Finite Group Databasebeta

← #25000376

Subgroups — #25000376

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#19144402C211yesmaximal, characteristic
2#19134607C211yesmaximal, characteristic
3#19133367C211yesmaximal, characteristic
4#19133250C211yesmaximal, characteristic
5#19133158C211yesmaximal, characteristic
6#19132918C211yesmaximal, characteristic
7C43×#1286C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×C4×Dic86C2211yescharacteristic
10#14583207—22no—
11#14583195—21no—
12#14583185—21no—
13#14582952C2211yescharacteristic
14#14582941—21no—
15C2×C4⋊(C43⋊C8)C2211yescharacteristic
16#14582909—21no—
17C2×#13063248—21no—
18#14582661—21no—
19#14582649—22no—
20#14582647—21no—
21#14582646—21no—
22#14582635—22no—
23#14582624—22no—
24C43×#431C2211yescharacteristic
25C43×#423C2211yescharacteristic
26C43×#382C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28C22×C43⋊C8—21no—
29#13063325D411yescharacteristic
30#13063325D411yescharacteristic
31#13063317—21no—
32#13063304—21no—
33#13063304—21no—
34C4×Dic86—21no—
35C4×Dic86—21no—
36C4×Dic86—21no—
37C4×Dic86—21no—
38C4×Dic86—21no—
39C4×Dic86—21no—
40#13063284—21no—
41C2×C4⋊Dic43D411yescharacteristic
42C2×Dic43⋊C4—21no—
43C2×C4×Dic43—21no—
44#13063259—22no—
45#13063257—22no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49#13063250—22no—
50#13063250—22no—
51#13063248—42no—
52C22⋊(C43⋊C8)D412yes—
53C4×C43⋊C8—21no—
54C2×M16×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C42×C43C2311yescharacteristic
57C4⋊C8×C43—21no—
58C4⋊C8×C43—21no—
59C4⋊C8×C43D412yes—
60C22⋊C8×C43—21no—
61C4×C8×C43—21no—
62#95×C43—21no—
63#95×C43—21no—
64C22×C4×C43—41no—
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43#4111yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C2×Dic86—21no—
71C2×Dic86—21no—
72C2×Dic86—21no—
73C2×Dic86—21no—
74C2×Dic86—21no—
75C2×Dic86—21no—
76C2×Dic86—21no—
77C2×Dic86SD1612yes—
78M16×C43—41no—
79M16×C43—41no—
80C2×C8×C43—22no—
81C2×C8×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C42×C43C2×D411yescharacteristic
85C42×C43C2×D411yescharacteristic
86C42×C43#4111yescharacteristic
87C42×C43#4111yescharacteristic
88C22⋊Dic43—41no—
89C4⋊Dic43—21no—
90C4⋊Dic43—21no—
91C4⋊Dic43—21no—
92C4⋊Dic43—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43—21no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97Dic43⋊C4—41no—
98Dic43⋊C4—41no—
99C4×Dic43—41no—
100C4×Dic43—41no—
101C4×Dic43—41no—
102C2×C43⋊C8—22no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106C23×C43#12111yescharacteristic
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—81no—
110C2×C4×C43—81no—
111C2×C4×C43—81no—
112C2×C4×C43#12011yescharacteristic
113C2×C4×C43#12111yescharacteristic
114C2×C4×C43#12111yescharacteristic
115C2×C4×C43#12311yescharacteristic
116C2×C4×C43#12311yescharacteristic
117C2×C4×C43#12411yescharacteristic
118C2×C4×C43C2×SD1611yescharacteristic
119C2×C4×C43#13511yescharacteristic
120C2×C4×C43#13711yescharacteristic
121C2×C4×C43#13711yescharacteristic
122C2×Dic43—22no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—81no—
129Dic86—22no—
130Dic86—22no—
131Dic86—41no—
132Dic86—41no—
133Dic86—81no—
134Dic86—81no—
135C8×C43—42no—
136C8×C43—81no—
137C43⋊C8—42no—
138C43⋊C8—81no—
139#10470—431nomaximal, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43#39411yescharacteristic
143C22×C43#46511yescharacteristic
144C22×C43#47011yescharacteristic
145C4×C43—21no—
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—161no—
150C4×C43#44811yescharacteristic
151C4×C43#45211yescharacteristic
152C4×C43#48311yescharacteristic
153C4×C43#48511yescharacteristic
154Dic43—42no—
155Dic43—81no—
156Dic43—81no—
157Dic43—81no—
158#3078—431no—
159#1805—431no—
160#1570—431no—
