Finite Group Databasebeta

← #19147077

Subgroups — #19147077

Order 5504.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583610C211yesmaximal, characteristic, complemented
2#14583599C211yesmaximal, characteristic
3#14583305C211yesmaximal, characteristic, complemented
4#14583242C211yesmaximal, characteristic, complemented
5#14583236C211yesmaximal, characteristic, complemented
6#14583216C211yesmaximal, characteristic, complemented
7#14583211C211yesmaximal, characteristic, complemented
8#14583207C211yesmaximal, characteristic, complemented
9#14583144C211yesmaximal, characteristic, complemented
10#14583127C211yesmaximal, characteristic, complemented
11#14582999C211yesmaximal, characteristic, complemented
12#14582969C211yesmaximal, characteristic, complemented
13#14582940C211yesmaximal, characteristic, complemented
14#107×D43C211yesmaximal, characteristic, complemented
15C43×#474C211yesmaximal, characteristic, complemented
16C2×#10621883C2211yescharacteristic
17C2×#10621872C2211yescharacteristic
18C2×C8×D43C2211yescharacteristic
19#13063318—21no—
20#13063317C2211yescharacteristic
21#13063316—21no—
22#13063308—21no—
23#13063305C2211yescharacteristic
24#13063305C2211yescharacteristic
25#13063301—21no—
26#13063301—21no—
27#13063298—21no—
28#13063296C2211yescharacteristic
29#13063296C2211yescharacteristic
30C4×Dic86C2211yescharacteristic
31C4×D172C2211yescharacteristic
32#13063287—21no—
33C4×C22⋊D43—21no—
34#13063283C2211yescharacteristic
35C4⋊C4×D43C2211yescharacteristic
36C4⋊C4×D43C2211yescharacteristic
37C4⋊C4×D43C2211yescharacteristic
38#13063259C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063258C2211yescharacteristic
42#13063257C2211yescharacteristic
43#13063256C2211yescharacteristic
44#13063256C2211yescharacteristic
45#13063250C2211yescharacteristic
46#13063250C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063246C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063236C2211yescharacteristic
52C4⋊Q8×C43C2211yescharacteristic
53C4×D4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C2×D172D411yescharacteristic
65C2×C4×D43—21no—
66C2×C4×D43—21no—
67C2×C4×D43—21no—
68C2×C4×D43C2311yescharacteristic
69C2×C4×D43C2311yescharacteristic
70C2×Dic86C2311yescharacteristic
71C2×C8×C43C2311yescharacteristic
72C2×C8×C43C2311yescharacteristic
73C4⋊C4×C43—21no—
74C4⋊C4×C43C2311yescharacteristic
75C4⋊C4×C43C2311yescharacteristic
76C4⋊C4×C43C2311yescharacteristic
77C22⋊C4×C43—21no—
78C42×C43C2311yescharacteristic
79C22⋊Dic43—21no—
80C22⋊Dic43—21no—
81#10621883—22no—
82(C2×D43)⋊C4—21no—
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4D411yescharacteristic
86(C2×D43)⋊C4D411yescharacteristic
87C4⋊Dic43—21no—
88C4⋊Dic43—21no—
89C4⋊Dic43D411yescharacteristic
90C4⋊Dic43C2311yescharacteristic
91C4⋊Dic43C2311yescharacteristic
92C4⋊Dic43C2311yescharacteristic
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C2×C43⋊C8C2311yescharacteristic
102C2×C43⋊C8C2311yescharacteristic
103#10621872—22no—
104C8×D43—22no—
105C23×C43—21no—
106C22×D43C2×D411yescharacteristic
107C22×D43C2×D411yescharacteristic
108Q8×C43—81no—
109D4×C43—21no—
110D4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—81no—
115C2×C4×C43C2×D411yescharacteristic
116C2×C4×C43C2×D411yescharacteristic
117C2×C4×C43C2411yescharacteristic
118C22⋊D43—42no—
119C22⋊D43—81no—
120C2×Dic43—21no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43C2×D411yescharacteristic
125C2×Dic43C2×D411yescharacteristic
126D172—22no—
127C4×D43—21no—
128C4×D43—21no—
129C4×D43—21no—
130C4×D43—21no—
131C4×D43—81no—
132C4×D43—81no—
133C4×D43—81no—
134Dic86—21no—
135Dic86—21no—
136C8×C43—21no—
137C8×C43—21no—
138C43⋊C8—21no—
139C43⋊C8#4112yes—
140C22×C43—41no—
141C22×C43—41no—
142C22×C43—41no—
143C22×C43C22×D411yescharacteristic
144C2×D43—21no—
145C2×D43—21no—
146C2×D43—21no—
147C2×D43—21no—
148C2×D43—21no—
149C2×D43#13712yes—
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—41no—
153C4×C43—41no—
154C4×C43—41no—
155C4×C43C2×#4111yescharacteristic
