Finite Group Databasebeta

← #28303295

Subgroups — #28303295

Order 13568.

642 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20290606C212yesmaximal
2#20289553C212yesmaximal
3#20289553C212yesmaximal
4C2×C4×#11719919C211yesmaximal, characteristic
5C2×C22⋊#88324C2214yes—
6#16811489—22no—
7#16811489—22no—
8C22×#11719919C411yescharacteristic
9C22×#11719919C411yescharacteristic
10C22×C4×Dic53C411yescharacteristic
11C22×C4×Dic53C2211yescharacteristic
12C4×#11719919—22no—
13C4×#11719919—22no—
14C2×#13133124C2211yescharacteristic
15C2×#13133124C2211yescharacteristic
16C22×C42×C53C411yescharacteristic
17C22×#88324—24no—
18C22⋊#88324—24no—
19C22⋊#88324—24no—
20C23×Dic53C2×C411yescharacteristic
21C23×Dic53C2×C411yescharacteristic
22C23×Dic53C2×C411yescharacteristic
23C23×Dic53C2311yescharacteristic
24C2×#11719919—22no—
25C2×#11719919—22no—
26C2×#11719919—22no—
27C2×#11719919—22no—
28C2×#11719919—22no—
29C2×#11719919C814yescomplemented
30C2×C4×Dic53—21no—
31C2×C4×Dic53—21no—
32C2×C4×Dic53—22no—
33C2×C4×Dic53—22no—
34C2×C4×Dic53—42no—
35C2×C4×Dic53D412yes—
36C2×C4×Dic53D412yes—
37#13133124—22no—
38#13133124—22no—
39C23×C4×C53C2×C411yescharacteristic
40C23×C4×C53C2×C411yescharacteristic
41C23×C4×C53C2×C411yescharacteristic
42C2×C42×C53—21no—
43C2×C42×C53—21no—
44C2×C42×C53—42no—
45C24×C53C22×C411yescharacteristic
46C22×C4×C53—21no—
47C22×C4×C53—21no—
48C22×C4×C53—22no—
49C22×C4×C53—22no—
50C22×C4×C53—21no—
51C22×C4×C53—21no—
52C22×C4×C53—21no—
53C22×C4×C53—21no—
54C22×C4×C53—41no—
55C22×C4×C53—41no—
56C22×C4×C53—41no—
57C22×C4×C53—41no—
58C22×C4×C53C22⋊C411yescharacteristic
59C22×C4×C53C22⋊C411yescharacteristic
60C22×C4×C53C2×C812yes—
61C22×C4×C53M1612yes—
62C22×Dic53—21no—
63C22×Dic53—21no—
64C22×Dic53—21no—
65C22×Dic53—21no—
66C22×Dic53—21no—
67C22×Dic53—21no—
68C22×Dic53—21no—
69C22×Dic53—21no—
70C22×Dic53—41no—
71C22×Dic53—41no—
72C22×Dic53—41no—
73C22×Dic53—41no—
74C22×Dic53—41no—
75C22×Dic53—41no—
76C22×Dic53C22⋊C412yes—
77C22×Dic53C2×C812yes—
78C22×Dic53C2×C812yes—
79C22×Dic53M1612yes—
80C22×Dic53M1612yes—
81C22×Dic53C2×D412yes—
82C22×Dic53#4112yes—
83C22×Dic53#4112yes—
84C2×#88324—44no—
85C2×#88324—44no—
86C2×#88324—44no—
87C42×C53—42no—
88C42×C53—42no—
89#11719919—28no—
90#11719919—28no—
91C4×Dic53—24no—
92C4×Dic53—24no—
93C4×Dic53—42no—
94C4×Dic53—42no—
95C23×C53—21no—
96C23×C53—21no—
97C23×C53—21no—
98C23×C53—21no—
99C23×C53C2×C22⋊C411yescharacteristic
100C23×C53#11711yescharacteristic
101C23×C53#11711yescharacteristic
102C23×C53C22×C811yescharacteristic
103C23×C53C2×M1611yescharacteristic
104C23×C53C2×M1611yescharacteristic
105C23×C53C2×M1611yescharacteristic
106C2×C4×C53—24no—
107C2×C4×C53—24no—
108C2×C4×C53—21no—
109C2×C4×C53—21no—
110C2×C4×C53—21no—
111C2×C4×C53—21no—
