Finite Group Databasebeta

← #27287487

Subgroups — #27287487

Order 13568.

516 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20279884C211yesmaximal, characteristic
2#20275516C211yesmaximal, characteristic, complemented
3#20274712C211yesmaximal, characteristic
4C2×#16810371C211yesmaximal, characteristic, complemented
5C2×#16810350C211yesmaximal, characteristic
6#20272556C211yesmaximal, characteristic, complemented
7C53×#1947C211yesmaximal, characteristic, complemented
8C2×#13133217C2211yescharacteristic
9C2×C4×D212C2211yescharacteristic
10C2×C4⋊#88322C2211yescharacteristic
11C2×#13133140—22no—
12C2×#13133137—21no—
13C2×C4×#88322C2211yescharacteristic
14#16810536—22no—
15#16810525—21no—
16#16810489—21no—
17#16810480—21no—
18#16810480—21no—
19#16810385—21no—
20#16810371—22no—
21#16810350—22no—
22C2×#107×C53—21no—
23C2×C4⋊C8×C53C2211yescharacteristic
24C53×#384C2211yescharacteristic
25C4×C4⋊C4×C53C2211yescharacteristic
26C53×#340—21no—
27C22×Dic106D412yes—
28C22×D212D411yescharacteristic
29C22×C4×D53—21no—
30C22×#88322—21no—
31C22×#88322—21no—
32#13133217—21no—
33#13133217—21no—
34#13133217—21no—
35#13133217—21no—
36C4×D212—21no—
37C4×D212—21no—
38C4×D212—21no—
39C4×D212—21no—
40C2×C4⋊Dic53—21no—
41C2×C4⋊Dic53—21no—
42C2×C4⋊Dic53D411yescharacteristic
43C2×#11719921—22no—
44C2×#11719921—22no—
45C2×#11719921—21no—
46C4⋊#88322—21no—
47C4⋊#88322—21no—
48#13133140—44no—
49#13133137—42no—
50C4×#88322—21no—
51C4×#88322—21no—
52#13133124—22no—
53#13133124—22no—
54C22×C8×C53—21no—
55C2×C4⋊C4×C53—21no—
56C2×C4⋊C4×C53—21no—
57C2×C4⋊C4×C53—21no—
58C2×C4⋊C4×C53D411yescharacteristic
59C2×C4⋊C4×C53D411yescharacteristic
60C2×C42×C53—21no—
61C2×C42×C53C2311yescharacteristic
62#107×C53—42no—
63C4⋊C8×C53—21no—
64C4⋊C8×C53D412yes—
65#95×C53—21no—
66C23×D53—21no—
67C22×C4×C53—21no—
68C22×C4×C53—21no—
69C22×C4×C53—41no—
70C22×C4×C53C2×D411yescharacteristic
71C22×C4×C53C2×D411yescharacteristic
72C22×C4×C53C2×D411yescharacteristic
73C22×Dic53—21no—
74C22×Dic53—22no—
75C2×D212—21no—
76C2×D212—21no—
77C2×D212—21no—
78C2×D212—21no—
79C2×D212—21no—
80C2×D212Q1612yes—
81C2×C4×D53—41no—
82C2×C4×D53—41no—
83C2×C4×D53—41no—
84C2×C4×D53—41no—
85C2×C4×D53—41no—
86C2×C4×D53—41no—
87C2×Dic106—22no—
88C2×Dic106—22no—
89C2×Dic106—42no—
90C2×Dic106—42no—
91C2×C8×C53—22no—
92C2×C8×C53—41no—
93C2×C8×C53—41no—
94C4⋊C4×C53—21no—
95C4⋊C4×C53—21no—
96C4⋊C4×C53—21no—
97C4⋊C4×C53—21no—
98C4⋊C4×C53—42no—
99C4⋊C4×C53—41no—
100C4⋊C4×C53—41no—
101C4⋊C4×C53—41no—
102C4⋊C4×C53—41no—
103C42×C53—41no—
104C42×C53—41no—
105C42×C53C2×D411yescharacteristic
106C42×C53#4111yescharacteristic
107C42×C53#4111yescharacteristic
108C42×C53#4111yescharacteristic
109#11719921—41no—
110#11719921—41no—
111#11719921—82no—
112#11719921—82no—
113C4⋊Dic53—21no—
114C4⋊Dic53—21no—
115C4⋊Dic53—41no—
116C4⋊Dic53—41no—
117C4⋊Dic53—41no—
118C4⋊Dic53—41no—
119C2×#88322—22no—
120C2×#88322—41no—
121C2×#88322—41no—
122C2×#88322—41no—
123C2×#88322—41no—
124C2×#88322—41no—
125C23×C53#12011yescharacteristic
126C22×D53—22no—
127C22×D53—41no—
128C22×D53—41no—
129C22×D53—41no—
130C22×D53—41no—
131C22×D53—41no—
132C22×D53—41no—
133C2×C4×C53—21no—
134C2×C4×C53—21no—
135C2×C4×C53—41no—
136C2×C4×C53—41no—
137C2×C4×C53—41no—
138C2×C4×C53—41no—
139C2×C4×C53—41no—
140C2×C4×C53—41no—
141C2×C4×C53—81no—
142C2×C4×C53—81no—
143C2×C4×C53—81no—
144C2×C4×C53#12111yescharacteristic
