Finite Group Databasebeta

← #19146714

Subgroups — #19146714

Order 5504.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583591C211yesmaximal, characteristic, complemented
2#14583568C211yesmaximal, characteristic
3#14583262C211yesmaximal, characteristic, complemented
4#14583222C211yesmaximal, characteristic, complemented
5#14583218C211yesmaximal, characteristic, complemented
6#14583204C211yesmaximal, characteristic, complemented
7#14583147C211yesmaximal, characteristic, complemented
8#14583125C211yesmaximal, characteristic, complemented
9#14583097C211yesmaximal, characteristic, complemented
10#14583060C211yesmaximal, characteristic, complemented
11#14583006C211yesmaximal, characteristic, complemented
12#14582973C211yesmaximal, characteristic, complemented
13#14582900C211yesmaximal, characteristic, complemented
14#14582894C211yesmaximal, characteristic, complemented
15C43×#452C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621884C2211yescharacteristic
18C2×#10621877C2211yescharacteristic
19C2×C8×D43C2211yescharacteristic
20#13063321—21no—
21#13063321C2211yescharacteristic
22#13063320—21no—
23#13063316—21no—
24#13063316C2211yescharacteristic
25#13063309—21no—
26#13063301C2211yescharacteristic
27#13063299—21no—
28#13063299C2211yescharacteristic
29#13063296—21no—
30#13063296C2211yescharacteristic
31Q8×Dic43C2211yescharacteristic
32Q8×Dic43C2211yescharacteristic
33C4×C22⋊D43—21no—
34C4×C22⋊D43C2211yescharacteristic
35#13063283C2211yescharacteristic
36#13063281—21no—
37C2×C4⋊Dic43C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063257C2211yescharacteristic
40#13063257C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42#13063249C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063235C2211yescharacteristic
52C2×#41×C43C2211yescharacteristic
53C2×Q16×C43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59#41×C43—22no—
60#41×C43—41no—
61C2×Q8×C43C2311yescharacteristic
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43D411yescharacteristic
72C22×Dic43—21no—
73#10621902—22no—
74#10621902—41no—
75C2×D172—21no—
76C2×D172C2311yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43C2311yescharacteristic
79Q16×C43—22no—
80SD16×C43—41no—
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C4⋊C4×C43—21no—
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43D411yescharacteristic
88#10621884—41no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4D411yescharacteristic
93C4⋊Dic43—21no—
94C4⋊Dic43—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4D411yescharacteristic
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107#10621877—41no—
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C8×D43—41no—
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43C2×D411yescharacteristic
115Q8×C43—21no—
116Q8×C43—21no—
117Q8×C43—21no—
118Q8×C43#4112yes—
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—42no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—42no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—41no—
131C22⋊D43—42no—
132C22⋊D43—81no—
133C22⋊D43—81no—
134C22⋊D43—81no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—42no—
139C2×Dic43C2×D411yescharacteristic
140C2×Dic43C2×D411yescharacteristic
141C2×Dic43C2×D411yescharacteristic
142D172—21no—
143D172—21no—
144D172—42no—
145C4×D43—21no—
146C4×D43—21no—
147C4×D43—42no—
148C8×C43—21no—
149C8×C43—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43C22×D411yescharacteristic
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C4×C43—22no—
166C4×C43—21no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43C2×#4111yescharacteristic
170C4×C43H(5,𝔽2)11yescharacteristic
171Dic43—21no—
172Dic43—21no—
173Dic43—21no—
174Dic43—41no—
175Dic43—41no—
176Dic43—41no—
177#3317—431nomaximal, Sylow
