Finite Group Databasebeta

← #27279373

Subgroups — #27279373

Order 13568.

618 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810970C211yesmaximal, characteristic
2#20277771C211yesmaximal, characteristic, complemented
3#20275642C211yesmaximal, characteristic
4#20275641C211yesmaximal, characteristic
5C2×#16810370C211yesmaximal, characteristic, complemented
6#20272555C211yesmaximal, characteristic, complemented
7C53×#1279C211yesmaximal, characteristic, complemented
8C2×#13133217C2211yescharacteristic
9C2×#13133214C2211yescharacteristic
10C2×C4×Dic106—21no—
11#16810970—22no—
12#16810970C414yescomplemented
13C2×C4⋊#88322C2211yescharacteristic
14C2×#13133139—22no—
15C2×#13133139—21no—
16C2×#13133139—21no—
17C2×#13133137—21no—
18C2×#13133137—21no—
19#16810529—21no—
20#16810519—21no—
21#16810506—22no—
22C4⋊C4×Dic53—21no—
23C4×C4⋊Dic53C2211yescharacteristic
24#16810370—22no—
25C2×C4⋊C8×C53C2211yescharacteristic
26C2×C4×C8×C53C2211yescharacteristic
27C4×C4⋊C4×C53C2211yescharacteristic
28C22×Dic106—21no—
29C22×D212—21no—
30C22×D212—21no—
31C22×D212—21no—
32C22×#88322—21no—
33#13133217—21no—
34#13133217—21no—
35#13133217C2×C412yes—
36#13133217D412yes—
37#13133214—21no—
38#13133214—21no—
39#13133214—21no—
40#13133214C2×C412yes—
41C4×Dic106—42no—
42C4×Dic106—42no—
43C2×C4⋊Dic53—21no—
44C2×C4⋊Dic53D411yescharacteristic
45C2×C4⋊Dic53D412yes—
46C2×C4⋊Dic53D411yescharacteristic
47C2×#11719919—22no—
48C2×C4×Dic53—22no—
49C2×C4×Dic53—21no—
50C4⋊#88322—21no—
51C4⋊#88322—21no—
52#13133139—28no—
53#13133139—42no—
54#13133139—42no—
55#13133137—42no—
56#13133137—42no—
57#13133124—22no—
58#13133124—22no—
59#13133124—21no—
60C22×C8×C53—21no—
61C22×C8×C53—21no—
62C2×C4⋊C4×C53D411yescharacteristic
63C2×C4⋊C4×C53D411yescharacteristic
64C2×C42×C53—21no—
65C2×C42×C53C2311yescharacteristic
66C4⋊C8×C53—21no—
67C4⋊C8×C53—21no—
68C4×C8×C53—21no—
69C4×C8×C53C2×C412yes—
70#95×C53—21no—
71C23×D53—41no—
72C22×C4×C53—21no—
73C22×C4×C53—21no—
74C22×C4×C53C2×D411yescharacteristic
75C22×C4×C53C2×D411yescharacteristic
76C22×C4×C53C2×D411yescharacteristic
77C22×Dic53—22no—
78C22×Dic53—21no—
79C22×Dic53—21no—
80C2×D212—22no—
81C2×D212—22no—
82C2×D212—22no—
83C2×D212—42no—
84C2×D212—42no—
85C2×D212—41no—
86C2×D212—41no—
87C2×D212—41no—
88C2×D212—41no—
89C2×D212—41no—
90C2×D212—41no—
91C2×D212—41no—
92C2×D212—41no—
93C2×D212—41no—
94C2×D212—41no—
95C2×D212—41no—
96C2×Dic106—22no—
97C2×Dic106—22no—
98C2×Dic106—41no—
99C2×Dic106—41no—
100C2×Dic106—41no—
101C2×Dic106—41no—
102C2×C8×C53—22no—
103C2×C8×C53—41no—
104C2×C8×C53—41no—
105C2×C8×C53—41no—
106C2×C8×C53—41no—
107C2×C8×C53—41no—
108C4⋊C4×C53—21no—
109C4⋊C4×C53—21no—
110C4⋊C4×C53—21no—
111C4⋊C4×C53SD1612yes—
112C42×C53—41no—
113C42×C53—41no—
114C42×C53C22×C411yescharacteristic
115C42×C53C2×D411yescharacteristic
116C42×C53#4111yescharacteristic
117C42×C53#4111yescharacteristic
118C4⋊Dic53—22no—
119C4⋊Dic53—22no—
120C4⋊Dic53—22no—
121C4⋊Dic53—21no—
122C4⋊Dic53—21no—
123C4⋊Dic53—21no—
124C4⋊Dic53C22⋊C414yes—
125C4⋊Dic53D812yes—
126#11719919—44no—
127C4×Dic53—44no—
128C4×Dic53—41no—
129C4×Dic53—41no—
130C2×#88322—41no—
131C2×#88322—41no—
132C2×#88322—41no—
133C23×C53#12011yescharacteristic
134C22×D53—42no—
135C22×D53—81no—
136C22×D53—81no—
137C22×D53—81no—
138C22×D53—81no—
139C22×D53—81no—
140C22×D53—81no—
141C2×C4×C53—21no—
142C2×C4×C53—21no—
143C2×C4×C53—22no—
144C2×C4×C53—41no—
145C2×C4×C53—41no—
146C2×C4×C53—41no—
147C2×C4×C53—41no—
148C2×C4×C53—41no—
149C2×C4×C53C2×C22⋊C411yescharacteristic
150C2×C4×C53C4×D411yescharacteristic