145C2×C4×C53#12111yescharacteristic
146C2×C4×C53#12111yescharacteristic
147C2×C4×C53#12311yescharacteristic
148C2×C4×C53#12311yescharacteristic
149C2×C4×C53#12411yescharacteristic
150C2×C4×C53C2×Q1611yescharacteristic
151C2×C4×C53#13511yescharacteristic
152C2×C4×C53#13511yescharacteristic
153C2×C4×C53#13511yescharacteristic
154C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C53#13711yescharacteristic
157C2×C4×C53#13711yescharacteristic
158C2×Dic53—42no—
159C2×Dic53—41no—
160C2×Dic53—41no—
161C2×Dic53—41no—
162C2×Dic53—42no—
163C2×Dic53—42no—
164D212—22no—
165D212—22no—
166D212—41no—
167D212—41no—
168C4×D53—81no—
169C4×D53—81no—
170C4×D53—81no—
171C4×D53—81no—
172Dic106—44no—
173Dic106—82no—
174C8×C53—42no—
175#88322—42no—
176#88322—81no—
177#10413—531nomaximal, Sylow
178C22×C53#39411yescharacteristic
179C22×C53#44911yescharacteristic
180C22×C53#44911yescharacteristic
181C22×C53#45111yescharacteristic
182C22×C53#45211yescharacteristic
183C22×C53#45311yescharacteristic
184C22×C53#45511yescharacteristic
185C2×D53—42no—
186C2×D53—42no—
187C2×D53—42no—
188C2×D53—81no—
189C2×D53—81no—
190C2×D53—81no—
191C2×D53—81no—
192C4×C53—21no—
193C4×C53—21no—
194C4×C53—81no—
195C4×C53—81no—
196C4×C53—161no—
197C4×C53#46311yescharacteristic
198C4×C53#46411yescharacteristic
199C4×C53#46711yescharacteristic
200C4×C53#46811yescharacteristic
201C4×C53#48411yescharacteristic
202C4×C53#48511yescharacteristic
203C4×C53#48811yescharacteristic
204C4×C53#48911yescharacteristic
205Dic53—82no—
206Dic53—81no—
207#2563—531no—
208#1956—531no—
209#1947D5311yescharacteristic, complemented
210#1802—531no—
211C2×#333—531no—
212C2×D4⋊C8—531no—
213#1279—531no—
214C2×C53#162411yescharacteristic
215C2×C53#163211yescharacteristic
216C2×C53#164411yescharacteristic
217C2×C53#164611yescharacteristic
218C2×C53#203611yescharacteristic
219C2×C53#203711yescharacteristic
220C2×C53#204211yescharacteristic
221D53—82no—
222C2×C4⋊Q8—531no—
223C2×C4×D4—531no—
224C2×#107—21no—
225C2×C4⋊C8—531no—
226C2×C4⋊C8C2×D5311yescharacteristic
227C2×#103—1062no—
228C2×#102—1061no—
229C2×C4×C8—531no—
230#393—1062no—
231#390—1061no—
232#384C2×D5311yescharacteristic
233#382—1061no—
234#380—1061no—
235#380—1061no—
236C4×C4⋊C4C2×D5311yescharacteristic
237#340—21no—
238#340—1061no—
239#333—1062no—
240D4⋊C8—1062no—
241C53#1041311yescharacteristic, complemented, Sylow
242C22×Q8—532no—
243C22×D4—531no—
244C23×C4—1061no—
245C22×C8—21no—
246C22×C8—1061no—
247C22×C8—1061no—
248C4⋊Q8—1061no—
249C4⋊Q8—1061no—
250C4⋊Q8—1061no—
251C4⋊Q8—1061no—
252C4×D4—1061no—
253C4×D4—1061no—
254C4×D4—1061no—
255C4×D4—1061no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—531no—
260C2×C4⋊C4—1061no—
261C2×C4⋊C4—1061no—
262C2×C4⋊C4C22⋊D5311yescharacteristic
263C2×C4⋊C4C22⋊D5311yescharacteristic
264C2×C22⋊C4—1062no—
265C2×C22⋊C4—1062no—
266C2×C22⋊C4—1061no—
267C2×C42—21no—
268C2×C42C22×D5311yescharacteristic
269#107—42no—
270C4⋊C8—21no—
271C4⋊C8—1061no—
272C4⋊C8—1061no—
273C4⋊C8D21212yes—
274#103—2124no—
275#102—2122no—
276C4×C8—1061no—
277C4×C8—1061no—
278#95—21no—
279#95—1062no—
280#95—1062no—
281C24—1061no—
282C2×Q8—1062no—
283C2×Q8—1062no—
284C2×Q8—2122no—
285C2×Q8—2122no—
286C2×D4—532no—
287C2×D4—1061no—
288C2×D4—1061no—
289C2×D4—1061no—
290C2×D4—1061no—
291C2×D4—1061no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—41no—
295C22×C4—1061no—
296C22×C4—1062no—
