Finite Group Databasebeta

← #28305742

Subgroups — #28305742

Order 13568.

640 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 122 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#20290569C211yesmaximal, characteristic
2#20290441C211yesmaximal, characteristic
3C2×#16811469C212yesmaximal
4C2×#16811468C212yesmaximal
5C2×#16810520C211yesmaximal, characteristic
6C2×C4⋊#88324—21no—
7C2×C22⋊#88324C2212yes—
8C2×C22⋊#88324C2212yes—
9C2×#13133272—21no—
10#16811489—21no—
11#16811489—21no—
12#16811469—24no—
13#16811468—24no—
14C22×C4⋊Dic53C2211yescharacteristic
15C22×#11719919C411yescharacteristic
16C22×#11719919C411yescharacteristic
17C22×#11719919C2211yescharacteristic
18C22×C4×Dic53C2211yescharacteristic
19#16810520—21no—
20#16810520—21no—
21#16810520—21no—
22#16810520—21no—
23C2×#13133124C411yescharacteristic
24C2×#95×C53C411yescharacteristic
25C22×#88324—22no—
26C22×#88324—22no—
27C4⋊#88324—42no—
28C22⋊#88324—22no—
29C22⋊#88324—22no—
30C22⋊#88324—22no—
31C22⋊#88324D414yes—
32#13133272—42no—
33C23×Dic53C2×C411yescharacteristic
34C23×Dic53C2×C411yescharacteristic
35C23×Dic53C2×C411yescharacteristic
36C23×Dic53C2311yescharacteristic
37C2×C4⋊Dic53—21no—
38C2×C4⋊Dic53—21no—
39C2×C4⋊Dic53—22no—
40C2×C4⋊Dic53—22no—
41C2×#11719919—22no—
42C2×#11719919—21no—
43C2×#11719919—21no—
44C2×#11719919—21no—
45C2×#11719919—21no—
46C2×#11719919—22no—
47C2×#11719919—21no—
48C2×#11719919—21no—
49C2×#11719919—22no—
50C2×#11719919—22no—
51C2×#11719919—42no—
52C2×C4×Dic53—42no—
53C2×C4×Dic53D411yescharacteristic
54C2×C4×Dic53D411yescharacteristic
55C2×C4×Dic53D411yescharacteristic
56C2×C4×Dic53D411yescharacteristic
57#13133124—21no—
58#13133124—21no—
59C23×C4×C53C2×C411yescharacteristic
60C23×C4×C53C2×C411yescharacteristic
61C23×C4×C53C2×C411yescharacteristic
62#95×C53—21no—
63#95×C53—21no—
64C24×C53C22×C411yescharacteristic
65C22×C4×C53—21no—
66C22×C4×C53—22no—
67C22×C4×C53—21no—
68C22×C4×C53—22no—
69C22×C4×C53—22no—
70C22×C4×C53—22no—
71C22×C4×C53—21no—
72C22×C4×C53—22no—
73C22×C4×C53—41no—
74C22×C4×C53—41no—
75C22×C4×C53—41no—
76C22×C4×C53C22⋊C411yescharacteristic
77C22×C4×C53C22⋊C411yescharacteristic
78C22×C4×C53M1612yes—
79C22×Dic53—21no—
80C22×Dic53—21no—
81C22×Dic53—22no—
82C22×Dic53—22no—
83C22×Dic53—21no—
84C22×Dic53—22no—
85C22×Dic53—21no—
86C22×Dic53—22no—
87C22×Dic53—21no—
88C22×Dic53—22no—
89C22×Dic53—41no—
90C22×Dic53—41no—
91C22×Dic53—41no—
92C22×Dic53—41no—
93C22×Dic53C22⋊C411yescharacteristic
94C22×Dic53C22⋊C411yescharacteristic
95C22×Dic53M1612yes—
96C22×Dic53C2×D411yescharacteristic
97C22×Dic53C2×D411yescharacteristic
98C22×Dic53C2×D412yes—
99C22×Dic53#4112yes—
100C2×#88324—24no—
101C2×#88324—42no—
102C2×#88324—42no—
103C2×#88324—42no—
104C2×#88324—42no—
105C2×#88324—42no—
106C4⋊Dic53—42no—
107C4⋊Dic53—41no—
108C4⋊Dic53—41no—
109#11719919—24no—
110#11719919—24no—
111#11719919—42no—
112#11719919—42no—
113#11719919—42no—
114#11719919—41no—
115#11719919—41no—
116C4×Dic53—22no—
117C4×Dic53—22no—
118C4×Dic53—41no—
119C4×Dic53—41no—
