Finite Group Databasebeta

← #20284994

Subgroups — #20284994

Order 6784.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16811244C211yesmaximal, characteristic, complemented
2#16811103C211yesmaximal, characteristic, complemented
3#16810954C211yesmaximal, characteristic, complemented
4#16810942C211yesmaximal, characteristic, complemented
5#16810914C211yesmaximal, characteristic, complemented
6#16810909C211yesmaximal, characteristic, complemented
7#16810846C211yesmaximal, characteristic, complemented
8#16810839C211yesmaximal, characteristic, complemented
9#16810787C211yesmaximal, characteristic, complemented
10#16810770C211yesmaximal, characteristic
11#16810736C211yesmaximal, characteristic, complemented
12#16810731C211yesmaximal, characteristic, complemented
13C4×#11719913C211yesmaximal, characteristic, complemented
14C4×#11719913C211yesmaximal, characteristic, complemented
15C53×#433C211yesmaximal, characteristic, complemented
16C2×#11719945C2211yescharacteristic
17C2×Dic212C2211yescharacteristic
18C2×#11719913C2211yescharacteristic
19C2×#11719913C2211yescharacteristic
20C2×D424C2211yescharacteristic
21#13133217C2211yescharacteristic
22#13133212—21no—
23#13133205C2211yescharacteristic
24#13133203—21no—
25#13133199—21no—
26#13133196C2211yescharacteristic
27#13133195—21no—
28#13133191C2211yescharacteristic
29C4×Dic106C2211yescharacteristic
30C4×Dic106C2211yescharacteristic
31C4×Dic106C2211yescharacteristic
32C4×D212C2211yescharacteristic
33C4×D212C2211yescharacteristic
34C4×D212C2211yescharacteristic
35#13133177—21no—
36#13133177—21no—
37#13133175—21no—
38C2×C4⋊Dic53C2211yescharacteristic
39C4⋊C4×D53—21no—
40#13133149C2211yescharacteristic
41#13133149C2211yescharacteristic
42#13133149C2211yescharacteristic
43#13133149C2211yescharacteristic
44#13133142C2211yescharacteristic
45#13133142C2211yescharacteristic
46#13133142C2211yescharacteristic
47#13133142C2211yescharacteristic
48#13133139C2211yescharacteristic
49#13133139C2211yescharacteristic
50#13133139C2211yescharacteristic
51#13133139C2211yescharacteristic
52#117×C53C2211yescharacteristic
53C4⋊C8×C53C2211yescharacteristic
54C4⋊C8×C53C2211yescharacteristic
55C22⋊C8×C53C2211yescharacteristic
56C22⋊C8×C53C2211yescharacteristic
57#97×C53C2211yescharacteristic
58C4×C8×C53C2211yescharacteristic
59C22×C4×C53C2311yescharacteristic
60C2×C22⋊D53—21no—
61C2×C22⋊D53—21no—
62C22×Dic53—21no—
63#11719945—22no—
64#11719945—22no—
65C2×D212C2311yescharacteristic
66C2×D212C2311yescharacteristic
67C2×C4×D53—21no—
68C2×C4×D53—21no—
69C2×C4×D53—21no—
70C2×C4×D53—21no—
71C2×Dic106—21no—
72C2×Dic106C2311yescharacteristic
73C2×Dic106C2311yescharacteristic
74C2×C8×C53C2311yescharacteristic
75C2×C8×C53C2311yescharacteristic
76C2×C8×C53C2311yescharacteristic
77C2×C8×C53C2311yescharacteristic
78C4⋊C4×C53D411yescharacteristic
79C4⋊C4×C53D411yescharacteristic
80C22⋊C4×C53D411yescharacteristic
81C22⋊C4×C53D411yescharacteristic
