Finite Group Databasebeta

← #19147035

Subgroups — #19147035

Order 5504.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583553C211yesmaximal, characteristic
2#14583309C211yesmaximal, characteristic, complemented
3#14583232C211yesmaximal, characteristic, complemented
4#14583227C211yesmaximal, characteristic, complemented
5#14583223C211yesmaximal, characteristic, complemented
6#14583212C211yesmaximal, characteristic, complemented
7#14583196C211yesmaximal, characteristic, complemented
8#14583194C211yesmaximal, characteristic, complemented
9#14583147C211yesmaximal, characteristic, complemented
10#14583130C211yesmaximal, characteristic, complemented
11#14582997C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582942C211yesmaximal, characteristic, complemented
14C2×#13063258C211yesmaximal, characteristic, complemented
15C43×#552C211yesmaximal, characteristic, complemented
16C2×#10621900—21no—
17C2×#10621884C2211yescharacteristic
18C2×#10621877C2211yescharacteristic
19C22×C43⋊C8C2211yescharacteristic
20#13063325C2211yescharacteristic
21#13063309—21no—
22#13063309—21no—
23#13063305—21no—
24#13063299C2211yescharacteristic
25#13063299C2211yescharacteristic
26C4×D172C2211yescharacteristic
27C2×C4⋊Dic43C2211yescharacteristic
28C2×C4⋊Dic43C2211yescharacteristic
29#13063258C2211yescharacteristic
30#13063258C2211yescharacteristic
31#13063258C2211yescharacteristic
32#13063258C2211yescharacteristic
33#13063258C2211yescharacteristic
34#13063258C2211yescharacteristic
35#13063256C2211yescharacteristic
36#13063256C2211yescharacteristic
37#13063256C2211yescharacteristic
38C4⋊(C43⋊C8)C2211yescharacteristic
39#13063249C2211yescharacteristic
40#13063249C2211yescharacteristic
41#13063249C2211yescharacteristic
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—
66C22×Dic43—21no—
67C22×Dic43—21no—
68#10621900—44no—
69C2×D172C2311yescharacteristic
70C2×C4×D43—21no—
71C2×Dic86—21no—
72C4⋊C4×C43—21no—
73C4⋊C4×C43—21no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43—21no—
76C4⋊C4×C43—21no—
77C4⋊C4×C43—21no—
78C4⋊C4×C43D411yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C4⋊C4×C43C2311yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C22⋊C4×C43—21no—
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C22⋊C4×C43D411yescharacteristic
86C22⋊C4×C43D411yescharacteristic
87C42×C43—21no—
88C42×C43—21no—
89C42×C43C2311yescharacteristic
90#10621884—22no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94C4⋊Dic43—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100#10621877—22no—
101C2×C43⋊C8—22no—
102C2×C43⋊C8C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C23×C43C2×D411yescharacteristic
107C23×C43C2×D411yescharacteristic
108C22×D43—21no—
109Q8×C43—21no—
110Q8×C43—21no—
111D4×C43—22no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—42no—
121C2×C4×C43C2×D411yescharacteristic
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2411yescharacteristic
126C22⋊D43—42no—
127C22⋊D43—42no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—42no—
132C2×Dic43—42no—
133D172—21no—
134D172—21no—
135C4×D43—42no—
136Dic86—42no—
137C43⋊C8—21no—
138C43⋊C8—21no—
139C43⋊C8—21no—
140C43⋊C8#4112yescomplemented
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43AGL(1,ℤ/8)12yes—
147C22×C43C22×D411yescharacteristic
148C2×D43—41no—
149C2×D43—41no—
150C2×D43—41no—
151C4×C43—21no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43C2×#4111yescharacteristic
160C4×C432−1+411yescharacteristic
161Dic43—41no—
162Dic43—41no—
163Dic43—41no—
164#3343—431nomaximal, Sylow
165C2×C43—22no—
166C2×C43—41no—
167C2×C43#54711yescharacteristic
168C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
