Finite Group Databasebeta

← #27279145

Subgroups — #27279145

Order 13568.

616 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810555C211yesmaximal, characteristic
2#20277317C211yesmaximal, characteristic
3#20274802C211yesmaximal, characteristic
4#20274799C211yesmaximal, characteristic
5C2×#16810348C211yesmaximal, characteristic
6#20272594C211yesmaximal, characteristic
7C53×#1294C211yesmaximal, characteristic
8C22×C4⋊Dic53—21no—
9C22×C4⋊Dic53C2211yescharacteristic
10C22×#11719919C2211yescharacteristic
11C2×C22⋊#88322C2211yescharacteristic
12#16810555—22no—
13#16810555C414yescomplemented
14#16810510—22no—
15#16810504—22no—
16#16810484—21no—
17#16810483C2211yescharacteristic
18C22⋊C4×Dic53—21no—
19C2×#13133124—21no—
20#16810386—22no—
21#16810385—22no—
22#16810348—22no—
23C2×C22⋊C8×C53C2211yescharacteristic
24C53×#380C2211yescharacteristic
25C2×#95×C53C2211yescharacteristic
26C23×Dic53—21no—
27C23×Dic53D411yescharacteristic
28C23×Dic53D411yescharacteristic
29C22×#88322—21no—
30C2×C4⋊Dic53—21no—
31C2×C4⋊Dic53—24no—
32C2×C4⋊Dic53—21no—
33C2×C4⋊Dic53—21no—
34C2×C4⋊Dic53—21no—
35C2×C4⋊Dic53—21no—
36C2×C4⋊Dic53—42no—
37C2×C4⋊Dic53—42no—
38C2×C4⋊Dic53C2×C412yes—
39C2×C4⋊Dic53D412yes—
40C2×#11719919—21no—
41C2×#11719919—21no—
42C2×#11719919—21no—
43C2×#11719919—21no—
44C2×#11719919C2×C412yes—
45C2×#11719919D412yes—
46C2×C22⋊Dic53—21no—
47C2×C4×Dic53—22no—
48C22⋊#88322—21no—
49C22⋊#88322—21no—
50#13133124—22no—
51#13133124—24no—
52#13133124—21no—
53#13133124—24no—
54C23×C4×C53—21no—
55C23×C4×C53C2311yescharacteristic
56C22×C8×C53—21no—
57C2×C4⋊C4×C53D412yes—
58C2×C22⋊C4×C53—21no—
59C22⋊C8×C53—21no—
60C22⋊C8×C53—21no—
61#95×C53—21no—
62#95×C53—21no—
63#95×C53C2×C412yes—
64C24×C53C2×D411yescharacteristic
65C22×C4×C53—24no—
66C22×C4×C53—22no—
67C22×C4×C53—22no—
68C22×C4×C53—42no—
69C22×C4×C53—42no—
70C22×C4×C53—41no—
71C22×C4×C53—41no—
72C22×C4×C53C22×C411yescharacteristic
73C22×C4×C53C2×D411yescharacteristic
74C22×C4×C53C2×D411yescharacteristic
75C22×C4×C53C2×D411yescharacteristic
76C22×C4×C53#4111yescharacteristic
77C22×C4×C53#4111yescharacteristic
78C22×Dic53—21no—
79C22×Dic53—21no—
80C22×Dic53—21no—
81C22×Dic53—21no—
82C22×Dic53—21no—
83C22×Dic53—21no—
84C22×Dic53—21no—
85C22×Dic53—21no—
86C22×Dic53—22no—
87C22×Dic53—22no—
88C22×Dic53—42no—
89C22×Dic53—41no—
90C22×Dic53—41no—
91C22×Dic53—41no—
92C22×Dic53—41no—
93C22×Dic53—41no—
94C22×Dic53—41no—
95C22×Dic53C22⋊C412yes—
96C22×Dic53C22⋊C412yes—
97C2×C8×C53—42no—
98C2×C8×C53—41no—
99C4⋊C4×C53—42no—
100C22⋊C4×C53—41no—
101C22⋊C4×C53—41no—
102C22⋊Dic53—41no—
103C22⋊Dic53—41no—
104C4⋊Dic53—22no—
105C4⋊Dic53—22no—
106C4⋊Dic53—48no—
107C4⋊Dic53—41no—
108C4⋊Dic53—41no—
109C4⋊Dic53—42no—
110#11719919—22no—
111#11719919—22no—
112#11719919—22no—
113#11719919—22no—
114C4×Dic53—82no—
115C2×#88322—42no—
116C2×#88322—41no—
117C23×C53—22no—
118C23×C53—22no—
119C23×C53C2×C22⋊C411yescharacteristic
120C23×C53#12011yescharacteristic
121C23×C53#12311yescharacteristic
122C23×C53#13511yescharacteristic
123C23×C53#13511yescharacteristic
