Finite Group Databasebeta

← #19144587

Subgroups — #19144587

Order 5504.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583478C211yesmaximal, characteristic
2#14583379C211yesmaximal, characteristic, complemented
3#14583242C211yesmaximal, characteristic, complemented
4#14583240C211yesmaximal, characteristic, complemented
5#14583231C211yesmaximal, characteristic, complemented
6#14583230C211yesmaximal, characteristic, complemented
7#14583222C211yesmaximal, characteristic, complemented
8#14583216C211yesmaximal, characteristic, complemented
9#14583215C211yesmaximal, characteristic, complemented
10#14582940C211yesmaximal, characteristic, complemented
11#106×D43C211yesmaximal, characteristic, complemented
12#14582897C211yesmaximal, characteristic, complemented
13#14582892C211yesmaximal, characteristic, complemented
14#14582864C211yesmaximal, characteristic, complemented
15C43×#482C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×#10621872C2211yescharacteristic
19C2×C8×D43C2211yescharacteristic
20#13063305C2211yescharacteristic
21#13063304C2211yescharacteristic
22#13063302—21no—
23#13063298—21no—
24#13063297—21no—
25#13063296—21no—
26#13063296C2211yescharacteristic
27C4×Dic86—21no—
28C4×D172—21no—
29(C22⋊D43)⋊C4—21no—
30(C22⋊D43)⋊C4—21no—
31#13063283C2211yescharacteristic
32#13063283C2211yescharacteristic
33C2×C4⋊Dic43C2211yescharacteristic
34C4⋊C4×D43C2211yescharacteristic
35C4⋊C4×D43C2211yescharacteristic
36C4⋊C4×D43C2211yescharacteristic
37#13063258C2211yescharacteristic
38#13063257C2211yescharacteristic
39#13063257C2211yescharacteristic
40#13063256C2211yescharacteristic
41#13063256C2211yescharacteristic
42#13063256C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52#121×C43C2211yescharacteristic
53#117×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43D411yescharacteristic
65C2×C22⋊D43D411yescharacteristic
66C22×Dic43—21no—
67C22×Dic43—21no—
68#10621900—22no—
69#10621900—22no—
70#10621898—22no—
71#10621898—22no—
72C2×D172D411yescharacteristic
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43C2311yescharacteristic
77C2×C4×D43C2311yescharacteristic
78C2×Dic86D411yescharacteristic
79C2×Dic86C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊C4×C43—21no—
87C42×C43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43—21no—
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106#10621872—22no—
107C8×D43—22no—
108C23×C43—21no—
109C23×C43C2×D411yescharacteristic
110C22×D43C2×D411yescharacteristic
111C22×D43C2×D411yescharacteristic
112D4×C43—21no—
113D4×C43—21no—
114D4×C43—81no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2411yescharacteristic
122C22⋊D43—22no—
123C22⋊D43—22no—
124C22⋊D43—42no—
125C22⋊D43—81no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—42no—
131C2×Dic43—81no—
132C2×Dic43C2×D411yescharacteristic
133C2×Dic43C2×D411yescharacteristic
134D172—22no—
135C4×D43—21no—
136C4×D43—21no—
137C4×D43—81no—
138C4×D43—81no—
139C4×D43—81no—
140C4×D43#4112yes—
141C4×D43#4112yes—
142Dic86—22no—
143Dic86—21no—
144Dic86—21no—
145C8×C43—21no—
146C8×C43—21no—
147C43⋊C8—21no—
148C43⋊C8—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43C22×D411yescharacteristic
156C2×D43—21no—
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—21no—
160C2×D43—21no—
161C2×D43#12312yes—
162C4×C43—21no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43C2×#4111yescharacteristic
167C4×C43C2×#4111yescharacteristic
168Dic43—21no—
169Dic43—41no—
170Dic43—41no—
171Dic43—41no—
172Dic43—41no—
173Dic43#12312yes—
174#3099—431nomaximal, Sylow
175C2×C43—41no—
176C2×C43—81no—
