Finite Group Databasebeta

← #19147657

Subgroups — #19147657

Order 5504.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583632C211yesmaximal, characteristic, complemented
2#14583621C211yesmaximal, characteristic, complemented
3#14583290C211yesmaximal, characteristic, complemented
4#14583285C211yesmaximal, characteristic
5#14583283C211yesmaximal, characteristic, complemented
6#14583124C211yesmaximal, characteristic, complemented
7#14583121C211yesmaximal, characteristic, complemented
8#14583114C211yesmaximal, characteristic, complemented
9#14583113C211yesmaximal, characteristic, complemented
10#14583103C211yesmaximal, characteristic, complemented
11#14583098C211yesmaximal, characteristic, complemented
12#14583029C211yesmaximal, characteristic, complemented
13#14583010C211yesmaximal, characteristic, complemented
14#14583005C211yesmaximal, characteristic, complemented
15C4×SD16×C43C211yesmaximal, characteristic, complemented
16C2×Dic172C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×#10621883C2211yescharacteristic
21C2×#10621884C2211yescharacteristic
22C2×D344C2211yescharacteristic
23C2×#10621882C2211yescharacteristic
24#13063323C2211yescharacteristic
25#13063321C2211yescharacteristic
26#13063320—21no—
27#13063319—21no—
28#13063314C2211yescharacteristic
29#13063313C2211yescharacteristic
30#13063313C2211yescharacteristic
31#13063312C2211yescharacteristic
32#13063311—21no—
33#13063308—21no—
34#13063307—21no—
35#13063303—21no—
36C4×Dic86C2211yescharacteristic
37#13063290C2211yescharacteristic
38#13063290C2211yescharacteristic
39#13063287C2211yescharacteristic
40#13063287C2211yescharacteristic
41C4×C22⋊D43—21no—
42#13063282—21no—
43C4⋊(C43⋊C8)C2211yescharacteristic
44Dic43⋊C8C2211yescharacteristic
45Dic43⋊C8C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic
50#13063235C2211yescharacteristic
51#13063235C2211yescharacteristic
52C2×SD16×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C4×C8×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C2×D172C2311yescharacteristic
65C2×D172C2311yescharacteristic
66C2×C4×D43—21no—
67C2×C4×D43—21no—
68C2×Dic86D411yescharacteristic
69C2×Dic86C2311yescharacteristic
70C2×Dic86C2311yescharacteristic
71SD16×C43—22no—
72C2×C8×C43C2311yescharacteristic
73C2×C8×C43C2311yescharacteristic
74C4⋊C4×C43—21no—
75C4⋊C4×C43C2311yescharacteristic
76C4⋊C4×C43C2311yescharacteristic
77C22⋊C4×C43—21no—
78C42×C43—21no—
79C42×C43C2311yescharacteristic
80C22⋊Dic43—21no—
81C22⋊Dic43—21no—
82#10621885—41no—
83#10621884—41no—
84#10621883—41no—
85#10621882—41no—
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4—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—
94C4⋊Dic43D411yescharacteristic
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4D411yescharacteristic
100Dic43⋊C4D411yescharacteristic
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43C2311yescharacteristic
104C4×Dic43C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107Dic172—22no—
108D344—22no—
109#10621873—41no—
110#10621873—41no—
111C23×C43—21no—
112C22×D43—21no—
113C22×D43—21no—
114Q8×C43—21no—
115Q8×C43—21no—
116D4×C43—21no—
117D4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—81no—
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2411yescharacteristic
125C22⋊D43—42no—
126C22⋊D43—81no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43C2×D411yescharacteristic
130C2×Dic43C2×D411yescharacteristic
131C2×Dic43C2×D411yescharacteristic
132C2×Dic43C2×D411yescharacteristic
133D172—21no—
134D172—21no—
135D172—21no—
136D172—21no—
137C4×D43—42no—
138C4×D43—81no—
139Dic86—21no—
140Dic86—21no—
141Dic86—21no—
142Dic86—21no—
143Dic86—41no—
144C8×C43—21no—
145C8×C43#4112yes—
146C43⋊C8—21no—
147C43⋊C8—21no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43C22×D411yescharacteristic
152C2×D43—41no—
153C2×D43—41no—
154C2×D43—41no—
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—41no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43C2×#4111yescharacteristic
