Finite Group Databasebeta

← #24993276

Subgroups — #24993276

Order 11008.

426 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 107 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#19145741C211yesmaximal, characteristic
2#19143532C211yesmaximal, characteristic
3#19135414C211yesmaximal, characteristic
4#19133268C211yesmaximal, characteristic
5#19133158C211yesmaximal, characteristic
6#19132425C211yesmaximal, characteristic
7C43×#1286C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×#13063325C2211yescharacteristic
10#14583297C412yescomplemented
11#14583250C412yescomplemented
12#14583230—22no—
13#14583185—22no—
14#14583028—22no—
15#14583028—22no—
16#14582952C2211yescharacteristic
17#14582927—21no—
18C2×#13063248—21no—
19C2×#13063248—21no—
20#14582857—21no—
21C2×#13063236C2211yescharacteristic
22#14582646—22no—
23#14582635—22no—
24C43×#431C2211yescharacteristic
25C43×#423C2211yescharacteristic
26C43×#382C2211yescharacteristic
27C22×Dic86—21no—
28C22×C43⋊C8D411yescharacteristic
29C22×C43⋊C8D411yescharacteristic
30#13063325—21no—
31#13063325—21no—
32#13063325—21no—
33#13063325C2×C412yes—
34#13063325C2×C411yescharacteristic
35#13063325C2×C411yescharacteristic
36#13063317—21no—
37#13063304—21no—
38#13063304D412yes—
39C4×Dic86—21no—
40C4×Dic86D412yes—
41#13063284—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44#13063257—24no—
45C4⋊(C43⋊C8)—21no—
46Dic43⋊C8—24no—
47#13063250—24no—
48#13063248—42no—
49#13063248—42no—
50C22⋊(C43⋊C8)—21no—
51#13063236—21no—
52#13063236—21no—
53#13063235—22no—
54C4×C43⋊C8—21no—
55C8×Dic43—22no—
56C2×M16×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C42×C43C2311yescharacteristic
59C4⋊C8×C43—21no—
60C4⋊C8×C43—21no—
61C4⋊C8×C43D412yes—
62C22⋊C8×C43—21no—
63C4×C8×C43C2×C412yes—
64#95×C43—21no—
65#95×C43—21no—
66C22×C4×C43—41no—
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43#4111yescharacteristic
70C22×Dic43—41no—
71C2×Dic86—22no—
72C2×Dic86—21no—
73C2×Dic86—41no—
74C2×Dic86—41no—
75C2×Dic86—41no—
76C2×Dic86—41no—
77C2×Dic86—41no—
78C2×Dic86C22⋊C412yes—
79M16×C43—41no—
80M16×C43—41no—
81C2×C8×C43—22no—
82C2×C8×C43—22no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C42×C43C22×C411yescharacteristic
86C42×C43C2×D411yescharacteristic
87C42×C43C2×D411yescharacteristic
88C42×C43#4111yescharacteristic
89C22⋊Dic43—22no—
90C4⋊Dic43—21no—
91C4⋊Dic43—21no—
92C4⋊Dic43—21no—
93C4⋊Dic43—22no—
94C4⋊Dic43—22no—
95C4⋊Dic43—41no—
96C4⋊Dic43—41no—
97C4⋊Dic43C22⋊C412yes—
98Dic43⋊C4—22no—
99Dic43⋊C4—22no—
100C4×Dic43—22no—
101C2×C43⋊C8—21no—
102C2×C43⋊C8—21no—
103C2×C43⋊C8—21no—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—21no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8SD1612yes—
108C23×C43#12111yescharacteristic
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—81no—
112C2×C4×C43—81no—
113C2×C4×C43—81no—
114C2×C4×C43C2×C22⋊C411yescharacteristic
115C2×C4×C43C4×D411yescharacteristic
116C2×C4×C43C4×D411yescharacteristic
117C2×C4×C43#12011yescharacteristic
118C2×C4×C43#12111yescharacteristic
119C2×C4×C43#12311yescharacteristic
120C2×C4×C43C2×SD1611yescharacteristic
121C2×C4×C43#13511yescharacteristic
122C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C43#13711yescharacteristic
124C2×Dic43—22no—
125C2×Dic43—22no—
126C2×Dic43—42no—
127C2×Dic43—81no—
128C2×Dic43—81no—
129Dic86—42no—
130Dic86—42no—
131Dic86—42no—
132Dic86—81no—
133Dic86—81no—
134Dic86—81no—
135C8×C43—42no—
136C8×C43—42no—
137C43⋊C8—22no—
138C43⋊C8—41no—
139C43⋊C8—81no—
140#9292—431nomaximal, Sylow
141C22×C43—21no—
142C22×C43—21no—
143C22×C43#38611yescharacteristic
144C22×C43#46011yescharacteristic
145C22×C43#46411yescharacteristic
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—161no—
151C4×C43C4×SD1611yescharacteristic
152C4×C43#44011yescharacteristic
153C4×C43#44811yescharacteristic
154C4×C43#44911yescharacteristic
