Finite Group Databasebeta

← #19146685

Subgroups — #19146685

Order 5504.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583554C211yesmaximal, characteristic
2#14583269C211yesmaximal, characteristic, complemented
3#14583240C211yesmaximal, characteristic, complemented
4#14583234C211yesmaximal, characteristic, complemented
5#14583196C211yesmaximal, characteristic, complemented
6#14583155C211yesmaximal, characteristic, complemented
7#14583138C211yesmaximal, characteristic, complemented
8#14583109C211yesmaximal, characteristic, complemented
9#14583059C211yesmaximal, characteristic, complemented
10#14583059C211yesmaximal, characteristic, complemented
11#14582997C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582898C211yesmaximal, characteristic, complemented
14#14582893C211yesmaximal, characteristic, complemented
15C43×#552C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621898C2211yescharacteristic
18C2×#10621885C2211yescharacteristic
19C2×#10621885C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
21C2×#10621877C2211yescharacteristic
22C22×C43⋊C8C2211yescharacteristic
23#13063325C2211yescharacteristic
24#13063307—21no—
25#13063307—21no—
26#13063304C2211yescharacteristic
27#13063304C2211yescharacteristic
28#13063296—21no—
29C4×D172C2211yescharacteristic
30C4⋊C4×D43—21no—
31#13063258C2211yescharacteristic
32#13063258C2211yescharacteristic
33#13063256C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic
35#13063249C2211yescharacteristic
36#13063248C2211yescharacteristic
37#13063248C2211yescharacteristic
38#13063248C2211yescharacteristic
39#13063248C2211yescharacteristic
40#13063248C2211yescharacteristic
41#13063248C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44#13063245C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic
47#13063236C2211yescharacteristic
48#126×C43—21no—
49#125×C43—21no—
50#125×C43C2211yescharacteristic
51#123×C43—21no—
52C22⋊Q8×C43C2211yescharacteristic
53C22⋊Q8×C43C2211yescharacteristic
54C4×Q8×C43C2211yescharacteristic
55C4×D4×C43C2211yescharacteristic
56#117×C43—21no—
57#117×C43C2211yescharacteristic
58C2×C4⋊C4×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43D411yescharacteristic
61C22×C4×C43—21no—
62C22×C4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66#10621898—22no—
67#10621898—22no—
68#10621898—41no—
69#10621898—41no—
70C2×D172C2311yescharacteristic
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×Dic86C2311yescharacteristic
75C2×Dic86C2311yescharacteristic
76C4⋊C4×C43—21no—
77C4⋊C4×C43—21no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43D411yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C22⋊C4×C43—21no—
87C22⋊C4×C43—21no—
88C22⋊C4×C43—21no—
89C22⋊C4×C43D411yescharacteristic
90C22⋊C4×C43D411yescharacteristic
91C42×C43—21no—
92C42×C43—21no—
93C42×C43C2311yescharacteristic
94C22⋊Dic43—21no—
95C22⋊Dic43—21no—
96#10621885—41no—
97#10621885—41no—
98#10621884—22no—
99(C2×D43)⋊C4—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43—21no—
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105#10621877—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C23×C43C2×D411yescharacteristic
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114Q8×C43—21no—
115Q8×C43—21no—
116D4×C43—41no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—42no—
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2411yescharacteristic
131C22⋊D43—42no—
132C22⋊D43—42no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136D172—21no—
137D172#4112yes—
138C4×D43—42no—
139C4×D43—42no—
140C4×D43—42no—
141Dic86—21no—
142Dic86—21no—
143Dic86—21no—
144Dic86—21no—
145C43⋊C8—21no—
146C43⋊C8—21no—
147C43⋊C8—21no—
148C43⋊C8—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43C22×D411yescharacteristic
156C2×D43—22no—
157C2×D43—41no—
158C2×D43—41no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43C2×#4111yescharacteristic
