Finite Group Databasebeta

← #14671273

Subgroups — #14671273

Order 2816.

894 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C22×#66898C211yesmaximal, characteristic
2C2×#10622177C212yesmaximal, complemented
3#13068537C211yesmaximal, characteristic
4#13066734C212yesmaximal, complemented
5C11×#2405C211yesmaximal, characteristic
6C23×D4×C11C2211yescharacteristic
7C2×C11×#123C411yescharacteristic, complemented
8C2×C11×#123C2211yescharacteristic
9C22×C11×C22⋊C4C411yescharacteristic, complemented
10C22×C22⋊Dic11—21no—
11C11×#394—21no—
12C11×#394—21no—
13C11×#386C411yescharacteristic, complemented
14C11×#386C2211yescharacteristic
15C11×#385—21no—
16C11×#379—21no—
17C11×#379C411yescharacteristic, complemented
18C2×#66898—21no—
19C2×#66898—24no—
20C2×#66898C2212yes—
21C2×#66897—21no—
22C2×#66897C2212yes—
23#10622820—21no—
24#10622177—24no—
25C25×C11C2×C411yescharacteristic
26C25×C11D411yescharacteristic
27C22×D4×C11—22no—
28C22×D4×C11—22no—
29C22×D4×C11—41no—
30C22×D4×C11—41no—
31C22×D4×C11—42no—
32C22×D4×C11C2×C411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C22×D4×C11D411yescharacteristic
35C22×D4×C11C2311yescharacteristic
36C23×C4×C11C2×C411yescharacteristic, complemented
37C23×C4×C11C2×C411yescharacteristic, complemented
38C23×C4×C11D411yescharacteristic
39C23×Dic11—41no—
40C11×#123—22no—
41C11×#123—22no—
42C11×#123—42no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—41no—
54C2×C11×C22⋊C4—41no—
55C2×C11×C22⋊C4C2×C411yescharacteristic, complemented
56C2×C11×C22⋊C4C2×C411yescharacteristic, complemented
57C2×C22⋊Dic11—24no—
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11—41no—
60C2×C22⋊Dic11—42no—
61C2×#4318—22no—
62C11×#95—21no—
63C11×#95—21no—
64#66898—24no—
65#66898—22no—
66#66898D414yes—
67#66897—22no—
68#66897—22no—
69#66897—42no—
70C22⋊(C11⋊C8)—41no—
71C22⋊(C11⋊C8)—41no—
72#13084—111nomaximal, Sylow
73C24×C11—21no—
74C24×C11—22no—
75C24×C11—21no—
76C24×C11—21no—
77C24×C11—21no—
78C24×C11—21no—
79C24×C11—21no—
80C24×C11—22no—
81C24×C11—41no—
82C24×C11—42no—
83C24×C11—42no—
84C24×C11—81no—
85C24×C11—81no—
86C24×C11C22⋊C411yescharacteristic
87C24×C11C22⋊C411yescharacteristic
88C24×C11C22⋊C411yescharacteristic
89C24×C11C22×C411yescharacteristic
90C24×C11C2×D411yescharacteristic
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C2×D4×C11—44no—
104C2×D4×C11—44no—
105C2×D4×C11—44no—
106C2×D4×C11—44no—
107C2×D4×C11C2×D412yes—
108C2×D4×C11#4112yes—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—41no—
118C22×C4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11—81no—
122C22×C4×C11C22⋊C411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×Dic11—44no—
125C22×Dic11—42no—
126C22×Dic11—82no—
127C22×Dic11—82no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4—42no—
130C11×C22⋊C4—22no—
131C11×C22⋊C4—42no—
132C11×C22⋊C4—42no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—42no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C11×C22⋊C4—81no—
140C11×C22⋊C4—81no—
141C11×C22⋊C4—81no—
142C22⋊Dic11—24no—
143C22⋊Dic11—44no—
144C22⋊Dic11—42no—
145#4318—42no—
146#4318—42no—
147C2×C11⋊C8—42no—
148C22×#99—111no—
149#2405D1111yescharacteristic
150C2×#352—112no—
151#1783—111no—
152#1390—112no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—41no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—42no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—42no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—81no—
