Finite Group Databasebeta

← #14726817

Subgroups — #14726817

Order 2816.

1338 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1338 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#13078612C212yesmaximal, complemented
2#13073513C211yesmaximal, characteristic, complemented
3#13067602C214yesmaximal, complemented
4#13067534C214yesmaximal, complemented
5#13067176C212yesmaximal, complemented
6#13066937C211yesmaximal, characteristic, complemented
7C11×#3496C211yesmaximal, characteristic, complemented
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×#66991—21no—
18C2×C4×D44C2211yescharacteristic, complemented
19#10622826—22no—
20#10622700—22no—
21#10622685—22no—
22#10622649C2214yescomplemented
23#10622646C2214yescomplemented
24C4×#4323—24no—
25#10622600—21no—
26#10622573C2212yescomplemented
27#10622566C2212yescomplemented
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×C22⋊D11—22no—
42C22×D44C2311yescharacteristic
43C22×C4×D11—21no—
44C11×C4⋊Q8D412yescomplemented
45C11×#127D412yescomplemented
46C11×#124—22no—
47C11×#123—28no—
48C11×C22⋊Q8—24no—
49C11×#121—24no—
50C11×#121—24no—
51C11×#121—24no—
52C11×#121—22no—
53C11×#121—24no—
54C11×#121C2314yes—
55C11×#120—28no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C4×D4×C11D414yescomplemented
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4C2312yes—
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—22no—
66#66991—44no—
67C2×#4323—24no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11C2311yescharacteristic
72C4×D44—22no—
73C4×D44—22no—
74#66896—24no—
75C11⋊#95—21no—
76C11⋊#95—22no—
77C11⋊#95C2312yes—
78C22⋊(C11⋊C8)C2314yes—
79#66873—24no—
80#66871—24no—
81C4⋊(C11⋊C8)—22no—
82C4×C11⋊C8—22no—
83#18210—111nomaximal, Sylow
84C24×C11—24no—
85C24×C11C2×D412yes—
86C23×D11—21no—
87C11×#41—416no—
88C11×#41—44no—
89C11×#41—44no—
90C2×Q8×C11—22no—
91C2×D4×C11—28no—
92C2×D4×C11—24no—
93C2×D4×C11—24no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—416no—
99C2×D4×C11—48no—
100C2×D4×C11—48no—
101C2×D4×C11—84no—
102C2×D4×C11D814yescomplemented
103C2×D4×C11C2×D414yes—
104C22×C4×C11—24no—
105C22×C4×C11—22no—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11—82no—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C2×C22⋊D11—44no—
114C2×C22⋊D11—44no—
115C2×C22⋊D11—82no—
116C22×Dic11—22no—
117C22×Dic11—21no—
118C2×D44—22no—
119C2×D44—42no—
120C2×C4×D11—42no—
121C2×C4×D11—42no—
122C2×C4×D11—42no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4C2×D414yes—
127C11×C22⋊C4—28no—
128C11×C22⋊C4—24no—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—24no—
131C42×C11C2×D412yes—
132C42×C11C2×D412yes—
133C22⋊Dic11—44no—
134#4323—48no—
135(C2×D11)⋊C4—41no—
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—82no—
138C4⋊Dic11—22no—
139C4⋊Dic11—42no—
140C2×C11⋊C8—24no—
141#3496D1111yescharacteristic, complemented
142#3100—112no—
143#2535—111no—
144#1607—114no—
145#1595—114no—
146#1517—112no—
147#1460—111no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11—24no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11—48no—
154C23×C11—84no—
155C23×C11—84no—
156C23×C11C2×D814yes—
157C23×C11C22×D411yescharacteristic
