Finite Group Databasebeta

← #27282083

Subgroups — #27282083

Order 13568.

478 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283350C211yesmaximal, characteristic
2#20279002C211yesmaximal, characteristic
3#20274796C211yesmaximal, characteristic
4#20273045C211yesmaximal, characteristic
5#20272624C211yesmaximal, characteristic
6#20272624C211yesmaximal, characteristic
7C53×#1463C211yesmaximal, characteristic
8C2×#13133176C2211yescharacteristic
9#16810681—22no—
10#16810681—22no—
11#16810646—21no—
12#16810587C2211yescharacteristic
13#16810587C2211yescharacteristic
14M16×Dic53—21no—
15#16810562—21no—
16#16810553—21no—
17#16810504—21no—
18#16810504—21no—
19#16810496C411yescharacteristic
20#16810496C411yescharacteristic
21#16810486C411yescharacteristic
22#16810486C411yescharacteristic
23#16810486C2211yescharacteristic
24#16810391—21no—
25#16810391—21no—
26#16810349—22no—
27C22×C4⋊C4×C53C2211yescharacteristic
28C53×#407C2211yescharacteristic
29C53×#407C2211yescharacteristic
30C53×#324—22no—
31C2×#11719917—21no—
32C2×#11719917—21no—
33#13133176—21no—
34#13133176—21no—
35#13133176—21no—
36#13133176—21no—
37C2×C4⋊Dic53D411yescharacteristic
38C2×C4⋊Dic53D411yescharacteristic
39C2×#11719919—21no—
40C2×#11719919—21no—
41C2×C22⋊Dic53C2×C411yescharacteristic
42C2×C22⋊Dic53C2×C411yescharacteristic
43C2×C22⋊Dic53C2×C411yescharacteristic
44C2×C22⋊Dic53C2×C411yescharacteristic
45C2×C4×Dic53D411yescharacteristic
46C2×C4×Dic53D411yescharacteristic
47#13133146—24no—
48C22⋊#88322—21no—
49C22⋊#88322—21no—
50C22⋊#88322—21no—
51C22⋊#88322D412yes—
52#13133127—22no—
53C8×Dic53—22no—
54#13133124—21no—
55#13133124—21no—
56#13133124—21no—
57#13133124—21no—
58#13133124—21no—
59#13133124—21no—
60#13133124—21no—
61#13133124—21no—
62C23×C4×C53C2×C411yescharacteristic
63C23×C4×C53C2×C411yescharacteristic
64C23×C4×C53C2311yescharacteristic
65C2×M16×C53—21no—
66C2×M16×C53—21no—
67C2×C4⋊C4×C53—21no—
68C2×C4⋊C4×C53—21no—
69C2×C4⋊C4×C53—21no—
70C2×C4⋊C4×C53—21no—
71C2×C4⋊C4×C53—21no—
72C2×C4⋊C4×C53—21no—
73C22⋊C8×C53—21no—
74C22⋊C8×C53—21no—
75C22⋊C8×C53—21no—
76C22⋊C8×C53D412yes—
77C24×C53C22×C411yescharacteristic
78C22×C4×C53—21no—
79C22×C4×C53—21no—
80C22×C4×C53—21no—
81C22×C4×C53—21no—
82C22×C4×C53—21no—
83C22×C4×C53—21no—
84C22×C4×C53—42no—
85C22×C4×C53—41no—
86C22×C4×C53—41no—
87C22×C4×C53—41no—
88C22×C4×C53—41no—
89C22×C4×C53C2×D411yescharacteristic
90C22×C4×C53C2×D411yescharacteristic
91C22×C4×C53C2×D411yescharacteristic
92C22×C4×C53C2×D411yescharacteristic
93C22×C4×C53#4111yescharacteristic
94C22×C4×C53#4111yescharacteristic
95C22×Dic53—21no—
96C22×Dic53—21no—
97C22×Dic53C22⋊C411yescharacteristic
98C22×Dic53C22⋊C411yescharacteristic
99C22×Dic53C22⋊C411yescharacteristic
100C22×Dic53C22⋊C411yescharacteristic
101M16×C53—41no—
102M16×C53—41no—
103M16×C53—41no—
104M16×C53—41no—
105C2×C8×C53—22no—
106C2×C8×C53—41no—
107C4⋊C4×C53—41no—
108C4⋊C4×C53—41no—
109C4⋊C4×C53—41no—
110C4⋊C4×C53—41no—
111C22⋊Dic53—21no—
112C22⋊Dic53—21no—
