Finite Group Databasebeta

← #20284185

Subgroups — #20284185

Order 6784.

484 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13133249C211yesmaximal, characteristic, complemented
2C2×#13133246C211yesmaximal, characteristic, complemented
3#16811172C211yesmaximal, characteristic
4C4×Q8×D53C211yesmaximal, characteristic, complemented
5#16810846C211yesmaximal, characteristic, complemented
6#16810845C211yesmaximal, characteristic, complemented
7#16810842C211yesmaximal, characteristic, complemented
8#16810832C211yesmaximal, characteristic, complemented
9#16810831C211yesmaximal, characteristic, complemented
10#16810822C211yesmaximal, characteristic, complemented
11#16810821C211yesmaximal, characteristic, complemented
12#16810645C211yesmaximal, characteristic, complemented
13#16810623C211yesmaximal, characteristic, complemented
14#16810621C211yesmaximal, characteristic, complemented
15C53×#464C211yesmaximal, characteristic, complemented
16C2×#11719949C2211yescharacteristic
17C2×#11719947C2211yescharacteristic
18C2×Q8×D53C2211yescharacteristic
19#13133249—24no—
20#13133246—24no—
21C2×Dic212C2211yescharacteristic
22C2×#11719925C2211yescharacteristic
23C2×#11719925C2211yescharacteristic
24C2×#11719913C2211yescharacteristic
25C2×#11719923C2211yescharacteristic
26C2×#11719924C2211yescharacteristic
27C2×#11719912C2211yescharacteristic
28C2×#11719912C2211yescharacteristic
29#13133215C2211yescharacteristic
30#13133213C2211yescharacteristic
31#13133205C2211yescharacteristic
32#13133190—21no—
33#13133190—21no—
34Q8×Dic53C2211yescharacteristic
35C4×Dic106—21no—
36C4×Dic106C2211yescharacteristic
37#13133182—21no—
38#13133182C2211yescharacteristic
39#13133177—21no—
40#13133177—21no—
41C4⋊C4×D53—21no—
42C4⋊C4×D53C2211yescharacteristic
43C42×D53—21no—
44C42×D53C2211yescharacteristic
45C4⋊#88322C2211yescharacteristic
46#13133146C2211yescharacteristic
47#13133146C2211yescharacteristic
48#13133142C2211yescharacteristic
49#13133141C2211yescharacteristic
50#13133140C2211yescharacteristic
51#13133139C2211yescharacteristic
52#13133138C2211yescharacteristic
53#13133137C2211yescharacteristic
54C2×Q16×C53C2211yescharacteristic
55C2×SD16×C53C2211yescharacteristic
56#124×C53C2211yescharacteristic
57C4×Q8×C53C2211yescharacteristic
58C4⋊C8×C53C2211yescharacteristic
59#103×C53C2211yescharacteristic
60#102×C53C2211yescharacteristic
61C2×Q8×C53C2311yescharacteristic
62C2×Q8×C53C2311yescharacteristic
63C2×D4×C53C2311yescharacteristic
64C2×C22⋊D53—21no—
65C2×C22⋊D53—21no—
66C2×C22⋊D53—21no—
67C22×Dic53—21no—
68#11719949—22no—
69#11719949—22no—
70Q8×D53—22no—
71Q8×D53D414yescomplemented
72#11719947—22no—
73#11719947—22no—
74C2×D212—21no—
75C2×D212C2311yescharacteristic
76C2×C4×D53—21no—
77C2×C4×D53—21no—
78C2×C4×D53—21no—
79C2×C4×D53D411yescharacteristic
80C2×C4×D53D411yescharacteristic
81C2×C4×D53C2311yescharacteristic
82C2×Dic106—21no—
83C2×Dic106C2311yescharacteristic
84C2×Dic106C2311yescharacteristic
85Q16×C53—22no—
86SD16×C53—22no—
87C2×C8×C53C2311yescharacteristic
88C2×C8×C53C2311yescharacteristic
89C4⋊C4×C53—21no—
90C4⋊C4×C53C2311yescharacteristic
91C22⋊C4×C53—21no—
92C22⋊C4×C53—21no—
