Finite Group Databasebeta

← #27300956

Subgroups — #27300956

Order 13568.

494 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D53C211yesmaximal, characteristic, complemented
2#20283411C211yesmaximal, characteristic
3C2×#16810408C211yesmaximal, characteristic, complemented
4C2×#16810406C211yesmaximal, characteristic, complemented
5C2×#16810402C211yesmaximal, characteristic, complemented
6#20272804C211yesmaximal, characteristic, complemented
7C53×#1379C211yesmaximal, characteristic, complemented
8C2×#13133223C2211yescharacteristic
9C22×C8×D53C2211yescharacteristic
10#16811135C411yescharacteristic
11C2×#13133157C2211yescharacteristic
12C2×#13133156—21no—
13M32×D53—22no—
14M32×D53—22no—
15C22×#11719908C2211yescharacteristic
16C2×C16×D53—21no—
17#16810696—21no—
18#16810696—21no—
19C8×D212—21no—
20C8×D212—21no—
21#16810650C411yescharacteristic
22#16810591C411yescharacteristic
23#16810586C411yescharacteristic
24#16810408—22no—
25#16810406—22no—
26#16810402—21no—
27#16810402—21no—
28C2×M32×C53C2211yescharacteristic
29C22×C16×C53C2211yescharacteristic
30C53×#405C2211yescharacteristic
31C2×#11719945C2×C411yescharacteristic
32C22×C4×D53C2×C411yescharacteristic
33#13133223—21no—
34#13133223—21no—
35#13133223—21no—
36#13133223—21no—
37C2×#11719917C2×C411yescharacteristic
38C2×#11719912—21no—
39C22×#88322C2×C411yescharacteristic
40C2×C8×D53—21no—
41C2×C8×D53—21no—
42C2×C8×D53—21no—
43C2×C8×D53—21no—
44C2×C8×D53—21no—
45C2×C8×D53D411yescharacteristic
46C2×C8×D53D411yescharacteristic
47C2×C8×D53D411yescharacteristic
48C2×C8×D53D411yescharacteristic
49#13133201—21no—
50#13133197C811yescharacteristic
51#13133197C811yescharacteristic
52#13133192C811yescharacteristic
53#13133192C811yescharacteristic
54#13133187—21no—
55C4×D212—21no—
56C4×D212—21no—
57#13133157—21no—
58#13133157D412yescomplemented
59#13133156—24no—
60C2×#11719908—21no—
61C2×#11719908—21no—
62C2×#11719908—21no—
63C2×#11719908—21no—
64C16×D53—24no—
65C4⋊#88322—21no—
66C4⋊#88322—21no—
67#13133129—21no—
68#13133129—21no—
69#13133129—21no—
70#13133129—21no—
71C2×M16×C53C2×C411yescharacteristic
72C22×C8×C53C2311yescharacteristic
73#117×C53C2×C411yescharacteristic
74M32×C53—21no—
75M32×C53D412yescomplemented
76C2×C16×C53—21no—
77C2×C16×C53—21no—
78C2×C16×C53—21no—
79C2×C16×C53—21no—
80#97×C53—21no—
81C4×C8×C53—21no—
82C23×D53M1611yescharacteristic
83C22×C4×C53C22×C411yescharacteristic
84C2×C22⋊D53—21no—
85C22×Dic53M1611yescharacteristic
86#11719945—21no—
87#11719945—21no—
88#11719945—21no—
89#11719945—21no—
90C2×D212—21no—
91C2×D212—21no—
92C2×D212C2×C811yescharacteristic
93C2×C4×D53—21no—
94C2×C4×D53—21no—
95C2×C4×D53—21no—
96C2×C4×D53—21no—
97C2×C4×D53—21no—
98C2×C4×D53C22⋊C411yescharacteristic
