Finite Group Databasebeta

← #14656161

Subgroups — #14656161

Order 2816.

658 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079534C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic, complemented
3#13067284C211yesmaximal, characteristic, complemented
4#13067110C211yesmaximal, characteristic, complemented
5#13067011C211yesmaximal, characteristic, complemented
6#13066519C211yesmaximal, characteristic, complemented
7C11×#2548C211yesmaximal, characteristic, complemented
8C2×C11×#127C2211yescharacteristic
9C2×C11×#124—21no—
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66995—21no—
12#10623008C2211yescharacteristic
13C11×#394—22no—
14C11×#390—22no—
15C11×#390—21no—
16C4×C11×C4⋊C4C2211yescharacteristic
17#10622830—22no—
18#10622686—21no—
19#10622685—22no—
20#10622683—21no—
21#10622644—21no—
22#10622641—22no—
23#10622640—21no—
24#10622579—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622182—22no—
29Q8⋊(C11⋊C8)—22no—
30#10622089—22no—
31C22×Q8×C11D411yescharacteristic
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11D412yes—
35C2×#4339—21no—
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127—21no—
40C11×#124—42no—
41C11×#124—42no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—24no—
50C2×C11×C22⋊C4—24no—
51C2×C42×C11—21no—
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C2×#4326—22no—
55#66995—42no—
56#66995—42no—
57C2×#4325—22no—
58C2×#4323—24no—
59#66983—21no—
60#66983—21no—
61C2×#4318—21no—
62#66928—21no—
63#66927D411yescharacteristic
64C4×D44—21no—
65C4×D44—21no—
66#66922D411yescharacteristic
67C11×#95D412yes—
68#66896—24no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71#66874—22no—
72#66873—22no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4⋊(C11⋊C8)D412yes—
77C4×C11⋊C8—21no—
78C4×C11⋊C8—21no—
79#10242—111nomaximal, Sylow
80C24×C11—22no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11D812yescomplemented
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—44no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—82no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C2×C22⋊D11—41no—
106#4339—41no—
107#4339—41no—
108#4339—41no—
109#4339—41no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×C4×D11—41no—
114C2×Dic22—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—48no—
121C11×C22⋊C4—84no—
122C42×C11—41no—
123C42×C11—41no—
124C42×C11—41no—
125C42×C11—41no—
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11#4111yescharacteristic
130#4326—44no—
131#4325—44no—
132#4323—84no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—41no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137#4318—41no—
138#4318—41no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—41no—
142#3205—111no—
143#3037—111no—
144#2548D1111yescharacteristic, complemented
145#1545—111no—
146#1502—111no—
147#1479—111no—
148#1303—111no—
149C23×C11—44no—
150C23×C11—44no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11—42no—
154C23×C11#12011yescharacteristic
155C22×D11—41no—
156Q8×C11—22no—
157Q8×C11—22no—
158Q8×C11—41no—
159Q8×C11—41no—
160D4×C11—44no—
161D4×C11—82no—
162D4×C11—82no—
163D4×C11—82no—
164D4×C11—81no—
165D4×C11—81no—
166D4×C11—81no—
167D4×C11—81no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12711yescharacteristic
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11#13511yescharacteristic
186C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
188C22⋊D11—81no—
189C22⋊D11—81no—
190C2×Dic11—41no—
191D44—41no—
192D44—41no—
193D44—42no—
194D44—81no—
195C4×D11—81no—
196C4×D11—81no—
197Dic22—41no—
198Dic22—41no—
199C11⋊C8—42no—
200C11⋊C8—42no—
201C11⋊C8—81no—
202C2×#137—221no—
203#532—111no—
204C2×#127C2×D1111yescharacteristic
205C2×#124—21no—
206C2×C4×Q8C2×D1111yescharacteristic
207#493—221no—
208#486—221no—
209#464—222no—
210#462—221no—
211#460—221no—
212#459—222no—
213#447—222no—
214#431—111no—
215#431—111no—
216#423—111no—
217#417—221no—
218#394—22no—
219#390—22no—
220#390—21no—
221C4×C4⋊C4C2×D1111yescharacteristic
222#331—222no—
223#327—222no—
224Q8⋊C8—222no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—84no—
228C22×C11—84no—
229C22×C11—82no—
230C22×C11—82no—
231C22×C11—82no—
232C22×C11#39211yescharacteristic
233C22×C11#44711yescharacteristic
234C22×C11#44911yescharacteristic
235C2×D11—81no—
236C2×D11—81no—
237C2×D11—81no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—42no—
242C4×C11—82no—
