Finite Group Databasebeta

← #14726824

Subgroups — #14726824

Order 2816.

1254 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1254 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#13078643C212yesmaximal, complemented
2#13073970C211yesmaximal, characteristic, complemented
3#13067636C214yesmaximal, complemented
4#13067568C214yesmaximal, complemented
5#13067176C212yesmaximal, complemented
6#13066937C211yesmaximal, characteristic, complemented
7C11×#3496C211yesmaximal, characteristic
8C2×C11×H(5,𝔽2)—21no—
9C11×#547—22no—
10C11×#546—24no—
11D42×C11—22no—
12C11×#537—21no—
13C11×#534C2214yes—
14C11×#532C2212yes—
15C2×C11×#121—22no—
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic, complemented
18#10622834—21no—
19#10622823—22no—
20#10622707—22no—
21#10622688—22no—
22#10622653C2214yescomplemented
23#10622647C2214yescomplemented
24C4×#4324—24no—
25#10622586—21no—
26#10622562C2212yescomplemented
27#10622560C2212yescomplemented
28#10622549C2211yescharacteristic, complemented
29#10622538C2212yescomplemented
30#10622175C2218yescomplemented
31#10622163C2214yescomplemented
32C11×H(5,𝔽2)—44no—
33C11×H(5,𝔽2)—44no—
34C2×C11×#41—24no—
35C2×C11×#41—22no—
36C22×D4×C11—24no—
37C22×D4×C11—24no—
38C22×D4×C11—22no—
39C22×D4×C11D411yescharacteristic
40C23×C4×C11D412yes—
41C22×Dic22C2311yescharacteristic
42C11×C4⋊Q8D412yes—
43C11×#127D412yes—
44C11×#124—22no—
45C11×#123—28no—
46C11×C22⋊Q8—24no—
47C11×#121—24no—
48C11×#121—24no—
49C11×#121—24no—
50C11×#121—22no—
51C11×#121—24no—
52C11×#121C2314yes—
53C11×#120—28no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C4×D4×C11D414yes—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C22⋊C4—24no—
61C2×C11×C22⋊C4C2312yes—
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11—22no—
64C2×C22⋊Dic11—22no—
65C2×#4324—24no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—22no—
70C2×C4×Dic11—21no—
71C4×Dic22—22no—
72C4×Dic22—22no—
73#66896—24no—
74C11⋊#95—21no—
75C11⋊#95—22no—
76C11⋊#95C2312yes—
77C22⋊(C11⋊C8)C2314yes—
78#66874—24no—
79#66872—24no—
80C4⋊(C11⋊C8)—22no—
81C4×C11⋊C8—22no—
82#18211—111nomaximal, Sylow
83C24×C11—24no—
84C24×C11C2×D412yes—
85C11×#41—416no—
86C11×#41—44no—
87C11×#41—44no—
88C2×Q8×C11—22no—
89C2×D4×C11—28no—
90C2×D4×C11—24no—
91C2×D4×C11—24no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—416no—
97C2×D4×C11—48no—
98C2×D4×C11—48no—
99C2×D4×C11—84no—
100C2×D4×C11SD1614yescomplemented
101C2×D4×C11C2×D414yes—
102C22×C4×C11—24no—
103C22×C4×C11—22no—
104C22×C4×C11—24no—
105C22×C4×C11—22no—
106C22×C4×C11—82no—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11—21no—
114C2×Dic22—22no—
115C2×Dic22—42no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4C2×D414yes—
120C11×C22⋊C4—28no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—24no—
124C42×C11C2×D412yes—
125C42×C11C2×D412yes—
126C22⋊Dic11—44no—
127C22⋊Dic11—82no—
128#4324—48no—
129C4⋊Dic11—22no—
130C4⋊Dic11—42no—
131Dic11⋊C4—41no—
132Dic11⋊C4—41no—
133Dic11⋊C4—82no—
134C4×Dic11—42no—
