Finite Group Databasebeta

← #20283593

Subgroups — #20283593

Order 6784.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13133238C211yesmaximal, characteristic
2#16811105C211yesmaximal, characteristic, complemented
3#16811102C211yesmaximal, characteristic, complemented
4#16810733C211yesmaximal, characteristic, complemented
5#16810732C211yesmaximal, characteristic, complemented
6#16810728C211yesmaximal, characteristic, complemented
7#16810727C211yesmaximal, characteristic, complemented
8C4×#11719913C211yesmaximal, characteristic, complemented
9SD16×Dic53C211yesmaximal, characteristic, complemented
10#16810710C211yesmaximal, characteristic, complemented
11#106×D53C211yesmaximal, characteristic, complemented
12#16810623C211yesmaximal, characteristic, complemented
13#16810621C211yesmaximal, characteristic, complemented
14#16810577C211yesmaximal, characteristic, complemented
15C4×SD16×C53C211yesmaximal, characteristic, complemented
16C2×#11719949C2211yescharacteristic
17C2×#11719947C2211yescharacteristic
18#13133238C418yescomplemented
19C2×#11719925C2211yescharacteristic
20C2×#11719913C2211yescharacteristic
21C2×#11719922C2211yescharacteristic
22C2×#11719912C2211yescharacteristic
23C2×C8×D53C2211yescharacteristic
24Q8×Dic53C2211yescharacteristic
25C4×Dic106C2211yescharacteristic
26#13133182C2211yescharacteristic
27C4×D212—21no—
28C4×D212C2211yescharacteristic
29D4×Dic53C2211yescharacteristic
30#13133179—21no—
31#13133179C2211yescharacteristic
32C4×C22⋊D53—21no—
33#13133177—21no—
34#13133174—21no—
35#13133174C2211yescharacteristic
36#13133173—21no—
37C2×#11719919—21no—
38C4⋊C4×D53—21no—
39C4⋊C4×D53C2211yescharacteristic
40C4⋊C4×D53C2211yescharacteristic
41#13133149C2211yescharacteristic
42#13133148C2211yescharacteristic
43#13133148C2211yescharacteristic
44#13133142C2211yescharacteristic
45#13133141C2211yescharacteristic
46#13133140C2211yescharacteristic
47#13133139C2211yescharacteristic
48#13133138C2211yescharacteristic
49#13133137C2211yescharacteristic
50#13133128C2211yescharacteristic
51#13133127C2211yescharacteristic
52C8×Dic53C2211yescharacteristic
53C2×SD16×C53C2211yescharacteristic
54C4×Q8×C53C2211yescharacteristic
55C4×D4×C53C2211yescharacteristic
56#106×C53C2211yescharacteristic
57#103×C53C2211yescharacteristic
58#102×C53C2211yescharacteristic
59C4×C8×C53C2211yescharacteristic
60C2×Q8×C53C2311yescharacteristic
61C2×D4×C53C2311yescharacteristic
62C22×C4×C53—21no—
63C2×C22⋊D53—21no—
64C22×Dic53—21no—
65C22×Dic53—21no—
66#11719949—22no—
67#11719949C2×C414yescomplemented
68#11719947—22no—
69#11719947C2×C414yescomplemented
70C2×D212—21no—
71C2×D212C2311yescharacteristic
72C2×C4×D53—21no—
73C2×C4×D53—21no—
74C2×C4×D53—21no—
75C2×C4×D53—21no—
76C2×C4×D53—21no—
77C2×C4×D53C2311yescharacteristic
78C2×Dic106C2311yescharacteristic
79SD16×C53C2×C414yescomplemented
80C2×C8×C53C2311yescharacteristic
81C2×C8×C53C2311yescharacteristic
82C4⋊C4×C53—21no—
83C4⋊C4×C53C2311yescharacteristic
84C4⋊C4×C53C2311yescharacteristic
85C22⋊C4×C53—21no—
86C42×C53—21no—
87C42×C53C2311yescharacteristic
88C22⋊Dic53—21no—
89#11719925C2×C414yescomplemented
90#11719922C2×C414yescomplemented