243C4×C11—81no—
244C4×C11#44711yescharacteristic
245C4×C11#44911yescharacteristic
246C4×C11#45512yes—
247C4×C11#46611yescharacteristic
248C4×C11#46911yescharacteristic
249Dic11—81no—
250C2×#41—221no—
251C22×Q8C22⋊D1111yescharacteristic
252C22×D4—21no—
253C22×D4—21no—
254C22×D4C22⋊D1112yes—
255#137—442no—
256#137—442no—
257C2×Q16—222no—
258C2×SD16—222no—
259C2×D8—224no—
260C2×M16—221no—
261C4⋊Q8—111no—
262#127—21no—
263#127—21no—
264#127—21no—
265#127—21no—
266#127—111no—
267#124—42no—
268#124—42no—
269#124—221no—
270#121—221no—
271#121—221no—
272C4×Q8—21no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×Q8—21no—
276C4×D4—221no—
277C4×D4—221no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4C22⋊D1111yescharacteristic
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42C22×D1111yescharacteristic
286C4⋊C8—112no—
287C4⋊C8—112no—
288C4⋊C8—221no—
289C4⋊C8—221no—
290#103—222no—
291#102—222no—
292#102—224no—
293C22⋊C8—221no—
294C22⋊C8—221no—
295C4×C8—221no—
296C4×C8—221no—
297#95C22⋊D1112yes—
298C2×C11—21no—
299C2×C11—21no—
300C2×C11—162no—
301C2×C11#199911yescharacteristic
302C2×C11#200411yescharacteristic
303C2×C11#200811yescharacteristic
304D11—161no—
305C24—22no—
306#41—441no—
307#41—441no—
308#41—441no—
309#41—441no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—221no—
316C2×Q8#432312yescomplemented
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—44no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—82no—
329C2×D4—221no—
330C2×D4—221no—
331C2×D4—221no—
332C2×D4—441no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—441no—
337C22×C4C2×C22⋊D1111yescharacteristic
338C22×C4C2×C22⋊D1111yescharacteristic
339C22×C4C2×C22⋊D1111yescharacteristic
340Q16—444no—
341SD16—444no—
342D8—884no—
343M16—441no—
344M16—441no—
345C2×C8—222no—
346C2×C8—222no—
347C2×C8—441no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—42no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—221no—
354C4⋊C4—221no—
355C22⋊C4—48no—
356C22⋊C4—84no—
357C22⋊C4—441no—
358C22⋊C4—441no—
359C42—41no—
360C42—41no—
361C42—41no—
362C42—41no—
363C42D4×D1111yescharacteristic
364C42D4×D1111yescharacteristic
365C42D4×D1111yescharacteristic
366C42#434111yescharacteristic
367C11#1024211yescharacteristic, complemented, Sylow
368C23—44no—
369C23—44no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23—441no—
374C23#6700611yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—41no—
378Q8—41no—
379Q8—441no—
380Q8—441no—
381D4—44no—
382D4—82no—
383D4—82no—
384D4—82no—
385D4—81no—
386D4—81no—
387D4—81no—
388D4—81no—
389D4—441no—
390D4—441no—
391D4—442no—
392D4—881no—
393D4—881no—
394D4—881no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—441no—
406C2×C4—881no—
407C2×C4—881no—
408C2×C4C2×#432311yescharacteristic
409C2×C4#6698511yescharacteristic
410C2×C4#6699011yescharacteristic
411C2×C4#6699011yescharacteristic
412C2×C4#6699111yescharacteristic
413C2×C4#6699211yescharacteristic
414C2×C4#6699211yescharacteristic
415C2×C4#6699311yescharacteristic
416C2×C4#6700211yescharacteristic
417C2×C4#6700311yescharacteristic
418C8—442no—
419C8—442no—
420C8—881no—
421C22—21no—
422C22—21no—
423C22—84no—
424C22—84no—
425C22—82no—
426C22—82no—
427C22—82no—
428C22—881no—
429C22—881no—
430C22—881no—
431C22#1062283011yescharacteristic
432C22#1062283611yescharacteristic
433C22#1062285111yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—42no—
438C4—82no—
439C4—81no—
440C4—881no—
441C4#1062264911yescharacteristic
442C4#1062265011yescharacteristic
443C4#1062265111yescharacteristic
444C4#1062265211yescharacteristic
445C4#1062267412yes—
446C2—21no—
447C2—21no—
448C2—162no—
449C2—1761no—
450C2#1306961211yescharacteristic
451C2#1306964511yescharacteristic
452C2#1306966911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2548C2
socleC22×C11#392
prime radical#13079534C2
hypercenter#2548D11
hypocenterC11#10242
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2548

Complements

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

NH ≅ G/Ntype
2. #13078088C2semidirect
3. #13067284C2semidirect
4. #13067110C2semidirect
5. #13067011C2semidirect
6. #13066519C2semidirect
7. C11×#2548C2semidirect
86. C2×Q8×C11D8semidirect
144. #2548D11semidirect
316. C2×Q8#4323semidirect
367. C11#10242semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130780882
#130672842
#130671102
#130670112
#130665192
C11×#25482
#1024211