Finite Group Databasebeta

← #19146501

Subgroups — #19146501

Order 5504.

398 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#14583601C211yesmaximal, characteristic, complemented
2#14583560C211yesmaximal, characteristic, complemented
3#14583255C211yesmaximal, characteristic, complemented
4#14583238C211yesmaximal, characteristic, complemented
5#14583218C211yesmaximal, characteristic, complemented
6#14583204C211yesmaximal, characteristic, complemented
7#14583133C211yesmaximal, characteristic, complemented
8#14583125C211yesmaximal, characteristic, complemented
9#14583116C211yesmaximal, characteristic, complemented
10#14583043C211yesmaximal, characteristic, complemented
11SD16×Dic43C211yesmaximal, characteristic, complemented
12(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
13#14582894C211yesmaximal, characteristic, complemented
14C2×#13063249C211yesmaximal, characteristic, complemented
15C43×#448C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621882C2211yescharacteristic
18C22×C43⋊C8C2211yescharacteristic
19C2×C8×D43C2211yescharacteristic
20#13063318—21no—
21#13063316C2211yescharacteristic
22#13063314—21no—
23#13063314C2211yescharacteristic
24#13063309—21no—
25#13063301—21no—
26#13063301C2211yescharacteristic
27#13063299—21no—
28#13063299C2211yescharacteristic
29#13063297—21no—
30#13063296C2211yescharacteristic
31Q8×Dic43C2211yescharacteristic
32D4×Dic43—21no—
33D4×Dic43C2211yescharacteristic
34C4×C22⋊D43—21no—
35C4×C22⋊D43C2211yescharacteristic
36#13063283C2211yescharacteristic
37C2×C4⋊Dic43C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063257C2211yescharacteristic
40#13063257C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42#13063249C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C22×Q8×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43—22no—
61C2×Q8×C43—41no—
62C2×Q8×C43C2311yescharacteristic
63C2×Q8×C43C2311yescharacteristic
64C2×D4×C43—21no—
65C2×D4×C43C2311yescharacteristic
66C22×C4×C43—21no—
67C22×C4×C43C2311yescharacteristic
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43D411yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73#10621902—22no—
74#10621902—41no—
75C2×D172—21no—
76C2×D172C2311yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43C2311yescharacteristic
79SD16×C43—22no—
80SD16×C43—41no—
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C22⋊C4×C43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43D411yescharacteristic
88#10621882—41no—
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)⋊C4D411yescharacteristic
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4D411yescharacteristic
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107C2×C43⋊C8—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—42no—
119Q8×C43#4112yes—
120D4×C43—21no—
121D4×C43—21no—
122D4×C43—42no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—42no—
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2411yescharacteristic
131C22⋊D43—22no—
132C22⋊D43—42no—
133C22⋊D43—81no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—81no—
138C2×Dic43—81no—
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—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43#13512yes—
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#3301—431nomaximal, Sylow
178C2×C43—22no—
179C2×C43—81no—
180C2×C43#54611yescharacteristic
181C2×C43C2×#13511yescharacteristic
182C2×C43#57711yescharacteristic
183D43—41no—
184D43—81no—
185#553—431no—
186#548—431no—
187#488—431no—
188#485—431no—
189#481—431no—
190#479—431no—
191#466—431no—
192#465—431no—
193#463—431no—
194#449—431no—
195#448D4311yescharacteristic, complemented
196C4×SD16—431no—
197C8×D4—431no—
198#416—431no—
199C2×#103—431no—
200C43#330111yescharacteristic, complemented, Sylow
201C2×#41—431no—
202C22×Q8C2×D4311yescharacteristic
203C2×SD16C2×D4311yescharacteristic
204C2×SD16C2×D4311yescharacteristic
205C2×D8—431no—
206C22×C8—431no—
207C22×C8—431no—
208#126—861no—
209#125—431no—
210#124—431no—
211#124—861no—
212#123—861no—
213C22⋊Q8—431no—
214C22⋊Q8—861no—
215#121—431no—
216#121—431no—
217#121—861no—
218#121—861no—
219#121C2×D4311yescharacteristic
220C4×Q8—431no—
221C4×D4—431no—
222C4×D4—431no—
223C4×D4—861no—
224C4×D4—861no—
225#117—431no—
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#103—431no—
235#103C2×D4311yescharacteristic
236#103C2×D4311yescharacteristic
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241C22⋊C8—431no—
242C22⋊C8C2×D4311yescharacteristic
243C4×C8—431no—
244#41—862no—
245#41—1721no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D4311yescharacteristic
250C2×Q8C22×D4311yescharacteristic
251C2×D4—21no—
252C2×D4—431no—
253C2×D4—431no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4C22×D4311yescharacteristic
258C22×C4—21no—
259C22×C4—431no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4C22×D4311yescharacteristic
264SD16—22no—
265SD16—41no—
266D8—1721no—
267C2×C8—431no—
268C2×C8—431no—
269C2×C8—1721no—
270C2×C8—1721no—
271C2×C8C22×D4311yescharacteristic
272C2×C8C22×D4311yescharacteristic
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—431no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4C22×D4311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—431no—
285C22⋊C4—431no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C42—431no—
294C42—861no—
295C42—861no—
296C23—21no—
297C23—431no—
298C23—861no—
299C23D4×D4311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#1062190012yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—862no—
309D4—861no—
310D4—861no—
311D4—3441no—
312D4—1722no—
313D4—1722no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—431no—
321C2×C4—431no—
322C2×C4—431no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—3441no—
329C2×C4—3441no—
330C2×C4—1722no—
331C2×C4D4×D4311yescharacteristic
332C2×C4C23×D4311yescharacteristic
333C8—21no—
334C8—21no—
335C8—861no—
336C8—861no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—861no—
343C22—861no—
344C22—861no—
345C22—1721no—
346C22—1721no—
347C22—1721no—
348C22#1306334612yes—
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—22no—
363C2—81no—
364C2—3441no—
365C2—1721no—
366C2#1458353611yescharacteristic
367C2C2×#1306334611yescharacteristic
368C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#448C2
socleC22×C43C22×D4
hypercenter#448D43
hypocenterC43#3301
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #14583601C2semidirect
2. #14583560C2semidirect
3. #14583255C2semidirect
4. #14583238C2semidirect
5. #14583218C2semidirect
6. #14583204C2semidirect
7. #14583133C2semidirect
8. #14583125C2semidirect
9. #14583116C2semidirect
10. #14583043C2semidirect
11. SD16×Dic43C2semidirect
12. (C22⋊D43)⋊C8C2semidirect
13. #14582894C2semidirect
14. C2×#13063249C2semidirect
15. C43×#448C2semidirect
195. #448D43semidirect
200. C43#3301semidirect