93C42×C53—21no—
94C42×C53C2311yescharacteristic
95#11719925—22no—
96#11719925—22no—
97#11719924—22no—
98#11719923—22no—
99#11719921—21no—
100#11719921—21no—
101C4⋊Dic53—21no—
102C4⋊Dic53C2311yescharacteristic
103#11719919—21no—
104#11719919—21no—
105#11719919—21no—
106#11719919—21no—
107#11719919—21no—
108C4×Dic53—21no—
109C4×Dic53—21no—
110C4×Dic53—21no—
111C4×Dic53D411yescharacteristic
112C4×Dic53D411yescharacteristic
113C4×Dic53C2311yescharacteristic
114C2×#88322C2311yescharacteristic
115C2×#88322C2311yescharacteristic
116Dic212—22no—
117#11719913—22no—
118#11719912—22no—
119#11719912—22no—
120C23×C53—21no—
121C22×D53—21no—
122C22×D53C2×D411yescharacteristic
123Q8×C53—21no—
124Q8×C53—21no—
125Q8×C53—21no—
126Q8×C53C2×D412yes—
127D4×C53—21no—
128D4×C53—21no—
129C2×C4×C53—21no—
130C2×C4×C53—21no—
131C2×C4×C53—21no—
132C2×C4×C53C2×D411yescharacteristic
133C2×C4×C53C2×D411yescharacteristic
134C2×C4×C53C2411yescharacteristic
135C22⋊D53—42no—
136C22⋊D53—42no—
137C22⋊D53—42no—
138C2×Dic53—21no—
139C2×Dic53—21no—
140C2×Dic53—21no—
141C2×Dic53—42no—
142C2×Dic53C2×D411yescharacteristic
143C2×Dic53C2×D411yescharacteristic
144C2×Dic53C2×D411yescharacteristic
145D212—21no—
146D212—21no—
147D212—42no—
148C4×D53—24no—
149C4×D53—22no—
150C4×D53—41no—
151C4×D53—42no—
152C4×D53—42no—
153C4×D53C2×D412yes—
154C4×D53#4112yes—
155Dic106—21no—
156Dic106—24no—
157Dic106—21no—
158Dic106—21no—
159Dic106C2×D412yes—
160C8×C53—21no—
161C8×C53—21no—
162#88322—21no—
163#88322—21no—
164C22×C53—41no—
165C22×C53—41no—
166C22×C53—41no—
167C22×C53C22×D411yescharacteristic
168C2×D53—21no—
169C2×D53—21no—
170C2×D53—41no—
171C2×D53—41no—
172C2×D53—41no—
173C2×D53#12112yes—
174C4×C53—22no—
175C4×C53—21no—
176C4×C53—21no—
177C4×C53—41no—
178C4×C53—41no—
179C4×C53C22×D411yescharacteristic
180C4×C53C2×#4111yescharacteristic
181Dic53—22no—
182Dic53—21no—
183Dic53—41no—
184Dic53—41no—
185Dic53#12112yes—
186Dic53#13712yescomplemented
187#3037—531nomaximal, Sylow
188C2×C53—81no—
189C2×C53C2×#12111yescharacteristic
190C2×C53C2×#13711yescharacteristic
191C2×C53#57511yescharacteristic
192D53—22no—
193D53—81no—
194C2×#137—531no—
195C2×#137—531no—
196#532—531no—
197C2×C4×Q8—531no—
198#464—531no—
199#464—531no—
200#464—531no—
201#464D5311yescharacteristic, complemented
202#462—531no—
203#462—531no—
204#460—531no—
205#460—531no—
206#423—531no—
207#417—531no—
208#417—531no—
209C53#303711yescharacteristic, complemented, Sylow
210C2×#41—531no—
211C2×#41—531no—
212C22×Q8—531no—
213#137—1064no—
214#137—1064no—
215C2×Q16—531no—
216C2×Q16—531no—
217C2×Q16—531no—
218C2×Q16C2×D5311yescharacteristic
219C2×SD16—531no—
220C2×SD16—531no—
221C2×SD16—531no—
222C2×SD16C2×D5311yescharacteristic
223C2×M16—531no—
224C2×M16—531no—
225C4⋊Q8—531no—
226#127—531no—
227#124—531no—
228#124C2×D5311yescharacteristic
229#121—1061no—
230#121—1061no—
231C4×Q8—531no—
232C4×Q8—531no—
233C4×Q8—531no—
234C4×Q8—1061no—
235C4×Q8—1061no—
236C4×Q8C2×D5311yescharacteristic
237C4×D4—1061no—
238C4×D4—1061no—
239C2×C4⋊C4—531no—
240C2×C4⋊C4—1061no—
241C2×C42—531no—
242C2×C42—1061no—
243C4⋊C8—531no—
244C4⋊C8—531no—
245C4⋊C8—531no—
246C4⋊C8C2×D5311yescharacteristic
