Finite Group Databasebeta

← #19135652

Subgroups — #19135652

Order 5504.

348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C2×#13063355C211yesmaximal, characteristic, complemented
2#14583470C211yesmaximal, characteristic, complemented
3#14582916C211yesmaximal, characteristic, complemented
4#14582909C211yesmaximal, characteristic, complemented
5#14582873C211yesmaximal, characteristic, complemented
6#14582670C211yesmaximal, characteristic, complemented
7C43×#575C211yesmaximal, characteristic
8C22×Dic86C2211yescharacteristic
9#13063355—22no—
10#13063355—22no—
11C2×#10621885—21no—
12C2×#10621883—21no—
13C2×#10621877C2211yescharacteristic
14#13063323—21no—
15#13063312—21no—
16#13063306—22no—
17#13063304—22no—
18#13063284C2211yescharacteristic
19#13063284C2211yescharacteristic
20#13063252—22no—
21#13063250—22no—
22#13063240—22no—
23C2×#41×C43C2211yescharacteristic
24C2×#41×C43C2211yescharacteristic
25#137×C43—21no—
26#137×C43—21no—
27AGL(1,ℤ/8)×C43—21no—
28AGL(1,ℤ/8)×C43—21no—
29#135×C43—22no—
30C2×M16×C43C2211yescharacteristic
31#41×C43—21no—
32#41×C43—21no—
33#41×C43—21no—
34#41×C43—21no—
35#41×C43—21no—
36#41×C43—21no—
37#41×C43—21no—
38#41×C43—21no—
39C2×Q8×C43D411yescharacteristic
40C2×Q8×C43D411yescharacteristic
41C2×D4×C43—21no—
42C2×D4×C43—21no—
43C2×D4×C43D411yescharacteristic
44C2×D4×C43D411yescharacteristic
45C22×C4×C43—21no—
46C22×C4×C43—21no—
47C22×C4×C43C2311yescharacteristic
48C22×Dic43—21no—
49C2×Dic86—21no—
50C2×Dic86—21no—
51C2×Dic86—21no—
52C2×Dic86—21no—
53C2×Dic86—21no—
54C2×Dic86D412yes—
55Q16×C43—22no—
56SD16×C43—22no—
57SD16×C43—22no—
58D8×C43—22no—
59M16×C43—21no—
60M16×C43—21no—
61C2×C8×C43D412yes—
62C22⋊Dic43—24no—
63C22⋊Dic43—21no—
64C22⋊Dic43D412yes—
65#10621885—24no—
66#10621883—24no—
67C4⋊Dic43—21no—
68C4⋊Dic43—21no—
69Dic43⋊C4—24no—
70C4×Dic43—21no—
71C4×Dic43—21no—
72#10621877—21no—
73#10621877D412yes—
74C2×C43⋊C8—21no—
75C23×C43—21no—
76C23×C43—21no—
77C23×C43C2×D411yescharacteristic
78Q8×C43—21no—
79Q8×C43—21no—
80Q8×C43—21no—
81Q8×C43—21no—
82D4×C43—21no—
83D4×C43—21no—
84D4×C43—21no—
85D4×C43—21no—
86D4×C43—41no—
87D4×C43—41no—
88D4×C43—41no—
89D4×C43—41no—
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43—41no—
96C2×C4×C43C2×D411yescharacteristic
97C2×C4×C43C2×D411yescharacteristic
98C2×C4×C43C2×D411yescharacteristic
99C2×C4×C43C2×D411yescharacteristic
100C2×C4×C43C2×D411yescharacteristic
101C2×C4×C43#4111yescharacteristic
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—41no—
105C2×Dic43—41no—
106C2×Dic43—41no—
107Dic86—22no—
108Dic86—22no—
109Dic86—41no—
110Dic86—41no—
111C8×C43—22no—
112C43⋊C8—22no—
113C22×C43—41no—
114C22×C43—42no—
115C22×C43—41no—
116C22×C43—41no—
117C22×C43—81no—
118C22×C43#12011yescharacteristic
119C22×C43#12111yescharacteristic
120C22×C43#12711yescharacteristic
121C4×C43—41no—
122C4×C43—41no—
123C4×C43#12011yescharacteristic
124C4×C43#12011yescharacteristic
125C4×C43#12111yescharacteristic
126C4×C43#12111yescharacteristic
127Dic43—42no—
128Dic43—42no—
