Finite Group Databasebeta

← #25009518

Subgroups — #25009518

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#19142419C211yesmaximal, characteristic
2#19135937C211yesmaximal, characteristic
3#19133637C211yesmaximal, characteristic
4#19132623C211yesmaximal, characteristic
5#19132601C211yesmaximal, characteristic
6#19132540C211yesmaximal, characteristic
7C43×#1611C211yesmaximal, characteristic
8#14583232—21no—
9#14582942—21no—
10#14582840—21no—
11#14582840—21no—
12#14582838C2211yescharacteristic
13#14582786—21no—
14#14582785—21no—
15#14582780—21no—
16#14582780—21no—
17#14582768C2211yescharacteristic
18#14582668C2211yescharacteristic
19#14582658—21no—
20#14582636—21no—
21#14582625C2211yescharacteristic
22C43×#544C2211yescharacteristic
23C43×#483—21no—
24C43×#398C2211yescharacteristic
25C43×#328—21no—
26C43×#324C2211yescharacteristic
27C2×#10621877—21no—
28C2×C4⋊Dic43D411yescharacteristic
29C2×C4⋊Dic43D411yescharacteristic
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C4×Dic43—21no—
34C2×C4×Dic43D411yescharacteristic
35#13063258—41no—
36#13063258—41no—
37#13063256—41no—
38#13063249—41no—
39C22⋊(C43⋊C8)—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95D411yescharacteristic
49C4⋊Q8×C43—41no—
50#125×C43—41no—
51C22⋊Q8×C43—21no—
52C22⋊Q8×C43—21no—
53#117×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43D411yescharacteristic
56C2×C4⋊C4×C43C2311yescharacteristic
57#106×C43—41no—
58#103×C43—41no—
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43D411yescharacteristic
62C2×Q8×C43—21no—
63C2×Q8×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C2×C8×C43—41no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43—21no—
76C4⋊C4×C43—21no—
77C4⋊C4×C43—21no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C22⋊C4×C43—41no—
85C42×C43—41no—
86C4⋊Dic43—41no—
87C4⋊Dic43—41no—
88Dic43⋊C4—42no—
89Dic43⋊C4—42no—
90Dic43⋊C4—42no—
91C4×Dic43—21no—
92C4×Dic43—21no—
93C4×Dic43—81no—
94#10621877—22no—
95#10621877—41no—
96C2×C43⋊C8—41no—
97C2×C43⋊C8—41no—
98C23×C43#12011yescharacteristic
99Q8×C43—81no—
100Q8×C43—81no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43#13511yescharacteristic
116C2×C4×C43#13711yescharacteristic
117C2×Dic43—22no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—42no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C8×C43—81no—
129C43⋊C8—42no—
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—
143C4×C43—81no—
144C4×C43—81no—
145Dic43—42no—
146Dic43—81no—
147Dic43—81no—
148Dic43—81no—
149#2794—431no—
150#2060—431no—
151#1617—431no—
152#1611D4311yescharacteristic
153#1353—431no—
154#1346—431no—
155#1325—431no—
156C2×C43—21no—
157C2×C43—21no—
158C2×C43#160311yescharacteristic
159C2×C43#219811yescharacteristic
160C2×C43#220311yescharacteristic
161#544C2×D4311yescharacteristic
162#484—861no—
163#483—21no—
164#428—861no—
165#400—431no—
166#400—861no—
167#400—861no—
168#398C2×D4311yescharacteristic
169#387—861no—
170#387—861no—
171#387—861no—
172#387—861no—
173#384—431no—
174#343—431no—
175#339—861no—
176#328—21no—
177#328—861no—
178#324—431no—
179#324C2×D4311yescharacteristic
180C43#1223611yescharacteristic, complemented, Sylow
181C2×M16—861no—
182C4⋊Q8—41no—
183#125—41no—
184C22⋊Q8—21no—
185C22⋊Q8—21no—
186#117—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—431no—
189C2×C4⋊C4—431no—
190C2×C4⋊C4—861no—
191C2×C4⋊C4—861no—
192C2×C4⋊C4—861no—
193C2×C4⋊C4C22⋊D4311yescharacteristic
194C2×C4⋊C4C22×D4311yescharacteristic
195C2×C42—431no—
196C2×C42—861no—
197#107—1721no—
198#107—1721no—
199#106—41no—
200#106—1721no—
201#103—41no—
202#103—1721no—
203C22⋊C8—21no—
204C22⋊C8—861no—
205#95—21no—
206#95—431no—
207#95—861no—
208#95—861no—
209#95—861no—
210#95—861no—
211#95—861no—
212#95—861no—
213#95—861no—
214#95—861no—
215#95C22⋊D4311yescharacteristic
216C2×Q8—21no—
217C2×Q8—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—861no—
221C22×C4—861no—
222C22×C4—861no—
223C22×C4—861no—
224C22×C4D4×D4311yescharacteristic
225C22×C4D4×D4311yescharacteristic
226C22×C4C2×C22⋊D4311yescharacteristic
227M16—862no—
228M16—1721no—
229C2×C8—41no—
230C2×C8—1721no—
231C2×C8—1721no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—1721no—
243C4⋊C4—1721no—
244C4⋊C4—1722no—
245C4⋊C4—1722no—
246C4⋊C4—1722no—
247C22⋊C4—41no—
248C42—41no—
249C42—861no—
250C42—861no—
251C42—3441no—
252C23#1306329311yescharacteristic
253Q8—81no—
254Q8—81no—
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—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—862no—
270C2×C4—1721no—
271C2×C4—1721no—
272C2×C4—1721no—
273C2×C4—1721no—
274C2×C4—1722no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4—1721no—
279C2×C4—1721no—
280C2×C4#1306334611yescharacteristic
281C2×C4#1306335411yescharacteristic
282C8—81no—
283C8—3441no—
284C8—1722no—
285C22—21no—
286C22—21no—
287C22#1458305811yescharacteristic
288C22#1458308011yescharacteristic
289C22#1458308511yescharacteristic
290C4—21no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—81no—
295C4—81no—
296C4—81no—
297C4—81no—
298C4—3441no—
299C4—3441no—
300C4—3441no—
301C4—1722no—
302C2—21no—
303C2—21no—
304C2#1913355511yescharacteristic
305C2#1913658911yescharacteristic
306C2#1913661411yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1611C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1611D43
hypocenterC43#12236
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1611

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
#191424192
#191359372
#191336372
#191326232
#191326012
#191325402
C43×#16112
#1223643