Finite Group Databasebeta

← #25074492

Subgroups — #25074492

Order 11008.

868 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 868 conjugacy classes of subgroups — too many to draw. Only its 163 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#19149009C211yesmaximal, characteristic
2#19145986C212yesmaximal, complemented
3#19133813C214yesmaximal, complemented
4#19133778C214yesmaximal, complemented
5#19133330C211yesmaximal, characteristic
6#19133051C212yesmaximal, complemented
7C43×#3131C211yesmaximal, characteristic
8#14583649—22no—
9#14583635C2212yes—
10#14583629C2212yes—
11#14583619—22no—
12D4×Dic86—22no—
13#14583516—24no—
14#14583470—22no—
15#14583456C2212yes—
16#14583184—22no—
17#14583181C2214yes—
18#14583155—24no—
19#14583109—22no—
20#14583106C2214yes—
21#14582923C2212yes—
22#14582648C2212yes—
23#14582643C2212yes—
24#14582631C2218yes—
25C43×#533C2211yescharacteristic
26C43×#532C2211yescharacteristic
27C43×#488—22no—
28C43×#487C2212yes—
29C43×#486C2212yes—
30C43×#416—22no—
31C2×C4×C8×C43C2211yescharacteristic
32C22×Dic86—22no—
33C2×#10621885—24no—
34C2×#10621877—22no—
35#13063325D412yes—
36#13063325D412yes—
37#13063324—24no—
38#13063323—24no—
39#13063318—28no—
40#13063317—22no—
41#13063312—24no—
42#13063312—24no—
43#13063306—24no—
44#13063306—24no—
45#13063304—24no—
46#13063304—22no—
47#13063304D414yes—
48#13063302—28no—
49C4×Dic86—22no—
50C4×Dic86C2314yes—
51#13063290—24no—
52D4×Dic43—24no—
53#13063284—22no—
54#13063284—22no—
55#13063256—24no—
56C4⋊(C43⋊C8)—22no—
57C4⋊(C43⋊C8)C2314yes—
58#13063249—24no—
59#13063248—24no—
60C2×#41×C43D412yes—
61C22×C8×C43—21no—
62C4⋊Q8×C43C2312yes—
63C4⋊Q8×C43C2311yescharacteristic
64#127×C43C2311yescharacteristic
65#125×C43—21no—
66#124×C43D412yes—
67C22⋊Q8×C43—22no—
68#121×C43—22no—
69C4×Q8×C43—22no—
70C4×D4×C43—22no—
71#117×C43—21no—
72C2×C42×C43C2311yescharacteristic
73#103×C43—24no—
74#102×C43—24no—
75C4×C8×C43—21no—
76C4×C8×C43C2312yes—
77#41×C43—44no—
78C2×Q8×C43—22no—
79C2×Q8×C43C2×D412yes—
80C2×D4×C43—22no—
81C2×D4×C43—22no—
82C2×D4×C43C2×D412yes—
83C22×C4×C43—22no—
84C22×C4×C43C2×D412yes—
85C22×C4×C43C2×D411yescharacteristic
86C22×Dic43—24no—
87C2×Dic86—22no—
88C2×Dic86—24no—
89C2×Dic86—84no—
90C2×Dic86C2×D414yes—
91C2×C8×C43—22no—
92C2×C8×C43—42no—
93C4⋊C4×C43—22no—
94C4⋊C4×C43—22no—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—42no—
97C22⋊C4×C43—24no—
98C22⋊C4×C43—41no—
99C42×C43—41no—
100C42×C43C2×D412yes—
101C42×C43C2×D411yescharacteristic
102C42×C43C2411yescharacteristic
103C22⋊Dic43—24no—
104C22⋊Dic43—28no—
105C22⋊Dic43—24no—
106#10621885—84no—
107C4⋊Dic43—22no—
108C4⋊Dic43—22no—
109C4⋊Dic43—22no—
110C4⋊Dic43C2×D414yes—
111Dic43⋊C4—28no—
112Dic43⋊C4—24no—
113Dic43⋊C4—24no—
114C4×Dic43—24no—
115C4×Dic43—24no—
116#10621877—82no—
117C2×C43⋊C8—24no—
118C23×C43—22no—
119C23×C43#12011yescharacteristic
120Q8×C43—42no—
121Q8×C43—42no—
122Q8×C43—42no—
123D4×C43—42no—
124D4×C43—42no—
125D4×C43—42no—
126D4×C43—82no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—44no—
132C2×C4×C43—42no—
133C2×C4×C43#12012yes—
134C2×C4×C43#12011yescharacteristic
135C2×C4×C43C22×D412yes—
136C2×C4×C43C22×D411yescharacteristic
137C2×Dic43—24no—
138C2×Dic43—24no—
139C2×Dic43—84no—
140Dic86—24no—
141Dic86—24no—
142Dic86—44no—
143Dic86—84no—
144C8×C43—42no—
145C43⋊C8—44no—
146#18693—431nomaximal, Sylow
147C22×C43—22no—
148C22×C43—21no—
149C22×C43—44no—
150C22×C43—42no—
151C22×C43C2×#12011yescharacteristic
152C4×C43—22no—
153C4×C43—21no—
154C4×C43—42no—
155C4×C43—82no—
156C4×C43#45512yes—
157C4×C43#57712yes—
