Finite Group Databasebeta

← #19135655

Subgroups — #19135655

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
1#14583697C211yesmaximal, characteristic
2C2×#13063356C211yesmaximal, characteristic, complemented
3#14582916C211yesmaximal, characteristic, complemented
4#14582908C211yesmaximal, characteristic, complemented
5#14582872C211yesmaximal, characteristic, complemented
6#14582669C211yesmaximal, characteristic, complemented
7C43×#536C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9#13063356—22no—
10#13063356—21no—
11#13063356—22no—
12#13063355—21no—
13#13063351—21no—
14#13063350—21no—
15#13063345—22no—
16C2×#10621885—21no—
17C2×#10621884—21no—
18C2×#10621877C2211yescharacteristic
19C2×#10621877C2211yescharacteristic
20#13063284C2211yescharacteristic
21#13063252—22no—
22#13063249—22no—
23#13063239—22no—
24C2×#41×C43C2211yescharacteristic
25C22×Q8×C43C2211yescharacteristic
26C4⋊Q8×C43—21no—
27#124×C43—21no—
28#123×C43—22no—
29C22⋊Q8×C43—22no—
30#117×C43C2211yescharacteristic
31#41×C43—21no—
32#41×C43—21no—
33#41×C43—21no—
34#41×C43—21no—
35C2×Q8×C43—21no—
36C2×Q8×C43—21no—
37C2×Q8×C43—21no—
38C2×Q8×C43—21no—
39C2×Q8×C43—21no—
40C2×Q8×C43D412yes—
41C2×Q8×C43D411yescharacteristic
42C2×D4×C43—21no—
43C2×D4×C43D411yescharacteristic
44C22×C4×C43—21no—
45C22×C4×C43—21no—
46C22×C4×C43C2311yescharacteristic
47C2×C22⋊D43—21no—
48#10621898—21no—
49#10621898—21no—
50#10621898—21no—
51#10621898—21no—
52C2×D172D411yescharacteristic
53C2×C4×D43—21no—
54C2×Dic86D411yescharacteristic
55C4⋊C4×C43—24no—
56C4⋊C4×C43—21no—
57C22⋊C4×C43—24no—
58C22⋊C4×C43D412yes—
59C42×C43—21no—
60C22⋊Dic43—21no—
61#10621885—24no—
62#10621885—22no—
63#10621884—24no—
64#10621884—22no—
65#10621883—22no—
66#10621882—22no—
67C4⋊Dic43—21no—
68C4×Dic43—21no—
69#10621877—21no—
70#10621877—21no—
71#10621877—21no—
72#10621877D412yes—
73C2×C43⋊C8—21no—
74C2×C43⋊C8D412yes—
75C23×C43—21no—
76C23×C43C2×D411yescharacteristic
77C22×D43—21no—
78Q8×C43—22no—
79Q8×C43—21no—
80Q8×C43—22no—
81Q8×C43—21no—
82Q8×C43—41no—
83Q8×C43—41no—
84D4×C43—21no—
85D4×C43—21no—
86D4×C43—41no—
87D4×C43—41no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—21no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43C2×D411yescharacteristic
96C2×C4×C43C2×D411yescharacteristic
97C2×C4×C43C2×D411yescharacteristic
98C2×C4×C43C2×D411yescharacteristic
99C2×C4×C43C2×D411yescharacteristic
100C2×C4×C43#4111yescharacteristic
101C22⋊D43—41no—
102C22⋊D43—41no—
103C2×Dic43—21no—
104C2×Dic43—41no—
105D172—21no—
106D172—21no—
107C4×D43—41no—
108C4×D43—41no—
109Dic86—21no—
110Dic86—21no—
111C43⋊C8—22no—
112C43⋊C8—22no—
113C22×C43—41no—
114C22×C43—42no—
115C22×C43—41no—
116C22×C43#12011yescharacteristic
117C22×C43#12111yescharacteristic
118C22×C43#12711yescharacteristic
119C2×D43—41no—
120C2×D43—81no—
121C4×C43—42no—
122C4×C43—41no—
123C4×C43—42no—
124C4×C43#12011yescharacteristic
125C4×C43#12011yescharacteristic
126C4×C43#12111yescharacteristic
127C4×C43#12111yescharacteristic
128Dic43—41no—
