Finite Group Databasebeta

← #25009524

Subgroups — #25009524

Order 11008.

324 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 55 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#19142420C211yesmaximal, characteristic
2#19135941C211yesmaximal, characteristic
3#19133636C211yesmaximal, characteristic
4#19133605C211yesmaximal, characteristic
5#19132600C211yesmaximal, characteristic
6#19132540C211yesmaximal, characteristic
7C43×#1353C211yesmaximal, characteristic
8#14583530C2211yescharacteristic
9#14583234—21no—
10#14583230—21no—
11#14582941—21no—
12#14582841—21no—
13#14582841—21no—
14#14582829C2211yescharacteristic
15#14582786—21no—
16#14582786—21no—
17#14582784—21no—
18#14582780—21no—
19#14582768C2211yescharacteristic
20#14582660—21no—
21#14582637—21no—
22#14582635—21no—
23#14582625C2211yescharacteristic
24C43×#400C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27#13063324—41no—
28#13063316—41no—
29#13063304—21no—
30#13063304—21no—
31#13063284—21no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43D411yescharacteristic
34C2×C4⋊Dic43D411yescharacteristic
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×C4×Dic43—21no—
39C2×C4×Dic43D411yescharacteristic
40#13063259—41no—
41#13063258—41no—
42#13063257—41no—
43#13063257—41no—
44#13063250—41no—
45#13063248—41no—
46C22⋊(C43⋊C8)—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95D411yescharacteristic
55C2×M16×C43—21no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C4⋊C4×C43C2311yescharacteristic
58C22⋊C8×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43D411yescharacteristic
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C2×Dic86—21no—
72C2×Dic86—21no—
73M16×C43—22no—
74M16×C43—41no—
75C2×C8×C43—41no—
76C2×C8×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C22⋊Dic43—41no—
80C4⋊Dic43—21no—
81C4⋊Dic43—21no—
82C4⋊Dic43—21no—
83C4⋊Dic43—21no—
84C4⋊Dic43—42no—
85C4⋊Dic43—41no—
86C4⋊Dic43—41no—
87Dic43⋊C4—42no—
88Dic43⋊C4—42no—
89Dic43⋊C4—41no—
90Dic43⋊C4—41no—
91Dic43⋊C4—41no—
92Dic43⋊C4—41no—
93C4×Dic43—21no—
94C4×Dic43—21no—
95C4×Dic43—41no—
96C4×Dic43—81no—
97C2×C43⋊C8—41no—
98C23×C43#12011yescharacteristic
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—42no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43#13511yescharacteristic
111C2×C4×C43#13711yescharacteristic
112C2×Dic43—22no—
113C2×Dic43—41no—
114C2×Dic43—41no—
115C2×Dic43—41no—
116C2×Dic43—41no—
117C2×Dic43—41no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126Dic86—81no—
127Dic86—81no—
128C8×C43—42no—
129C8×C43—81no—
130C43⋊C8—81no—
131#12236—431nomaximal, Sylow
132C22×C43—21no—
133C22×C43—21no—
134C22×C43#45211yescharacteristic
135C22×C43#45611yescharacteristic
136C22×C43B(4,𝔽2)11yescharacteristic
137C4×C43—21no—
138C4×C43—21no—
139C4×C43—41no—
140C4×C43—41no—
141C4×C43—81no—
142C4×C43—81no—
143Dic43—42no—
144Dic43—81no—
145Dic43—81no—
146Dic43—81no—
147Dic43—81no—
148Dic43—81no—
149#2794—431no—
150#2060—431no—
151#1617—431no—
152#1611—431no—
153#1353D4311yescharacteristic
154#1346—431no—
155#1325—431no—
156C2×C43—21no—
157C2×C43—21no—
158C2×C43#160311yescharacteristic
159C2×C43#219811yescharacteristic
160C2×C43#220311yescharacteristic
161#544—431no—
162#484—861no—
163#483—861no—
164#428—861no—
165#400—861no—
166#400—861no—
167#400C2×D4311yescharacteristic
168#398—431no—
169#387—861no—
170#387—861no—
171#387—861no—
172#387—861no—
173#384—431no—
174#343C2×D4311yescharacteristic
175#339—861no—
176#328—861no—
177#328—861no—
178#324—431no—
179#324C2×D4311yescharacteristic
180C43#1223611yescharacteristic, complemented, Sylow
181C2×M16—21no—
182C4⋊Q8—1721no—
183#125—1721no—
184C22⋊Q8—861no—
185C22⋊Q8—861no—
186#117—861no—
187C2×C4⋊C4—431no—
188C2×C4⋊C4—431no—
189C2×C4⋊C4—861no—
190C2×C4⋊C4—861no—
191C2×C4⋊C4—861no—
192C2×C4⋊C4—861no—
193C2×C4⋊C4D17211yescharacteristic
194C2×C4⋊C4C22×D4311yescharacteristic
195C2×C42—431no—
196C2×C42—861no—
197#107—1721no—
198#107—1721no—
199#106—1721no—
200#106—1721no—
201#103—1721no—
202#103—1721no—
203C22⋊C8—21no—
204C22⋊C8—861no—
205#95—21no—
206#95—21no—
207#95—431no—
208#95—861no—
209#95—861no—
210#95—861no—
211#95—861no—
212#95—861no—
213#95—861no—
214#95—861no—
215#95D17211yescharacteristic
216C2×Q8—861no—
217C2×Q8—861no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—861no—
221C22×C4—861no—
222C22×C4—861no—
223C22×C4—861no—
224C22×C4C2×D17211yescharacteristic
225C22×C4D4×D4311yescharacteristic
226C22×C4D4×D4311yescharacteristic
227M16—22no—
228M16—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—1721no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—861no—
235C4⋊C4—861no—
236C4⋊C4—861no—
237C4⋊C4—861no—
238C4⋊C4—1721no—
239C4⋊C4—1721no—
240C4⋊C4—1721no—
241C4⋊C4—1721no—
242C4⋊C4—1722no—
243C4⋊C4—1722no—
244C4⋊C4—1722no—
245C4⋊C4—1721no—
246C4⋊C4—1721no—
247C22⋊C4—1721no—
248C42—861no—
249C42—861no—
250C42—3441no—
251C42—1721no—
252C23#1306329511yescharacteristic
253Q8—3441no—
254Q8—3441no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—862no—
267C2×C4—1721no—
268C2×C4—1721no—
269C2×C4—1721no—
270C2×C4—1721no—
271C2×C4—1721no—
272C2×C4—1721no—
273C2×C4—1721no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4—1721no—
279C2×C4—1721no—
280C2×C4#1306334611yescharacteristic
281C2×C4#1306335711yescharacteristic
282C8—42no—
283C8—81no—
284C8—3441no—
285C22—21no—
286C22—21no—
287C22#1458306411yescharacteristic
288C22#1458308311yescharacteristic
289C22#1458308711yescharacteristic
290C4—21no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—81no—
295C4—81no—
296C4—3441no—
297C4—3441no—
298C4—3441no—
299C4—3441no—
300C4—3441no—
301C4—1722no—
302C2—21no—
303C2—21no—
304C2#1913356111yescharacteristic
305C2#1913659211yescharacteristic
306C2#1913661811yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1353C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1353D43
hypocenterC43#12236
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
180. C43#12236semidirect

Maximal subgroups

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

subgroupindex
#191424202
#191359412
#191336362
#191336052
#191326002
#191325402
C43×#13532
#1223643