161#1542—431no—
162#1518—431no—
163#1461—431no—
164#1286D4311yescharacteristic
165C2×C43—21no—
166C2×C43—21no—
167C2×C43#203511yescharacteristic
168C2×C43#204911yescharacteristic
169C2×C43#205311yescharacteristic
170#533—431no—
171C2×C4×Q8—431no—
172#479—862no—
173#477—861no—
174#475—861no—
175#431—431no—
176#431C2×D4311yescharacteristic
177#428—861no—
178#423C2×D4311yescharacteristic
179C2×C4⋊C8—431no—
180#419—861no—
181C2×#103—861no—
182#382C2×D4311yescharacteristic
183#340—861no—
184#334—862no—
185#333—861no—
186#332—861no—
187#328—862no—
188#324—862no—
189C43#1047011yescharacteristic, complemented, Sylow
190C22×Q8—431no—
191C2×M16—21no—
192C22×C8—861no—
193C4⋊Q8—431no—
194C4⋊Q8—431no—
195#125—861no—
196C22⋊Q8—861no—
197C22⋊Q8—861no—
198C4×Q8—861no—
199C4×Q8—861no—
200C4×Q8—861no—
201C4×Q8—861no—
202C4×Q8—861no—
203C4×Q8—861no—
204#117—861no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—431no—
207C2×C4⋊C4—861no—
208C2×C42—861no—
209C2×C42C22×D4311yescharacteristic
210#107—862no—
211#106—862no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—861no—
215C4⋊C8—861no—
216C4⋊C8—861no—
217C4⋊C8D17212yes—
218#103—862no—
219#103—862no—
220#103—1722no—
221C22⋊C8—21no—
222C22⋊C8—432no—
223C4×C8—21no—
224C4×C8—861no—
225#95—21no—
226#95—21no—
227C2×Q8—432no—
228C2×Q8—861no—
229C2×Q8—861no—
230C2×Q8—861no—
231C2×Q8—861no—
232C2×Q8—861no—
233C2×Q8—861no—
234C2×Q8—861no—
235C22×C4—41no—
236C22×C4—861no—
237C22×C4—861no—
238C22×C4#1062189811yescharacteristic
239C22×C4D4×D4311yescharacteristic
240C22×C4D4×D4311yescharacteristic
241M16—41no—
242M16—41no—
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—862no—
246C2×C8—1721no—
247C2×C8—1721no—
248C2×C8—1721no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—861no—
252C4⋊C4—861no—
253C4⋊C4—861no—
254C4⋊C4—861no—
255C4⋊C4—861no—
256C4⋊C4—861no—
257C4⋊C4—1721no—
258C4⋊C4—1721no—
259C4⋊C4—1721no—
260C4⋊C4—1721no—
261C22⋊C4—1721no—
262C42—1721no—
263C42—1721no—
264C42—1721no—
265C42C2×D17211yescharacteristic
266C42#1062189811yescharacteristic
267C42D4×D4311yescharacteristic
268C42#1062190211yescharacteristic
269C23#1306329811yescharacteristic
270Q8—862no—
271Q8—862no—
272Q8—3441no—
273Q8—3441no—
274Q8—1721no—
275Q8—1721no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—862no—
282C2×C4—3441no—
283C2×C4—1721no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4#1306329511yescharacteristic
289C2×C4#1306329811yescharacteristic
290C2×C4#1306330011yescharacteristic
291C2×C4#1306331011yescharacteristic
292C2×C4#1306331011yescharacteristic
293C2×C4#1306331311yescharacteristic
294C2×C4SD16×D4311yescharacteristic
295C2×C4#1306334411yescharacteristic
296C2×C4#1306335411yescharacteristic
297C2×C4#1306335711yescharacteristic
298C8—42no—
299C8—81no—
300C8—3441no—
301C8—1722no—
302C22—21no—
303C22—21no—
304C22#1458281711yescharacteristic
305C22#1458312711yescharacteristic
306C22#1458315611yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—161no—
312C4—3441no—
313C4—3441no—
314C4—3441no—
315C4—1722no—
316C4#1458303911yescharacteristic
317C4#1458306211yescharacteristic
318C4#1458323111yescharacteristic
319C4#1458324211yescharacteristic
320C2—21no—
321C2—21no—
322C2#1913579411yescharacteristic
323C2#1913587811yescharacteristic
324C2#1913590211yescharacteristic
subgroupG/H
centerC22#14582817
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1286C2
socleC22×C43#394
prime radicalC23×C43#121
hypercenter#1286D43
hypocenterC43#10470
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
189. C43#10470semidirect

Maximal subgroups

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

subgroupindex
#191444022
#191346072
#191333672
#191332502
#191331582
#191329182
C43×#12862
#1047043