Finite Group Databasebeta

← #14726899

Subgroups — #14726899

Order 2816.

958 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 203 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#13078620C212yesmaximal
2#13073521C211yesmaximal, characteristic
3#13067624C214yesmaximal, complemented
4#13067556C214yesmaximal
5#13067180C212yesmaximal, complemented
6#13066940C211yesmaximal, characteristic, complemented
7C11×#3502C211yesmaximal, characteristic, complemented
8Q82×C11—22no—
9C11×#557—22no—
10C11×#557—24no—
11C11×#544—21no—
12C11×#544C2214yes—
13C11×#533—22no—
14C11×#533C2212yes—
15C11×#519—21no—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999—21no—
18C2×C4×D44C2211yescharacteristic
19#10622697—22no—
20#10622696—22no—
21#10622659C2214yes—
22#10622656C2214yes—
23C4×#4325—24no—
24#10622604C2212yes—
25#10622600—21no—
26#10622596C2212yes—
27#10622553—22no—
28#10622549C2211yescharacteristic
29#10622538C2212yes—
30#10622176C2218yes—
31#10622166C2214yes—
32C22×Q8×C11D411yescharacteristic
33C22×D44C2311yescharacteristic
34C22×C4×D11—21no—
35C11×C4⋊Q8—22no—
36C11×C4⋊Q8—22no—
37C11×C4⋊Q8—24no—
38C11×C4⋊Q8—28no—
39C11×C4⋊Q8D412yes—
40C11×C4⋊Q8D412yes—
41C11×#125—24no—
42C11×#125—24no—
43C11×#125—28no—
44C11×#125—22no—
45C11×C22⋊Q8—22no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8C2314yes—
48C4×Q8×C11—24no—
49C4×Q8×C11—24no—
50C4×Q8×C11—24no—
51C4×Q8×C11—24no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C4×Q8×C11D414yes—
56C11×#117—24no—
57C11×#117—22no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C42×C11D412yes—
61C2×C42×C11C2311yescharacteristic
62#66999—44no—
63C2×#4325—24no—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—22no—
70C4×D44—22no—
71C4×D44—22no—
72#66899—24no—
73C11⋊#95—21no—
74C11⋊#95—22no—
75C11⋊#95C2312yes—
76C22⋊(C11⋊C8)C2314yes—
77#66873—24no—
78#66872—24no—
79C4⋊(C11⋊C8)—22no—
80C4×C11⋊C8—22no—
81#18220—111nomaximal, Sylow
82C23×D11—21no—
83C2×Q8×C11—24no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11SD1614yescomplemented
88C2×Q8×C11C2×D414yes—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2411yescharacteristic
94C22×Dic11—22no—
95C22×Dic11—21no—
96C2×D44—22no—
97C2×D44—42no—
98C2×C4×D11—42no—
99C2×C4×D11—42no—
100C2×C4×D11—42no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—28no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4C2×D414yes—
113C11×C22⋊C4—24no—
114C42×C11—28no—
115C42×C11—22no—
116C42×C11—22no—
117C42×C11—24no—
118C42×C11C2×D412yes—
119C42×C11C2×D412yes—
120#4325—48no—
121(C2×D11)⋊C4—44no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—44no—
125C4⋊Dic11—22no—
126C4⋊Dic11—42no—
127Dic11⋊C4—44no—
128C2×C11⋊C8—24no—
129#3502D1111yescharacteristic, complemented
130#3101—112no—
131#2536—111no—
132#1611—114no—
133#1599—114no—
134#1518—112no—
135#1461—111no—
136C23×C11C22×D411yescharacteristic
137C22×D11—22no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144Q8×C11—28no—
145Q8×C11—44no—
146Q8×C11—44no—
147Q8×C11—84no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12012yes—
159C2×C4×C11C2×SD1614yes—
160C2×C4×C11C2×SD1612yes—
161C2×C4×C11#13712yes—
162C2×C4×C11C22×D412yes—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—42no—
168C2×Dic11—41no—
169D44—24no—
170D44—42no—
171C4×D11—84no—
172C11⋊C8—44no—
173Q82—22no—
174#557—22no—
175#557—24no—
176#544—21no—
177#544C2×D1114yes—
178#533—22no—
179#533C2×D1112yes—
180C2×C22⋊Q8—221no—
181#519—21no—
182C2×C4×Q8C2×D1111yescharacteristic
183C2×C4×D4—111no—
184#483—114no—
185#476—222no—
186#461—222no—
187#450—114no—
188C4×SD16—224no—
189#431—112no—
190#398—112no—
191#394—112no—
192#388—222no—
193#382—111no—
194#380—221no—
195#328—118no—
196#324—114no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11C2×#12011yescharacteristic
200C22×C11C22×SD1611yescharacteristic
201C22×C11C2×#13711yescharacteristic
202C2×D11—42no—
203C2×D11—42no—