185C23×C11—81no—
186C23×C11—81no—
187C23×C11—81no—
188C23×C11—84no—
189C23×C11—82no—
190C23×C11—82no—
191C23×C11—84no—
192C23×C11—84no—
193C23×C11#9911yescharacteristic
194C23×C11#9911yescharacteristic
195C23×C11#9912yes—
196C23×C11C2×C22⋊C411yescharacteristic
197C23×C11C4×D412yes—
198C23×C11#12011yescharacteristic
199C23×C11#12311yescharacteristic
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—44no—
203D4×C11—44no—
204D4×C11—42no—
205D4×C11—42no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—82no—
226C2×C4×C11—82no—
227C2×C4×C11#12112yes—
228C2×Dic11—44no—
229C2×Dic11—88no—
230C2×Dic11—82no—
231C2×Dic11—82no—
232C11⋊C8—82no—
233C23×D4C2×D1111yescharacteristic
234C2×#123Dic1111yescharacteristic, complemented
235C2×#123C2×D1111yescharacteristic
236C22×C22⋊C4—221no—
237C22×C22⋊C4Dic1111yescharacteristic, complemented
238C2×#100—112no—
239C2×#100—221no—
240C2×#99—112no—
241C2×#99—224no—
242C2×#99—221no—
243#407—221no—
244#394—21no—
245#394—21no—
246#386Dic1111yescharacteristic, complemented
247#386C2×D1111yescharacteristic
248#385—21no—
249#379—21no—
250#379Dic1111yescharacteristic, complemented
251#352—224no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11—42no—
270C22×C11—44no—
271C22×C11—44no—
272C22×C11—41no—
273C22×C11—41no—
274C22×C11—41no—
275C22×C11—41no—
276C22×C11—41no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—41no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11—84no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11—84no—
289C22×C11#35212yescomplemented
290C22×C11#38611yescharacteristic
291C22×C11C2×#9911yescharacteristic
292C22×C11C2×#9911yescharacteristic
293C4×C11—22no—
294C4×C11—41no—
295C4×C11—81no—
296C4×C11—81no—
297C4×C11—81no—
298C4×C11—81no—
299Dic11—84no—
300C25C2×Dic1111yescharacteristic
301C25C22⋊D1111yescharacteristic
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—41no—
305C22×D4—41no—
306C22×D4—42no—
307C22×D4C2×Dic1111yescharacteristic
308C22×D4C22⋊D1111yescharacteristic
309C22×D4C22⋊D1111yescharacteristic
310C22×D4C22×D1111yescharacteristic
311C23×C4—441no—
312C23×C4C2×Dic1111yescharacteristic, complemented
313C23×C4C2×Dic1111yescharacteristic, complemented
314C23×C4C22⋊D1111yescharacteristic
315C2×M16—222no—
316#123—22no—
317#123—22no—
318#123—42no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—41no—
330C2×C22⋊C4—41no—
331C2×C22⋊C4—224no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—441no—
334C2×C22⋊C4—442no—
335C2×C22⋊C4C2×Dic1111yescharacteristic, complemented
336C2×C22⋊C4C2×Dic1111yescharacteristic, complemented
337#100—222no—
338#100—222no—
339#100—442no—
340#99—114no—
341#99—224no—
342#99—222no—
343C22⋊C8—441no—
344C22⋊C8—441no—
345#95—21no—
346#95—21no—
347C2×C11—21no—
348C2×C11—21no—
349C2×C11—22no—
350C2×C11—41no—
351C2×C11—41no—
352C2×C11—42no—
353C2×C11—41no—
354C2×C11—42no—
355C2×C11—81no—
356C2×C11#189811yescharacteristic
357C2×C11C2×#35211yescharacteristic
358C2×C11#212111yescharacteristic
359C24—21no—
360C24—22no—
361C24—21no—
362C24—21no—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—22no—
367C24—41no—
368C24—42no—
369C24—42no—
370C24—81no—
371C24—81no—
372C24C22⋊Dic1111yescharacteristic
373C24C22⋊Dic1111yescharacteristic
374C24C22⋊Dic1111yescharacteristic
375C24C22×Dic1111yescharacteristic
376C24C2×C22⋊D1111yescharacteristic