135C2×C11⋊C8—24no—
136#3496D1111yescharacteristic
137#3103—112no—
138#2580—111no—
139#1613—114no—
140#1601—114no—
141#1517—112no—
142#1460—111no—
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—24no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11—48no—
149C23×C11—84no—
150C23×C11—84no—
151C23×C11C2×SD1614yes—
152C23×C11C22×D411yescharacteristic
153Q8×C11—44no—
154D4×C11—28no—
155D4×C11—44no—
156D4×C11—44no—
157D4×C11—416no—
158D4×C11—44no—
159D4×C11—44no—
160D4×C11—44no—
161D4×C11—84no—
162C2×C4×C11—22no—
163C2×C4×C11—24no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—44no—
167C2×C4×C11—48no—
168C2×C4×C11—48no—
169C2×C4×C11—42no—
170C2×C4×C11—82no—
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12012yes—
174C2×C4×C11C2×SD1612yes—
175C2×C4×C11AGL(1,ℤ/8)12yes—
176C2×C4×C11C22×D412yes—
177C2×Dic11—22no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—42no—
186Dic22—24no—
187Dic22—42no—
188C11⋊C8—44no—
189C2×H(5,𝔽2)—21no—
190#547—22no—
191#546—24no—
192D42—22no—
193#537—21no—
194#534C2×D1114yes—
195#532C2×D1112yes—
196C2×#121—22no—
197C2×C4×Q8—111no—
198C2×C4×D4C2×D1111yescharacteristic
199#481—114no—
200#475—222no—
201#460—222no—
202#448—114no—
203C4×SD16—224no—
204#431—112no—
205#399—112no—
206#393—112no—
207#390—221no—
208#389—221no—
209#385—222no—
210#382—111no—
211#327—118no—
212#323—114no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—24no—
216C22×C11—44no—
217C22×C11—42no—
218C22×C11—42no—
219C22×C11—44no—
220C22×C11—44no—
221C22×C11—44no—
222C22×C11—82no—
223C22×C11—168no—
224C22×C11C2×#12011yescharacteristic
225C22×C11C22×SD1611yescharacteristic
226C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—22no—
230C4×C11—44no—
231C4×C11—42no—
232C4×C11#45014yes—
233Dic11—42no—
234Dic11—82no—
235Dic11—81no—
236H(5,𝔽2)—44no—
237H(5,𝔽2)—44no—
238C2×#41—24no—
239C2×#41—22no—
240C22×Q8—111no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—22no—
244C22×D4C22⋊D1111yescharacteristic
245C23×C4C22⋊D1112yes—
246C2×SD16—224no—
247C4⋊Q8C22⋊D1112yes—
248#127C22⋊D1112yes—
249#124—22no—
250#123—28no—
251C22⋊Q8—24no—
252#121—24no—
253#121—24no—
254#121—24no—
255#121—22no—
256#121—24no—
257#121C22×D1114yes—
258#120—28no—
259C4×Q8—222no—
260C4×Q8—222no—
261C4×D4—22no—
262C4×D4—22no—
263C4×D4—22no—
264C4×D4C22⋊D1114yes—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—222no—
270C2×C4⋊C4C22⋊D1111yescharacteristic
271C2×C22⋊C4—24no—
272C2×C22⋊C4—222no—
273C2×C22⋊C4—222no—
274C2×C22⋊C4C22×D1112yes—
275C2×C42—221no—
276C2×C42C22×D1111yescharacteristic
277#106—224no—
278C4⋊C8—222no—
279#103—224no—
280#102—224no—
281C22⋊C8—114no—
282C4×C8—222no—
283#95—112no—
284#95—221no—
285#95—222no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—44no—
289C2×C11—84no—
290C2×C11C2×#45011yescharacteristic
291C2×C11#301911yescharacteristic
292C2×C11#302511yescharacteristic
293C24—24no—
294C24C2×C22⋊D1112yes—
295#41—416no—
296#41—44no—
297#41—44no—
298C2×Q8—22no—
299C2×Q8—222no—
300C2×Q8—442no—
301C2×D4—28no—