177C2×C43C2×#12311yescharacteristic
178C2×C43#57711yescharacteristic
179C2×C43#57711yescharacteristic
180D43—22no—
181D43—41no—
182#537—431no—
183#520—431no—
184#485—431no—
185#485—431no—
186#483—431no—
187#483—431no—
188#482—431no—
189#482D4311yescharacteristic, complemented
190#481—431no—
191#481—431no—
192#428—431no—
193C2×#106—431no—
194#417—431no—
195#416—431no—
196#408—431no—
197C43#309911yescharacteristic, complemented, Sylow
198C2×#41—431no—
199C2×#41—431no—
200C2×M16—431no—
201C22×C8—431no—
202C22⋊Q8—431no—
203C22⋊Q8—431no—
204C22⋊Q8—861no—
205#121—431no—
206#121—861no—
207#121—861no—
208#121—861no—
209#121C2×D4311yescharacteristic
210C4×Q8—861no—
211C4×D4—861no—
212C4×D4—861no—
213C4×D4—861no—
214#117—431no—
215#117—431no—
216#117C2×D4311yescharacteristic
217C2×C4⋊C4—431no—
218C2×C4⋊C4—431no—
219C2×C4⋊C4—431no—
220C2×C4⋊C4—431no—
221#107—431no—
222#107C2×D4311yescharacteristic
223#106—431no—
224#106—431no—
225#106—431no—
226#106—431no—
227#106—431no—
228#106C2×D4311yescharacteristic
229#103—431no—
230#103—431no—
231#103—431no—
232#103—431no—
233#102—431no—
234#102—431no—
235#102C2×D4311yescharacteristic
236#102C2×D4311yescharacteristic
237C22⋊C8—431no—
238C22⋊C8—431no—
239C22⋊C8—431no—
240C22⋊C8C2×D4311yescharacteristic
241#41—862no—
242#41—862no—
243#41—862no—
244#41—862no—
245C2×Q8—431no—
246C2×Q8—431no—
247C2×D4—21no—
248C2×D4—431no—
249C2×D4—431no—
250C2×D4—431no—
251C2×D4—861no—
252C2×D4—861no—
253C2×D4C22×D4311yescharacteristic
254C22×C4—431no—
255C22×C4—431no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4C22×D4311yescharacteristic
262M16—862no—
263C2×C8—431no—
264C2×C8—431no—
265C2×C8—862no—
266C2×C8C22×D4311yescharacteristic
267C2×C8C22×D4311yescharacteristic
268C4⋊C4—431no—
269C4⋊C4—431no—
270C4⋊C4—431no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4C22×D4311yescharacteristic
278C4⋊C4C22×D4311yescharacteristic
279C4⋊C4C22×D4311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C42—21no—
288C42—861no—
289C42—861no—
290C23—21no—
291C23—431no—
292C23—431no—
293C23D4×D4311yescharacteristic
294Q8—862no—
295Q8—861no—
296Q8—861no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—862no—
301D4—862no—
302D4—862no—
303D4—3441no—
304D4—1722no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—431no—
311C2×C4—432no—
312C2×C4—432no—
313C2×C4—431no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4—3441no—
324C2×C4—1722no—
325C2×C4D4×D4311yescharacteristic
326C2×C4C23×D4311yescharacteristic
327C8—21no—
328C8—21no—
329C8—861no—
330C8—861no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—432no—
338C22—861no—
339C22—861no—
340C22—861no—
341C22—861no—
342C22—861no—
343C22C2×D4×D4311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—432no—
349C4—861no—
350C4—1721no—
351C4—1721no—
352C4—1721no—
353C4—1721no—
354C4#41×D4311yescharacteristic
355C4#41×D4311yescharacteristic
356C2—41no—
357C2—81no—
358C2—862no—
359C2—1721no—
360C2#123×D4311yescharacteristic
361C2#1458370611yescharacteristic
362C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#482C2
socleC22×C43C22×D4
hypercenter#482D43
hypocenterC43#3099
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #14583379C2semidirect
3. #14583242C2semidirect
4. #14583240C2semidirect
5. #14583231C2semidirect
6. #14583230C2semidirect
7. #14583222C2semidirect
8. #14583216C2semidirect
9. #14583215C2semidirect
10. #14582940C2semidirect
11. #106×D43C2semidirect
12. #14582897C2semidirect
13. #14582892C2semidirect
14. #14582864C2semidirect
15. C43×#482C2semidirect
189. #482D43semidirect
197. C43#3099semidirect