Finite Group Databasebeta

← #28306249

Subgroups — #28306249

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
1#20290571C211yesmaximal, characteristic
2C4×C22⋊#88324C211yesmaximal, characteristic
3#20289553C212yesmaximal
4#20289553C212yesmaximal
5C2×#16810518C211yesmaximal, characteristic
6C2×#13133284—21no—
7C2×C22⋊#88324C2212yes—
8C2×C22⋊#88324C2212yes—
9C2×C4×#88324—21no—
10#16811489—21no—
11#16811489—21no—
12C22×#11719919C411yescharacteristic
13C22×#11719919C411yescharacteristic
14C22×#11719919C411yescharacteristic
15C22×C4×Dic53C2211yescharacteristic
16#16810518—21no—
17#16810518—21no—
18#16810518—21no—
19#16810518—21no—
20C2×#13133124C2211yescharacteristic
21C2×#13133124C2211yescharacteristic
22C22×C4⋊C4×C53C411yescharacteristic
23C22×#88324—22no—
24C22×#88324—22no—
25#13133284—42no—
26C22⋊#88324—22no—
27C22⋊#88324—24no—
28C22⋊#88324Q814yes—
29C4×#88324—42no—
30C23×Dic53C2×C411yescharacteristic
31C23×Dic53C2×C411yescharacteristic
32C23×Dic53C2×C411yescharacteristic
33C23×Dic53C2311yescharacteristic
34C2×#11719919—21no—
35C2×#11719919—21no—
36C2×#11719919—21no—
37C2×#11719919—21no—
38C2×#11719919—21no—
39C2×#11719919—21no—
40C2×#11719919—22no—
41C2×#11719919—42no—
42C2×#11719919—42no—
43C2×#11719919C814yescomplemented
44C2×C4×Dic53—42no—
45C2×C4×Dic53D411yescharacteristic
46C2×C4×Dic53D411yescharacteristic
47C2×C4×Dic53D411yescharacteristic
48C2×C4×Dic53D411yescharacteristic
49#13133124—21no—
50#13133124—21no—
51#13133124—21no—
52#13133124—21no—
53C23×C4×C53C2×C411yescharacteristic
54C23×C4×C53C2×C411yescharacteristic
55C23×C4×C53C2×C411yescharacteristic
56C2×C4⋊C4×C53—21no—
57C2×C4⋊C4×C53—21no—
58C2×C4⋊C4×C53—42no—
59C24×C53C22×C411yescharacteristic
60C22×C4×C53—21no—
61C22×C4×C53—21no—
62C22×C4×C53—22no—
63C22×C4×C53—22no—
64C22×C4×C53—21no—
65C22×C4×C53—22no—
66C22×C4×C53—41no—
67C22×C4×C53—41no—
68C22×C4×C53—41no—
69C22×C4×C53—41no—
70C22×C4×C53—41no—
71C22×C4×C53C22⋊C411yescharacteristic
72C22×C4×C53C22⋊C411yescharacteristic
73C22×C4×C53C2×C812yes—
74C22×Dic53—22no—
75C22×Dic53—22no—
76C22×Dic53—21no—
77C22×Dic53—21no—
78C22×Dic53—21no—
79C22×Dic53—22no—
80C22×Dic53—41no—
81C22×Dic53—41no—
82C22×Dic53—41no—
83C22×Dic53—41no—
84C22×Dic53—41no—
85C22×Dic53—41no—
86C22×Dic53C22⋊C411yescharacteristic
87C22×Dic53C22⋊C411yescharacteristic
88C22×Dic53C2×C812yes—
89C22×Dic53C2×C812yes—
90C22×Dic53M1612yes—
91C22×Dic53C2×D411yescharacteristic
92C22×Dic53C2×D411yescharacteristic
93C22×Dic53C2×Q812yes—
94C22×Dic53#4112yes—
95C2×#88324—24no—
96C2×#88324—42no—
97C2×#88324—42no—
98C2×#88324—42no—
99C2×#88324—42no—
100C2×#88324—42no—
101C4⋊C4×C53—42no—
102C4⋊C4×C53—42no—
103#11719919—24no—
104#11719919—24no—
105#11719919—42no—
106#11719919—42no—
107#11719919—42no—
108#11719919—42no—
109C4×Dic53—22no—
110C4×Dic53—22no—
111C4×Dic53—41no—
112C4×Dic53—41no—
113C23×C53—21no—
114C23×C53—21no—
115C23×C53—21no—
116C23×C53—21no—
117C23×C53C2×C22⋊C411yescharacteristic
