Finite Group Databasebeta

← #19146694

Subgroups — #19146694

Order 5504.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583584C211yesmaximal, characteristic, complemented
2#14583551C211yesmaximal, characteristic
3#14583266C211yesmaximal, characteristic, complemented
4#14583242C211yesmaximal, characteristic, complemented
5#14583202C211yesmaximal, characteristic, complemented
6#14583155C211yesmaximal, characteristic, complemented
7#14583141C211yesmaximal, characteristic, complemented
8#14583108C211yesmaximal, characteristic, complemented
9#14583064C211yesmaximal, characteristic, complemented
10#14583063C211yesmaximal, characteristic, complemented
11#14582998C211yesmaximal, characteristic, complemented
12#14582973C211yesmaximal, characteristic, complemented
13#14582898C211yesmaximal, characteristic, complemented
14#14582894C211yesmaximal, characteristic, complemented
15C43×#484C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621898C2211yescharacteristic
18C2×Dic172C2211yescharacteristic
19C2×#10621885C2211yescharacteristic
20C2×#10621873C2211yescharacteristic
21C2×#10621877C2211yescharacteristic
22C2×C8×D43C2211yescharacteristic
23#13063323C2211yescharacteristic
24#13063320—21no—
25#13063316C2211yescharacteristic
26#13063315—21no—
27#13063310—21no—
28#13063308—21no—
29#13063307—21no—
30#13063305C2211yescharacteristic
31#13063305C2211yescharacteristic
32#13063304C2211yescharacteristic
33#13063298—21no—
34#13063290C2211yescharacteristic
35#13063287C2211yescharacteristic
36C4×C22⋊D43C2211yescharacteristic
37#13063284—21no—
38#13063283C2211yescharacteristic
39C4⋊C4×D43—21no—
40#13063256C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063235C2211yescharacteristic
52C22⋊Q8×C43C2211yescharacteristic
53C2×C4⋊C4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C22×C4×C43—21no—
61C22×C4×C43C2311yescharacteristic
62C2×C22⋊D43—21no—
63C2×C22⋊D43D411yescharacteristic
64#10621902—22no—
65#10621902—41no—
66#10621898—22no—
67#10621898—41no—
68C2×D172—21no—
69C2×D172C2311yescharacteristic
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×C4×D43C2311yescharacteristic
74C2×Dic86C2311yescharacteristic
75C2×Dic86C2311yescharacteristic
76C2×C8×C43C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43C2311yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43D411yescharacteristic
86#10621885—41no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4D411yescharacteristic
92C4⋊Dic43—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43—21no—
95C4⋊Dic43C2311yescharacteristic
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4D411yescharacteristic
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105#10621877—41no—
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108Dic172—41no—
109#10621873—22no—
110C8×D43—41no—
111C23×C43C2×D411yescharacteristic
112C22×D43—21no—
113C22×D43C2×D411yescharacteristic
114Q8×C43—21no—
115Q8×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—42no—
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2411yescharacteristic
125C22⋊D43—41no—
126C22⋊D43—42no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43C2×D411yescharacteristic
131C2×Dic43C2×D411yescharacteristic
132C2×Dic43C2×D411yescharacteristic
133D172—21no—
134D172—42no—
135D172#4112yes—
136C4×D43—21no—
137C4×D43—21no—
138C4×D43—42no—
139C4×D43—42no—
140C4×D43—42no—
141Dic86—21no—
142Dic86—21no—
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×C43C22×D411yescharacteristic
153C2×D43—22no—
154C2×D43—21no—
155C2×D43—21no—
156C2×D43—21no—
157C2×D43—41no—
158C2×D43—41no—
159C4×C43—21no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43C2×#4111yescharacteristic
165C4×C43H(5,𝔽2)11yescharacteristic
166Dic43—21no—
167Dic43—21no—
168Dic43—21no—
169Dic43—41no—
