Finite Group Databasebeta

← #25010535

Subgroups — #25010535

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#19136744C211yesmaximal, characteristic, complemented
3#19134110C211yesmaximal, characteristic, complemented
4#19132638C211yesmaximal, characteristic
5#19132578C211yesmaximal, characteristic, complemented
6#19132566C211yesmaximal, characteristic, complemented
7C43×#2243C211yesmaximal, characteristic
8#14583618—21no—
9#14583290—21no—
10#14583118—21no—
11#14583112—21no—
12#14583107—21no—
13#14583106—21no—
14#14583029C2211yescharacteristic
15#14583000—21no—
16C4×Dic172C2211yescharacteristic
17#14582724—21no—
18C4⋊(C43⋊C16)C2211yescharacteristic
19#14582702—21no—
20#14582650C2211yescharacteristic
21#14582645—21no—
22C43×#500C2211yescharacteristic
23C43×#495C2211yescharacteristic
24C43×#358—21no—
25C43×#357—21no—
26C43×#346C2211yescharacteristic
27C2×Dic172D411yescharacteristic
28C2×#10621885—21no—
29C2×#10621885—41no—
30C2×#10621883—21no—
31#13063323—21no—
32#13063318—41no—
33#13063318—41no—
34#13063312—21no—
35#13063302—41no—
36Q8×Dic43—21no—
37C4×Dic86—21no—
38C4×Dic86D411yescharacteristic
39D4×Dic43—21no—
40#13063281—41no—
41C2×C43⋊C16—21no—
42#13063259D411yescharacteristic
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)D411yescharacteristic
45Dic43⋊C8—21no—
46#13063250—21no—
47#13063249—21no—
48#13063249—41no—
49#13063246—21no—
50#13063235—21no—
51C2×Q16×C43D411yescharacteristic
52C2×SD16×C43—21no—
53C2×D8×C43D411yescharacteristic
54C4⋊Q8×C43—21no—
55#124×C43—21no—
56C2×C16×C43—21no—
57#107×C43—21no—
58#107×C43—21no—
59C4×C8×C43C2311yescharacteristic
60C2×Q8×C43—21no—
61C2×Q8×C43—41no—
62C2×D4×C43—21no—
63C22×Dic43—41no—
64C2×Dic86—21no—
65C2×Dic86D811yescharacteristic
66Q16×C43—41no—
67SD16×C43—41no—
68SD16×C43—41no—
69D8×C43—41no—
70C2×C8×C43C2×D411yescharacteristic
71C2×C8×C43C2×D411yescharacteristic
72C4⋊C4×C43—41no—
73C4⋊C4×C43—41no—
74C22⋊C4×C43—41no—
75C22⋊C4×C43—41no—
76C42×C43C2×D411yescharacteristic
77C22⋊Dic43—41no—
78C22⋊Dic43—41no—
79C22⋊Dic43—41no—
80#10621885—81no—
81#10621885—82no—
82#10621883—81no—
83C4⋊Dic43—21no—
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—
94C2×C43⋊C8—41no—
95Dic172—21no—
96Dic172—21no—
97C16×C43—41no—
98C43⋊C16—41no—
99C23×C43—41no—
100Q8×C43—41no—
101Q8×C43—41no—
102Q8×C43—81no—
103Q8×C43—81no—
104D4×C43—41no—
105D4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—81no—
108C2×C4×C43#12011yescharacteristic
109C2×C4×C43C2×D811yescharacteristic
110C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
111C2×Dic43—21no—
112C2×Dic43—21no—
113C2×Dic43—41no—
114C2×Dic43—41no—
115C2×Dic43—82no—
116Dic86—41no—
117Dic86—41no—
118Dic86—41no—
119C8×C43—21no—
120C8×C43#13511yescharacteristic
121C8×C43#13711yescharacteristic
122C43⋊C8—41no—
123C43⋊C8—81no—
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—161no—
133C4×C43#45211yescharacteristic
134C4×C43#45511yescharacteristic
135Dic43—41no—
136Dic43—41no—
137Dic43—81no—
138Dic43—81no—
139#3402—431no—
140#2243D4311yescharacteristic
141#2227—431no—
142#1694—431no—
143#1360—431no—
144#1338—431no—
145#1334—431no—
146C2×C43—161no—
147C2×C43#164111yescharacteristic
148C2×C43#219011yescharacteristic
149C2×C43#219511yescharacteristic
150#556—861no—
151#500C2×D4311yescharacteristic
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⋊C16—431no—
163#358—21no—
164#358—861no—
165#357—21no—
166#346C2×D4311yescharacteristic
167#334—431no—
168#332—861no—
169C43#1239111yescharacteristic, complemented, Sylow
170C2×Q16—431no—
171C2×Q16—861no—
172C2×Q16—1721no—
173C2×Q16C22⋊D4311yescharacteristic
174C2×SD16—21no—
175C2×SD16—861no—
176C2×D8C22⋊D4311yescharacteristic
177C4⋊Q8—21no—
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—21no—
192#107—21no—
193#107—431no—
194C4⋊C8—431no—
195C4⋊C8—861no—
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—41no—
205C2×Q8—431no—
206C2×Q8—861no—
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—861no—
219C2×C8—1721no—
220C2×C8D4×D4311yescharacteristic
221C2×C8C2×C22⋊D4311yescharacteristic
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—431no—
225C4⋊C4—861no—
226C4⋊C4—861no—
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—81no—
246Q8—81no—
247Q8—1721no—
248Q8—1721no—
249Q8—1721no—
250D4—41no—
251D4—41no—
252C2×C4—41no—
253C2×C4—81no—
254C2×C4—861no—
255C2×C4—861no—
256C2×C4—3442no—
257C2×C4—1721no—
258C2×C4—1721no—
259C2×C4#1306329311yescharacteristic
260C2×C4D8×D4311yescharacteristic
261C2×C4#1306334911yescharacteristic
262C8—21no—
263C8—3441no—
264C8—1721no—
265C8#1306334611yescharacteristic
266C8#1306335411yescharacteristic
267C22—81no—
268C22—81no—
269C22—81no—
270C22#1458303111yescharacteristic
271C4—21no—
272C4—21no—
273C4—81no—
274C4—161no—
275C4—3441no—
276C4—3441no—
277C4—1721no—
278C4—1721no—
279C4#1458305811yescharacteristic
280C4#1458307611yescharacteristic
281C2—161no—
282C2#1913378511yescharacteristic
283C2#1913653911yescharacteristic
284C2#1913657011yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2243C2
socleC22×C43#447
prime radicalC2×D8×C43D4
hypercenter#2243D43
hypocenterC43#12391
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2243

Complements

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

NH ≅ G/Ntype
2. #19136744C2semidirect
3. #19134110C2semidirect
5. #19132578C2semidirect
6. #19132566C2semidirect
169. C43#12391semidirect

Maximal subgroups

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

subgroupindex
#191476772
#191367442
#191341102
#191326382
#191325782
#191325662
C43×#22432
#1239143