Finite Group Databasebeta

← #27303444

Subgroups — #27303444

Order 13568.

482 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811007C211yesmaximal, characteristic
2C2×#16810428C211yesmaximal, characteristic, complemented
3C2×#16810428C211yesmaximal, characteristic, complemented
4C2×#16810425C211yesmaximal, characteristic
5C2×#16810425C211yesmaximal, characteristic
6#20275448C211yesmaximal, characteristic, complemented
7C53×#1374C211yesmaximal, characteristic, complemented
8C22×Dic212C2211yescharacteristic
9C22×#11719913—21no—
10C22×D424C2211yescharacteristic
11C2×#13133205—21no—
12#16811007—22no—
13#16811007—22no—
14C2×#13133151C2211yescharacteristic
15C2×#13133151C2211yescharacteristic
16#16810521—21no—
17#16810428—22no—
18#16810428—22no—
19#16810425—22no—
20#16810425—22no—
21#16810386—21no—
22C22×C16×C53C2211yescharacteristic
23C22×C16×C53C2211yescharacteristic
24C2×C4×C8×C53C2211yescharacteristic
25C22×Dic106—21no—
26C22×D212—21no—
27C2×Dic212—21no—
28C2×Dic212—21no—
29C2×Dic212—21no—
30C2×Dic212—21no—
31C2×Dic212—21no—
32C2×Dic212D412yes—
33C2×#11719913—24no—
34C2×#11719913—42no—
35C2×#11719913—42no—
36C2×D424—21no—
37C2×D424—21no—
38C2×D424—21no—
39C2×D424—21no—
40C2×D424—21no—
41C2×D424D412yes—
42#13133205—24no—
43#13133205—42no—
44C2×C4⋊Dic53—21no—
45C2×C4⋊Dic53—21no—
46C2×#11719919—41no—
47C2×#11719921—41no—
48C2×#11719921—41no—
49#13133151—21no—
50#13133151—21no—
51#13133151—21no—
52#13133151D412yes—
53#13133124—41no—
54C22×C8×C53D411yescharacteristic
55C22×C8×C53C2311yescharacteristic
56C2×C42×C53D411yescharacteristic
57C2×C16×C53—21no—
58C2×C16×C53—21no—
59C2×C16×C53—21no—
60C2×C16×C53—21no—
61C2×C16×C53—21no—
62C2×C16×C53—21no—
63C4×C8×C53—21no—
64C4×C8×C53—21no—
65C23×D53—41no—
66C22×C4×C53D811yescharacteristic
67C22×C4×C53D811yescharacteristic
68C22×C4×C53C2×D411yescharacteristic
69C22×Dic53—41no—
70C22×Dic53—41no—
71C22×Dic53—41no—
72C2×D212—22no—
73C2×D212—41no—
74C2×D212—41no—
75C2×D212—41no—
76C2×D212—41no—
77C2×D212—41no—
78C2×Dic106—22no—
79C2×Dic106—41no—
80C2×Dic106—41no—
81C2×Dic106—41no—
82C2×Dic106—41no—
83C2×Dic106—41no—
84C2×C8×C53—21no—
85C2×C8×C53—21no—
86C2×C8×C53SD1612yes—
87C2×C8×C53C2×D411yescharacteristic
88C2×C8×C53C2×D411yescharacteristic
89C2×C8×C53C2×D411yescharacteristic
90C2×C8×C53#4111yescharacteristic
91C2×C8×C53#4111yescharacteristic
92C2×C8×C53#4111yescharacteristic
93C42×C53—21no—
94C42×C53—21no—
95#11719921—44no—
96#11719921—44no—
97C4⋊Dic53—22no—
98C4⋊Dic53—41no—
99C4⋊Dic53—41no—
100C4⋊Dic53—41no—
101#11719919—82no—
102Dic212—22no—
103Dic212—22no—
104Dic212—41no—
105Dic212—41no—
106D424—22no—
107D424—22no—
108D424—41no—
109D424—41no—
110#11719913—48no—
111C16×C53—41no—
112C16×C53—41no—
113C23×C53C2×D811yescharacteristic
114C22×D53—42no—
115C22×D53—81no—
116C22×D53—81no—
117C22×D53—81no—
118C22×D53—81no—
119C22×D53—81no—
120C22×D53—81no—
121C2×C4×C53—21no—
122C2×C4×C53—21no—
123C2×C4×C53—21no—
124C2×C4×C53—21no—
125C2×C4×C53—21no—