99C2×C4×D53C22⋊C411yescharacteristic
100C2×C4×D53C2×C811yescharacteristic
101C2×C4×D53C2×C811yescharacteristic
102C2×Dic106C2×C811yescharacteristic
103M16×C53—21no—
104M16×C53—21no—
105C2×C8×C53—21no—
106C2×C8×C53C2×D411yescharacteristic
107C2×C8×C53C2×D411yescharacteristic
108C2×C8×C53C2×D411yescharacteristic
109C2×C8×C53C2×D411yescharacteristic
110C2×C8×C53#4111yescharacteristic
111C2×C8×C53#4111yescharacteristic
112C4⋊C4×C53C2×C811yescharacteristic
113C4⋊C4×C53C2×C811yescharacteristic
114C22⋊C4×C53—21no—
115C42×C53—21no—
116#11719921—21no—
117#11719921—21no—
118#11719921—21no—
119#11719921—21no—
120C4⋊Dic53—21no—
121C4⋊Dic53—21no—
122#11719917—21no—
123#11719917—21no—
124C2×#88322—21no—
125C2×#88322—21no—
126C2×#88322—21no—
127C2×#88322C22⋊C411yescharacteristic
128C2×#88322C22⋊C411yescharacteristic
129#11719912—41no—
130#11719912—41no—
131C8×D53—21no—
132C8×D53—21no—
133C8×D53—21no—
134C8×D53—21no—
135C8×D53—21no—
136C8×D53—21no—
137C8×D53—21no—
138C8×D53—21no—
139C8×D53—41no—
140C8×D53—41no—
141C16×C53—22no—
142C16×C53—41no—
143#11719908—22no—
144#11719908—41no—
145C23×C53C2×M1611yescharacteristic
146C22×D53—21no—
147C22×D53—21no—
148C22×D53—22no—
149C22×D53—21no—
150C22×D53—41no—
151C22×D53C22⋊C811yescharacteristic
152C22×D53C22⋊C811yescharacteristic
153C2×C4×C53—21no—
154C2×C4×C53—21no—
155C2×C4×C53C2×C22⋊C411yescharacteristic
156C2×C4×C53C4×D411yescharacteristic
157C2×C4×C53C4×D411yescharacteristic
158C2×C4×C53C22×C811yescharacteristic
159C2×C4×C53#13111yescharacteristic
160C2×C4×C53#13111yescharacteristic
161C22⋊D53—41no—
162C22⋊D53—41no—
163C2×Dic53—21no—
164C2×Dic53—21no—
165C2×Dic53—21no—
166C2×Dic53C22⋊C811yescharacteristic
167C2×Dic53C22⋊C811yescharacteristic
168D212—21no—
169D212—21no—
170D212—42no—
171D212—42no—
172C4×D53—21no—
173C4×D53—21no—
174C4×D53—21no—
175C4×D53—21no—
176C4×D53—21no—
177C4×D53—21no—
178C4×D53—21no—
179C4×D53—21no—
180C4×D53—41no—
181C4×D53—41no—
182Dic106—21no—
183Dic106—21no—
184C8×C53—41no—
185C8×C53#12011yescharacteristic
186C8×C53#12111yescharacteristic
187C8×C53#12111yescharacteristic
188C8×C53#12311yescharacteristic
189#88322—21no—
190#88322—21no—
191#88322—41no—
192#12978—531nomaximal, Sylow
193C22×C53—21no—
194C22×C53—21no—
195C22×C53C2×C22⋊C811yescharacteristic
196C22×C53#43511yescharacteristic
197C22×C53#43511yescharacteristic
198C2×D53—21no—
199C2×D53—21no—
200C2×D53—21no—
201C2×D53—21no—
202C2×D53—21no—
203C2×D53—42no—
204C2×D53—42no—
205C2×D53—41no—
206C2×D53—41no—
207C2×D53—41no—
208C2×D53#35012yescomplemented
209C4×C53—41no—
210C4×C53—41no—
211C4×C53#38611yescharacteristic
212C4×C53#40811yescharacteristic
213C4×C53C8×D411yescharacteristic
214C4×C53C8×D411yescharacteristic
215Dic53—21no—