156C4×C432−1+411yescharacteristic
157Dic43—21no—
158Dic43—21no—
159Dic43—41no—
160Dic43—41no—
161Dic43—41no—
162Dic43—41no—
163#3346—431nomaximal, Sylow
164C2×C43—81no—
165C2×C43#54711yescharacteristic
166C2×C43C2×#13711yescharacteristic
167C2×C43#57611yescharacteristic
168D43—22no—
169D43—41no—
170#554—431no—
171#553—431no—
172#501—431no—
173#485—431no—
174#484—431no—
175#481—431no—
176#480—431no—
177#479—431no—
178#474D4311yescharacteristic, complemented
179#468—431no—
180#465—431no—
181#440—431no—
182#435—431no—
183#428—431no—
184C2×#107—431no—
185C43#334611yescharacteristic, complemented, Sylow
186C2×SD16—431no—
187C2×M16—431no—
188C22×C8—431no—
189C4⋊Q8C2×D4311yescharacteristic
190#126—861no—
191#125—431no—
192#125—861no—
193#123—861no—
194C22⋊Q8—431no—
195C22⋊Q8—431no—
196C22⋊Q8—861no—
197C22⋊Q8—861no—
198#121—431no—
199#121—431no—
200#121—861no—
201C4×Q8—431no—
202C4×D4—431no—
203C4×D4—861no—
204C4×D4—861no—
205C4×D4C2×D4311yescharacteristic
206#117—431no—
207C2×C4⋊C4—431no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4—431no—
210#107—431no—
211#107—431no—
212#107—431no—
213#107—431no—
214#107C2×D4311yescharacteristic
215#107C2×D4311yescharacteristic
216#106—431no—
217#106—431no—
218#106—431no—
219C4⋊C8C2×D4311yescharacteristic
220#103—431no—
221#103—431no—
222#103—431no—
223#102—431no—
224#102C2×D4311yescharacteristic
225#102C2×D4311yescharacteristic
226C22⋊C8—431no—
227C22⋊C8—431no—
228#97—431no—
229C2×Q8—21no—
230C2×Q8—431no—
231C2×D4—431no—
232C2×D4—861no—
233C2×D4—861no—
234C2×D4C22×D4311yescharacteristic
235C22×C4—21no—
236C22×C4—431no—
237C22×C4—431no—
238C22×C4—861no—
239C22×C4—861no—
240C22×C4—861no—
241SD16—862no—
242M16—862no—
243C2×C8—431no—
244C2×C8—431no—
245C2×C8—862no—
246C2×C8C22×D4311yescharacteristic
247C2×C8C22×D4311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—431no—
250C4⋊C4—431no—
251C4⋊C4—431no—
252C4⋊C4—431no—
253C4⋊C4—861no—
254C4⋊C4—861no—
255C4⋊C4—861no—
256C4⋊C4—861no—
257C4⋊C4—861no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4C22×D4311yescharacteristic
262C4⋊C4C22×D4311yescharacteristic
263C4⋊C4C22×D4311yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—431no—
266C22⋊C4—431no—
267C22⋊C4—861no—
268C22⋊C4—861no—
269C22⋊C4—861no—
270C22⋊C4—861no—
271C22⋊C4—861no—
272C42—861no—
273C42—861no—
274C42C22×D4311yescharacteristic
275C23—21no—
276C23—431no—
277C23—431no—
278Q8—81no—
279Q8—861no—
280Q8—861no—
281D4—21no—
282D4—21no—
283D4—862no—
284D4—3441no—
285D4—1722no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—81no—
290C2×C4—431no—
291C2×C4—431no—
292C2×C4—861no—
293C2×C4—861no—
294C2×C4—861no—
295C2×C4—861no—
296C2×C4—861no—
297C2×C4—861no—
298C2×C4—861no—
299C2×C4—861no—
300C2×C4—3441no—
301C2×C4—3441no—
302C2×C4—3441no—
303C2×C4D4×D4311yescharacteristic
304C2×C4D4×D4311yescharacteristic
305C2×C4C23×D4311yescharacteristic
306C8—21no—
307C8—21no—
308C8—432no—
309C8—861no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—432no—
314C22—861no—
315C22—861no—
316C22—861no—
317C22—861no—
318C22—861no—
319C22C2×D4×D4311yescharacteristic
320C4—21no—
321C4—21no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—861no—
326C4—861no—
327C4—1721no—
328C4—1721no—
329C4—1721no—
330C4—1721no—
331C4#41×D4311yescharacteristic
332C4#1306337311yescharacteristic
333C2—81no—
334C2—862no—
335C2—1721no—
336C2#1458355111yescharacteristic
337C2#137×D4311yescharacteristic
338C2#1458370011yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#474C2
socleC22×C43C22×D4
hypercenter#474D43
hypocenterC43#3346
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #14583610C2semidirect
3. #14583305C2semidirect
4. #14583242C2semidirect
5. #14583236C2semidirect
6. #14583216C2semidirect
7. #14583211C2semidirect
8. #14583207C2semidirect
9. #14583144C2semidirect
10. #14583127C2semidirect
11. #14582999C2semidirect
12. #14582969C2semidirect
13. #14582940C2semidirect
14. #107×D43C2semidirect
15. C43×#474C2semidirect
178. #474D43semidirect
185. C43#3346semidirect