Finite Group Databasebeta

← #27277459

Subgroups — #27277459

Order 13568.

496 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20277111C211yesmaximal, characteristic
2#20274692C211yesmaximal, characteristic
3C4×#13133129C211yesmaximal, characteristic
4#20272556C211yesmaximal, characteristic, complemented
5#20272555C211yesmaximal, characteristic, complemented
6#20272554C211yesmaximal, characteristic, complemented
7C53×#1279C211yesmaximal, characteristic, complemented
8C2×C42×D53C2211yescharacteristic
9C2×C4⋊#88322C2211yescharacteristic
10C2×#13133129—21no—
11C2×#13133129—21no—
12C2×C4×#88322C2211yescharacteristic
13#16810490—21no—
14#16810488C411yescharacteristic
15#16810488C411yescharacteristic
16#16810485—21no—
17#16810480C411yescharacteristic
18#16810480C411yescharacteristic
19C4×C4⋊Dic53C2211yescharacteristic
20C4×#11719921—21no—
21#16810469—21no—
22#16810377—21no—
23#16810377—21no—
24C2×C4⋊C8×C53C2211yescharacteristic
25C2×C4×C8×C53C2211yescharacteristic
26C4×C4⋊C4×C53C2211yescharacteristic
27C22×C4×D53C2×C411yescharacteristic
28C22×C4×D53D411yescharacteristic
29C22×C4×D53D411yescharacteristic
30C22×#88322—21no—
31C22×#88322—21no—
32C2×C4⋊Dic53C2×C411yescharacteristic
33C2×C4⋊Dic53C2×C411yescharacteristic
34C2×#11719921—21no—
35C2×#11719921—21no—
36C2×C4×Dic53—21no—
37C2×C4×Dic53C2×C411yescharacteristic
38C2×C4×Dic53D411yescharacteristic
39C2×C4×Dic53D411yescharacteristic
40C42×D53—21no—
41C42×D53—21no—
42C42×D53—21no—
43C42×D53—21no—
44C4⋊#88322—21no—
45C4⋊#88322—21no—
46#13133129—24no—
47#13133129—42no—
48C4×#88322—21no—
49C4×#88322—21no—
50#13133124—21no—
51#13133124—21no—
52#13133124—21no—
53#13133124—21no—
54#13133124—21no—
55#13133124—21no—
56#13133124—21no—
57C22×C8×C53—21no—
58C22×C8×C53—21no—
59C2×C4⋊C4×C53C2×C411yescharacteristic
60C2×C4⋊C4×C53C2×C411yescharacteristic
61C2×C42×C53—21no—
62C2×C42×C53C2311yescharacteristic
63C4⋊C8×C53—21no—
64C4⋊C8×C53—21no—
65C4×C8×C53—21no—
66C4×C8×C53—21no—
67#95×C53—21no—
68C23×D53C22⋊C411yescharacteristic
69C22×C4×C53—21no—
70C22×C4×C53—21no—
71C22×C4×C53C22×C411yescharacteristic
72C22×C4×C53C2×D411yescharacteristic
73C22×C4×C53C2×D411yescharacteristic
74C22×Dic53—21no—
75C22×Dic53—21no—
76C22×Dic53C22⋊C411yescharacteristic
77C22×Dic53C22⋊C411yescharacteristic
78C22×Dic53C22⋊C411yescharacteristic
79C2×C4×D53—22no—
80C2×C4×D53—21no—
81C2×C4×D53—21no—
82C2×C4×D53—21no—
83C2×C4×D53—21no—
84C2×C4×D53—21no—
85C2×C4×D53—21no—
86C2×C4×D53—21no—
87C2×C4×D53—21no—
88C2×C4×D53—21no—
89C2×C4×D53—21no—
90C2×C4×D53—21no—
91C2×C4×D53—21no—
92C2×C4×D53—21no—
93C2×C4×D53—21no—
94C2×C4×D53—41no—
95C2×C8×C53—22no—
96C2×C8×C53—41no—
97C2×C8×C53—41no—
98C2×C8×C53—41no—
99C2×C8×C53—41no—
100C2×C8×C53—41no—
101C4⋊C4×C53—21no—
