Finite Group Databasebeta

← #28299546

Subgroups — #28299546

Order 13568.

514 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 110 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#20290572C211yesmaximal, characteristic
2#20290572C211yesmaximal, characteristic
3#20289534C212yesmaximal, complemented
4#20289533C212yesmaximal, complemented
5#20277196C211yesmaximal, characteristic
6C2×#13133284—21no—
7C2×#13133284—21no—
8C2×#13133274—21no—
9C2×#13133274—21no—
10#16811489C2212yes—
11#16811489C2212yes—
12C2×#13133175C411yescharacteristic
13C2×#13133175C411yescharacteristic
14C2×C42×D53C2211yescharacteristic
15#16810522C2211yescharacteristic
16#16810521C411yescharacteristic
17#16810519C2211yescharacteristic
18#16810497—21no—
19#16810494—21no—
20C4⋊C4×Dic53—21no—
21#16810474—21no—
22C53×#389C411yescharacteristic
23C22×#88324—22no—
24C22×#88324—22no—
25#13133284—42no—
26#13133284—42no—
27#13133274—42no—
28#13133274—42no—
29C22×C4×D53C2×C411yescharacteristic
30C22×C4×D53D411yescharacteristic
31C22×C4×D53D411yescharacteristic
32#13133175—22no—
33#13133175—42no—
34#13133175C814yescomplemented
35C2×C4⋊Dic53—21no—
36C2×C4⋊Dic53C2×C411yescharacteristic
37C2×C4⋊Dic53C2×C411yescharacteristic
38C2×#11719919—21no—
39C2×#11719919—21no—
40C2×#11719921—21no—
41C2×#11719921—21no—
42C2×C4×Dic53—21no—
43C2×C4×Dic53—21no—
44C2×C4×Dic53D411yescharacteristic
45C2×C4×Dic53D411yescharacteristic
46C2×C4×Dic53C2311yescharacteristic
47C42×D53—42no—
48#13133124—21no—
49#13133124—21no—
50#13133124—21no—
51C2×C4⋊C4×C53—21no—
52C2×C4⋊C4×C53C2×C411yescharacteristic
53C2×C4⋊C4×C53C2×C411yescharacteristic
54C2×C42×C53C2×C411yescharacteristic
55#95×C53—21no—
56C23×D53C22⋊C411yescharacteristic
57C22×C4×C53—21no—
58C22×C4×C53—21no—
59C22×C4×C53C22⋊C411yescharacteristic
60C22×C4×C53C22⋊C411yescharacteristic
61C22×C4×C53C22×C411yescharacteristic
62C22×Dic53—21no—
63C22×Dic53—21no—
64C22×Dic53C22⋊C411yescharacteristic
65C22×Dic53C2×D411yescharacteristic
66C22×Dic53C2×D411yescharacteristic
67C2×C4×D53—22no—
68C2×C4×D53—22no—
69C2×C4×D53—21no—
70C2×C4×D53—21no—
71C2×C4×D53—21no—
72C2×C4×D53—21no—
73C2×C4×D53—41no—
74C2×C4×D53—41no—
75C2×C4×D53—41no—
76C2×C4×D53—41no—
77C2×C4×D53C2×C812yes—
78C2×C4×D53M1612yes—
79C2×#88324—42no—
80C2×#88324—42no—
81C2×#88324—42no—
82C2×#88324—42no—
83C2×#88324—42no—
84C2×#88324—42no—
85C4⋊C4×C53—21no—
86C4⋊C4×C53—42no—
87C4⋊C4×C53—41no—
88C4⋊C4×C53C2×C812yes—
89C42×C53—41no—
90#11719921—24no—
91#11719921—42no—
92C4⋊Dic53—21no—
93C4⋊Dic53—41no—
94C4⋊Dic53—41no—
95C4⋊Dic53—41no—
96C4⋊Dic53C2×C812yes—
97#11719919—42no—
98#11719919—41no—
99#11719919—41no—
100C4×Dic53—24no—
101C4×Dic53—22no—
102C4×Dic53—22no—
103C4×Dic53—41no—
104C4×Dic53—42no—
105C23×C53C2×C22⋊C411yescharacteristic
106C22×D53—21no—
107C22×D53—21no—
108C22×D53—21no—
109C22×D53—21no—
110C22×D53—21no—
111C22×D53—21no—
112C22×D53C22⋊C812yes—
