Finite Group Databasebeta

← #19146937

Subgroups — #19146937

Order 5504.

420 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583550C211yesmaximal, characteristic, complemented
2#14583549C211yesmaximal, characteristic, complemented
3#14583303C211yesmaximal, characteristic, complemented
4#14583214C211yesmaximal, characteristic, complemented
5#14583213C211yesmaximal, characteristic, complemented
6#14583211C211yesmaximal, characteristic, complemented
7#14583178C211yesmaximal, characteristic, complemented
8#14583177C211yesmaximal, characteristic, complemented
9#14583134C211yesmaximal, characteristic, complemented
10#14583133C211yesmaximal, characteristic, complemented
11#14582979C211yesmaximal, characteristic, complemented
12(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
13C2×#13063258C211yesmaximal, characteristic, complemented
14#107×D43C211yesmaximal, characteristic, complemented
15C43×#480C211yesmaximal, characteristic, complemented
16C2×#10621898—21no—
17C2×#10621900—21no—
18C2×#10621882C2211yescharacteristic
19C22×C43⋊C8C2211yescharacteristic
20C2×C8×D43C2211yescharacteristic
21#13063324C2211yescharacteristic
22#13063324C2211yescharacteristic
23#13063310—21no—
24#13063308—21no—
25#13063307—21no—
26#13063306—21no—
27#13063303—21no—
28#13063302—21no—
29#13063300C2211yescharacteristic
30#13063299C2211yescharacteristic
31#13063296C2211yescharacteristic
32D4×Dic43C2211yescharacteristic
33#13063287C2211yescharacteristic
34C4×C22⋊D43C2211yescharacteristic
35C2×C4⋊Dic43C2211yescharacteristic
36C4⋊C4×D43C2211yescharacteristic
37C4⋊C4×D43C2211yescharacteristic
38#13063259C2211yescharacteristic
39#13063259C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063258C2211yescharacteristic
42#13063258C2211yescharacteristic
43#13063258C2211yescharacteristic
44#13063258C2211yescharacteristic
45Dic43⋊C8C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52#121×C43C2211yescharacteristic
53C2×C4⋊C4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43D411yescharacteristic
66C22×Dic43—21no—
67C22×Dic43—21no—
68#10621900—44no—
69#10621898—44no—
70C2×D172—21no—
71C2×D172C2311yescharacteristic
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43C2311yescharacteristic
76C2×Dic86—21no—
77C2×Dic86—21no—
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C4⋊C4×C43—21no—
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C22⋊C4×C43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43D411yescharacteristic
88#10621882—22no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4D411yescharacteristic
93C4⋊Dic43—21no—
94C4⋊Dic43C2311yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4D411yescharacteristic
102C4×Dic43C2311yescharacteristic
103C2×C43⋊C8—22no—
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C8×D43—22no—
107C23×C43—21no—
108C23×C43C2×D411yescharacteristic
109C22×D43—21no—
110C22×D43C2×D411yescharacteristic
111D4×C43—21no—
112D4×C43—21no—
113D4×C43—42no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—42no—
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2411yescharacteristic
122C22⋊D43—42no—
123C22⋊D43—42no—
124C22⋊D43D814yescomplemented
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—42no—
129C2×Dic43—42no—
130C2×Dic43C2×D411yescharacteristic
131C2×Dic43C2×D411yescharacteristic
132C2×Dic43C2×D411yescharacteristic
133D172—21no—
134D172—21no—
135D172—42no—
136C4×D43—21no—
137C4×D43—21no—
138C4×D43—42no—
139C4×D43—42no—
140C4×D43—42no—
141Dic86—42no—
142Dic86—42no—
143C8×C43—21no—
144C8×C43—21no—
145C43⋊C8—21no—
146C43⋊C8#4112yescomplemented
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43C2×D812yes—
153C22×C43C22×D411yescharacteristic
154C2×D43—21no—
155C2×D43—21no—
156C2×D43—41no—
157C2×D43—41no—
158C2×D43—41no—
159C2×D43C2×D812yes—
160C4×C43—21no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43C2×#4111yescharacteristic
165C4×C432−1+411yescharacteristic
166Dic43—21no—
167Dic43—21no—