247#103—531no—
248#103—531no—
249#103—531no—
250#103C2×D5311yescharacteristic
251#102—531no—
252#102—531no—
253#102—531no—
254#102C2×D5311yescharacteristic
255#41—1062no—
256#41—1062no—
257#41—1062no—
258#41—1062no—
259C2×Q8—534no—
260C2×Q8—531no—
261C2×Q8—531no—
262C2×Q8—1061no—
263C2×Q8—1062no—
264C2×Q8C22×D5311yescharacteristic
265C2×Q8C22×D5311yescharacteristic
266C2×D4—531no—
267C2×D4—1061no—
268C2×D4—1061no—
269C2×D4—1061no—
270C2×D4—1061no—
271C2×D4C22×D5311yescharacteristic
272C22×C4—531no—
273C22×C4—531no—
274C22×C4—531no—
275C22×C4—1061no—
276C22×C4—1061no—
277C22×C4—1061no—
278C22×C4—1061no—
279Q16—22no—
280Q16—1062no—
281Q16—1062no—
282Q16—1062no—
283SD16—22no—
284SD16—1062no—
285SD16—1062no—
286SD16—1062no—
287M16—1062no—
288M16—1062no—
289C2×C8—531no—
290C2×C8—531no—
291C2×C8C22×D5311yescharacteristic
292C2×C8C22×D5311yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—531no—
295C4⋊C4—1061no—
296C4⋊C4—1061no—
297C4⋊C4—1061no—
298C4⋊C4—1061no—
299C4⋊C4—1061no—
300C4⋊C4—1061no—
301C4⋊C4C22×D5311yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—1061no—
305C22⋊C4—1061no—
306C42—21no—
307C42—531no—
308C42—531no—
309C42—531no—
310C42—1061no—
311C42—1061no—
312C42—1061no—
313C42C22×D5311yescharacteristic
314C23—21no—
315C23—531no—
316C23—1061no—
317Q8—21no—
318Q8—21no—
319Q8—21no—
320Q8—532no—
321Q8—1064no—
322Q8—1061no—
323Q8—1061no—
324Q8—1061no—
325Q8D4×D5312yes—
326D4—21no—
327D4—21no—
328D4—1061no—
329D4—1061no—
330D4—2122no—
331D4—2122no—
332D4—2122no—
333D4—2122no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—531no—
338C2×C4—531no—
339C2×C4—532no—
340C2×C4—532no—
341C2×C4—531no—
342C2×C4—1062no—
343C2×C4—1064no—
344C2×C4—1061no—
345C2×C4—1061no—
346C2×C4—1061no—
347C2×C4—2121no—
348C2×C4—2122no—
349C2×C4—2122no—
350C2×C4—2122no—
351C2×C4D4×D5311yescharacteristic
352C2×C4D4×D5311yescharacteristic
353C2×C4C23×D5311yescharacteristic
354C8—21no—
355C8—21no—
356C8—1061no—
357C8—1061no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—532no—
362C22—1061no—
363C22—1061no—
364C22—2121no—
365C22—2121no—
366C22—2121no—
367C22C2×D4×D5311yescharacteristic
368C4—22no—
369C4—21no—
370C4—21no—
371C4—41no—
372C4—41no—
373C4—532no—
374C4—532no—
375C4—1062no—
376C4—1061no—
377C4—2121no—
378C4—2121no—
379C4C2×D4×D5311yescharacteristic
380C4#41×D5311yescharacteristic
381C2—81no—
382C2—1062no—
383C2—4241no—
384C2#121×D5311yescharacteristic
385C2#137×D5311yescharacteristic
386C2#1681142011yescharacteristic
subgroupG/H
centerC22C2×D4×D53
commutatorC2×C4×C53C24
FrattiniC2×C4C23×D53
FittingC53×#464C2
socleC22×C53C22×D4
hypercenter#464D53
hypocenterC53#3037
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#13133249C2semidirect
2. C2×#13133246C2semidirect
4. C4×Q8×D53C2semidirect
5. #16810846C2semidirect
6. #16810845C2semidirect
7. #16810842C2semidirect
8. #16810832C2semidirect
9. #16810831C2semidirect
10. #16810822C2semidirect
11. #16810821C2semidirect
12. #16810645C2semidirect
13. #16810623C2semidirect
14. #16810621C2semidirect
15. C53×#464C2semidirect
71. Q8×D53D4semidirect
186. Dic53#137semidirect
201. #464D53semidirect
209. C53#3037semidirect