120C23×C53—21no—
121C23×C53—21no—
122C23×C53—21no—
123C23×C53—21no—
124C23×C53C2×C22⋊C411yescharacteristic
125C23×C53C4×D412yes—
126C23×C53C2×M1611yescharacteristic
127C23×C53C2×M1611yescharacteristic
128C23×C53#13112yes—
129C2×C4×C53—21no—
130C2×C4×C53—21no—
131C2×C4×C53—22no—
132C2×C4×C53—21no—
133C2×C4×C53—21no—
134C2×C4×C53—21no—
135C2×C4×C53—24no—
136C2×C4×C53—44no—
137C2×C4×C53—41no—
138C2×C4×C53—41no—
139C2×C4×C53—42no—
140C2×C4×C53—41no—
141C2×C4×C53—41no—
142C2×C4×C53—41no—
143C2×C4×C53—82no—
144C2×C4×C53#10112yes—
145C2×Dic53—24no—
146C2×Dic53—24no—
147C2×Dic53—21no—
148C2×Dic53—21no—
149C2×Dic53—21no—
150C2×Dic53—21no—
151C2×Dic53—21no—
152C2×Dic53—21no—
153C2×Dic53—21no—
154C2×Dic53—21no—
155C2×Dic53—22no—
156C2×Dic53—24no—
157C2×Dic53—42no—
158C2×Dic53—42no—
159C2×Dic53—41no—
160C2×Dic53—41no—
161C2×Dic53—42no—
162C2×Dic53—41no—
163C2×Dic53—41no—
164C2×Dic53—41no—
165C2×Dic53—82no—
166C2×Dic53#9912yes—
167C2×Dic53#10112yes—
168C2×Dic53#12112yes—
169C2×Dic53#12411yescharacteristic
170C2×Dic53#12711yescharacteristic
171#88324—44no—
172#88324—82no—
173#9654—531nomaximal, Sylow
174C22×C53—22no—
175C22×C53—22no—
176C22×C53—21no—
177C22×C53—21no—
178C22×C53—21no—
179C22×C53—21no—
180C22×C53—22no—
181C22×C53—22no—
182C22×C53#39011yescharacteristic
183C22×C53#40711yescharacteristic
184C22×C53#40811yescharacteristic
185C22×C53C2×#9911yescharacteristic
186C22×C53#41011yescharacteristic
187C22×C53C2×#10111yescharacteristic
188C22×C53C2×#10111yescharacteristic
189C22×C53#43512yes—
190C22×C53#43512yes—
191C4×C53—22no—
192C4×C53—42no—
193C4×C53—41no—
194C4×C53—81no—
195Dic53—22no—
196Dic53—21no—
197Dic53—21no—
198Dic53—22no—
199Dic53—22no—
200Dic53—42no—
201Dic53—81no—
202C2×#389—531no—
203#1797—531no—
204#1749—531no—
205C2×#324—532no—
206C2×#324—532no—
207C2×C53—22no—
208C2×C53—22no—
209C2×C53#146311yescharacteristic
210C2×C53#146711yescharacteristic
211C2×C53#147011yescharacteristic
212C2×C53#147211yescharacteristic
213C2×C53#195511yescharacteristic
214C2×C53#196411yescharacteristic
215C2×C53#196611yescharacteristic
216C22×C4⋊C4—531no—
217C22×C4⋊C4—531no—
218C22×C4⋊C4—531no—
219C22×C4⋊C4—531no—
220C22×C42—531no—
221C2×C4⋊C8—1061no—
222C2×C22⋊C8—532no—
223C2×C22⋊C8—532no—
224C2×#97—1061no—
225#389—1061no—
226#389—1061no—
227#389—1061no—
228#389—1061no—
229C2×#95—531no—
230C2×#95#615711yescharacteristic
231#336—1061no—
232#336—1061no—
233#324—1064no—
234#324—1064no—
235C53#965411yescharacteristic, complemented, Sylow
236C23×C4—531no—
237C23×C4—531no—
238C23×C4—531no—
239C23×C4—531no—
240C23×C4C2×#615711yescharacteristic
241C23×C4C2×#615711yescharacteristic
242C23×C4C2×#615711yescharacteristic
243C22×C8—1062no—
244C22×C8—1062no—
245C2×C4⋊C4—1062no—
246C2×C4⋊C4—1061no—
247C2×C4⋊C4—1061no—
248C2×C4⋊C4—1062no—
249C2×C4⋊C4—1062no—
250C2×C4⋊C4—1062no—
251C2×C4⋊C4—1062no—
252C2×C4⋊C4—1061no—
253C2×C4⋊C4—1061no—
254C2×C4⋊C4—1061no—
255C2×C4⋊C4—1061no—
256C2×C4⋊C4—1062no—
257C2×C4⋊C4—1061no—
258C2×C4⋊C4—1061no—
259C2×C4⋊C4—2122no—
260C2×C42—531no—
