Finite Group Databasebeta

← #19144825

Subgroups — #19144825

Order 5504.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583522C211yesmaximal, characteristic
2#14583377C211yesmaximal, characteristic, complemented
3#14583237C211yesmaximal, characteristic, complemented
4#14583224C211yesmaximal, characteristic
5#14583192C211yesmaximal, characteristic, complemented
6#14583182C211yesmaximal, characteristic, complemented
7#14583123C211yesmaximal, characteristic, complemented
8#14583123C211yesmaximal, characteristic, complemented
9#14583038C211yesmaximal, characteristic
10#14583006C211yesmaximal, characteristic, complemented
11#14583002C211yesmaximal, characteristic, complemented
12Q16×Dic43C211yesmaximal, characteristic, complemented
13#14582984C211yesmaximal, characteristic, complemented
14#14582957C211yesmaximal, characteristic, complemented
15C43×#451C211yesmaximal, characteristic, complemented
16C2×#10621884C2211yescharacteristic
17C2×#10621884C2211yescharacteristic
18#13063324C2211yescharacteristic
19#13063320—21no—
20#13063314C2211yescharacteristic
21#13063311—21no—
22#13063307—21no—
23#13063305—21no—
24#13063299C2211yescharacteristic
25Q8×Dic43—21no—
26Q8×Dic43—21no—
27Q8×Dic43C2211yescharacteristic
28Q8×Dic43C2211yescharacteristic
29Q8×Dic43C2211yescharacteristic
30Q8×Dic43C2211yescharacteristic
31Q8×Dic43C2211yescharacteristic
32#13063287C2211yescharacteristic
33#13063284—21no—
34#13063284—21no—
35#13063284C2211yescharacteristic
36#13063284C2211yescharacteristic
37#13063259C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063257C2211yescharacteristic
40#13063256C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063249C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063247C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C22×Q8×C43C2211yescharacteristic
53C2×Q16×C43C2211yescharacteristic
54C2×Q16×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×Q8×C43—22no—
60C2×Q8×C43—22no—
61C2×Q8×C43—21no—
62C2×Q8×C43C2311yescharacteristic
63C2×Q8×C43C2311yescharacteristic
64C2×Q8×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—21no—
68C2×D172C2311yescharacteristic
69C2×C4×D43—21no—
70C2×Dic86—21no—
71Q16×C43—22no—
72Q16×C43—22no—
73C2×C8×C43C2311yescharacteristic
74C2×C8×C43C2311yescharacteristic
75C4⋊C4×C43—21no—
76C4⋊C4×C43C2311yescharacteristic
77C22⋊C4×C43—21no—
78C22⋊Dic43—21no—
79C22⋊Dic43D411yescharacteristic
80C22⋊Dic43D411yescharacteristic
81#10621884—22no—
82#10621884—22no—
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4—21no—
87C4⋊Dic43—21no—
88C4⋊Dic43—21no—
89C4⋊Dic43—21no—
90C4⋊Dic43—21no—
91C4⋊Dic43—21no—
92C4⋊Dic43D411yescharacteristic
93C4⋊Dic43D411yescharacteristic
94C4⋊Dic43C2311yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105C4×Dic43C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43C2×D411yescharacteristic
109C22×D43—21no—
110Q8×C43—24no—
111Q8×C43—21no—
112Q8×C43—21no—
113Q8×C43—21no—
114Q8×C43—21no—
115Q8×C43#4112yes—
116Q8×C43#4112yes—
117C2×C4×C43—24no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2411yescharacteristic
126C22⋊D43—81no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43C2×D411yescharacteristic
131C2×Dic43C2×D411yescharacteristic
132C2×Dic43C2×D411yescharacteristic
133C2×Dic43C2×D411yescharacteristic
134D172—21no—
135D172—21no—
136C4×D43—81no—
137Dic86—81no—
138C8×C43—21no—
139C8×C43—21no—
140C43⋊C8—21no—
141C43⋊C8—21no—
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43C22×D411yescharacteristic
146C2×D43—41no—
147C2×D43—41no—
148C2×D43—41no—
149C4×C43—22no—
150C4×C43—22no—
151C4×C43—21no—
152C4×C43—41no—
153C4×C43—41no—
154C4×C43C2×#4111yescharacteristic
155C4×C43C2×#4111yescharacteristic
156Dic43—21no—
157Dic43—21no—
158Dic43—21no—
159Dic43—21no—
160Dic43—41no—
161Dic43—41no—
