Finite Group Databasebeta

← #27279308

Subgroups — #27279308

Order 13568.

488 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283854C211yesmaximal, characteristic, complemented
2#20275514C211yesmaximal, characteristic, complemented
3#20273303C211yesmaximal, characteristic, complemented
4#20273158C211yesmaximal, characteristic, complemented
5#20272615C211yesmaximal, characteristic, complemented
6#20272564C211yesmaximal, characteristic, complemented
7C53×#3105C211yesmaximal, characteristic
8#16810754—21no—
9#16810695—21no—
10#16810695—21no—
11D4×#88322—21no—
12#16810684—21no—
13#16810680C2211yescharacteristic
14#16810650—21no—
15C2×C4⋊#88322C2211yescharacteristic
16C2×C22⋊#88322—21no—
17C2×C22⋊#88322—21no—
18C4×#11719917C2211yescharacteristic
19C2×#13133128C2211yescharacteristic
20#16810365—21no—
21#16810363—21no—
22D4⋊#88322—21no—
23D4⋊#88322—21no—
24C53×#529C2211yescharacteristic
25C2×C4×D4×C53C2211yescharacteristic
26C53×#484C411yescharacteristic
27C53×#481C411yescharacteristic
28C53×#478—21no—
29C53×#463—21no—
30C53×#450C411yescharacteristic
31C53×#447C411yescharacteristic
32C4×SD16×C53—21no—
33C4×D8×C53—21no—
34C53×#431C2211yescharacteristic
35C2×#11719917—21no—
36C2×#11719917—21no—
37C22×#88322—21no—
38C22×#88322—21no—
39C22×#88322D411yescharacteristic
40C22×#88322D411yescharacteristic
41C4⋊#88322—21no—
42C4⋊#88322—21no—
43C4⋊#88322—21no—
44C4⋊#88322—21no—
45C4⋊#88322D411yescharacteristic
46C4⋊#88322D411yescharacteristic
47C22⋊#88322—21no—
48C22⋊#88322—21no—
49C22⋊#88322—21no—
50C22⋊#88322—42no—
51C22⋊#88322—42no—
52#13133128—21no—
53#13133128—21no—
54#13133128—21no—
55#13133128—21no—
56#13133128—21no—
57C4×#88322—21no—
58C4×#88322—21no—
59C22×D4×C53C2×C411yescharacteristic
60C23×C4×C53—21no—
61C2×SD16×C53—21no—
62C2×D8×C53—21no—
63#126×C53—21no—
64#125×C53D411yescharacteristic
65#124×C53D411yescharacteristic
66#123×C53—21no—
67C22⋊Q8×C53C2×C411yescharacteristic
68#121×C53C2×C411yescharacteristic
69C4×Q8×C53D411yescharacteristic
70C4×D4×C53—21no—
71C4×D4×C53—21no—
72C4×D4×C53—21no—
73C4×D4×C53—21no—
74C4×D4×C53—21no—
75C4×D4×C53D411yescharacteristic
76#117×C53—21no—
77C2×C4⋊C4×C53C2×C411yescharacteristic
78C2×C22⋊C4×C53—21no—
79C2×C42×C53C2311yescharacteristic
80#107×C53—21no—
81#106×C53—21no—
82C4⋊C8×C53—21no—
83#103×C53—21no—
84#102×C53—21no—
85#102×C53—21no—
86#102×C53—21no—
87C22⋊C8×C53C2×C411yescharacteristic
88C22⋊C8×C53C2×C411yescharacteristic
89C4×C8×C53—21no—
90C24×C53—21no—
91C2×Q8×C53C22⋊C411yescharacteristic
92C2×D4×C53—21no—
93C2×D4×C53—21no—
94C2×D4×C53—21no—
95C2×D4×C53—42no—
96C2×D4×C53C22⋊C411yescharacteristic
97C22×C4×C53—21no—
98C22×C4×C53—21no—
99C22×C4×C53—41no—
100C22×C4×C53—41no—
101C22×C4×C53—41no—
102C22×C4×C53—41no—
103C22×C4×C53—41no—
104C22×C4×C53—41no—
105C22×C4×C53C22×C411yescharacteristic
106C22×C4×C53C2×D411yescharacteristic
107C22×C4×C53#4111yescharacteristic
108SD16×C53—42no—
109D8×C53—42no—
110C2×C8×C53—21no—
111C2×C8×C53—21no—
112C4⋊C4×C53—21no—
113C4⋊C4×C53—21no—
114C4⋊C4×C53—21no—
115C4⋊C4×C53—21no—
116C4⋊C4×C53—21no—
117C4⋊C4×C53—21no—
118C4⋊C4×C53C22⋊C411yescharacteristic
119C4⋊C4×C53C22⋊C411yescharacteristic
120C22⋊C4×C53—21no—
121C22⋊C4×C53—21no—
122C22⋊C4×C53—21no—
123C22⋊C4×C53—21no—
124C22⋊C4×C53—21no—
125C22⋊C4×C53—41no—
126C22⋊C4×C53—41no—
127C42×C53—21no—
128C42×C53C2×D411yescharacteristic