216Dic53—21no—
217Dic53—41no—
218C22×M32—531no—
219#2929—531no—
220C2×#350—531no—
221C2×#350—531no—
222C2×C22⋊C16—531no—
223#1379—531no—
224#1379D5311yescharacteristic, complemented
225C2×C53—21no—
226C2×C53—21no—
227C2×C53#186911yescharacteristic
228C2×C53C2×#35011yescharacteristic
229C2×C53#211711yescharacteristic
230D53—22no—
231D53—41no—
232D53—81no—
233C2×#131—531no—
234C23×C8—531no—
235#525—531no—
236C2×M32—531no—
237C2×M32—1061no—
238C2×M32—1062no—
239C2×M32—1062no—
240C2×M32C2×D5311yescharacteristic
241C22×C16—531no—
242C22×C16—1061no—
243C22×C16C2×D5311yescharacteristic
244#435—1061no—
245#435—1061no—
246C8×D4—1061no—
247C8×D4—1061no—
248#424—531no—
249#408—531no—
250#407—531no—
251#405C2×D5311yescharacteristic
252#350—1062no—
253#350—1062no—
254C22⋊C16—1061no—
255C22⋊C16—1061no—
256C53#1297811yescharacteristic, complemented, Sylow
257C2×#41—531no—
258C23×C4—531no—
259#131—1061no—
260#131—1061no—
261#131—1061no—
262#131—1061no—
263C2×M16—531no—
264C2×M16—1061no—
265C2×M16C4×D5311yescharacteristic
266C22×C8—531no—
267C22×C8—531no—
268C22×C8—531no—
269C22×C8—531no—
270C22×C8—531no—
271C22×C8—1061no—
272C22×C8—1061no—
273C22×C8—1061no—
274C22×C8—1061no—
275C22×C8—1061no—
276C22×C8C22×D5311yescharacteristic
277#123—1061no—
278C22⋊Q8—531no—
279C22⋊Q8—531no—
280#121—531no—
281#121—531no—
282#120—1061no—
283C4×D4—1061no—
284C4×D4—1061no—
285#117C4×D5311yescharacteristic
286M32—21no—
287M32—532no—
288M32—1064no—
289M32—1061no—
290M32D21212yescomplemented
291C2×C16—21no—
292C2×C16—21no—
293C2×C16—21no—
294C2×C16—21no—
295C2×C16—1064no—
296C2×C16—1061no—
297C2×C16—1061no—
298C2×C16—1061no—
299C2×C16—1061no—
300C4⋊C8—1061no—
301C4⋊C8—1061no—
302C22⋊C8—1061no—
303C22⋊C8—1061no—
304C22⋊C8—1061no—
305C22⋊C8—1061no—
306#97—21no—
307C4×C8—21no—
308C24—531no—
309#41—1061no—
310#41—1061no—
311#41—1061no—
312#41—1061no—
313C2×Q8—531no—
314C2×D4—531no—
315C2×D4—1061no—
316C2×D4—1061no—
317C2×D4—1061no—
318C22×C4—531no—
319C22×C4—531no—
320C22×C4—531no—
321C22×C4—531no—
322C22×C4—531no—
323C22×C4—1061no—
324C22×C4—1061no—
325C22×C4—1061no—
326C22×C4—1061no—
327C22×C4—1061no—
328C22×C4C2×C4×D5311yescharacteristic
329M16—21no—
330M16—21no—
331M16—1061no—
332M16—1061no—
333M16—2121no—
334M16—2121no—
335C2×C8—21no—
336C2×C8—531no—
337C2×C8—531no—
338C2×C8—1061no—
339C2×C8—1061no—
340C2×C8—1061no—
341C2×C8—1061no—
342C2×C8—1061no—
343C2×C8—1061no—
344C2×C8—1061no—
345C2×C8—1061no—
346C2×C8—1061no—
347C2×C8—1061no—
348C2×C8—1061no—
349C2×C8—2121no—
350C2×C8—2121no—
351C2×C8C2×D21211yescharacteristic
352C2×C8#1171994511yescharacteristic
353C2×C8D4×D5311yescharacteristic
354C2×C8D4×D5311yescharacteristic
355C2×C8D4×D5311yescharacteristic