91#11719921—21no—
92#11719921—21no—
93#11719921D411yescharacteristic
94#11719921D411yescharacteristic
95C4⋊Dic53—21no—
96C4⋊Dic53C2311yescharacteristic
97C4⋊Dic53C2311yescharacteristic
98#11719919—21no—
99#11719919—21no—
100#11719919—21no—
101#11719919—21no—
102#11719919D411yescharacteristic
103#11719919D411yescharacteristic
104C4×Dic53—21no—
105C4×Dic53—21no—
106C4×Dic53—21no—
107C4×Dic53C2311yescharacteristic
108C2×#88322C2311yescharacteristic
109C2×#88322C2311yescharacteristic
110#11719913C2×C414yescomplemented
111#11719912—22no—
112C8×D53C2×C414yescomplemented
113C23×C53—21no—
114C22×D53—21no—
115C22×D53C2×D411yescharacteristic
116Q8×C53—21no—
117Q8×C53C22×C412yes—
118D4×C53—21no—
119D4×C53C22×C412yes—
120C2×C4×C53—21no—
121C2×C4×C53—21no—
122C2×C4×C53—21no—
123C2×C4×C53—81no—
124C2×C4×C53C2×D411yescharacteristic
125C2×C4×C53C2×D411yescharacteristic
126C2×C4×C53C2411yescharacteristic
127C22⋊D53—24no—
128C2×Dic53—21no—
129C2×Dic53—24no—
130C2×Dic53—21no—
131C2×Dic53—21no—
132C2×Dic53—81no—
133C2×Dic53C2×D411yescharacteristic
134C2×Dic53C2×D411yescharacteristic
135C2×Dic53C2×D411yescharacteristic
136D212—24no—
137D212—21no—
138D212C22×C412yes—
139C4×D53—24no—
140C4×D53—81no—
141C4×D53—81no—
142C4×D53—81no—
143C4×D53—81no—
144C4×D53C22×C412yes—
145C4×D53#4112yes—
146Dic106—21no—
147Dic106C22×C412yes—
148C8×C53—21no—
149C8×C53C22×C412yes—
150#88322—21no—
151#88322C22×C412yes—
152C22×C53—22no—
153C22×C53—41no—
154C22×C53—41no—
155C22×C53C22×D411yescharacteristic
156C2×D53—21no—
157C2×D53—21no—
158C2×D53—22no—
159C2×D53—41no—
160C2×D53—41no—
161C2×D53C4×D412yes—
162C4×C53—22no—
163C4×C53—21no—
164C4×C53—21no—
165C4×C53—41no—
166C4×C53—41no—
167C4×C53C23×C411yescharacteristic
168C4×C53C2×#4111yescharacteristic
169Dic53—22no—
170Dic53—21no—
171Dic53—21no—
172Dic53—41no—
173Dic53—41no—
174Dic53C4×D412yes—
175#2952—531nomaximal, Sylow
176C2×C53—42no—
177C2×C53C2×C4×D411yescharacteristic
178C2×C53#57711yescharacteristic
179C2×C53#57711yescharacteristic
180D53—22no—
181D53—42no—
182C2×#135—531no—
183#520—531no—
184#520—531no—
185#442—531no—
186#442—531no—
187#441—531no—
188#441—531no—
189C4×SD16—531no—
190C4×SD16—531no—
191C4×SD16—531no—
192C4×SD16D5311yescharacteristic, complemented
193C2×#106—531no—
194#417—531no—
195#417—531no—
196#405—531no—
197C53#295211yescharacteristic, complemented, Sylow
198C2×#41—531no—
199C2×#41—531no—
200#135—538no—
201C2×Q16—531no—
202C2×SD16—531no—
203C2×SD16C2×D5311yescharacteristic
204C2×D8—531no—
205C2×M16—531no—
206C22×C8—531no—
207C4×Q8—531no—
208C4×Q8—531no—
209C4×Q8—531no—
210C4×Q8C2×D5311yescharacteristic
211C4×D4—531no—
212C4×D4—531no—
213C4×D4—531no—
214C4×D4—1061no—
215C4×D4—1061no—
216C4×D4—1061no—
217C4×D4—1061no—
218C4×D4C2×D5311yescharacteristic
219#117—531no—
220#117—1061no—
221#117—1061no—
222C2×C4⋊C4—531no—
223C2×C4⋊C4—531no—
224C2×C4⋊C4—1061no—
225C2×C4⋊C4—1061no—
226#106—531no—
227#106—531no—
228#106—531no—
229#106C2×D5311yescharacteristic
230#103—531no—
231#103—531no—
232#103—531no—
233#103C2×D5311yescharacteristic
234#102—531no—
235#102—531no—
236#102—531no—
237#102C2×D5311yescharacteristic
238#97—531no—