118C23×C53C4×Q812yes—
119C23×C53C22×C811yescharacteristic
120C23×C53C2×M1611yescharacteristic
121C23×C53#13112yes—
122C2×C4×C53—21no—
123C2×C4×C53—21no—
124C2×C4×C53—22no—
125C2×C4×C53—21no—
126C2×C4×C53—21no—
127C2×C4×C53—21no—
128C2×C4×C53—44no—
129C2×C4×C53—42no—
130C2×C4×C53—41no—
131C2×C4×C53—41no—
132C2×C4×C53—42no—
133C2×C4×C53—41no—
134C2×C4×C53—41no—
135C2×C4×C53—41no—
136C2×C4×C53—82no—
137C2×C4×C53#10012yes—
138C2×Dic53—21no—
139C2×Dic53—21no—
140C2×Dic53—21no—
141C2×Dic53—21no—
142C2×Dic53—21no—
143C2×Dic53—21no—
144C2×Dic53—24no—
145C2×Dic53—24no—
146C2×Dic53—22no—
147C2×Dic53—42no—
148C2×Dic53—42no—
149C2×Dic53—42no—
150C2×Dic53—41no—
151C2×Dic53—41no—
152C2×Dic53—42no—
153C2×Dic53—41no—
154C2×Dic53—41no—
155C2×Dic53—41no—
156C2×Dic53—82no—
157C2×Dic53C22⋊C812yes—
158C2×Dic53C22⋊C812yes—
159C2×Dic53#9912yes—
160C2×Dic53#10112yes—
161C2×Dic53C22⋊Q812yes—
162C2×Dic53#12411yescharacteristic
163C2×Dic53C4⋊Q811yescharacteristic
164#88324—44no—
165#88324—82no—
166#9879—531nomaximal, Sylow
167C22×C53—21no—
168C22×C53—21no—
169C22×C53—21no—
170C22×C53—21no—
171C22×C53—22no—
172C22×C53—22no—
173C22×C53—22no—
174C22×C53—22no—
175C22×C53#39111yescharacteristic
176C22×C53C2×C22⋊C811yescharacteristic
177C22×C53#40811yescharacteristic
178C22×C53C2×#9911yescharacteristic
179C22×C53#41011yescharacteristic
180C22×C53C2×#10011yescharacteristic
181C22×C53C2×#10111yescharacteristic
182C22×C53C8×Q812yes—
183C22×C53#44612yes—
184C4×C53—22no—
185C4×C53—42no—
186C4×C53—41no—
187C4×C53—81no—
188Dic53—22no—
189Dic53—22no—
190Dic53—21no—
191Dic53—21no—
192Dic53—42no—
193Dic53—81no—
194Dic53#32414yes—
195C2×#389—531no—
196#1797—531no—
197C4×C22⋊C8—531no—
198#1280—532no—
199#1280—532no—
200C2×C53—22no—
201C2×C53—22no—
202C2×C53C2×#32411yescharacteristic
203C2×C53#146011yescharacteristic
204C2×C53#147011yescharacteristic
205C2×C53#147111yescharacteristic
206C2×C53#198411yescharacteristic
207C2×C53#199611yescharacteristic
208C2×C53#199711yescharacteristic
209C22×C4⋊C4—531no—
210C22×C4⋊C4—531no—
211C22×C4⋊C4—531no—
212C22×C4⋊C4#615711yescharacteristic
213C22×C42—531no—
214C2×C4⋊C8—1061no—
215C2×C22⋊C8—532no—
216C2×C22⋊C8—532no—
217C2×C4×C8—1061no—
218#389—1061no—
219#389—1061no—
220#389—1061no—
221#389—1061no—
222C2×#95—531no—
223C2×#95—531no—
224#336—1061no—
225#336—1061no—
226C53#987911yescharacteristic, complemented, Sylow
227C23×C4—531no—
228C23×C4—531no—
229C23×C4—531no—
230C23×C4—531no—
231C23×C4C2×#615711yescharacteristic
232C23×C4C2×#615711yescharacteristic
233C23×C4C2×#615711yescharacteristic
234C22×C8—1062no—
235C22×C8—1062no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—42no—
239C2×C4⋊C4—534no—
240C2×C4⋊C4—1062no—
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—2122no—
248C2×C4⋊C4—2122no—
249C2×C42—531no—
250C2×C42—531no—
251C2×C42—531no—
252C2×C42—531no—
253C2×C42—2122no—
254C4⋊C8—2122no—
255C22⋊C8—534no—
256C22⋊C8—1062no—
257C22⋊C8—1064no—
258C4×C8—2122no—