297C22×C4—2121no—
298C22×C4—2121no—
299C22×C4—2121no—
300C22×C4—2121no—
301C22×C4—2121no—
302C22×C4—2121no—
303C22×C4D4×D5311yescharacteristic
304C22×C4D4×D5311yescharacteristic
305C22×C4C2×C22⋊D5311yescharacteristic
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—1062no—
310C2×C8—2121no—
311C2×C8—2121no—
312C2×C8—2121no—
313C2×C8—2121no—
314C2×C8—2121no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—42no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—1061no—
325C4⋊C4—1061no—
326C4⋊C4—2121no—
327C4⋊C4—2121no—
328C4⋊C4—2121no—
329C4⋊C4—2121no—
330C22⋊C4—4242no—
331C22⋊C4—4242no—
332C22⋊C4—2121no—
333C22⋊C4—2121no—
334C42—41no—
335C42—41no—
336C42C2×D21211yescharacteristic
337C42#1171994511yescharacteristic
338C42#1171994911yescharacteristic
339C42#1171994911yescharacteristic
340C23—1062no—
341C23—2121no—
342C23—2121no—
343C23—2121no—
344C23—2121no—
345C23—2121no—
346C23—2121no—
347C23#1313318511yescharacteristic
348Q8—4242no—
349Q8—2124no—
350D4—1062no—
351D4—1062no—
352D4—2121no—
353D4—2121no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—4241no—
366C2×C4—4241no—
367C2×C4—4241no—
368C2×C4—4241no—
369C2×C4—2121no—
370C2×C4—2121no—
371C2×C4—2122no—
372C2×C4—2121no—
373C2×C4—2122no—
374C2×C4—2122no—
375C2×C4#1313319111yescharacteristic
376C2×C4#1313319211yescharacteristic
377C2×C4#1313319211yescharacteristic
378C2×C4#1313320211yescharacteristic
379C2×C4#1313320211yescharacteristic
380C2×C4#1313320611yescharacteristic
381C2×C4Q16×D5311yescharacteristic
382C2×C4#1313323611yescharacteristic
383C2×C4#1313323711yescharacteristic
384C2×C4#1313323711yescharacteristic
385C2×C4#1313324111yescharacteristic
386C2×C4#1313324311yescharacteristic
387C2×C4#1313324811yescharacteristic
388C2×C4#1313324911yescharacteristic
389C8—42no—
390C8—4241no—
391C8—2122no—
392C22—4241no—
393C22—4241no—
394C22—4241no—
395C22—4241no—
396C22—2122no—
397C22—2122no—
398C22—2122no—
399C22#1681054011yescharacteristic
400C22#1681076511yescharacteristic
401C22#1681076611yescharacteristic
402C22#1681077711yescharacteristic
403C22#1681078311yescharacteristic
404C22#1681078911yescharacteristic
405C22#1681079911yescharacteristic
406C4—21no—
407C4—21no—
408C4—81no—
409C4—81no—
410C4—161no—
411C4—4242no—
412C4—4241no—
413C4#1681083811yescharacteristic
414C4#1681084511yescharacteristic
415C4#1681086511yescharacteristic
416C4#1681087011yescharacteristic
417C4#1681096011yescharacteristic
418C4#1681096611yescharacteristic
419C4#1681098011yescharacteristic
420C4#1681098511yescharacteristic
421C2—4242no—
422C2#2027379711yescharacteristic
423C2#2027384811yescharacteristic
424C2#2027392711yescharacteristic
425C2#2027394211yescharacteristic
426C2#2027592011yescharacteristic
427C2#2027592711yescharacteristic
428C2#2027595611yescharacteristic
subgroupG/H
centerC23#13133185
commutator, cosocleC2×C42×C53C23
FrattiniC2×C42C22×D53
FittingC53×#1947C2
socleC23×C53#120
prime radicalC22×D212D4
hypercenter#1947D53
hypocenterC53#10413
LCSG ▷ C2×C42×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
2. #20275516C2semidirect
4. C2×#16810371C2semidirect
6. #20272556C2semidirect
7. C53×#1947C2semidirect
209. #1947D53semidirect
241. C53#10413semidirect

Maximal subgroups

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

subgroupindex
#202798842
#202755162
#202747122
C2×#168103712
C2×#168103502
#202725562
C53×#19472
#1041353