152
C43×#12722
#756343