158C4×C43#57812yes—
159Dic43—44no—
160Dic43—44no—
161#3550—431no—
162#3255—432no—
163#3131D4311yescharacteristic
164#1645—434no—
165#1640—434no—
166#1560—431no—
167#1493—432no—
168C2×C43—41no—
169C2×C43—82no—
170C2×C43#301312yes—
171C2×C43C2×#45511yescharacteristic
172#563—862no—
173#559—432no—
174Q82—432no—
175#556—862no—
176D4×Q8—862no—
177#542—864no—
178#536—862no—
179#533—432no—
180#533C2×D4311yescharacteristic
181#532C2×D4311yescharacteristic
182#488—22no—
183#487C2×D4312yes—
184#486C2×D4312yes—
185#475—434no—
186#475—862no—
187#470—864no—
188#462—434no—
189#462—862no—
190#423—432no—
191#416—22no—
192C2×C4×C8C2×D4311yescharacteristic
193#333—432no—
194#331—432no—
195Q8⋊C8—438no—
196C43#1869311yescharacteristic, complemented, Sylow
197C2×#41C22⋊D4312yes—
198C22×Q8—862no—
199C2×Q16—864no—
200C2×M16—862no—
201C22×C8—21no—
202C4⋊Q8—432no—
203C4⋊Q8—432no—
204C4⋊Q8—864no—
205C4⋊Q8—864no—
206C4⋊Q8C22×D4312yes—
207C4⋊Q8C22×D4311yescharacteristic
208#127C22×D4311yescharacteristic
209#126—868no—
210#125—21no—
211#125—862no—
212#124—864no—
213#124—864no—
214#124C22⋊D4312yes—
215#123—864no—
216#123—864no—
217C22⋊Q8—22no—
218C22⋊Q8—434no—
219C22⋊Q8—868no—
220C22⋊Q8—864no—
221C22⋊Q8—862no—
222#121—22no—
223C4×Q8—22no—
224C4×Q8—434no—
225C4×Q8—864no—
226C4×Q8—862no—
227C4×D4—22no—
228C4×D4—864no—
229#117—21no—
230#117—862no—
231#117—862no—
232C2×C42C22×D4311yescharacteristic
233#106—864no—
234C4⋊C8—434no—
235C4⋊C8—862no—
236#103—24no—
237#103—864no—
238#103—864no—
239#102—24no—
240C4×C8—21no—
241C4×C8C22×D4312yes—
242#41—44no—
243C2×Q8—22no—
244C2×Q8—434no—
245C2×Q8—864no—
246C2×Q8—862no—
247C2×Q8—3444no—
248C2×Q8C2×C22⋊D4312yes—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4C2×C22⋊D4312yes—
252C22×C4—22no—
253C22×C4—864no—
254C22×C4D4×D4312yes—
255C22×C4C2×C22⋊D4311yescharacteristic
256Q16—3444no—
257M16—3442no—
258C2×C8—22no—
259C2×C8—42no—
260C2×C8—864no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—42no—
265C4⋊C4—434no—
266C4⋊C4—868no—
267C4⋊C4—862no—
268C4⋊C4—862no—
269C4⋊C4—862no—
270C4⋊C4—864no—
271C4⋊C4—864no—
272C22⋊C4—24no—
273C22⋊C4—41no—
274C22⋊C4—864no—
275C22⋊C4—868no—
276C22⋊C4—864no—
277C42—41no—
278C42—864no—
279C42—864no—
280C42D4×D4312yes—
281C42C2×C22⋊D4311yescharacteristic
282C42C23×D4311yescharacteristic
283C23—22no—
284C23#1306329311yescharacteristic
285Q8—42no—
286Q8—42no—
287Q8—42no—
288Q8—864no—
289Q8—864no—
290Q8—3444no—
291Q8—1724no—
292D4—42no—
293D4—42no—
294D4—42no—
295D4—82no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—44no—
301C2×C4—42no—
302C2×C4—864no—
303C2×C4—864no—
304C2×C4—3444no—
305C2×C4#1306329312yes—
306C2×C4#1306329311yescharacteristic
307C2×C4C2×D4×D4312yes—
308C2×C4C22×C22⋊D4311yescharacteristic
309C8—42no—
310C8—1724no—
311C22—22no—
312C22—21no—
313C22—44no—
314C22—42no—
315C22C2×#1306329311yescharacteristic
316C4—22no—
317C4—21no—
318C4—42no—
319C4—82no—
320C4—1724no—
321C4—1724no—
322C4#1458307612yes—
323C4#1458370612yes—
324C4#1458371312yes—
325C2—41no—
326C2—82no—
327C2#1914390612yes—
328C2C2×#1458307611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3131C2
socleC22×C43C2×#120
prime radicalC43×#532C22
hypercenter#3131D43
hypocenterC43#18693
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
2. #19145986C2semidirect
3. #19133813C2semidirect
4. #19133778C2semidirect
6. #19133051C2semidirect
196. C43#18693semidirect

Maximal subgroups

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

subgroupindex
#191490092
#191459862
#191338132
#191337782
#191333302
#191330512
C43×#31312
#1869343