113C22⋊Dic53—21no—
114C22⋊Dic53—21no—
115C22⋊Dic53—41no—
116C22⋊Dic53—41no—
117C4⋊Dic53—21no—
118C4⋊Dic53—21no—
119C4⋊Dic53—21no—
120C4⋊Dic53—21no—
121#11719919—42no—
122#11719919—42no—
123C4×Dic53—21no—
124C4×Dic53—21no—
125C4×Dic53—21no—
126C4×Dic53—21no—
127#11719917—41no—
128#11719917—41no—
129#11719917—41no—
130#11719917—41no—
131C2×#88322—22no—
132C2×#88322—41no—
133C23×C53—21no—
134C23×C53—21no—
135C23×C53—41no—
136C23×C53—41no—
137C23×C53C2×C22⋊C411yescharacteristic
138C23×C53C4×D411yescharacteristic
139C23×C53C4×D411yescharacteristic
140C2×C4×C53—21no—
141C2×C4×C53—21no—
142C2×C4×C53—21no—
143C2×C4×C53—21no—
144C2×C4×C53—22no—
145C2×C4×C53—22no—
146C2×C4×C53—22no—
147C2×C4×C53—41no—
148C2×C4×C53—41no—
149C2×C4×C53—41no—
150C2×C4×C53—41no—
151C2×C4×C53—41no—
152C2×C4×C53—41no—
153C2×C4×C53—41no—
154C2×C4×C53—41no—
155C2×C4×C53—41no—
156C2×C4×C53—41no—
157C2×C4×C53—41no—
158C2×C4×C53—81no—
159C2×C4×C53—81no—
160C2×C4×C53#12011yescharacteristic
161C2×C4×C53#12111yescharacteristic
162C2×C4×C53#12111yescharacteristic
163C2×C4×C53#12311yescharacteristic
164C2×Dic53—21no—
165C2×Dic53—21no—
166C2×Dic53—21no—
167C2×Dic53—21no—
168C2×Dic53—41no—
169C2×Dic53—41no—
170C2×Dic53—41no—
171C2×Dic53—41no—
172C2×Dic53—41no—
173C2×Dic53—41no—
174C2×Dic53—41no—
175C2×Dic53—41no—
176C2×Dic53—41no—
177C2×Dic53—41no—
178C8×C53—42no—
179C8×C53—81no—
180#88322—42no—
181#88322—81no—
182#9514—531nomaximal, Sylow
183C22×C53—21no—
184C22×C53—21no—
185C22×C53—21no—
186C22×C53—21no—
187C22×C53—21no—
188C22×C53—21no—
189C22×C53—21no—
190C22×C53—21no—
191C22×C53—42no—
192C22×C53—42no—
193C22×C53#38611yescharacteristic
194C22×C53#41011yescharacteristic
195C22×C53#41011yescharacteristic
196C4×C53—21no—
197C4×C53—21no—
198C4×C53—21no—
199C4×C53—21no—
200C4×C53—42no—
201C4×C53—81no—
202Dic53—41no—
203Dic53—41no—
204Dic53—41no—
205Dic53—41no—
206Dic53—81no—
207Dic53—81no—
208#2921—531no—
209#2484—531no—
210#1822—531no—
211#1463—531no—
212#1463D5311yescharacteristic
213#1306—531no—
214#1306—531no—
215C2×C53—21no—
216C2×C53—21no—
217C2×C53—41no—
218C2×C53—41no—
219C2×C53#189111yescharacteristic
220C2×C53#189911yescharacteristic
221C2×C53#191511yescharacteristic
222C2×#117—531no—
223C22×C4⋊C4C2×D5311yescharacteristic
224#433—1062no—
225#433—1062no—
226#423—1061no—
227#407—531no—
228#407—531no—
229#407C2×D5311yescharacteristic
230#407C2×D5311yescharacteristic
231C4×M16—1061no—
232#400—1061no—
233#398—1061no—
234#387—1061no—
235#387—1061no—
236#385—531no—
237#385—531no—
238#381—531no—
239#381—531no—
240#381—531no—
241#343—1061no—
242#343—1061no—
243#324—22no—
244#324—1062no—
245C53#951411yescharacteristic, complemented, Sylow
246C23×C4C4×D5311yescharacteristic
247C23×C4C4×D5311yescharacteristic
248C23×C4C22×D5311yescharacteristic
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—1061no—
252C2×M16—1061no—
253#117—1061no—
254#117—1061no—
255#117—1061no—
256#117—1061no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—531no—