112C2×C4×C53—22no—
113C2×C4×C53—22no—
114C2×C4×C53—42no—
115C2×C4×C53—42no—
116C2×C4×C53—41no—
117C2×C4×C53—41no—
118C2×C4×C53—41no—
119C2×C4×C53—41no—
120C2×C4×C53—42no—
121C2×C4×C53—42no—
122C2×C4×C53#10012yes—
123C2×C4×C53#10112yes—
124C2×Dic53—22no—
125C2×Dic53—22no—
126C2×Dic53—22no—
127C2×Dic53—22no—
128C2×Dic53—22no—
129C2×Dic53—22no—
130C2×Dic53—22no—
131C2×Dic53—22no—
132C2×Dic53—22no—
133C2×Dic53—22no—
134C2×Dic53—42no—
135C2×Dic53—42no—
136C2×Dic53—42no—
137C2×Dic53—42no—
138C2×Dic53—41no—
139C2×Dic53—41no—
140C2×Dic53—41no—
141C2×Dic53—41no—
142C2×Dic53—42no—
143C2×Dic53—42no—
144C2×Dic53C22⋊C814yes—
145C2×Dic53#12314yes—
146#88324—84no—
147#8701—531nomaximal, Sylow
148C22×C53—21no—
149C22×C53—21no—
150C22×C53—21no—
151C22×C53—21no—
152C22×C53—21no—
153C22×C53—21no—
154C22×C53—21no—
155C22×C53—21no—
156C22×C53—21no—
157C22×C53—21no—
158C22×C53—21no—
159C22×C53—21no—
160C22×C53#38111yescharacteristic
161C22×C53C2×C22⋊C811yescharacteristic
162C22×C53#40711yescharacteristic
163C22×C53#41011yescharacteristic
164C22×C53#41011yescharacteristic
165C22×C53C2×#10011yescharacteristic
166C22×C53C2×#10111yescharacteristic
167C22×C53#43111yescharacteristic
168C22×C53#43111yescharacteristic
169C22×C53#43211yescharacteristic
170C22×C53#43211yescharacteristic
171C4×C53—22no—
172C4×C53—22no—
173C4×C53—42no—
174C4×C53—42no—
175Dic53—24no—
176Dic53—24no—
177Dic53—42no—
178Dic53—42no—
179C2×C4×C4⋊C4—531no—
180#1817—532no—
181#1280—532no—
182#1280—532no—
183C2×C53—21no—
184C2×C53—21no—
185C2×C53—21no—
186C2×C53—21no—
187C2×C53#146011yescharacteristic
188C2×C53#146111yescharacteristic
189C2×C53#146611yescharacteristic
190C2×C53#146711yescharacteristic
191C2×C53#181711yescharacteristic
192C2×C53#182011yescharacteristic
193C2×C53#182111yescharacteristic
194C22×C4⋊C4—531no—
195C22×C4⋊C4—531no—
196C22×C42—531no—
197C22×C42—531no—
198C22×C42#615711yescharacteristic
199C2×C22⋊C8—534no—
200C4×C4⋊C4—1062no—
201C4×C4⋊C4—1062no—
202C2×#95—531no—
203C2×#95—531no—
204#336—1062no—
205#336—1062no—
206C53#870111yescharacteristic, complemented, Sylow
207C23×C4—531no—
208C23×C4—531no—
209C23×C4—531no—
210C23×C4—531no—
211C23×C4C2×#615711yescharacteristic
212C23×C4C2×#615711yescharacteristic
213C23×C4C2×#615711yescharacteristic
214C22×C8—1064no—
215C2×C4⋊C4—534no—
216C2×C4⋊C4—1062no—
217C2×C4⋊C4—1062no—
218C2×C4⋊C4—1062no—
219C2×C4⋊C4—1062no—
220C2×C4⋊C4—1062no—
221C2×C42—21no—
222C2×C42—21no—
223C2×C42—42no—
224C2×C42—532no—
225C2×C42—532no—
226C2×C42—1062no—
227C2×C42—1062no—
228C2×C42—1061no—
229C2×C42—1061no—
230C2×C42—2122no—
231C22⋊C8—1064no—
232C22⋊C8—1064no—
233#95—1062no—
234#95—1062no—
235C24C22×#615711yescharacteristic
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—532no—
