Finite Group Databasebeta

← #28306246

Subgroups — #28306246

Order 13568.

680 conjugacy classes of subgroups.

The subgroup lattice has 416 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×#16810527C211yesmaximal, characteristic
6C2×#13133284—21no—
7C2×C22⋊#88324C2212yes—
8C2×C22⋊#88324C2212yes—
9C2×C4×#88324—21no—
10#16811489—21no—
11#16811489—21no—
12C23×Dic106C411yescharacteristic
13C22×#11719919C411yescharacteristic
14C22×C4×Dic53C2211yescharacteristic
15#16810527—21no—
16#16810527—21no—
17#16810527—21no—
18#16810527—21no—
19C2×#13133124C411yescharacteristic
20C2×#13133124C2211yescharacteristic
21C2×#13133124C2211yescharacteristic
22C2×#95×C53C411yescharacteristic
23C22×#88324—22no—
24C22×#88324—22no—
25#13133284—42no—
26C22⋊#88324—22no—
27C22⋊#88324—24no—
28C22⋊#88324Q814yescomplemented
29C4×#88324—42no—
30C22×Dic106—21no—
31C22×Dic106—21no—
32C22×Dic106—22no—
33C22×Dic106—42no—
34C22×Dic106—42no—
35C22×Dic106C814yescomplemented
36C23×Dic53C2×C411yescharacteristic
37C23×Dic53C2×C411yescharacteristic
38C23×Dic53C2×C411yescharacteristic
39C23×Dic53C2311yescharacteristic
40C2×#11719919—21no—
41C2×#11719919—21no—
42C2×#11719919—42no—
43C2×C4×Dic53—42no—
44C2×C4×Dic53D411yescharacteristic
45C2×C4×Dic53D411yescharacteristic
46C2×C4×Dic53D411yescharacteristic
47C2×C4×Dic53D411yescharacteristic
48#13133124—21no—
49#13133124—21no—
50#13133124—21no—
51#13133124—21no—
52#13133124—21no—
53#13133124—21no—
54C23×C4×C53C2×C411yescharacteristic
55C23×C4×C53C2×C411yescharacteristic
56C23×C4×C53C2×C411yescharacteristic
57#95×C53—21no—
58#95×C53—21no—
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×Dic106—24no—
96C2×Dic106—24no—
97C2×Dic106—42no—
98C2×Dic106—42no—
99C2×Dic106—48no—
100C2×Dic106—42no—
101C2×Dic106—42no—
102C2×Dic106—48no—
103C2×#88324—24no—
104C2×#88324—42no—
105C2×#88324—42no—
106C2×#88324—42no—
107C2×#88324—42no—
108C2×#88324—42no—
109#11719919—42no—
110#11719919—42no—
111C4×Dic53—22no—
112C4×Dic53—22no—
113C4×Dic53—41no—
114C4×Dic53—41no—
115C23×C53—21no—
116C23×C53—21no—
117C23×C53—21no—
118C23×C53—21no—
119C23×C53C2×C22⋊C411yescharacteristic
120C23×C53C4×Q812yes—
121C23×C53C22×C811yescharacteristic
122C23×C53C2×M1611yescharacteristic
123C23×C53#13112yes—
124C2×C4×C53—21no—
125C2×C4×C53—21no—
126C2×C4×C53—22no—
127C2×C4×C53—21no—
128C2×C4×C53—21no—
129C2×C4×C53—21no—
130C2×C4×C53—44no—
131C2×C4×C53—42no—
132C2×C4×C53—41no—
133C2×C4×C53—41no—
134C2×C4×C53—42no—
135C2×C4×C53—41no—
136C2×C4×C53—41no—
137C2×C4×C53—41no—
138C2×C4×C53—82no—
139C2×C4×C53#10112yes—
140C2×Dic53—21no—
141C2×Dic53—21no—
142C2×Dic53—21no—
143C2×Dic53—21no—
144C2×Dic53—21no—
145C2×Dic53—21no—
146C2×Dic53—24no—
147C2×Dic53—24no—
148C2×Dic53—22no—
149C2×Dic53—42no—
150C2×Dic53—42no—
151C2×Dic53—42no—
152C2×Dic53—41no—
153C2×Dic53—41no—
154C2×Dic53—42no—
155C2×Dic53—41no—
156C2×Dic53—41no—
157C2×Dic53—41no—
158C2×Dic53—82no—
159C2×Dic53C22⋊C812yes—
160C2×Dic53C22⋊C812yes—
161C2×Dic53#9912yes—
162C2×Dic53#10012yes—
163C2×Dic53C22⋊Q812yes—
164C2×Dic53#12411yescharacteristic
165C2×Dic53C4⋊Q811yescharacteristic
166Dic106—48no—
167Dic106—48no—
168#88324—44no—
169#88324—82no—
170#9878—531nomaximal, Sylow
171C22×C53—21no—
172C22×C53—21no—
173C22×C53—21no—
174C22×C53—21no—
175C22×C53—22no—
176C22×C53—22no—
177C22×C53—22no—
178C22×C53—22no—
179C22×C53#39111yescharacteristic
180C22×C53C2×C22⋊C811yescharacteristic
181C22×C53#40811yescharacteristic
182C22×C53C2×#9911yescharacteristic
183C22×C53#41011yescharacteristic
184C22×C53C2×#10011yescharacteristic
185C22×C53C2×#10111yescharacteristic
186C22×C53C8×Q812yes—
187C22×C53#44612yes—
188C4×C53—22no—
189C4×C53—42no—
190C4×C53—41no—
191C4×C53—81no—
192Dic53—22no—
193Dic53—22no—
194Dic53—21no—
195Dic53—21no—
196Dic53—42no—
197Dic53—81no—
198Dic53#32314yes—
199C2×#391—531no—
200#1797—531no—
201C4×C22⋊C8—531no—
202#1280—532no—
203#1280—532no—
204C2×C53—22no—
205C2×C53—22no—
206C2×C53C2×#32311yescharacteristic
207C2×C53#146111yescharacteristic
