Finite Group Databasebeta

← #19143667

Subgroups — #19143667

Order 5504.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583446C211yesmaximal, characteristic
2#14582975C211yesmaximal, characteristic, complemented
3#14582974C211yesmaximal, characteristic, complemented
4#14582972C211yesmaximal, characteristic, complemented
5#14582971C211yesmaximal, characteristic, complemented
6#14582969C211yesmaximal, characteristic, complemented
7C8×C22⋊D43C211yesmaximal, characteristic, complemented
8(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
9#14582954C211yesmaximal, characteristic, complemented
10#14582951C211yesmaximal, characteristic, complemented
11#14582867C211yesmaximal, characteristic, complemented
12#14582865C211yesmaximal, characteristic, complemented
13#14582864C211yesmaximal, characteristic, complemented
14#14582864C211yesmaximal, characteristic, complemented
15C43×#435C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621898C2211yescharacteristic
18C2×#10621877C2211yescharacteristic
19C2×#10621872C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21C22×C43⋊C8C2211yescharacteristic
22C2×C8×D43C2211yescharacteristic
23C2×C8×D43C2211yescharacteristic
24#13063324C411yescharacteristic
25#13063321C411yescharacteristic
26#13063311C411yescharacteristic
27#13063311C411yescharacteristic
28#13063300C411yescharacteristic
29#13063298C411yescharacteristic
30#13063298C411yescharacteristic
31#13063296C411yescharacteristic
32C4×D172C2211yescharacteristic
33C4×C22⋊D43C2211yescharacteristic
34C4×C22⋊D43C2211yescharacteristic
35C42×D43C2211yescharacteristic
36C4⋊(C43⋊C8)C2211yescharacteristic
37Dic43⋊C8C2211yescharacteristic
38Dic43⋊C8C2211yescharacteristic
39C22⋊(C43⋊C8)C2211yescharacteristic
40C22⋊(C43⋊C8)C2211yescharacteristic
41(C2×D43)⋊C8C2211yescharacteristic
42(C2×D43)⋊C8C2211yescharacteristic
43(C2×D43)⋊C8C2211yescharacteristic
44(C2×D43)⋊C8C2211yescharacteristic
45(C2×D43)⋊C8C2211yescharacteristic
46(C2×D43)⋊C8C2211yescharacteristic
47(C2×D43)⋊C8C2211yescharacteristic
48(C2×D43)⋊C8C2211yescharacteristic
49#13063236C2211yescharacteristic
50C8×Dic43C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×M16×C43C2211yescharacteristic
53C22×C8×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55C4⋊C8×C43C2211yescharacteristic
56C22⋊C8×C43C2211yescharacteristic
57C22⋊C8×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×D4×C43C2×C411yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C2×C22⋊D43C2×C411yescharacteristic
63C2×C22⋊D43C2×C411yescharacteristic
64C2×C22⋊D43C2×C411yescharacteristic
65C2×C22⋊D43C2×C411yescharacteristic
66C2×C22⋊D43C2×C411yescharacteristic
67C2×C22⋊D43C2×C411yescharacteristic
68#10621898—41no—
69#10621898—41no—
70#10621898—41no—
71#10621898—41no—
72C2×D172C2×C411yescharacteristic
73C2×D172C2×C411yescharacteristic
74C2×D172C2×C411yescharacteristic
75C2×C4×D43C2×C411yescharacteristic
76C2×C4×D43C2×C411yescharacteristic
77C2×C4×D43C2311yescharacteristic
78C2×C4×D43C2311yescharacteristic
79C2×C4×D43C2311yescharacteristic
80C2×Dic86C2×C411yescharacteristic
81C2×Dic86C2×C411yescharacteristic
82M16×C43—41no—
83C2×C8×C43—41no—
84C2×C8×C43C2311yescharacteristic
85C2×C8×C43C2311yescharacteristic
86C2×C8×C43C2311yescharacteristic
