Finite Group Databasebeta

← #14677253

Subgroups — #14677253

Order 2816.

2358 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66928C211yesmaximal, characteristic
2C22×#66940C211yesmaximal, characteristic, complemented
3C2×#10622587C211yesmaximal, characteristic, complemented
4C2×#10622601C211yesmaximal, characteristic
5C2×#10622601C211yesmaximal, characteristic
6#13066860C214yesmaximal, complemented
7#13066852C214yesmaximal, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C11×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2214yes—
17C22×(C2×D11)⋊C4C2214yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23C2×#66940—24no—
24C2×#66940—24no—
25C2×#66940—24no—
26C2×#66928—24no—
27C2×#66928—24no—
28C2×#66928C418yescomplemented
29C2×C11×#95C2214yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2214yes—
33#10622601—24no—
34#10622601—24no—
35#10622587—24no—
36C24×D11C2312yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×Dic11C2311yescharacteristic
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C23×Dic11C2311yescharacteristic
45C22×D44—22no—
46C22×D44—22no—
47C22×D44—22no—
48C22×D44—22no—
49C22×D44—22no—
50C22×D44—22no—
51C22×D44C2×C414yes—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22C2×C414yes—
57C22×Dic22D414yes—
58C22×Dic22D414yes—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4D414yes—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11C2×C414yes—
68C2×(C2×D11)⋊C4—28no—
69C2×(C2×D11)⋊C4—28no—
70C2×(C2×D11)⋊C4—28no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—28no—
74C2×(C2×D11)⋊C4—28no—
75C2×(C2×D11)⋊C4—44no—
76C2×(C2×D11)⋊C4—44no—
77C2×(C2×D11)⋊C4C2×C4116yes—
78C2×Dic11⋊C4—24no—
79C2×Dic11⋊C4—24no—
80C2×Dic11⋊C4—24no—
81C2×C4×Dic11—24no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—24no—
85C2×C4×Dic11—24no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11—22no—
89C2×C4×Dic11D414yes—
90#66940—232no—
91#66928—232no—
92C11×#95—44no—
93C11⋊#95—28no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96#14026—111nomaximal, Sylow
97C24×C11C2411yescharacteristic
98C23×D11—22no—
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—24no—
103C23×D11—24no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—24no—
107C23×D11—24no—
108C23×D11C22×C414yes—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11C22×C414yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C2×D414yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11#4112yes—
132C22×C4×C11#4112yes—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11C22×C414yes—
151C22×Dic11C2×D412yes—
152C22×Dic11C2×D414yes—
153C22×Dic11C2×D414yes—
154C22×Dic11C2×D412yes—
155C22×Dic11#4114yes—
156C22×Dic11#4114yes—
157C2×D44—28no—
158C2×D44—28no—
159C2×D44—28no—
160C2×D44—44no—
161C2×D44—44no—
162C2×D44—44no—
163C2×D44—44no—
164C2×Dic22—28no—
165C2×Dic22—28no—
166C2×Dic22—28no—
167C2×Dic22—28no—
168C2×Dic22—28no—
169C2×Dic22—28no—
170C2×Dic22C22⋊C4116yescomplemented
171C11×C4⋊C4—28no—
172C11×C4⋊C4—44no—
173C42×C11—28no—
174(C2×D11)⋊C4—232no—
175(C2×D11)⋊C4—416no—
176(C2×D11)⋊C4—48no—
177(C2×D11)⋊C4—48no—
178Dic11⋊C4—216no—
179C4×Dic11—216no—
180C4×Dic11—28no—
181C4×Dic11—44no—
182C22×#124—111no—
183C22×C4×Q8—111no—
184C2×#391—111no—
185C2×#390—111no—
186C2×#390—111no—
187#1439—114no—
188#1437—114no—
189C4⋊#95D1111yescharacteristic, complemented
190C4×#95—111no—
191C23×C11C23×C411yescharacteristic
192C23×C11C22×D411yescharacteristic
193C23×C11C22×D411yescharacteristic
194C23×C11C22×D411yescharacteristic
195C23×C11C22×D411yescharacteristic
196C23×C11C2×#4111yescharacteristic
197C23×C11C2×#4111yescharacteristic
198C23×C11C2×#4112yes—
199C23×C11C2×#4112yes—
200C23×C11H(5,𝔽2)12yes—
201C23×C112−1+412yes—
202C22×D11—24no—
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—28no—
206C22×D11—28no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—44no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—44no—
