Finite Group Databasebeta

← #27282087

Subgroups — #27282087

Order 13568.

478 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 103 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#20283353C211yesmaximal, characteristic
2#20274798C211yesmaximal, characteristic
3#20273045C212yesmaximal
4#20272623C212yesmaximal
5C53×#2484C211yesmaximal, characteristic
6#16810684—24no—
7#16810647—21no—
8#16810587C2212yes—
9#16810587C2212yes—
10C4×#11719917—21no—
11#16810392—21no—
12#16810392—21no—
13#16810349—24no—
14C2×#117×C53C2211yescharacteristic
15C22×C4⋊C4×C53C2211yescharacteristic
16C53×#400—21no—
17C53×#398—21no—
18C53×#387—21no—
19C53×#387—21no—
20C53×#385C411yescharacteristic
21C53×#385C411yescharacteristic
22C53×#381C411yescharacteristic
23C53×#381C411yescharacteristic
24C53×#381C2211yescharacteristic
25C2×#11719917—22no—
26C2×#11719917—22no—
27C4⋊#88322—24no—
28C22⋊#88322—22no—
29C22⋊#88322—22no—
30C22⋊#88322—22no—
31C22⋊#88322D414yes—
32#13133128—22no—
33C4×#88322—22no—
34C23×C4×C53C2×C411yescharacteristic
35C23×C4×C53C2×C411yescharacteristic
36C23×C4×C53C2311yescharacteristic
37#117×C53—22no—
38#117×C53—22no—
39C2×C4⋊C4×C53—21no—
40C2×C4⋊C4×C53—21no—
41C2×C4⋊C4×C53—22no—
42C2×C4⋊C4×C53—21no—
43C2×C4⋊C4×C53—21no—
44C2×C4⋊C4×C53—22no—
45C2×C4⋊C4×C53D411yescharacteristic
46C2×C4⋊C4×C53D411yescharacteristic
47C2×C22⋊C4×C53C2×C411yescharacteristic
48C2×C22⋊C4×C53C2×C411yescharacteristic
49C2×C22⋊C4×C53C2×C411yescharacteristic
50C2×C22⋊C4×C53C2×C411yescharacteristic
51C2×C42×C53D411yescharacteristic
52C2×C42×C53D411yescharacteristic
53#95×C53—21no—
54#95×C53—21no—
55#95×C53—21no—
56#95×C53—21no—
57#95×C53—21no—
58#95×C53—21no—
59#95×C53—21no—
60#95×C53—21no—
61C24×C53C22×C411yescharacteristic
62C22×C4×C53—21no—
63C22×C4×C53—22no—
64C22×C4×C53—21no—
65C22×C4×C53—21no—
66C22×C4×C53—21no—
67C22×C4×C53—22no—
68C22×C4×C53—42no—
69C22×C4×C53—41no—
70C22×C4×C53—41no—
71C22×C4×C53—41no—
72C22×C4×C53—41no—
73C22×C4×C53C22⋊C411yescharacteristic
74C22×C4×C53C22⋊C411yescharacteristic
75C22×C4×C53C22⋊C411yescharacteristic
76C22×C4×C53C22⋊C411yescharacteristic
77C22×C4×C53C2×D411yescharacteristic
78C22×C4×C53C2×D411yescharacteristic
79C22×C4×C53C2×D412yes—
80C22×C4×C53#4112yes—
81C4⋊C4×C53—22no—
82C4⋊C4×C53—22no—
83C4⋊C4×C53—42no—
84C4⋊C4×C53—42no—
85C4⋊C4×C53—41no—
86C4⋊C4×C53—42no—
87C4⋊C4×C53—41no—
88C22⋊C4×C53—22no—
89C22⋊C4×C53—22no—
90C22⋊C4×C53—41no—
91C22⋊C4×C53—41no—
92C42×C53—21no—
93C42×C53—21no—
94C42×C53—21no—
95C42×C53—21no—
96#11719917—42no—
97#11719917—42no—
98#11719917—42no—
99#11719917—42no—
100C2×#88322—24no—
101C2×#88322—42no—
102C23×C53—21no—
103C23×C53—21no—
104C23×C53—41no—
105C23×C53—41no—
106C23×C53C2×C22⋊C411yescharacteristic
107C23×C53C4×D412yes—
108C2×C4×C53—21no—
109C2×C4×C53—21no—
110C2×C4×C53—21no—
111C2×C4×C53—21no—
112C2×C4×C53—24no—
113C2×C4×C53—22no—
114C2×C4×C53—21no—
115C2×C4×C53—21no—
116C2×C4×C53—21no—
117C2×C4×C53—21no—
118C2×C4×C53—42no—
119C2×C4×C53—42no—
120C2×C4×C53—41no—
121C2×C4×C53—42no—
122C2×C4×C53—41no—
123C2×C4×C53—41no—
124C2×C4×C53—41no—
125C2×C4×C53—41no—
126C2×C4×C53—41no—
127C2×C4×C53—41no—
128C2×C4×C53—41no—
129C2×C4×C53—41no—
130C2×C4×C53—41no—
131C2×C4×C53—41no—
132C2×C4×C53—41no—
133C2×C4×C53—41no—
134C2×C4×C53—41no—
135C2×C4×C53—41no—
136C2×C4×C53—82no—
137C2×C4×C53#12011yescharacteristic
138C2×C4×C53#12112yes—
139C2×C4×C53#12311yescharacteristic
140#88322—44no—
141#88322—82no—
142#9514—531nomaximal, Sylow
143C22×C53—21no—
