Finite Group Databasebeta

← #19144863

Subgroups — #19144863

Order 5504.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583521C211yesmaximal, characteristic, complemented
2#14583381C211yesmaximal, characteristic, complemented
3#14583233C211yesmaximal, characteristic, complemented
4#14583214C211yesmaximal, characteristic, complemented
5#14583192C211yesmaximal, characteristic, complemented
6#14583178C211yesmaximal, characteristic, complemented
7#14583123C211yesmaximal, characteristic, complemented
8#14583117C211yesmaximal, characteristic, complemented
9#14583060C211yesmaximal, characteristic, complemented
10#14583047C211yesmaximal, characteristic
11#14582997C211yesmaximal, characteristic, complemented
12#14582997C211yesmaximal, characteristic, complemented
13C4×D344C211yesmaximal, characteristic, complemented
14#14582958C211yesmaximal, characteristic, complemented
15C4×Q16×C43C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621884C2211yescharacteristic
18C2×#10621884C2211yescharacteristic
19C2×D344C2211yescharacteristic
20#13063324C2211yescharacteristic
21#13063319—21no—
22#13063314C2211yescharacteristic
23#13063313—21no—
24#13063310—21no—
25#13063303—21no—
26#13063301C2211yescharacteristic
27#13063300C2211yescharacteristic
28Q8×Dic43C2211yescharacteristic
29C4×D172—21no—
30C4×D172C2211yescharacteristic
31C4×D172C2211yescharacteristic
32#13063287—21no—
33#13063287C2211yescharacteristic
34#13063282—21no—
35#13063282C2211yescharacteristic
36C4⋊C4×D43—21no—
37C4⋊C4×D43C2211yescharacteristic
38#13063259C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063258C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063236C2211yescharacteristic
52C2×Q16×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54C4×Q8×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58C4×C8×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×Q8×C43C2311yescharacteristic
61#10621902—22no—
62#10621902—22no—
63C2×D172—21no—
64C2×D172—21no—
65C2×D172C2311yescharacteristic
66C2×D172C2311yescharacteristic
67C2×C4×D43—21no—
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43C2311yescharacteristic
73C2×Dic86—21no—
74Q16×C43—22no—
75C2×C8×C43C2311yescharacteristic
76C2×C8×C43C2311yescharacteristic
77C4⋊C4×C43—21no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43C2311yescharacteristic
80C4⋊C4×C43C2311yescharacteristic
81C42×C43—21no—
82C42×C43—21no—
83C42×C43C2311yescharacteristic
84#10621884—22no—
85#10621884—22no—
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)⋊C4D411yescharacteristic
94(C2×D43)⋊C4D411yescharacteristic
95C4⋊Dic43—21no—
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4D411yescharacteristic
102Dic43⋊C4D411yescharacteristic
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107D344—22no—
108C22×D43—21no—
109C22×D43—21no—
110C22×D43C2×D411yescharacteristic
111Q8×C43—21no—
112Q8×C43—21no—
113Q8×C43—21no—
114Q8×C43#4112yes—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43C2×D411yescharacteristic
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2411yescharacteristic
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43C2×D411yescharacteristic
125C2×Dic43C2×D411yescharacteristic
126C2×Dic43C2×D411yescharacteristic
127D172—24no—
128D172—21no—
129D172—21no—
130D172—21no—
131D172—81no—
132D172#4112yes—
133C4×D43—24no—
134C4×D43—21no—
135C4×D43—21no—
136C4×D43—81no—
137C4×D43—81no—
138C4×D43—81no—
139C4×D43—81no—
140Dic86—81no—
141C8×C43—21no—
142C8×C43—21no—
143C43⋊C8—21no—
144C43⋊C8—21no—
145C22×C43C22×D411yescharacteristic
146C2×D43—22no—
147C2×D43—21no—
148C2×D43—21no—
149C2×D43—21no—
150C2×D43—41no—
151C2×D43—41no—
152C2×D43—41no—
153C2×D43—41no—
154C2×D43—41no—
155C4×C43—22no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—41no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43C2×#4111yescharacteristic
