Finite Group Databasebeta

← #19135601

Subgroups — #19135601

Order 5504.

444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×#10621873C211yesmaximal, characteristic, complemented
2C2×#13063305C211yesmaximal, characteristic, complemented
3C2×#13063300C211yesmaximal, characteristic
4C2×#13063248C211yesmaximal, characteristic, complemented
5C2×#13063245C211yesmaximal, characteristic, complemented
6C2×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
7C43×#340C211yesmaximal, characteristic, complemented
8C22×Dic86C2211yescharacteristic
9C22×D172—21no—
10C22×D172C2211yescharacteristic
11C22×C4×D43C2211yescharacteristic
12C2×#10621873—22no—
13C2×#10621873—22no—
14C2×#10621873—22no—
15C22×C43⋊C8C2211yescharacteristic
16#13063305—22no—
17#13063305—22no—
18#13063300—22no—
19#13063300—22no—
20C2×C4⋊Dic43—21no—
21C2×(C2×D43)⋊C4—21no—
22C2×(C2×D43)⋊C4—21no—
23#13063248—22no—
24#13063245—22no—
25(C2×D43)⋊C8—22no—
26C22×C8×C43C2211yescharacteristic
27C2×C4⋊C4×C43C2211yescharacteristic
28C2×C4⋊C4×C43C2211yescharacteristic
29C23×D43—21no—
30C23×D43D411yescharacteristic
31C22×C4×C43—21no—
32C22×C4×C43—21no—
33C22×C4×C43C2311yescharacteristic
34C22×Dic43—21no—
35C22×Dic43D411yescharacteristic
36C2×D172—24no—
37C2×D172—21no—
38C2×D172—21no—
39C2×D172—21no—
40C2×D172—21no—
41C2×D172—21no—
42C2×D172—42no—
43C2×D172—42no—
44C2×D172D412yes—
45C2×C4×D43—21no—
46C2×C4×D43—21no—
47C2×C4×D43—21no—
48C2×C4×D43—21no—
49C2×C4×D43—21no—
50C2×C4×D43—21no—
51C2×Dic86—21no—
52C2×Dic86—21no—
53C2×Dic86—21no—
54C2×Dic86—21no—
55C2×Dic86—21no—
56C2×Dic86D412yescomplemented
57C2×C8×C43—21no—
58C2×C8×C43—21no—
59C2×C8×C43D412yescomplemented
60C4⋊C4×C43—21no—
61C4⋊C4×C43—21no—
62C4⋊C4×C43D412yes—
63C4⋊C4×C43D412yescomplemented
64(C2×D43)⋊C4—24no—
65(C2×D43)⋊C4—24no—
66C4⋊Dic43—24no—
67C2×C43⋊C8—21no—
68C2×C43⋊C8—21no—
69C2×C43⋊C8—21no—
70#10621873—28no—
71C23×C43C2×D411yescharacteristic
72C22×D43—21no—
73C22×D43—21no—
74C22×D43—21no—
75C22×D43—21no—
76C22×D43—21no—
77C22×D43—21no—
78C22×D43—22no—
79C22×D43—41no—
80C22×D43—41no—
81C22×D43—41no—
82C22×D43—41no—
83C22×D43—41no—
84C22×D43—41no—
85C22×D43SD1612yescomplemented
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—41no—
89C2×C4×C43—41no—
90C2×C4×C43—41no—
91C2×C4×C43—41no—
92C2×C4×C43C2×D411yescharacteristic
93C2×C4×C43C2×D411yescharacteristic
94C2×C4×C43C2×D411yescharacteristic
95C2×C4×C43C2×D411yescharacteristic
96C2×C4×C43C2×D411yescharacteristic
97C2×C4×C43#4111yescharacteristic
98C2×Dic43—21no—
99C2×Dic43—22no—
100C2×Dic43—21no—
101C2×Dic43—21no—
102C2×Dic43—41no—
103C2×Dic43—41no—
104D172—22no—
105D172—22no—
106D172—48no—
107D172—41no—
108D172—41no—
109C4×D43—41no—
110C4×D43—41no—
111C4×D43—41no—
112C4×D43—41no—
113Dic86—22no—
114Dic86—22no—
115Dic86—41no—
116Dic86—41no—
117C8×C43—22no—
118C43⋊C8—41no—
119C22×C43#12011yescharacteristic
120C22×C43#12011yescharacteristic
121C22×C43#12111yescharacteristic
122C22×C43C2×SD1611yescharacteristic
123C22×C43#13511yescharacteristic
124C22×C43AGL(1,ℤ/8)11yescharacteristic
125C22×C43#13711yescharacteristic
126C2×D43—22no—
127C2×D43—22no—
128C2×D43—22no—
129C2×D43—41no—
130C2×D43—41no—
131C2×D43—41no—
132C2×D43—41no—
133C2×D43—42no—
134C2×D43—42no—
135C2×D43—42no—
136C2×D43—81no—
137C2×D43—81no—
138C2×D43—81no—
139C2×D43—81no—
140C4×C43—42no—
141C4×C43—42no—
142C4×C43#12011yescharacteristic
143C4×C43#12111yescharacteristic
144C4×C43#12111yescharacteristic
145C4×C43#12711yescharacteristic
146Dic43—42no—
147Dic43—41no—
148#2000—431nomaximal, Sylow
149C2×C43#39211yescharacteristic
150C2×C43#44811yescharacteristic
151C2×C43#44911yescharacteristic
152C2×C43#45011yescharacteristic
153C2×C43#45211yescharacteristic
154C2×C43#46511yescharacteristic
155C2×C43#46811yescharacteristic