239#97—531no—
240C4×C8—531no—
241C4×C8C2×D5311yescharacteristic
242#41—534no—
243#41—534no—
244#41—1062no—
245#41—1062no—
246C2×Q8—531no—
247C2×Q8C22×D5311yescharacteristic
248C2×D4—531no—
249C2×D4—1061no—
250C2×D4—1061no—
251C2×D4C22×D5311yescharacteristic
252C22×C4—21no—
253C22×C4—531no—
254C22×C4—1061no—
255C22×C4—1061no—
256C22×C4—1061no—
257C22×C4—1061no—
258C22×C4—1061no—
259C22×C4—1061no—
260C22×C4—1061no—
261Q16—534no—
262SD16—534no—
263SD16C4×D5314yescomplemented
264D8—534no—
265M16—1062no—
266C2×C8—531no—
267C2×C8—534no—
268C2×C8—531no—
269C2×C8C22×D5311yescharacteristic
270C2×C8C22×D5311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—531no—
273C4⋊C4—531no—
274C4⋊C4—531no—
275C4⋊C4—531no—
276C4⋊C4—1061no—
277C4⋊C4—1061no—
278C4⋊C4—1061no—
279C4⋊C4—1061no—
280C4⋊C4—1061no—
281C4⋊C4C22×D5311yescharacteristic
282C4⋊C4C22×D5311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—531no—
285C22⋊C4—531no—
286C22⋊C4—1061no—
287C22⋊C4—1061no—
288C22⋊C4—1061no—
289C42—21no—
290C42—531no—
291C42—1061no—
292C42—1061no—
293C42—1061no—
294C42C22×D5311yescharacteristic
295C23—21no—
296C23—531no—
297C23—1061no—
298Q8—21no—
299Q8—532no—
300Q8—1061no—
301Q8C2×C4×D5312yes—
302D4—21no—
303D4—532no—
304D4—1064no—
305D4—1064no—
306D4—1061no—
307D4C2×C4×D5312yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—531no—
313C2×C4—532no—
314C2×C4—532no—
315C2×C4—531no—
316C2×C4—531no—
317C2×C4—1064no—
318C2×C4—1064no—
319C2×C4—1061no—
320C2×C4—1061no—
321C2×C4—1061no—
322C2×C4—4241no—
323C2×C4—4241no—
324C2×C4—4241no—
325C2×C4—4241no—
326C2×C4—4241no—
327C2×C4D4×D5311yescharacteristic
328C2×C4D4×D5311yescharacteristic
329C2×C4C23×D5311yescharacteristic
330C8—21no—
331C8—532no—
332C8—1061no—
333C8C2×C4×D5312yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—532no—
338C22—1061no—
339C22—1061no—
340C22—1062no—
341C22—2121no—
342C22—2121no—
343C22C2×D4×D5311yescharacteristic
344C4—22no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—532no—
350C4—1062no—
351C4—1061no—
352C4—1061no—
353C4—2121no—
354C4—2121no—
355C4C22×C4×D5311yescharacteristic
356C4#41×D5311yescharacteristic
357C2—42no—
358C2—1062no—
359C2—2122no—
360C2C4×D4×D5311yescharacteristic
361C2#1681142911yescharacteristic
362C2#1681143011yescharacteristic
subgroupG/H
centerC22C2×D4×D53
commutatorC4×C53C23×C4
FrattiniC2×C4C23×D53
FittingC4×SD16×C53C2
socleC22×C53C22×D4
hypercenterC4×SD16D53
hypocenterC53#2952
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #16811105C2semidirect
3. #16811102C2semidirect
4. #16810733C2semidirect
5. #16810732C2semidirect
6. #16810728C2semidirect
7. #16810727C2semidirect
8. C4×#11719913C2semidirect
9. SD16×Dic53C2semidirect
10. #16810710C2semidirect
11. #106×D53C2semidirect
12. #16810623C2semidirect
13. #16810621C2semidirect
14. #16810577C2semidirect
15. C4×SD16×C53C2semidirect
18. #13133238C4semidirect
67. #11719949C2×C4semidirect
69. #11719947C2×C4semidirect
79. SD16×C53C2×C4semidirect
89. #11719925C2×C4semidirect
90. #11719922C2×C4semidirect
110. #11719913C2×C4semidirect
112. C8×D53C2×C4semidirect
192. C4×SD16D53semidirect
197. C53#2952semidirect
263. SD16C4×D53semidirect