217C22×D11—44no—
218C22×D11—44no—
219C22×D11—44no—
220C22×D11—44no—
221C22×D11—44no—
222C22×D11—44no—
223C22×D11—44no—
224C22×D11—44no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—28no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—44no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—44no—
241C2×C4×C11—44no—
242C2×C4×C11C2×C22⋊C414yes—
243C2×C4×C11C4×D414yes—
244C2×C4×C11C4×D414yes—
245C2×C4×C11#12014yes—
246C2×C4×C11#12114yes—
247C2×C4×C11#12114yes—
248C2×C4×C11#12314yes—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—22no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11C2×C22⋊C418yes—
272C2×Dic11#12414yescomplemented
273D44—416no—
274Dic22—232no—
275C23×Q8—111no—
276C23×D4—111no—
277C2×#124—118no—
278C2×#124—224no—
279C2×#124—224no—
280C2×C4×Q8—224no—
281C2×C4×Q8—224no—
282C2×C4×Q8—224no—
283C22×C4⋊C4—112no—
284C22×C4⋊C4C2×D1111yescharacteristic
285C22×C4⋊C4C2×D1111yescharacteristic
286C22×C22⋊C4—114no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—114no—
289C22×C22⋊C4—112no—
290C22×C42—111no—
291C22×C42—112no—
292C22×C42—111no—
293C22×C42C2×D1111yescharacteristic
294#391—224no—
295#390—224no—
296#390—224no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—114no—
300C2×#95C2×D1114yes—
301C22×C11C22×C22⋊C411yescharacteristic
302C22×C11C2×C4×D411yescharacteristic
303C22×C11C2×C4×D411yescharacteristic
304C22×C11C4×#4112yes—
305C22×C11#52012yes—
306C22×C11C2×#12011yescharacteristic
307C22×C11C2×#12111yescharacteristic
308C22×C11C2×#12111yescharacteristic
309C22×C11C2×#12311yescharacteristic
310C22×C11C2×#12411yescharacteristic
311C22×C11#52912yes—
312C22×C11#53211yescharacteristic
313C22×C11#53511yescharacteristic
314C22×C11#53611yescharacteristic
315C22×C11#54212yes—
316C22×C11#54612yes—
317C22×C11#54812yes—
318C22×C11#54812yes—
319C22×C11#54812yes—
320C22×C11#55012yes—
321C22×C11#55012yes—
322C22×C11#55612yes—
323C22×C11#55912yes—
324C2×D11—44no—
325C2×D11—48no—
326C2×D11—48no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—84no—
330C2×D11—82no—
331C2×D11—82no—
332C2×D11—84no—
333C2×D11—82no—
334C2×D11—82no—
335C4×C11—44no—
336C4×C11—44no—
337C4×C11—82no—
338C4×C11#38618yes—
339Dic11—24no—
340Dic11—28no—
341Dic11—44no—
342Dic11—42no—
343C25—112no—
344C22×Q8—114no—
345C22×Q8—114no—
346C22×Q8—114no—
347C22×Q8—222no—
348C22×Q8—222no—
349C22×Q8—222no—
350C22×Q8—222no—
351C22×D4—114no—
352C22×D4—222no—
353C22×D4—222no—
354C22×D4—222no—
355C22×D4—222no—
356C22×D4—222no—
357C22×D4—222no—
358C23×C4—112no—
359C23×C4—111no—
360C23×C4—111no—
361C23×C4—112no—
362C23×C4C22×D1112yes—
363C23×C4C22×D1112yes—
364C23×C4C22×D1112yes—
365C23×C4C22×D1111yescharacteristic
366#124—2232no—
367C4×Q8—2232no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—224no—
376C2×C4⋊C4D4414yes—
377C2×C22⋊C4—1116no—
378C2×C22⋊C4—228no—
379C2×C22⋊C4—228no—
380C2×C22⋊C4—224no—
381C2×C22⋊C4—224no—
382C2×C22⋊C4—228no—
383C2×C22⋊C4—228no—
384C2×C22⋊C4—228no—
385C2×C22⋊C4—444no—
386C2×C22⋊C4—444no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—114no—
390C2×C42—224no—
391C2×C42—224no—
392C2×C42—224no—
393C2×C42—222no—
394C2×C42—222no—
395C2×C42—222no—
396C2×C42—222no—
397C2×C42—222no—
398C2×C42C4×D1114yes—
399#95—44no—
400#95—224no—
401#95—224no—
402#95—228no—
403C2×C11C2×#38611yescharacteristic
404C2×C11C4×#12411yescharacteristic
405C2×C11#232611yescharacteristic
406C2×C11#234112yes—
407C2×C11#236712yes—
408C2×C11#242612yes—
409C2×C11#243111yescharacteristic
410C2×C11#243611yescharacteristic
411C2×C11#244812yes—
412C2×C11#254511yescharacteristic
413C2×C11#254811yescharacteristic
414D11—84no—
415C24—114no—
416C24—222no—
417C24—222no—
418C24—222no—
419C24—222no—
420C24—222no—
421C24—224no—
422C24—222no—
423C24—224no—
424C24—224no—
425C24—224no—
426C24C23×D1111yescharacteristic
427C2×Q8—1116no—
428C2×Q8—228no—
429C2×Q8—228no—
430C2×Q8—228no—
431C2×Q8—228no—
432C2×Q8—228no—
433C2×Q8—228no—
