Finite Group Databasebeta

← #19134894

Subgroups — #19134894

Order 5504.

376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D43C211yesmaximal, characteristic, complemented
2#14583406C211yesmaximal, characteristic
3C2×#13063252C211yesmaximal, characteristic, complemented
4C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
5#14582660C211yesmaximal, characteristic, complemented
6#14582659C211yesmaximal, characteristic, complemented
7C2×#104×C43C211yesmaximal, characteristic, complemented
8C22×C4×D43C2211yescharacteristic
9C2×#10621877C2211yescharacteristic
10C2×#10621872—21no—
11M16×D43—22no—
12M16×D43—22no—
13C2×C8×D43—21no—
14#13063306—21no—
15#13063301C411yescharacteristic, complemented
16#13063301C411yescharacteristic, complemented
17#13063296C411yescharacteristic, complemented
18#13063296C411yescharacteristic, complemented
19#13063293—21no—
20C4×C22⋊D43—21no—
21C4×C22⋊D43—21no—
22#13063284C2211yescharacteristic
23C2×(C2×D43)⋊C4—21no—
24C2×C4×Dic43C2211yescharacteristic
25#13063252—22no—
26C43⋊#95—21no—
27C2×#41×C43C2211yescharacteristic
28C2×M16×C43C2211yescharacteristic
29C2×C42×C43C2211yescharacteristic
30#104×C43—22no—
31C23×D43D411yescharacteristic
32#41×C43—21no—
33#41×C43—21no—
34#41×C43—21no—
35#41×C43—21no—
36C2×Q8×C43C2×C411yescharacteristic
37C2×D4×C43—21no—
38C2×D4×C43C2×C411yescharacteristic
39C22×C4×C43—21no—
40C22×C4×C43—21no—
41C22×C4×C43C2311yescharacteristic
42C2×C22⋊D43—21no—
43C2×C22⋊D43—21no—
44C22×Dic43—21no—
45C22×Dic43D411yescharacteristic
46C2×C4×D43—21no—
47C2×C4×D43—21no—
48C2×C4×D43—21no—
49C2×C4×D43—21no—
50C2×C4×D43C2×C411yescharacteristic
51C2×C4×D43C2×C411yescharacteristic
52C2×C4×D43D411yescharacteristic
53C2×C4×D43D411yescharacteristic
54M16×C43—21no—
55M16×C43D412yescomplemented
56C2×C8×C43—21no—
57C42×C43—21no—
58C42×C43—21no—
59C22⋊Dic43—21no—
60C22⋊Dic43—21no—
61C22⋊Dic43—21no—
62(C2×D43)⋊C4—24no—
63(C2×D43)⋊C4—21no—
64(C2×D43)⋊C4—21no—
65C4⋊Dic43C2×C411yescharacteristic
66C4⋊Dic43C2×C411yescharacteristic
67Dic43⋊C4—21no—
68Dic43⋊C4—21no—
69C4×Dic43—21no—
70C4×Dic43—21no—
71C4×Dic43—21no—
72#10621877—21no—
73#10621877D412yescomplemented
74C2×C43⋊C8—21no—
75#10621872—24no—
76C8×D43—24no—
77C23×C43—21no—
78C23×C43C2×D411yescharacteristic
79C22×D43—21no—
80C22×D43—21no—
81C22×D43—22no—
82C22×D43—41no—
83C22×D43C22⋊C411yescharacteristic
84C22×D43C22⋊C411yescharacteristic
85Q8×C43—21no—
86Q8×C43—21no—
87D4×C43—21no—
88D4×C43—21no—
89D4×C43—41no—
90D4×C43—41no—
91C2×C4×C43—22no—
92C2×C4×C43—21no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43—41no—
96C2×C4×C43—41no—
97C2×C4×C43C22×C411yescharacteristic
98C2×C4×C43C2×D411yescharacteristic
99C2×C4×C43C2×D411yescharacteristic
100C2×C4×C43C2×D411yescharacteristic
101C2×C4×C43#4111yescharacteristic
102C2×C4×C43#4111yescharacteristic
103C22⋊D43—42no—
104C22⋊D43—42no—
105C2×Dic43—21no—
106C2×Dic43—21no—
107C2×Dic43—22no—
108C2×Dic43—21no—
109C2×Dic43—21no—
110C2×Dic43—41no—
111C2×Dic43—41no—
112C2×Dic43C22⋊C411yescharacteristic
113C2×Dic43C22⋊C411yescharacteristic
114C4×D43—21no—
115C4×D43—21no—
116C4×D43—21no—
117C4×D43—21no—
118C4×D43—21no—
119C4×D43—21no—
120C4×D43—21no—
121C4×D43—21no—
122C8×C43—22no—
123C43⋊C8—22no—
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—41no—
127C22×C43—41no—
128C22×C43—41no—
129C22×C43C2×C22⋊C411yescharacteristic
130C22×C43#12111yescharacteristic
131C22×C43#12111yescharacteristic
132C2×D43—21no—
133C2×D43—21no—
134C2×D43—21no—
135C2×D43—21no—
136C2×D43—21no—
137C2×D43—42no—
138C2×D43—42no—
139C2×D43#10412yescomplemented
140C4×C43—42no—
141C4×C43—41no—
142C4×C43C4×D411yescharacteristic
143C4×C43C4×D411yescharacteristic
144C4×C43#12011yescharacteristic
145C4×C43#12311yescharacteristic
146Dic43—21no—
147Dic43—21no—
148Dic43—42no—
149Dic43—41no—
