Finite Group Databasebeta

← #27284140

Subgroups — #27284140

Order 13568.

572 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810507C211yesmaximal, characteristic
2#20274695C211yesmaximal, characteristic
3#20272557C212yesmaximal
4#20272557C212yesmaximal
5C4×C22⋊C8×C53C211yesmaximal, characteristic
6C22×#11719919C411yescharacteristic
7C22×#11719919C411yescharacteristic
8C2×C4⋊#88322—21no—
9C2×C22⋊#88322C2212yes—
10#16810507—21no—
11#16810507—21no—
12#16810507—21no—
13#16810507—21no—
14C2×#13133124C411yescharacteristic
15C2×#13133124C411yescharacteristic
16C2×#13133124C2211yescharacteristic
17C2×#13133124C2211yescharacteristic
18#16810378—21no—
19C22×C42×C53C2211yescharacteristic
20C2×C22⋊C8×C53C2212yes—
21C2×C4×C8×C53—21no—
22C53×#336—21no—
23C23×Dic53C2×C411yescharacteristic
24C23×Dic53C2×C411yescharacteristic
25C23×Dic53C2×C411yescharacteristic
26C23×Dic53C2×C411yescharacteristic
27C22×#88322—22no—
28C2×#11719919—21no—
29C2×#11719919—21no—
30C2×#11719919—21no—
31C2×#11719919—21no—
32C2×#11719919—22no—
33C2×#11719919—42no—
34C2×#11719919C814yescomplemented
35C4⋊#88322—42no—
36C22⋊#88322—24no—
37#13133124—21no—
38#13133124—21no—
39#13133124—21no—
40#13133124—21no—
41#13133124—21no—
42#13133124—21no—
43#13133124—21no—
44#13133124—21no—
45C23×C4×C53C2×C411yescharacteristic
46C23×C4×C53C2×C411yescharacteristic
47C23×C4×C53C2311yescharacteristic
48C22×C8×C53—22no—
49C2×C42×C53—42no—
50C2×C42×C53D411yescharacteristic
51C2×C42×C53D411yescharacteristic
52C2×C42×C53D411yescharacteristic
53C2×C42×C53D411yescharacteristic
54C22⋊C8×C53—22no—
55C22⋊C8×C53Q814yes—
56C4×C8×C53—42no—
57C24×C53C22×C411yescharacteristic
58C22×C4×C53—22no—
59C22×C4×C53—22no—
60C22×C4×C53—41no—
61C22×C4×C53—41no—
62C22×C4×C53—41no—
63C22×C4×C53—41no—
64C22×C4×C53—41no—
65C22×C4×C53C22⋊C411yescharacteristic
66C22×C4×C53C22⋊C411yescharacteristic
67C22×C4×C53C22⋊C411yescharacteristic
68C22×C4×C53C22⋊C411yescharacteristic
69C22×C4×C53C2×C812yes—
70C22×C4×C53M1612yes—
71C22×C4×C53C2×D411yescharacteristic
72C22×C4×C53C2×D411yescharacteristic
73C22×C4×C53C2×Q812yes—
74C22×C4×C53#4112yes—
75C22×Dic53—21no—
76C22×Dic53—21no—
77C22×Dic53—21no—
78C22×Dic53—21no—
79C22×Dic53—21no—
80C22×Dic53—21no—
81C22×Dic53—22no—
82C22×Dic53—22no—
83C22×Dic53—41no—
84C22×Dic53—41no—
85C22×Dic53—41no—
86C22×Dic53—41no—
87C22×Dic53—41no—
88C22×Dic53—41no—
89C22×Dic53—41no—
90C22×Dic53—41no—
91C22×Dic53C2×C812yes—
92C22×Dic53C2×C812yes—
93C2×C8×C53—24no—
94C2×C8×C53—42no—
95C2×C8×C53—42no—
96C42×C53—22no—
97C42×C53—22no—
98C42×C53—41no—
99C42×C53—41no—
100#11719919—24no—
101#11719919—24no—
102#11719919—42no—
103#11719919—42no—
104C2×#88322—42no—
105C2×#88322—42no—
106C2×#88322—42no—
107C23×C53—21no—
108C23×C53—21no—
109C23×C53—21no—
110C23×C53—21no—
111C23×C53C2×C22⋊C411yescharacteristic
112C23×C53C4×Q812yes—
113C23×C53C22×C811yescharacteristic
114C23×C53C2×M1611yescharacteristic
115C23×C53#13112yes—
116C2×C4×C53—21no—