113C2×C4×C53—21no—
114C2×C4×C53—21no—
115C2×C4×C53—22no—
116C2×C4×C53—21no—
117C2×C4×C53—21no—
118C2×C4×C53—21no—
119C2×C4×C53—21no—
120C2×C4×C53—21no—
121C2×C4×C53—21no—
122C2×C4×C53—41no—
123C2×C4×C53—41no—
124C2×C4×C53—41no—
125C2×C4×C53—41no—
126C2×C4×C53—41no—
127C2×C4×C53C22×C811yescharacteristic
128C2×C4×C53C2×M1611yescharacteristic
129C2×Dic53—21no—
130C2×Dic53—21no—
131C2×Dic53—21no—
132C2×Dic53—21no—
133C2×Dic53—22no—
134C2×Dic53—41no—
135C2×Dic53—41no—
136C2×Dic53—41no—
137C2×Dic53—41no—
138C2×Dic53—41no—
139C2×Dic53C22⋊C812yes—
140C2×Dic53#9912yes—
141C2×Dic53#10112yes—
142C2×Dic53AGL(1,ℤ/8)11yescharacteristic
143C2×Dic53AGL(1,ℤ/8)11yescharacteristic
144C2×Dic53#13711yescharacteristic
145C2×Dic53#13711yescharacteristic
146C4×D53—24no—
147C4×D53—24no—
148C4×D53—42no—
149C4×D53—42no—
150C4×D53—42no—
151C4×D53—42no—
152#88324—82no—
153#88324—82no—
154#7598—531nomaximal, Sylow
155C22×C53C2×C22⋊C811yescharacteristic
156C22×C53C2×#9911yescharacteristic
157C22×C53C2×#10111yescharacteristic
158C22×C53#41711yescharacteristic
159C22×C53#41711yescharacteristic
160C22×C53#42111yescharacteristic
161C22×C53#42111yescharacteristic
162C2×D53—22no—
163C2×D53—22no—
164C2×D53—22no—
165C2×D53—41no—
166C2×D53—41no—
167C2×D53—41no—
168C2×D53—41no—
169C4×C53—21no—
170C4×C53—21no—
171C4×C53—42no—
172C4×C53—41no—
173C4×C53—41no—
174C4×C53—81no—
175Dic53—21no—
176Dic53—21no—
177Dic53—21no—
178Dic53—21no—
179Dic53—42no—
180Dic53—81no—
181Dic53#32414yes—
182#2296—531no—
183#1797—531no—
184#1797—531no—
185#1271—532no—
186#1271—532no—
187C2×C53C2×#32411yescharacteristic
188C2×C53#147711yescharacteristic
189C2×C53#147711yescharacteristic
190C2×C53#151311yescharacteristic
191C2×C53#151311yescharacteristic
192C2×C53#153711yescharacteristic
193C2×C53#156111yescharacteristic
194D53—42no—
195C2×#117—531no—
196C2×#117—531no—
197C22×C42—531no—
198C2×C4⋊C8—1061no—
199C2×C4⋊C8—1061no—
200C2×C22⋊C8—1061no—
201C2×C22⋊C8—1061no—
202#389—531no—
203#389—531no—
204#389—531no—
205#389#615711yescharacteristic
206#385—1061no—
207#385—1061no—
208C4×C4⋊C4—1061no—
209C4×C4⋊C4—1061no—
210#336—532no—
211#336—532no—
212C53#759811yescharacteristic, complemented, Sylow
213C23×C4—531no—
214C23×C4—531no—
215C23×C4—531no—
216C22×C8—1062no—
217C22×C8—1062no—
218#117—534no—
219#117—1062no—
220#117—2122no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—531no—
223C2×C4⋊C4—531no—
224C2×C4⋊C4—1061no—
225C2×C4⋊C4—1061no—
226C2×C4⋊C4—1061no—
227C2×C4⋊C4C2×#615711yescharacteristic
228C2×C4⋊C4C2×#615711yescharacteristic
229C2×C22⋊C4—1061no—
230C2×C22⋊C4—1061no—
231C2×C42—531no—
232C2×C42—531no—
233C2×C42—531no—
234C2×C42—1061no—
235C2×C42—1061no—
236C2×C42—2122no—
237C2×C42C2×#615711yescharacteristic
238C4⋊C8—2122no—
239C4⋊C8—2122no—
240C22⋊C8—2122no—
241C22⋊C8—2122no—
242#95—21no—
243#95—1061no—
244#95—1061no—
245#95—1061no—