87C2×C8×C43C2311yescharacteristic
88C4⋊C4×C43C2×C411yescharacteristic
89C22⋊C4×C43C2×C411yescharacteristic
90C22⋊C4×C43C2×C411yescharacteristic
91C42×C43C2311yescharacteristic
92C22⋊Dic43C2×C411yescharacteristic
93C22⋊Dic43C2×C411yescharacteristic
94(C2×D43)⋊C4C2×C411yescharacteristic
95(C2×D43)⋊C4C2×C411yescharacteristic
96(C2×D43)⋊C4C2×C411yescharacteristic
97(C2×D43)⋊C4C2×C411yescharacteristic
98C4⋊Dic43C2×C411yescharacteristic
99Dic43⋊C4C2×C411yescharacteristic
100Dic43⋊C4C2×C411yescharacteristic
101C4×Dic43C2×C411yescharacteristic
102C4×Dic43C2×C411yescharacteristic
103C4×Dic43C2311yescharacteristic
104#10621877—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110#10621872—41no—
111#10621872—41no—
112C8×D43—41no—
113C8×D43—41no—
114C23×C43C22×C411yescharacteristic
115C23×C43C22×C411yescharacteristic
116C22×D43C22×C411yescharacteristic
117C22×D43C22×C411yescharacteristic
118C22×D43C22×C411yescharacteristic
119D4×C43—41no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43C22×C411yescharacteristic
125C2×C4×C43C22×C411yescharacteristic
126C2×C4×C43C22×C411yescharacteristic
127C2×C4×C43C22×C411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43—22no—
130C22⋊D43—22no—
131C22⋊D43—41no—
132C22⋊D43—41no—
133C22⋊D43—41no—
134C22⋊D43—41no—
135C2×Dic43C22×C411yescharacteristic
136C2×Dic43C22×C411yescharacteristic
137C2×Dic43C22×C411yescharacteristic
138C2×Dic43C22×C411yescharacteristic
139C2×Dic43C22×C411yescharacteristic
140D172—41no—
141D172—41no—
142D172—41no—
143C4×D43—21no—
144C4×D43—21no—
145C4×D43—21no—
146C4×D43—21no—
147C4×D43—21no—
148C4×D43—21no—
149C4×D43—22no—
150C4×D43—41no—
151Dic86—41no—
152Dic86—41no—
153C8×C43—21no—
154C8×C43—21no—
155C8×C43—21no—
156C8×C43—21no—
157C43⋊C8—21no—
158C43⋊C8—21no—
159C43⋊C8—21no—
160C43⋊C8—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43C23×C411yescharacteristic
168C2×D43—21no—
169C2×D43—21no—
170C2×D43—21no—
171C2×D43—21no—
172C2×D43—21no—
173C2×D43—21no—
174C2×D43—21no—
175C2×D43—21no—
176C2×D43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43H(5,𝔽2)11yescharacteristic
182C4×C43H(5,𝔽2)11yescharacteristic
183Dic43—21no—
184Dic43—21no—
185Dic43—21no—
186Dic43—21no—
187Dic43#13112yes—
188#2981—431nomaximal, Sylow
189C2×C43—41no—
190C2×C43—41no—
191C2×C43#51811yescharacteristic
192C2×C43C2×#13111yescharacteristic
193C2×C43#56811yescharacteristic
194D43—41no—
195D43—41no—
196D43—41no—
197#532—431no—
198#436—431no—
199#436—431no—
200#435—431no—
201#435—431no—
202#435—431no—
203#435D4311yescharacteristic, complemented
204C8×D4—431no—
205C8×D4—431no—
206#432—431no—
207#431—431no—
208#408—431no—
209#408—431no—
210#408—431no—
211#408—431no—
212C43#298111yescharacteristic, complemented, Sylow
213C2×#41—431no—
214C2×#41—431no—
215C2×M16—431no—
216C2×M16—431no—
217C2×M16—431no—
218C2×M16C2×D4311yescharacteristic
219C22×C8—431no—
220C22×C8—431no—
221C22×C8—431no—
222C22×C8C2×D4311yescharacteristic
223C4⋊Q8—431no—
224#127—431no—
225#124—431no—
226#124—431no—
227#121—431no—
228#121—431no—
229#121—431no—
230#121—431no—
231C4×D4—431no—
232C4×D4—431no—
233C4×D4—431no—
234C4×D4C2×D4311yescharacteristic
235C2×C42—431no—
236C4⋊C8—431no—
237C4⋊C8—431no—
238C4⋊C8—431no—
239C4⋊C8C2×D4311yescharacteristic
240C22⋊C8—431no—
241C22⋊C8—431no—
