Finite Group Databasebeta

← #19145472

Subgroups — #19145472

Order 5504.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583478C211yesmaximal, characteristic
2#14583472C211yesmaximal, characteristic, complemented
3#14583242C211yesmaximal, characteristic, complemented
4#14583236C211yesmaximal, characteristic, complemented
5#14583228C211yesmaximal, characteristic, complemented
6#14583222C211yesmaximal, characteristic, complemented
7#14583157C211yesmaximal, characteristic, complemented
8#14583138C211yesmaximal, characteristic, complemented
9#14583126C211yesmaximal, characteristic, complemented
10#14583062C211yesmaximal, characteristic, complemented
11#14583058C211yesmaximal, characteristic, complemented
12#14583056C211yesmaximal, characteristic, complemented
13#14583036C211yesmaximal, characteristic, complemented
14#14582867C211yesmaximal, characteristic, complemented
15C43×#468C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×Q8×D43C2211yescharacteristic
19C2×Dic172C2211yescharacteristic
20C2×#10621885C2211yescharacteristic
21C2×#10621883C2211yescharacteristic
22C22×C43⋊C8C2211yescharacteristic
23#13063324—21no—
24#13063311—21no—
25#13063310—21no—
26#13063307—21no—
27#13063305C2211yescharacteristic
28#13063305C2211yescharacteristic
29#13063304C2211yescharacteristic
30#13063304C2211yescharacteristic
31#13063302—21no—
32#13063301C2211yescharacteristic
33#13063298—21no—
34#13063297—21no—
35#13063296—21no—
36#13063296C2211yescharacteristic
37#13063283C2211yescharacteristic
38C4⋊C4×D43C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063257C2211yescharacteristic
41#13063256C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063246C2211yescharacteristic
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52C2×SD16×C43C2211yescharacteristic
53C2×M16×C43C2211yescharacteristic
54C22⋊Q8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#107×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43D411yescharacteristic
66C2×C22⋊D43D411yescharacteristic
67C22×Dic43—21no—
68Q8×D43—41no—
69Q8×D43—41no—
70#10621900—41no—
71#10621900—41no—
72#10621898—41no—
73#10621898—41no—
74C2×D172D411yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43C2311yescharacteristic
78C2×C4×D43C2311yescharacteristic
79C2×Dic86—21no—
80C2×Dic86D411yescharacteristic
81C2×Dic86C2311yescharacteristic
82C2×Dic86C2311yescharacteristic
83SD16×C43—41no—
84M16×C43—41no—
85C2×C8×C43C2311yescharacteristic
86C2×C8×C43C2311yescharacteristic
87C4⋊C4×C43—21no—
88C4⋊C4×C43C2311yescharacteristic
89C4⋊C4×C43C2311yescharacteristic
90C22⋊C4×C43—21no—
91C22⋊C4×C43—21no—
92C22⋊Dic43—21no—
93C22⋊Dic43—21no—
94C22⋊Dic43—21no—
95#10621885—41no—
96#10621883—41no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101C4⋊Dic43—21no—
102C4⋊Dic43—21no—
103C4⋊Dic43C2311yescharacteristic
104C4⋊Dic43C2311yescharacteristic
105Dic43⋊C4—21no—
106Dic43⋊C4—21no—
107Dic43⋊C4—21no—
108Dic43⋊C4—21no—
109C4×Dic43—21no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8C2311yescharacteristic
112C2×C43⋊C8C2311yescharacteristic
113Dic172—41no—
114C23×C43—21no—
115C23×C43C2×D411yescharacteristic
116C22×D43C2×D411yescharacteristic
117C22×D43C2×D411yescharacteristic
118Q8×C43—21no—
119Q8×C43—21no—
120D4×C43—21no—
121D4×C43—21no—
122D4×C43—81no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—41no—
131C22⋊D43—41no—
132C22⋊D43—42no—
133C22⋊D43—81no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—42no—
139C2×Dic43C2×D411yescharacteristic
140C2×Dic43C2×D411yescharacteristic
141D172—41no—
142C4×D43—21no—
143C4×D43—21no—
144C4×D43—21no—
145C4×D43—21no—
146C4×D43—42no—
147C4×D43—81no—
148Dic86—21no—
149Dic86—21no—
150Dic86—21no—
151Dic86—21no—
152Dic86—41no—
153Dic86—42no—
154C8×C43—21no—
155C8×C43—21no—
156C43⋊C8—21no—
157C43⋊C8—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43C22×D411yescharacteristic
165C2×D43—21no—
166C2×D43—21no—
167C2×D43—21no—
168C2×D43—21no—
169C2×D43—21no—
170C2×D43—21no—
171C4×C43—21no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43—41no—