259#95—1061no—
260#95—1061no—
261#95—1061no—
262#95—1061no—
263C24C22×#615711yescharacteristic
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—531no—
276C22×C4—531no—
277C22×C4—531no—
278C22×C4—531no—
279C22×C4—532no—
280C22×C4—532no—
281C22×C4—532no—
282C22×C4—532no—
283C22×C4—532no—
284C22×C4—1062no—
285C22×C4—1062no—
286C22×C4—1061no—
287C22×C4—1061no—
288C22×C4—1062no—
289C22×C4—1061no—
290C22×C4—2121no—
291C22×C4—2121no—
292C22×C4—2121no—
293C22×C4—2121no—
294C22×C4—2121no—
295C22×C4—2121no—
296C22×C4D53⋊C812yes—
297C22×C4C22⋊#615711yescharacteristic
298C22×C4C22⋊#615711yescharacteristic
299C2×C8—1064no—
300C2×C8—2122no—
301C2×C8—2122no—
302C2×C8—2122no—
303C2×C8—2122no—
304C2×C8—2122no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—1064no—
308C4⋊C4—1064no—
309C4⋊C4—2122no—
310C4⋊C4—2122no—
311C4⋊C4—2122no—
312C4⋊C4—2122no—
313C42—1062no—
314C42—1062no—
315C42—2121no—
316C42—2121no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×C22⋊#615711yescharacteristic
322C23Q8×#615712yes—
323C23C2×D53⋊C811yescharacteristic
324C23D53⋊M1611yescharacteristic
325C23#1313330412yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—82no—
341C2×C4—532no—
342C2×C4—532no—
343C2×C4—532no—
344C2×C4—532no—
345C2×C4—531no—
346C2×C4—531no—
347C2×C4—532no—
348C2×C4—1064no—
349C2×C4—1064no—
350C2×C4—1061no—
351C2×C4—1061no—
352C2×C4—1061no—
353C2×C4—1061no—
354C2×C4—1061no—
355C2×C4—1061no—
356C2×C4—1062no—
357C2×C4—4242no—
358C2×C4—2122no—
359C2×C4—2122no—
360C2×C4—2121no—
361C2×C4—2121no—
362C2×C4—2121no—
363C2×C4—2122no—
364C2×C4—2121no—
365C2×C4—2121no—
366C2×C4—2122no—
367C2×C4#1313327712yes—
368C8—4242no—
369C8—2124no—
370C22—22no—
371C22—22no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—22no—
377C22—22no—
378C22(C2×#6157)⋊Q811yescharacteristic
379C22D53⋊(C22⋊C8)11yescharacteristic
380C22#1681159611yescharacteristic
381C22D53⋊#9911yescharacteristic
382C22#1681160211yescharacteristic
383C22C2×#1313327711yescharacteristic
384C22D53⋊#10111yescharacteristic
385C22#1681167212yes—
386C22#1681167512yes—
387C4—22no—
388C4—42no—
389C4—41no—
390C4—81no—
391C4—534no—
392C4—1061no—
393C4—1062no—
394C4—1061no—
395C4—1062no—
396C4—4241no—
397C4—2122no—
398C2—22no—
399C2—22no—
400C2D53⋊#32411yescharacteristic
401C2#2028995411yescharacteristic
402C2#2028998711yescharacteristic
403C2#2028999111yescharacteristic
404C2#2029088611yescharacteristic
405C2#2029090611yescharacteristic
406C2#2029090711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6157
commutatorC23×C53C22×C8
FrattiniC24C22×#6157
FittingC22×C4⋊C4×C53C4
socleC23×C53C2×C22⋊C4
prime radicalC24×C53C22×C4
cosocleC23×Dic53C23
hypercenterC22×C4⋊C4#6157
hypocenterC53#9879
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
43. C2×#11719919C8semidirect
226. C53#9879semidirect

Maximal subgroups

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

subgroupindex
#202905712
C4×C22⋊#883242
#202895532
C2×#168105182
#987953