102C4⋊C4×C53—21no—
103C4⋊C4×C53—21no—
104C4⋊C4×C53—21no—
105C42×C53—41no—
106C42×C53—41no—
107C42×C53#4111yescharacteristic
108C42×C53#4111yescharacteristic
109C42×C53#4111yescharacteristic
110C42×C53#4111yescharacteristic
111#11719921—42no—
112#11719921—42no—
113C4⋊Dic53—21no—
114C4⋊Dic53—21no—
115C4⋊Dic53—21no—
116C4⋊Dic53—21no—
117C4×Dic53—21no—
118C4×Dic53—21no—
119C4×Dic53—21no—
120C4×Dic53—21no—
121C4×Dic53—21no—
122C4×Dic53—21no—
123C4×Dic53—41no—
124C4×Dic53—41no—
125C2×#88322—22no—
126C2×#88322—41no—
127C2×#88322—41no—
128C2×#88322—41no—
129C2×#88322—41no—
130C2×#88322—41no—
131C23×C53C2×C22⋊C411yescharacteristic
132C22×D53—21no—
133C22×D53—21no—
134C22×D53—21no—
135C22×D53—21no—
136C22×D53—21no—
137C22×D53—21no—
138C22×D53#10412yes—
139C2×C4×C53—21no—
140C2×C4×C53—21no—
141C2×C4×C53—41no—
142C2×C4×C53—41no—
143C2×C4×C53—41no—
144C2×C4×C53—41no—
145C2×C4×C53—41no—
146C2×C4×C53—41no—
147C2×C4×C53#11711yescharacteristic
148C2×C4×C53#11711yescharacteristic
149C2×C4×C53#12311yescharacteristic
150C2×C4×C53#12311yescharacteristic
151C2×C4×C53#12311yescharacteristic
152C2×C4×C53#12311yescharacteristic
153C2×C4×C53#13111yescharacteristic
154C2×C4×C53#13111yescharacteristic
155C2×C4×C53#13111yescharacteristic
156C2×C4×C53#13111yescharacteristic
157C2×C4×C53#13511yescharacteristic
158C2×C4×C53#13511yescharacteristic
159C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C53#13711yescharacteristic
161C2×Dic53—21no—
162C2×Dic53—21no—
163C2×Dic53—21no—
164C2×Dic53—21no—
165C2×Dic53—21no—
166C2×Dic53—21no—
167C2×Dic53—21no—
168C2×Dic53—21no—
169C2×Dic53—21no—
170C2×Dic53—41no—
171C2×Dic53—41no—
172C2×Dic53—41no—
173C2×Dic53—41no—
174C2×Dic53—41no—
175C2×Dic53—41no—
176C4×D53—42no—
177C4×D53—42no—
178C4×D53—41no—
179C4×D53—41no—
180C4×D53—41no—
181C4×D53—41no—
182C4×D53—41no—
183C4×D53—41no—
184C4×D53—41no—
185C4×D53—41no—
186C8×C53—42no—
187C8×C53—81no—
188#88322—42no—
189#88322—81no—
190#8711—531nomaximal, Sylow
191C22×C53#38111yescharacteristic
192C22×C53#40811yescharacteristic
193C22×C53#40811yescharacteristic
194C22×C53#41611yescharacteristic
195C22×C53#41711yescharacteristic
196C22×C53C2×#10411yescharacteristic
197C22×C53#42111yescharacteristic
198C2×D53—22no—
199C2×D53—22no—
200C2×D53—22no—
201C2×D53—41no—
202C2×D53—41no—
203C2×D53—41no—
204C2×D53—41no—
205C4×C53—21no—
206C4×C53—21no—
207C4×C53—81no—
208C4×C53—81no—
209C4×C53#43311yescharacteristic
210C4×C53#43311yescharacteristic
211C4×C53#43311yescharacteristic
212C4×C53#43311yescharacteristic
213C4×C53#48211yescharacteristic
214C4×C53#48211yescharacteristic
215C4×C53#48511yescharacteristic
216C4×C53#48511yescharacteristic
217Dic53—41no—
218Dic53—41no—
219Dic53—41no—
220Dic53—81no—
221Dic53—81no—
222#2283—531no—
223#1797—531no—
