Finite Group Databasebeta

← #19144955

Subgroups — #19144955

Order 5504.

372 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583526C211yesmaximal, characteristic, complemented
2#14583474C211yesmaximal, characteristic
3#14583267C211yesmaximal, characteristic, complemented
4#14583266C211yesmaximal, characteristic, complemented
5#14583261C211yesmaximal, characteristic, complemented
6#14583260C211yesmaximal, characteristic, complemented
7#14583255C211yesmaximal, characteristic, complemented
8#14583254C211yesmaximal, characteristic, complemented
9#14583248C211yesmaximal, characteristic, complemented
10#14582906C211yesmaximal, characteristic, complemented
11#14582899C211yesmaximal, characteristic
12#14582894C211yesmaximal, characteristic
13#103×D43C211yesmaximal, characteristic, complemented
14#14582853C211yesmaximal, characteristic, complemented
15C43×#487C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18C2×#10621872C2211yescharacteristic
19C2×C8×D43C2211yescharacteristic
20#13063324C2211yescharacteristic
21#13063323—21no—
22#13063323C2211yescharacteristic
23#13063317C2211yescharacteristic
24#13063316C2211yescharacteristic
25#13063315—21no—
26#13063314C2211yescharacteristic
27#13063313C2211yescharacteristic
28#13063310—21no—
29#13063310—21no—
30#13063303—21no—
31#13063303—21no—
32#13063303—21no—
33#13063301—21no—
34#13063283C2211yescharacteristic
35#13063282C2211yescharacteristic
36C4⋊C4×D43C2211yescharacteristic
37#13063250C2211yescharacteristic
38#13063250C2211yescharacteristic
39#13063249C2211yescharacteristic
40#13063249C2211yescharacteristic
41#13063249C2211yescharacteristic
42#13063249C2211yescharacteristic
43#13063248C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063236C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C4⋊Q8×C43C2211yescharacteristic
53C4⋊Q8×C43C2211yescharacteristic
54#103×C43C2211yescharacteristic
55#103×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58C4×C8×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62#10621902—22no—
63#10621902—22no—
64Q8×D43—22no—
65Q8×D43—22no—
66C2×D172—21no—
67C2×D172C2311yescharacteristic
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43C2311yescharacteristic
72C2×Dic86—21no—
73C2×Dic86—21no—
74C2×Dic86C2311yescharacteristic
75C2×C8×C43C2311yescharacteristic
76C2×C8×C43C2311yescharacteristic
77C4⋊C4×C43—21no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43C2311yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C42×C43C2311yescharacteristic
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4D411yescharacteristic
89(C2×D43)⋊C4D411yescharacteristic
90C4⋊Dic43—21no—
91C4⋊Dic43C2311yescharacteristic
92C4⋊Dic43C2311yescharacteristic
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4D411yescharacteristic
101Dic43⋊C4D411yescharacteristic
102C4×Dic43—21no—
103C4×Dic43C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106#10621872—22no—
107C8×D43—22no—
108C22×D43—21no—
109C22×D43C2×D411yescharacteristic
110Q8×C43—21no—
111Q8×C43—21no—
112Q8×C43—21no—
113Q8×C43—21no—
114Q8×C43—81no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43C2×D411yescharacteristic
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2411yescharacteristic
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43C2×D411yescharacteristic
126C2×Dic43C2×D411yescharacteristic
127C2×Dic43C2×D411yescharacteristic
128D172—21no—
129D172—21no—
130D172—42no—
131C4×D43—42no—
132C4×D43—42no—
133C4×D43—81no—
134C4×D43#4112yes—
135C4×D43#4112yes—
136Dic86—21no—
137Dic86—21no—
138Dic86—42no—
139Dic86—81no—
140C8×C43—21no—
141C8×C43—21no—
142C43⋊C8—21no—
143C43⋊C8—21no—
144C22×C43C22×D411yescharacteristic
145C2×D43—21no—
146C2×D43—21no—
147C2×D43—41no—
148C2×D43—41no—
149C2×D43—41no—
150C2×D43#12412yes—
151C4×C43—21no—
152C4×C43—21no—
153C4×C43—41no—
