Finite Group Databasebeta

← #20277430

Subgroups — #20277430

Order 6784.

516 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13133216C211yesmaximal, characteristic
2C2×C4×Dic106C211yesmaximal, characteristic
3C2×#13133182C211yesmaximal, characteristic
4#16810527C211yesmaximal, characteristic
5#16810527C211yesmaximal, characteristic
6#16810510C211yesmaximal, characteristic
7#16810509C211yesmaximal, characteristic
8#16810508C211yesmaximal, characteristic
9#16810507C211yesmaximal, characteristic
10#16810506C211yesmaximal, characteristic
11#16810505C211yesmaximal, characteristic
12#16810504C211yesmaximal, characteristic
13#16810487C211yesmaximal, characteristic
14#16810468C211yesmaximal, characteristic
15C53×#387C211yesmaximal, characteristic
16C22×Dic106C2211yescharacteristic
17C22×Dic106C2211yescharacteristic
18#13133216C418yescomplemented
19C4×Dic106—24no—
20#13133182—24no—
21C2×C4⋊Dic53C2211yescharacteristic
22C2×C4⋊Dic53C2211yescharacteristic
23C2×#11719919C2211yescharacteristic
24C2×#11719919C2211yescharacteristic
25C2×#11719919C2211yescharacteristic
26C2×#11719919C2211yescharacteristic
27C2×#11719919C2211yescharacteristic
28C2×#11719919C2211yescharacteristic
29C2×C4×Dic53C2211yescharacteristic
30C2×C4×Dic53C2211yescharacteristic
31C2×C4×Dic53C2211yescharacteristic
32C2×C4×Dic53C2211yescharacteristic
33C2×C4×Dic53C2211yescharacteristic
34C2×C4×Dic53C2211yescharacteristic
35#13133124C2211yescharacteristic
36#13133124C2211yescharacteristic
37#13133124C2211yescharacteristic
38#13133124C2211yescharacteristic
39#13133124C2211yescharacteristic
40#13133124C2211yescharacteristic
41#13133124C2211yescharacteristic
42#13133124C2211yescharacteristic
43#13133124C2211yescharacteristic
44#13133124C2211yescharacteristic
45#13133124C2211yescharacteristic
46#13133124C2211yescharacteristic
47C2×C4⋊C4×C53C2211yescharacteristic
48C2×C4⋊C4×C53C2211yescharacteristic
49C2×C42×C53C2211yescharacteristic
50#95×C53C2211yescharacteristic
51#95×C53C2211yescharacteristic
52#95×C53C2211yescharacteristic
53#95×C53C2211yescharacteristic
54C22×C4×C53C2311yescharacteristic
55C22×C4×C53C2311yescharacteristic
56C22×C4×C53C2311yescharacteristic
57C22×C4×C53C2311yescharacteristic
58C22×C4×C53C2311yescharacteristic
59C22×C4×C53C2311yescharacteristic
60C22×C4×C53C2311yescharacteristic
61C22×Dic53C2311yescharacteristic
62C22×Dic53C2311yescharacteristic
63C22×Dic53C2311yescharacteristic
64C22×Dic53C2311yescharacteristic
65C22×Dic53C2311yescharacteristic
66C22×Dic53C2311yescharacteristic
67C22×Dic53C2311yescharacteristic
68C22×Dic53C2311yescharacteristic
69C2×Dic106—22no—
70C2×Dic106—22no—
71C2×Dic106—22no—
72C2×Dic106—22no—
73C2×Dic106C2×C414yes—
74C2×Dic106C2×C414yes—