261C2×C42—531no—
262C2×C42—531no—
263C2×C42—531no—
264C2×C42—2122no—
265C4⋊C8—2122no—
266C22⋊C8—534no—
267C22⋊C8—1062no—
268C22⋊C8—1062no—
269C22⋊C8—1062no—
270#97—2122no—
271#95—21no—
272#95—21no—
273#95—1061no—
274#95—1061no—
275C24C22×#615711yescharacteristic
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—22no—
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—1062no—
295C22×C4—1062no—
296C22×C4—1061no—
297C22×C4—1061no—
298C22×C4—1061no—
299C22×C4—1062no—
300C22×C4—1061no—
301C22×C4—1062no—
302C22×C4—1062no—
303C22×C4—1061no—
304C22×C4—2121no—
305C22×C4—2121no—
306C22×C4—2121no—
307C22×C4—2121no—
308C22×C4#1171993612yes—
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—1064no—
318C4⋊C4—1064no—
319C4⋊C4—2122no—
320C4⋊C4—2121no—
321C4⋊C4—2121no—
322C4⋊C4—2122no—
323C4⋊C4—2121no—
324C4⋊C4—2121no—
325C4⋊C4—2122no—
326C4⋊C4—2122no—
327C42—1062no—
328C42—1062no—
329C42—2121no—
330C42—2121no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23C2×C22⋊#615711yescharacteristic
336C23D4×#615712yes—
337C23D53⋊M1611yescharacteristic
338C23C2×#1171993611yescharacteristic
339C23#1313330412yes—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—24no—
347C2×C4—44no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—82no—
355C2×C4—532no—
356C2×C4—531no—
357C2×C4—531no—
358C2×C4—532no—
359C2×C4—532no—
360C2×C4—1064no—
361C2×C4—1064no—
362C2×C4—1061no—
363C2×C4—1061no—
364C2×C4—1061no—
365C2×C4—1061no—
366C2×C4—1061no—
367C2×C4—1061no—
368C2×C4—1061no—
369C2×C4—1061no—
370C2×C4—1062no—
371C2×C4—1064no—
372C2×C4—4242no—
373C2×C4—2122no—
374C2×C4—2122no—
375C2×C4—2121no—
376C2×C4—2121no—
377C2×C4—2121no—
378C2×C4—2121no—
379C2×C4—2121no—
380C2×C4—2122no—
381C2×C4#1313327812yes—
382C8—4242no—
383C8—2124no—
384C22—22no—
385C22—22no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—22no—
391C22—22no—
392C22#1681157511yescharacteristic
393C22#1681159411yescharacteristic
394C22#1681159611yescharacteristic
395C22D53⋊#9911yescharacteristic
396C22#1681160211yescharacteristic
397C22C2×#1313327811yescharacteristic
398C22D53⋊#10111yescharacteristic
399C22#1681165212yes—
400C22#1681165512yes—
401C4—22no—
402C4—42no—
403C4—41no—
404C4—81no—
405C4—1061no—
406C4—1062no—
407C4—1061no—
408C4—1062no—
409C4—1062no—
410C4—4241no—
411C4—2122no—
412C2—22no—
413C2—22no—
414C2#2028996411yescharacteristic
415C2#2028997711yescharacteristic
416C2#2028998711yescharacteristic
417C2#2028999411yescharacteristic
418C2#2029084011yescharacteristic
419C2#2029085611yescharacteristic
420C2#2029085811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6157
commutator, prime radicalC24×C53C22×C4
FrattiniC24C22×#6157
FittingC2×#95×C53C4
socleC23×C53C2×C22⋊C4
cosocleC23×Dic53C23
hypercenterC2×#95#6157
hypocenterC53#9654
LCSG ▷ C24×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
235. C53#9654semidirect

Maximal subgroups

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

subgroupindex
#202905692
#202904412
C2×#168114692
C2×#168114682
C2×#168105202
#965453