Finite Group Databasebeta

← #19146706

Subgroups — #19146706

Order 5504.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583606C211yesmaximal, characteristic, complemented
2#14583258C211yesmaximal, characteristic, complemented
3#14583227C211yesmaximal, characteristic, complemented
4#14583215C211yesmaximal, characteristic, complemented
5#14583184C211yesmaximal, characteristic, complemented
6#14583155C211yesmaximal, characteristic, complemented
7#14583126C211yesmaximal, characteristic, complemented
8#14583118C211yesmaximal, characteristic, complemented
9#14583061C211yesmaximal, characteristic, complemented
10#14583055C211yesmaximal, characteristic, complemented
11#14583004C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582900C211yesmaximal, characteristic, complemented
14C2×#13063249C211yesmaximal, characteristic, complemented
15C43×#548C211yesmaximal, characteristic
16C2×#10621885C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621877C2211yescharacteristic
20C22×C43⋊C8C2211yescharacteristic
21#13063325C2211yescharacteristic
22#13063316—21no—
23#13063304C2211yescharacteristic
24#13063304C2211yescharacteristic
25#13063302—21no—
26#13063302—21no—
27C4×Dic86C2211yescharacteristic
28D4×Dic43—21no—
29C2×C4⋊Dic43C2211yescharacteristic
30C2×C4⋊Dic43C2211yescharacteristic
31#13063256C2211yescharacteristic
32#13063256C2211yescharacteristic
33#13063256C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic
35#13063249C2211yescharacteristic
36#13063249C2211yescharacteristic
37#13063249C2211yescharacteristic
38#13063249C2211yescharacteristic
39#13063249C2211yescharacteristic
40#13063249C2211yescharacteristic
41#13063248C2211yescharacteristic
42#13063246C2211yescharacteristic
43#13063246C2211yescharacteristic
44#13063246C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic
47#13063236C2211yescharacteristic
48C2×#41×C43C2211yescharacteristic
49C22×Q8×C43C2211yescharacteristic
50#124×C43—21no—
51#124×C43C2211yescharacteristic
52C22⋊Q8×C43—21no—
53C22⋊Q8×C43C2211yescharacteristic
54#121×C43—21no—
55#121×C43C2211yescharacteristic
56C4×Q8×C43C2211yescharacteristic
57C4×D4×C43—21no—
58C4×D4×C43C2211yescharacteristic
59#41×C43—22no—
60#41×C43—41no—
61C2×Q8×C43—21no—
62C2×Q8×C43—22no—
63C2×Q8×C43—41no—
64C2×Q8×C43C2311yescharacteristic
65C2×Q8×C43C2311yescharacteristic
66C2×D4×C43—21no—
67C2×D4×C43—21no—
68C2×D4×C43D411yescharacteristic
69C2×D4×C43C2311yescharacteristic
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43C2311yescharacteristic
73C22×C4×C43C2311yescharacteristic
74C22×Dic43—21no—
75C22×Dic43—21no—
76C2×Dic86—21no—
77C2×Dic86C2311yescharacteristic
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43D411yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C22⋊C4×C43—21no—
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C22⋊C4×C43—21no—
86C22⋊C4×C43D411yescharacteristic
87C22⋊C4×C43D411yescharacteristic
88C42×C43—21no—
89C42×C43C2311yescharacteristic
90C22⋊Dic43—21no—
91C22⋊Dic43—21no—
92#10621885—22no—
93#10621885—41no—
94#10621883—41no—
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
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
114Q8×C43—21no—
115Q8×C43—21no—
116Q8×C43—21no—
117Q8×C43—42no—
118Q8×C43#4112yes—
119D4×C43—22no—
120D4×C43—21no—
121D4×C43—21no—
122D4×C43—42no—
123D4×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—21no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2×D411yescharacteristic
135C2×C4×C43C2×D411yescharacteristic
136C2×C4×C43C2×D411yescharacteristic
137C2×C4×C43C2411yescharacteristic
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—81no—
143C2×Dic43—81no—
144Dic86—21no—
145Dic86—21no—
146Dic86—81no—
147C43⋊C8—21no—
148C43⋊C8—21no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43#13712yes—
160C22×C43C22×D411yescharacteristic
