Finite Group Databasebeta

← #25010539

Subgroups — #25010539

Order 11008.

290 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 61 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#19147677C211yesmaximal, characteristic
2#19136831C211yesmaximal, characteristic
3#19136748C211yesmaximal, characteristic, complemented
4#19134114C211yesmaximal, characteristic, complemented
5#19132576C211yesmaximal, characteristic, complemented
6#19132564C211yesmaximal, characteristic, complemented
7C43×#1360C211yesmaximal, characteristic
8#14583618—21no—
9#14583304C2211yescharacteristic
10#14583290—21no—
11#14583118—21no—
12#14583112—21no—
13#14583110—21no—
14#14583107—21no—
15#14583029C2211yescharacteristic
16#14583000—21no—
17C4×Dic172C2211yescharacteristic
18#14582725—21no—
19#14582704—21no—
20#14582703—21no—
21#14582700—21no—
22#14582675C2211yescharacteristic
23#14582646—21no—
24C43×#495C2211yescharacteristic
25C43×C4⋊C16C2211yescharacteristic
26C43×#334C2211yescharacteristic
27C2×Dic172—41no—
28C2×Dic172D411yescharacteristic
29C2×#10621885—21no—
30C2×#10621883—21no—
31#13063325—21no—
32#13063323—21no—
33#13063318—41no—
34#13063318—41no—
35#13063312—21no—
36#13063302—41no—
37Q8×Dic43—21no—
38C4×Dic86—21no—
39C4×Dic86D411yescharacteristic
40D4×Dic43—21no—
41#13063281—41no—
42C2×C43⋊C16—21no—
43#13063259—21no—
44#13063259—21no—
45#13063259D411yescharacteristic
46C4⋊(C43⋊C8)D411yescharacteristic
47Dic43⋊C8—21no—
48#13063250—21no—
49#13063250—41no—
50#13063249—21no—
51#13063246—21no—
52#13063235—21no—
53C2×Q16×C43D411yescharacteristic
54C2×SD16×C43—21no—
55C2×D8×C43D411yescharacteristic
56#124×C43—21no—
57C2×C16×C43—21no—
58C4⋊C8×C43—21no—
59C4×C8×C43C2311yescharacteristic
60C2×Q8×C43—21no—
61C2×D4×C43—21no—
62C22×Dic43—41no—
63C2×Dic86—21no—
64C2×Dic86—41no—
65C2×Dic86D811yescharacteristic
66Q16×C43—41no—
67SD16×C43—41no—
68SD16×C43—41no—
69D8×C43—41no—
70C2×C8×C43—41no—
71C2×C8×C43C2×D411yescharacteristic
72C2×C8×C43C2×D411yescharacteristic
73C22⋊C4×C43—41no—
74C22⋊C4×C43—41no—
75C42×C43C2×D411yescharacteristic
76C22⋊Dic43—41no—
77C22⋊Dic43—41no—
78C22⋊Dic43—41no—
79#10621885—81no—
80#10621883—81no—
81C4⋊Dic43—21no—
82C4⋊Dic43—41no—
83C4⋊Dic43—41no—
84C4⋊Dic43—41no—
85C4⋊Dic43D811yescharacteristic
86Dic43⋊C4—21no—
87Dic43⋊C4—41no—
88Dic43⋊C4—41no—
89Dic43⋊C4—41no—
90C4×Dic43—21no—
91C4×Dic43—41no—
92C4×Dic43—41no—
93C2×C43⋊C8—21no—
94Dic172—21no—
95Dic172—21no—
96Dic172—82no—
97C16×C43—41no—
98C43⋊C16—41no—
99C23×C43—41no—
100Q8×C43—41no—
101Q8×C43—41no—
102D4×C43—41no—
103D4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43#12011yescharacteristic
106C2×C4×C43C2×D811yescharacteristic
107C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
108C2×Dic43—21no—
109C2×Dic43—21no—
110C2×Dic43—41no—
111C2×Dic43—41no—
112C2×Dic43—82no—
113C2×Dic43—81no—
114Dic86—41no—
115Dic86—41no—
116Dic86—41no—
117Dic86—81no—
118Dic86—81no—
119C8×C43—21no—
120C8×C43—81no—
121C8×C43#13511yescharacteristic
122C8×C43#13711yescharacteristic
123C43⋊C8—41no—
124#12391—431nomaximal, Sylow
125C22×C43—81no—
126C22×C43—81no—
127C22×C43—81no—
128C22×C43#44711yescharacteristic
129C4×C43—21no—
130C4×C43—21no—
131C4×C43—81no—
132C4×C43#45211yescharacteristic
133C4×C43#45511yescharacteristic
134Dic43—41no—
135Dic43—41no—
136Dic43—81no—
137Dic43—81no—
138Dic43—161no—
