Finite Group Databasebeta

← #14684465

Subgroups — #14684465

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622842C211yesmaximal, characteristic
2C2×#10622546C211yesmaximal, characteristic
3#13066887C211yesmaximal, characteristic
4#13066882C212yesmaximal
5#13066877C212yesmaximal
6#13066876C212yesmaximal
7#13066875C211yesmaximal, characteristic
8#13066867C212yesmaximal
9#13066866C211yesmaximal, characteristic
10#13066843C211yesmaximal, characteristic
11C2×C11×#391C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×Dic11⋊C4C2211yescharacteristic
16C22×Dic11⋊C4C2211yescharacteristic
17C22×Dic11⋊C4C2212yes—
18C11×#391—24no—
19C2×C11×#95C2212yes—
20C2×C11×#95C2212yes—
21#10622842C418yescomplemented
22C2×C11⋊#95C2211yescharacteristic
23C2×C11⋊#95C2211yescharacteristic
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2211yescharacteristic
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37#10622546—24no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—42no—
41C22×Q8×C11—42no—
42C22×Q8×C11C2×C414yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2312yes—
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2312yes—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—42no—
56C2×C42×C11—42no—
57C2×C42×C11D414yes—
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—42no—
62C2×Dic11⋊C4—42no—
63C2×Dic11⋊C4—42no—
64C2×Dic11⋊C4C2×C414yes—
65C2×Dic11⋊C4C2×C418yes—
66C11×#95—24no—
67C11×#95—24no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95—42no—
74C11⋊#95—42no—
75C11⋊#95—42no—
76C11⋊#95—42no—
77C11⋊#95—42no—
78C11⋊#95—42no—
79C11⋊#95—42no—
80C11⋊#95—42no—
81C11⋊#95C2×C418yes—
82C11⋊#95C2×C414yes—
83#14626—111nomaximal, Sylow
84C24×C11C2411yescharacteristic
85C2×Q8×C11—28no—
86C2×Q8×C11—48no—
87C2×Q8×C11—44no—
88C2×Q8×C11—44no—
89C2×Q8×C11—48no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11C22×C414yes—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11#4112yes—
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—22no—
126C22×Dic11—21no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—21no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—21no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11—21no—
150C22×Dic11—22no—
151C22×Dic11—21no—
152C22×Dic11C22×C412yes—
153C22×Dic11C22×C414yes—
154C22×Dic11C22×C412yes—
155C11×C4⋊C4—44no—
156C42×C11—44no—
157Dic11⋊C4—28no—
158Dic11⋊C4—48no—
159Dic11⋊C4—44no—
160C2×#395—111no—
161C2×#391D1111yescharacteristic
162C2×#387—111no—
163#1446—111no—
164#1445—112no—
165#1443—112no—
166#1443—112no—
167#1442—111no—
168#1441—112no—
169#1441—111no—
170#1434—111no—
171C23×C11C23×C411yescharacteristic
172C23×C11C22×D411yescharacteristic
173C23×C11C2×#4111yescharacteristic
174C23×C11H(5,𝔽2)12yes—
175C23×C11H(5,𝔽2)12yes—
176C23×C11H(5,𝔽2)11yescharacteristic
177C23×C112−1+412yes—
178C23×C112−1+411yescharacteristic
179C23×C112−1+411yescharacteristic
180C23×C112−1+412yes—
181C23×C112−1+411yescharacteristic
182Q8×C11—416no—
183C2×C4×C11—24no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11C4×D414yes—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—24no—
215C2×Dic11—24no—
216C2×Dic11—22no—
217C2×Dic11—24no—
218C2×Dic11—22no—
219C2×Dic11—24no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—42no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C23×Q8C2×D1111yescharacteristic
249C22×C4⋊C4—111no—
250C22×C4⋊C4—112no—
251C22×C4⋊C4—111no—
252C22×C4⋊C4C2×D1111yescharacteristic
253C22×C42C2×D1111yescharacteristic
254#395—118no—
255#391—24no—
256#387—224no—
257C2×#95—111no—
258C2×#95—112no—
259C2×#95—111no—
260C2×#95—111no—
261C2×#95—111no—
262C2×#95—111no—
263C2×#95—111no—
264C2×#95—112no—
265C2×#95—112no—
266C2×#95—112no—
267C2×#95—112no—
268C2×#95—112no—
269C2×#95—112no—
270C2×#95—112no—
271C2×#95—112no—
272C2×#95C2×D1112yes—
273C2×#95C2×D1112yes—
274C22×C11C2×C4×D411yescharacteristic
275C22×C11#51812yes—
276C22×C11#51911yescharacteristic
277C22×C11#51912yes—
278C22×C11#52011yescharacteristic
279C22×C11#53411yescharacteristic
280C22×C11#53511yescharacteristic
281C22×C11#53611yescharacteristic
282C22×C11#53611yescharacteristic
283C22×C11#53611yescharacteristic
284C22×C11#53711yescharacteristic
285C22×C11#53812yes—
286C22×C11#54112yes—
287C22×C11#54111yescharacteristic
288C22×C11#54211yescharacteristic
289C22×C11#56212yes—
290C22×C11#56212yes—
291C22×C11#56312yes—
292C22×C11#56312yes—
293C22×C11#56312yes—
294C22×C11#56312yes—
295C22×C11#56312yes—
296C22×C11#56312yes—
297C4×C11—24no—
298C4×C11—42no—
299C4×C11—44no—
300C4×C11—42no—
301C4×C11—82no—
302Dic11—42no—