129C42×C53C2×D411yescharacteristic
130C42×C53C2×D411yescharacteristic
131C42×C53#4111yescharacteristic
132#11719917—22no—
133#11719917—41no—
134#11719917—81no—
135C2×#88322—22no—
136C2×#88322—21no—
137C2×#88322—21no—
138C2×#88322—21no—
139C2×#88322—21no—
140C2×#88322—41no—
141C2×#88322—41no—
142C2×#88322—41no—
143C2×#88322—41no—
144C2×#88322—41no—
145C2×#88322—81no—
146C23×C53—22no—
147C23×C53—21no—
148C23×C53—41no—
149C23×C53—41no—
150C23×C53—41no—
151C23×C53—41no—
152C23×C53—41no—
153C23×C53—41no—
154C23×C53C4×D411yescharacteristic
155Q8×C53—41no—
156D4×C53—22no—
157D4×C53—22no—
158D4×C53—41no—
159D4×C53—41no—
160D4×C53—41no—
161D4×C53—41no—
162D4×C53—41no—
163C2×C4×C53—21no—
164C2×C4×C53—21no—
165C2×C4×C53—21no—
166C2×C4×C53—21no—
167C2×C4×C53—21no—
168C2×C4×C53—21no—
169C2×C4×C53—21no—
170C2×C4×C53—41no—
171C2×C4×C53—41no—
172C2×C4×C53—41no—
173C2×C4×C53—41no—
174C2×C4×C53—41no—
175C2×C4×C53—41no—
176C2×C4×C53—81no—
177C2×C4×C53—81no—
178C2×C4×C53—81no—
179C2×C4×C53—81no—
180C2×C4×C53C2×C22⋊C411yescharacteristic
181C2×C4×C53C4×D411yescharacteristic
182C2×C4×C53#12011yescharacteristic
183C2×C4×C53#12111yescharacteristic
184C2×C4×C53#12111yescharacteristic
185C2×C4×C53#12311yescharacteristic
186C8×C53—41no—
187C8×C53—41no—
188#88322—42no—
189#88322—42no—
190#88322—41no—
191#88322—41no—
192#88322—41no—
193#88322—41no—
194#9052—531nomaximal, Sylow
195C22×C53—21no—
196C22×C53—21no—
197C22×C53—42no—
198C22×C53—42no—
199C22×C53—41no—
200C22×C53—41no—
201C22×C53—42no—
202C22×C53—41no—
203C22×C53—81no—
204C22×C53—81no—
205C22×C53—81no—
206C22×C53—81no—
207C22×C53#38611yescharacteristic
208C22×C53#44311yescharacteristic
209C22×C53#44411yescharacteristic
210C4×C53—21no—
211C4×C53—21no—
212C4×C53—21no—
213C4×C53—21no—
214C4×C53—21no—
215C4×C53—41no—
216C4×C53—41no—
217C4×C53—41no—
218C4×C53—81no—
219C4×C53#45311yescharacteristic
220C4×C53#45411yescharacteristic
221#3105D5311yescharacteristic
222#2992—531no—
223#1955—531no—
224#1524—531no—
225#1490—531no—
226#1302—531no—
227#1283—531no—
228C2×C53—21no—
229C2×C53—21no—
230C2×C53—81no—
231C2×C53—82no—
232C2×C53#187611yescharacteristic
233C2×C53#188311yescharacteristic
234C2×C53#189111yescharacteristic
235#529C2×D5311yescharacteristic
236C2×C4×D4C2×D5311yescharacteristic
237#484Dic5311yescharacteristic
238#481Dic5311yescharacteristic
239#478—21no—
240#463—21no—
241#450Dic5311yescharacteristic
242#447Dic5311yescharacteristic
243#446—1061no—
244C4×SD16—21no—
245C4×D8—21no—
246#435—1061no—
247#435—1061no—
248C8×D4—1061no—
249#433—1061no—
250#432—531no—
251#431C2×D5311yescharacteristic
252#424—1061no—
253C2×C4⋊C8—531no—
254C2×C22⋊C8—1061no—
255C2×C22⋊C8—1061no—
256C4×M16—531no—
257C2×#97—531no—
258#330—1061no—
259#329—1061no—
260D4⋊C8—1061no—
261D4⋊C8—1061no—
262C53#905211yescharacteristic, complemented, Sylow
263C22×D4C2×Dic5311yescharacteristic
264C23×C4—21no—
265C2×SD16—21no—
266C2×D8—21no—
267C2×M16—1061no—
268C2×M16—1061no—
269C22×C8—531no—
270C22×C8—531no—
271C22×C8—1061no—
272C22×C8—1061no—
273#126—21no—
274#125C22⋊D5311yescharacteristic
275#124C22⋊D5311yescharacteristic
276#123—21no—
277C22⋊Q8C2×Dic5311yescharacteristic
278#121C2×Dic5311yescharacteristic
279C4×Q8C22⋊D5311yescharacteristic
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4C22⋊D5311yescharacteristic
286#117—21no—
