Finite Group Databasebeta

← #24988361

Subgroups — #24988361

Order 11008.

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

normal subgroups only

This group has 782 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
1C2×#14583606C211yesmaximal, characteristic
2#19133281C212yesmaximal, complemented
3#19133023C212yesmaximal, complemented
4#19132916C211yesmaximal, characteristic
5C43×#1800C211yesmaximal, characteristic
6#14583606—24no—
7#14583606—24no—
8C2×#13063325C2211yescharacteristic
9C2×#13063316—21no—
10C2×#13063304C412yes—
11C2×#13063302—22no—
12C2×C4×Dic86C2211yescharacteristic
13C2×D4×Dic43—21no—
14C22×C4⋊Dic43C412yes—
15#14582952C2212yes—
16#14582644—24no—
17#14582629—24no—
18#14582623—22no—
19C2×C4×D4×C43C2211yescharacteristic
20C43×#423C2212yes—
21C2×#100×C43—21no—
22C43×#343—21no—
23C22×Dic86—21no—
24C22×Dic86C2×C411yescharacteristic
25C23×Dic43—22no—
26#13063325—22no—
27#13063325D414yes—
28#13063316—28no—
29#13063304—24no—
30#13063304—24no—
31#13063302—216no—
32C4×Dic86—22no—
33C4×Dic86D414yes—
34D4×Dic43—28no—
35C2×C4⋊Dic43—22no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43—24no—
38C2×C4⋊Dic43—24no—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×C4⋊Dic43C2×C412yes—
41C2×Dic43⋊C4—22no—
42C2×Dic43⋊C4—21no—
43C2×C22⋊Dic43—22no—
44C2×C4×Dic43—21no—
45C4⋊(C43⋊C8)—22no—
46C22⋊(C43⋊C8)—22no—
47C4×C43⋊C8—22no—
48C22×D4×C43D411yescharacteristic
49C23×C4×C43C2×C412yes—
50C2×M16×C43—22no—
51C4×D4×C43—22no—
52C4×D4×C43—22no—
53C2×C4⋊C4×C43D411yescharacteristic
54C2×C22⋊C4×C43D412yes—
55C2×C42×C43C2311yescharacteristic
56C4⋊C8×C43—22no—
57C4⋊C8×C43—22no—
58#100×C43—42no—
59C24×C43C22⋊C412yes—
60C2×D4×C43—22no—
61C2×D4×C43—22no—
62C2×D4×C43SD1612yes—
63C2×D4×C43Q1612yes—
64C22×C4×C43—22no—
65C22×C4×C43—22no—
66C22×C4×C43—44no—
67C22×C4×C43C22⋊C412yes—
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—28no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—22no—
75C22×Dic43—84no—
76C2×Dic86—21no—
77C2×Dic86—24no—
78C2×Dic86—42no—
79C2×Dic86—82no—
80C2×Dic86C22⋊C412yes—
81M16×C43—42no—
82M16×C43—42no—
83C2×C8×C43—42no—
84C4⋊C4×C43—22no—
85C22⋊C4×C43—24no—
86C42×C43C2×D412yes—
87C42×C43C2×D412yes—
88C22⋊Dic43—28no—
89C4⋊Dic43—28no—
90C4⋊Dic43—21no—
91C4⋊Dic43—22no—
92C4⋊Dic43—24no—
93C4⋊Dic43C22⋊C412yes—
94C4⋊Dic43C22⋊C414yes—
95Dic43⋊C4—28no—
96Dic43⋊C4—24no—
97C4×Dic43—24no—
98C2×C43⋊C8—42no—
99C23×C43—22no—
100C23×C43—22no—
101C23×C43—42no—
102C23×C43—42no—
103C23×C43#10314yes—
104C23×C43C2×C22⋊C411yescharacteristic
105D4×C43—24no—
106D4×C43—24no—
107C2×C4×C43—22no—
108C2×C4×C43—22no—
109C2×C4×C43—41no—
110C2×C4×C43—44no—
111C2×C4×C43—44no—
112C2×C4×C43—42no—
113C2×C4×C43C2×C22⋊C411yescharacteristic
114C2×C4×C43C2×C22⋊C411yescharacteristic
115C2×C4×C43#12012yes—
116C2×C4×C43#12012yes—
117C2×C4×C43C2×SD1611yescharacteristic
118C2×C4×C43C2×Q1611yescharacteristic
119C2×C4×C43#13712yes—
120C2×Dic43—22no—
121C2×Dic43—22no—
122C2×Dic43—24no—
123C2×Dic43—42no—
124C2×Dic43—44no—
125C2×Dic43—42no—
126C2×Dic43—88no—
127Dic86—24no—
128Dic86—42no—
129Dic86—84no—
130C8×C43—82no—
131C43⋊C8—82no—
132#8395—431nomaximal, Sylow
133C22×C43—21no—
134C22×C43—21no—
135C22×C43—24no—
136C22×C43—44no—
137C22×C43—44no—
138C22×C43—42no—
139C22×C43—42no—
140C22×C43#37911yescharacteristic
141C22×C43C2×#10311yescharacteristic
142C22×C43#41911yescharacteristic
143C4×C43—22no—
144C4×C43—21no—
145C4×C43—42no—
146C4×C43#41312yes—
147C4×C43#44812yes—
148C4×C43#45112yes—
149Dic43—44no—
150Dic43—42no—
151Dic43—42no—
152C2×#554—431no—
153#1800D4311yescharacteristic
