Finite Group Databasebeta

← #14666393

Subgroups — #14666393

Order 2816.

554 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 59 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#13069742C211yesmaximal, characteristic
2#13067601C211yesmaximal, characteristic, complemented
3#13067567C211yesmaximal, characteristic, complemented
4#13066637C211yesmaximal, characteristic, complemented
5#13066616C211yesmaximal, characteristic, complemented
6#13066544C211yesmaximal, characteristic, complemented
7C11×#2736C211yesmaximal, characteristic, complemented
8C2×#67006—21no—
9#10623024C2211yescharacteristic
10C11×#397—21no—
11C11×#397C2211yescharacteristic
12C11×#393—21no—
13C11×#393C2211yescharacteristic
14C11×#388—21no—
15C11×#388—21no—
16C11×#388—21no—
17C11×#379—21no—
18C11×#379C2211yescharacteristic
19#10622840—21no—
20#10622580—21no—
21C2×#66870—21no—
22#10622164C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C25×C11D411yescharacteristic
28C22×Q8×C11D411yescharacteristic, complemented
29C22×C22⋊D11—21no—
30C22×C22⋊D11—41no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic, complemented
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4D411yescharacteristic
42C2×C11×C22⋊C4C2311yescharacteristic
43C2×C42×C11—21no—
44#67006—42no—
45#67006—42no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—41no—
48C2×#4325—41no—
49#66983—21no—
50#66983—21no—
51#66939—41no—
52#66935—41no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95D411yescharacteristic, complemented
58C11×#95D411yescharacteristic, complemented
59#66899—41no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66873—41no—
63#66871—41no—
64#66870—42no—
65#12188—111nomaximal, Sylow
66C24×C11—21no—
67C24×C11—21no—
68C24×C11—21no—
69C24×C11—41no—
70C24×C11—41no—
71C24×C11—42no—
72C24×C11—81no—
73C24×C11C2×D411yescharacteristic
74C23×D11—21no—
75C2×Q8×C11—41no—
76C2×Q8×C11—81no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—44no—
88C2×C22⋊D11—41no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11—82no—
92C2×C22⋊D11—82no—
93C22×Dic11—21no—
94C22×Dic11—41no—
95C2×D44—21no—
96C2×D44—21no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—81no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—42no—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—81no—
106C11×C22⋊C4—81no—
107C11×C22⋊C4—81no—
108C11×C22⋊C4—81no—
109C11×C22⋊C4—81no—
110C42×C11—81no—
111C22⋊Dic11—22no—
112C22⋊Dic11—44no—
113C22⋊Dic11—41no—
114#4325—82no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121#2736D1111yescharacteristic, complemented
122#2021—111no—
123#1607—111no—
124#1601—111no—
125#1351—111no—
126#1344—111no—
127#1316—111no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—22no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—42no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—42no—
138C23×C11—42no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—81no—
143C23×C11—82no—
144C23×C11—81no—
145C23×C11—82no—
146C23×C11—84no—
147C23×C11—81no—
148C23×C11#12011yescharacteristic
149C23×C11#13511yescharacteristic
150C23×C11AGL(1,ℤ/8)11yescharacteristic
151C22×D11—41no—
152C22×D11—41no—
153C22×D11—41no—
154C22×D11—81no—
155C22×D11—81no—
156Q8×C11—42no—
157Q8×C11—81no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C22⋊D11—81no—
178C22⋊D11—81no—
179C22⋊D11—88no—
180C22⋊D11—81no—
181C22⋊D11—81no—
182C2×Dic11—42no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—81no—
187C2×Dic11—81no—
188D44—81no—
189D44—81no—
190C11⋊C8—81no—
191C11⋊C8—81no—
192#534—111no—
193C2×#120—221no—
194#480—221no—
195#448—221no—
196C2×#99—221no—
197#397—21no—
198#397C2×D1111yescharacteristic
199#393—21no—
200#393C2×D1111yescharacteristic
201#388—21no—
202#388—21no—
203#388—21no—
204#379—21no—
205#379C2×D1111yescharacteristic
206#342—111no—
207#327—221no—
208#327—221no—
209#323—111no—
210#323—111no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—42no—
218C22×C11—42no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—44no—
222C22×C11—42no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11—82no—
227C22×C11—82no—
228C22×C11—82no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11#44911yescharacteristic
232C22×C11#45311yescharacteristic
233C22×C11B(4,𝔽2)11yescharacteristic
234C2×D11—82no—
235C2×D11—81no—
236C2×D11—81no—
237C2×D11—81no—
238C2×D11—161no—
