Finite Group Databasebeta

← #25000378

Subgroups — #25000378

Order 11008.

366 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 91 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#19144396C211yesmaximal, characteristic
2#19134611C211yesmaximal, characteristic
3#19133369C211yesmaximal, characteristic
4#19133159C211yesmaximal, characteristic
5#19132918C211yesmaximal, characteristic
6#19132454C211yesmaximal, characteristic
7C43×#1542C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9#14583203—22no—
10#14583191—21no—
11#14583181—21no—
12#14582952C2211yescharacteristic
13#14582942—21no—
14#14582923C2211yescharacteristic
15#14582907—21no—
16C2×#13063250—21no—
17#14582765C2211yescharacteristic
18#14582662—21no—
19#14582651—22no—
20#14582636—22no—
21#14582624—22no—
22C43×#533C2211yescharacteristic
23C43×#431C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C43×#333—21no—
26C43×#332—21no—
27C22×Dic86D411yescharacteristic
28C2×#10621877—21no—
29C4×Dic86—21no—
30C4×Dic86—21no—
31C4×Dic86—21no—
32C4×Dic86—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43D411yescharacteristic
35C2×Dic43⋊C4—21no—
36C2×C4×Dic43—21no—
37#13063258—22no—
38#13063256—22no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)D412yes—
42#13063250—42no—
43#13063248—22no—
44#13063248—22no—
45C22⋊(C43⋊C8)D412yes—
46C4×C43⋊C8—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C22×C8×C43—21no—
50C4⋊Q8×C43D411yescharacteristic
51C4⋊Q8×C43D411yescharacteristic
52#125×C43—21no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43—21no—
55C4×Q8×C43—21no—
56C4×Q8×C43—21no—
57#117×C43—21no—
58C2×C42×C43C2311yescharacteristic
59C4⋊C8×C43—21no—
60C4⋊C8×C43—21no—
61C4⋊C8×C43—21no—
62C22⋊C8×C43—21no—
63C4×C8×C43—21no—
64C2×Q8×C43—21no—
65C2×Q8×C43—21no—
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43#4111yescharacteristic
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—41no—
72C2×Dic86—21no—
73C2×Dic86—21no—
74C2×Dic86—21no—
75C2×Dic86—21no—
76C2×Dic86—21no—
77C2×Dic86Q1612yes—
78C2×C8×C43—41no—
79C2×C8×C43—41no—
80C2×C8×C43—41no—
81C2×C8×C43—41no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—41no—
88C22⋊C4×C43—41no—
89C42×C43—41no—
90C42×C43C2×D411yescharacteristic
91C42×C43C2×D411yescharacteristic
92C42×C43#4111yescharacteristic
93C42×C43#4111yescharacteristic
94C4⋊Dic43—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43—41no—
97C4⋊Dic43—41no—
98Dic43⋊C4—41no—
99Dic43⋊C4—41no—
100C4×Dic43—41no—
101C4×Dic43—41no—
102#10621877—41no—
103#10621877—41no—
104C2×C43⋊C8—22no—
105C2×C43⋊C8—22no—
106C23×C43#12111yescharacteristic
107Q8×C43—81no—
108Q8×C43—81no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43#12011yescharacteristic
114C2×C4×C43#12111yescharacteristic
115C2×C4×C43#12111yescharacteristic
116C2×C4×C43#12311yescharacteristic
117C2×C4×C43#12311yescharacteristic
118C2×C4×C43#12411yescharacteristic
119C2×C4×C43C2×Q1611yescharacteristic
120C2×C4×C43#13511yescharacteristic
121C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C43#13711yescharacteristic
123C2×Dic43—22no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—81no—
128C2×Dic43—81no—
129C2×Dic43—81no—
130C2×Dic43—81no—
131Dic86—22no—
132Dic86—22no—
133Dic86—41no—
134Dic86—41no—
135C8×C43—81no—
136C8×C43—81no—
137C43⋊C8—42no—
138C43⋊C8—42no—
139#10471—431nomaximal, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43#39411yescharacteristic
143C22×C43#46711yescharacteristic
144C22×C43#46811yescharacteristic
145C4×C43—21no—
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—81no—
150C4×C43—81no—
151C4×C43#44911yescharacteristic
152C4×C43#45111yescharacteristic
153C4×C43#48411yescharacteristic
154C4×C43#48511yescharacteristic
155Dic43—42no—
156Dic43—81no—
