Finite Group Databasebeta

← #14787636

Subgroups — #14787636

Order 2816.

1122 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1122 conjugacy classes of subgroups — too many to draw. Only its 191 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#13076935C212yesmaximal, complemented
2#13071098C211yesmaximal, characteristic, complemented
3#13069968C212yesmaximal, complemented
4#13069864C212yesmaximal
5#13069075C212yesmaximal, complemented
6#13068897C214yesmaximal, complemented
7#13068693C211yesmaximal, characteristic, complemented
8C11×#3491C211yesmaximal, characteristic
9C11×#552—24no—
10C11×#551—24no—
11C11×#543C2211yescharacteristic
12C11×#539—22no—
13C11×#534C2211yescharacteristic
14C11×#529—22no—
15C2×C11×#123C2212yes—
16C11×#518C2212yes—
17C2×C11×#117C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20#10622833C2214yes—
21C2×#66898C2214yes—
22#10622824C2212yes—
23#10622591—24no—
24#10622586—22no—
25#10622559C2212yes—
26#10622559C2212yes—
27#10622559C2214yes—
28#10622557—24no—
29C4×Dic11⋊C4—22no—
30#10622164C2214yes—
31#10622164C2212yes—
32#10622164C2212yes—
33C22×D4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×Dic11C2312yes—
36C11×#126—24no—
37C11×#126—24no—
38C11×#125—22no—
39C11×#125—24no—
40C11×#124—22no—
41C11×#123—24no—
42C11×#123—22no—
43C11×#123—22no—
44C11×#123—24no—
45C11×#123—22no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—22no—
48C11×C22⋊Q8—24no—
49C11×#121—22no—
50C11×#120—22no—
51C4×Q8×C11—22no—
52C4×D4×C11—22no—
53C4×D4×C11—24no—
54C4×D4×C11—24no—
55C11×#117—24no—
56C11×#117—24no—
57C11×#117—22no—
58C2×C11×C4⋊C4D412yes—
59C2×C11×C4⋊C4D414yes—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4D414yes—
62C2×C11×C22⋊C4C2311yescharacteristic
63C2×C11×C22⋊C4C2311yescharacteristic
64C2×C11×C22⋊C4C2312yes—
65C2×C42×C11D412yes—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11C2314yes—
68C2×C22⋊Dic11C2312yes—
69#66979—24no—
70C2×C4⋊Dic11—21no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—24no—
74C2×C4×Dic11—21no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—21no—
78#66898—28no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84#24113—111nomaximal, Sylow
85C24×C11C2×D412yes—
86C24×C11C2411yescharacteristic
87C2×Q8×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—24no—
91C2×D4×C11—24no—
92C2×D4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—24no—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D414yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D414yes—
103C22×Dic11—22no—
104C22×Dic11—24no—
105C22×Dic11—22no—
106C22×Dic11—24no—
107C22×Dic11—44no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—24no—
115C11×C22⋊C4—24no—
116C11×C22⋊C4—24no—
117C11×C22⋊C4—22no—
118C11×C22⋊C4—22no—
119C11×C22⋊C4—22no—
120C11×C22⋊C4—22no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—24no—
123C42×C11—24no—
124C42×C11—22no—
125C42×C11—22no—
126C22⋊Dic11—22no—
127C22⋊Dic11—24no—
128C22⋊Dic11—24no—
129C22⋊Dic11—48no—
130C22⋊Dic11#4114yes—
131C4⋊Dic11—24no—
132Dic11⋊C4—44no—
133Dic11⋊C4—44no—
134Dic11⋊C4—48no—
135C4×Dic11—24no—
136C4×Dic11—42no—
137C4×Dic11—42no—
138#3491D1111yescharacteristic
139#2853—112no—
140#2296—111no—
141#2062—112no—
142#2044—112no—
143#1899—112no—
144#1867—114no—
145#1820—111no—
146C23×C11—22no—
147C23×C11—24no—
148C23×C11—42no—
149C23×C11—44no—
150C23×C11C22×D411yescharacteristic
151C23×C11C22×D412yes—
152C23×C11C2×#4112yes—
153C23×C112−1+412yes—
154Q8×C11—82no—
155D4×C11—42no—
156D4×C11—42no—
157D4×C11—44no—
158D4×C11—82no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—28no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—42no—
170C2×C4×C11—44no—
171C2×C4×C11—42no—
172C2×C4×C11—84no—
173C2×C4×C11#12012yes—
174C2×C4×C11#12012yes—
175C2×Dic11—24no—
176C2×Dic11—28no—
177C2×Dic11—24no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—44no—
182C2×Dic11—42no—
183C2×Dic11—44no—
184C2×Dic11—44no—
185C2×Dic11—44no—
186#552—24no—
187#551—24no—
188#543C2×D1111yescharacteristic
189#539—22no—
190#534C2×D1111yescharacteristic
191#529—22no—
192C2×#123C2×D1112yes—
193#518C2×D1112yes—
194C2×#117—111no—
195C2×#117C2×D1111yescharacteristic
196C22×C42—111no—
197C2×#99—114no—
198#389—222no—
199#388—224no—
200#387—224no—
201#386—114no—
202#385—114no—