154#1549—432no—
155#1487—432no—
156#1460—431no—
157C2×C43—21no—
158C2×C43—21no—
159C2×C43—44no—
160C2×C43#178511yescharacteristic
161C2×C43#178711yescharacteristic
162C2×C43#179511yescharacteristic
163#554—864no—
164#554—864no—
165C2×C4⋊Q8—431no—
166C2×#125—861no—
167C2×C22⋊Q8—432no—
168C2×C22⋊Q8—862no—
169C2×C4×Q8—431no—
170C2×C4×D4—861no—
171C2×C4×D4C2×D4311yescharacteristic
172C22×C4⋊C4—432no—
173#431—432no—
174#423C2×D4312yes—
175C2×#100—21no—
176#343—21no—
177#332—864no—
178Q8⋊C8—864no—
179#323—862no—
180C43#839511yescharacteristic, complemented, Sylow
181C22×Q8—431no—
182C22×Q8—861no—
183C22×D4C22⋊D4311yescharacteristic
184C23×C4—862no—
185C23×C4C4×D4312yes—
186C2×M16—22no—
187C4⋊Q8—434no—
188C4⋊Q8—862no—
189#125—868no—
190C22⋊Q8—8616no—
191C22⋊Q8—864no—
192C22⋊Q8—864no—
193C4×Q8—434no—
194C4×Q8—862no—
195C4×D4—22no—
196C4×D4—22no—
197C4×D4—868no—
198C2×C4⋊C4—431no—
199C2×C4⋊C4—432no—
200C2×C4⋊C4—864no—
201C2×C4⋊C4—864no—
202C2×C4⋊C4—862no—
203C2×C4⋊C4—862no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4—861no—
206C2×C4⋊C4C22⋊D4311yescharacteristic
207C2×C22⋊C4—862no—
208C2×C22⋊C4D17212yes—
209C2×C42—861no—
210C2×C42C22×D4311yescharacteristic
211C4⋊C8—22no—
212C4⋊C8—22no—
213C4⋊C8—862no—
214#100—42no—
215C22⋊C8—862no—
216C4×C8—862no—
217C24(C2×D43)⋊C412yes—
218C2×Q8—432no—
219C2×Q8—861no—
220C2×Q8—864no—
221C2×Q8—3442no—
222C2×Q8—1722no—
223C2×D4—22no—
224C2×D4—22no—
225C2×D4#1062188312yes—
226C2×D4#1062188512yes—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—44no—
230C22×C4—868no—
231C22×C4—861no—
232C22×C4—861no—
233C22×C4—862no—
234C22×C4—3444no—
235C22×C4(C2×D43)⋊C412yes—
236C22×C4C2×C4×D4311yescharacteristic
237C22×C4C2×D17211yescharacteristic
238C22×C4C2×C22⋊D4311yescharacteristic
239M16—42no—
240M16—42no—
241C2×C8—42no—
242C2×C8—1722no—
243C4⋊C4—22no—
244C4⋊C4—432no—
245C4⋊C4—434no—
246C4⋊C4—868no—
247C4⋊C4—868no—
248C4⋊C4—861no—
249C4⋊C4—862no—
250C4⋊C4—864no—
251C4⋊C4—864no—
252C22⋊C4—24no—
253C22⋊C4—868no—
254C42—864no—
255C42D4×D4312yes—
256C42D4×D4312yes—
257C23—22no—
258C23—22no—
259C23—42no—
260C23—42no—
261C23#1306324814yes—
262C23C2×(C2×D43)⋊C411yescharacteristic
263Q8—864no—
264Q8—3444no—
265Q8—1722no—
266D4—24no—
267D4—24no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—42no—
274C2×C4—862no—
275C2×C4—862no—
276C2×C4—864no—
277C2×C4—3448no—
278C2×C4—1722no—
279C2×C4—1724no—
280C2×C4—1722no—
281C2×C4C22⋊C4×D4311yescharacteristic
282C2×C4C22⋊C4×D4311yescharacteristic
283C2×C4#1306329312yes—
284C2×C4#1306329512yes—
285C2×C4C2×#1062188311yescharacteristic
286C2×C4C2×#1062188511yescharacteristic
287C2×C4#1306335512yes—
288C8—82no—
289C8—3442no—
290C22—21no—
291C22—21no—
292C22—24no—
293C22—44no—
294C22—44no—
295C22—42no—
296C22—42no—
297C22#1458275411yescharacteristic
298C22C2×#1306324811yescharacteristic
299C22#1458290711yescharacteristic
300C4—21no—
301C4—22no—
302C4—42no—
303C4—1722no—
304C4—1722no—
305C4—1724no—
306C4#1458288012yes—
307C4#1458303712yes—
308C4#1458305412yes—
309C2—21no—
310C2—21no—
311C2—44no—
312C2#1913452011yescharacteristic
313C2#1913452911yescharacteristic
314C2#1913456611yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1800C2
socleC22×C43#379
prime radicalC22×D4×C43D4
cosocleC2×C42×C43C23
hypercenter#1800D43
hypocenterC43#8395
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
2. #19133281C2semidirect
3. #19133023C2semidirect
180. C43#8395semidirect

Maximal subgroups

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

subgroupindex
C2×#145836062
#191332812
#191330232
#191329162
C43×#18002
#839543