75C4⋊C4×C53—22no—
76C4⋊C4×C53C2×C414yes—
77C42×C53—22no—
78C4⋊Dic53—22no—
79C4⋊Dic53C2×C414yes—
80#11719919—22no—
81#11719919—22no—
82#11719919—22no—
83#11719919—22no—
84#11719919C2×C414yes—
85#11719919C2×C414yes—
86C4×Dic53—22no—
87C4×Dic53—22no—
88C4×Dic53—22no—
89C4×Dic53—22no—
90C4×Dic53C2×C414yes—
91C4×Dic53D414yes—
92C23×C53C2411yescharacteristic
93C2×C4×C53—21no—
94C2×C4×C53—21no—
95C2×C4×C53—21no—
96C2×C4×C53—21no—
97C2×C4×C53—21no—
98C2×C4×C53—21no—
99C2×C4×C53—21no—
100C2×C4×C53—21no—
101C2×C4×C53—21no—
102C2×C4×C53—21no—
103C2×C4×C53—21no—
104C2×C4×C53—21no—
105C2×C4×C53—21no—
106C2×C4×C53—21no—
107C2×C4×C53—21no—
108C2×C4×C53—21no—
109C2×C4×C53—21no—
110C2×C4×C53C22×C412yes—
111C2×C4×C53C22×C412yes—
112C2×C4×C53C22×C412yes—
113C2×C4×C53C2×D412yes—
114C2×Dic53—21no—
115C2×Dic53—21no—
116C2×Dic53—21no—
117C2×Dic53—21no—
118C2×Dic53—21no—
119C2×Dic53—21no—
120C2×Dic53—21no—
121C2×Dic53—21no—
122C2×Dic53—21no—
123C2×Dic53—21no—
124C2×Dic53—21no—
125C2×Dic53—21no—
126C2×Dic53—21no—
127C2×Dic53—21no—
128C2×Dic53—21no—
129C2×Dic53—21no—
130C2×Dic53—21no—
131C2×Dic53C22×C412yes—
132C2×Dic53C22×C412yes—
133C2×Dic53C22×C412yes—
134C2×Dic53C22×C412yes—
135C2×Dic53C2×D412yes—
136C2×Dic53C2×D412yes—
137C2×Dic53#4112yes—
138Dic106—28no—
139Dic106—28no—
140C22×C53C23×C411yescharacteristic
141C22×C53C22×D411yescharacteristic
142C22×C53C2×#4111yescharacteristic
143C22×C532−1+411yescharacteristic
144C22×C532−1+411yescharacteristic
145C22×C532−1+411yescharacteristic
146C22×C532−1+411yescharacteristic
147C4×C53—22no—
148C4×C53—22no—
149C4×C53—22no—
150C4×C53—22no—
151C4×C53—41no—
152C4×C53—41no—
153C4×C53—41no—
154Dic53—22no—
155Dic53—22no—
156Dic53—22no—
157Dic53—22no—
158Dic53—41no—
159Dic53—41no—
160Dic53—41no—
161Dic53C4×D414yes—
162#2327—531nomaximal, Sylow
163C2×C53C2×C4×D411yescharacteristic
164C2×C53#51911yescharacteristic
165C2×C53#51911yescharacteristic
166C2×C53#53611yescharacteristic
167C2×C53#53611yescharacteristic
168C2×C53#54111yescharacteristic
169C2×C53#54111yescharacteristic
170C2×C4⋊Q8—531no—
171C2×C4×Q8—531no—
172C2×C4×Q8—531no—
173#391—531no—
174#391—531no—
175#387—531no—
176#387—531no—
177#387—531no—
178#387—531no—
179#387—531no—
180#387—531no—
181#387—531no—
182#387D5311yescharacteristic
183#382—531no—
184#376—531no—
185C53#232711yescharacteristic, complemented, Sylow
186C22×Q8—531no—
187C22×Q8—531no—
188C4⋊Q8—538no—
189C4×Q8—1064no—
190C4×Q8—1064no—
191C2×C4⋊C4—531no—
192C2×C4⋊C4—531no—
193C2×C4⋊C4—531no—
194C2×C4⋊C4—531no—
195C2×C4⋊C4—531no—
196C2×C4⋊C4—531no—
197C2×C4⋊C4—531no—
198C2×C4⋊C4—531no—
199C2×C4⋊C4C2×D5311yescharacteristic
200C2×C4⋊C4C2×D5311yescharacteristic
201C2×C42—531no—
202C2×C42—531no—
