Finite Group Databasebeta

← #19146571

Subgroups — #19146571

Order 5504.

394 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#14583595C211yesmaximal, characteristic, complemented
2#14583267C211yesmaximal, characteristic, complemented
3#14583237C211yesmaximal, characteristic, complemented
4#14583227C211yesmaximal, characteristic, complemented
5#14583199C211yesmaximal, characteristic, complemented
6#14583147C211yesmaximal, characteristic, complemented
7#14583130C211yesmaximal, characteristic, complemented
8#14583101C211yesmaximal, characteristic, complemented
9#14583044C211yesmaximal, characteristic, complemented
10#14583044C211yesmaximal, characteristic, complemented
11#14583009C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582900C211yesmaximal, characteristic, complemented
14#14582895C211yesmaximal, characteristic, complemented
15C43×#547C211yesmaximal, characteristic, complemented
16C2×#10621884C2211yescharacteristic
17C2×#10621884C2211yescharacteristic
18C2×#10621882C2211yescharacteristic
19C2×#10621877C2211yescharacteristic
20C22×C43⋊C8C2211yescharacteristic
21#13063320—21no—
22#13063317C2211yescharacteristic
23#13063307—21no—
24#13063299C2211yescharacteristic
25#13063299C2211yescharacteristic
26#13063297—21no—
27C4×D172C2211yescharacteristic
28(C22⋊D43)⋊C4—21no—
29#13063284C2211yescharacteristic
30C2×C4⋊Dic43C2211yescharacteristic
31#13063258C2211yescharacteristic
32#13063256C2211yescharacteristic
33#13063256C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic
35#13063249C2211yescharacteristic
36#13063249C2211yescharacteristic
37#13063249C2211yescharacteristic
38#13063249C2211yescharacteristic
39#13063249C2211yescharacteristic
40#13063249C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063246C2211yescharacteristic
43#13063246C2211yescharacteristic
44#13063245C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic
47#13063236C2211yescharacteristic
48C2×#41×C43C2211yescharacteristic
49C2×#41×C43C2211yescharacteristic
50C4⋊Q8×C43C2211yescharacteristic
51#123×C43—21no—
52#123×C43—21no—
53C22⋊Q8×C43C2211yescharacteristic
54C22⋊Q8×C43C2211yescharacteristic
55#121×C43—21no—
56C4×D4×C43C2211yescharacteristic
57C4×D4×C43C2211yescharacteristic
58C2×C4⋊C4×C43—21no—
59#41×C43—22no—
60#41×C43—22no—
61#41×C43—41no—
62#41×C43—41no—
63C2×Q8×C43C2311yescharacteristic
64C2×Q8×C43C2311yescharacteristic
65C2×D4×C43—21no—
66C2×D4×C43—21no—
67C2×D4×C43D411yescharacteristic
68C2×D4×C43C2311yescharacteristic
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43C2311yescharacteristic
73C22×C4×C43C2311yescharacteristic
74C2×C22⋊D43—21no—
75C2×C22⋊D43—21no—
76C22×Dic43—21no—
77C2×D172C2311yescharacteristic
78C2×C4×D43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43D411yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊C4×C43—21no—
87C22⋊C4×C43—21no—
88C22⋊C4×C43D411yescharacteristic
89C22⋊C4×C43D411yescharacteristic
90C42×C43C2311yescharacteristic
91C22⋊Dic43—21no—
92#10621884—41no—
93#10621884—41no—
94#10621882—22no—
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—
104C4×Dic43—21no—
105#10621877—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C23×C43C2×D411yescharacteristic
114C22×D43—21no—
115Q8×C43—21no—
116Q8×C43—21no—
117Q8×C43—21no—
118Q8×C43—21no—
119D4×C43—21no—
120D4×C43—41no—
121D4×C43—42no—
122D4×C43—42no—
123D4×C43#4112yes—
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—21no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43—42no—
134C2×C4×C43C2×D411yescharacteristic
135C2×C4×C43C2×D411yescharacteristic
136C2×C4×C43C2×D411yescharacteristic
137C2×C4×C43C2×D411yescharacteristic
138C2×C4×C43C2411yescharacteristic
139C22⋊D43—42no—
140C22⋊D43—81no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—81no—
145D172—21no—
146D172—21no—
147C4×D43—81no—
148C43⋊C8—21no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—22no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43C22×D411yescharacteristic
