Finite Group Databasebeta

← #19147649

Subgroups — #19147649

Order 5504.

362 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583632C211yesmaximal, characteristic
2#14583627C211yesmaximal, characteristic, complemented
3#14583293C211yesmaximal, characteristic, complemented
4#14583290C211yesmaximal, characteristic, complemented
5#14583270C211yesmaximal, characteristic
6#14583121C211yesmaximal, characteristic, complemented
7#14583120C211yesmaximal, characteristic, complemented
8#14583108C211yesmaximal, characteristic, complemented
9#14583104C211yesmaximal, characteristic, complemented
10#14583103C211yesmaximal, characteristic, complemented
11#14583098C211yesmaximal, characteristic
12#14583027C211yesmaximal, characteristic, complemented
13#14582998C211yesmaximal, characteristic, complemented
14#14582993C211yesmaximal, characteristic, complemented
15C43×#440C211yesmaximal, characteristic, complemented
16C2×Dic172C2211yescharacteristic
17C2×Dic172C2211yescharacteristic
18C2×#10621885C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×#10621873C2211yescharacteristic
21C2×#10621883C2211yescharacteristic
22C2×#10621883C2211yescharacteristic
23C2×#10621884C2211yescharacteristic
24#13063325C2211yescharacteristic
25#13063323C2211yescharacteristic
26#13063323C2211yescharacteristic
27#13063321C2211yescharacteristic
28#13063317—21no—
29#13063315—21no—
30#13063315—21no—
31#13063313C2211yescharacteristic
32#13063312C2211yescharacteristic
33#13063311—21no—
34#13063308—21no—
35#13063307—21no—
36C4×Dic86—21no—
37C4×Dic86C2211yescharacteristic
38#13063290C2211yescharacteristic
39#13063290C2211yescharacteristic
40#13063290C2211yescharacteristic
41#13063287C2211yescharacteristic
42C4×C22⋊D43—21no—
43C4⋊(C43⋊C8)C2211yescharacteristic
44Dic43⋊C8C2211yescharacteristic
45Dic43⋊C8C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063248C2211yescharacteristic
49#13063245C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×SD16×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C2×D172C2311yescharacteristic
65C2×C4×D43—21no—
66C2×Dic86D411yescharacteristic
67C2×Dic86C2311yescharacteristic
68C2×Dic86C2311yescharacteristic
69C2×Dic86C2311yescharacteristic
70SD16×C43—22no—
71C2×C8×C43C2311yescharacteristic
72C2×C8×C43C2311yescharacteristic
73C4⋊C4×C43—21no—
74C4⋊C4×C43C2311yescharacteristic
75C4⋊C4×C43C2311yescharacteristic
76C22⋊C4×C43—21no—
77C42×C43—21no—
78C42×C43C2311yescharacteristic
79C22⋊Dic43—21no—
80C22⋊Dic43—21no—
81#10621885—41no—
82#10621884—41no—
83#10621883—41no—
84#10621883—41no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4—21no—
88C4⋊Dic43—21no—
89C4⋊Dic43—21no—
90C4⋊Dic43D411yescharacteristic
91Dic43⋊C4—21no—
92Dic43⋊C4—21no—
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4D411yescharacteristic
99Dic43⋊C4D411yescharacteristic
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43C2311yescharacteristic
104C4×Dic43C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107Dic172—22no—
108Dic172—41no—
109#10621873—22no—
110#10621873—41no—
111C23×C43—21no—
112C22×D43—21no—
113Q8×C43—21no—
114Q8×C43—21no—
115D4×C43—21no—
116D4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—81no—
121C2×C4×C43C2×D411yescharacteristic
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2411yescharacteristic
124C22⋊D43—42no—
125C22⋊D43—81no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43C2×D411yescharacteristic
130C2×Dic43C2×D411yescharacteristic
131C2×Dic43C2×D411yescharacteristic
132C2×Dic43C2×D411yescharacteristic
133D172—21no—
134D172—21no—
135C4×D43—81no—
136Dic86—22no—
137Dic86—21no—
138Dic86—21no—
139Dic86—21no—
140Dic86—21no—
141Dic86—21no—
142Dic86—21no—
143C8×C43—21no—
144C8×C43#4112yes—
145C43⋊C8—21no—
146C43⋊C8—21no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43C22×D411yescharacteristic
151C2×D43—41no—
152C2×D43—41no—