169C2×C43#57811yescharacteristic
170D43—81no—
171#552D4311yescharacteristic, complemented
172#547—431no—
173#501—431no—
174#484—431no—
175#483—431no—
176#482—431no—
177#480—431no—
178#478—431no—
179#477—431no—
180#468—431no—
181#465—431no—
182#440—431no—
183#435—431no—
184#428—431no—
185C2×#107—431no—
186C43#334311yescharacteristic, complemented, Sylow
187C2×#41—861no—
188C2×SD16—431no—
189C2×M16—431no—
190C22×C8—431no—
191C4⋊Q8—431no—
192#126—21no—
193#125—21no—
194#125C2×D4311yescharacteristic
195#123—21no—
196#123—861no—
197#123—861no—
198C22⋊Q8—861no—
199C22⋊Q8C2×D4311yescharacteristic
200C22⋊Q8C2×D4311yescharacteristic
201#121—431no—
202#121—431no—
203C4×Q8C2×D4311yescharacteristic
204C4×D4—431no—
205C4×D4C2×D4311yescharacteristic
206#117—21no—
207#117C2×D4311yescharacteristic
208C2×C4⋊C4—431no—
209C2×C4⋊C4—431no—
210C2×C4⋊C4C2×D4311yescharacteristic
211#107—431no—
212#107—431no—
213#107—431no—
214#107—431no—
215#107—431no—
216#107—431no—
217#106—431no—
218#106—431no—
219#106—431no—
220C4⋊C8—431no—
221#103—431no—
222#103—431no—
223#103—431no—
224#102—431no—
225#102—431no—
226#102—431no—
227C22⋊C8—431no—
228C22⋊C8—431no—
229#97—431no—
230#41—1724no—
231C2×Q8—861no—
232C2×Q8C22×D4311yescharacteristic
233C2×D4—431no—
234C2×D4—861no—
235C2×D4—861no—
236C2×D4C22⋊D4311yescharacteristic
237C22×C4—21no—
238C22×C4—861no—
239C22×C4—861no—
240C22×C4—861no—
241C22×C4C22×D4311yescharacteristic
242C22×C4C22×D4311yescharacteristic
243SD16—862no—
244M16—862no—
245C2×C8—431no—
246C2×C8—431no—
247C2×C8—431no—
248C2×C8—431no—
249C2×C8—862no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—431no—
257C4⋊C4—431no—
258C4⋊C4—431no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4—861no—
262C4⋊C4C22⋊D4311yescharacteristic
263C4⋊C4C22×D4311yescharacteristic
264C4⋊C4C22×D4311yescharacteristic
265C4⋊C4C22×D4311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—861no—
270C22⋊C4—861no—
271C22⋊C4—861no—
272C22⋊C4C22⋊D4311yescharacteristic
273C22⋊C4C22⋊D4311yescharacteristic
274C42—21no—
275C42—21no—
276C42C22×D4311yescharacteristic
277C23—861no—
278C23C2×C22⋊D4311yescharacteristic
279C23C2×C22⋊D4311yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—1722no—
283D4—22no—
284D4—861no—
285D4—861no—
286D4—1722no—
287D4—1722no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—861no—
298C2×C4—861no—
299C2×C4—861no—
300C2×C4—1722no—
301C2×C4—1722no—
302C2×C4—1722no—
303C2×C4C2×C22⋊D4311yescharacteristic
304C2×C4C2×C22⋊D4311yescharacteristic
305C2×C4C2×C22⋊D4311yescharacteristic
306C2×C4C2×C22⋊D4311yescharacteristic
307C2×C4C23×D4311yescharacteristic
308C8—432no—
309C8—861no—
310C8—861no—
311C8—861no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—1721no—
318C22—1721no—
319C22—1721no—
320C22#1306335012yes—
321C22C22×C22⋊D4311yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—1721no—
331C4—1721no—
332C4—1721no—
333C4#41×D4311yescharacteristic
334C4#1306337211yescharacteristic
335C2—22no—
336C2—41no—
337C2—3441no—
338C2#1458354811yescharacteristic
339C2C2×#1306335011yescharacteristic
340C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#552C2
socleC22×C43C22×D4
hypercenter#552D43
hypocenterC43#3343
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. #14583309C2semidirect
3. #14583232C2semidirect
4. #14583227C2semidirect
5. #14583223C2semidirect
6. #14583212C2semidirect
7. #14583196C2semidirect
8. #14583194C2semidirect
9. #14583147C2semidirect
10. #14583130C2semidirect
11. #14582997C2semidirect
12. #14582971C2semidirect
13. #14582942C2semidirect
14. C2×#13063258C2semidirect
15. C43×#552C2semidirect
140. C43⋊C8#41semidirect
171. #552D43semidirect
186. C43#3343semidirect