246C24—531no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—531no—
250C22×C4—531no—
251C22×C4—531no—
252C22×C4—532no—
253C22×C4—532no—
254C22×C4—1062no—
255C22×C4—1062no—
256C22×C4—1061no—
257C22×C4—1061no—
258C22×C4—1061no—
259C22×C4—1061no—
260C22×C4—1061no—
261C22×C4—1061no—
262C22×C4—2121no—
263C22×C4—2121no—
264C22×C4—2121no—
265C22×C4—2121no—
266C22×C4C22⋊#615711yescharacteristic
267C22×C4C22⋊#615711yescharacteristic
268C22×C4C22×#615711yescharacteristic
269C2×C8—2122no—
270C2×C8—2122no—
271C2×C8—2122no—
272C2×C8—2122no—
273C2×C8—2122no—
274C2×C8—2122no—
275C4⋊C4—21no—
276C4⋊C4—41no—
277C4⋊C4—42no—
278C4⋊C4—532no—
279C4⋊C4—1061no—
280C4⋊C4—2121no—
281C4⋊C4—2122no—
282C4⋊C4—2121no—
283C4⋊C4—2121no—
284C4⋊C4—2121no—
285C4⋊C4—2121no—
286C4⋊C4D53⋊C812yes—
287C22⋊C4—1064no—
288C22⋊C4—2122no—
289C42—41no—
290C42—1062no—
291C42—1062no—
292C42—1064no—
293C42—2121no—
294C42—2122no—
295C23—532no—
296C23—1061no—
297C23—1061no—
298C23—1061no—
299C23—1061no—
300C23—1061no—
301C23—1061no—
302C23C2×C22⋊#615711yescharacteristic
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—532no—
318C2×C4—532no—
319C2×C4—532no—
320C2×C4—531no—
321C2×C4—531no—
322C2×C4—531no—
323C2×C4—531no—
324C2×C4—1064no—
325C2×C4—1064no—
326C2×C4—1061no—
327C2×C4—1061no—
328C2×C4—1061no—
329C2×C4—1061no—
330C2×C4—1062no—
331C2×C4—2122no—
332C2×C4—2122no—
333C2×C4—2122no—
334C2×C4—2122no—
335C2×C4—2121no—
336C2×C4—2121no—
337C2×C4—2121no—
338C2×C4—2121no—
339C2×C4—2121no—
340C2×C4C2×D53⋊C811yescharacteristic
341C2×C4D53⋊M1611yescharacteristic
342C8—4242no—
343C8—4242no—
344C22—1062no—
345C22—1062no—
346C22—1062no—
347C22—2121no—
348C22—2121no—
349C22—2121no—
350C22—2121no—
351C22D53⋊(C22⋊C8)11yescharacteristic
352C22D53⋊#9911yescharacteristic
353C22D53⋊#10111yescharacteristic
354C22#1681161411yescharacteristic
355C22#1681161411yescharacteristic
356C22#1681162111yescharacteristic
357C22#1681162211yescharacteristic
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—42no—
363C4—81no—
364C4—534no—
365C4—1061no—
366C4—1061no—
367C4—1061no—
368C4—1061no—
369C4—4241no—
370C4—2122no—
371C2—2122no—
372C2D53⋊#32411yescharacteristic
373C2#2029001111yescharacteristic
374C2#2029001311yescharacteristic
375C2#2029013111yescharacteristic
376C2#2029013311yescharacteristic
377C2#2029020711yescharacteristic
378C2#2029025511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6157
commutatorC2×C4×C53C22×C8
FrattiniC22×C4C22×#6157
FittingC53×#389C4
socleC23×C53C2×C22⋊C4
prime radicalC23×D53C22⋊C4
cosocleC2×C4×Dic53C23
hypercenter#389#6157
hypocenterC53#7598
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
3. #20289534C2semidirect
4. #20289533C2semidirect
34. #13133175C8semidirect
212. C53#7598semidirect

Maximal subgroups

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

subgroupindex
#202905722
#202895342
#202895332
#202771962
#759853