Finite Group Databasebeta

← #19135657

Subgroups — #19135657

Order 5504.

348 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 69 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#14583699C211yesmaximal, characteristic
2C2×#13063356C211yesmaximal, characteristic, complemented
3#14583473C211yesmaximal, characteristic, complemented
4#14582917C211yesmaximal, characteristic, complemented
5#14582872C211yesmaximal, characteristic, complemented
6#14582670C211yesmaximal, characteristic, complemented
7C43×#419C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C2×#10621898C2211yescharacteristic
10#13063358—21no—
11#13063358—21no—
12#13063356—22no—
13#13063356—22no—
14#13063353—21no—
15#13063353—21no—
16#13063347—22no—
17C2×#10621885—21no—
18C2×#10621884—21no—
19C2×#10621877C2211yescharacteristic
20#13063323—21no—
21#13063314—21no—
22#13063308—22no—
23#13063301—22no—
24#13063284C2211yescharacteristic
25#13063253—22no—
26#13063239—22no—
27C22×Q8×C43C2211yescharacteristic
28C2×M16×C43C2211yescharacteristic
29#117×C43C2211yescharacteristic
30#103×C43—22no—
31C2×Q8×C43—21no—
32C2×Q8×C43—21no—
33C2×Q8×C43—21no—
34C2×Q8×C43—21no—
35C2×Q8×C43—21no—
36C2×Q8×C43D412yes—
37C22×C4×C43—21no—
38C22×C4×C43C2311yescharacteristic
39C2×C22⋊D43—21no—
40C2×C22⋊D43—21no—
41#10621898—21no—
42#10621898—21no—
43#10621898—21no—
44#10621898—21no—
45#10621898—21no—
46#10621898—21no—
47#10621898—21no—
48#10621898—21no—
49C2×D172D411yescharacteristic
50C2×D172D411yescharacteristic
51C2×C4×D43—21no—
52C2×C4×D43—21no—
53C2×Dic86D411yescharacteristic
54C2×Dic86D411yescharacteristic
55M16×C43—21no—
56M16×C43—21no—
57C2×C8×C43D412yes—
58C4⋊C4×C43—21no—
59C22⋊C4×C43—21no—
60C42×C43—21no—
61C22⋊Dic43D412yes—
62#10621885—24no—
63#10621884—24no—
64(C2×D43)⋊C4—24no—
65C4⋊Dic43—21no—
66Dic43⋊C4—24no—
67C4×Dic43—21no—
68#10621877—21no—
69#10621877D412yes—
70C2×C43⋊C8—21no—
71Dic172—22no—
72D344—22no—
73#10621873—22no—
74#10621873—22no—
75C23×C43C2×D411yescharacteristic
76C22×D43—21no—
77C22×D43—21no—
78Q8×C43—22no—
79Q8×C43—22no—
80Q8×C43—41no—
81Q8×C43—41no—
82C2×C4×C43—22no—
83C2×C4×C43—41no—
84C2×C4×C43—41no—
85C2×C4×C43—41no—
86C2×C4×C43C2×D411yescharacteristic
87C2×C4×C43C2×D411yescharacteristic
88C2×C4×C43C2×D411yescharacteristic
89C2×C4×C43C2×D411yescharacteristic
90C2×C4×C43C2×D411yescharacteristic
91C2×C4×C43#4111yescharacteristic
92C22⋊D43—41no—
93C22⋊D43—41no—
94C22⋊D43—41no—
95C22⋊D43—41no—
96C2×Dic43—22no—
97C2×Dic43—21no—
98C2×Dic43—21no—
99D172—21no—
100D172—21no—
101D172—21no—
102D172—21no—
103C4×D43—41no—
104C4×D43—41no—
105C4×D43—41no—
106C4×D43—41no—
107Dic86—21no—
108Dic86—21no—
109Dic86—21no—
110Dic86—21no—
111C8×C43—22no—
112C43⋊C8—22no—
113C22×C43—41no—
114C22×C43#12011yescharacteristic
115C22×C43#12111yescharacteristic
116C22×C43#12711yescharacteristic
117C2×D43—42no—
118C2×D43—41no—
119C2×D43—41no—
120C2×D43—81no—
121C4×C43—42no—
122C4×C43—81no—
123C4×C43#12011yescharacteristic