356C2×C8#1171994911yescharacteristic
357C4⋊C4—1061no—
358C4⋊C4—1061no—
359C4⋊C4C8×D5311yescharacteristic
360C4⋊C4C8×D5311yescharacteristic
361C22⋊C4—21no—
362C22⋊C4—1061no—
363C22⋊C4—1061no—
364C22⋊C4—1061no—
365C22⋊C4—1061no—
366C42—21no—
367C16—22no—
368C16—41no—
369C16—1062no—
370C16—2121no—
371C23—531no—
372C23—531no—
373C23—1062no—
374C23—1061no—
375C23—1061no—
376C23—1061no—
377C23—2121no—
378C23M16×D5311yescharacteristic
379Q8—1061no—
380Q8—1061no—
381D4—1061no—
382D4—1061no—
383D4—2122no—
384D4—2122no—
385D4—2121no—
386D4—2121no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—531no—
390C2×C4—531no—
391C2×C4—1061no—
392C2×C4—1061no—
393C2×C4—1061no—
394C2×C4—1061no—
395C2×C4—1061no—
396C2×C4—1061no—
397C2×C4—1061no—
398C2×C4—1061no—
399C2×C4—1061no—
400C2×C4—1061no—
401C2×C4—1061no—
402C2×C4—2121no—
403C2×C4—2121no—
404C2×C4C22⋊C4×D5311yescharacteristic
405C2×C4#1313317911yescharacteristic
406C2×C4C4×D21211yescharacteristic
407C2×C4C2×C8×D5311yescharacteristic
408C2×C4#1313322311yescharacteristic
409C2×C4#1313322511yescharacteristic
410C8—41no—
411C8—1061no—
412C8—1061no—
413C8—2121no—
414C8#1313318711yescharacteristic
415C8#1313319011yescharacteristic
416C8#1313319211yescharacteristic
417C8#1313320211yescharacteristic
418C22—21no—
419C22—21no—
420C22—532no—
421C22—1061no—
422C22—1061no—
423C22—1061no—
424C22—1061no—
425C22—1061no—
426C22—2122no—
427C22—2122no—
428C22—2121no—
429C22—2121no—
430C22—2121no—
431C22C22⋊C8×D5311yescharacteristic
432C22#1681069311yescharacteristic
433C22#1681069611yescharacteristic
434C4—41no—
435C4—41no—
436C4—1061no—
437C4—1061no—
438C4—2121no—
439C4#1681050111yescharacteristic
440C4#1681058811yescharacteristic
441C4#1681068811yescharacteristic
442C4C8×D21211yescharacteristic
443C2—21no—
444C2—21no—
445C2—1062no—
446C2—4241no—
447C2—2121no—
448C2#2027500611yescharacteristic
449C2#350×D5311yescharacteristic
450C2#2027634111yescharacteristic
subgroupG/H
centerC2×C8D4×D53
commutatorC2×C4×C53C22×C8
FrattiniC22×C8C22×D53
FittingC53×#1379C2
socleC22×C53C2×C22⋊C8
prime radical#16811135C4
cosocleC22×C8×C53C23
hypercenter#1379D53
hypocenterC53#12978
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #1379

Complements

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

NH ≅ G/Ntype
1. C2×M32×D53C2semidirect
3. C2×#16810408C2semidirect
4. C2×#16810406C2semidirect
5. C2×#16810402C2semidirect
6. #20272804C2semidirect
7. C53×#1379C2semidirect
58. #13133157D4semidirect
75. M32×C53D4semidirect
208. C2×D53#350semidirect
224. #1379D53semidirect
256. C53#12978semidirect
290. M32D212semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D532
#202834112
C2×#168104082
C2×#168104062
C2×#168104022
#202728042
C53×#13792
#1297853