175C4×C43H(5,𝔽2)11yescharacteristic
176C4×C43H(5,𝔽2)11yescharacteristic
177Dic43—21no—
178Dic43—21no—
179Dic43—41no—
180Dic43—41no—
181Dic43—41no—
182Dic43—41no—
183#3201—431nomaximal, Sylow
184C2×C43—41no—
185C2×C43—81no—
186C2×C43#53411yescharacteristic
187C2×C43#57711yescharacteristic
188C2×C43#57811yescharacteristic
189D43—41no—
190D43—41no—
191#537—431no—
192#536—431no—
193#485—431no—
194#484—431no—
195#483—431no—
196#482—431no—
197#470—431no—
198#468D4311yescharacteristic, complemented
199#467—431no—
200#465—431no—
201#452—431no—
202#452—431no—
203#451—431no—
204#448—431no—
205#408—431no—
206C43#320111yescharacteristic, complemented, Sylow
207C2×#41—431no—
208C2×#41—431no—
209C22×Q8—431no—
210C2×Q16—431no—
211C2×Q16—431no—
212C2×SD16—431no—
213C2×SD16C2×D4311yescharacteristic
214C2×M16C2×D4311yescharacteristic
215C22×C8—431no—
216C4⋊Q8—861no—
217#124—861no—
218#123—861no—
219#123—861no—
220C22⋊Q8—431no—
221C22⋊Q8—431no—
222C22⋊Q8—431no—
223C22⋊Q8—431no—
224C22⋊Q8—431no—
225C22⋊Q8—861no—
226C22⋊Q8C2×D4311yescharacteristic
227#121—431no—
228#121—861no—
229#121—861no—
230#121—861no—
231#121C2×D4311yescharacteristic
232#117—431no—
233C2×C4⋊C4—431no—
234#107—431no—
235#107C2×D4311yescharacteristic
236#106—431no—
237#106—431no—
238#103—431no—
239#103—431no—
240#103—431no—
241#103—431no—
242#103—431no—
243#103C2×D4311yescharacteristic
244#102—431no—
245#102C2×D4311yescharacteristic
246C22⋊C8—431no—
247C22⋊C8—431no—
248C22⋊C8—431no—
249C22⋊C8—431no—
250#41—1721no—
251#41—1721no—
252#41—1721no—
253#41—1721no—
254C2×Q8—431no—
255C2×Q8—431no—
256C2×Q8—431no—
257C2×Q8—861no—
258C2×Q8—1721no—
259C2×Q8—1721no—
260C2×Q8C22×D4311yescharacteristic
261C2×D4—21no—
262C2×D4—431no—
263C2×D4—431no—
264C2×D4—431no—
265C2×D4—861no—
266C2×D4—861no—
267C2×D4C22×D4311yescharacteristic
268C22×C4—431no—
269C22×C4—431no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4C22×D4311yescharacteristic
274Q16—1721no—
275Q16—1721no—
276SD16—41no—
277SD16—1721no—
278M16—41no—
279C2×C8—431no—
280C2×C8—431no—
281C2×C8—1721no—
282C2×C8C22×D4311yescharacteristic
283C2×C8C22×D4311yescharacteristic
284C4⋊C4—21no—
285C4⋊C4—431no—
286C4⋊C4—431no—
287C4⋊C4—861no—
288C4⋊C4—861no—
289C4⋊C4—861no—
290C4⋊C4—861no—
291C4⋊C4—861no—
292C4⋊C4—861no—
293C4⋊C4C22×D4311yescharacteristic
294C4⋊C4C22×D4311yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C42—861no—
305C23—21no—
306C23—431no—
307C23—431no—
308C23D4×D4311yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—861no—
312Q8—861no—
313Q8—861no—
314Q8—861no—
315Q8—1721no—
316Q8—1722no—
317D4—21no—
318D4—21no—
319D4—81no—
320D4—3441no—
321D4—1721no—
322D4—1721no—
323D4—1721no—
324D4—1722no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—431no—
331C2×C4—431no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—3441no—
341C2×C4—1722no—
342C2×C4—1722no—
343C2×C4D4×D4311yescharacteristic
344C2×C4C23×D4311yescharacteristic
345C8—21no—
346C8—21no—
347C8—861no—
348C8—861no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—861no—
356C22—861no—
357C22—861no—
358C22—861no—
359C22—861no—
360C22—861no—
361C22C2×D4×D4311yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—861no—
367C4—861no—
368C4—1721no—
369C4—1721no—
370C4—1721no—
371C4—1721no—
372C4#1306337011yescharacteristic
373C4#1306337111yescharacteristic
374C2—41no—
375C2—81no—
376C2—1721no—
377C2—1721no—
378C2#1458345711yescharacteristic
379C2#1458370911yescharacteristic
380C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#468C2
socleC22×C43C22×D4
hypercenter#468D43
hypocenterC43#3201
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
2. #14583472C2semidirect
3. #14583242C2semidirect
4. #14583236C2semidirect
5. #14583228C2semidirect
6. #14583222C2semidirect
7. #14583157C2semidirect
8. #14583138C2semidirect
9. #14583126C2semidirect
10. #14583062C2semidirect
11. #14583058C2semidirect
12. #14583056C2semidirect
13. #14583036C2semidirect
14. #14582867C2semidirect
15. C43×#468C2semidirect
198. #468D43semidirect
206. C43#3201semidirect