239C4×C11—41no—
240C4×C11—41no—
241C4×C11—81no—
242C4×C11—81no—
243C4×C11—81no—
244C4×C11—81no—
245C4×C11—81no—
246Dic11—82no—
247Dic11—81no—
248C25C22⋊D1111yescharacteristic
249C22×Q8C22⋊D1111yescharacteristic, complemented
250C22×D4—221no—
251C22×D4—441no—
252C2×SD16—441no—
253#123—441no—
254#121—221no—
255#121—221no—
256#120—441no—
257#120—442no—
258#120—442no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4C22⋊D1111yescharacteristic, complemented
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4—441no—
271C2×C22⋊C4C22⋊D1111yescharacteristic
272C2×C22⋊C4C22×D1111yescharacteristic
273C2×C42—21no—
274#107—441no—
275#103—441no—
276#102—441no—
277#99—442no—
278C22⋊C8—221no—
279C22⋊C8—221no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—21no—
284#95C22⋊D1111yescharacteristic, complemented
285#95C22⋊D1111yescharacteristic, complemented
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—41no—
289C2×C11—41no—
290C2×C11—82no—
291C2×C11#160011yescharacteristic
292C2×C11#219711yescharacteristic
293C2×C11#219911yescharacteristic
294D11—161no—
295C24—21no—
296C24—21no—
297C24—21no—
298C24—41no—
299C24—41no—
300C24—42no—
301C24—81no—
302C24—221no—
303C24C2×C22⋊D1111yescharacteristic
304C2×Q8—41no—
305C2×Q8—81no—
306C2×D4—221no—
307C2×D4—221no—
308C2×D4—441no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—444no—
312C2×D4—441no—
313C2×D4—441no—
314C2×D4—441no—
315C2×D4—882no—
316C2×D4—882no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—221no—
323C22×C4—441no—
324C22×C4C2×C22⋊D1111yescharacteristic
325C22×C4C2×C22⋊D1111yescharacteristic
326SD16—882no—
327C2×C8—441no—
328C2×C8—441no—
329C4⋊C4—41no—
330C4⋊C4—81no—
331C4⋊C4—221no—
332C4⋊C4—221no—
333C22⋊C4—41no—
334C22⋊C4—42no—
335C22⋊C4—42no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—81no—
340C22⋊C4—81no—
341C22⋊C4—81no—
342C22⋊C4—81no—
343C22⋊C4—81no—
344C22⋊C4—222no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—444no—
348C22⋊C4—441no—
349C42—81no—
350C11#1218811yescharacteristic, complemented, Sylow
351C23—21no—
352C23—21no—
353C23—22no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—42no—
359C23—41no—
360C23—42no—
361C23—42no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—81no—
366C23—82no—
367C23—81no—
368C23—82no—
369C23—84no—
370C23—81no—
371C23—441no—
372C23—441no—
373C23—441no—
374C23—881no—
375C23—881no—
376C23#6700211yescharacteristic
377C23#6700311yescharacteristic
378C23#6700611yescharacteristic
379Q8—42no—
380Q8—81no—
381D4—881no—
382D4—881no—
383D4—881no—
384D4—881no—
385D4—888no—
386D4—881no—
387D4—881no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—442no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—881no—
412C2×C4—881no—
413C8—881no—
414C8—881no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—41no—
420C22—41no—
421C22—42no—
422C22—42no—
423C22—41no—
424C22—41no—
425C22—44no—
426C22—42no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—82no—
431C22—82no—
432C22—82no—
433C22—81no—
434C22—81no—
435C22—882no—
436C22—881no—
437C22—881no—
438C22—881no—
439C22—1761no—
440C22#1062285111yescharacteristic
441C22#1062285411yescharacteristic
442C22#1062285711yescharacteristic
443C4—41no—
444C4—41no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—81no—
450C4—882no—
451C4—881no—
452C2—21no—
453C2—21no—
454C2—41no—
455C2—41no—
456C2—82no—
457C2—1761no—
458C2#1306756211yescharacteristic
459C2#1307060611yescharacteristic
460C2#1307061711yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2736C2
socleC22×C11B(4,𝔽2)
prime radical#13069742C2
hypercenter#2736D11
hypocenterC11#12188
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2736

Complements

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

NH ≅ G/Ntype
2. #13067601C2semidirect
3. #13067567C2semidirect
4. #13066637C2semidirect
5. #13066616C2semidirect
6. #13066544C2semidirect
7. C11×#2736C2semidirect
28. C22×Q8×C11D4semidirect
32. C2×C11×C4⋊C4D4semidirect
57. C11×#95D4semidirect
58. C11×#95D4semidirect
121. #2736D11semidirect
249. C22×Q8C22⋊D11semidirect
260. C2×C4⋊C4C22⋊D11semidirect
284. #95C22⋊D11semidirect
285. #95C22⋊D11semidirect
350. C11#12188semidirect

Maximal subgroups

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

subgroupindex
#130697422
#130676012
#130675672
#130666372
#130666162
#130665442
C11×#27362
#1218811