Finite Group Databasebeta

← #19145706

Subgroups — #19145706

Order 5504.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583520C211yesmaximal, characteristic, complemented
2#14583475C211yesmaximal, characteristic, complemented
3#14583293C211yesmaximal, characteristic, complemented
4#14583283C211yesmaximal, characteristic, complemented
5#14583259C211yesmaximal, characteristic, complemented
6#14583250C211yesmaximal, characteristic, complemented
7#14583122C211yesmaximal, characteristic, complemented
8#14583115C211yesmaximal, characteristic, complemented
9#14583110C211yesmaximal, characteristic, complemented
10#14583105C211yesmaximal, characteristic, complemented
11#14583063C211yesmaximal, characteristic, complemented
12#14583057C211yesmaximal, characteristic, complemented
13#14583046C211yesmaximal, characteristic
14#14583040C211yesmaximal, characteristic, complemented
15C43×#433C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×Dic86C2211yescharacteristic
18C2×Dic172C2211yescharacteristic
19C2×Dic172C2211yescharacteristic
20C2×Dic172C2211yescharacteristic
21C2×#10621873C2211yescharacteristic
22C2×#10621873C2211yescharacteristic
23C2×#10621873C2211yescharacteristic
24C2×#10621873C2211yescharacteristic
25C2×D344C2211yescharacteristic
26#13063325C2211yescharacteristic
27#13063325C2211yescharacteristic
28#13063325C2211yescharacteristic
29#13063320—21no—
30#13063313C2211yescharacteristic
31#13063313C2211yescharacteristic
32#13063313C2211yescharacteristic
33#13063311—21no—
34#13063309—21no—
35#13063309—21no—
36#13063307—21no—
37#13063305—21no—
38#13063305—21no—
39#13063304C2211yescharacteristic
40#13063303—21no—
41#13063299C2211yescharacteristic
42C4×Dic86C2211yescharacteristic
43C4×D172C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063250C2211yescharacteristic
46#13063250C2211yescharacteristic
47#13063250C2211yescharacteristic
48#13063250C2211yescharacteristic
49#13063250C2211yescharacteristic
50#13063247C2211yescharacteristic
51#13063247C2211yescharacteristic
52#117×C43C2211yescharacteristic
53C4⋊C8×C43C2211yescharacteristic
54C4⋊C8×C43C2211yescharacteristic
55C22⋊C8×C43C2211yescharacteristic
56C22⋊C8×C43C2211yescharacteristic
57#97×C43C2211yescharacteristic
58C4×C8×C43C2211yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C2×C22⋊D43—21no—
61C2×C22⋊D43—21no—
62C22×Dic43—21no—
63#10621898—41no—
64#10621898—41no—
65C2×D172C2311yescharacteristic
66C2×D172C2311yescharacteristic
67C2×C4×D43—21no—
68C2×C4×D43—21no—
69C2×Dic86—21no—
70C2×Dic86—21no—
71C2×Dic86—41no—
72C2×Dic86—41no—
73C2×Dic86C2311yescharacteristic
74C2×Dic86C2311yescharacteristic
75C2×Dic86C2311yescharacteristic
76C2×Dic86C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43D411yescharacteristic
82C4⋊C4×C43D411yescharacteristic
83C22⋊C4×C43D411yescharacteristic
84C22⋊C4×C43D411yescharacteristic
85C42×C43C2311yescharacteristic
86C42×C43C2311yescharacteristic
87C22⋊Dic43—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43C2311yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105C4×Dic43—21no—
106Dic172—41no—
107Dic172—41no—
108Dic172—41no—
109D344—41no—
110#10621873—41no—
111#10621873—41no—
112#10621873—41no—
113#10621873—41no—
114C23×C43C2×D411yescharacteristic
115C22×D43—21no—
116C22×D43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43C2×D411yescharacteristic
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2×D411yescharacteristic
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2411yescharacteristic
125C22⋊D43—42no—
126C22⋊D43—81no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—42no—
134D172—21no—
135D172—21no—
136D172—21no—
137D172—21no—
138C4×D43—42no—
139C4×D43—81no—
140Dic86—21no—
141Dic86—21no—
142Dic86—21no—
143Dic86—21no—
144Dic86—21no—
145Dic86—21no—
146Dic86—21no—
147Dic86—21no—
148Dic86—42no—
149Dic86—81no—
150C8×C43—21no—
151C8×C43—21no—
152C8×C43—21no—
153C8×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43C22×D411yescharacteristic
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43H(5,𝔽2)11yescharacteristic
