Finite Group Databasebeta

← #14669608

Subgroups — #14669608

Order 2816.

852 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 127 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#13070301C211yesmaximal, characteristic, complemented
2#13070257C212yesmaximal, complemented
3#13069035C212yesmaximal, complemented
4#13069000C211yesmaximal, characteristic, complemented
5C11×#3481C211yesmaximal, characteristic
6C11×#559C411yescharacteristic, complemented
7C11×#554—21no—
8C11×#553—22no—
9C11×#551—21no—
10C11×#551C412yescomplemented
11C11×#546—22no—
12D42×C11C411yescharacteristic, complemented
13C11×#532C2211yescharacteristic
14C11×#529—22no—
15C11×#525—21no—
16C11×#525C2212yes—
17C4×C11×#41—21no—
18C2×C4×D4×C11—22no—
19#10623350C2211yescharacteristic, complemented
20#10622853C2211yescharacteristic, complemented
21#10622850C2212yescomplemented
22#10622849—21no—
23#10622820—22no—
24#10622186—21no—
25#10622180—21no—
26#10622177—22no—
27#10622174—22no—
28#10622171—22no—
29#10622161—21no—
30C2×C11×#41—21no—
31C2×C11×#41D411yescharacteristic
32C2×C11×#41C2311yescharacteristic
33C22×D4×C11—22no—
34C23×C4×C11—21no—
35C23×C4×C11D412yes—
36C11×C4⋊Q8D411yescharacteristic
37C11×#127C2×C411yescharacteristic
38C11×#126—22no—
39C11×#126—22no—
40C11×#125—22no—
41C11×#124—22no—
42C11×#124C2×C411yescharacteristic
43C11×#124D411yescharacteristic
44C11×#123—21no—
45C11×#123—22no—
46C11×#123—21no—
47C11×#123—22no—
48C11×#123C2×C412yes—
49C11×#123D412yes—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—22no—
53C11×#121—22no—
54C11×#121—22no—
55C11×#121—22no—
56C11×#121—22no—
57C11×#120—21no—
58C11×#120—21no—
59C11×#120C2×C412yes—
60C11×#120D412yes—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—21no—
74C11×#117—21no—
75C11×#117—21no—
76C11×#117—22no—
77C11×#117D412yes—
78C2×C11×C4⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C42×C11—22no—
82C2×C42×C11D411yescharacteristic
83#67001—42no—
84#66979—21no—
85C2×#4318—22no—
86C2×#4318—21no—
87C2×#4318—22no—
88#66901—42no—
89#66900—22no—
90#66898—22no—
91#66897—22no—
92C22⋊(C11⋊C8)—44no—
93#12765—111nomaximal, Sylow
94C24×C11—21no—
95C24×C11C22⋊C412yes—
96C11×#41—41no—
97C11×#41—41no—
98C11×#41—41no—
99C11×#41—41no—
100C11×#41—44no—
101C2×Q8×C11—21no—
102C2×Q8×C11C22⋊C411yescharacteristic
103C2×Q8×C11C2×D411yescharacteristic
104C2×D4×C11—21no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—21no—
110C2×D4×C11—48no—
111C2×D4×C11C22⋊C411yescharacteristic
112C2×D4×C11C22×C411yescharacteristic
113C2×D4×C11C2×D412yes—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—81no—
125C22×C4×C11—81no—
126C22×C4×C11C22⋊C412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—21no—
142C11×C22⋊C4—21no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—22no—
147C11×C22⋊C4—22no—
148C11×C22⋊C4—22no—
149C11×C22⋊C4C22⋊C412yes—
150C11×C22⋊C4C22⋊C412yes—
151C42×C11—22no—
152C42×C11—22no—
153C42×C11—21no—
154C42×C11—22no—
155C42×C11C22⋊C411yescharacteristic
156C42×C11C22⋊C411yescharacteristic
157C22⋊Dic11—41no—
158C4⋊Dic11—41no—
159C4×Dic11—41no—
160#4318—22no—
161#4318—42no—