264C2×C4⋊C4—531no—
265C2×C4⋊C4—1061no—
266C2×C4⋊C4—1061no—
267C2×C22⋊C4—531no—
268C2×C22⋊C4—531no—
269C2×C22⋊C4—531no—
270C2×C22⋊C4—531no—
271C2×C42—531no—
272C2×C42—531no—
273C4⋊C8—1064no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—532no—
278C22⋊C8—1061no—
279C22⋊C8—1061no—
280C22⋊C8—1061no—
281C22⋊C8C22⋊D5312yes—
282#97—1062no—
283C4×C8—1062no—
284#95—1061no—
285#95—1061no—
286#95—1061no—
287#95—1061no—
288#95—1061no—
289#95—1061no—
290#95—1061no—
291#95—1061no—
292C24C2×C4×D5311yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—42no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—531no—
305C22×C4—531no—
306C22×C4—531no—
307C22×C4—531no—
308C22×C4—1061no—
309C22×C4—1061no—
310C22×C4#1171994511yescharacteristic
311C22×C4D4×D5311yescharacteristic
312C22×C4D4×D5311yescharacteristic
313C22×C4D4×D5311yescharacteristic
314C22×C4#1171994711yescharacteristic
315C22×C4C2×C22⋊D5311yescharacteristic
316M16—41no—
317M16—41no—
318M16—41no—
319M16—41no—
320M16—2121no—
321M16—2121no—
322M16—2121no—
323M16—2121no—
324C2×C8—22no—
325C2×C8—41no—
326C2×C8—1062no—
327C2×C8—2121no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—1061no—
333C4⋊C4—1061no—
334C4⋊C4—1061no—
335C4⋊C4—1061no—
336C4⋊C4—2122no—
337C4⋊C4—2122no—
338C22⋊C4—1061no—
339C22⋊C4—1061no—
340C22⋊C4—1061no—
341C22⋊C4—1061no—
342C22⋊C4—2121no—
343C22⋊C4—2121no—
344C42—1061no—
345C42—1061no—
346C42—1061no—
347C42—1061no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23C22⋊C4×D5311yescharacteristic
353C23#1313317711yescharacteristic
354C23C4×C22⋊D5311yescharacteristic
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—1061no—
376C2×C4—1061no—
377C2×C4—1061no—
378C2×C4—1061no—
379C2×C4—2121no—
380C2×C4—2121no—
381C2×C4—2121no—
382C2×C4—2121no—
383C2×C4—2121no—
384C2×C4—2121no—
385C2×C4—2121no—
386C2×C4—2121no—
387C2×C4—2121no—
388C2×C4—2121no—
389C2×C4#1313318511yescharacteristic
390C2×C4#1313318811yescharacteristic
391C2×C4#1313319011yescharacteristic
392C2×C4#1313319911yescharacteristic
393C8—42no—
394C8—81no—
395C8—4241no—
396C8—2122no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—42no—
406C22—42no—
407C22#1681049911yescharacteristic
408C22#1681059511yescharacteristic
409C22#1681059511yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—42no—
415C4—81no—
416C4—4241no—
417C4—4241no—
418C4—2121no—
419C4—2121no—
420C4—2121no—
421C4—2121no—
422C2—21no—
423C2—21no—
424C2—41no—
425C2—41no—
426C2#2027513011yescharacteristic
427C2#2027517011yescharacteristic
428C2#2027526411yescharacteristic
subgroupG/H
centerC22#16810499
commutator, prime radicalC24×C53C22×C4
FrattiniC23×C4C22×D53
FittingC53×#1463C2
socleC22×C53#386
cosocleC23×C4×C53C23
hypercenter#1463D53
hypocenterC53#9514
LCSG ▷ C24×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
245. C53#9514semidirect

Maximal subgroups

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

subgroupindex
#202833502
#202790022
#202747962
#202730452
#202726242
C53×#14632
#951453