153C2×D43—41no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43C2×#4111yescharacteristic
160C4×C43H(5,𝔽2)11yescharacteristic
161Dic43—21no—
162Dic43—21no—
163Dic43—21no—
164Dic43—41no—
165Dic43—41no—
166Dic43—41no—
167Dic43#13712yes—
168#3400—431nomaximal, Sylow
169C2×C43—81no—
170C2×C43#55011yescharacteristic
171C2×C43C2×#13711yescharacteristic
172C2×C43#57711yescharacteristic
173D43—81no—
174#559—431no—
175#557—431no—
176#497—431no—
177#497—431no—
178#492—431no—
179#464—431no—
180#464—431no—
181#462—431no—
182#461—431no—
183#461—431no—
184#460—431no—
185#446—431no—
186#440—431no—
187#440D4311yescharacteristic, complemented
188C4×Q16—431no—
189C43#340011yescharacteristic, complemented, Sylow
190C2×Q16—431no—
191C2×Q16—431no—
192C2×Q16—431no—
193C2×SD16—431no—
194C2×SD16—431no—
195C2×SD16—431no—
196C2×SD16—431no—
197C2×SD16—431no—
198C2×SD16C2×D4311yescharacteristic
199C4⋊Q8—431no—
200C4⋊Q8—431no—
201C4⋊Q8—431no—
202#127—431no—
203#125—861no—
204#125—861no—
205#125—861no—
206#124—431no—
207#124—431no—
208#124—861no—
209#123—861no—
210#123—861no—
211C4×Q8—431no—
212C4×Q8—431no—
213C4×Q8—431no—
214C4×Q8—431no—
215C4×Q8—861no—
216C4×Q8C2×D4311yescharacteristic
217C4×D4—431no—
218C4×D4—861no—
219C4×D4C2×D4311yescharacteristic
220#107C2×D4311yescharacteristic
221C4⋊C8—431no—
222C4⋊C8—431no—
223C4⋊C8—431no—
224#103—431no—
225#103—431no—
226#103—431no—
227#103C2×D4311yescharacteristic
228#102—431no—
229#102C2×D4311yescharacteristic
230#97—431no—
231#97C2×D4311yescharacteristic
232C4×C8—431no—
233C2×Q8—431no—
234C2×Q8—431no—
235C2×Q8—431no—
236C2×Q8—431no—
237C2×Q8C22×D4311yescharacteristic
238C2×D4—431no—
239C2×D4—861no—
240C2×D4—861no—
241C2×D4C22×D4311yescharacteristic
242C22×C4—21no—
243C22×C4—861no—
244Q16—862no—
245Q16—1721no—
246Q16—1721no—
247SD16—22no—
248SD16—862no—
249SD16—1721no—
250SD16—1721no—
251SD16—1721no—
252SD16—1721no—
253C2×C8—431no—
254C2×C8—431no—
255C2×C8C22×D4311yescharacteristic
256C2×C8C22×D4311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—431no—
259C4⋊C4—431no—
260C4⋊C4—431no—
261C4⋊C4—861no—
262C4⋊C4—861no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4C22×D4311yescharacteristic
271C4⋊C4C22×D4311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C22⋊C4—861no—
277C22⋊C4—861no—
278C42—21no—
279C42—431no—
280C42—431no—
281C42—861no—
282C42—861no—
283C42—861no—
284C42C22×D4311yescharacteristic
285C23—21no—
286C23—861no—
287Q8—21no—
288Q8—21no—
289Q8—862no—
290Q8—861no—
291Q8—861no—
292Q8—861no—
293Q8—861no—
294Q8—861no—
295Q8—861no—
296D4—21no—
297D4—21no—
298D4—861no—
299D4—861no—
300D4—3441no—
301D4—1722no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—81no—
306C2×C4—431no—
307C2×C4—431no—
308C2×C4—431no—
309C2×C4—431no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—3441no—
314C2×C4D4×D4311yescharacteristic
315C2×C4D4×D4311yescharacteristic
316C2×C4C23×D4311yescharacteristic
317C8—21no—
318C8—861no—
319C8—861no—
320C8#1062189812yes—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—1721no—
325C22—1721no—
326C22—1721no—
327C22C2×D4×D4311yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—432no—
334C4—861no—
335C4—861no—
336C4—861no—
337C4—1721no—
338C4—1721no—
339C4—1721no—
340C4C2×#1062189811yescharacteristic
341C4#1306337111yescharacteristic
342C2—81no—
343C2—3441no—
344C2#1458357011yescharacteristic
345C2#137×D4311yescharacteristic
346C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#440C2
socleC22×C43C22×D4
hypercenter#440D43
hypocenterC43#3400
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #14583627C2semidirect
3. #14583293C2semidirect
4. #14583290C2semidirect
6. #14583121C2semidirect
7. #14583120C2semidirect
8. #14583108C2semidirect
9. #14583104C2semidirect
10. #14583103C2semidirect
12. #14583027C2semidirect
13. #14582998C2semidirect
14. #14582993C2semidirect
15. C43×#440C2semidirect
187. #440D43semidirect
189. C43#3400semidirect