203C2×C42—531no—
204C2×C42—531no—
205C2×C42—531no—
206C2×C42—531no—
207C2×C42C2×D5311yescharacteristic
208#95—531no—
209#95—531no—
210#95—531no—
211#95—531no—
212#95—531no—
213#95—531no—
214#95—531no—
215#95—531no—
216#95—531no—
217#95—531no—
218#95—531no—
219#95—531no—
220#95C2×D5311yescharacteristic
221#95C2×D5311yescharacteristic
222#95C2×D5311yescharacteristic
223#95C2×D5311yescharacteristic
224C2×Q8—534no—
225C2×Q8—534no—
226C2×Q8—1062no—
227C2×Q8—1062no—
228C2×Q8—1062no—
229C2×Q8—1062no—
230C22×C4—531no—
231C22×C4—531no—
232C22×C4—531no—
233C22×C4—531no—
234C22×C4—531no—
235C22×C4—531no—
236C22×C4—531no—
237C22×C4—531no—
238C22×C4C22×D5311yescharacteristic
239C22×C4C22×D5311yescharacteristic
240C22×C4C22×D5311yescharacteristic
241C22×C4C22×D5311yescharacteristic
242C22×C4C22×D5311yescharacteristic
243C22×C4C22×D5311yescharacteristic
244C22×C4C22×D5311yescharacteristic
245C4⋊C4—22no—
246C4⋊C4—534no—
247C4⋊C4—534no—
248C4⋊C4—534no—
249C4⋊C4—1062no—
250C4⋊C4—1062no—
251C4⋊C4—1062no—
252C4⋊C4—1062no—
253C4⋊C4—1062no—
254C4⋊C4C4×D5314yes—
255C42—22no—
256C42—534no—
257C42—534no—
258C42—1062no—
259C42—1062no—
260C42—1062no—
261C42—1062no—
262C23C23×D5311yescharacteristic
263Q8—1068no—
264Q8—1068no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—532no—
283C2×C4—532no—
284C2×C4—532no—
285C2×C4—532no—
286C2×C4—532no—
287C2×C4—532no—
288C2×C4—532no—
289C2×C4—1061no—
290C2×C4—1061no—
291C2×C4—1061no—
292C2×C4—1061no—
293C2×C4—1061no—
294C2×C4—1061no—
295C2×C4—1061no—
296C2×C4—1061no—
297C2×C4—1061no—
298C2×C4—1061no—
299C2×C4—1061no—
300C2×C4—1061no—
301C2×C4—1061no—
302C2×C4—1061no—
303C2×C4—1061no—
304C2×C4—1061no—
305C2×C4—1061no—
306C2×C4C2×C4×D5312yes—
307C2×C4C2×C4×D5312yes—
308C2×C4C2×C4×D5312yes—
309C2×C4D4×D5312yes—
310C22C22×C4×D5311yescharacteristic
311C22C2×D4×D5311yescharacteristic
312C22#41×D5311yescharacteristic
313C22#1313326411yescharacteristic
314C22#1313326411yescharacteristic
315C22#1313326411yescharacteristic
316C22#1313326511yescharacteristic
317C4—22no—
318C4—22no—
319C4—22no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—534no—
325C4—1062no—
326C4—1062no—
327C4—1062no—
328C4—1062no—
329C4—2121no—
330C4—2121no—
331C4—2121no—
332C2C4×D4×D5311yescharacteristic
333C2#1681109911yescharacteristic
334C2#1681110011yescharacteristic
335C2#1681119511yescharacteristic
336C2#1681119611yescharacteristic
337C2#1681123011yescharacteristic
338C2#1681123211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D53
commutatorC22×C53C23×C4
FittingC53×#387C2
socleC23×C53C24
hypercenter#387D53
hypocenterC53#2327
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
18. #13133216C4semidirect
185. C53#2327semidirect