129Dic43—81no—
130#2009—431nomaximal, Sylow
131C2×C43—21no—
132C2×C43—21no—
133C2×C43—21no—
134C2×C43—81no—
135C2×C43—81no—
136C2×C43#39211yescharacteristic
137#575D4311yescharacteristic
138C2×#137—431no—
139#536—431no—
140#421—431no—
141#419—431no—
142#410—431no—
143#344—431no—
144C43#200911yescharacteristic, complemented, Sylow
145C2×#41C2×D4311yescharacteristic
146C2×#41C2×D4311yescharacteristic
147C22×Q8—431no—
148#137—21no—
149#137—21no—
150#137—862no—
151#137—862no—
152AGL(1,ℤ/8)—21no—
153AGL(1,ℤ/8)—21no—
154#135—22no—
155C2×Q16—861no—
156C2×SD16—861no—
157C2×M16—431no—
158C2×M16C2×D4311yescharacteristic
159C4⋊Q8—861no—
160#124—861no—
161#123—862no—
162C22⋊Q8—862no—
163#117—431no—
164#117—431no—
165#104—862no—
166#103—862no—
167#99—862no—
168#41—21no—
169#41—21no—
170#41—21no—
171#41—21no—
172#41—21no—
173#41—21no—
174#41—21no—
175#41—21no—
176C2×Q8—432no—
177C2×Q8—861no—
178C2×Q8—861no—
179C2×Q8—861no—
180C2×Q8—861no—
181C2×Q8—861no—
182C2×Q8C22⋊D4311yescharacteristic
183C2×Q8C22⋊D4311yescharacteristic
184C2×D4—21no—
185C2×D4—21no—
186C2×D4C22⋊D4311yescharacteristic
187C2×D4C22⋊D4311yescharacteristic
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—861no—
191C22×C4C22×D4311yescharacteristic
192Q16—22no—
193Q16—864no—
194SD16—22no—
195SD16—22no—
196SD16—864no—
197D8—22no—
198M16—21no—
199M16—21no—
200M16—432no—
201M16—861no—
202C2×C8—861no—
203C2×C8C22⋊D4312yes—
204C4⋊C4—864no—
205C4⋊C4—861no—
206C4⋊C4—861no—
207C22⋊C4—432no—
208C22⋊C4—864no—
209C22⋊C4—861no—
210C42—861no—
211C42—861no—
212C23—21no—
213C23—21no—
214C23D4×D4311yescharacteristic
215Q8—21no—
216Q8—21no—
217Q8—21no—
218Q8—21no—
219Q8—862no—
220Q8—862no—
221Q8—1721no—
222Q8—1721no—
223D4—21no—
224D4—21no—
225D4—21no—
226D4—21no—
227D4—41no—
228D4—41no—
229D4—41no—
230D4—41no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—862no—
238C2×C4—862no—
239C2×C4—1721no—
240C2×C4—1721no—
241C2×C4—1721no—
242C2×C4D4×D4311yescharacteristic
243C2×C4D4×D4311yescharacteristic
244C2×C4#1062190011yescharacteristic
245C2×C4C2×C22⋊D4311yescharacteristic
246C2×C4C2×C22⋊D4311yescharacteristic
247C2×C4C2×C22⋊D4311yescharacteristic
248C8—22no—
249C8—862no—
250C22—41no—
251C22—42no—
252C22—41no—
253C22—41no—
254C22—81no—
255C22#1306329311yescharacteristic
256C22#1306329711yescharacteristic
257C22#1306332111yescharacteristic
258C4—41no—
259C4—41no—
260C4—3441no—
261C4—1722no—
262C4—1722no—
263C4#1306329311yescharacteristic
264C4#1306329411yescharacteristic
265C4#1306329611yescharacteristic
266C4#1306329711yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—81no—
271C2—81no—
272C2#1458280711yescharacteristic
subgroupG/H
centerC2#14582807
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#575C2
socleC2×C43#392
hypercenter#575D43
hypocenterC43#2009
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C2×#13063355C2semidirect
2. #14583470C2semidirect
3. #14582916C2semidirect
4. #14582909C2semidirect
5. #14582873C2semidirect
6. #14582670C2semidirect
144. C43#2009semidirect