Finite Group Databasebeta

← #19147186

Subgroups — #19147186

Order 5504.

386 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583612C211yesmaximal, characteristic, complemented
2#14583550C211yesmaximal, characteristic, complemented
3#14583296C211yesmaximal, characteristic, complemented
4#14583226C211yesmaximal, characteristic, complemented
5#14583223C211yesmaximal, characteristic, complemented
6#14583219C211yesmaximal, characteristic, complemented
7#14583217C211yesmaximal, characteristic, complemented
8#14583188C211yesmaximal, characteristic, complemented
9#14583178C211yesmaximal, characteristic, complemented
10#14583153C211yesmaximal, characteristic, complemented
11#14583152C211yesmaximal, characteristic, complemented
12#14582981C211yesmaximal, characteristic, complemented
13#14582975C211yesmaximal, characteristic, complemented
14#14582940C211yesmaximal, characteristic, complemented
15C43×#428C211yesmaximal, characteristic, complemented
16C2×#10621898—21no—
17C2×D344C2211yescharacteristic
18C2×#10621872C2211yescharacteristic
19#13063324C2211yescharacteristic
20#13063324C2211yescharacteristic
21#13063313—21no—
22#13063311—21no—
23#13063310—21no—
24#13063308—21no—
25#13063303—21no—
26#13063300C2211yescharacteristic
27#13063300C2211yescharacteristic
28#13063299C2211yescharacteristic
29#13063299C2211yescharacteristic
30#13063298—21no—
31#13063287C2211yescharacteristic
32#13063287C2211yescharacteristic
33C4×C22⋊D43C2211yescharacteristic
34#13063283C2211yescharacteristic
35#13063282—21no—
36C4⋊C4×D43C2211yescharacteristic
37#13063258C2211yescharacteristic
38#13063257C2211yescharacteristic
39#13063256C2211yescharacteristic
40#13063256C2211yescharacteristic
41#13063256C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063245C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×M16×C43C2211yescharacteristic
53#117×C43C2211yescharacteristic
54C2×C4⋊C4×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#107×C43C2211yescharacteristic
57#106×C43C2211yescharacteristic
58#106×C43C2211yescharacteristic
59C22×C4×C43—21no—
60C22×C4×C43C2311yescharacteristic
61C2×C22⋊D43—21no—
62C2×C22⋊D43—21no—
63C2×C22⋊D43D411yescharacteristic
64#10621898—44no—
65C2×D172—21no—
66C2×D172—21no—
67C2×D172C2311yescharacteristic
68C2×D172C2311yescharacteristic
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43C2311yescharacteristic
73C2×Dic86—21no—
74C2×Dic86—21no—
75M16×C43—22no—
76C2×C8×C43C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C4⋊C4×C43—21no—
79C4⋊C4×C43C2311yescharacteristic
80C4⋊C4×C43C2311yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C42×C43—21no—
85C22⋊Dic43D411yescharacteristic
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4D411yescharacteristic
94C4⋊Dic43C2311yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4D411yescharacteristic
100C4×Dic43—21no—
101C4×Dic43C2311yescharacteristic
102C2×C43⋊C8C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104D344—22no—
105#10621872—22no—
106C23×C43C2×D411yescharacteristic
107C22×D43—21no—
108C22×D43—21no—
109C22×D43C2×D411yescharacteristic
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—42no—
117C2×C4×C43C2×D411yescharacteristic
118C2×C4×C43C2411yescharacteristic
119C22⋊D43—22no—
120C22⋊D43—42no—
121C22⋊D43—81no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43C2×D411yescharacteristic
125C2×Dic43C2×D411yescharacteristic
126C2×Dic43C2×D411yescharacteristic
127D172—21no—
128D172—21no—
129D172—21no—
130D172—21no—
131D172—42no—
132D172—81no—
133C4×D43—21no—
134C4×D43—21no—
135C4×D43—42no—
136C4×D43—42no—
137C4×D43—42no—
138Dic86—42no—
139Dic86—81no—
140C8×C43—21no—
141C8×C43#4112yescomplemented
142C43⋊C8—21no—
143C43⋊C8—21no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43C22×D411yescharacteristic
148C2×D43—21no—
149C2×D43—21no—
150C2×D43—21no—
151C2×D43—41no—
152C2×D43—41no—
153C2×D43—41no—
154C2×D43—41no—
155C2×D43—41no—
156C2×D43—41no—
157C4×C43—21no—
158C4×C43—41no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43C2×#4111yescharacteristic