170Dic43—41no—
171Dic43—41no—
172#3315—431nomaximal, Sylow
173C2×C43—41no—
174C2×C43#54611yescharacteristic
175C2×C43#57511yescharacteristic
176C2×C43#57811yescharacteristic
177D43—41no—
178D43—42no—
179#552—431no—
180#547—431no—
181#491—431no—
182#485—431no—
183#484D4311yescharacteristic, complemented
184#478—431no—
185#470—431no—
186#467—431no—
187#462—431no—
188#452—431no—
189#452—431no—
190#440—431no—
191#435—431no—
192#417—431no—
193#416—431no—
194C43#331511yescharacteristic, complemented, Sylow
195C2×#41—431no—
196C2×#41—431no—
197C2×Q16—431no—
198C2×Q16—431no—
199C2×SD16—431no—
200C2×M16—431no—
201C22×C8—431no—
202C4⋊Q8—431no—
203#126—861no—
204#125—431no—
205#125—861no—
206#123—861no—
207#123—861no—
208#123—861no—
209C22⋊Q8—431no—
210C22⋊Q8—431no—
211C22⋊Q8—431no—
212C22⋊Q8C2×D4311yescharacteristic
213#121—861no—
214C4×Q8—431no—
215C4×D4—431no—
216C4×D4—431no—
217#117—431no—
218#117—861no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4C2×D4311yescharacteristic
221#107C2×D4311yescharacteristic
222#107C2×D4311yescharacteristic
223#106—431no—
224C4⋊C8—431no—
225#103—431no—
226#103—431no—
227#103—431no—
228#103—431no—
229#103—431no—
230#103C2×D4311yescharacteristic
231#103C2×D4311yescharacteristic
232#102—431no—
233#102—431no—
234#102—431no—
235C22⋊C8—431no—
236C22⋊C8C2×D4311yescharacteristic
237#97—431no—
238#41—862no—
239#41—862no—
240#41—1721no—
241#41—1721no—
242C2×Q8—431no—
243C2×Q8—431no—
244C2×Q8C22×D4311yescharacteristic
245C2×D4—431no—
246C2×D4—431no—
247C2×D4—861no—
248C2×D4—861no—
249C22×C4—21no—
250C22×C4—431no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4C22×D4311yescharacteristic
255Q16—1721no—
256Q16—1721no—
257SD16—862no—
258M16—1721no—
259C2×C8—431no—
260C2×C8—431no—
261C2×C8—1721no—
262C2×C8C22×D4311yescharacteristic
263C2×C8C22×D4311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—431no—
267C4⋊C4—431no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4C22×D4311yescharacteristic
277C4⋊C4C22×D4311yescharacteristic
278C4⋊C4C22×D4311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—431no—
281C22⋊C4—431no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C42—431no—
288C42—861no—
289C42—861no—
290C23—431no—
291C23—861no—
292C23D4×D4311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—861no—
296Q8—861no—
297Q8—861no—
298Q8—861no—
299D4—432no—
300D4—861no—
301D4—1722no—
302D4—1721no—
303D4—1722no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—431no—
312C2×C4—431no—
313C2×C4—431no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—1722no—
320C2×C4—1722no—
321C2×C4—1722no—
322C2×C4D4×D4311yescharacteristic
323C2×C4C23×D4311yescharacteristic
324C8—21no—
325C8—21no—
326C8—861no—
327C8—861no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—861no—
332C22—861no—
333C22—861no—
334C22—862no—
335C22—1721no—
336C22—1721no—
337C22C2×D4×D4311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—861no—
344C4—861no—
345C4—861no—
346C4—1721no—
347C4—1721no—
348C4—1721no—
349C4#41×D4311yescharacteristic
350C4#1306337111yescharacteristic
351C2—41no—
352C2—1721no—
353C2—1722no—
354C2#1458354111yescharacteristic
355C2#1458369511yescharacteristic
356C2#1458371211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#484C2
socleC22×C43C22×D4
hypercenter#484D43
hypocenterC43#3315
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #14583584C2semidirect
3. #14583266C2semidirect
4. #14583242C2semidirect
5. #14583202C2semidirect
6. #14583155C2semidirect
7. #14583141C2semidirect
8. #14583108C2semidirect
9. #14583064C2semidirect
10. #14583063C2semidirect
11. #14582998C2semidirect
12. #14582973C2semidirect
13. #14582898C2semidirect
14. #14582894C2semidirect
15. C43×#484C2semidirect
183. #484D43semidirect
194. C43#3315semidirect