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—22no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43C2×#4111yescharacteristic
169C4×C43H(5,𝔽2)11yescharacteristic
170Dic43—41no—
171Dic43—41no—
172Dic43—41no—
173Dic43—41no—
174#3316—431nomaximal, Sylow
175C2×C43—22no—
176C2×C43—41no—
177C2×C43—81no—
178C2×C43#54611yescharacteristic
179C2×C43C2×#13711yescharacteristic
180C2×C43#57711yescharacteristic
181#554—431no—
182#548D4311yescharacteristic
183#489—431no—
184#483—431no—
185#481—431no—
186#475—431no—
187#470—431no—
188#465—431no—
189#464—431no—
190#452—431no—
191#451—431no—
192#441—431no—
193#435—431no—
194#417—431no—
195C2×#103—431no—
196C43#331611yescharacteristic, complemented, Sylow
197C2×#41C2×D4311yescharacteristic
198C22×Q8C2×D4311yescharacteristic
199C2×Q16—431no—
200C2×Q16—431no—
201C2×SD16—431no—
202C2×M16—431no—
203C22×C8—431no—
204C4⋊Q8—431no—
205#125—861no—
206#124—21no—
207#124C2×D4311yescharacteristic
208C22⋊Q8—21no—
209C22⋊Q8—431no—
210C22⋊Q8—431no—
211C22⋊Q8—861no—
212C22⋊Q8—861no—
213C22⋊Q8C2×D4311yescharacteristic
214#121—21no—
215#121C2×D4311yescharacteristic
216C4×Q8—431no—
217C4×Q8C2×D4311yescharacteristic
218C4×D4—21no—
219C4×D4—861no—
220C4×D4C2×D4311yescharacteristic
221C2×C4⋊C4—431no—
222C2×C4⋊C4—431no—
223#106—431no—
224#106—431no—
225#106—431no—
226C4⋊C8—431no—
227#103—431no—
228#103—431no—
229#103—431no—
230#103—431no—
231#103—431no—
232#103—431no—
233#103—431no—
234#102—431no—
235#102—431no—
236#102—431no—
237C22⋊C8—431no—
238C22⋊C8—431no—
239#97—431no—
240#41—22no—
241#41—41no—
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—431no—
246C2×Q8—861no—
247C2×Q8C22×D4311yescharacteristic
248C2×Q8C22×D4311yescharacteristic
249C2×D4—21no—
250C2×D4—21no—
251C2×D4C22⋊D4311yescharacteristic
252C2×D4C22×D4311yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4C22×D4311yescharacteristic
258C22×C4C22×D4311yescharacteristic
259Q16—862no—
260Q16—1721no—
261SD16—1721no—
262M16—1721no—
263C2×C8—431no—
264C2×C8—431no—
265C2×C8—431no—
266C2×C8—431no—
267C2×C8—1721no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—431no—
271C4⋊C4—431no—
272C4⋊C4—431no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4C22⋊D4311yescharacteristic
280C4⋊C4C22×D4311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4C22⋊D4311yescharacteristic
288C22⋊C4C22⋊D4311yescharacteristic
289C42—21no—
290C42—861no—
291C42C22×D4311yescharacteristic
292C23—21no—
293C23C2×C22⋊D4311yescharacteristic
294C23C2×C22⋊D4311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—861no—
300Q8—861no—
301Q8—3441no—
302Q8#1062190012yes—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—42no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4C2×C22⋊D4311yescharacteristic
324C2×C4C2×C22⋊D4311yescharacteristic
325C2×C4C2×C22⋊D4311yescharacteristic
326C2×C4C2×C22⋊D4311yescharacteristic
327C2×C4C23×D4311yescharacteristic
328C8—861no—
329C8—861no—
330C8—861no—
331C8—861no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#1306335512yes—
341C22C22×C22⋊D4311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—1721no—
350C4—1721no—
351C4—1721no—
352C4—1721no—
353C4C2×#1062190011yescharacteristic
354C4#1306337011yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2#1458354311yescharacteristic
359C2C2×#1306335511yescharacteristic
360C2#1458370711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#548C2
socleC22×C43C22×D4
hypercenter#548D43
hypocenterC43#3316
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #14583606C2semidirect
2. #14583258C2semidirect
3. #14583227C2semidirect
4. #14583215C2semidirect
5. #14583184C2semidirect
6. #14583155C2semidirect
7. #14583126C2semidirect
8. #14583118C2semidirect
9. #14583061C2semidirect
10. #14583055C2semidirect
11. #14583004C2semidirect
12. #14582971C2semidirect
13. #14582900C2semidirect
14. C2×#13063249C2semidirect
196. C43#3316semidirect