129Dic43—81no—
130#2009—431nomaximal, Sylow
131C2×C43—21no—
132C2×C43—21no—
133C2×C43—21no—
134C2×C43—81no—
135C2×C43#39211yescharacteristic
136D43—81no—
137#575—431no—
138C2×#137—431no—
139#536D4311yescharacteristic, complemented
140#421—431no—
141#419—431no—
142#410—431no—
143#344—431no—
144C43#200911yescharacteristic, complemented, Sylow
145C2×#41—431no—
146C2×#41C2×D4311yescharacteristic
147C22×Q8C2×D4311yescharacteristic
148#137—862no—
149#137—861no—
150#137—862no—
151#137—861no—
152AGL(1,ℤ/8)—861no—
153AGL(1,ℤ/8)—861no—
154#135—862no—
155C2×Q16—861no—
156C2×SD16—861no—
157C2×M16—431no—
158C2×M16—431no—
159C4⋊Q8—21no—
160#124—21no—
161#123—22no—
162C22⋊Q8—22no—
163#117—431no—
164#117C2×D4311yescharacteristic
165#104—862no—
166#103—862no—
167#99—862no—
168#41—21no—
169#41—21no—
170#41—21no—
171#41—21no—
172#41—861no—
173#41—861no—
174#41—861no—
175#41—861no—
176C2×Q8—21no—
177C2×Q8—21no—
178C2×Q8—21no—
179C2×Q8—21no—
180C2×Q8—21no—
181C2×Q8—431no—
182C2×Q8C22⋊D4312yes—
183C2×Q8C22⋊D4311yescharacteristic
184C2×D4—21no—
185C2×D4—431no—
186C2×D4—861no—
187C2×D4C22⋊D4311yescharacteristic
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—861no—
191C22×C4C22×D4311yescharacteristic
192Q16—864no—
193Q16—862no—
194SD16—862no—
195SD16—864no—
196SD16—862no—
197D8—862no—
198M16—432no—
199M16—861no—
200M16—861no—
201M16—861no—
202C2×C8—432no—
203C2×C8—861no—
204C4⋊C4—24no—
205C4⋊C4—21no—
206C4⋊C4—861no—
207C22⋊C4—24no—
208C22⋊C4—861no—
209C22⋊C4C22⋊D4312yes—
210C42—21no—
211C42—861no—
212C23—21no—
213C23—861no—
214C23C2×C22⋊D4311yescharacteristic
215Q8—22no—
216Q8—21no—
217Q8—22no—
218Q8—21no—
219Q8—41no—
220Q8—41no—
221Q8—861no—
222Q8—861no—
223D4—21no—
224D4—21no—
225D4—41no—
226D4—41no—
227D4—861no—
228D4—861no—
229D4—1721no—
230D4—1721no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—861no—
239C2×C4—1721no—
240C2×C4—1721no—
241C2×C4—1721no—
242C2×C4D4×D4311yescharacteristic
243C2×C4D4×D4311yescharacteristic
244C2×C4D4×D4311yescharacteristic
245C2×C4#1062190011yescharacteristic
246C2×C4C2×C22⋊D4311yescharacteristic
247C2×C4C2×C22⋊D4311yescharacteristic
248C8—862no—
249C8—862no—
250C22—41no—
251C22—42no—
252C22—41no—
253C22—3441no—
254C22—1721no—
255C22#1306329411yescharacteristic
256C22#1306329611yescharacteristic
257C22#1306332111yescharacteristic
258C4—42no—
259C4—41no—
260C4—42no—
261C4—3441no—
262C4—1721no—
263C4#1306329311yescharacteristic
264C4#1306329311yescharacteristic
265C4#1306329711yescharacteristic
266C4#1306329711yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—81no—
271C2—3441no—
272C2#1458280711yescharacteristic
subgroupG/H
centerC2#14582807
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#536C2
socleC2×C43#392
hypercenter#536D43
hypocenterC43#2009
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C2×#13063356C2semidirect
3. #14582916C2semidirect
4. #14582908C2semidirect
5. #14582872C2semidirect
6. #14582669C2semidirect
7. C43×#536C2semidirect
139. #536D43semidirect
144. C43#2009semidirect