Finite Group Databasebeta

← #19144803

Subgroups — #19144803

Order 5504.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583379C211yesmaximal, characteristic
2#14583232C211yesmaximal, characteristic, complemented
3#14583227C211yesmaximal, characteristic, complemented
4#14583203C211yesmaximal, characteristic, complemented
5#14583196C211yesmaximal, characteristic, complemented
6#14583106C211yesmaximal, characteristic, complemented
7#14583101C211yesmaximal, characteristic, complemented
8#14583059C211yesmaximal, characteristic
9#14583059C211yesmaximal, characteristic
10#14583004C211yesmaximal, characteristic, complemented
11#14582997C211yesmaximal, characteristic, complemented
12C4×#10621885C211yesmaximal, characteristic, complemented
13C4×#10621884C211yesmaximal, characteristic, complemented
14#14582960C211yesmaximal, characteristic, complemented
15C43×#541C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621885C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
21C4×Dic86C2211yescharacteristic
22C4×Dic86C2211yescharacteristic
23C4×D172C2211yescharacteristic
24C4×D172C2211yescharacteristic
25(C22⋊D43)⋊C4—21no—
26(C22⋊D43)⋊C4—21no—
27#13063283—21no—
28C2×C4⋊Dic43C2211yescharacteristic
29C4⋊C4×D43—21no—
30#13063258C2211yescharacteristic
31#13063258C2211yescharacteristic
32#13063256C2211yescharacteristic
33#13063256C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic
35C4⋊(C43⋊C8)C2211yescharacteristic
36#13063249C2211yescharacteristic
37#13063249C2211yescharacteristic
38#13063249C2211yescharacteristic
39#13063249C2211yescharacteristic
40#13063248C2211yescharacteristic
41#13063248C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44C22⋊(C43⋊C8)C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46#13063236C2211yescharacteristic
47C4×C43⋊C8C2211yescharacteristic
48C4⋊Q8×C43C2211yescharacteristic
49#126×C43—21no—
50#126×C43—21no—
51#125×C43—21no—
52#125×C43—21no—
53#125×C43C2211yescharacteristic
54C22⋊Q8×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56C4×Q8×C43C2211yescharacteristic
57C4×Q8×C43C2211yescharacteristic
58#117×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×Q8×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C2×C22⋊D43—21no—
63C22×Dic43—21no—
64#10621898—22no—
65#10621898—22no—
66C2×D172C2311yescharacteristic
67C2×C4×D43—21no—
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×Dic86C2311yescharacteristic
71C4⋊C4×C43—21no—
72C4⋊C4×C43—21no—
73C4⋊C4×C43—21no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43—21no—
76C4⋊C4×C43—21no—
77C4⋊C4×C43—21no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43D411yescharacteristic
80C4⋊C4×C43D411yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C22⋊C4×C43D411yescharacteristic
86C22⋊C4×C43D411yescharacteristic
87C42×C43—21no—
88C42×C43—21no—
89C42×C43C2311yescharacteristic
90C42×C43C2311yescharacteristic
91#10621885—22no—
92#10621885—22no—
93#10621884—22no—
94#10621884—22no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43C2×D411yescharacteristic
109C22×D43—21no—
110Q8×C43—21no—
111Q8×C43—21no—
112Q8×C43—21no—
113Q8×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2×D411yescharacteristic
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2411yescharacteristic
126C22⋊D43—24no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—81no—
131D172—21no—
132D172#4112yes—
133C4×D43—24no—
134C4×D43—81no—
135C4×D43—81no—
136Dic86—21no—
137Dic86#4112yes—
138C43⋊C8—21no—
139C43⋊C8—21no—
140C43⋊C8—21no—
141C43⋊C8—21no—
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43C22×D411yescharacteristic
146C2×D43—22no—
147C2×D43—41no—
148C2×D43—41no—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—41no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43C2×#4111yescharacteristic