82C42×C53C2311yescharacteristic
83C42×C53C2311yescharacteristic
84C22⋊Dic53—21no—
85#11719921—21no—
86#11719921—21no—
87#11719921—21no—
88#11719921—21no—
89#11719921—21no—
90#11719921—21no—
91C4⋊Dic53—21no—
92C4⋊Dic53—21no—
93C4⋊Dic53C2311yescharacteristic
94C4⋊Dic53C2311yescharacteristic
95C4⋊Dic53C2311yescharacteristic
96C4⋊Dic53C2311yescharacteristic
97#11719919—21no—
98#11719919—21no—
99#11719919—21no—
100#11719919—21no—
101C4×Dic53—21no—
102C4×Dic53—21no—
103C4×Dic53—21no—
104Dic212—22no—
105D424—22no—
106#11719913—22no—
107#11719913—22no—
108C23×C53C2×D411yescharacteristic
109C22×D53—21no—
110C22×D53—21no—
111C2×C4×C53—21no—
112C2×C4×C53—21no—
113C2×C4×C53C2×D411yescharacteristic
114C2×C4×C53C2×D411yescharacteristic
115C2×C4×C53C2×D411yescharacteristic
116C2×C4×C53C2×D411yescharacteristic
117C2×C4×C53C2×D411yescharacteristic
118C2×C4×C53C2411yescharacteristic
119C22⋊D53—24no—
120C22⋊D53—81no—
121C2×Dic53—21no—
122C2×Dic53—21no—
123C2×Dic53—21no—
124C2×Dic53—21no—
125C2×Dic53—21no—
126C2×Dic53—21no—
127C2×Dic53—81no—
128D212—21no—
129D212—21no—
130D212—21no—
131D212#4112yes—
132C4×D53—24no—
133C4×D53—81no—
134C4×D53—81no—
135C4×D53—81no—
136Dic106—21no—
137Dic106—21no—
138Dic106—21no—
139Dic106—81no—
140Dic106#4112yes—
141C8×C53—21no—
142C8×C53—21no—
143C8×C53—21no—
144C8×C53—21no—
145C22×C53—21no—
146C22×C53—21no—
147C22×C53—21no—
148C22×C53C22×D411yescharacteristic
149C2×D53—22no—
150C2×D53—41no—
151C2×D53—41no—
152C2×D53—41no—
153C2×D53—41no—
154C2×D53—41no—
155C4×C53—21no—
156C4×C53—21no—
157C4×C53—21no—
158C4×C53—21no—
159C4×C53—21no—
160C4×C53C2×#4111yescharacteristic
161C4×C53C2×#4111yescharacteristic
162Dic53—22no—
163Dic53—41no—
164Dic53—41no—
165Dic53—41no—
166Dic53—41no—
167Dic53—41no—
168#3125—531nomaximal, Sylow
169C2×C53—41no—
170C2×C53#52511yescharacteristic
171C2×C53#57711yescharacteristic
172C2×C53#57711yescharacteristic
173D53—42no—
174D53—81no—
175#542—531no—
176#520—531no—
177#483—531no—
178#481—531no—
179#476—531no—
180#475—531no—
181#464—531no—
182#463—531no—
183#452—531no—
184#449—531no—
185#442—531no—
186#441—531no—
187C4×SD16—531no—
188C4×SD16—531no—
189#433D5311yescharacteristic, complemented
190C53#312511yescharacteristic, complemented, Sylow
191C2×#41—531no—
192C2×Q16—531no—
193C2×SD16—531no—
194C2×SD16—531no—
195C2×D8—531no—
196C4⋊Q8—531no—
197#126—1061no—
198#124—531no—
199#124—1061no—
200#123—1061no—
201C22⋊Q8—531no—
202C22⋊Q8—1061no—
203#121—531no—
204C4×Q8—531no—
205C4×Q8—531no—
206C4×Q8—531no—
207C4×D4—531no—
208C4×D4—531no—
209C4×D4—531no—
210C4×D4—1061no—
211C4×D4—1061no—
212#117—1061no—
213#117C2×D5311yescharacteristic
214C2×C4⋊C4—531no—
215C2×C4⋊C4—1061no—
216#106—531no—
217#106—531no—
218#106—531no—
219#106—531no—
220C4⋊C8C2×D5311yescharacteristic
221C4⋊C8C2×D5311yescharacteristic
222#103—531no—
223#103—531no—
224#103—531no—
225#103—531no—
226#102—531no—
227#102—531no—
228#102—531no—