242C22⋊C8—431no—
243C22⋊C8—431no—
244C22⋊C8—431no—
245C22⋊C8—431no—
246C22⋊C8—431no—
247C22⋊C8—431no—
248C22⋊C8—431no—
249C22⋊C8—431no—
250C22⋊C8C2×D4311yescharacteristic
251C22⋊C8C2×D4311yescharacteristic
252#97—431no—
253#97C2×D4311yescharacteristic
254C4×C8—431no—
255C4×C8—431no—
256#41—1721no—
257#41—1721no—
258#41—1721no—
259#41—1721no—
260C2×Q8—431no—
261C2×Q8—431no—
262C2×D4—431no—
263C2×D4—431no—
264C2×D4—431no—
265C2×D4—431no—
266C2×D4—431no—
267C2×D4—431no—
268C2×D4—431no—
269C2×D4—431no—
270C2×D4—431no—
271C2×D4C4×D4311yescharacteristic
272C22×C4—431no—
273C22×C4—431no—
274C22×C4—431no—
275C22×C4—431no—
276C22×C4—431no—
277C22×C4C22×D4311yescharacteristic
278C22×C4C22×D4311yescharacteristic
279M16—41no—
280M16—1721no—
281M16—1721no—
282M16—1721no—
283C2×C8—41no—
284C2×C8—431no—
285C2×C8—431no—
286C2×C8—431no—
287C2×C8—431no—
288C2×C8—1721no—
289C2×C8—1721no—
290C2×C8—1721no—
291C2×C8C22×D4311yescharacteristic
292C2×C8C22×D4311yescharacteristic
293C2×C8C22×D4311yescharacteristic
294C2×C8C22×D4311yescharacteristic
295C4⋊C4—431no—
296C4⋊C4—431no—
297C4⋊C4—431no—
298C4⋊C4C4×D4311yescharacteristic
299C22⋊C4—431no—
300C22⋊C4—431no—
301C22⋊C4—431no—
302C22⋊C4—431no—
303C22⋊C4—431no—
304C22⋊C4—431no—
305C22⋊C4C4×D4311yescharacteristic
306C22⋊C4C4×D4311yescharacteristic
307C42—431no—
308C42—431no—
309C42—431no—
310C42C22×D4311yescharacteristic
311C23—431no—
312C23—431no—
313C23—431no—
314C23C2×C4×D4311yescharacteristic
315C23C2×C4×D4311yescharacteristic
316Q8—1721no—
317Q8—1721no—
318D4—41no—
319D4—862no—
320D4—862no—
321D4—1721no—
322D4—1721no—
323D4—1721no—
324D4—1721no—
325D4—1721no—
326D4—1721no—
327D4—1721no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—431no—
333C2×C4—431no—
334C2×C4—431no—
335C2×C4—431no—
336C2×C4—431no—
337C2×C4—862no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—1721no—
345C2×C4C2×C4×D4311yescharacteristic
346C2×C4C2×C4×D4311yescharacteristic
347C2×C4C2×C4×D4311yescharacteristic
348C2×C4C2×C4×D4311yescharacteristic
349C2×C4C23×D4311yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C8—861no—
355C8—861no—
356C8—861no—
357C8—861no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—861no—
365C22—861no—
366C22—861no—
367C22—861no—
368C22—861no—
369C22—861no—
370C22—861no—
371C22—861no—
372C22—861no—
373C22C22×C4×D4311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—432no—
379C4—861no—
380C4—861no—
381C4—861no—
382C4—861no—
383C4#1306337011yescharacteristic
384C4#1306337111yescharacteristic
385C2—41no—
386C2—41no—
387C2—1721no—
388C2—1721no—
389C2—1721no—
390C2#1458337111yescharacteristic
391C2#131×D4311yescharacteristic
392C2#1458366511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D43
commutator, socleC22×C43C23×C4
FittingC43×#435C2
hypercenter#435D43
hypocenterC43#2981
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #14582975C2semidirect
3. #14582974C2semidirect
4. #14582972C2semidirect
5. #14582971C2semidirect
6. #14582969C2semidirect
7. C8×C22⋊D43C2semidirect
8. (C22⋊D43)⋊C8C2semidirect
9. #14582954C2semidirect
10. #14582951C2semidirect
11. #14582867C2semidirect
12. #14582865C2semidirect
13. #14582864C2semidirect
14. #14582864C2semidirect
15. C43×#435C2semidirect
203. #435D43semidirect
212. C43#2981semidirect