Finite Group Databasebeta

← #14648880

Subgroups — #14648880

Order 2816.

676 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 99 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#13077832C211yesmaximal, characteristic
2#13077664C211yesmaximal, characteristic, complemented
3#13068561C211yesmaximal, characteristic, complemented
4#13068527C211yesmaximal, characteristic, complemented
5#13066504C211yesmaximal, characteristic, complemented
6#13066464C211yesmaximal, characteristic, complemented
7C11×#1501C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C11×#525C2211yescharacteristic
10C2×#67003—21no—
11C2×C11×C22⋊C8C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13#10622847—21no—
14#10622820C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×(C2×D11)⋊C8—21no—
18C2×(C2×D11)⋊C8—21no—
19#10622663C411yescharacteristic, complemented
20#10622660—21no—
21#10622659C411yescharacteristic, complemented
22#10622653C411yescharacteristic, complemented
23#10622650—21no—
24#10622649C411yescharacteristic, complemented
25#10622625—21no—
26#10622624—21no—
27#10622624—21no—
28D4×C11⋊C8—21no—
29#10622615—21no—
30#10622613—21no—
31C2×#66869—21no—
32C2×#66869—21no—
33C11×#328—21no—
34C11×#327—21no—
35C2×C11×#41D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×C22⋊D11—21no—
38C2×#4339—21no—
39C2×#4339—21no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—42no—
43C2×#4339—42no—
44C22×D44C2×C411yescharacteristic
45C22×C4×D11—21no—
46C22×Dic22C2×C411yescharacteristic
47C22×C8×C11—21no—
48C11×#123—21no—
49C11×C22⋊Q8C2×C411yescharacteristic
50C11×C22⋊Q8D411yescharacteristic
51C11×#121C2×C411yescharacteristic
52C11×#121D411yescharacteristic
53C11×#120—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C11×#117D411yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C42×C11—21no—
59#67003—42no—
60#67003—42no—
61C2×#4326—21no—
62C2×#4325—21no—
63C2×#4324—21no—
64C2×#4323—21no—
65C2×#4318—21no—
66C2×#4318D411yescharacteristic
67C2×#4318D411yescharacteristic
68C22×C11⋊C8—21no—
69C22×C11⋊C8—21no—
70C22×C11⋊C8D411yescharacteristic
71C22×C11⋊C8D411yescharacteristic
72C11×C22⋊C8—21no—
73C11×C22⋊C8—21no—
74C11×#95—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)—21no—
78C22⋊(C11⋊C8)—21no—
79C22⋊(C11⋊C8)—21no—
80C22⋊(C11⋊C8)—21no—
81C22⋊(C11⋊C8)—21no—
82C22⋊(C11⋊C8)C2×C411yescharacteristic
83C22⋊(C11⋊C8)C2×C411yescharacteristic
84(C2×D11)⋊C8—42no—
85(C2×D11)⋊C8—42no—
86#66874—21no—
87#66874—21no—
88#66873—21no—
89#66873—21no—
90#66869—42no—
91#66869—42no—
92C4⋊(C11⋊C8)—21no—
93C4⋊(C11⋊C8)—21no—
94#66867—21no—
95C4×C11⋊C8—21no—
96#9037—111nomaximal, Sylow
97C24×C11#4111yescharacteristic
98C23×D11—21no—
99C11×#41—41no—
100C11×#41—41no—
101C2×Q8×C11C22⋊C411yescharacteristic
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11C22⋊C411yescharacteristic
106C22×C4×C11—21no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C2×C22⋊D11—42no—
117C2×C22⋊D11—42no—
118C2×C22⋊D11—41no—
119C2×C22⋊D11—41no—
120C22×Dic11—21no—
121#4339—22no—
122#4339—22no—
123#4339—22no—
124#4339—22no—
125#4339—41no—
126#4339—41no—
127#4339—41no—
128#4339—41no—
129#4339—42no—
130#4339—42no—
131#4339—42no—
132#4339—42no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—42no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×C4×D11—41no—
141C2×C4×D11—41no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—42no—
145C2×C8×C11—41no—
146C2×C8×C11—41no—
147C2×C8×C11—41no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4C22⋊C411yescharacteristic
151C11×C4⋊C4C22⋊C411yescharacteristic
152C11×C22⋊C4—21no—
153C11×C22⋊C4—21no—
154C11×C22⋊C4—21no—
155C11×C22⋊C4—21no—
156C11×C22⋊C4—21no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—41no—
159C42×C11—21no—
160C42×C11—41no—