164C4×C43H(5,𝔽2)11yescharacteristic
165Dic43—21no—
166Dic43—21no—
167Dic43—21no—
168Dic43—21no—
169Dic43—41no—
170Dic43—41no—
171#3401—431nomaximal, Sylow
172C2×C43—81no—
173C2×C43#55011yescharacteristic
174C2×C43#57511yescharacteristic
175C2×C43#57711yescharacteristic
176D43—81no—
177D43—81no—
178#559—431no—
179#556—431no—
180#497—431no—
181#496—431no—
182#495—431no—
183#464—431no—
184#464—431no—
185#463—431no—
186#463—431no—
187#461—431no—
188#460—431no—
189#446—431no—
190#442—431no—
191#441—431no—
192C4×SD16D4311yescharacteristic, complemented
193C43#340111yescharacteristic, complemented, Sylow
194C2×Q16—431no—
195C2×Q16—431no—
196C2×SD16—431no—
197C2×SD16—431no—
198C2×SD16—431no—
199C2×SD16—431no—
200C2×SD16C2×D4311yescharacteristic
201C2×D8—431no—
202C2×D8—431no—
203C4⋊Q8—431no—
204#127—431no—
205#126—861no—
206#126—861no—
207#124—431no—
208#124—431no—
209#124—431no—
210#124—431no—
211#124—861no—
212#123—861no—
213#123—861no—
214C22⋊Q8—861no—
215C4×Q8—431no—
216C4×Q8—431no—
217C4×Q8—431no—
218C4×Q8C2×D4311yescharacteristic
219C4×D4—431no—
220C4×D4—431no—
221C4×D4—861no—
222C4×D4C2×D4311yescharacteristic
223#117—861no—
224#106C2×D4311yescharacteristic
225C4⋊C8—431no—
226C4⋊C8—431no—
227C4⋊C8—431no—
228#103—431no—
229#103—431no—
230#103C2×D4311yescharacteristic
231#102—431no—
232#102—431no—
233#102C2×D4311yescharacteristic
234#97—431no—
235#97—431no—
236C4×C8C2×D4311yescharacteristic
237C2×Q8—431no—
238C2×Q8—431no—
239C2×Q8—431no—
240C2×Q8C22×D4311yescharacteristic
241C2×D4—431no—
242C2×D4—431no—
243C2×D4—861no—
244C2×D4—861no—
245C2×D4C22×D4311yescharacteristic
246C22×C4—21no—
247C22×C4—861no—
248C22×C4—861no—
249Q16—862no—
250Q16—1721no—
251SD16—22no—
252SD16—1721no—
253SD16—1721no—
254SD16—1721no—
255SD16—1721no—
256D8—862no—
257D8—1721no—
258C2×C8—431no—
259C2×C8—431no—
260C2×C8C22×D4311yescharacteristic
261C2×C8C22×D4311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—431no—
264C4⋊C4—431no—
265C4⋊C4—431no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4C22×D4311yescharacteristic
271C4⋊C4C22×D4311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C22⋊C4—861no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C42—21no—
284C42—431no—
285C42—431no—
286C42—861no—
287C42—861no—
288C42C22×D4311yescharacteristic
289C23—21no—
290C23—861no—
291C23—861no—
292Q8—21no—
293Q8—21no—
294Q8—861no—
295Q8—861no—
296Q8—861no—
297Q8—861no—
298Q8—1721no—
299D4—21no—
300D4—21no—
301D4—861no—
302D4—861no—
303D4—861no—
304D4—861no—
305D4—3441no—
306D4—1722no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—431no—
312C2×C4—431no—
313C2×C4—431no—
314C2×C4—431no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—3441no—
318C2×C4—1722no—
319C2×C4D4×D4311yescharacteristic
320C2×C4D4×D4311yescharacteristic
321C2×C4C23×D4311yescharacteristic
322C8—21no—
323C8—861no—
324C8—861no—
325C8#1062189812yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—1721no—
330C22—1721no—
331C22—1721no—
332C22—1721no—
333C22—1721no—
334C22—1721no—
335C22C2×D4×D4311yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—861no—
342C4—861no—
343C4—861no—
344C4—861no—
345C4—1721no—
346C4—1721no—
347C4C2×#1062189811yescharacteristic
348C4#1306337111yescharacteristic
349C2—81no—
350C2—3441no—
351C2—3441no—
352C2#1458357011yescharacteristic
353C2#1458369611yescharacteristic
354C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC4×SD16×C43C2
socleC22×C43C22×D4
hypercenterC4×SD16D43
hypocenterC43#3401
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #14583632C2semidirect
2. #14583621C2semidirect
3. #14583290C2semidirect
5. #14583283C2semidirect
6. #14583124C2semidirect
7. #14583121C2semidirect
8. #14583114C2semidirect
9. #14583113C2semidirect
10. #14583103C2semidirect
11. #14583098C2semidirect
12. #14583029C2semidirect
13. #14583010C2semidirect
14. #14583005C2semidirect
15. C4×SD16×C43C2semidirect
192. C4×SD16D43semidirect
193. C43#3401semidirect