203#385—112no—
204#385—112no—
205#381—112no—
206C4×C4⋊C4—222no—
207#342—112no—
208#342—114no—
209#342—112no—
210C22×C11—22no—
211C22×C11—24no—
212C22×C11—42no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—44no—
216C22×C11—84no—
217C22×C11C2×#12011yescharacteristic
218C22×C11#52511yescharacteristic
219C22×C11#53611yescharacteristic
220C22×C11#54714yes—
221C4×C11—22no—
222C4×C11—22no—
223C4×C11—42no—
224C4×C11—42no—
225C4×C11—44no—
226C4×C11—42no—
227Dic11—44no—
228Dic11—44no—
229Dic11—84no—
230C22×D4C22×D1112yes—
231C23×C4—112no—
232C23×C4C22×D1111yescharacteristic
233#126—24no—
234#126—24no—
235#125—22no—
236#125—24no—
237#124—22no—
238#123—24no—
239#123—22no—
240#123—22no—
241#123—24no—
242#123—22no—
243C22⋊Q8—24no—
244C22⋊Q8—22no—
245C22⋊Q8—24no—
246#121—22no—
247#120—22no—
248C4×Q8—22no—
249C4×D4—22no—
250C4×D4—24no—
251C4×D4—24no—
252#117—24no—
253#117—24no—
254#117—22no—
255#117—224no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—222no—
258C2×C4⋊C4—222no—
259C2×C4⋊C4—224no—
260C2×C4⋊C4C22⋊D1112yes—
261C2×C4⋊C4C22⋊D1114yes—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—112no—
264C2×C22⋊C4—114no—
265C2×C22⋊C4—224no—
266C2×C22⋊C4C22⋊D1114yes—
267C2×C22⋊C4C22×D1111yescharacteristic
268C2×C22⋊C4C22×D1111yescharacteristic
269C2×C22⋊C4C22×D1112yes—
270C2×C42—221no—
271C2×C42—221no—
272C2×C42—224no—
273C2×C42—221no—
274C2×C42C22⋊D1112yes—
275#99—228no—
276#95—222no—
277#95—222no—
278#95—224no—
279#95—224no—
280#95—224no—
281C2×C11—21no—
282C2×C11—24no—
283C2×C11—21no—
284C2×C11—82no—
285C2×C11#240611yescharacteristic
286C2×C11#302512yes—
287C24C2×C22⋊D1112yes—
288C24C23×D1111yescharacteristic
289C2×Q8—22no—
290C2×D4—24no—
291C2×D4—24no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—24no—
298C22×C4—224no—
299C22×C4—222no—
300C22×C4—222no—
301C22×C4—224no—
302C22×C4—444no—
303C22×C4C2×C22⋊D1112yes—
304C22×C4C2×C22⋊D1114yes—
305C22×C4C2×C22⋊D1111yescharacteristic
306C22×C4C2×C22⋊D1111yescharacteristic
307C22×C4C2×C22⋊D1112yes—
308C22×C4C2×C22⋊D1112yes—
309C22×C4C2×C22⋊D1114yes—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—24no—
315C4⋊C4—24no—
316C4⋊C4—24no—
317C4⋊C4—224no—
318C4⋊C4—448no—
319C4⋊C4—444no—
320C4⋊C4—444no—
321C22⋊C4—24no—
322C22⋊C4—24no—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—24no—
328C22⋊C4—24no—
329C22⋊C4—114no—
330C22⋊C4—222no—
331C22⋊C4—224no—
332C22⋊C4—224no—
333C22⋊C4—448no—
334C42—24no—
335C42—22no—
336C42—22no—
337C42—224no—
338C42—442no—
339C42—442no—
340C11#2411311yescharacteristic, complemented, Sylow
341C23—22no—
342C23—24no—
343C23—42no—
344C23—44no—
345C23#41×D1112yes—
346C23#6704312yes—
347C23C22×C22⋊D1112yes—
348C23C22×C22⋊D1111yescharacteristic
349Q8—82no—
350D4—44no—
351D4—42no—
352D4—42no—
353D4—82no—
354C2×C4—28no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—24no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—24no—
364C2×C4—42no—
365C2×C4—44no—
366C2×C4—42no—
367C2×C4—84no—
368C2×C4—228no—
369C2×C4—224no—
370C2×C4—224no—
371C2×C4—442no—
372C2×C4—442no—
373C2×C4—442no—
374C2×C4—444no—
375C2×C4—442no—
376C2×C4—444no—
377C2×C4—444no—
378C2×C4—444no—
379C2×C4#6700612yes—
380C2×C4#6700612yes—
381C22—22no—
382C22—24no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—44no—
387C22—84no—
388C22#1062335514yes—
389C22#1062335611yescharacteristic
390C22#1062335911yescharacteristic
391C22C2×#6700611yescharacteristic
392C4—22no—
393C4—22no—
394C4—42no—
395C4—42no—
396C4—44no—
397C4—42no—
398C4—444no—
399C4—444no—
400C4—884no—
401C2—21no—
402C2—24no—
403C2—21no—
404C2—82no—
405C2#1307194711yescharacteristic
406C2#1307800812yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#3491C2
socleC22×C11C2×#120
prime radicalC11×#534C22
hypercenter#3491D11
hypocenterC11#24113
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3491

Complements

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

NH ≅ G/Ntype
1. #13076935C2semidirect
2. #13071098C2semidirect
3. #13069968C2semidirect
5. #13069075C2semidirect
6. #13068897C2semidirect
7. #13068693C2semidirect
340. C11#24113semidirect

Maximal subgroups

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

subgroupindex
#130769352
#130710982
#130699682
#130698642
#130690752
#130688972
#130686932
C11×#34912
#2411311