224C4×C22⋊C8—531no—
225#1279—531no—
226#1279—531no—
227#1279—531no—
228#1279D5311yescharacteristic, complemented
229C2×C53#148211yescharacteristic
230C2×C53#148311yescharacteristic
231C2×C53#149411yescharacteristic
232C2×C53#149511yescharacteristic
233C2×C53#181811yescharacteristic
234C2×C53#182511yescharacteristic
235C2×C53#182611yescharacteristic
236D53—42no—
237C22×C42—531no—
238C2×C4⋊C8—531no—
239C2×C4⋊C8C2×D5311yescharacteristic
240C2×C22⋊C8—1061no—
241C2×C22⋊C8—1061no—
242C2×C4×C8—531no—
243C2×C4×C8C2×D5311yescharacteristic
244#383—1061no—
245#382—531no—
246#382—531no—
247#381—1061no—
248#380—531no—
249#380—531no—
250C4×C4⋊C4—531no—
251C4×C4⋊C4C2×D5311yescharacteristic
252C4×C22⋊C4—1061no—
253#376—1061no—
254#336—1061no—
255#336—1061no—
256C53#871111yescharacteristic, complemented, Sylow
257C23×C4—531no—
258C23×C4—531no—
259C23×C4—531no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—1061no—
263C22×C8—1061no—
264C2×C4⋊C4—531no—
265C2×C4⋊C4—531no—
266C2×C4⋊C4C4×D5311yescharacteristic
267C2×C4⋊C4C4×D5311yescharacteristic
268C2×C22⋊C4—1061no—
269C2×C22⋊C4—1061no—
270C2×C42—21no—
271C2×C42—531no—
272C2×C42—531no—
273C2×C42—531no—
274C2×C42—1061no—
275C2×C42—1061no—
276C2×C42—1061no—
277C2×C42—1061no—
278C2×C42—1061no—
279C2×C42C22×D5311yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—1061no—
283C4⋊C8—1061no—
284C22⋊C8—1064no—
285C22⋊C8—2122no—
286C4×C8—21no—
287C4×C8—21no—
288C4×C8—1061no—
289C4×C8—1061no—
290#95—21no—
291#95—1061no—
292#95—1061no—
293#95—1061no—
294#95—1061no—
295#95—1061no—
296#95—1061no—
297#95—1061no—
298C24—531no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—531no—
302C22×C4—531no—
303C22×C4—531no—
304C22×C4—1062no—
305C22×C4—1061no—
306C22×C4—1061no—
307C22×C4—1061no—
308C22×C4—1061no—
309C22×C4—1061no—
310C22×C4—1061no—
311C22×C4—1061no—
312C22×C4—1061no—
313C22×C4—1061no—
314C22×C4—1061no—
315C22×C4—1061no—
316C22×C4—1061no—
317C22×C4—1061no—
318C22×C4—1061no—
319C22×C4—1061no—
320C22×C4—1061no—
321C22×C4—2121no—
322C22×C4C2×C4×D5311yescharacteristic
323C22×C4D4×D5311yescharacteristic
324C22×C4D4×D5311yescharacteristic
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—1062no—
332C2×C8—2121no—
333C2×C8—2121no—
334C2×C8—2121no—
335C2×C8—2121no—
336C2×C8—2121no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—1061no—
342C4⋊C4—1061no—
343C4⋊C4—1061no—
344C4⋊C4—1061no—
345C22⋊C4—2122no—
346C22⋊C4—2122no—
347C42—41no—
348C42—41no—
349C42—1061no—
350C42—1061no—
351C42—1061no—
352C42—1061no—
353C42—1061no—
354C42—1061no—
355C42—2121no—
356C42—2121no—
357C42#1171994511yescharacteristic
358C42#1171994511yescharacteristic
359C42#1171994711yescharacteristic
360C42#1171994911yescharacteristic
361C23—532no—
362C23—1061no—