158C22×D11—22no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165Q8×C11—44no—
166D4×C11—28no—
167D4×C11—44no—
168D4×C11—44no—
169D4×C11—416no—
170D4×C11—44no—
171D4×C11—44no—
172D4×C11—44no—
173D4×C11—84no—
174C2×C4×C11—22no—
175C2×C4×C11—24no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—44no—
179C2×C4×C11—48no—
180C2×C4×C11—48no—
181C2×C4×C11—42no—
182C2×C4×C11—82no—
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12012yes—
186C2×C4×C11C2×D812yes—
187C2×C4×C11AGL(1,ℤ/8)12yes—
188C2×C4×C11C22×D412yes—
189C22⋊D11—88no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—41no—
193C2×Dic11—42no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196D44—24no—
197D44—42no—
198C4×D11—84no—
199C11⋊C8—44no—
200C2×H(5,𝔽2)—21no—
201#547—22no—
202#546—24no—
203D42—22no—
204#537—21no—
205#534C2×D1114yes—
206#532C2×D1112yes—
207C2×#121—22no—
208C2×#121—221no—
209C2×C4×D4—111no—
210C2×C4×D4C2×D1111yescharacteristic
211#480—114no—
212#474—222no—
213#459—222no—
214#447—114no—
215C4×D8—224no—
216#431—112no—
217#397—112no—
218#392—112no—
219#386—222no—
220#382—111no—
221#380—221no—
222#327—118no—
223#323—114no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—24no—
227C22×C11—44no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—44no—
231C22×C11—44no—
232C22×C11—44no—
233C22×C11—82no—
234C22×C11—168no—
235C22×C11C2×#12011yescharacteristic
236C22×C11C22×D811yescharacteristic
237C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
238C2×D11—42no—
239C2×D11—42no—
240C2×D11—42no—
241C2×D11—81no—
242C2×D11—81no—
243C2×D11—81no—
244C2×D11—81no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—22no—
248C4×C11—44no—
249C4×C11—42no—
250C4×C11#44714yes—
251Dic11—82no—
252Dic11—81no—
253H(5,𝔽2)—44no—
254H(5,𝔽2)—44no—
255C2×#41—24no—
256C2×#41—22no—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—22no—
260C22×D4—111no—
261C22×D4—222no—
262C22×D4C22⋊D1111yescharacteristic
263C23×C4—221no—
264C23×C4C22⋊D1112yes—
265C2×D8—224no—
266C4⋊Q8C22⋊D1112yescomplemented
267#127C22⋊D1112yescomplemented
268#124—22no—
269#123—28no—
270C22⋊Q8—24no—
271#121—24no—
272#121—24no—
273#121—24no—
274#121—22no—
275#121—24no—
276#121—444no—
277#121C22×D1114yes—
278#120—28no—
279C4×D4—22no—
280C4×D4—22no—
281C4×D4—22no—
282C4×D4—222no—
283C4×D4—222no—
284C4×D4C22⋊D1114yescomplemented
285C2×C4⋊C4—22no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4C22⋊D1111yescharacteristic
289C2×C22⋊C4—24no—
290C2×C22⋊C4—222no—
291C2×C22⋊C4—221no—
292C2×C22⋊C4—222no—
293C2×C22⋊C4C22×D1112yes—
294C2×C42C22×D1111yescharacteristic
295#107—224no—
296C4⋊C8—222no—
297#102—224no—
298#102—224no—
299C22⋊C8—114no—
300C4×C8—222no—
301#95—112no—
302#95—222no—
303#95—221no—
304C2×C11—21no—
305C2×C11—21no—
306C2×C11—44no—
307C2×C11—84no—
308C2×C11C2×#44711yescharacteristic
309C2×C11#301911yescharacteristic
310C2×C11#302511yescharacteristic
311D11—82no—
312C24—24no—
313C24—221no—
314C24C2×C22⋊D1112yes—
315#41—416no—
316#41—44no—
317#41—44no—
318C2×Q8—22no—
319C2×D4—28no—
320C2×D4—24no—
321C2×D4—24no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—416no—
327C2×D4—48no—
328C2×D4—48no—
329C2×D4—84no—
330C2×D4—222no—
331C2×D4—442no—
332C2×D4—444no—
333C2×D4—444no—