302C2×D4—24no—
303C2×D4—24no—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—416no—
309C2×D4—48no—
310C2×D4—48no—
311C2×D4—84no—
312C2×D4#432414yescomplemented
313C2×D4C2×C22⋊D1114yes—
314C22×C4—24no—
315C22×C4—22no—
316C22×C4—24no—
317C22×C4—22no—
318C22×C4—82no—
319C22×C4—221no—
320C22×C4—222no—
321C22×C4—221no—
322C22×C4C2×C22⋊D1112yes—
323C22×C4C2×C22⋊D1111yescharacteristic
324C22×C4C2×C22⋊D1111yescharacteristic
325C22×C4C23×D1111yescharacteristic
326SD16—448no—
327C2×C8—224no—
328C4⋊C4—24no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—222no—
332C4⋊C4—442no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C4⋊C4—882no—
336C4⋊C4C2×C22⋊D1114yes—
337C22⋊C4—28no—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—444no—
342C22⋊C4—882no—
343C42—442no—
344C42C2×C22⋊D1112yes—
345C42C2×C22⋊D1112yes—
346C11#1821111yescharacteristic, complemented, Sylow
347C23—22no—
348C23—22no—
349C23—24no—
350C23—42no—
351C23—42no—
352C23—48no—
353C23—84no—
354C23—84no—
355C23C2×#432414yes—
356C23C22×C22⋊D1111yescharacteristic
357Q8—44no—
358Q8—224no—
359Q8—442no—
360D4—28no—
361D4—44no—
362D4—44no—
363D4—416no—
364D4—44no—
365D4—44no—
366D4—44no—
367D4—84no—
368C2×C4—22no—
369C2×C4—24no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—44no—
373C2×C4—48no—
374C2×C4—48no—
375C2×C4—42no—
376C2×C4—82no—
377C2×C4—222no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—442no—
381C2×C4—441no—
382C2×C4—442no—
383C2×C4—441no—
384C2×C4—442no—
385C2×C4—441no—
386C2×C4#6698512yes—
387C2×C4C2×#432412yes—
388C2×C4#6700611yescharacteristic
389C2×C4#6700611yescharacteristic
390C2×C4#6700612yes—
391C2×C4C22×C22⋊D1112yes—
392C8—444no—
393C22—21no—
394C22—21no—
395C22—24no—
396C22—44no—
397C22—42no—
398C22—42no—
399C22—44no—
400C22—44no—
401C22—44no—
402C22—82no—
403C22—168no—
404C22C2×#6698511yescharacteristic
405C22C22×#432411yescharacteristic
406C22C2×#6700611yescharacteristic
407C4—21no—
408C4—21no—
409C4—22no—
410C4—44no—
411C4—42no—
412C4—442no—
413C4—882no—
414C4—881no—
415C4#1062283114yes—
416C2—21no—
417C2—21no—
418C2—44no—
419C2—84no—
420C2C2×#1062283111yescharacteristic
421C2#1307797311yescharacteristic
422C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3496C2
socleC22×C11C2×#120
hypercenter#3496D11
hypocenterC11#18211
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #13078643C2semidirect
2. #13073970C2semidirect
3. #13067636C2semidirect
4. #13067568C2semidirect
5. #13067176C2semidirect
6. #13066937C2semidirect
17. C2×C4×Dic22C22semidirect
22. #10622653C22semidirect
23. #10622647C22semidirect
26. #10622562C22semidirect
27. #10622560C22semidirect
28. #10622549C22semidirect
29. #10622538C22semidirect
30. #10622175C22semidirect
31. #10622163C22semidirect
100. C2×D4×C11SD16semidirect
312. C2×D4#4324semidirect
346. C11#18211semidirect

Maximal subgroups

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

subgroupindex
#130786432
#130739702
#130676362
#130675682
#130671762
#130669372
C11×#34962
#1821111