434C2×D4—228no—
435C2×D4—228no—
436C2×D4—228no—
437C2×D4—444no—
438C2×D4—444no—
439C2×D4—444no—
440C2×D4—444no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—112no—
459C22×C4—114no—
460C22×C4—114no—
461C22×C4—112no—
462C22×C4—114no—
463C22×C4—221no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—221no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—221no—
472C22×C4—222no—
473C22×C4—221no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4C2×C4×D1114yes—
481C22×C4C2×C4×D1112yes—
482C22×C4C2×D4414yes—
483C22×C4C2×D4412yes—
484C22×C4#433912yes—
485C22×C4D4×D1112yes—
486C22×C4D4×D1112yes—
487C22×C4D4×D1112yes—
488C22×C4#434312yes—
489C4⋊C4—28no—
490C4⋊C4—44no—
491C4⋊C4—2216no—
492C22⋊C4—2232no—
493C22⋊C4—4416no—
494C22⋊C4—448no—
495C22⋊C4—448no—
496C42—28no—
497C42—2216no—
498C42—228no—
499C42—444no—
500C11#1402611yescharacteristic, complemented, Sylow
501C23—224no—
502C23—224no—
503C23—224no—
504C23—228no—
505C23—228no—
506C23—442no—
507C23—442no—
508C23—444no—
509C23—442no—
510C23—442no—
511C23—442no—
512C23—442no—
513C23—444no—
514C23—444no—
515C23—444no—
516C23—444no—
517C23—444no—
518C23—444no—
519C23—444no—
520C23—444no—
521C23—442no—
522C23—442no—
523C23—444no—
524C23C22×C4×D1111yescharacteristic
525C23C22×D4411yescharacteristic
526C23C2×#433911yescharacteristic
527C23C2×D4×D1111yescharacteristic
528C23C2×D4×D1111yescharacteristic
529C23C2×D4×D1111yescharacteristic
530C23#6703712yes—
531C23C2×#434311yescharacteristic
532C23#6704012yes—
533C23#41×D1112yes—
534C23#41×D1112yes—
535Q8—2232no—
536D4—4416no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—28no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—42no—
554C2×C4—118no—
555C2×C4—114no—
556C2×C4—222no—
557C2×C4—224no—
558C2×C4—222no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—222no—
571C2×C4—224no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4C4×D4414yes—
579C2×C4C22⋊C4×D1114yes—
580C2×C4#6693514yes—
581C2×C4#6693714yes—
582C2×C4#6694614yes—
583C2×C4#6694714yes—
584C2×C4#6694814yes—
585C22—444no—
586C22—448no—
587C22—448no—
588C22—444no—
589C22—444no—
590C22—884no—
591C22—884no—
592C22—882no—
593C22—882no—
594C22—882no—
595C22—882no—
596C22C2×C4×D4411yescharacteristic
597C22C2×C22⋊C4×D1111yescharacteristic
598C22C2×#6693511yescharacteristic
599C22C2×#6693711yescharacteristic
600C22C2×#6694611yescharacteristic
601C22#1062303512yes—
602C22C2×#6694711yescharacteristic
603C22C2×#6694811yescharacteristic
604C22#1062305312yes—
605C22#1062308512yes—
606C22#1062309012yes—
607C22#1062309912yes—
608C22#1062310712yes—
609C22#1062313012yes—
610C22#1062313012yes—
611C22#1062316412yes—
612C22#1062316412yes—
613C22#1062319911yescharacteristic
614C22D11×#12411yescharacteristic
615C22#1062322212yes—
616C22#1062324611yescharacteristic
617C22#1062325511yescharacteristic
618C22#1062326412yes—
619C4—44no—
620C4—44no—
621C4—82no—
622C4—224no—
623C4—228no—
624C4—444no—
625C4—442no—
626C4#1062227818yes—
627C2—884no—
628C2C2×#1062227811yescharacteristic
629C2#1307115511yescharacteristic
630C2#1307132411yescharacteristic
631C2#1307145312yes—
632C2#1307168712yes—
633C2#1307218012yes—
634C2#1307223411yescharacteristic
635C2#1307227311yescharacteristic
636C2#1307241612yes—
637C2#1307359911yescharacteristic
638C2#1307362011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4⋊#95D11
hypocenterC11#14026
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×#66940C2semidirect
3. C2×#10622587C2semidirect
6. #13066860C2semidirect
7. #13066852C2semidirect
8. C4×C11⋊#95C2semidirect
9. C11×C4⋊#95C2semidirect
28. C2×#66928C4semidirect
170. C2×Dic22C22⋊C4semidirect
189. C4⋊#95D11semidirect
272. C2×Dic11#124semidirect
500. C11#14026semidirect

Maximal subgroups

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

subgroupindex
C22×#669282
C22×#669402
C2×#106225872
C2×#106226012
#130668602
#130668522
C4×C11⋊#952
C11×C4⋊#952
#1402611