168Dic43—41no—
169Dic43—41no—
170Dic43—41no—
171Dic43C2×D812yes—
172#3334—431nomaximal, Sylow
173C2×C43—22no—
174C2×C43—81no—
175C2×C43#54711yescharacteristic
176C2×C43C22×D811yescharacteristic
177C2×C43#57811yescharacteristic
178D43—22no—
179D43—81no—
180#547—431no—
181#547—431no—
182#500—431no—
183#480—431no—
184#480—431no—
185#480—431no—
186#480D4311yescharacteristic, complemented
187#474—431no—
188#474—431no—
189#466—431no—
190#466—431no—
191C4×D8—431no—
192C8×D4—431no—
193C2×#107—431no—
194C2×#107—431no—
195C43#333411yescharacteristic, complemented, Sylow
196C2×#41—861no—
197C2×#41—861no—
198C2×D8—431no—
199C22×C8—431no—
200C22×C8—431no—
201C4⋊Q8—431no—
202C4⋊Q8—431no—
203#123—861no—
204#123—861no—
205#123—861no—
206#123—861no—
207C22⋊Q8—861no—
208C22⋊Q8—861no—
209#121—431no—
210#121—431no—
211#121—431no—
212#121C2×D4311yescharacteristic
213C4×D4—431no—
214C4×D4—431no—
215C4×D4—431no—
216C2×C4⋊C4—431no—
217C2×C4⋊C4—431no—
218C2×C4⋊C4—431no—
219C2×C4⋊C4C2×D4311yescharacteristic
220#107—431no—
221#107—431no—
222#107—431no—
223#107—431no—
224#107—431no—
225#107—431no—
226#107—431no—
227#107C2×D4311yescharacteristic
228#107C2×D4311yescharacteristic
229C4⋊C8—431no—
230#102—431no—
231#102—431no—
232#102—431no—
233#102—431no—
234#102C2×D4311yescharacteristic
235#102C2×D4311yescharacteristic
236C22⋊C8—431no—
237C22⋊C8C2×D4311yescharacteristic
238C4×C8—431no—
239#41—1724no—
240#41—1724no—
241C2×Q8—861no—
242C2×Q8—861no—
243C2×D4—21no—
244C2×D4—431no—
245C2×D4—431no—
246C2×D4—861no—
247C2×D4—861no—
248C2×D4—861no—
249C2×D4C22×D4311yescharacteristic
250C22×C4—21no—
251C22×C4—431no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4C22×D4311yescharacteristic
258D8—862no—
259C2×C8—431no—
260C2×C8—431no—
261C2×C8—862no—
262C2×C8—862no—
263C2×C8C22×D4311yescharacteristic
264C2×C8C22×D4311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—431no—
267C4⋊C4—431no—
268C4⋊C4—431no—
269C4⋊C4—431no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4C22×D4311yescharacteristic
276C4⋊C4C22×D4311yescharacteristic
277C4⋊C4C22×D4311yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—431no—
280C22⋊C4—431no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C42—431no—
287C23—21no—
288C23—431no—
289C23—861no—
290C23D4×D4311yescharacteristic
291Q8—1722no—
292Q8—1722no—
293D4—21no—
294D4—21no—
295D4—42no—
296D4—434no—
297D4—861no—
298D4—861no—
299D4—1722no—
300D4—1722no—
301D4—1722no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—431no—
309C2×C4—431no—
310C2×C4—431no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—1722no—
317C2×C4—1722no—
318C2×C4—1722no—
319C2×C4—1722no—
320C2×C4—1722no—
321C2×C4D4×D4311yescharacteristic
322C2×C4C23×D4311yescharacteristic
323C8—21no—
324C8—21no—
325C8—432no—
326C8—861no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—432no—
333C22—861no—
334C22—861no—
335C22—1721no—
336C22—1721no—
337C22—1721no—
338C22D8×D4312yes—
339C22C2×D4×D4311yescharacteristic
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—432no—
345C4—861no—
346C4—861no—
347C4—1721no—
348C4—1721no—
349C4—1721no—
350C4#41×D4311yescharacteristic
351C4#1306337211yescharacteristic
352C2—22no—
353C2—81no—
354C2—862no—
355C2—3441no—
356C2#1458354711yescharacteristic
357C2C2×D8×D4311yescharacteristic
358C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#480C2
socleC22×C43C22×D4
hypercenter#480D43
hypocenterC43#3334
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #14583550C2semidirect
2. #14583549C2semidirect
3. #14583303C2semidirect
4. #14583214C2semidirect
5. #14583213C2semidirect
6. #14583211C2semidirect
7. #14583178C2semidirect
8. #14583177C2semidirect
9. #14583134C2semidirect
10. #14583133C2semidirect
11. #14582979C2semidirect
12. (C22⋊D43)⋊C8C2semidirect
13. C2×#13063258C2semidirect
14. #107×D43C2semidirect
15. C43×#480C2semidirect
124. C22⋊D43D8semidirect
146. C43⋊C8#41semidirect
186. #480D43semidirect
195. C43#3334semidirect