117C2×C4×C53—21no—
118C2×C4×C53—21no—
119C2×C4×C53—21no—
120C2×C4×C53—21no—
121C2×C4×C53—21no—
122C2×C4×C53—21no—
123C2×C4×C53—21no—
124C2×C4×C53—21no—
125C2×C4×C53—21no—
126C2×C4×C53—21no—
127C2×C4×C53—21no—
128C2×C4×C53—21no—
129C2×C4×C53—42no—
130C2×C4×C53—42no—
131C2×C4×C53—42no—
132C2×C4×C53—42no—
133C2×C4×C53—44no—
134C2×C4×C53C22⋊C812yes—
135C2×C4×C53C22⋊C812yes—
136C2×C4×C53#9912yes—
137C2×C4×C53C22⋊Q812yes—
138C2×C4×C53#12411yescharacteristic
139C2×C4×C53C4⋊Q811yescharacteristic
140C2×Dic53—22no—
141C2×Dic53—22no—
142C2×Dic53—42no—
143C2×Dic53—42no—
144C2×Dic53—41no—
145C2×Dic53—41no—
146C2×Dic53—41no—
147C2×Dic53—41no—
148C2×Dic53—42no—
149C2×Dic53—42no—
150C2×Dic53—41no—
151C2×Dic53—41no—
152C2×Dic53—41no—
153C2×Dic53—41no—
154C2×Dic53—41no—
155C2×Dic53—41no—
156C2×Dic53—82no—
157C2×Dic53—82no—
158C8×C53—44no—
159#88322—82no—
160#9880—531nomaximal, Sylow
161C22×C53—21no—
162C22×C53—21no—
163C22×C53—21no—
164C22×C53—21no—
165C22×C53—22no—
166C22×C53—22no—
167C22×C53—22no—
168C22×C53—22no—
169C22×C53#39111yescharacteristic
170C22×C53C2×C22⋊C811yescharacteristic
171C22×C53#40811yescharacteristic
172C22×C53C2×#9911yescharacteristic
173C22×C53#41011yescharacteristic
174C22×C53#41311yescharacteristic
175C22×C53#41311yescharacteristic
176C22×C53C8×Q812yes—
177C22×C53#44612yes—
178C4×C53—22no—
179C4×C53—22no—
180C4×C53—22no—
181C4×C53—21no—
182C4×C53—22no—
183C4×C53—21no—
184C4×C53—41no—
185Dic53—42no—
186Dic53—42no—
187Dic53—81no—
188Dic53—81no—
189C2×#387—531no—
190#1797—531no—
191C4×C22⋊C8D5311yescharacteristic
192#1280—532no—
193#1280—532no—
194C2×C53—22no—
195C2×C53—22no—
196C2×C53#145811yescharacteristic
197C2×C53#145911yescharacteristic
198C2×C53#146811yescharacteristic
199C2×C53#147311yescharacteristic
200C2×C53#198411yescharacteristic
201C2×C53#199611yescharacteristic
202C2×C53#199811yescharacteristic
203C22×C4⋊C4—531no—
204C22×C4⋊C4—531no—
205C22×C42C2×D5311yescharacteristic
206C2×C4⋊C8—1061no—
207C2×C22⋊C8—532no—
208C2×C22⋊C8C2×D5312yes—
209C2×C4×C8—21no—
210#387—1061no—
211#387—1061no—
212#387—1061no—
213#387—1061no—
214C2×#95—531no—
215C2×#95—531no—
216C2×#95—531no—
217C2×#95—531no—
218#336—21no—
219#336—1061no—
220C53#988011yescharacteristic, complemented, Sylow
221C23×C4—531no—
222C23×C4—531no—
223C23×C4—531no—
224C23×C4—531no—
225C23×C4C4×D5311yescharacteristic
226C23×C4C4×D5311yescharacteristic
227C23×C4C22×D5311yescharacteristic
228C22×C8—22no—
229C22×C8—1062no—
230C2×C4⋊C4—534no—
231C2×C4⋊C4—1062no—
232C2×C4⋊C4—1061no—
233C2×C4⋊C4—1061no—
234C2×C4⋊C4—1061no—
235C2×C4⋊C4—1061no—
236C2×C4⋊C4—2122no—
237C2×C42—42no—
238C2×C42D21211yescharacteristic
239C2×C42D21211yescharacteristic
240C2×C42C22⋊D5311yescharacteristic
241C2×C42C22⋊D5311yescharacteristic
242C4⋊C8—2122no—
243C22⋊C8—22no—
244C22⋊C8—1064no—
245C22⋊C8Dic10614yes—
246C4×C8—42no—
247#95—1061no—
248#95—1061no—
249#95—1061no—
250#95—1061no—
251#95—1061no—
252#95—1061no—
253#95—1061no—
254#95—1061no—
