Finite Group Databasebeta

← #19145488

Subgroups — #19145488

Order 5504.

378 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583473C211yesmaximal, characteristic
2#14583472C211yesmaximal, characteristic
3#14583241C211yesmaximal, characteristic, complemented
4#14583239C211yesmaximal, characteristic, complemented
5#14583238C211yesmaximal, characteristic, complemented
6#14583237C211yesmaximal, characteristic, complemented
7#14583156C211yesmaximal, characteristic, complemented
8#14583154C211yesmaximal, characteristic, complemented
9#14583139C211yesmaximal, characteristic, complemented
10#14583137C211yesmaximal, characteristic, complemented
11#14583055C211yesmaximal, characteristic, complemented
12#14583053C211yesmaximal, characteristic, complemented
13#14583053C211yesmaximal, characteristic, complemented
14#14582864C211yesmaximal, characteristic
15C43×#451C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18C2×#10621885C2211yescharacteristic
19C2×#10621885C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21C2×C8×D43C2211yescharacteristic
22#13063324—21no—
23#13063323—21no—
24#13063314—21no—
25#13063311—21no—
26#13063310—21no—
27#13063308—21no—
28#13063308—21no—
29#13063307—21no—
30#13063305C2211yescharacteristic
31#13063304C2211yescharacteristic
32#13063301C2211yescharacteristic
33#13063301C2211yescharacteristic
34#13063301C2211yescharacteristic
35#13063301C2211yescharacteristic
36#13063301C2211yescharacteristic
37#13063284C2211yescharacteristic
38#13063283C2211yescharacteristic
39#13063259C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063257C2211yescharacteristic
42#13063256C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063249C2211yescharacteristic
47#13063249C2211yescharacteristic
48#13063249C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52C22×Q8×C43C2211yescharacteristic
53C2×Q16×C43C2211yescharacteristic
54C2×Q16×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43—41no—
61C2×Q8×C43—41no—
62C2×Q8×C43C2311yescharacteristic
63C2×Q8×C43C2311yescharacteristic
64C2×Q8×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43D411yescharacteristic
68C2×C22⋊D43D411yescharacteristic
69Q8×D43—41no—
70Q8×D43—41no—
71#10621898—41no—
72#10621898—41no—
73C2×D172D411yescharacteristic
74C2×C4×D43—21no—
75C2×C4×D43C2311yescharacteristic
76C2×C4×D43C2311yescharacteristic
77C2×Dic86—21no—
78C2×Dic86D411yescharacteristic
79C2×Dic86C2311yescharacteristic
80Q16×C43—41no—
81Q16×C43—41no—
82C2×C8×C43C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C4⋊C4×C43—21no—
85C4⋊C4×C43C2311yescharacteristic
86C22⋊C4×C43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89#10621885—41no—
90#10621885—41no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106Dic43⋊C4—21no—
107Dic43⋊C4—21no—
108C4×Dic43—21no—
109C4×Dic43—21no—
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112#10621872—41no—
113C8×D43—41no—
114C23×C43C2×D411yescharacteristic
115C22×D43C2×D411yescharacteristic
116C22×D43C2×D411yescharacteristic
117Q8×C43—21no—
118Q8×C43—21no—
119Q8×C43—21no—
120Q8×C43—21no—
121Q8×C43—21no—
122Q8×C43—21no—
123Q8×C43—42no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—42no—
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2411yescharacteristic
133C22⋊D43—41no—
134C22⋊D43—41no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43C2×D411yescharacteristic
140C2×Dic43C2×D411yescharacteristic
141D172—41no—
142C4×D43—21no—
143C4×D43—21no—
144C4×D43—21no—
145C4×D43—21no—
146C4×D43—42no—
147Dic86—21no—
148Dic86—21no—
149Dic86—41no—
150Dic86—42no—
151C8×C43—21no—
152C8×C43—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43C22×D411yescharacteristic
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—21no—