229#102—531no—
230C22⋊C8C2×D5311yescharacteristic
231C22⋊C8C2×D5311yescharacteristic
232#97C2×D5311yescharacteristic
233C4×C8C2×D5311yescharacteristic
234#41—1062no—
235#41—1062no—
236C2×Q8—531no—
237C2×Q8—531no—
238C2×Q8—1061no—
239C2×D4—531no—
240C2×D4—531no—
241C2×D4—1061no—
242C2×D4—1061no—
243C22×C4—1061no—
244C22×C4—1061no—
245C22×C4—1061no—
246C22×C4—1061no—
247C22×C4—1061no—
248C22×C4C22×D5311yescharacteristic
249Q16—1062no—
250SD16—1062no—
251SD16—1062no—
252D8—1062no—
253C2×C8C22×D5311yescharacteristic
254C2×C8C22×D5311yescharacteristic
255C2×C8C22×D5311yescharacteristic
256C2×C8C22×D5311yescharacteristic
257C4⋊C4—531no—
258C4⋊C4—531no—
259C4⋊C4—531no—
260C4⋊C4—531no—
261C4⋊C4—1061no—
262C4⋊C4—1061no—
263C4⋊C4—1061no—
264C4⋊C4—1061no—
265C4⋊C4—1061no—
266C4⋊C4—1061no—
267C4⋊C4D21211yescharacteristic
268C4⋊C4D21211yescharacteristic
269C22⋊C4—1061no—
270C22⋊C4—1061no—
271C22⋊C4—1061no—
272C22⋊C4—1061no—
273C22⋊C4—1061no—
274C22⋊C4—1061no—
275C22⋊C4—1061no—
276C22⋊C4D21211yescharacteristic
277C22⋊C4D21211yescharacteristic
278C42—1061no—
279C42—1061no—
280C42—1061no—
281C42C22×D5311yescharacteristic
282C42C22×D5311yescharacteristic
283C23—1061no—
284C23—1061no—
285C23C2×D21211yescharacteristic
286Q8—532no—
287Q8—1061no—
288Q8—1061no—
289Q8—1061no—
290Q8—4241no—
291D4—532no—
292D4—1064no—
293D4—1061no—
294D4—1061no—
295D4—1061no—
296D4—4241no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—1064no—
300C2×C4—1061no—
301C2×C4—1061no—
302C2×C4—1061no—
303C2×C4—1061no—
304C2×C4—1061no—
305C2×C4—1061no—
306C2×C4—4241no—
307C2×C4—4241no—
308C2×C4—4241no—
309C2×C4—4241no—
310C2×C4C2×D21211yescharacteristic
311C2×C4C2×D21211yescharacteristic
312C2×C4C2×D21211yescharacteristic
313C2×C4C2×D21211yescharacteristic
314C2×C4C2×D21211yescharacteristic
315C2×C4C23×D5311yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—1062no—
324C22—2121no—
325C22—2121no—
326C22—2121no—
327C22—2121no—
328C22—2121no—
329C22C22×D21211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—1062no—
336C4—2121no—
337C4—2121no—
338C4—2121no—
339C4—2121no—
340C4—2121no—
341C4#41×D5311yescharacteristic
342C4#41×D5311yescharacteristic
343C2—41no—
344C2—4241no—
345C2—2122no—
346C2#1681113511yescharacteristic
347C2#1681143511yescharacteristic
348C2#1681143511yescharacteristic
subgroupG/H
centerC22C22×D212
commutatorC2×C4×C53C24
FrattiniC2×C4C23×D53
FittingC53×#433C2
socleC22×C53C22×D4
hypercenter#433D53
hypocenterC53#3125
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16811244C2semidirect
2. #16811103C2semidirect
3. #16810954C2semidirect
4. #16810942C2semidirect
5. #16810914C2semidirect
6. #16810909C2semidirect
7. #16810846C2semidirect
8. #16810839C2semidirect
9. #16810787C2semidirect
11. #16810736C2semidirect
12. #16810731C2semidirect
13. C4×#11719913C2semidirect
14. C4×#11719913C2semidirect
15. C53×#433C2semidirect
189. #433D53semidirect
190. C53#3125semidirect