150Dic43—41no—
151#1871—431nomaximal, Sylow
152C2×C43—21no—
153C2×C43—21no—
154C2×C43—81no—
155C2×C43#38611yescharacteristic
156C2×C43C2×#10411yescharacteristic
157C2×C43#42111yescharacteristic
158D43—22no—
159D43—41no—
160C22×M16—431no—
161#525—431no—
162C2×#104—431no—
163C2×#104D4311yescharacteristic, complemented
164C4×C22⋊C4—431no—
165#339—431no—
166#339—431no—
167C43#187111yescharacteristic, complemented, Sylow
168C2×#41C2×D4311yescharacteristic
169C23×C4—431no—
170C2×M16—431no—
171C2×M16—861no—
172C2×M16—862no—
173C2×M16—862no—
174C2×M16C2×D4311yescharacteristic
175C22×C8—861no—
176#123—861no—
177C22⋊Q8—431no—
178C22⋊Q8—431no—
179#121—431no—
180#121—431no—
181#120—861no—
182C4×D4—861no—
183C4×D4—861no—
184#117—431no—
185C2×C22⋊C4—861no—
186C2×C42—431no—
187C2×C42C2×D4311yescharacteristic
188#104—22no—
189#104—862no—
190#95—861no—
191C24—431no—
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196C2×Q8C4×D4311yescharacteristic
197C2×D4—21no—
198C2×D4—861no—
199C2×D4—861no—
200C2×D4C4×D4311yescharacteristic
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—431no—
204C22×C4—431no—
205C22×C4—431no—
206C22×C4—431no—
207C22×C4—431no—
208C22×C4—861no—
209C22×C4—861no—
210C22×C4—861no—
211C22×C4—861no—
212C22×C4—861no—
213C22×C4C22×D4311yescharacteristic
214M16—21no—
215M16—432no—
216M16—864no—
217M16—861no—
218M16C22⋊D4312yescomplemented
219C2×C8—21no—
220C2×C8—864no—
221C2×C8—861no—
222C4⋊C4—431no—
223C4⋊C4—431no—
224C4⋊C4—861no—
225C4⋊C4—861no—
226C22⋊C4—861no—
227C22⋊C4—861no—
228C22⋊C4—864no—
229C22⋊C4—861no—
230C22⋊C4—861no—
231C22⋊C4—861no—
232C42—21no—
233C42—21no—
234C42—861no—
235C42—861no—
236C42—861no—
237C23—21no—
238C23—431no—
239C23—431no—
240C23—862no—
241C23—861no—
242C23—861no—
243C23—1721no—
244C23D4×D4311yescharacteristic
245Q8—21no—
246Q8—21no—
247D4—21no—
248D4—21no—
249D4—41no—
250D4—41no—
251D4—1722no—
252D4—1722no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—431no—
260C2×C4—431no—
261C2×C4—861no—
262C2×C4—861no—
263C2×C4—861no—
264C2×C4—861no—
265C2×C4—861no—
266C2×C4—861no—
267C2×C4—861no—
268C2×C4—861no—
269C2×C4—861no—
270C2×C4—861no—
271C2×C4—862no—
272C2×C4—861no—
273C2×C4—861no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4C2×C4×D4311yescharacteristic
277C2×C4#1062189811yescharacteristic
278C2×C4D4×D4311yescharacteristic
279C2×C4D4×D4311yescharacteristic
280C2×C4#1062190011yescharacteristic
281C2×C4C2×C22⋊D4311yescharacteristic
282C8—22no—
283C8—862no—
284C22—21no—
285C22—21no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—432no—
290C22—861no—
291C22—861no—
292C22—861no—
293C22—861no—
294C22—861no—
295C22—1722no—
296C22—1722no—
297C22C22⋊C4×D4311yescharacteristic
298C22#1306329611yescharacteristic
299C22#1306329811yescharacteristic
300C4—42no—
301C4—41no—
302C4—861no—
303C4—861no—
304C4—1722no—
305C4—1721no—
306C4—1721no—
307C4(C22⋊D43)⋊C411yescharacteristic
308C4C4×C22⋊D4311yescharacteristic
309C4#1306329311yescharacteristic
310C4#1306330711yescharacteristic
311C2—21no—
312C2—21no—
313C2—81no—
314C2—862no—
315C2—1721no—
316C2#1458277511yescharacteristic
317C2#104×D4311yescharacteristic
318C2#1458291411yescharacteristic
subgroupG/H
centerC2×C4D4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC2×#104×C43C2
socleC22×C43C2×C22⋊C4
hypercenterC2×#104D43
hypocenterC43#1871
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×M16×D43C2semidirect
3. C2×#13063252C2semidirect
4. C4×(C2×D43)⋊C4C2semidirect
5. #14582660C2semidirect
6. #14582659C2semidirect
7. C2×#104×C43C2semidirect
15. #13063301C4semidirect
16. #13063301C4semidirect
17. #13063296C4semidirect
18. #13063296C4semidirect
55. M16×C43D4semidirect
73. #10621877D4semidirect
139. C2×D43#104semidirect
163. C2×#104D43semidirect
167. C43#1871semidirect
218. M16C22⋊D43semidirect