255C24C2×C4×D5311yescharacteristic
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—532no—
264C22×C4—532no—
265C22×C4—1061no—
266C22×C4—1061no—
267C22×C4—1061no—
268C22×C4—1061no—
269C22×C4—1062no—
270C22×C4—1062no—
271C22×C4—1061no—
272C22×C4—1061no—
273C22×C4—2121no—
274C22×C4—2121no—
275C22×C4—2121no—
276C22×C4—2121no—
277C22×C4—2121no—
278C22×C4—2121no—
279C22×C4—2121no—
280C22×C4—2121no—
281C22×C4C8×D5312yes—
282C22×C4#1171991212yes—
283C22×C4#1171992111yescharacteristic
284C22×C4#1171992111yescharacteristic
285C22×C4#1171992111yescharacteristic
286C22×C4#1171992111yescharacteristic
287C22×C4C2×Dic10612yes—
288C22×C4C2×D21211yescharacteristic
289C22×C4#1171994512yes—
290C22×C4C2×C22⋊D5311yescharacteristic
291C2×C8—24no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—2122no—
295C2×C8—2122no—
296C2×C8—2122no—
297C4⋊C4—1064no—
298C4⋊C4—1064no—
299C4⋊C4—2122no—
300C4⋊C4—2122no—
301C42—22no—
302C42—22no—
303C42—41no—
304C42—41no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C2×#1171992111yescharacteristic
310C23C4×Dic10612yes—
311C23C2×C8×D5311yescharacteristic
312C23C2×#1171991211yescharacteristic
313C23#1313322312yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—1062no—
333C2×C4—1062no—
334C2×C4—4242no—
335C2×C4—4242no—
336C2×C4—2121no—
337C2×C4—2121no—
338C2×C4—2121no—
339C2×C4—2121no—
340C2×C4—2121no—
341C2×C4—2121no—
342C2×C4—2122no—
343C2×C4—2122no—
344C2×C4—2121no—
345C2×C4—2121no—
346C2×C4—2121no—
347C2×C4—2121no—
348C2×C4—2122no—
349C2×C4—2122no—
350C2×C4#1313312912yes—
351C2×C4#1313312912yes—
352C2×C4#1313313112yes—
353C2×C4#1313319612yes—
354C2×C4#1313320511yescharacteristic
355C2×C4#1313321711yescharacteristic
356C8—44no—
357C8—4242no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22#1681052911yescharacteristic
367C22C2×#1313312911yescharacteristic
368C22#1681058911yescharacteristic
369C22C2×#1313313111yescharacteristic
370C22#1681059611yescharacteristic
371C22#1681060511yescharacteristic
372C22#1681060511yescharacteristic
373C22C8×Dic10612yes—
374C22#1681075312yes—
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—21no—
380C4—21no—
381C4—41no—
382C4—4241no—
383C4—4241no—
384C4—2122no—
385C4—2122no—
386C2—22no—
387C2—22no—
388C2#2027302711yescharacteristic
389C2#2027303111yescharacteristic
390C2#2027306111yescharacteristic
391C2#2027308211yescharacteristic
392C2#2027565111yescharacteristic
393C2#2027570011yescharacteristic
394C2#2027570811yescharacteristic
subgroupG/H
centerC23C2×#11719921
commutatorC23×C53C22×C8
FrattiniC23×C4C22×D53
FittingC4×C22⋊C8×C53C2
socleC23×C53C2×C22⋊C4
prime radicalC24×C53C22×C4
cosocleC23×C4×C53C23
hypercenterC4×C22⋊C8D53
hypocenterC53#9880
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
34. C2×#11719919C8semidirect
220. C53#9880semidirect

Maximal subgroups

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

subgroupindex
C2×#168105072
#202746952
#202725572
C4×C22⋊C8×C532
#988053