151C2×C4×C53C4×D411yescharacteristic
152C2×C4×C53#12111yescharacteristic
153C2×C4×C53#12111yescharacteristic
154C2×C4×C53#12311yescharacteristic
155C2×C4×C53C2×D811yescharacteristic
156C2×C4×C53C2×SD1611yescharacteristic
157C2×C4×C53#13511yescharacteristic
158C2×C4×C53#13511yescharacteristic
159C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C53#13711yescharacteristic
163C2×Dic53—24no—
164C2×Dic53—22no—
165C2×Dic53—42no—
166C2×Dic53—42no—
167C2×Dic53—41no—
168C2×Dic53—41no—
169C2×Dic53—41no—
170C2×Dic53—41no—
171C2×Dic53—41no—
172D212—44no—
173D212—42no—
174D212—42no—
175D212—42no—
176D212—42no—
177D212—82no—
178D212—81no—
179D212—81no—
180D212—81no—
181D212—81no—
182Dic106—42no—
183Dic106—42no—
184Dic106—42no—
185Dic106—42no—
186C8×C53—42no—
187C8×C53—81no—
188#88322—81no—
189#9062—531nomaximal, Sylow
190C22×C53#38611yescharacteristic
191C22×C53#44711yescharacteristic
192C22×C53#44811yescharacteristic
193C22×C53#44911yescharacteristic
194C22×C53#44911yescharacteristic
195C22×C53#45411yescharacteristic
196C22×C53#45411yescharacteristic
197C2×D53—82no—
198C2×D53—82no—
199C2×D53—82no—
200C2×D53—161no—
201C2×D53—161no—
202C2×D53—161no—
203C2×D53—161no—
204C4×C53—21no—
205C4×C53—21no—
206C4×C53—42no—
207C4×C53—81no—
208C4×C53C4×D811yescharacteristic
209C4×C53C4×SD1611yescharacteristic
210C4×C53#44011yescharacteristic
211C4×C53#44211yescharacteristic
212C4×C53#45911yescharacteristic
213C4×C53#46011yescharacteristic
214C4×C53#46311yescharacteristic
215C4×C53#46411yescharacteristic
216Dic53—44no—
217Dic53—42no—
218Dic53—81no—
219C2×#486—531no—
220#2365—531no—
221#1982—531no—
222#1982—531no—
223C2×#332—531no—
224#1279—531no—
225#1279D5311yescharacteristic, complemented
226C2×C53#162511yescharacteristic
227C2×C53#162611yescharacteristic
228C2×C53#162711yescharacteristic
229C2×C53#162811yescharacteristic
230C2×C53#187911yescharacteristic
231C2×C53#188011yescharacteristic
232C2×C53#188811yescharacteristic
233D53—162no—
234C2×C4⋊Q8—531no—
235C2×#127—531no—
236C2×C4×Q8—1061no—
237#486—534no—
238#486—1062no—
239C2×C4⋊C8—531no—
240C2×C4⋊C8C2×D5311yescharacteristic
241C2×#102—1062no—
242C2×#102—1061no—
243C2×#102—1061no—
244C2×#102—1061no—
245C2×#102—1061no—
246C2×C4×C8C2×D5311yescharacteristic
247#391—1061no—
248#389—1061no—
249#387—1062no—
250C4×C4⋊C4—531no—
251C4×C4⋊C4—1061no—
252C4×C4⋊C4C2×D5311yescharacteristic
253#332—1062no—
254C53#906211yescharacteristic, complemented, Sylow
255C22×Q8—1061no—
256C22×D4—1061no—
257C22×D4—1061no—
258C22×D4—1061no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—1061no—
262C4⋊Q8—532no—
263C4⋊Q8—532no—
264C4⋊Q8—1061no—
265C4⋊Q8—1061no—
266#127—532no—
267#127—1061no—
268#127—1061no—
269#127—1061no—
270C4×Q8—2122no—
271C4×Q8—2122no—
272C2×C4⋊C4—531no—
273C2×C4⋊C4—532no—
274C2×C4⋊C4—531no—
275C2×C4⋊C4—1061no—
276C2×C4⋊C4—1062no—
277C2×C4⋊C4D21211yescharacteristic
278C2×C4⋊C4D21211yescharacteristic
279C2×C42—21no—
280C2×C42—1062no—
281C2×C42—1061no—
282C2×C42C22×D5311yescharacteristic
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—1061no—
286C4⋊C8—1061no—
287#102—1068no—
288#102—2122no—
289#102—2122no—
290#102—2122no—
291#102—2122no—
292C4×C8—21no—
293C4×C8C4×D5312yes—
294#95—21no—
295#95—1062no—
296#95—1062no—
297#95—1061no—
298C24—2121no—
299C2×Q8—1062no—
300C2×Q8—1062no—
301C2×Q8—2121no—
302C2×Q8—2121no—
303C2×Q8—2121no—
304C2×Q8—2121no—
305C2×D4—1062no—
306C2×D4—1062no—
307C2×D4—1062no—
308C2×D4—2122no—
309C2×D4—2122no—
310C2×D4—2121no—
311C2×D4—2121no—
312C2×D4—2121no—
313C2×D4—2121no—
314C2×D4—2121no—