124C23×C53AGL(1,ℤ/8)11yescharacteristic
125C23×C53AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C53—22no—
127C2×C4×C53—22no—
128C2×C4×C53—24no—
129C2×C4×C53—41no—
130C2×C4×C53—41no—
131C2×C4×C53—41no—
132C2×C4×C53—41no—
133C2×C4×C53—44no—
134C2×C4×C53—44no—
135C2×C4×C53—42no—
136C2×C4×C53—42no—
137C2×C4×C53—42no—
138C2×C4×C53—42no—
139C2×C4×C53—42no—
140C2×C4×C53C4×D411yescharacteristic
141C2×C4×C53C4×D411yescharacteristic
142C2×C4×C53#12111yescharacteristic
143C2×C4×C53#12111yescharacteristic
144C2×Dic53—22no—
145C2×Dic53—22no—
146C2×Dic53—22no—
147C2×Dic53—22no—
148C2×Dic53—41no—
149C2×Dic53—41no—
150C2×Dic53—42no—
151C2×Dic53—41no—
152C2×Dic53—41no—
153C2×Dic53—42no—
154C2×Dic53—42no—
155C2×Dic53—42no—
156C2×Dic53—42no—
157C2×Dic53—42no—
158C2×Dic53—42no—
159C2×Dic53—42no—
160C2×Dic53—81no—
161C2×Dic53—81no—
162C2×Dic53—81no—
163C2×Dic53—81no—
164C2×Dic53—81no—
165C8×C53—81no—
166#88322—81no—
167#9026—531nomaximal, Sylow
168C22×C53—22no—
169C22×C53—22no—
170C22×C53—22no—
171C22×C53—22no—
172C22×C53—21no—
173C22×C53—21no—
174C22×C53—21no—
175C22×C53—21no—
176C22×C53#38611yescharacteristic
177C22×C53#41611yescharacteristic
178C22×C53#41811yescharacteristic
179C22×C53#44911yescharacteristic
180C22×C53#44911yescharacteristic
181C22×C53#45612yes—
182C22×C53#45812yes—
183C22×C53#48211yescharacteristic
184C22×C53#48211yescharacteristic
185C4×C53—21no—
186C4×C53—21no—
187C4×C53—21no—
188C4×C53—21no—
189C4×C53—44no—
190C4×C53—82no—
191Dic53—42no—
192Dic53—42no—
193Dic53—82no—
194Dic53—82no—
195C2×#398—531no—
196#2313—531no—
197#1823—531no—
198#1823—531no—
199C2×#324—531no—
200#1294—531no—
201#1294D5311yescharacteristic
202C2×C53—21no—
203C2×C53—21no—
204C2×C53—21no—
205C2×C53—21no—
206C2×C53#160912yes—
207C2×C53#160912yes—
208C2×C53#187511yescharacteristic
209C2×C53#188611yescharacteristic
210C2×C53#189011yescharacteristic
211C22×C4⋊C4—531no—
212C22×C4⋊C4—531no—
213C22×C4⋊C4—1061no—
214C2×C22⋊C8—531no—
215C2×C22⋊C8C2×D5311yescharacteristic
216#398—534no—
217#398—1062no—
218#387—1062no—
219#387—1062no—
220#381—1061no—
221#380—531no—
222#380C2×D5311yescharacteristic
223C4×C22⋊C4—1061no—
224C2×#95—1061no—
225C2×#95C2×D5311yescharacteristic
226#340—1062no—
227#340—1062no—
228#324—1062no—
229C53#902611yescharacteristic, complemented, Sylow
230C23×C4—21no—
231C23×C4—531no—
232C23×C4—531no—
233C23×C4—1061no—
234C23×C4C22×D5311yescharacteristic
235C22×C8—21no—
236C22×C8—1061no—
237C2×C4⋊C4—532no—
238C2×C4⋊C4—532no—
239C2×C4⋊C4—532no—
240C2×C4⋊C4—532no—
241C2×C4⋊C4—1061no—
242C2×C4⋊C4—1061no—
243C2×C4⋊C4—1061no—
244C2×C4⋊C4—1061no—
245C2×C4⋊C4—1061no—
246C2×C4⋊C4—1061no—
247C2×C4⋊C4—1061no—
248C2×C4⋊C4—1061no—
249C2×C4⋊C4—1064no—
250C2×C4⋊C4—1061no—
251C2×C4⋊C4—2122no—
252C2×C4⋊C4—2122no—
253C2×C4⋊C4D21212yes—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—1061no—
256C2×C42—1062no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—1061no—
260C22⋊C8—1061no—
261#95—21no—
262#95—21no—
263#95—1064no—
264#95—1062no—
265#95—1064no—
266#95—1061no—
267#95C4×D5312yes—
268C24D4×D5311yescharacteristic