139#3402—431no—
140#2243—431no—
141#2227—431no—
142#1694—431no—
143#1360D4311yescharacteristic
144#1338—431no—
145#1334—431no—
146C2×C43—161no—
147C2×C43#164111yescharacteristic
148C2×C43#219011yescharacteristic
149C2×C43#219511yescharacteristic
150#556—861no—
151#500—431no—
152#497—861no—
153#495C2×D4311yescharacteristic
154#464—861no—
155#463—861no—
156#462—861no—
157#462—861no—
158#446—431no—
159#440—861no—
160C4×Q16—431no—
161#366—861no—
162C4⋊C16C2×D4311yescharacteristic
163#358—861no—
164#358—861no—
165#357—861no—
166#346—431no—
167#334C2×D4311yescharacteristic
168#332—861no—
169C43#1239111yescharacteristic, complemented, Sylow
170C2×Q16—431no—
171C2×Q16—861no—
172C2×Q16—1721no—
173C2×Q16D17211yescharacteristic
174C2×SD16—21no—
175C2×SD16—861no—
176C2×D8D17211yescharacteristic
177C4⋊Q8—861no—
178C4⋊Q8—861no—
179#126—1721no—
180#126—1721no—
181#124—21no—
182#124—861no—
183C22⋊Q8—1721no—
184C4×Q8—431no—
185C4×Q8—861no—
186C4×Q8—861no—
187C4×D4—861no—
188#117—1721no—
189C2×C16—21no—
190C2×C16—861no—
191#107—431no—
192#107—861no—
193#107—861no—
194C4⋊C8—21no—
195C4⋊C8—431no—
196C4⋊C8—861no—
197#103—861no—
198#103—861no—
199#103—1721no—
200#102—861no—
201#97—861no—
202C4×C8C22×D4311yescharacteristic
203C2×Q8—21no—
204C2×Q8—431no—
205C2×Q8—861no—
206C2×Q8—1721no—
207C2×D4—21no—
208C22×C4—1721no—
209Q16—41no—
210Q16—861no—
211Q16—861no—
212Q16—3442no—
213Q16—3441no—
214SD16—41no—
215SD16—41no—
216SD16—3441no—
217D8—41no—
218C2×C8—41no—
219C2×C8—861no—
220C2×C8C2×D17211yescharacteristic
221C2×C8D4×D4311yescharacteristic
222C4⋊C4—431no—
223C4⋊C4—861no—
224C4⋊C4—861no—
225C4⋊C4—1721no—
226C4⋊C4—1721no—
227C4⋊C4—1721no—
228C4⋊C4—1721no—
229C4⋊C4—1721no—
230C4⋊C4—1721no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—1721no—
234C22⋊C4—1721no—
235C22⋊C4—1721no—
236C42—861no—
237C42—1721no—
238C42—1721no—
239C42D4×D4311yescharacteristic
240C16—41no—
241C16—1721no—
242C23—41no—
243Q8—41no—
244Q8—41no—
245Q8—3441no—
246Q8—3441no—
247Q8—1721no—
248Q8—1721no—
249Q8—1721no—
250D4—41no—
251D4—41no—
252C2×C4—41no—
253C2×C4—861no—
254C2×C4—861no—
255C2×C4—3442no—
256C2×C4—3441no—
257C2×C4—1721no—
258C2×C4—1721no—
259C2×C4#1306329511yescharacteristic
260C2×C4D8×D4311yescharacteristic
261C2×C4#1306335211yescharacteristic
262C8—21no—
263C8—81no—
264C8—1721no—
265C8#1306334411yescharacteristic
266C8#1306335411yescharacteristic
267C22—81no—
268C22—81no—
269C22—81no—
270C22#1458303411yescharacteristic
271C4—21no—
272C4—21no—
273C4—81no—
274C4—3441no—
275C4—3441no—
276C4—1721no—
277C4—1721no—
278C4—6881no—
279C4#1458306211yescharacteristic
280C4#1458307911yescharacteristic
281C2—161no—
282C2#1913378911yescharacteristic
283C2#1913654211yescharacteristic
284C2#1913657411yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1360C2
socleC22×C43#447
prime radicalC2×D8×C43D4
hypercenter#1360D43
hypocenterC43#12391
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1360

Complements

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

NH ≅ G/Ntype
3. #19136748C2semidirect
4. #19134114C2semidirect
5. #19132576C2semidirect
6. #19132564C2semidirect
169. C43#12391semidirect

Maximal subgroups

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

subgroupindex
#191476772
#191368312
#191367482
#191341142
#191325762
#191325642
C43×#13602
#1239143