303Dic11—42no—
304Dic11—44no—
305Dic11—81no—
306Dic11—82no—
307Dic11—81no—
308C22×Q8—22no—
309C22×Q8—22no—
310C22×Q8—42no—
311C22×Q8—42no—
312C22×Q8C4×D1114yes—
313C23×C4—111no—
314C23×C4—111no—
315C23×C4—112no—
316C23×C4—111no—
317C23×C4—112no—
318C23×C4—111no—
319C23×C4C22×D1112yes—
320C23×C4C22×D1112yes—
321C23×C4C22×D1111yescharacteristic
322C23×C4C22×D1111yescharacteristic
323C23×C4C22×D1111yescharacteristic
324C2×C4⋊C4—22no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—114no—
327C2×C4⋊C4—118no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—222no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—442no—
332C2×C4⋊C4—442no—
333C2×C4⋊C4—442no—
334C2×C42—42no—
335C2×C42C22⋊D1114yes—
336#95—24no—
337#95—24no—
338#95—118no—
339#95—114no—
340#95—222no—
341#95—222no—
342#95—222no—
343#95—222no—
344#95—222no—
345#95—442no—
346#95—442no—
347#95—442no—
348#95—442no—
349#95—442no—
350#95—442no—
351#95—442no—
352#95—442no—
353C2×C11#232111yescharacteristic
354C2×C11#232311yescharacteristic
355C2×C11#232711yescharacteristic
356C2×C11#237812yes—
357C2×C11#238112yes—
358C2×C11#281411yescharacteristic
359C2×C11#281711yescharacteristic
360C2×C11#282011yescharacteristic
361C2×C11#282111yescharacteristic
362C2×C11#283112yes—
363C2×C11#283312yes—
364C24C23×D1111yescharacteristic
365C2×Q8—28no—
366C2×Q8—48no—
367C2×Q8—48no—
368C2×Q8—44no—
369C2×Q8—44no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—114no—
394C22×C4—112no—
395C22×C4—112no—
396C22×C4—221no—
397C22×C4—221no—
398C22×C4—222no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—221no—
404C22×C4—222no—
405C22×C4—221no—
406C22×C4—221no—
407C22×C4—222no—
408C22×C4—221no—
409C22×C4—222no—
410C22×C4—221no—
411C22×C4—221no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—221no—
418C22×C4—222no—
419C22×C4—221no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—221no—
424C22×C4—222no—
425C22×C4—221no—
426C22×C4—222no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4C2×C4×D1114yes—
430C22×C4C2×C4×D1112yes—
431C22×C4#433912yes—
432C22×C4C2×C22⋊D1112yes—
433C22×C4C2×C22⋊D1112yes—
434C22×C4C2×C22⋊D1112yes—
435C4⋊C4—44no—
436C4⋊C4—228no—
437C4⋊C4—448no—
438C4⋊C4—444no—
439C42—44no—
440C11#1462611yescharacteristic, complemented, Sylow
441C23C22×C4×D1111yescharacteristic
442C23C2×#433911yescharacteristic
443C23#6703712yes—
444C23#6703712yes—
445C23#6704011yescharacteristic
446C23#6704012yes—
447C23#6704011yescharacteristic
448C23#6704211yescharacteristic
449C23#6704312yes—
450C23#6704311yescharacteristic
451C23C22×C22⋊D1111yescharacteristic
452Q8—416no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—224no—
482C2×C4—224no—
483C2×C4—222no—
484C2×C4—222no—
485C2×C4—224no—
486C2×C4—222no—
487C2×C4—224no—
488C2×C4—222no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4—441no—
495C2×C4—441no—
496C2×C4—441no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—441no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4C4×C22⋊D1114yes—
518C22#1062301712yes—
519C22#1062302512yes—
520C22#1062310312yes—
521C22#1062310311yescharacteristic
522C22#1062310511yescharacteristic
523C22#1062311311yescharacteristic
524C22#1062311412yes—
525C22#1062311411yescharacteristic
526C22#1062317712yes—
527C22#1062317712yes—
528C22#1062317712yes—
529C22#1062317812yes—
530C22#1062320312yes—
531C22#1062321512yes—
532C22#1062326612yes—
533C22#1062326612yes—
534C22C2×C4×C22⋊D1111yescharacteristic
535C22#1062333511yescharacteristic
536C22#1062333611yescharacteristic
537C22#1062334711yescharacteristic
538C22#1062334711yescharacteristic
539C22#1062335611yescharacteristic
540C22#1062336411yescharacteristic
541C4—24no—
542C4—42no—
543C4—44no—
544C4—42no—
545C4—82no—
546C4—444no—
547C4—442no—
548C4—442no—
549C4—882no—
550C4—881no—
551C4—881no—
552C2#1307127411yescharacteristic
553C2#1307129211yescharacteristic
554C2#1307133211yescharacteristic
555C2#1307177712yes—
556C2#1307179512yes—
557C2#1307662711yescharacteristic
558C2#1307665111yescharacteristic
559C2#1307666711yescharacteristic
560C2#1307667511yescharacteristic
561C2#1307676812yes—
562C2#1307679212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#391C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#391D11
hypocenterC11#14626
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
21. #10622842C4semidirect
440. C11#14626semidirect

Maximal subgroups

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

subgroupindex
C2×#106228422
C2×#106225462
#130668872
#130668822
#130668772
#130668762
#130668752
#130668672
#130668662
#130668432
C2×C11×#3912
#1462611