154C4×C43—41no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43C2×#4111yescharacteristic
158C4×C43C2×#4111yescharacteristic
159Dic43—21no—
160Dic43—21no—
161Dic43—41no—
162Dic43—41no—
163Dic43—41no—
164Dic43#12412yes—
165#3137—431nomaximal, Sylow
166C2×C43C2×#12411yescharacteristic
167C2×C43#57711yescharacteristic
168C2×C43#57811yescharacteristic
169D43—22no—
170D43—81no—
171#544—431no—
172#536—431no—
173#491—431no—
174#491—431no—
175#489—431no—
176#489—431no—
177#488—431no—
178#488—431no—
179#487—431no—
180#487D4311yescharacteristic, complemented
181#419—431no—
182#417—431no—
183#416—431no—
184C2×#103—431no—
185#405—431no—
186C43#313711yescharacteristic, complemented, Sylow
187C2×#41—431no—
188C22×Q8—431no—
189C2×M16—431no—
190C22×C8—431no—
191C4⋊Q8—431no—
192C4⋊Q8—431no—
193C4⋊Q8—861no—
194C4⋊Q8C2×D4311yescharacteristic
195C4⋊Q8C2×D4311yescharacteristic
196#125—431no—
197#125—431no—
198#125—861no—
199#124—431no—
200#124—431no—
201#123—861no—
202#123—861no—
203C22⋊Q8—861no—
204C22⋊Q8—861no—
205C22⋊Q8—861no—
206C22⋊Q8—861no—
207#117—431no—
208#117—431no—
209C2×C4⋊C4—431no—
210#103—431no—
211#103—431no—
212#103—431no—
213#103—431no—
214#103—431no—
215#103—431no—
216#103—431no—
217#103—431no—
218#103C2×D4311yescharacteristic
219#103C2×D4311yescharacteristic
220#103C2×D4311yescharacteristic
221#103C2×D4311yescharacteristic
222#102—431no—
223#102—431no—
224#102—431no—
225#102—431no—
226#97—431no—
227#97—431no—
228C4×C8—431no—
229C4×C8C2×D4311yescharacteristic
230#41—862no—
231#41—862no—
232C2×Q8—21no—
233C2×Q8—431no—
234C2×Q8—861no—
235C2×Q8—861no—
236C2×Q8—862no—
237C2×Q8—862no—
238C2×Q8C22×D4311yescharacteristic
239C2×Q8C22×D4311yescharacteristic
240C2×D4—431no—
241C2×D4—861no—
242C22×C4—431no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4—861no—
246M16—862no—
247C2×C8—431no—
248C2×C8—431no—
249C2×C8—862no—
250C2×C8C22×D4311yescharacteristic
251C2×C8C22×D4311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—431no—
256C4⋊C4—431no—
257C4⋊C4—431no—
258C4⋊C4—431no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4—861no—
262C4⋊C4—861no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4C22×D4311yescharacteristic
268C4⋊C4C22×D4311yescharacteristic
269C22⋊C4—431no—
270C22⋊C4—431no—
271C22⋊C4—861no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C42—431no—
277C42—861no—
278C42C22×D4311yescharacteristic
279C23—431no—
280C23—861no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—21no—
285Q8—81no—
286Q8—861no—
287Q8—861no—
288Q8—3441no—
289Q8—1722no—
290D4—861no—
291D4—861no—
292D4—1722no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—431no—
298C2×C4—432no—
299C2×C4—432no—
300C2×C4—431no—
301C2×C4—431no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—3441no—
306C2×C4—1722no—
307C2×C4—1722no—
308C2×C4D4×D4311yescharacteristic
309C2×C4D4×D4311yescharacteristic
310C2×C4C23×D4311yescharacteristic
311C8—21no—
312C8—21no—
313C8—861no—
314C8—861no—
315C22—432no—
316C22—861no—
317C22—861no—
318C22—1721no—
319C22—1721no—
320C22—1721no—
321C22C2×D4×D4311yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—432no—
329C4—861no—
330C4—861no—
331C4—1721no—
332C4—1721no—
333C4—1721no—
334C4#41×D4311yescharacteristic
335C4#41×D4311yescharacteristic
336C2—862no—
337C2—3441no—
338C2#124×D4311yescharacteristic
339C2#1458370511yescharacteristic
340C2#1458371211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#487C2
socleC22×C43C22×D4
hypercenter#487D43
hypocenterC43#3137
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #14583526C2semidirect
3. #14583267C2semidirect
4. #14583266C2semidirect
5. #14583261C2semidirect
6. #14583260C2semidirect
7. #14583255C2semidirect
8. #14583254C2semidirect
9. #14583248C2semidirect
10. #14582906C2semidirect
13. #103×D43C2semidirect
14. #14582853C2semidirect
15. C43×#487C2semidirect
180. #487D43semidirect
186. C43#3137semidirect