157Dic43—161no—
158#3078—431no—
159#1805—431no—
160#1571—431no—
161#1542D4311yescharacteristic
162#1518—431no—
163#1461—431no—
164#1286—431no—
165C2×C43—21no—
166C2×C43—21no—
167C2×C43#203611yescharacteristic
168C2×C43#204911yescharacteristic
169C2×C43#205311yescharacteristic
170#533C2×D4311yescharacteristic
171C2×C4×Q8—431no—
172#479—862no—
173#477—861no—
174#475—861no—
175#431—431no—
176#431C2×D4311yescharacteristic
177#428—861no—
178#423—431no—
179C2×C4⋊C8C2×D4311yescharacteristic
180#419—861no—
181C2×#103—861no—
182#382—431no—
183#340—861no—
184#335—862no—
185#333—21no—
186#332—21no—
187#328—862no—
188#324—862no—
189C43#1047111yescharacteristic, complemented, Sylow
190C22×Q8—431no—
191C2×M16—861no—
192C22×C8—21no—
193C4⋊Q8C22⋊D4311yescharacteristic
194C4⋊Q8C22⋊D4311yescharacteristic
195#125—21no—
196C22⋊Q8—21no—
197C22⋊Q8—21no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—861no—
201C4×Q8—861no—
202C4×Q8—861no—
203C4×Q8—861no—
204#117—21no—
205C2×C4⋊C4—431no—
206C2×C4⋊C4—861no—
207C2×C4⋊C4—861no—
208C2×C42—861no—
209C2×C42C22×D4311yescharacteristic
210#107—862no—
211#106—862no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—432no—
216C4⋊C8—861no—
217C4⋊C8—861no—
218#103—862no—
219#103—862no—
220#103—1722no—
221C22⋊C8—21no—
222C22⋊C8—432no—
223C4×C8—21no—
224C4×C8—861no—
225#95—861no—
226#95—861no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—432no—
230C2×Q8—861no—
231C2×Q8—861no—
232C2×Q8—861no—
233C2×Q8—861no—
234C2×Q8—861no—
235C22×C4—861no—
236C22×C4—861no—
237C22×C4—1721no—
238C22×C4#1062189811yescharacteristic
239C22×C4D4×D4311yescharacteristic
240C22×C4D4×D4311yescharacteristic
241M16—1721no—
242M16—1721no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—862no—
248C2×C8—862no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—861no—
256C4⋊C4—861no—
257C4⋊C4—1721no—
258C4⋊C4—1721no—
259C4⋊C4—1721no—
260C4⋊C4—1721no—
261C22⋊C4—41no—
262C42—41no—
263C42—1721no—
264C42—1721no—
265C42#1062189811yescharacteristic
266C42D4×D4311yescharacteristic
267C42#1062190011yescharacteristic
268C42C2×C22⋊D4311yescharacteristic
269C23#1306329811yescharacteristic
270Q8—81no—
271Q8—81no—
272Q8—862no—
273Q8—862no—
274Q8—1721no—
275Q8—1721no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—862no—
281C2×C4—3441no—
282C2×C4—3441no—
283C2×C4—3441no—
284C2×C4—3441no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4#1306329311yescharacteristic
289C2×C4#1306329711yescharacteristic
290C2×C4#1306329811yescharacteristic
291C2×C4#1306330711yescharacteristic
292C2×C4#1306330811yescharacteristic
293C2×C4#1306331111yescharacteristic
294C2×C4Q16×D4311yescharacteristic
295C2×C4#1306334611yescharacteristic
296C2×C4#1306335211yescharacteristic
297C2×C4#1306335711yescharacteristic
298C8—81no—
299C8—81no—
300C8—1722no—
301C8—1722no—
302C22—21no—
303C22—21no—
304C22#1458281411yescharacteristic
305C22#1458313911yescharacteristic
306C22#1458314811yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—81no—
312C4—81no—
313C4—3441no—
314C4—1722no—
315C4—6881no—
316C4#1458304311yescharacteristic
317C4#1458305311yescharacteristic
318C4#1458323311yescharacteristic
319C4#1458323811yescharacteristic
320C2—21no—
321C2—21no—
322C2#1913579611yescharacteristic
323C2#1913587511yescharacteristic
324C2#1913589911yescharacteristic
subgroupG/H
centerC22#14582814
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1542C2
socleC22×C43#394
prime radicalC23×C43#121
hypercenter#1542D43
hypocenterC43#10471
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
189. C43#10471semidirect

Maximal subgroups

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

subgroupindex
#191443962
#191346112
#191333692
#191331592
#191329182
#191324542
C43×#15422
#1047143