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—22no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—44no—
390C2×D4—44no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4D4×D1112yes—
394C2×D4#434112yes—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—81no—
408C22×C4—444no—
409C22×C4—442no—
410C22×C4—882no—
411C22×C4—882no—
412C22×C4C22⋊Dic1111yescharacteristic
413C22×C4C2×C22⋊D1111yescharacteristic
414M16—442no—
415M16—442no—
416C2×C8—442no—
417C4⋊C4—42no—
418C4⋊C4—42no—
419C22⋊C4—22no—
420C22⋊C4—42no—
421C22⋊C4—42no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—42no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—81no—
429C22⋊C4—81no—
430C22⋊C4—81no—
431C22⋊C4—224no—
432C22⋊C4—444no—
433C22⋊C4—442no—
434C11#1308411yescharacteristic, complemented, Sylow
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—22no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—41no—
452C23—42no—
453C23—42no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—42no—
462C23—41no—
463C23—41no—
464C23—42no—
465C23—42no—
466C23—81no—
467C23—81no—
468C23—81no—
469C23—81no—
470C23—84no—
471C23—82no—
472C23—82no—
473C23—84no—
474C23—84no—
475C23#6689811yescharacteristic
476C23#6689811yescharacteristic
477C23#6689812yes—
478C23D4×Dic1112yes—
479C23#6698811yescharacteristic
480C23#6699011yescharacteristic
481C23C2×C22⋊Dic1111yescharacteristic
482D4—42no—
483D4—42no—
484D4—44no—
485D4—44no—
486D4—42no—
487D4—42no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—82no—
508C2×C4—82no—
509C2×C4—444no—
510C2×C4—888no—
511C2×C4—882no—
512C2×C4—882no—
513C2×C4#6699212yes—
514C8—882no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—22no—
521C22—21no—
522C22—22no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—41no—
531C22—41no—
532C22—44no—
533C22—42no—
534C22—44no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—81no—
545C22—81no—
546C22—84no—
547C22—81no—
548C22—81no—
549C22—82no—
550C22—82no—
551C22—84no—
552C22#1062217712yescomplemented
553C22C2×#6689811yescharacteristic
554C22C2×#6689811yescharacteristic
555C22#1062283311yescharacteristic
556C4—22no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—884no—
563C2—21no—
564C2—21no—
565C2—22no—
566C2—41no—
567C2—41no—
568C2—42no—
569C2—41no—
570C2—42no—
571C2—81no—
572C2#1306907011yescharacteristic
573C2C2×#1062217711yescharacteristic
574C2#1307026211yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#2405C2
socleC22×C11C2×#99
prime radicalC23×D4×C11C22
cosocleC22×D4×C11C23
hypercenter#2405D11
hypocenterC11#13084
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ #2405

Complements

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

NH ≅ G/Ntype
2. C2×#10622177C2semidirect
4. #13066734C2semidirect
7. C2×C11×#123C4semidirect
9. C22×C11×C22⋊C4C4semidirect
13. C11×#386C4semidirect
17. C11×#379C4semidirect
36. C23×C4×C11C2×C4semidirect
37. C23×C4×C11C2×C4semidirect
55. C2×C11×C22⋊C4C2×C4semidirect
56. C2×C11×C22⋊C4C2×C4semidirect
234. C2×#123Dic11semidirect
237. C22×C22⋊C4Dic11semidirect
246. #386Dic11semidirect
250. #379Dic11semidirect
289. C22×C11#352semidirect
312. C23×C4C2×Dic11semidirect
313. C23×C4C2×Dic11semidirect
335. C2×C22⋊C4C2×Dic11semidirect
336. C2×C22⋊C4C2×Dic11semidirect
434. C11#13084semidirect
552. C22#10622177semidirect

Maximal subgroups

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

subgroupindex
C22×#668982
C2×#106221772
#130685372
#130667342
C11×#24052
#1308411