163C4×C432−1+411yescharacteristic
164Dic43—21no—
165Dic43—21no—
166Dic43—41no—
167Dic43—41no—
168Dic43AGL(1,ℤ/8)12yes—
169#3354—431nomaximal, Sylow
170C2×C43—41no—
171C2×C43#54711yescharacteristic
172C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C43#57711yescharacteristic
174D43—41no—
175D43—81no—
176D43—81no—
177#555—431no—
178#547—431no—
179#498—431no—
180#482—431no—
181#482—431no—
182#481—431no—
183#481—431no—
184#476—431no—
185#474—431no—
186#469—431no—
187#469—431no—
188C4×D8—431no—
189#436—431no—
190#428—431no—
191#428D4311yescharacteristic, complemented
192C43#335411yescharacteristic, complemented, Sylow
193C2×#41—861no—
194C2×D8—431no—
195C2×M16—431no—
196C2×M16C2×D4311yescharacteristic
197C4⋊Q8—431no—
198C4⋊Q8—431no—
199#124—861no—
200#124—861no—
201#123—861no—
202#123—861no—
203C22⋊Q8—861no—
204#121—431no—
205#121—431no—
206#121—431no—
207#121—431no—
208#121—861no—
209C4×D4—431no—
210C4×D4—431no—
211C4×D4—431no—
212#117—431no—
213#117—861no—
214#117C2×D4311yescharacteristic
215C2×C4⋊C4—431no—
216C2×C4⋊C4C2×D4311yescharacteristic
217#107—431no—
218#107C2×D4311yescharacteristic
219#107C2×D4311yescharacteristic
220#106—431no—
221#106—431no—
222#106—431no—
223#106—431no—
224#106C2×D4311yescharacteristic
225#106C2×D4311yescharacteristic
226C4⋊C8—431no—
227#102—431no—
228#102—431no—
229#102—431no—
230#102—431no—
231#102—431no—
232#102—431no—
233C22⋊C8—431no—
234C22⋊C8—431no—
235C4×C8—431no—
236#41—1724no—
237C2×Q8—861no—
238C2×Q8—861no—
239C2×D4—431no—
240C2×D4—431no—
241C2×D4—431no—
242C2×D4—861no—
243C2×D4—861no—
244C2×D4—861no—
245C2×D4—861no—
246C22×C4—21no—
247C22×C4—431no—
248C22×C4—861no—
249C22×C4—861no—
250C22×C4—861no—
251C22×C4C22×D4311yescharacteristic
252D8—862no—
253M16—22no—
254M16—862no—
255C2×C8—431no—
256C2×C8—431no—
257C2×C8C22×D4311yescharacteristic
258C2×C8C22×D4311yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—431no—
261C4⋊C4—431no—
262C4⋊C4—431no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4C22×D4311yescharacteristic
267C4⋊C4C22×D4311yescharacteristic
268C4⋊C4C22×D4311yescharacteristic
269C4⋊C4C22×D4311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—431no—
272C22⋊C4—431no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C22⋊C4—861no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C42—21no—
281C42—431no—
282C42—861no—
283C23—431no—
284C23—861no—
285C23—861no—
286C23D4×D4311yescharacteristic
287Q8—3441no—
288Q8—1722no—
289D4—862no—
290D4—861no—
291D4—861no—
292D4—861no—
293D4—861no—
294D4—3441no—
295D4—3441no—
296D4—1722no—
297D4—1722no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—431no—
306C2×C4—431no—
307C2×C4—431no—
308C2×C4—861no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—1722no—
313C2×C4—1722no—
314C2×C4—1722no—
315C2×C4D4×D4311yescharacteristic
316C2×C4C23×D4311yescharacteristic
317C8—21no—
318C8—861no—
319C8—861no—
320C8#1062189812yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—861no—
325C22—861no—
326C22—861no—
327C22—1721no—
328C22—1721no—
329C22—1721no—
330C22—1721no—
331C22—1721no—
332C22—1721no—
333C22C2×D4×D4311yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—432no—
340C4—861no—
341C4—861no—
342C4—1721no—
343C4—1721no—
344C4C2×#1062189811yescharacteristic
345C4#1306337311yescharacteristic
346C2—41no—
347C2—3441no—
348C2—3441no—
349C2—1721no—
350C2#1458355011yescharacteristic
351C2AGL(1,ℤ/8)×D4311yescharacteristic
352C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#428C2
socleC22×C43C22×D4
hypercenter#428D43
hypocenterC43#3354
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #14583612C2semidirect
2. #14583550C2semidirect
3. #14583296C2semidirect
4. #14583226C2semidirect
5. #14583223C2semidirect
6. #14583219C2semidirect
7. #14583217C2semidirect
8. #14583188C2semidirect
9. #14583178C2semidirect
10. #14583153C2semidirect
11. #14583152C2semidirect
12. #14582981C2semidirect
13. #14582975C2semidirect
14. #14582940C2semidirect
15. C43×#428C2semidirect
141. C8×C43#41semidirect
191. #428D43semidirect
192. C43#3354semidirect
320. C8#10621898semidirect