144C22×C53—21no—
145C22×C53—22no—
146C22×C53—22no—
147C22×C53—22no—
148C22×C53—42no—
149C22×C53—42no—
150C22×C53#38611yescharacteristic
151C22×C53#41011yescharacteristic
152C22×C53#41011yescharacteristic
153C4×C53—21no—
154C4×C53—22no—
155C4×C53—21no—
156C4×C53—42no—
157C4×C53—41no—
158C4×C53—41no—
159C4×C53—41no—
160C4×C53—41no—
161C4×C53—81no—
162C4×C53—81no—
163C4×C53—81no—
164#2921—531no—
165#2484D5311yescharacteristic
166#1822—531no—
167#1463—532no—
168#1306—532no—
169C2×C53—21no—
170C2×C53—21no—
171C2×C53—42no—
172C2×C53#189111yescharacteristic
173C2×C53#189911yescharacteristic
174C2×C53#191511yescharacteristic
175C2×#117C2×D5311yescharacteristic
176C22×C4⋊C4C2×D5311yescharacteristic
177#433—1064no—
178#423—1061no—
179#407—532no—
180#407—532no—
181C4×M16—1061no—
182#400—21no—
183#398—21no—
184#387—21no—
185#387—21no—
186#385Dic5311yescharacteristic
187#385Dic5311yescharacteristic
188#381Dic5311yescharacteristic
189#381Dic5311yescharacteristic
190#381C2×D5311yescharacteristic
191#343—1061no—
192#343—1061no—
193#324—1064no—
194C53#951411yescharacteristic, complemented, Sylow
195C23×C4C2×Dic5311yescharacteristic
196C23×C4C2×Dic5311yescharacteristic
197C23×C4C22×D5311yescharacteristic
198C2×M16—1062no—
199C2×M16—1062no—
200#117—22no—
201#117—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4C22⋊D5311yescharacteristic
209C2×C4⋊C4C22⋊D5311yescharacteristic
210C2×C22⋊C4C2×Dic5311yescharacteristic
211C2×C22⋊C4C2×Dic5311yescharacteristic
212C2×C22⋊C4C2×Dic5311yescharacteristic
213C2×C22⋊C4C2×Dic5311yescharacteristic
214C2×C42C22⋊D5311yescharacteristic
215C2×C42C22⋊D5311yescharacteristic
216C4⋊C8—1064no—
217C22⋊C8—534no—
218C22⋊C8—1062no—
219C22⋊C8—1062no—
220C22⋊C8—1062no—
221#97—1062no—
222C4×C8—1062no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231C24C22×Dic5311yescharacteristic
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—42no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4C22⋊Dic5311yescharacteristic
244C22×C4C22⋊Dic5311yescharacteristic
245C22×C4C22⋊Dic5311yescharacteristic
246C22×C4C22⋊Dic5311yescharacteristic
247C22×C4D4×D5312yes—
248C22×C4#1171994712yes—
249C22×C4C2×C22⋊D5311yescharacteristic
250C22×C4C2×C22⋊D5311yescharacteristic
251M16—2122no—
252M16—2122no—
253M16—2122no—
254M16—2122no—
255C2×C8—1064no—
256C2×C8—2122no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23C2×C22⋊Dic5311yescharacteristic
277C23D4×Dic5312yes—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—82no—
307C2×C4#1313318511yescharacteristic
308C2×C4#1313318912yes—
309C2×C4#1313319811yescharacteristic
310C8—4242no—
311C8—2124no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—42no—
318C22—42no—
319C22#1681050311yescharacteristic
320C22#1681059711yescharacteristic
321C22#1681059711yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—42no—
328C4—41no—
329C4—41no—
330C4—81no—
331C4—81no—
332C4—81no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#2027513411yescharacteristic
337C2#2027517411yescharacteristic
338C2#2027526811yescharacteristic
subgroupG/H
centerC22#16810503
commutator, prime radicalC24×C53C22×C4
FrattiniC23×C4C22×D53
FittingC53×#2484C2
socleC22×C53#386
cosocleC23×C4×C53C23
hypercenter#2484D53
hypocenterC53#9514
LCSG ▷ C24×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
194. C53#9514semidirect

Maximal subgroups

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

subgroupindex
#202833532
#202747982
#202730452
#202726232
C53×#24842
#951453