124C4×C43#12011yescharacteristic
125C4×C43#12111yescharacteristic
126C4×C43#12111yescharacteristic
127Dic43—42no—
128Dic43—41no—
129Dic43—41no—
130#2009—431nomaximal, Sylow
131C2×C43—21no—
132C2×C43—21no—
133C2×C43—21no—
134C2×C43#39211yescharacteristic
135D43—81no—
136D43—81no—
137#575—431no—
138C2×#137—431no—
139#536—431no—
140#421—431no—
141#419D4311yescharacteristic, complemented
142#410—431no—
143#344—431no—
144C43#200911yescharacteristic, complemented, Sylow
145C2×#41—431no—
146C2×#41—431no—
147C22×Q8C2×D4311yescharacteristic
148#137—861no—
149#137—861no—
150#137—862no—
151#137—862no—
152AGL(1,ℤ/8)—861no—
153AGL(1,ℤ/8)—861no—
154#135—862no—
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#117C2×D4311yescharacteristic
165#104—862no—
166#103—22no—
167#99—862no—
168#41—861no—
169#41—861no—
170#41—861no—
171#41—861no—
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×Q8—431no—
183C2×Q8D17212yes—
184C2×D4—431no—
185C2×D4—431no—
186C2×D4—861no—
187C2×D4—861no—
188C22×C4—21no—
189C22×C4—861no—
190C22×C4—861no—
191C22×C4C22×D4311yescharacteristic
192Q16—862no—
193Q16—864no—
194SD16—862no—
195SD16—862no—
196SD16—864no—
197D8—862no—
198M16—21no—
199M16—21no—
200M16—432no—
201M16—861no—
202C2×C8—861no—
203C2×C8C22⋊D4312yes—
204C4⋊C4—21no—
205C4⋊C4—864no—
206C4⋊C4—861no—
207C22⋊C4—21no—
208C22⋊C4—432no—
209C22⋊C4—864no—
210C42—21no—
211C42—861no—
212C23—861no—
213C23—861no—
214C23D4×D4311yescharacteristic
215Q8—22no—
216Q8—22no—
217Q8—41no—
218Q8—41no—
219Q8—861no—
220Q8—861no—
221Q8—861no—
222Q8—861no—
223D4—861no—
224D4—861no—
225D4—861no—
226D4—861no—
227D4—1721no—
228D4—1721no—
229D4—1721no—
230D4—1721no—
231C2×C4—22no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—862no—
236C2×C4—861no—
237C2×C4—861no—
238C2×C4—1721no—
239C2×C4—1721no—
240C2×C4—1721no—
241C2×C4—1721no—
242C2×C4C2×D17211yescharacteristic
243C2×C4#1062189811yescharacteristic
244C2×C4D4×D4311yescharacteristic
245C2×C4D4×D4311yescharacteristic
246C2×C4D4×D4311yescharacteristic
247C2×C4C2×C22⋊D4311yescharacteristic
248C8—22no—
249C8—862no—
250C22—41no—
251C22—3441no—
252C22—1722no—
253C22—1721no—
254C22—1721no—
255C22#1306329511yescharacteristic
256C22#1306329811yescharacteristic
257C22#1306332111yescharacteristic
258C4—42no—
259C4—81no—
260C4—1722no—
261C4—1721no—
262C4—1721no—
263C4#1306329311yescharacteristic
264C4#1306329511yescharacteristic
265C4#1306329811yescharacteristic
266C4#1306329911yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—3441no—
271C2—3441no—
272C2#1458280811yescharacteristic
subgroupG/H
centerC2#14582808
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#419C2
socleC2×C43#392
hypercenter#419D43
hypocenterC43#2009
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. C2×#13063356C2semidirect
3. #14583473C2semidirect
4. #14582917C2semidirect
5. #14582872C2semidirect
6. #14582670C2semidirect
7. C43×#419C2semidirect
141. #419D43semidirect
144. C43#2009semidirect