165C4×C43—21no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43H(5,𝔽2)11yescharacteristic
171C4×C43H(5,𝔽2)11yescharacteristic
172Dic43—21no—
173Dic43—21no—
174Dic43—41no—
175Dic43—41no—
176Dic43—41no—
177Dic43—41no—
178#3202—431nomaximal, Sylow
179C2×C43—41no—
180C2×C43#53411yescharacteristic
181C2×C43#57811yescharacteristic
182C2×C43#57811yescharacteristic
183D43—41no—
184D43—41no—
185#536—431no—
186#536—431no—
187#485—431no—
188#485—431no—
189#485—431no—
190#485—431no—
191#470—431no—
192#470—431no—
193#467—431no—
194#467—431no—
195#451—431no—
196#451—431no—
197#451—431no—
198#451D4311yescharacteristic, complemented
199#408—431no—
200C43#320211yescharacteristic, complemented, Sylow
201C2×#41—431no—
202C22×Q8—431no—
203C22×Q8C2×D4311yescharacteristic
204C2×Q16—431no—
205C2×Q16—431no—
206C2×Q16C2×D4311yescharacteristic
207C2×Q16C2×D4311yescharacteristic
208C2×M16—431no—
209C22×C8—431no—
210C4⋊Q8—861no—
211C4⋊Q8—861no—
212#124—861no—
213#124—861no—
214#123—861no—
215#123—861no—
216#123—861no—
217#123—861no—
218C22⋊Q8—431no—
219C22⋊Q8—431no—
220C22⋊Q8—431no—
221C22⋊Q8—431no—
222C22⋊Q8—431no—
223C22⋊Q8—431no—
224C22⋊Q8—431no—
225C22⋊Q8C2×D4311yescharacteristic
226#117—431no—
227#117—431no—
228#107—431no—
229#107—431no—
230#106—431no—
231#106—431no—
232#103—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#103—431no—
237#103—431no—
238#103C2×D4311yescharacteristic
239#103C2×D4311yescharacteristic
240C22⋊C8—431no—
241C22⋊C8—431no—
242C22⋊C8—431no—
243C22⋊C8C2×D4311yescharacteristic
244#41—1721no—
245#41—1721no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—431no—
250C2×Q8—431no—
251C2×Q8—861no—
252C2×Q8—1721no—
253C2×Q8—1721no—
254C2×Q8C22×D4311yescharacteristic
255C2×Q8C22×D4311yescharacteristic
256C2×Q8C22×D4311yescharacteristic
257C2×D4—431no—
258C2×D4—431no—
259C2×D4—431no—
260C22×C4—21no—
261C22×C4—431no—
262C22×C4—431no—
263C22×C4—861no—
264C22×C4C22×D4311yescharacteristic
265Q16—41no—
266Q16—41no—
267Q16—1721no—
268Q16—1721no—
269M16—1721no—
270C2×C8—431no—
271C2×C8—431no—
272C2×C8—1721no—
273C2×C8C22×D4311yescharacteristic
274C2×C8C22×D4311yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—431no—
277C4⋊C4—431no—
278C4⋊C4—431no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4C22×D4311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C42—861no—
298C42—861no—
299C23—431no—
300C23—431no—
301C23D4×D4311yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—42no—
309Q8—861no—
310Q8—861no—
311Q8—1721no—
312Q8—1722no—
313D4—1721no—
314D4—1721no—
315D4—1721no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—431no—
324C2×C4—431no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—1722no—
334C2×C4D4×D4311yescharacteristic
335C2×C4C23×D4311yescharacteristic
336C8—21no—
337C8—21no—
338C8—861no—
339C8—861no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—861no—
344C22—861no—
345C22—861no—
346C22—861no—
347C22—861no—
348C22—861no—
349C22C2×D4×D4311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—861no—
356C4—861no—
357C4—1721no—
358C4—1721no—
359C4—1721no—
360C4—1721no—
361C4#1306337011yescharacteristic
362C4#1306337011yescharacteristic
363C2—41no—
364C2—1721no—
365C2—1721no—
366C2#1458345911yescharacteristic
367C2#1458371211yescharacteristic
368C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#451C2
socleC22×C43C22×D4
hypercenter#451D43
hypocenterC43#3202
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #14583241C2semidirect
4. #14583239C2semidirect
5. #14583238C2semidirect
6. #14583237C2semidirect
7. #14583156C2semidirect
8. #14583154C2semidirect
9. #14583139C2semidirect
10. #14583137C2semidirect
11. #14583055C2semidirect
12. #14583053C2semidirect
13. #14583053C2semidirect
15. C43×#451C2semidirect
198. #451D43semidirect
200. C43#3202semidirect