Finite Group Databasebeta

← #19135660

Subgroups — #19135660

Order 5504.

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

normal subgroups only

This group has 394 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, complemented
2#14583410C211yesmaximal, characteristic, complemented
3#14582917C211yesmaximal, characteristic, complemented
4#14582916C211yesmaximal, characteristic, complemented
5#14582863C211yesmaximal, characteristic, complemented
6#14582655C211yesmaximal, characteristic, complemented
7C43×#525C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9#13063356—21no—
10#13063355—21no—
11#13063351—21no—
12#13063350—21no—
13#13063345—22no—
14C2×#10621877C2211yescharacteristic
15C2×#10621877C2211yescharacteristic
16#13063308—21no—
17#13063304—21no—
18#13063299—21no—
19#13063294—21no—
20C4×C22⋊D43—22no—
21#13063284C2211yescharacteristic
22#13063253—22no—
23#13063252—22no—
24C22⋊(C43⋊C8)—22no—
25C2×#41×C43C2211yescharacteristic
26C23×C4×C43C2211yescharacteristic
27#123×C43—21no—
28C22⋊Q8×C43—21no—
29#121×C43—21no—
30#120×C43—21no—
31C4×D4×C43—22no—
32#117×C43C2211yescharacteristic
33C24×C43D411yescharacteristic
34#41×C43—21no—
35#41×C43—21no—
36#41×C43—21no—
37#41×C43—21no—
38C2×Q8×C43D411yescharacteristic, complemented
39C2×D4×C43—22no—
40C2×D4×C43—21no—
41C2×D4×C43D411yescharacteristic, complemented
42C22×C4×C43—21no—
43C22×C4×C43—21no—
44C22×C4×C43—21no—
45C22×C4×C43—21no—
46C22×C4×C43—21no—
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43D411yescharacteristic
50C22×C4×C43C2311yescharacteristic
51C2×C22⋊D43—22no—
52C2×C22⋊D43—21no—
53#10621898—21no—
54#10621898—21no—
55#10621898—21no—
56#10621898—21no—
57C2×D172D411yescharacteristic, complemented
58C2×C4×D43—21no—
59C2×Dic86D411yescharacteristic, complemented
60C4⋊C4×C43—22no—
61C4⋊C4×C43—21no—
62C22⋊C4×C43—22no—
63C22⋊C4×C43—22no—
64C22⋊C4×C43—21no—
65C42×C43D412yescomplemented
66C22⋊Dic43—22no—
67C22⋊Dic43—21no—
68#10621885—22no—
69#10621884—22no—
70#10621883—22no—
71#10621882—22no—
72(C2×D43)⋊C4—22no—
73C4⋊Dic43—21no—
74Dic43⋊C4—22no—
75C4×Dic43D412yescomplemented
76#10621877—21no—
77#10621877—21no—
78#10621877—21no—
79#10621877—21no—
80C2×C43⋊C8—21no—
81C2×C43⋊C8D412yescomplemented
82C23×C43—21no—
83C23×C43—21no—
84C23×C43—21no—
85C23×C43—21no—
86C23×C43—42no—
87C23×C43C2×D411yescharacteristic
88C22×D43—21no—
89Q8×C43—21no—
90Q8×C43—21no—
91D4×C43—21no—
92D4×C43—21no—
93D4×C43—44no—
94D4×C43—41no—
95D4×C43—41no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—41no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43C2×D411yescharacteristic
108C2×C4×C43C2×D411yescharacteristic
109C2×C4×C43C2×D411yescharacteristic
110C2×C4×C43C2×D411yescharacteristic
111C2×C4×C43C2×D411yescharacteristic
112C2×C4×C43#4111yescharacteristic
113C22⋊D43—44no—
114C22⋊D43—41no—
115C22⋊D43—41no—
116C2×Dic43—22no—
117C2×Dic43—21no—
118D172—21no—
119D172—21no—
120C4×D43—41no—
121C4×D43—41no—
122Dic86—21no—
123Dic86—21no—
124C43⋊C8—22no—
125C43⋊C8—41no—
126C22×C43—22no—
127C22×C43—22no—
128C22×C43—22no—
129C22×C43—41no—
130C22×C43—41no—
131C22×C43—41no—
132C22×C43—41no—
133C22×C43—42no—
134C22×C43—41no—
135C22×C43—41no—
136C22×C43#12011yescharacteristic
137C22×C43#12011yescharacteristic
138C22×C43#12111yescharacteristic
139C2×D43—42no—
140C2×D43—41no—
141C4×C43—42no—
142C4×C43—41no—
143C4×C43—41no—
144C4×C43#12011yescharacteristic
145C4×C43#12111yescharacteristic
146C4×C43#12111yescharacteristic
147C4×C43#12711yescharacteristic