168C4×C43H(5,𝔽2)11yescharacteristic
169Dic43—41no—
170Dic43—41no—
171Dic43—41no—
172#3315—431nomaximal, Sylow
173C2×C43—41no—
174C2×C43—41no—
175C2×C43#54611yescharacteristic
176C2×C43#57511yescharacteristic
177C2×C43#57811yescharacteristic
178D43—42no—
179#552D4311yescharacteristic, complemented
180#547—431no—
181#491—431no—
182#485—431no—
183#484—431no—
184#478—431no—
185#470—431no—
186#467—431no—
187#462—431no—
188#452—431no—
189#452—431no—
190#440—431no—
191#435—431no—
192#417—431no—
193#416—431no—
194C43#331511yescharacteristic, complemented, Sylow
195C2×#41—431no—
196C2×#41—431no—
197C2×Q16—431no—
198C2×Q16—431no—
199C2×SD16—431no—
200C2×M16—431no—
201C22×C8—431no—
202C4⋊Q8—431no—
203#126—21no—
204#125—21no—
205#125C2×D4311yescharacteristic
206#123—21no—
207#123—861no—
208#123—861no—
209C22⋊Q8—431no—
210C22⋊Q8—431no—
211C22⋊Q8C2×D4311yescharacteristic
212C22⋊Q8C2×D4311yescharacteristic
213#121—861no—
214C4×Q8C2×D4311yescharacteristic
215C4×D4—431no—
216C4×D4C2×D4311yescharacteristic
217#117—21no—
218#117C2×D4311yescharacteristic
219C2×C4⋊C4—861no—
220C2×C4⋊C4C2×D4311yescharacteristic
221#107—431no—
222#107—431no—
223#106—431no—
224C4⋊C8—431no—
225#103—431no—
226#103—431no—
227#103—431no—
228#103—431no—
229#103—431no—
230#103—431no—
231#103—431no—
232#102—431no—
233#102—431no—
234#102—431no—
235C22⋊C8—431no—
236C22⋊C8—431no—
237#97—431no—
238#41—862no—
239#41—862no—
240#41—1721no—
241#41—1721no—
242C2×Q8—431no—
243C2×Q8—431no—
244C2×Q8C22×D4311yescharacteristic
245C2×D4—431no—
246C2×D4—861no—
247C2×D4—861no—
248C2×D4C22⋊D4311yescharacteristic
249C22×C4—21no—
250C22×C4—861no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4C22×D4311yescharacteristic
254C22×C4C22×D4311yescharacteristic
255Q16—1721no—
256Q16—1721no—
257SD16—862no—
258M16—1721no—
259C2×C8—431no—
260C2×C8—431no—
261C2×C8—431no—
262C2×C8—431no—
263C2×C8—1721no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—431no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4C22⋊D4311yescharacteristic
276C4⋊C4C22×D4311yescharacteristic
277C4⋊C4C22×D4311yescharacteristic
278C4⋊C4C22×D4311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4C22⋊D4311yescharacteristic
286C22⋊C4C22⋊D4311yescharacteristic
287C42—21no—
288C42—21no—
289C42C22×D4311yescharacteristic
290C23—861no—
291C23C2×C22⋊D4311yescharacteristic
292C23C2×C22⋊D4311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—861no—
296Q8—861no—
297Q8—861no—
298Q8—861no—
299D4—41no—
300D4—432no—
301D4—861no—
302D4—1722no—
303D4—1722no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—1722no—
317C2×C4—1722no—
318C2×C4—1722no—
319C2×C4C2×C22⋊D4311yescharacteristic
320C2×C4C2×C22⋊D4311yescharacteristic
321C2×C4C2×C22⋊D4311yescharacteristic
322C2×C4C2×C22⋊D4311yescharacteristic
323C2×C4C23×D4311yescharacteristic
324C8—861no—
325C8—861no—
326C8—861no—
327C8—861no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—862no—
335C22—1721no—
336C22—1721no—
337C22C22×C22⋊D4311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—1721no—
347C4—1721no—
348C4—1721no—
349C4#41×D4311yescharacteristic
350C4#1306337111yescharacteristic
351C2—41no—
352C2—41no—
353C2—1722no—
354C2#1458353711yescharacteristic
355C2#1458369711yescharacteristic
356C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#552C2
socleC22×C43C22×D4
hypercenter#552D43
hypocenterC43#3315
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #14583269C2semidirect
3. #14583240C2semidirect
4. #14583234C2semidirect
5. #14583196C2semidirect
6. #14583155C2semidirect
7. #14583138C2semidirect
8. #14583109C2semidirect
9. #14583059C2semidirect
10. #14583059C2semidirect
11. #14582997C2semidirect
12. #14582971C2semidirect
13. #14582898C2semidirect
14. #14582893C2semidirect
15. C43×#552C2semidirect
179. #552D43semidirect
194. C43#3315semidirect