170C4×C43H(5,𝔽2)11yescharacteristic
171Dic43—41no—
172Dic43—41no—
173Dic43—41no—
174Dic43—41no—
175Dic43—41no—
176Dic43—41no—
177#3225—431nomaximal, Sylow
178C2×C43—41no—
179C2×C43#53511yescharacteristic
180C2×C43#57711yescharacteristic
181C2×C43#57811yescharacteristic
182D43—81no—
183D43—81no—
184#542—431no—
185#536—431no—
186#497—431no—
187#495—431no—
188#489—431no—
189#487—431no—
190#464—431no—
191#463—431no—
192#462—431no—
193#461—431no—
194#452—431no—
195#451—431no—
196#449—431no—
197#448—431no—
198#433D4311yescharacteristic, complemented
199C43#322511yescharacteristic, complemented, Sylow
200C2×#41—431no—
201C22×Q8—431no—
202C2×Q16—431no—
203C2×Q16—431no—
204C2×Q16—431no—
205C2×SD16—431no—
206C2×SD16—431no—
207C2×SD16—431no—
208C2×SD16—431no—
209C2×D8—431no—
210C4⋊Q8—431no—
211C4⋊Q8—431no—
212C4⋊Q8—431no—
213#126—861no—
214#124—431no—
215#124—431no—
216#124—431no—
217#124—861no—
218#123—861no—
219#123—861no—
220#123—861no—
221C22⋊Q8—431no—
222C22⋊Q8—861no—
223C22⋊Q8—861no—
224C22⋊Q8—861no—
225#121—431no—
226C4×Q8—431no—
227C4×D4—431no—
228#117C2×D4311yescharacteristic
229C4⋊C8C2×D4311yescharacteristic
230C4⋊C8C2×D4311yescharacteristic
231#103—431no—
232#103—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#103—431no—
237#102—431no—
238#102—431no—
239C22⋊C8C2×D4311yescharacteristic
240C22⋊C8C2×D4311yescharacteristic
241#97C2×D4311yescharacteristic
242C4×C8C2×D4311yescharacteristic
243#41—1721no—
244#41—1721no—
245C2×Q8—431no—
246C2×Q8—431no—
247C2×Q8—431no—
248C2×Q8—431no—
249C2×Q8—861no—
250C2×Q8—861no—
251C2×Q8—1721no—
252C2×Q8—1721no—
253C2×D4—431no—
254C2×D4—431no—
255C2×D4—861no—
256C2×D4—861no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4C22×D4311yescharacteristic
261Q16—1721no—
262Q16—1721no—
263Q16—1721no—
264SD16—1721no—
265SD16—1721no—
266SD16—1721no—
267SD16—1721no—
268D8—1721no—
269C2×C8C22×D4311yescharacteristic
270C2×C8C22×D4311yescharacteristic
271C2×C8C22×D4311yescharacteristic
272C2×C8C22×D4311yescharacteristic
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4D17211yescharacteristic
283C4⋊C4D17211yescharacteristic
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4D17211yescharacteristic
294C22⋊C4D17211yescharacteristic
295C42—861no—
296C42C22×D4311yescharacteristic
297C42C22×D4311yescharacteristic
298C23—861no—
299C23—861no—
300C23C2×D17211yescharacteristic
301Q8—861no—
302Q8—861no—
303Q8—861no—
304Q8—861no—
305Q8—861no—
306Q8—861no—
307Q8—861no—
308Q8—861no—
309Q8—3441no—
310Q8—1722no—
311D4—861no—
312D4—861no—
313D4—861no—
314D4—861no—
315D4—3441no—
316D4—1722no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—861no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—3441no—
326C2×C4—1722no—
327C2×C4—1722no—
328C2×C4C2×D17211yescharacteristic
329C2×C4C2×D17211yescharacteristic
330C2×C4C2×D17211yescharacteristic
331C2×C4C2×D17211yescharacteristic
332C2×C4C2×D17211yescharacteristic
333C2×C4C23×D4311yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—1721no—
342C22—1721no—
343C22—1721no—
344C22—1721no—
345C22—1721no—
346C22—1721no—
347C22C22×D17211yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—1721no—
354C4—1721no—
355C4—1721no—
356C4—1721no—
357C4—1721no—
358C4—1721no—
359C4#1306337111yescharacteristic
360C4#1306337111yescharacteristic
361C2—41no—
362C2—3441no—
363C2—3441no—
364C2#1458346811yescharacteristic
365C2#1458371111yescharacteristic
366C2#1458371611yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#433C2
socleC22×C43C22×D4
hypercenter#433D43
hypocenterC43#3225
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #14583520C2semidirect
2. #14583475C2semidirect
3. #14583293C2semidirect
4. #14583283C2semidirect
5. #14583259C2semidirect
6. #14583250C2semidirect
7. #14583122C2semidirect
8. #14583115C2semidirect
9. #14583110C2semidirect
10. #14583105C2semidirect
11. #14583063C2semidirect
12. #14583057C2semidirect
14. #14583040C2semidirect
15. C43×#433C2semidirect
198. #433D43semidirect
199. C43#3225semidirect