363C23—1061no—
364C23—1061no—
365C23—1061no—
366C23—1061no—
367C23—1061no—
368C23C22⋊C4×D5311yescharacteristic
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—1061no—
378C2×C4—1061no—
379C2×C4—1061no—
380C2×C4—1061no—
381C2×C4—1061no—
382C2×C4—1061no—
383C2×C4—1061no—
384C2×C4—1061no—
385C2×C4—1061no—
386C2×C4—2122no—
387C2×C4—2122no—
388C2×C4—2121no—
389C2×C4—2121no—
390C2×C4—2121no—
391C2×C4—2121no—
392C2×C4—2121no—
393C2×C4—2121no—
394C2×C4—2121no—
395C2×C4—2121no—
396C2×C4—2121no—
397C2×C4—2121no—
398C2×C4—2121no—
399C2×C4—2121no—
400C2×C4—2121no—
401C2×C4—2121no—
402C2×C4#1313317411yescharacteristic
403C2×C4#1313317511yescharacteristic
404C2×C4#1313319911yescharacteristic
405C2×C4#1313319911yescharacteristic
406C2×C4#1313320211yescharacteristic
407C2×C4#1313320211yescharacteristic
408C2×C4#1313322311yescharacteristic
409C2×C4#1313322311yescharacteristic
410C2×C4#1313322511yescharacteristic
411C2×C4#1313322511yescharacteristic
412C2×C4#1313323611yescharacteristic
413C2×C4#1313323811yescharacteristic
414C2×C4#1313324411yescharacteristic
415C2×C4#1313324911yescharacteristic
416C8—42no—
417C8—81no—
418C8—4241no—
419C8—2122no—
420C22—1062no—
421C22—1062no—
422C22—1062no—
423C22—2121no—
424C22—2121no—
425C22—2121no—
426C22—2121no—
427C22#1681048511yescharacteristic
428C22#1681058811yescharacteristic
429C22#1681058811yescharacteristic
430C22#1681061611yescharacteristic
431C22#1681062311yescharacteristic
432C22#104×D5311yescharacteristic
433C22#1681063811yescharacteristic
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—4241no—
439C4—4241no—
440C4—2121no—
441C4—2121no—
442C4—2121no—
443C4#1681068211yescharacteristic
444C4#1681068311yescharacteristic
445C4#1681068311yescharacteristic
446C4#1681068511yescharacteristic
447C4#1681094511yescharacteristic
448C4#1681094911yescharacteristic
449C4#1681096211yescharacteristic
450C4#1681096611yescharacteristic
451C2—2122no—
452C2#2027312011yescharacteristic
453C2#2027312711yescharacteristic
454C2#2027317211yescharacteristic
455C2#2027317911yescharacteristic
456C2#2027478511yescharacteristic
457C2#2027480811yescharacteristic
458C2#2027481311yescharacteristic
subgroupG/H
centerC22×C4D4×D53
commutatorC22×C4×C53C22×C4
FrattiniC2×C42C22×D53
FittingC53×#1279C2
socleC23×C53C2×C22⋊C4
prime radicalC23×D53C22⋊C4
cosocleC2×C42×C53C23
hypercenter#1279D53
hypocenterC53#8711
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #20272556C2semidirect
5. #20272555C2semidirect
6. #20272554C2semidirect
7. C53×#1279C2semidirect
228. #1279D53semidirect
256. C53#8711semidirect

Maximal subgroups

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

subgroupindex
#202771112
#202746922
C4×#131331292
#202725562
#202725552
#202725542
C53×#12792
#871153