249C22×C4—532no—
250C22×C4—532no—
251C22×C4—532no—
252C22×C4—532no—
253C22×C4—532no—
254C22×C4—532no—
255C22×C4—532no—
256C22×C4—1061no—
257C22×C4—1061no—
258C22×C4—1061no—
259C22×C4—1061no—
260C22×C4—1061no—
261C22×C4—1061no—
262C22×C4—1061no—
263C22×C4—1061no—
264C22×C4—2121no—
265C22×C4—2121no—
266C22×C4—2121no—
267C22×C4—2121no—
268C22×C4—2121no—
269C22×C4—2121no—
270C22×C4D53⋊C812yes—
271C22×C4#1171993612yes—
272C22×C4C22⋊#615711yescharacteristic
273C22×C4C22⋊#615711yescharacteristic
274C2×C8—2124no—
275C2×C8—2124no—
276C2×C8—2124no—
277C4⋊C4—1068no—
278C4⋊C4—1068no—
279C42—42no—
280C42—42no—
281C42—1064no—
282C42—1064no—
283C42—2122no—
284C42—2122no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23C2×C22⋊#615711yescharacteristic
290C23#1313329611yescharacteristic
291C23#1313329611yescharacteristic
292C23C2×D53⋊C811yescharacteristic
293C23D53⋊M1611yescharacteristic
294C23D53⋊M1611yescharacteristic
295C23C2×#1171993611yescharacteristic
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—534no—
313C2×C4—534no—
314C2×C4—1062no—
315C2×C4—1062no—
316C2×C4—1062no—
317C2×C4—1062no—
318C2×C4—1062no—
319C2×C4—1062no—
320C2×C4—1062no—
321C2×C4—1062no—
322C2×C4—1062no—
323C2×C4—1062no—
324C2×C4—2122no—
325C2×C4—2122no—
326C2×C4—2122no—
327C2×C4—2122no—
328C2×C4—2121no—
329C2×C4—2121no—
330C2×C4—2121no—
331C2×C4—2121no—
332C2×C4—2122no—
333C2×C4—2122no—
334C2×C4#1313327712yes—
335C2×C4#1313327812yes—
336C8—4244no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22#1681156611yescharacteristic
350C22D53⋊(C22⋊C8)11yescharacteristic
351C22#1681159411yescharacteristic
352C22#1681160211yescharacteristic
353C22#1681160211yescharacteristic
354C22C2×#1313327711yescharacteristic
355C22C2×#1313327811yescharacteristic
356C22#1681164111yescharacteristic
357C22#1681164211yescharacteristic
358C22#1681164511yescharacteristic
359C22#1681164611yescharacteristic
360C4—22no—
361C4—22no—
362C4—42no—
363C4—42no—
364C4—1064no—
365C4—1064no—
366C4—2122no—
367C4—2122no—
368C2—21no—
369C2—21no—
370C2—21no—
371C2—21no—
372C2#2028995411yescharacteristic
373C2#2028995711yescharacteristic
374C2#2028997411yescharacteristic
375C2#2028997711yescharacteristic
376C2#2029060711yescharacteristic
377C2#2029061211yescharacteristic
378C2#2029061411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6157
commutatorC23×C53C22×C8
FrattiniC24C22×#6157
FittingC22×C42×C53C4
socleC23×C53C2×C22⋊C4
prime radicalC24×C53C22×C4
cosocleC23×Dic53C23
hypercenterC22×C42#6157
hypocenterC53#8701
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
29. C2×#11719919C8semidirect
206. C53#8701semidirect

Maximal subgroups

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

subgroupindex
#202906062
#202895532
C2×C4×#117199192
#870153