162#4318—42no—
163#4318—41no—
164#4318—42no—
165C2×C11⋊C8—24no—
166C2×C11⋊C8—41no—
167C2×C11⋊C8—42no—
168#3481D1111yescharacteristic
169#2132—111no—
170#2120—112no—
171#1891—112no—
172#1884—111no—
173C23×C11—22no—
174C23×C11—21no—
175C23×C11—42no—
176C23×C11—44no—
177C23×C11—44no—
178C23×C11—81no—
179C23×C11C2×C22⋊C412yes—
180C23×C11#12011yescharacteristic
181Q8×C11—41no—
182Q8×C11—41no—
183Q8×C11—42no—
184D4×C11—24no—
185D4×C11—41no—
186D4×C11—42no—
187D4×C11—41no—
188D4×C11—44no—
189D4×C11—44no—
190D4×C11—44no—
191D4×C11—44no—
192D4×C11—81no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—21no—
203C2×C4×C11—44no—
204C2×C4×C11—42no—
205C2×C4×C11—44no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—82no—
212C2×C4×C11—81no—
213C2×C4×C11—82no—
214C2×C4×C11C2×C22⋊C411yescharacteristic
215C2×C4×C11#12012yes—
216C2×C4×C11#12011yescharacteristic
217C2×Dic11—81no—
218C11⋊C8—42no—
219C11⋊C8—82no—
220#568—111no—
221#559Dic1111yescharacteristic, complemented
222#554—21no—
223#553—22no—
224#551—21no—
225#551Dic1112yescomplemented
226#546—22no—
227D42Dic1111yescharacteristic, complemented
228#532C2×D1111yescharacteristic
229#529—22no—
230#525—21no—
231#525C2×D1112yes—
232C4×#41—21no—
233C2×C4×D4—22no—
234#421—221no—
235#413—112no—
236#410—111no—
237#407—222no—
238#356—221no—
239#355—221no—
240#352—222no—
241AΣL(1,𝔽16)—222no—
242#344—222no—
243#339—221no—
244C22×C11—24no—
245C22×C11—22no—
246C22×C11—21no—
247C22×C11—41no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—42no—
251C22×C11—44no—
252C22×C11—42no—
253C22×C11—41no—
254C22×C11—82no—
255C22×C11—84no—
256C22×C11#37911yescharacteristic
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—21no—
260C4×C11—41no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—41no—
265C4×C11B(4,𝔽2)11yescharacteristic
266C4×C11#45811yescharacteristic
267Dic11—161no—
268C2×#41—21no—
269C2×#41C22⋊D1111yescharacteristic
270C2×#41C22×D1111yescharacteristic
271C22×D4—22no—
272C23×C4—21no—
273C23×C4C22⋊D1112yes—
274#131—442no—
275C2×M16—222no—
276C2×M16—221no—
277C2×M16—222no—
278C4⋊Q8C22⋊D1111yescharacteristic
279#127C2×Dic1111yescharacteristic
280#126—22no—
281#126—22no—
282#125—22no—
283#124—22no—
284#124C2×Dic1111yescharacteristic
285#124C22⋊D1111yescharacteristic
286#123—21no—
287#123—22no—
288#123—21no—
289#123—22no—
290#123C2×Dic1112yes—
291#123C22⋊D1112yes—
292C22⋊Q8—22no—
293C22⋊Q8—22no—
294C22⋊Q8—22no—
295#121—22no—
296#121—22no—
297#121—22no—
298#121—22no—
299#120—21no—
300#120—21no—
301#120C2×Dic1112yes—
302#120C22⋊D1112yes—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×D4—21no—
306C4×D4—22no—
307C4×D4—22no—
308C4×D4—22no—
309C4×D4—22no—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4—22no—
315C4×D4—21no—
316#117—21no—
317#117—21no—
318#117—22no—
319#117—221no—
320#117C22⋊D1112yes—
321C2×C4⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C42—22no—
325C2×C42C22⋊D1111yescharacteristic
326#104—442no—
327#101—222no—
328#100—222no—
329#99—222no—
330C22⋊C8—444no—
331C2×C11—21no—
332C2×C11—41no—
333C2×C11—42no—
334C2×C11—44no—
335C2×C11—81no—