161C42×C11—41no—
162#4326—42no—
163#4325—42no—
164#4324—42no—
165#4323—42no—
166#4318—41no—
167#4318—41no—
168#4318—81no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—41no—
176C2×C11⋊C8—41no—
177C2×C11⋊C8—41no—
178C2×C11⋊C8—41no—
179C2×C11⋊C8—81no—
180#3002—111no—
181#2976—111no—
182#1789—111no—
183#1780—111no—
184#1501D1111yescharacteristic, complemented
185#1298—111no—
186#1282—111no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11C4×D411yescharacteristic
193C23×C11#12111yescharacteristic
194C23×C11#12311yescharacteristic
195C22×D11—22no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—41no—
202Q8×C11—41no—
203D4×C11—41no—
204D4×C11—41no—
205D4×C11—41no—
206D4×C11—81no—
207D4×C11—81no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—81no—
224C2×C4×C11—81no—
225C2×C4×C11C2×C22⋊C411yescharacteristic
226C2×C4×C11C4×D411yescharacteristic
227C2×C4×C11#12011yescharacteristic
228C2×C4×C11#12111yescharacteristic
229C22⋊D11—42no—
230C22⋊D11—42no—
231C22⋊D11—42no—
232C22⋊D11—42no—
233C2×Dic11—22no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236D44—22no—
237D44—22no—
238D44—41no—
239D44—41no—
240C4×D11—42no—
241C4×D11—42no—
242C4×D11—42no—
243C4×D11—42no—
244Dic22—22no—
245Dic22—22no—
246Dic22—41no—
247Dic22—41no—
248C8×C11—81no—
249C11⋊C8—41no—
250C11⋊C8—41no—
251C11⋊C8—41no—
252C11⋊C8—41no—
253C11⋊C8—41no—
254C11⋊C8—41no—
255C22×#41—111no—
256C2×#135—221no—
257#525C2×D1111yescharacteristic
258#452—221no—
259#451—111no—
260#450—111no—
261#449—221no—
262#448—111no—
263#447—111no—
264#436—221no—
265#435—221no—
266#435—221no—
267C8×D4—221no—
268#433—221no—
269C2×#104—221no—
270C2×#104—221no—
271#416—221no—
272#408—221no—
273#407—111no—
274C2×C22⋊C8—111no—
275C2×C22⋊C8—111no—
276C2×C22⋊C8—221no—
277C2×C22⋊C8—221no—
278C2×C22⋊C8C2×D1111yescharacteristic
279C4×C22⋊C4C2×D1111yescharacteristic
280#328—21no—
281#327—21no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—41no—
291C22×C11—41no—
292C22×C11—41no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11#38611yescharacteristic
296C22×C11#44311yescharacteristic
297C22×C11#44411yescharacteristic
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—81no—
302C2×D11—81no—
303C2×D11—81no—
304C2×D11—81no—
305C4×C11—21no—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—41no—
309C4×C11—41no—
310C4×C11—41no—
311C4×C11—82no—
312C4×C11B(4,𝔽2)11yescharacteristic
313C4×C11B(4,𝔽2)11yescharacteristic
314Dic11—42no—
315C2×#41—221no—
316C2×#41—221no—
317C2×#41—221no—
318C2×#41—221no—
319C2×#41—442no—
320C2×#41—442no—
321C2×#41D4411yescharacteristic
322C22×Q8—111no—
323C22×D4—111no—
324C22×D4—221no—
325C23×C4—221no—
326C23×C4C22×D1111yescharacteristic
327#135—442no—
328#135—442no—
329C2×Q16—221no—
330C2×SD16—221no—
331C2×SD16—221no—
332C2×D8—221no—
333C2×M16—111no—
334C2×M16—111no—
335C2×M16—221no—
336C22×C8—21no—
337C22×C8—111no—
338C22×C8—111no—
339C22×C8—221no—
340C22×C8—221no—
341#123—21no—
342C22⋊Q8C4×D1111yescharacteristic
343C22⋊Q8C22⋊D1111yescharacteristic
344#121C4×D1111yescharacteristic
345#121C22⋊D1111yescharacteristic
346#120—21no—
347C4×D4—21no—
348C4×D4—21no—
349#117D4411yescharacteristic
350C2×C22⋊C4—21no—
351C2×C42—21no—
352C4⋊C8—221no—
353C4⋊C8—221no—
354#104—442no—
355#104—442no—
356#103—221no—
357#103—221no—
358#102—221no—
359#102—221no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—111no—
363C22⋊C8—111no—
364C22⋊C8—221no—
365C22⋊C8—221no—
366C22⋊C8—221no—
367C22⋊C8—221no—
368C22⋊C8—221no—
369C22⋊C8—221no—
370C22⋊C8—221no—
371C22⋊C8—442no—
372C22⋊C8—442no—
373#97—221no—
374C4×C8—221no—
375#95—21no—
376C2×C11—21no—
377C2×C11—21no—
378C2×C11—41no—
379C2×C11—41no—
380C2×C11—81no—
381C2×C11#187611yescharacteristic
382C2×C11#188111yescharacteristic