162Dic43—41no—
163#3121—431nomaximal, Sylow
164C2×C43—41no—
165C2×C43#52511yescharacteristic
166C2×C43#57711yescharacteristic
167C2×C43#57811yescharacteristic
168D43—81no—
169#542—431no—
170#519—431no—
171#485—431no—
172#482—431no—
173#477—431no—
174#475—431no—
175#464—431no—
176#464—431no—
177#451D4311yescharacteristic, complemented
178#448—431no—
179#441—431no—
180#440—431no—
181C4×Q16—431no—
182C4×SD16—431no—
183#433—431no—
184C43#312111yescharacteristic, complemented, Sylow
185C22×Q8C2×D4311yescharacteristic
186C2×Q16C2×D4311yescharacteristic
187C2×Q16C2×D4311yescharacteristic
188C2×SD16—431no—
189C2×SD16—431no—
190C4⋊Q8—431no—
191#126—861no—
192#124—431no—
193#124—861no—
194#123—861no—
195C22⋊Q8—861no—
196C22⋊Q8C2×D4311yescharacteristic
197#121—431no—
198C4×Q8—431no—
199C4×Q8—431no—
200C4×Q8—431no—
201C4×Q8—431no—
202C4×Q8—431no—
203C4×Q8—861no—
204C4×Q8—861no—
205C4×D4—431no—
206#117—431no—
207#117—431no—
208#117—861no—
209#117—861no—
210#107—431no—
211#107—431no—
212#106—431no—
213#106—431no—
214C4⋊C8—431no—
215C4⋊C8—431no—
216#103—431no—
217#103—431no—
218#103—431no—
219#103—431no—
220#103C2×D4311yescharacteristic
221#103C2×D4311yescharacteristic
222#102—431no—
223#102—431no—
224C22⋊C8—431no—
225C22⋊C8C2×D4311yescharacteristic
226#97—431no—
227C4×C8—431no—
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—21no—
231C2×Q8—861no—
232C2×Q8C22×D4311yescharacteristic
233C2×Q8C22×D4311yescharacteristic
234C2×Q8C22×D4311yescharacteristic
235C2×D4—431no—
236C2×D4—861no—
237C22×C4—21no—
238C22×C4—861no—
239C22×C4C22×D4311yescharacteristic
240Q16—22no—
241Q16—22no—
242SD16—862no—
243SD16—862no—
244C2×C8—431no—
245C2×C8—431no—
246C2×C8C22×D4311yescharacteristic
247C2×C8C22×D4311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—431no—
250C4⋊C4—431no—
251C4⋊C4—431no—
252C4⋊C4—431no—
253C4⋊C4—431no—
254C4⋊C4—861no—
255C4⋊C4—861no—
256C4⋊C4—861no—
257C4⋊C4—861no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4C22×D4311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—431no—
263C22⋊C4—431no—
264C22⋊C4—861no—
265C22⋊C4—861no—
266C22⋊C4—861no—
267C22⋊C4—861no—
268C22⋊C4—861no—
269C42—431no—
270C42—431no—
271C42—861no—
272C42—861no—
273C42—861no—
274C42—861no—
275C42—861no—
276C42—861no—
277C23—861no—
278C23D4×D4311yescharacteristic
279Q8—24no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—3441no—
285Q8#1062190012yes—
286Q8#1062190012yes—
287D4—861no—
288D4—861no—
289D4—3441no—
290C2×C4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—431no—
298C2×C4—431no—
299C2×C4—431no—
300C2×C4—431no—
301C2×C4—861no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—3441no—
305C2×C4D4×D4311yescharacteristic
306C2×C4C23×D4311yescharacteristic
307C8—21no—
308C8—21no—
309C8—861no—
310C8—861no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—1721no—
315C22—1721no—
316C22—1721no—
317C22C2×D4×D4311yescharacteristic
318C4—22no—
319C4—22no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—861no—
324C4—861no—
325C4—861no—
326C4—861no—
327C4—1721no—
328C4—1721no—
329C4—1721no—
330C4C2×#1062190011yescharacteristic
331C4C2×#1062190011yescharacteristic
332C2—41no—
333C2—3441no—
334C2#1458340511yescharacteristic
335C2#1458370811yescharacteristic
336C2#1458371211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#451C2
socleC22×C43C22×D4
hypercenter#451D43
hypocenterC43#3121
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #14583377C2semidirect
3. #14583237C2semidirect
5. #14583192C2semidirect
6. #14583182C2semidirect
7. #14583123C2semidirect
8. #14583123C2semidirect
10. #14583006C2semidirect
11. #14583002C2semidirect
12. Q16×Dic43C2semidirect
13. #14582984C2semidirect
14. #14582957C2semidirect
15. C43×#451C2semidirect
177. #451D43semidirect
184. C43#3121semidirect