336C2×C11#179011yescharacteristic
337C24—21no—
338C24C22⋊Dic1112yes—
339#41—41no—
340#41—41no—
341#41—41no—
342#41—41no—
343#41—44no—
344C2×Q8—21no—
345C2×Q8C22⋊Dic1111yescharacteristic
346C2×Q8C2×C22⋊D1111yescharacteristic
347C2×D4—21no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—21no—
353C2×D4—48no—
354C2×D4C22⋊Dic1111yescharacteristic
355C2×D4C22×Dic1111yescharacteristic
356C2×D4C2×C22⋊D1112yes—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—81no—
368C22×C4—81no—
369C22×C4C22⋊Dic1112yes—
370C22×C4C2×C22⋊D1111yescharacteristic
371C22×C4C2×C22⋊D1112yes—
372M16—222no—
373M16—442no—
374M16—441no—
375M16—442no—
376M16—442no—
377C2×C8—224no—
378C2×C8—441no—
379C2×C8—442no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—441no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—21no—
394C22⋊C4—21no—
395C22⋊C4—22no—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C22⋊C4—441no—
402C22⋊C4C22⋊Dic1112yes—
403C22⋊C4C22⋊Dic1112yes—
404C42—22no—
405C42—22no—
406C42—21no—
407C42—22no—
408C42—441no—
409C42C22⋊Dic1111yescharacteristic
410C42C22⋊Dic1111yescharacteristic
411C11#1276511yescharacteristic, complemented, Sylow
412C23—22no—
413C23—21no—
414C23—42no—
415C23—44no—
416C23—44no—
417C23—81no—
418C23C2×C22⋊Dic1112yes—
419C23#6700611yescharacteristic
420Q8—41no—
421Q8—41no—
422Q8—42no—
423D4—24no—
424D4—41no—
425D4—42no—
426D4—41no—
427D4—44no—
428D4—44no—
429D4—44no—
430D4—44no—
431D4—81no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—21no—
442C2×C4—44no—
443C2×C4—42no—
444C2×C4—44no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—82no—
451C2×C4—81no—
452C2×C4—82no—
453C2×C4—881no—
454C2×C4C2×C22⋊Dic1111yescharacteristic
455C2×C4#6700612yes—
456C2×C4#6700611yescharacteristic
457C8—442no—
458C8—882no—
459C22—24no—
460C22—22no—
461C22—21no—
462C22—41no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—44no—
467C22—42no—
468C22—41no—
469C22—82no—
470C22—84no—
471C22#1062286011yescharacteristic
472C4—22no—
473C4—22no—
474C4—21no—
475C4—41no—
476C4—42no—
477C4—42no—
478C4—42no—
479C4—41no—
480C4—1761no—
481C4#1062285611yescharacteristic
482C4#1062285711yescharacteristic
483C2—21no—
484C2—41no—
485C2—44no—
486C2—42no—
487C2—81no—
488C2#1306856411yescharacteristic
subgroupG/H
centerC4#10622857
commutatorC2×D4×C11C22×C4
FrattiniC2×#41C22×D11
Fitting, prime radicalC11×#3481C2
socleC2×C11#1790
cosocleC2×C11×#41C23
hypercenter#3481D11
hypocenterC11#12765
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #3481

Complements

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

NH ≅ G/Ntype
1. #13070301C2semidirect
2. #13070257C2semidirect
3. #13069035C2semidirect
4. #13069000C2semidirect
6. C11×#559C4semidirect
10. C11×#551C4semidirect
12. D42×C11C4semidirect
19. #10623350C22semidirect
20. #10622853C22semidirect
21. #10622850C22semidirect
221. #559Dic11semidirect
225. #551Dic11semidirect
227. D42Dic11semidirect
411. C11#12765semidirect

Maximal subgroups

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

subgroupindex
#130703012
#130702572
#130690352
#130690002
C11×#34812
#1276511