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43C2×#4111yescharacteristic
173C4×C43H(5,𝔽2)11yescharacteristic
174Dic43—41no—
175Dic43—41no—
176Dic43—41no—
177#3307—431nomaximal, Sylow
178C2×C43—41no—
179C2×C43—41no—
180C2×C43—42no—
181C2×C43#54611yescharacteristic
182C2×C43#57511yescharacteristic
183C2×C43#57711yescharacteristic
184D43—81no—
185#553—431no—
186#547D4311yescharacteristic, complemented
187#491—431no—
188#485—431no—
189#483—431no—
190#478—431no—
191#468—431no—
192#465—431no—
193#461—431no—
194#449—431no—
195#449—431no—
196#442—431no—
197#435—431no—
198#417—431no—
199#416—431no—
200C43#330711yescharacteristic, complemented, Sylow
201C2×#41C2×D4311yescharacteristic
202C2×#41C2×D4311yescharacteristic
203C2×SD16—431no—
204C2×SD16—431no—
205C2×D8—431no—
206C2×M16—431no—
207C22×C8—431no—
208C4⋊Q8C2×D4311yescharacteristic
209#126—861no—
210#125—431no—
211#123—21no—
212#123—21no—
213#123—861no—
214C22⋊Q8C2×D4311yescharacteristic
215C22⋊Q8C2×D4311yescharacteristic
216#121—21no—
217#121—431no—
218#121—431no—
219#121—861no—
220C4×D4—431no—
221C4×D4—861no—
222C4×D4C2×D4311yescharacteristic
223C4×D4C2×D4311yescharacteristic
224#117—431no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—431no—
227#107—431no—
228#106—431no—
229#106—431no—
230C4⋊C8—431no—
231#103—431no—
232#103—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#103—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241C22⋊C8—431no—
242C22⋊C8—431no—
243#97—431no—
244#41—22no—
245#41—22no—
246#41—41no—
247#41—41no—
248C2×Q8C22×D4311yescharacteristic
249C2×Q8C22×D4311yescharacteristic
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—431no—
253C2×D4—861no—
254C2×D4—861no—
255C2×D4C22⋊D4311yescharacteristic
256C2×D4C22×D4311yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4C22×D4311yescharacteristic
263C22×C4C22×D4311yescharacteristic
264SD16—1721no—
265SD16—1721no—
266D8—862no—
267M16—1721no—
268C2×C8—431no—
269C2×C8—431no—
270C2×C8—431no—
271C2×C8—431no—
272C2×C8—1721no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—431no—
278C4⋊C4—431no—
279C4⋊C4—431no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4C22⋊D4311yescharacteristic
284C4⋊C4C22×D4311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4C22⋊D4311yescharacteristic
293C22⋊C4C22⋊D4311yescharacteristic
294C42—861no—
295C42C22×D4311yescharacteristic
296C23—21no—
297C23—861no—
298C23C2×C22⋊D4311yescharacteristic
299C23C2×C22⋊D4311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—21no—
304D4—21no—
305D4—41no—
306D4—42no—
307D4—42no—
308D4—861no—
309D4—861no—
310D4—3441no—
311D4—1722no—
312D4#1062190012yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—3441no—
327C2×C4—3441no—
328C2×C4C2×C22⋊D4311yescharacteristic
329C2×C4C2×C22⋊D4311yescharacteristic
330C2×C4C2×C22⋊D4311yescharacteristic
331C2×C4C2×C22⋊D4311yescharacteristic
332C2×C4C23×D4311yescharacteristic
333C8—861no—
334C8—861no—
335C8—861no—
336C8—861no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—22no—
344C22—41no—
345C22—41no—
346C22—1721no—
347C22—1721no—
348C22—1721no—
349C22C22×C22⋊D4311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—1721no—
358C4—1721no—
359C4—1721no—
360C4C2×#1062190011yescharacteristic
361C4#1306337011yescharacteristic
362C2—41no—
363C2—41no—
364C2—42no—
365C2—3441no—
366C2#1458354311yescharacteristic
367C2#1458369711yescharacteristic
368C2#1458370711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#547C2
socleC22×C43C22×D4
hypercenter#547D43
hypocenterC43#3307
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #14583595C2semidirect
2. #14583267C2semidirect
3. #14583237C2semidirect
4. #14583227C2semidirect
5. #14583199C2semidirect
6. #14583147C2semidirect
7. #14583130C2semidirect
8. #14583101C2semidirect
9. #14583044C2semidirect
10. #14583044C2semidirect
11. #14583009C2semidirect
12. #14582971C2semidirect
13. #14582900C2semidirect
14. #14582895C2semidirect
15. C43×#547C2semidirect
186. #547D43semidirect
200. C43#3307semidirect