148Dic43—42no—
149Dic43—41no—
150#2010—431nomaximal, Sylow
151C2×C43—21no—
152C2×C43—21no—
153C2×C43—21no—
154C2×C43—42no—
155C2×C43—81no—
156C2×C43#39211yescharacteristic
157D43—81no—
158#575—431no—
159#525—431no—
160#525D4311yescharacteristic, complemented
161#421—431no—
162#421—431no—
163#407—431no—
164H(3,ℤ/4)—431no—
165C43#201011yescharacteristic, complemented, Sylow
166C2×#41—431no—
167C2×#41C2×D4311yescharacteristic
168C23×C4C2×D4311yescharacteristic
169#137—861no—
170#137—861no—
171AGL(1,ℤ/8)—861no—
172AGL(1,ℤ/8)—861no—
173#135—862no—
174C2×M16—431no—
175C2×M16—431no—
176#123—21no—
177#123—861no—
178C22⋊Q8—21no—
179C22⋊Q8—861no—
180#121—21no—
181#121—861no—
182#120—21no—
183#120—861no—
184C4×D4—22no—
185C4×D4—862no—
186#117—431no—
187#117C2×D4311yescharacteristic
188#104—862no—
189#104—862no—
190C22⋊C8—862no—
191C24C22⋊D4311yescharacteristic
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—861no—
197#41—861no—
198#41—861no—
199#41—861no—
200C2×Q8—431no—
201C2×Q8C22⋊D4311yescharacteristic, complemented
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—431no—
205C2×D4—862no—
206C2×D4—861no—
207C2×D4C22⋊D4311yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—861no—
216C22×C4C22⋊D4311yescharacteristic
217C22×C4C22×D4311yescharacteristic
218Q16—862no—
219SD16—862no—
220SD16—862no—
221D8—862no—
222M16—861no—
223M16—861no—
224M16—861no—
225M16—861no—
226C2×C8—432no—
227C2×C8—861no—
228C4⋊C4—22no—
229C4⋊C4—21no—
230C4⋊C4—862no—
231C4⋊C4—861no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C22⋊C4—21no—
235C22⋊C4—862no—
236C22⋊C4—862no—
237C22⋊C4—861no—
238C42—432no—
239C42C22⋊D4312yescomplemented
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—42no—
245C23—861no—
246C23C2×C22⋊D4311yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—861no—
250Q8—861no—
251D4—21no—
252D4—21no—
253D4—44no—
254D4—41no—
255D4—41no—
256D4—861no—
257D4—861no—
258D4—1724no—
259D4—1721no—
260D4—1721no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—862no—
273C2×C4—861no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4D4×D4311yescharacteristic
277C2×C4D4×D4311yescharacteristic
278C2×C4D4×D4311yescharacteristic
279C2×C4#1062190011yescharacteristic
280C2×C4C2×C22⋊D4311yescharacteristic
281C2×C4C2×C22⋊D4311yescharacteristic
282C8—862no—
283C8—1721no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—1722no—
295C22—1721no—
296C22#1306329311yescharacteristic
297C22#1306329411yescharacteristic
298C22#1306329711yescharacteristic
299C4—42no—
300C4—41no—
301C4—41no—
302C4—1722no—
303C4—1721no—
304C4#1306329311yescharacteristic
305C4#1306329611yescharacteristic
306C4#1306329711yescharacteristic
307C4#1306332111yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—42no—
312C2—81no—
313C2—3441no—
314C2#1458280711yescharacteristic
subgroupG/H
centerC4#13063321
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#525C2
socleC2×C43#392
hypercenter#525D43
hypocenterC43#2010
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #14583697C2semidirect
2. #14583410C2semidirect
3. #14582917C2semidirect
4. #14582916C2semidirect
5. #14582863C2semidirect
6. #14582655C2semidirect
7. C43×#525C2semidirect
38. C2×Q8×C43D4semidirect
41. C2×D4×C43D4semidirect
57. C2×D172D4semidirect
59. C2×Dic86D4semidirect
65. C42×C43D4semidirect
75. C4×Dic43D4semidirect
81. C2×C43⋊C8D4semidirect
160. #525D43semidirect
165. C43#2010semidirect
201. C2×Q8C22⋊D43semidirect
207. C2×D4C22⋊D43semidirect
239. C42C22⋊D43semidirect