178C2×C43—41no—
179C2×C43—81no—
180C2×C43#54611yescharacteristic
181C2×C43#57511yescharacteristic
182C2×C43#57711yescharacteristic
183D43—41no—
184D43—81no—
185#552—431no—
186#550—431no—
187#490—431no—
188#482—431no—
189#481—431no—
190#479—431no—
191#468—431no—
192#465—431no—
193#460—431no—
194#452—431no—
195#452D4311yescharacteristic, complemented
196#441—431no—
197#435—431no—
198#417—431no—
199#416—431no—
200C43#331711yescharacteristic, complemented, Sylow
201C2×#41—431no—
202C2×#41C2×D4311yescharacteristic
203C2×Q16C2×D4311yescharacteristic
204C2×SD16—431no—
205C2×SD16C2×D4311yescharacteristic
206C2×M16—431no—
207C22×C8—431no—
208#127—431no—
209#127—861no—
210#126—861no—
211#125—431no—
212#125—861no—
213#123—861no—
214C22⋊Q8—431no—
215C22⋊Q8C2×D4311yescharacteristic
216#121—431no—
217#121—431no—
218#121—861no—
219#121—861no—
220C4×Q8—431no—
221C4×Q8—431no—
222C4×D4—431no—
223C4×D4—861no—
224#117—431no—
225#117—861no—
226C2×C4⋊C4—431no—
227#107—431no—
228#106—431no—
229#106—431no—
230C4⋊C8—431no—
231#103—431no—
232#103—431no—
233#103—431no—
234#103C2×D4311yescharacteristic
235#102—431no—
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102C2×D4311yescharacteristic
241C22⋊C8—431no—
242C22⋊C8C2×D4311yescharacteristic
243#97—431no—
244#41—22no—
245#41—41no—
246#41—862no—
247#41—1721no—
248C2×Q8C22×D4311yescharacteristic
249C2×Q8C22×D4311yescharacteristic
250C2×D4—21no—
251C2×D4—431no—
252C2×D4—431no—
253C2×D4—861no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4C22×D4311yescharacteristic
259C22×C4—21no—
260C22×C4—431no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4C22×D4311yescharacteristic
264Q16—22no—
265SD16—41no—
266SD16—1721no—
267M16—1721no—
268C2×C8—431no—
269C2×C8—431no—
270C2×C8—1721no—
271C2×C8C22×D4311yescharacteristic
272C2×C8C22×D4311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—431no—
277C4⋊C4—431no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4C22×D4311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—431no—
287C22⋊C4—431no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C42—431no—
293C42—861no—
294C42—861no—
295C42—861no—
296C23—21no—
297C23—431no—
298C23—861no—
299C23D4×D4311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8#1062190012yes—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—861no—
308D4—861no—
309D4—3441no—
310D4—3441no—
311D4—3441no—
312D4—1722no—
313D4—1721no—
314D4—1722no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—431no—
322C2×C4—431no—
323C2×C4—431no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—1722no—
330C2×C4—1722no—
331C2×C4D4×D4311yescharacteristic
332C2×C4C23×D4311yescharacteristic
333C8—21no—
334C8—21no—
335C8—861no—
336C8—861no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—861no—
344C22—861no—
345C22—861no—
346C22—1721no—
347C22—1721no—
348C22—1721no—
349C22C2×D4×D4311yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—861no—
355C4—861no—
356C4—861no—
357C4—1721no—
358C4—1721no—
359C4—1721no—
360C4C2×#1062190011yescharacteristic
361C4#1306337011yescharacteristic
362C2—41no—
363C2—81no—
364C2—3441no—
365C2—1721no—
366C2#1458353611yescharacteristic
367C2#1458369811yescharacteristic
368C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#452C2
socleC22×C43C22×D4
hypercenter#452D43
hypocenterC43#3317
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #14583591C2semidirect
3. #14583262C2semidirect
4. #14583222C2semidirect
5. #14583218C2semidirect
6. #14583204C2semidirect
7. #14583147C2semidirect
8. #14583125C2semidirect
9. #14583097C2semidirect
10. #14583060C2semidirect
11. #14583006C2semidirect
12. #14582973C2semidirect
13. #14582900C2semidirect
14. #14582894C2semidirect
15. C43×#452C2semidirect
195. #452D43semidirect
200. C43#3317semidirect