334C2×D4—882no—
335C2×D4#432314yescomplemented
336C2×D4C2×C22⋊D1114yes—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—82no—
342C22×C4—222no—
343C22×C4—221no—
344C22×C4—442no—
345C22×C4—442no—
346C22×C4—442no—
347C22×C4C2×C22⋊D1112yes—
348C22×C4C2×C22⋊D1111yescharacteristic
349C22×C4C2×C22⋊D1111yescharacteristic
350C22×C4C23×D1111yescharacteristic
351D8—448no—
352C2×C8—224no—
353C4⋊C4—24no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—222no—
357C4⋊C4—442no—
358C4⋊C4C2×C22⋊D1114yes—
359C22⋊C4—28no—
360C22⋊C4—24no—
361C22⋊C4—24no—
362C22⋊C4—24no—
363C22⋊C4—444no—
364C22⋊C4—441no—
365C22⋊C4—441no—
366C22⋊C4—882no—
367C42C2×C22⋊D1112yes—
368C42C2×C22⋊D1112yes—
369C11#1821011yescharacteristic, complemented, Sylow
370C23—22no—
371C23—22no—
372C23—24no—
373C23—42no—
374C23—42no—
375C23—48no—
376C23—84no—
377C23—84no—
378C23—222no—
379C23—441no—
380C23—441no—
381C23—441no—
382C23—441no—
383C23—441no—
384C23—441no—
385C23C2×#432314yes—
386C23C22×C22⋊D1111yescharacteristic
387Q8—44no—
388D4—28no—
389D4—44no—
390D4—44no—
391D4—416no—
392D4—44no—
393D4—44no—
394D4—44no—
395D4—84no—
396D4—224no—
397D4—442no—
398D4—888no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—44no—
404C2×C4—48no—
405C2×C4—48no—
406C2×C4—42no—
407C2×C4—82no—
408C2×C4—442no—
409C2×C4—442no—
410C2×C4—441no—
411C2×C4—442no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—884no—
415C2×C4C2×#432312yes—
416C2×C4#6698512yes—
417C2×C4#6700611yescharacteristic
418C2×C4#6700611yescharacteristic
419C2×C4#6700612yes—
420C2×C4C22×C22⋊D1112yes—
421C8—444no—
422C22—21no—
423C22—21no—
424C22—24no—
425C22—44no—
426C22—42no—
427C22—42no—
428C22—44no—
429C22—44no—
430C22—44no—
431C22—82no—
432C22—168no—
433C22—442no—
434C22—442no—
435C22—442no—
436C22—881no—
437C22—881no—
438C22—881no—
439C22—881no—
440C22C22×#432311yescharacteristic
441C22C2×#6698511yescharacteristic
442C22C2×#6700611yescharacteristic
443C4—21no—
444C4—21no—
445C4—22no—
446C4—44no—
447C4—42no—
448C4—882no—
449C4—881no—
450C4#1062283014yes—
451C2—21no—
452C2—21no—
453C2—44no—
454C2—84no—
455C2—882no—
456C2C2×#1062283011yescharacteristic
457C2#1307797311yescharacteristic
458C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3496C2
socleC22×C11C2×#120
hypercenter#3496D11
hypocenterC11#18210
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. #13078612C2semidirect
2. #13073513C2semidirect
3. #13067602C2semidirect
4. #13067534C2semidirect
5. #13067176C2semidirect
6. #13066937C2semidirect
7. C11×#3496C2semidirect
18. C2×C4×D44C22semidirect
22. #10622649C22semidirect
23. #10622646C22semidirect
26. #10622573C22semidirect
27. #10622566C22semidirect
28. #10622549C22semidirect
29. #10622538C22semidirect
30. #10622175C22semidirect
31. #10622163C22semidirect
44. C11×C4⋊Q8D4semidirect
45. C11×#127D4semidirect
59. C4×D4×C11D4semidirect
102. C2×D4×C11D8semidirect
141. #3496D11semidirect
266. C4⋊Q8C22⋊D11semidirect
267. #127C22⋊D11semidirect
284. C4×D4C22⋊D11semidirect
335. C2×D4#4323semidirect
369. C11#18210semidirect

Maximal subgroups

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

subgroupindex
#130786122
#130735132
#130676022
#130675342
#130671762
#130669372
C11×#34962
#1821011