162C4×C43C2×#4111yescharacteristic
163Dic43—21no—
164Dic43—21no—
165Dic43—21no—
166Dic43—41no—
167Dic43—41no—
168#3124—431nomaximal, Sylow
169C2×C43#52511yescharacteristic
170C2×C43#57611yescharacteristic
171C2×C43#57811yescharacteristic
172D43—41no—
173D43—42no—
174D43—81no—
175#542—431no—
176#520—431no—
177#484—431no—
178#480—431no—
179#477—431no—
180#474—431no—
181#464—431no—
182#463—431no—
183#452—431no—
184#449—431no—
185#440—431no—
186#440—431no—
187C4×Q16D4311yescharacteristic, complemented
188C4×D8—431no—
189#433—431no—
190C43#312411yescharacteristic, complemented, Sylow
191C2×#41—431no—
192C2×Q16C2×D4311yescharacteristic
193C2×SD16—431no—
194C2×SD16—431no—
195C2×D8—431no—
196C4⋊Q8—431no—
197#126—861no—
198#124—431no—
199#124—861no—
200#123—861no—
201C22⋊Q8—431no—
202C22⋊Q8—861no—
203#121—431no—
204C4×Q8—431no—
205C4×Q8C2×D4311yescharacteristic
206C4×Q8C2×D4311yescharacteristic
207C4×D4—431no—
208C4×D4—431no—
209C4×D4—431no—
210C4×D4—861no—
211C4×D4—861no—
212#117—431no—
213#117—861no—
214C2×C4⋊C4—431no—
215C2×C4⋊C4—861no—
216#107—431no—
217#107—431no—
218#107—431no—
219#107C2×D4311yescharacteristic
220C4⋊C8—431no—
221C4⋊C8—431no—
222#103—431no—
223#103—431no—
224#103C2×D4311yescharacteristic
225#103C2×D4311yescharacteristic
226#102—431no—
227#102—431no—
228#102—431no—
229#102—431no—
230C22⋊C8—431no—
231C22⋊C8—431no—
232#97—431no—
233C4×C8C2×D4311yescharacteristic
234#41—862no—
235#41—862no—
236C2×Q8—861no—
237C2×Q8C22×D4311yescharacteristic
238C2×Q8C22×D4311yescharacteristic
239C2×D4—431no—
240C2×D4—431no—
241C2×D4—861no—
242C2×D4—861no—
243C22×C4—431no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4—861no—
249Q16—22no—
250SD16—862no—
251SD16—862no—
252D8—862no—
253C2×C8—431no—
254C2×C8—431no—
255C2×C8C22×D4311yescharacteristic
256C2×C8C22×D4311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—431no—
260C4⋊C4—431no—
261C4⋊C4—431no—
262C4⋊C4—431no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4C22×D4311yescharacteristic
268C4⋊C4C22×D4311yescharacteristic
269C22⋊C4—431no—
270C22⋊C4—431no—
271C22⋊C4—861no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C22⋊C4—861no—
277C22⋊C4—861no—
278C42—21no—
279C42—21no—
280C42—431no—
281C42—861no—
282C42C22×D4311yescharacteristic
283C23—431no—
284C23—861no—
285C23—861no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—3441no—
290Q8#1062189812yes—
291D4—432no—
292D4—864no—
293D4—861no—
294D4—861no—
295D4—861no—
296D4—3441no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—431no—
302C2×C4—431no—
303C2×C4—431no—
304C2×C4—864no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—3441no—
310C2×C4—3441no—
311C2×C4—3441no—
312C2×C4—3441no—
313C2×C4D4×D4311yescharacteristic
314C2×C4D4×D4311yescharacteristic
315C2×C4C23×D4311yescharacteristic
316C8—21no—
317C8—21no—
318C8—861no—
319C8—861no—
320C22—862no—
321C22—861no—
322C22—861no—
323C22—861no—
324C22—1721no—
325C22—1721no—
326C22—1721no—
327C22—1721no—
328C22—1721no—
329C22C2×D4×D4311yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—861no—
337C4—861no—
338C4—861no—
339C4—1721no—
340C4—1721no—
341C4#41×D4311yescharacteristic
342C4C2×#1062189811yescharacteristic
343C2—3441no—
344C2—1721no—
345C2—1722no—
346C2#1458340811yescharacteristic
347C2#1458370111yescharacteristic
348C2#1458371211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC4×Q16×C43C2
socleC22×C43C22×D4
hypercenterC4×Q16D43
hypocenterC43#3124
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #14583521C2semidirect
2. #14583381C2semidirect
3. #14583233C2semidirect
4. #14583214C2semidirect
5. #14583192C2semidirect
6. #14583178C2semidirect
7. #14583123C2semidirect
8. #14583117C2semidirect
9. #14583060C2semidirect
11. #14582997C2semidirect
12. #14582997C2semidirect
13. C4×D344C2semidirect
14. #14582958C2semidirect
15. C4×Q16×C43C2semidirect
187. C4×Q16D43semidirect
190. C43#3124semidirect