155Dic43—42no—
156Dic43—42no—
157Dic43—82no—
158#3229—431no—
159#2961—431no—
160#1960—431no—
161#1546—431no—
162#1518—431no—
163#1286D4311yescharacteristic
164#1275—431no—
165C2×C43—21no—
166C2×C43—21no—
167C2×C43#188011yescharacteristic
168C2×C43#190211yescharacteristic
169C2×C43#190911yescharacteristic
170#533—431no—
171C2×C4⋊Q8—431no—
172#498—432no—
173#487—432no—
174#483—862no—
175#475—862no—
176#446—862no—
177#446—862no—
178#431—431no—
179#431C2×D4311yescharacteristic
180#424—861no—
181#423C2×D4311yescharacteristic
182C2×#103—861no—
183C2×#103—861no—
184#405—861no—
185C2×#97—431no—
186#382C2×D4311yescharacteristic
187#332—862no—
188#328—862no—
189C43#929211yescharacteristic, complemented, Sylow
190C22×Q8—861no—
191C2×M16—21no—
192C22×C8—431no—
193C22×C8—431no—
194C4⋊Q8—431no—
195C4⋊Q8—431no—
196C4⋊Q8—432no—
197C4⋊Q8—861no—
198C4⋊Q8—861no—
199C4⋊Q8—861no—
200#125—861no—
201C22⋊Q8—432no—
202C22⋊Q8—861no—
203C4×Q8—432no—
204C4×Q8—861no—
205#117—861no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4—861no—
209C2×C42C22×D4311yescharacteristic
210#106—864no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—864no—
214C4⋊C8—861no—
215C4⋊C8D17212yes—
216#103—864no—
217#103—1722no—
218#103—1722no—
219C22⋊C8—21no—
220C22⋊C8—861no—
221#97—862no—
222#97—861no—
223#97—861no—
224C4×C8—862no—
225C4×C8—861no—
226C4×C8C4×D4312yes—
227#95—21no—
228#95—21no—
229C2×Q8—432no—
230C2×Q8—861no—
231C2×Q8—862no—
232C2×Q8—1721no—
233C2×Q8—1721no—
234C2×Q8—1721no—
235C2×Q8—1721no—
236C2×Q8—1721no—
237C22×C4—41no—
238C22×C4—1721no—
239C22×C4#1062189811yescharacteristic
240C22×C4D4×D4311yescharacteristic
241C22×C4D4×D4311yescharacteristic
242M16—41no—
243M16—41no—
244C2×C8—22no—
245C2×C8—22no—
246C2×C8—432no—
247C2×C8—861no—
248C2×C8—861no—
249C2×C8—861no—
250C2×C8—861no—
251C2×C8—861no—
252C2×C8—1721no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—432no—
256C4⋊C4—861no—
257C4⋊C4—861no—
258C4⋊C4—861no—
259C4⋊C4—862no—
260C4⋊C4—862no—
261C4⋊C4—862no—
262C4⋊C4—862no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C22⋊C4—862no—
266C42—862no—
267C42C2×C4×D4311yescharacteristic
268C42C2×D17211yescharacteristic
269C42D4×D4311yescharacteristic
270C42#1062190211yescharacteristic
271C23#1306329811yescharacteristic
272Q8—3441no—
273Q8—3441no—
274Q8—3441no—
275Q8—1722no—
276Q8—1722no—
277Q8—1722no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—862no—
284C2×C4—862no—
285C2×C4—3441no—
286C2×C4—3441no—
287C2×C4—1722no—
288C2×C4C22⋊C4×D4311yescharacteristic
289C2×C4#1306328711yescharacteristic
290C2×C4C4×D17211yescharacteristic
291C2×C4#1306329511yescharacteristic
292C2×C4#1306330011yescharacteristic
293C2×C4#1306331011yescharacteristic
294C2×C4SD16×D4311yescharacteristic
295C2×C4#1306334611yescharacteristic
296C2×C4#1306334911yescharacteristic
297C2×C4#1306335711yescharacteristic
298C8—42no—
299C8—42no—
300C8—862no—
301C8—3441no—
302C8—1721no—
303C22—21no—
304C22—21no—
305C22#1458277711yescharacteristic
306C22#1458309811yescharacteristic
307C22#1458312411yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—161no—
313C4—3442no—
314C4—1722no—
315C4—1722no—
316C4#1458298611yescharacteristic
317C4#1458299811yescharacteristic
318C4#1458303911yescharacteristic
319C4#1458304511yescharacteristic
320C2—21no—
321C2—21no—
322C2#1913495111yescharacteristic
323C2#1913506711yescharacteristic
324C2#1913511611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1286C2
socleC22×C43#386
prime radicalC23×C43#121
cosocleC2×C42×C43C23
hypercenter#1286D43
hypocenterC43#9292
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
10. #14583297C4semidirect
11. #14583250C4semidirect
189. C43#9292semidirect

Maximal subgroups

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

subgroupindex
#191457412
#191435322
#191354142
#191332682
#191331582
#191324252
C43×#12862
#929243