159C4×C43C2×#4111yescharacteristic
160Dic43—22no—
161Dic43—41no—
162Dic43—41no—
163#3120—431nomaximal, Sylow
164C2×C43—41no—
165C2×C43#52511yescharacteristic
166C2×C43#57711yescharacteristic
167C2×C43#57811yescharacteristic
168D43—42no—
169#541D4311yescharacteristic, complemented
170#520—431no—
171#484—431no—
172#483—431no—
173#479—431no—
174#478—431no—
175#462—431no—
176#461—431no—
177#452—431no—
178#452—431no—
179#441—431no—
180#440—431no—
181C4×Q16—431no—
182C4×SD16—431no—
183#433—431no—
184C43#312011yescharacteristic, complemented, Sylow
185C2×#41—431no—
186C2×Q16—431no—
187C2×Q16—431no—
188C2×SD16—431no—
189C2×SD16—431no—
190C4⋊Q8C2×D4311yescharacteristic
191#126—21no—
192#126—21no—
193#125—21no—
194#125—21no—
195#125C2×D4311yescharacteristic
196C22⋊Q8C2×D4311yescharacteristic
197C22⋊Q8C2×D4311yescharacteristic
198C4×Q8—431no—
199C4×Q8—431no—
200C4×Q8C2×D4311yescharacteristic
201C4×Q8C2×D4311yescharacteristic
202C4×D4—431no—
203C4×D4—431no—
204C4×D4—861no—
205C4×D4—861no—
206#117—861no—
207#117C2×D4311yescharacteristic
208C2×C4⋊C4—431no—
209C2×C4⋊C4—861no—
210#107—431no—
211#107—431no—
212#106—431no—
213#106—431no—
214C4⋊C8—431no—
215C4⋊C8—431no—
216#103—431no—
217#103—431no—
218#103—431no—
219#103—431no—
220#103—431no—
221#103—431no—
222#102—431no—
223#102—431no—
224C22⋊C8—431no—
225C22⋊C8—431no—
226#97—431no—
227C4×C8—431no—
228#41—862no—
229#41—862no—
230C2×Q8—431no—
231C2×Q8C22×D4311yescharacteristic
232C2×Q8C22×D4311yescharacteristic
233C2×D4—431no—
234C2×D4—861no—
235C22×C4—861no—
236C22×C4—861no—
237C22×C4—861no—
238C22×C4—861no—
239C22×C4C22×D4311yescharacteristic
240Q16—862no—
241Q16—862no—
242SD16—862no—
243SD16—862no—
244C2×C8—431no—
245C2×C8—431no—
246C2×C8—431no—
247C2×C8—431no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—431no—
257C4⋊C4—431no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4C22⋊D4311yescharacteristic
262C4⋊C4C22⋊D4311yescharacteristic
263C4⋊C4C22×D4311yescharacteristic
264C4⋊C4C22×D4311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—861no—
268C22⋊C4—861no—
269C22⋊C4C22⋊D4311yescharacteristic
270C22⋊C4C22⋊D4311yescharacteristic
271C42—21no—
272C42—21no—
273C42—861no—
274C42—861no—
275C42C22×D4311yescharacteristic
276C42C22×D4311yescharacteristic
277C23—861no—
278C23C2×C22⋊D4311yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—432no—
284Q8—861no—
285D4—432no—
286D4—864no—
287D4—861no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—864no—
295C2×C4—861no—
296C2×C4—861no—
297C2×C4—861no—
298C2×C4—3441no—
299C2×C4—3441no—
300C2×C4—3441no—
301C2×C4C2×C22⋊D4311yescharacteristic
302C2×C4C2×C22⋊D4311yescharacteristic
303C2×C4C2×C22⋊D4311yescharacteristic
304C2×C4C2×C22⋊D4311yescharacteristic
305C2×C4C2×C22⋊D4311yescharacteristic
306C2×C4C23×D4311yescharacteristic
307C8—861no—
308C8—861no—
309C8—861no—
310C8—861no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—862no—
315C22—1721no—
316C22—1721no—
317C22C22×C22⋊D4311yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—862no—
328C4—1721no—
329C4—1721no—
330C4#41×D4311yescharacteristic
331C4#41×D4311yescharacteristic
332C2—41no—
333C2—1722no—
334C2#1458340611yescharacteristic
335C2#1458370711yescharacteristic
336C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#541C2
socleC22×C43C22×D4
hypercenter#541D43
hypocenterC43#3120
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #14583232C2semidirect
3. #14583227C2semidirect
4. #14583203C2semidirect
5. #14583196C2semidirect
6. #14583106C2semidirect
7. #14583101C2semidirect
10. #14583004C2semidirect
11. #14582997C2semidirect
12. C4×#10621885C2semidirect
13. C4×#10621884C2semidirect
14. #14582960C2semidirect
15. C43×#541C2semidirect
169. #541D43semidirect
184. C43#3120semidirect