Finite Group Databasebeta

← #19147412

Subgroups — #19147412

Order 5504.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583632C211yesmaximal, characteristic
2#14583629C211yesmaximal, characteristic, complemented
3#14583261C211yesmaximal, characteristic, complemented
4#14583257C211yesmaximal, characteristic, complemented
5#14583244C211yesmaximal, characteristic
6#14583193C211yesmaximal, characteristic, complemented
7#14583178C211yesmaximal, characteristic, complemented
8#14583122C211yesmaximal, characteristic, complemented
9#14583120C211yesmaximal, characteristic, complemented
10#14583098C211yesmaximal, characteristic
11#14583028C211yesmaximal, characteristic, complemented
12#14582999C211yesmaximal, characteristic, complemented
13#14582998C211yesmaximal, characteristic, complemented
14#14582993C211yesmaximal, characteristic, complemented
15C43×#474C211yesmaximal, characteristic, complemented
16C2×Dic172C2211yescharacteristic
17C2×#10621873C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19#13063324—21no—
20#13063324C2211yescharacteristic
21#13063324C2211yescharacteristic
22#13063323—21no—
23#13063323—21no—
24#13063321C2211yescharacteristic
25#13063313C2211yescharacteristic
26#13063312C2211yescharacteristic
27#13063311—21no—
28#13063308—21no—
29#13063307—21no—
30C4×Dic86C2211yescharacteristic
31C4×Dic86C2211yescharacteristic
32#13063290—21no—
33#13063290C2211yescharacteristic
34#13063290C2211yescharacteristic
35#13063290C2211yescharacteristic
36#13063287C2211yescharacteristic
37C4×C22⋊D43—21no—
38#13063258C2211yescharacteristic
39Dic43⋊C8C2211yescharacteristic
40Dic43⋊C8C2211yescharacteristic
41#13063250C2211yescharacteristic
42#13063248C2211yescharacteristic
43#13063248C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063236C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C4⋊Q8×C43C2211yescharacteristic
53C4×D4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C2×D172C2311yescharacteristic
65C2×C4×D43—21no—
66C2×Dic86—21no—
67C2×Dic86—21no—
68C2×Dic86D411yescharacteristic
69C2×Dic86C2311yescharacteristic
70C2×Dic86C2311yescharacteristic
71C2×C8×C43C2311yescharacteristic
72C2×C8×C43C2311yescharacteristic
73C4⋊C4×C43—21no—
74C4⋊C4×C43C2311yescharacteristic
75C4⋊C4×C43C2311yescharacteristic
76C4⋊C4×C43C2311yescharacteristic
77C22⋊C4×C43—21no—
78C42×C43C2311yescharacteristic
79C22⋊Dic43—21no—
80C22⋊Dic43—21no—
81#10621883—22no—
82(C2×D43)⋊C4—21no—
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85C4⋊Dic43D411yescharacteristic
86C4⋊Dic43C2311yescharacteristic
87Dic43⋊C4—21no—
88Dic43⋊C4—21no—
89Dic43⋊C4—21no—
90Dic43⋊C4—21no—
91Dic43⋊C4—21no—
92Dic43⋊C4—21no—
93Dic43⋊C4D411yescharacteristic
94Dic43⋊C4D411yescharacteristic
95C4×Dic43—21no—
96C4×Dic43—21no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43C2311yescharacteristic
100C4×Dic43C2311yescharacteristic
101C2×C43⋊C8C2311yescharacteristic
102C2×C43⋊C8C2311yescharacteristic
103Dic172—22no—
104#10621873—22no—
105C23×C43—21no—
106C22×D43—21no—
107Q8×C43—81no—
108D4×C43—21no—
109D4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—81no—
114C2×C4×C43C2×D411yescharacteristic
115C2×C4×C43C2×D411yescharacteristic
116C2×C4×C43C2411yescharacteristic
117C22⋊D43—42no—
118C22⋊D43—81no—
119C2×Dic43—21no—
120C2×Dic43—21no—
121C2×Dic43—21no—
122C2×Dic43C2×D411yescharacteristic
123C2×Dic43C2×D411yescharacteristic
124C2×Dic43C2×D411yescharacteristic
125C2×Dic43C2×D411yescharacteristic
126D172—21no—
127D172—21no—
128C4×D43—81no—
129Dic86—21no—
130Dic86—22no—
131Dic86—21no—
132Dic86—21no—
133Dic86—81no—
134Dic86—81no—
135Dic86#4112yes—
136C8×C43—21no—
137C8×C43—21no—
138C43⋊C8—21no—
139C43⋊C8—21no—
140C22×C43—41no—
141C22×C43—41no—
142C22×C43—41no—
143C22×C43C22×D411yescharacteristic
144C2×D43—41no—
145C2×D43—41no—
146C2×D43—41no—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—41no—