269C22×C4—24no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—532no—
277C22×C4—532no—
278C22×C4—1061no—
279C22×C4—1061no—
280C22×C4—1061no—
281C22×C4—1061no—
282C22×C4—1061no—
283C22×C4—1061no—
284C22×C4—1061no—
285C22×C4—1061no—
286C22×C4—1062no—
287C22×C4—1062no—
288C22×C4—2121no—
289C22×C4—2121no—
290C22×C4—2121no—
291C22×C4—2121no—
292C22×C4—2121no—
293C22×C4—2121no—
294C22×C4—2122no—
295C22×C4C2×C4×D5311yescharacteristic
296C22×C4C2×D21211yescharacteristic
297C22×C4#1171994511yescharacteristic
298C22×C4D4×D5311yescharacteristic
299C22×C4D4×D5311yescharacteristic
300C22×C4#1171994911yescharacteristic
301C2×C8—42no—
302C2×C8—41no—
303C2×C8—2122no—
304C2×C8—2121no—
305C4⋊C4—42no—
306C4⋊C4—1062no—
307C4⋊C4—1062no—
308C4⋊C4—1062no—
309C4⋊C4—1062no—
310C4⋊C4—1062no—
311C4⋊C4—1062no—
312C4⋊C4—2122no—
313C4⋊C4—2128no—
314C4⋊C4—2121no—
315C4⋊C4—2121no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—2121no—
319C22⋊C4—2121no—
320C42—4242no—
321C23—22no—
322C23—22no—
323C23C22⋊C4×D5311yescharacteristic
324C23#1313318711yescharacteristic
325C23#1313320211yescharacteristic
326C23#1313323811yescharacteristic
327C23#1313324011yescharacteristic
328C23#1313324111yescharacteristic
329C23#1313324411yescharacteristic
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—44no—
338C2×C4—44no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—1062no—
345C2×C4—1062no—
346C2×C4—1062no—
347C2×C4—1062no—
348C2×C4—4241no—
349C2×C4—4241no—
350C2×C4—4241no—
351C2×C4—4241no—
352C2×C4—4241no—
353C2×C4—2122no—
354C2×C4—2122no—
355C2×C4—2122no—
356C2×C4—2122no—
357C2×C4—2122no—
358C2×C4—2122no—
359C2×C4—2121no—
360C2×C4—2121no—
361C2×C4—2122no—
362C2×C4—2121no—
363C2×C4—2121no—
364C2×C4—2122no—
365C2×C4#1313317911yescharacteristic
366C2×C4C4×D21211yescharacteristic
367C2×C4#1313319011yescharacteristic
368C2×C4#1313319211yescharacteristic
369C8—81no—
370C8—4241no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22#1681050111yescharacteristic
380C22#1681061811yescharacteristic
381C22#1681062611yescharacteristic
382C22#1681076911yescharacteristic
383C22#1681077111yescharacteristic
384C22#1681080712yes—
385C22#1681081412yes—
386C22#1681094911yescharacteristic
387C22#1681095011yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—44no—
393C4—82no—
394C4—4242no—
395C4—4242no—
396C4—2122no—
397C4—2122no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2#2027371312yes—
403C2#2027371512yes—
404C2#2027503611yescharacteristic
405C2#2027510711yescharacteristic
406C2#2027512711yescharacteristic
subgroupG/H
centerC23#13133187
commutatorC22×C4×C53C22×C4
FrattiniC23×C4C22×D53
FittingC53×#1294C2
socleC23×C53#120
prime radicalC24×C53C2×D4
cosocleC23×C4×C53C23
hypercenter#1294D53
hypocenterC53#9026
LCSG ▷ C22×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
13. #16810555C4semidirect
229. C53#9026semidirect

Maximal subgroups

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

subgroupindex
C2×#168105552
#202773172
#202748022
#202747992
C2×#168103482
#202725942
C53×#12942
#902653