204C2×D11—42no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C2×D11—81no—
209C4×C11—24no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—22no—
213C4×C11—44no—
214C4×C11—42no—
215C4×C11—44no—
216C4×C11#44814yes—
217Dic11—82no—
218Dic11—81no—
219C22×Q8C22⋊D1111yescharacteristic
220C22×D4—111no—
221C23×C4—221no—
222C2×SD16—224no—
223C4⋊Q8—22no—
224C4⋊Q8—22no—
225C4⋊Q8—24no—
226C4⋊Q8—28no—
227C4⋊Q8C22⋊D1112yes—
228C4⋊Q8C22⋊D1112yes—
229#125—24no—
230#125—24no—
231#125—28no—
232#125—22no—
233C22⋊Q8—22no—
234C22⋊Q8—24no—
235C22⋊Q8—444no—
236C22⋊Q8C22×D1114yes—
237C4×Q8—24no—
238C4×Q8—24no—
239C4×Q8—24no—
240C4×Q8—24no—
241C4×Q8—22no—
242C4×Q8—22no—
243C4×Q8—22no—
244C4×Q8C22⋊D1114yes—
245C4×D4—222no—
246C4×D4—222no—
247#117—24no—
248#117—22no—
249C2×C4⋊C4—111no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4—222no—
252C2×C4⋊C4C22⋊D1111yescharacteristic
253C2×C4⋊C4C22×D1112yes—
254C2×C22⋊C4—221no—
255C2×C22⋊C4—222no—
256C2×C22⋊C4—222no—
257C2×C42C22⋊D1112yes—
258C2×C42C22×D1111yescharacteristic
259#106—224no—
260C4⋊C8—222no—
261#103—224no—
262#102—224no—
263C22⋊C8—114no—
264C4×C8—222no—
265#95—112no—
266#95—222no—
267#95—221no—
268C2×C11—21no—
269C2×C11—21no—
270C2×C11C2×#44811yescharacteristic
271C2×C11#302011yescharacteristic
272C2×C11#302511yescharacteristic
273D11—82no—
274C24—221no—
275C2×Q8—24no—
276C2×Q8—22no—
277C2×Q8—22no—
278C2×Q8—22no—
279C2×Q8#432514yescomplemented
280C2×Q8C2×C22⋊D1114yes—
281C2×D4—222no—
282C2×D4—442no—
283C22×C4—222no—
284C22×C4—221no—
285C22×C4—442no—
286C22×C4—442no—
287C22×C4—442no—
288C22×C4C2×C22⋊D1112yes—
289C22×C4C2×C22⋊D1112yes—
290C22×C4C2×C22⋊D1111yescharacteristic
291C22×C4C2×C22⋊D1111yescharacteristic
292C22×C4C23×D1111yescharacteristic
293SD16—448no—
294C2×C8—224no—
295C4⋊C4—24no—
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—28no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—24no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—222no—
307C4⋊C4—444no—
308C4⋊C4—442no—
309C4⋊C4C2×C22⋊D1114yes—
310C22⋊C4—24no—
311C22⋊C4—444no—
312C22⋊C4—444no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C42—28no—
316C42—22no—
317C42—22no—
318C42—24no—
319C42C2×C22⋊D1112yes—
320C42C2×C22⋊D1112yes—
321C11#1822011yescharacteristic, complemented, Sylow
322C23—222no—
323C23—441no—
324C23—441no—
325C23—441no—
326C23—441no—
327C23—441no—
328C23—441no—
329C23C22×C22⋊D1111yescharacteristic
330Q8—28no—
331Q8—44no—
332Q8—44no—
333Q8—84no—
334D4—224no—
335D4—442no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—884no—
351C2×C4C2×#432514yes—
352C2×C4C2×#432512yes—
353C2×C4#6699512yes—
354C2×C4#6700611yescharacteristic
355C2×C4#6700611yescharacteristic
356C2×C4#6700612yes—
357C2×C4C22×C22⋊D1112yes—
358C8—444no—
359C22—21no—
360C22—21no—
361C22—442no—
362C22—442no—
363C22—442no—
364C22—881no—
365C22—881no—
366C22—881no—
367C22—881no—
368C22C22×#432511yescharacteristic
369C22C2×#6699511yescharacteristic
370C22C2×#6700611yescharacteristic
371C4—24no—
372C4—21no—
373C4—21no—
374C4—22no—
375C4—44no—
376C4—42no—
377C4—44no—
378C4—882no—
379C4—881no—
380C4#1062284014yes—
381C2—21no—
382C2—21no—
383C2—882no—
384C2C2×#1062284011yescharacteristic
385C2#1307798011yescharacteristic
386C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3502C2
socleC22×C11C2×#120
prime radicalC22×D44C23
hypercenter#3502D11
hypocenterC11#18220
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3502

Complements

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

NH ≅ G/Ntype
3. #13067624C2semidirect
5. #13067180C2semidirect
6. #13066940C2semidirect
7. C11×#3502C2semidirect
87. C2×Q8×C11SD16semidirect
129. #3502D11semidirect
279. C2×Q8#4325semidirect
321. C11#18220semidirect

Maximal subgroups

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

subgroupindex
#130786202
#130735212
#130676242
#130675562
#130671802
#130669402
C11×#35022
#1822011