315C2×D4—2121no—
316C2×D4—2121no—
317C2×D4—2121no—
318C2×D4—2121no—
319C2×D4—2121no—
320C2×D4—2121no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—1062no—
324C22×C4—1061no—
325C22×C4—1061no—
326C22×C4C2×D21211yescharacteristic
327C22×C4D4×D5311yescharacteristic
328C22×C4D4×D5311yescharacteristic
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—2121no—
336C2×C8—2121no—
337C2×C8—2121no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—534no—
342C4⋊C4—532no—
343C4⋊C4—1062no—
344C4⋊C4—1062no—
345C4⋊C4—1062no—
346C4⋊C4—1061no—
347C4⋊C4—1061no—
348C4⋊C4—1061no—
349C4⋊C4—2124no—
350C4⋊C4#1171991312yes—
351C42—41no—
352C42—41no—
353C42—2124no—
354C42—2121no—
355C42—2121no—
356C42C2×C4×D5311yescharacteristic
357C42#1171994511yescharacteristic
358C42D4×D5311yescharacteristic
359C42#1171994911yescharacteristic
360C23—4241no—
361C23—4241no—
362C23—4241no—
363C23—4241no—
364C23—4241no—
365C23—4241no—
366C23—2122no—
367C23#1313318711yescharacteristic
368Q8—2122no—
369Q8—2122no—
370Q8—2122no—
371Q8—2122no—
372D4—4242no—
373D4—4241no—
374D4—4241no—
375D4—4241no—
376D4—4241no—
377D4—2124no—
378D4—2122no—
379D4—2122no—
380D4—2122no—
381D4—2122no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—1064no—
391C2×C4—1062no—
392C2×C4—2121no—
393C2×C4—2121no—
394C2×C4—2121no—
395C2×C4—2122no—
396C2×C4—2121no—
397C2×C4—2122no—
398C2×C4—2121no—
399C2×C4C22⋊C4×D5311yescharacteristic
400C2×C4#1313317911yescharacteristic
401C2×C4C4×D21211yescharacteristic
402C2×C4#1313319011yescharacteristic
403C2×C4#1313319211yescharacteristic
404C2×C4#1313320211yescharacteristic
405C2×C4D8×D5311yescharacteristic
406C2×C4C2×#1171991311yescharacteristic
407C2×C4#1313323911yescharacteristic
408C2×C4#1313324011yescharacteristic
409C2×C4#1313324411yescharacteristic
410C2×C4#1313324411yescharacteristic
411C2×C4#1313324511yescharacteristic
412C2×C4#1313325011yescharacteristic
413C8—42no—
414C8—81no—
415C8—4241no—
416C22—8481no—
417C22—8481no—
418C22—8481no—
419C22—8481no—
420C22—4242no—
421C22—4242no—
422C22—4242no—
423C22#1681050111yescharacteristic
424C22#1681075811yescharacteristic
425C22#1681076411yescharacteristic
426C22#1681077011yescharacteristic
427C22#1681077111yescharacteristic
428C22#1681079711yescharacteristic
429C22#1681079711yescharacteristic
430C4—21no—
431C4—21no—
432C4—42no—
433C4—81no—
434C4—4241no—
435C4—2124no—
436C4—2122no—
437C4#1681070511yescharacteristic
438C4C4×#1171991311yescharacteristic
439C4#1681072511yescharacteristic
440C4#1681073411yescharacteristic
441C4#1681081711yescharacteristic
442C4#1681082411yescharacteristic
443C4#1681084111yescharacteristic
444C4#1681084611yescharacteristic
445C2—8482no—
446C2#2027380711yescharacteristic
447C2#2027381411yescharacteristic
448C2#2027382111yescharacteristic
449C2#2027382811yescharacteristic
450C2#2027506411yescharacteristic
451C2#2027506911yescharacteristic
452C2#2027511711yescharacteristic
subgroupG/H
centerC23#13133187
commutatorC42×C53C22×C4
FrattiniC2×C42C22×D53
FittingC53×#1279C2
socleC23×C53#120
prime radicalC2×#13133214C22
cosocleC2×C42×C53C23
hypercenter#1279D53
hypocenterC53#9062
LCSG ▷ C42×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #20277771C2semidirect
5. C2×#16810370C2semidirect
6. #20272555C2semidirect
7. C53×#1279C2semidirect
12. #16810970C4semidirect
225. #1279D53semidirect
254. C53#9062semidirect

Maximal subgroups

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

subgroupindex
C2×#168109702
#202777712
#202756422
#202756412
C2×#168103702
#202725552
C53×#12792
#906253