208C2×C53#146911yescharacteristic
209C2×C53#147211yescharacteristic
210C2×C53#198411yescharacteristic
211C2×C53#199611yescharacteristic
212C2×C53#199711yescharacteristic
213C23×Q8—531no—
214C22×C4⋊C4—531no—
215C22×C42—531no—
216C2×C4⋊C8—1061no—
217C2×C22⋊C8—532no—
218C2×C22⋊C8—532no—
219C2×C4×C8—1061no—
220#391—1061no—
221#391—1061no—
222#391—1061no—
223#391—1061no—
224C2×#95—531no—
225C2×#95—531no—
226C2×#95—531no—
227C2×#95#615711yescharacteristic
228#336—1061no—
229#336—1061no—
230C53#987811yescharacteristic, complemented, Sylow
231C22×Q8—534no—
232C22×Q8—1061no—
233C22×Q8—1061no—
234C22×Q8—1062no—
235C22×Q8—2122no—
236C22×Q8—2122no—
237C23×C4—531no—
238C23×C4—531no—
239C23×C4—531no—
240C23×C4—531no—
241C23×C4C2×#615711yescharacteristic
242C23×C4C2×#615711yescharacteristic
243C23×C4C2×#615711yescharacteristic
244C22×C8—1062no—
245C22×C8—1062no—
246C2×C4⋊C4—1061no—
247C2×C4⋊C4—1061no—
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—21no—
260#95—21no—
261#95—1061no—
262#95—1061no—
263#95—1061no—
264#95—1061no—
265#95—1061no—
266#95—1061no—
267C24C22×#615711yescharacteristic
268C2×Q8—1064no—
269C2×Q8—1064no—
270C2×Q8—2122no—
271C2×Q8—2122no—
272C2×Q8—2128no—
273C2×Q8—2128no—
274C2×Q8—2122no—
275C2×Q8—2122no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—531no—
288C22×C4—531no—
289C22×C4—531no—
290C22×C4—531no—
291C22×C4—532no—
292C22×C4—532no—
293C22×C4—532no—
294C22×C4—532no—
295C22×C4—532no—
296C22×C4—1062no—
297C22×C4—1062no—
298C22×C4—1061no—
299C22×C4—1061no—
300C22×C4—1062no—
301C22×C4—1061no—
302C22×C4—2121no—
303C22×C4—2121no—
304C22×C4—2121no—
305C22×C4—2121no—
306C22×C4—2121no—
307C22×C4—2121no—
308C22×C4D53⋊C812yes—
309C22×C4C22⋊#615711yescharacteristic
310C22×C4C22⋊#615711yescharacteristic
311C2×C8—1064no—
312C2×C8—2122no—
313C2×C8—2122no—
314C2×C8—2122no—
315C2×C8—2122no—
316C2×C8—2122no—
317C4⋊C4—2122no—
318C4⋊C4—2122no—
319C42—1062no—
320C42—1062no—
321C42—2121no—
322C42—2121no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23C2×C22⋊#615711yescharacteristic
328C23Q8×#615712yes—
329C23C2×D53⋊C811yescharacteristic
330C23D53⋊M1611yescharacteristic
331C23#1313330412yes—
332Q8—2128no—
333Q8—2128no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—82no—
349C2×C4—532no—
350C2×C4—532no—
351C2×C4—532no—
352C2×C4—532no—
353C2×C4—531no—
354C2×C4—531no—
355C2×C4—532no—
356C2×C4—1064no—
357C2×C4—1064no—
358C2×C4—1061no—
359C2×C4—1061no—
360C2×C4—1061no—
361C2×C4—1061no—
362C2×C4—1061no—
363C2×C4—1061no—
364C2×C4—1062no—
365C2×C4—4242no—
366C2×C4—2122no—
367C2×C4—2122no—
368C2×C4—2121no—
369C2×C4—2121no—
370C2×C4—2121no—
371C2×C4—2122no—
372C2×C4—2121no—
373C2×C4—2121no—
374C2×C4—2122no—
375C2×C4#1313327812yes—
376C8—4242no—
377C8—2124no—
378C22—22no—
379C22—22no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22(C2×#6157)⋊Q811yescharacteristic
387C22D53⋊(C22⋊C8)11yescharacteristic
388C22#1681159611yescharacteristic
389C22D53⋊#9911yescharacteristic
390C22#1681160211yescharacteristic
391C22D53⋊#10011yescharacteristic
392C22C2×#1313327811yescharacteristic
393C22#1681167212yes—
394C22#1681167512yes—
395C4—22no—
396C4—42no—
397C4—41no—
398C4—81no—
399C4—534no—
400C4—1061no—
401C4—1062no—
402C4—1061no—
403C4—1062no—
404C4—4241no—
405C4—2122no—
406C2—22no—
407C2—22no—
408C2D53⋊#32311yescharacteristic
409C2#2028995711yescharacteristic
410C2#2028998411yescharacteristic
411C2#2028999411yescharacteristic
412C2#2029088611yescharacteristic
413C2#2029090611yescharacteristic
414C2#2029090811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6157
commutatorC23×C53C22×C8
FrattiniC24C22×#6157
FittingC2×#95×C53C4
socleC23×C53C2×C22⋊C4
prime radicalC24×C53C22×C4
cosocleC23×Dic53C23
hypercenterC2×#95#6157
hypocenterC53#9878
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
28. C22⋊#88324Q8semidirect
35. C22×Dic106C8semidirect
230. C53#9878semidirect

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×#168105272
#987853