383C2×C11#188911yescharacteristic
384D11—82no—
385C24—221no—
386C24#434111yescharacteristic
387#41—41no—
388#41—41no—
389#41—222no—
390#41—222no—
391#41—222no—
392#41—222no—
393#41—441no—
394#41—441no—
395#41—441no—
396#41—441no—
397#41—442no—
398#41—442no—
399#41—442no—
400#41—442no—
401C2×Q8—221no—
402C2×Q8—221no—
403C2×Q8—442no—
404C2×Q8(C2×D11)⋊C411yescharacteristic
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—221no—
409C2×D4—221no—
410C2×D4—442no—
411C2×D4—442no—
412C2×D4—442no—
413C2×D4—441no—
414C2×D4—441no—
415C2×D4(C2×D11)⋊C411yescharacteristic
416C22×C4—21no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—221no—
423C22×C4—441no—
424C22×C4—441no—
425C22×C4—441no—
426C22×C4—441no—
427C22×C4C2×C4×D1111yescharacteristic
428C22×C4C2×D4411yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4D4×D1111yescharacteristic
431C22×C4#434111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433Q16—442no—
434SD16—442no—
435SD16—442no—
436D8—442no—
437M16—441no—
438M16—441no—
439M16—881no—
440C2×C8—41no—
441C2×C8—41no—
442C2×C8—41no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—441no—
450C2×C8—441no—
451C2×C8—441no—
452C2×C8—441no—
453C2×C8—881no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4(C2×D11)⋊C411yescharacteristic
457C4⋊C4(C2×D11)⋊C411yescharacteristic
458C22⋊C4—21no—
459C22⋊C4—21no—
460C22⋊C4—21no—
461C22⋊C4—21no—
462C22⋊C4—21no—
463C22⋊C4—22no—
464C22⋊C4—41no—
465C42—21no—
466C42—41no—
467C42—41no—
468C11#903711yescharacteristic, complemented, Sylow
469C23—21no—
470C23—21no—
471C23—21no—
472C23—41no—
473C23—41no—
474C23—222no—
475C23—441no—
476C23—441no—
477C23—441no—
478C23—441no—
479C23—441no—
480C23—441no—
481C23(C22⋊D11)⋊C411yescharacteristic
482C23#6693911yescharacteristic
483C23#6699211yescharacteristic
484Q8—41no—
485Q8—222no—
486Q8—222no—
487Q8—441no—
488Q8—441no—
489D4—41no—
490D4—41no—
491D4—41no—
492D4—81no—
493D4—81no—
494D4—222no—
495D4—222no—
496D4—441no—
497D4—441no—
498D4—442no—
499D4—442no—
500D4—442no—
501D4—442no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—81no—
518C2×C4—81no—
519C2×C4—222no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4(C22⋊D11)⋊C411yescharacteristic
527C2×C4#6693511yescharacteristic
528C2×C4C2×(C2×D11)⋊C411yescharacteristic
529C2×C4#6699211yescharacteristic
530C8—81no—
531C8—441no—
532C8—441no—
533C8—441no—
534C8—441no—
535C8—441no—
536C8—441no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—81no—
549C22—81no—
550C22—442no—
551C22—442no—
552C22—442no—
553C22—881no—
554C22—881no—
555C22—881no—
556C22—881no—
557C22#1062243611yescharacteristic
558C22#1062243711yescharacteristic
559C22#1062257111yescharacteristic
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—82no—
567C4—442no—
568C4#1062235411yescharacteristic
569C4#1062235411yescharacteristic
570C2—21no—
571C2—21no—
572C2—41no—
573C2—41no—
574C2—81no—
575C2—882no—
576C2#1306894111yescharacteristic
577C2#1306897611yescharacteristic
578C2#1306902211yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1501C2
socleC22×C11#386
prime radical#13077832C2
cosocleC23×C4×C11C23
hypercenter#1501D11
hypocenterC11#9037
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1501

Complements

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

NH ≅ G/Ntype
2. #13077664C2semidirect
3. #13068561C2semidirect
4. #13068527C2semidirect
5. #13066504C2semidirect
6. #13066464C2semidirect
7. C11×#1501C2semidirect
19. #10622663C4semidirect
21. #10622659C4semidirect
22. #10622653C4semidirect
24. #10622649C4semidirect
184. #1501D11semidirect
468. C11#9037semidirect

Maximal subgroups

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

subgroupindex
#130778322
#130776642
#130685612
#130685272
#130665042
#130664642
C11×#15012
#903711