150C4×C43—41no—
151C4×C43—41no—
152C4×C43C2×#4111yescharacteristic
153C4×C432−1+411yescharacteristic
154Dic43—22no—
155Dic43—21no—
156Dic43—21no—
157Dic43—21no—
158Dic43—41no—
159Dic43—41no—
160Dic43#13712yes—
161#3375—431nomaximal, Sylow
162C2×C43—81no—
163C2×C43#54811yescharacteristic
164C2×C43C2×#13711yescharacteristic
165C2×C43#57611yescharacteristic
166D43—81no—
167#559—431no—
168Q82—431no—
169#489—431no—
170#489—431no—
171#486—431no—
172#477—431no—
173#474—431no—
174#474D4311yescharacteristic, complemented
175#464—431no—
176#464—431no—
177#460—431no—
178#446—431no—
179#440—431no—
180#440—431no—
181C4×Q16—431no—
182C43#337511yescharacteristic, complemented, Sylow
183C2×Q16—431no—
184C2×SD16—431no—
185C2×SD16—431no—
186C4⋊Q8—431no—
187C4⋊Q8—431no—
188C4⋊Q8—861no—
189C4⋊Q8—861no—
190C4⋊Q8—861no—
191C4⋊Q8C2×D4311yescharacteristic
192#127—431no—
193#124—431no—
194#124—431no—
195#124—861no—
196#123—861no—
197#123—861no—
198C4×Q8—431no—
199C4×Q8—431no—
200C4×Q8—431no—
201C4×Q8—431no—
202C4×Q8—431no—
203C4×Q8—861no—
204C4×D4—431no—
205C4×D4—861no—
206C4×D4C2×D4311yescharacteristic
207#107—431no—
208#107C2×D4311yescharacteristic
209#107C2×D4311yescharacteristic
210C4⋊C8—431no—
211C4⋊C8—431no—
212C4⋊C8C2×D4311yescharacteristic
213#103—431no—
214#103—431no—
215#103—431no—
216#103—431no—
217#102—431no—
218#102—431no—
219#102—431no—
220#102—431no—
221#102C2×D4311yescharacteristic
222#102C2×D4311yescharacteristic
223#97—431no—
224#97—431no—
225C4×C8—431no—
226C2×Q8—21no—
227C2×Q8—431no—
228C2×Q8—431no—
229C2×Q8—431no—
230C2×Q8—861no—
231C2×Q8—861no—
232C2×D4—431no—
233C2×D4—861no—
234C2×D4—861no—
235C2×D4C22×D4311yescharacteristic
236C22×C4—21no—
237C22×C4—861no—
238Q16—862no—
239SD16—862no—
240SD16—862no—
241C2×C8—431no—
242C2×C8—431no—
243C2×C8C22×D4311yescharacteristic
244C2×C8C22×D4311yescharacteristic
245C4⋊C4—21no—
246C4⋊C4—431no—
247C4⋊C4—431no—
248C4⋊C4—431no—
249C4⋊C4—431no—
250C4⋊C4—861no—
251C4⋊C4—861no—
252C4⋊C4—861no—
253C4⋊C4—861no—
254C4⋊C4—861no—
255C4⋊C4—861no—
256C4⋊C4C22×D4311yescharacteristic
257C4⋊C4C22×D4311yescharacteristic
258C4⋊C4C22×D4311yescharacteristic
259C22⋊C4—21no—
260C22⋊C4—861no—
261C22⋊C4—861no—
262C22⋊C4—861no—
263C22⋊C4—861no—
264C22⋊C4—861no—
265C42—431no—
266C42—431no—
267C42—861no—
268C42—861no—
269C42—861no—
270C42—861no—
271C42C22×D4311yescharacteristic
272C23—21no—
273C23—861no—
274Q8—81no—
275Q8—432no—
276Q8—862no—
277Q8—861no—
278Q8—861no—
279Q8—861no—
280Q8—3441no—
281Q8—3441no—
282D4—21no—
283D4—21no—
284D4—861no—
285D4—861no—
286D4—3441no—
287D4—1722no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—81no—
292C2×C4—431no—
293C2×C4—431no—
294C2×C4—431no—
295C2×C4—431no—
296C2×C4—861no—
297C2×C4—861no—
298C2×C4—861no—
299C2×C4—3441no—
300C2×C4D4×D4311yescharacteristic
301C2×C4D4×D4311yescharacteristic
302C2×C4C23×D4311yescharacteristic
303C8—21no—
304C8—21no—
305C8—861no—
306C8—861no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—1721no—
311C22—1721no—
312C22—1721no—
313C22C2×D4×D4311yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—432no—
320C4—862no—
321C4—861no—
322C4—861no—
323C4—861no—
324C4—1721no—
325C4—1721no—
326C4#41×D4311yescharacteristic
327C4#1306337311yescharacteristic
328C2—81no—
329C2—3441no—
330C2#1458355911yescharacteristic
331C2#137×D4311yescharacteristic
332C2#1458370011yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#474C2
socleC22×C43C22×D4
hypercenter#474D43
hypocenterC43#3375
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #14583629C2semidirect
3. #14583261C2semidirect
4. #14583257C2semidirect
6. #14583193C2semidirect
7. #14583178C2semidirect
8. #14583122C2semidirect
9. #14583120C2semidirect
11. #14583028C2semidirect
12. #14582999C2semidirect
13. #14582998C2semidirect
14. #14582993C2semidirect
15. C43×#474C2semidirect
174. #474D43semidirect
182. C43#3375semidirect