287C2×C4⋊C4C2×Dic5311yescharacteristic
288C2×C22⋊C4—21no—
289C2×C42C22×D5311yescharacteristic
290#107—21no—
291#106—21no—
292C4⋊C8—21no—
293C4⋊C8—531no—
294C4⋊C8—531no—
295C4⋊C8—1061no—
296C4⋊C8—1061no—
297C4⋊C8—1061no—
298C4⋊C8—1061no—
299#103—21no—
300#102—21no—
301#102—21no—
302#102—21no—
303C22⋊C8—1061no—
304C22⋊C8—1061no—
305C22⋊C8—1061no—
306C22⋊C8—2122no—
307C22⋊C8—2122no—
308C22⋊C8C2×Dic5311yescharacteristic
309C22⋊C8C2×Dic5311yescharacteristic
310#97—1061no—
311#97—1061no—
312#97—1061no—
313#97—1061no—
314#97—1061no—
315C4×C8—21no—
316C4×C8—1061no—
317C4×C8—1061no—
318C24—21no—
319C2×Q8C22⋊Dic5311yescharacteristic
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—42no—
324C2×D4C22⋊Dic5311yescharacteristic
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4D4×D5311yescharacteristic
334C22×C4#1171994711yescharacteristic
335C22×C4C22×Dic5311yescharacteristic
336SD16—42no—
337D8—42no—
338M16—1062no—
339M16—4241no—
340M16—2121no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—1062no—
344C2×C8—1061no—
345C2×C8—1061no—
346C2×C8—1061no—
347C2×C8—1061no—
348C2×C8—4241no—
349C2×C8—2121no—
350C2×C8—2121no—
351C2×C8—2121no—
352C2×C8—2121no—
353C2×C8—2121no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4C22⋊Dic5311yescharacteristic
361C4⋊C4C22⋊Dic5311yescharacteristic
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C42—21no—
370C42D4×D5311yescharacteristic
371C42#1171994711yescharacteristic
372C42C2×C22⋊D5311yescharacteristic
373C42C2×C22⋊D5311yescharacteristic
374C23—22no—
375C23—21no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23D4×Dic5311yescharacteristic
383Q8—41no—
384D4—22no—
385D4—22no—
386D4—41no—
387D4—41no—
388D4—41no—
389D4—41no—
390D4—41no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4C2×C22⋊Dic5311yescharacteristic
409C2×C4D4×Dic5311yescharacteristic
410C2×C4#1313318511yescharacteristic
411C2×C4#1313318911yescharacteristic
412C2×C4#1313318911yescharacteristic
413C2×C4#1313319811yescharacteristic
414C8—41no—
415C8—41no—
416C8—2122no—
417C8—2122no—
418C8—2121no—
419C8—2121no—
420C8—2121no—
421C8—2121no—
422C22—21no—
423C22—21no—
424C22—42no—
425C22—42no—
426C22—41no—
427C22—41no—
428C22—42no—
429C22—41no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22#1681050311yescharacteristic
435C22#1681074011yescharacteristic
436C22#1681074511yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—81no—
446C4#1681078911yescharacteristic
447C4#1681079411yescharacteristic
448C2—21no—
449C2—21no—
450C2—82no—
451C2—81no—
452C2#2027504411yescharacteristic
453C2#2027509311yescharacteristic
454C2#2027513411yescharacteristic
subgroupG/H
centerC2×C4#13133185
commutatorC22×C4×C53C22×C4
FrattiniC2×C42C22×D53
FittingC53×#3105C2
socleC22×C53#386
prime radicalC53×#447C4
cosocleC2×C42×C53C23
hypercenter#3105D53
hypocenterC53#9052
LCSG ▷ C22×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3105

Complements

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

NH ≅ G/Ntype
1. #20283854C2semidirect
2. #20275514C2semidirect
3. #20273303C2semidirect
4. #20273158C2semidirect
5. #20272615C2semidirect
6. #20272564C2semidirect
262. C53#9052semidirect

Maximal subgroups

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

subgroupindex
#202838542
#202755142
#202733032
#202731582
#202726152
#202725642
C53×#31052
#905253