156D43—42no—
157D43—82no—
158C22×SD16—431no—
159C2×C22⋊Q8—431no—
160C2×#121—431no—
161C2×#103—431no—
162C2×#102—431no—
163C2×C22⋊C8—431no—
164#340D4311yescharacteristic, complemented
165C43#200011yescharacteristic, complemented, Sylow
166C22×Q8—431no—
167C22×D4—431no—
168C22×D4—861no—
169C23×C4—431no—
170C2×SD16—862no—
171C2×SD16—862no—
172C2×SD16—862no—
173C22×C8—431no—
174C22×C8C2×D4311yescharacteristic
175C22⋊Q8—862no—
176C22⋊Q8—862no—
177#121—862no—
178#121—862no—
179C2×C4⋊C4—861no—
180C2×C4⋊C4C2×D4311yescharacteristic
181C2×C4⋊C4C2×D4311yescharacteristic
182C2×C22⋊C4—861no—
183C2×C22⋊C4—861no—
184#103—862no—
185#102—862no—
186C22⋊C8—862no—
187C24—431no—
188C24—861no—
189C2×Q8—432no—
190C2×Q8—861no—
191C2×Q8—861no—
192C2×Q8—861no—
193C2×Q8—861no—
194C2×Q8—861no—
195C2×D4—432no—
196C2×D4—864no—
197C2×D4—861no—
198C2×D4—861no—
199C2×D4—861no—
200C2×D4—861no—
201C2×D4—861no—
202C2×D4—1722no—
203C2×D4—1722no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—431no—
207C22×C4—861no—
208C22×C4—861no—
209C22×C4—861no—
210C22×C4—861no—
211C22×C4—861no—
212C22×C4—861no—
213C22×C4—861no—
214C22×C4C22×D4311yescharacteristic
215SD16—868no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—861no—
219C2×C8—861no—
220C2×C8—861no—
221C2×C8D17212yescomplemented
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—864no—
225C4⋊C4D17212yes—
226C4⋊C4D17212yescomplemented
227C22⋊C4—864no—
228C22⋊C4—864no—
229C23—432no—
230C23—861no—
231C23—861no—
232C23—861no—
233C23—861no—
234C23—861no—
235C23—861no—
236C23—862no—
237C23—1721no—
238C23—1721no—
239C23—1721no—
240C23—1721no—
241C23—1721no—
242C23—1721no—
243C23D4×D4311yescharacteristic
244Q8—862no—
245Q8—862no—
246Q8—1721no—
247Q8—1721no—
248D4—862no—
249D4—862no—
250D4—1728no—
251D4—1721no—
252D4—1721no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—861no—
260C2×C4—862no—
261C2×C4—861no—
262C2×C4—861no—
263C2×C4—1721no—
264C2×C4—1721no—
265C2×C4—1721no—
266C2×C4—1721no—
267C2×C4—1721no—
268C2×C4—1721no—
269C2×C4C2×D17211yescharacteristic
270C2×C4C2×D17211yescharacteristic
271C2×C4C2×D17211yescharacteristic
272C2×C4D4×D4311yescharacteristic
273C2×C4D4×D4311yescharacteristic
274C2×C4#1062190211yescharacteristic
275C8—22no—
276C8—1721no—
277C22—862no—
278C22—862no—
279C22—862no—
280C22—3441no—
281C22—3441no—
282C22—3441no—
283C22—3441no—
284C22—1722no—
285C22—1722no—
286C22—1722no—
287C22—1721no—
288C22—1721no—
289C22—1721no—
290C22—1721no—
291C22#1306329511yescharacteristic
292C22#1306329511yescharacteristic
293C22#1306330011yescharacteristic
294C22SD16×D4311yescharacteristic
295C22#1306334611yescharacteristic
296C22#1306334911yescharacteristic
297C22#1306335711yescharacteristic
298C4—42no—
299C4—42no—
300C4—1721no—
301C4—1722no—
302C4#1306329511yescharacteristic
303C4#1306330011yescharacteristic
304C4#1306330011yescharacteristic
305C4#1306332211yescharacteristic
306C2—3442no—
307C2—1722no—
308C2#1458280911yescharacteristic
309C2#1458303911yescharacteristic
310C2#1458304511yescharacteristic
311C2#1458305111yescharacteristic
312C2#1458306411yescharacteristic
313C2#1458312911yescharacteristic
314C2#1458314611yescharacteristic
subgroupG/H
centerC23D4×D43
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#340C2
socleC23×C43C2×D4
hypercenter#340D43
hypocenterC43#2000
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
1. C22×#10621873C2semidirect
2. C2×#13063305C2semidirect
4. C2×#13063248C2semidirect
5. C2×#13063245C2semidirect
6. C2×(C2×D43)⋊C8C2semidirect
7. C43×#340C2semidirect
56. C2×Dic86D4semidirect
59. C2×C8×C43D4semidirect
63. C4⋊C4×C43D4semidirect
85. C22×D43SD16semidirect
164. #340D43semidirect
165. C43#2000semidirect
221. C2×C8D172semidirect
226. C4⋊C4D172semidirect