126C2×C4×C53—21no—
127C2×C4×C53#12011yescharacteristic
128C2×C4×C53#12111yescharacteristic
129C2×C4×C53#12411yescharacteristic
130C2×C4×C53C2×SD1611yescharacteristic
131C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
133C2×Dic53—42no—
134C2×Dic53—42no—
135C2×Dic53—81no—
136C2×Dic53—81no—
137C2×Dic53—81no—
138C2×Dic53—81no—
139C2×Dic53—81no—
140C2×Dic53—81no—
141C2×Dic53—81no—
142D212—42no—
143D212—42no—
144D212—81no—
145D212—81no—
146Dic106—42no—
147Dic106—42no—
148Dic106—81no—
149Dic106—81no—
150C8×C53—22no—
151C8×C53#12111yescharacteristic
152C8×C53#12111yescharacteristic
153C8×C53#12311yescharacteristic
154C8×C53#12311yescharacteristic
155#13408—531nomaximal, Sylow
156C22×C53#44711yescharacteristic
157C22×C53#45911yescharacteristic
158C22×C53#48611yescharacteristic
159C22×C53#50811yescharacteristic
160C22×C53#50811yescharacteristic
161C22×C53#50911yescharacteristic
162C22×C53#51011yescharacteristic
163C2×D53—82no—
164C2×D53—82no—
165C2×D53—82no—
166C2×D53—161no—
167C2×D53—161no—
168C2×D53—161no—
169C2×D53—161no—
170C4×C53—41no—
171C4×C53—41no—
172C4×C53#39411yescharacteristic
173C4×C53#45011yescharacteristic
174C4×C53#46011yescharacteristic
175C4×C53#49011yescharacteristic
176Dic53—82no—
177Dic53—82no—
178Dic53—161no—
179C2×#495—531no—
180C2×#358—531no—
181C2×#358—531no—
182C2×#357—531no—
183C2×#357—531no—
184#1942—531no—
185#1374D5311yescharacteristic, complemented
186C2×C53#204111yescharacteristic
187C2×C53#218611yescharacteristic
188C2×C53#218911yescharacteristic
189C2×C53#221011yescharacteristic
190C2×C53#221111yescharacteristic
191C2×C53#224211yescharacteristic
192C2×C53#224311yescharacteristic
193D53—162no—
194C22×Q16—531no—
195C22×SD16—1061no—
196C22×D8—531no—
197C2×#124—1061no—
198C22×C16C2×D5311yescharacteristic
199C22×C16C2×D5311yescharacteristic
200#495—1062no—
201#495—1062no—
202C2×#107—531no—
203C2×#107—531no—
204C2×C4×C8C2×D5311yescharacteristic
205#389—1061no—
206#358—1062no—
207#358—1062no—
208#357—1062no—
209#357—1062no—
210#340—1061no—
211C53#1340811yescharacteristic, complemented, Sylow
212C22×Q8—1061no—
213C22×D4—1061no—
214C2×Q16—532no—
215C2×Q16—1061no—
216C2×Q16—1061no—
217C2×Q16—1061no—
218C2×Q16—1061no—
219C2×Q16—1061no—
220C2×SD16—1064no—
221C2×SD16—2122no—
222C2×SD16—2122no—
223C2×D8—532no—
224C2×D8—1061no—
225C2×D8—1061no—
226C2×D8—1061no—
227C2×D8—1061no—
228C2×D8—1061no—
229C22×C8D21211yescharacteristic
230C22×C8C22×D5311yescharacteristic
231#124—1064no—
232#124—2122no—
233C2×C4⋊C4—1061no—
234C2×C4⋊C4—1061no—
235C2×C4⋊C4—2121no—
236C2×C22⋊C4—2121no—
237C2×C22⋊C4—2121no—
238C2×C42D21211yescharacteristic
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—21no—
245#107—532no—
246#107—1061no—
247#107—1061no—
248#107—1061no—
249C4×C8—21no—
250C4×C8—21no—
251#95—2121no—
252C24—2121no—
253C2×Q8—1062no—
254C2×Q8—2121no—
255C2×Q8—2121no—
256C2×Q8—2121no—
257C2×Q8—2121no—
258C2×Q8—2121no—
259C2×D4—1062no—
260C2×D4—2121no—
261C2×D4—2121no—
