Finite Group Databasebeta

← #19146715

Subgroups — #19146715

Order 5504.

392 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#14583570C211yesmaximal, characteristic
2#14583265C211yesmaximal, characteristic, complemented
3#14583223C211yesmaximal, characteristic, complemented
4#14583217C211yesmaximal, characteristic, complemented
5#14583203C211yesmaximal, characteristic, complemented
6#14583147C211yesmaximal, characteristic, complemented
7#14583130C211yesmaximal, characteristic, complemented
8#14583099C211yesmaximal, characteristic, complemented
9#14583059C211yesmaximal, characteristic, complemented
10#14583059C211yesmaximal, characteristic, complemented
11#14583004C211yesmaximal, 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×#10621884C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
21C2×#10621877C2211yescharacteristic
22C22×C43⋊C8C2211yescharacteristic
23#13063322C2211yescharacteristic
24#13063321—21no—
25#13063299C2211yescharacteristic
26#13063299C2211yescharacteristic
27#13063298—21no—
28#13063298—21no—
29C4×Dic86C2211yescharacteristic
30#13063287—21no—
31#13063258C2211yescharacteristic
32#13063256C2211yescharacteristic
33#13063256C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic
35#13063249C2211yescharacteristic
36#13063248C2211yescharacteristic
37#13063248C2211yescharacteristic
38#13063248C2211yescharacteristic
39#13063245C2211yescharacteristic
40#13063245C2211yescharacteristic
41#13063245C2211yescharacteristic
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—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68#10621898—22no—
69#10621898—22no—
70#10621898—41no—
71#10621898—41no—
72C2×D172—21no—
73C2×D172—21no—
74C2×D172C2311yescharacteristic
75C2×D172C2311yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×Dic86C2311yescharacteristic
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43D411yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C4⋊C4×C43C2311yescharacteristic
88C4⋊C4×C43C2311yescharacteristic
89C22⋊C4×C43—21no—
90C22⋊C4×C43—21no—
91C22⋊C4×C43—21no—
92C22⋊C4×C43D411yescharacteristic
93C22⋊C4×C43D411yescharacteristic
94C42×C43—21no—
95C42×C43—21no—
96C42×C43C2311yescharacteristic
97#10621885—22no—
98#10621884—41no—
99#10621884—41no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102C4⋊Dic43C2311yescharacteristic
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×C43C2×D411yescharacteristic
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43—21no—
115Q8×C43—21no—
116Q8×C43—21no—
117D4×C43—41no—
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—21no—
126C2×C4×C43—42no—
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2411yescharacteristic
132C22⋊D43—42no—
133C22⋊D43—42no—
134C22⋊D43—81no—
135C22⋊D43—81no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138D172—21no—
139D172—21no—
140D172—21no—
141D172—21no—
142D172—42no—
143D172—81no—
144C4×D43—42no—
145C4×D43—42no—
146Dic86—21no—
147Dic86#4112yes—
148C43⋊C8—21no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43C22×D411yescharacteristic
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—41no—
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×C43—41no—
173C4×C43C2×#4111yescharacteristic
174C4×C43H(5,𝔽2)11yescharacteristic
175Dic43—22no—
176Dic43—41no—
177#3317—431nomaximal, Sylow
178C2×C43—41no—
179C2×C43—41no—
180C2×C43#54611yescharacteristic
181C2×C43#57511yescharacteristic
182C2×C43#57711yescharacteristic
183D43—81no—
184D43—81no—
185#552D4311yescharacteristic, complemented
186#550—431no—
187#490—431no—
188#482—431no—
189#481—431no—
190#479—431no—
191#468—431no—
192#465—431no—
193#460—431no—
194#452—431no—
195#452—431no—
196#441—431no—
197#435—431no—
198#417—431no—
199#416—431no—
200C43#331711yescharacteristic, complemented, Sylow
201C2×#41—431no—
202C2×#41—431no—
203C2×Q16—431no—
204C2×SD16—431no—
205C2×SD16—431no—
206C2×M16—431no—
207C22×C8—431no—
208#127—431no—
209#127—861no—
210#126—21no—
211#125—21no—
212#125C2×D4311yescharacteristic
213#123—21no—
214C22⋊Q8C2×D4311yescharacteristic
215C22⋊Q8C2×D4311yescharacteristic
216#121—431no—
217#121—431no—
218#121—861no—
219#121—861no—
220C4×Q8—431no—
221C4×Q8C2×D4311yescharacteristic
222C4×D4—861no—
223C4×D4C2×D4311yescharacteristic
224#117—21no—
225#117C2×D4311yescharacteristic
226C2×C4⋊C4C2×D4311yescharacteristic
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#102—431no—
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241C22⋊C8—431no—
242C22⋊C8—431no—
243#97—431no—
244#41—862no—
245#41—862no—
246#41—1721no—
247#41—1721no—
248C2×Q8—431no—
249C2×Q8C22×D4311yescharacteristic
250C2×D4—431no—
251C2×D4—431no—
252C2×D4—861no—
253C2×D4—861no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4C22⋊D4311yescharacteristic
259C22×C4—21no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4C22×D4311yescharacteristic
263C22×C4C22×D4311yescharacteristic
264Q16—862no—
265SD16—1721no—
266SD16—1721no—
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—21no—
278C4⋊C4—21no—
279C4⋊C4—431no—
280C4⋊C4—861no—
281C4⋊C4C22⋊D4311yescharacteristic
282C4⋊C4C22×D4311yescharacteristic
283C4⋊C4C22×D4311yescharacteristic
284C4⋊C4C22×D4311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4C22⋊D4311yescharacteristic
291C22⋊C4C22⋊D4311yescharacteristic
292C42—21no—
293C42—21no—
294C42—861no—
295C42C22×D4311yescharacteristic
296C23—861no—
297C23—861no—
298C23C2×C22⋊D4311yescharacteristic
299C23C2×C22⋊D4311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—432no—
303Q8—861no—
304D4—41no—
305D4—861no—
306D4—861no—
307D4—861no—
308D4—861no—
309D4—3441no—
310D4—3441no—
311D4—3441no—
312D4—1722no—
313D4—1722no—
314D4—1722no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—1722no—
327C2×C4—1722no—
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—1721no—
344C22—1721no—
345C22—1721no—
346C22—1721no—
347C22—1721no—
348C22—1721no—
349C22C22×C22⋊D4311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—862no—
359C4—1721no—
360C4#41×D4311yescharacteristic
361C4#1306337111yescharacteristic
362C2—41no—
363C2—41no—
364C2—3441no—
365C2—3441no—
366C2#1458353711yescharacteristic
367C2#1458369711yescharacteristic
368C2#1458370711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#552C2
socleC22×C43C22×D4
hypercenter#552D43
hypocenterC43#3317
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. #14583265C2semidirect
3. #14583223C2semidirect
4. #14583217C2semidirect
5. #14583203C2semidirect
6. #14583147C2semidirect
7. #14583130C2semidirect
8. #14583099C2semidirect
9. #14583059C2semidirect
10. #14583059C2semidirect
11. #14583004C2semidirect
12. #14582971C2semidirect
13. #14582898C2semidirect
14. #14582893C2semidirect
15. C43×#552C2semidirect
185. #552D43semidirect
200. C43#3317semidirect