262C2×D4—2121no—
263C2×D4—2121no—
264C2×D4—2121no—
265C22×C4—2121no—
266C22×C4—2121no—
267C22×C4—2121no—
268C22×C4D42411yescharacteristic
269C22×C4D42411yescharacteristic
270C22×C4C2×D21211yescharacteristic
271Q16—1062no—
272Q16—1062no—
273Q16—2121no—
274Q16—2121no—
275SD16—2128no—
276D8—1062no—
277D8—1062no—
278D8—2121no—
279D8—2121no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8#1171991312yes—
283C2×C8#1171994511yescharacteristic
284C2×C8#1171994511yescharacteristic
285C2×C8D4×D5311yescharacteristic
286C2×C8D4×D5311yescharacteristic
287C2×C8D4×D5311yescharacteristic
288C2×C8#1171994911yescharacteristic
289C4⋊C4—1062no—
290C4⋊C4—4242no—
291C4⋊C4—2121no—
292C4⋊C4—2121no—
293C4⋊C4—2121no—
294C22⋊C4—2124no—
295C22⋊C4—2124no—
296C42—21no—
297C42—21no—
298C16—41no—
299C16—41no—
300C23—4241no—
301C23—4241no—
302C23—4241no—
303C23—4241no—
304C23—4241no—
305C23—4241no—
306C23—2122no—
307C23C2×D42411yescharacteristic
308Q8—4241no—
309Q8—4241no—
310Q8—2122no—
311Q8—2122no—
312D4—4241no—
313D4—4241no—
314D4—2122no—
315D4—2122no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—4241no—
323C2×C4—4241no—
324C2×C4—4241no—
325C2×C4—4241no—
326C2×C4—4241no—
327C2×C4—4241no—
328C2×C4—4241no—
329C2×C4—2122no—
330C2×C4—2122no—
331C2×C4#1313318711yescharacteristic
332C2×C4#1313319211yescharacteristic
333C2×C4#1313320511yescharacteristic
334C2×C4C2×#1171991311yescharacteristic
335C2×C4#1313324511yescharacteristic
336C2×C4#1313324511yescharacteristic
337C8—22no—
338C8#1313319011yescharacteristic
339C8#1313319011yescharacteristic
340C8#1313320211yescharacteristic
341C8#1313320211yescharacteristic
342C22—8481no—
343C22—8481no—
344C22—8481no—
345C22—8481no—
346C22—4242no—
347C22—4242no—
348C22—4242no—
349C22#1681075911yescharacteristic
350C22#1681081911yescharacteristic
351C22#1681097011yescharacteristic
352C22#1681105511yescharacteristic
353C22#1681105511yescharacteristic
354C22#1681106111yescharacteristic
355C22#1681106611yescharacteristic
356C4—41no—
357C4—41no—
358C4—8481no—
359C4—4242no—
360C4—4242no—
361C4#1681054111yescharacteristic
362C4#1681077611yescharacteristic
363C4#1681082411yescharacteristic
364C4#1681098811yescharacteristic
365C2—8482no—
366C2#2027595011yescharacteristic
367C2#2027664011yescharacteristic
368C2#2027665711yescharacteristic
369C2#2027677111yescharacteristic
370C2#2027677811yescharacteristic
371C2#2027694711yescharacteristic
372C2#2027695211yescharacteristic
subgroupG/H
centerC23C2×D424
commutator, cosocleC22×C8×C53C23
FrattiniC22×C8C22×D53
FittingC53×#1374C2
socleC23×C53C2×D8
prime radicalC22×D424C22
hypercenter#1374D53
hypocenterC53#13408
LCSG ▷ C22×C8×C53 ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
2. C2×#16810428C2semidirect
3. C2×#16810428C2semidirect
6. #20275448C2semidirect
7. C53×#1374C2semidirect
185. #1374D53semidirect
211. C53#13408semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168110072
C2×#168104282
C2×#168104252
#202754482
C53×#13742
#1340853