Finite Group Databasebeta

← #14914046

Subgroups — #14914046

Order 2816.

3190 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66988C211yesmaximal, characteristic
2C2×#10623329C211yesmaximal, characteristic
3C22×#66930C211yesmaximal, characteristic, complemented
4#13071614C218yesmaximal, complemented
5#13071480C214yesmaximal, complemented
6#13071467C214yesmaximal, complemented
7#13071290C214yesmaximal, complemented
8#13071228C211yesmaximal, characteristic, complemented
9#13071141C214yesmaximal, complemented
10C2×#10622556C211yesmaximal, characteristic, complemented
11#13070969C211yesmaximal, characteristic, complemented
12C11×#2308C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22#10623329—28no—
23C2×#66988C4116yescomplemented
24C2×#66988C2212yes—
25C2×#66988C2212yes—
26C2×#66988C2214yes—
27C2×D4×Dic11C2214yes—
28C2×D4×Dic11C2214yes—
29C2×#66979C2212yes—
30C22×Dic11⋊C4C2212yes—
31C22×Dic11⋊C4C2212yescomplemented
32C22×C4×Dic11C2212yescomplemented
33C2×#66930—28no—
34C2×#66930C2214yes—
35C2×#66930C2214yescomplemented
36C11×#386C2214yes—
37C11×#386C2214yes—
38C11×#381C2212yes—
39C11×#379C2212yes—
40#10622823C2214yescomplemented
41C4×C22⋊Dic11C2214yescomplemented
42C2×C11⋊#95C2214yescomplemented
43#10622559C2218yescomplemented
44#10622559C2214yescomplemented
45#10622558C2218yescomplemented
46#10622557C2218yescomplemented
47#10622556C2214yes—
48#10622556C2212yescomplemented
49#10622556C2212yescomplemented
50#10622555C2214yes—
51C22⋊C4×Dic11C2214yes—
52C22⋊C4×Dic11C2218yescomplemented
53C22⋊C4×Dic11C2214yescomplemented
54#10622268C2218yescomplemented
55#10622265C2218yescomplemented
56#10622262C2218yescomplemented
57#10622260C2218yescomplemented
58C25×C11C2311yescharacteristic
59C25×C11C2311yescharacteristic
60C22×D4×C11—24no—
61C22×D4×C11—24no—
62C22×D4×C11C2×C418yes—
63C22×D4×C11C2312yes—
64C22×D4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2312yes—
67C23×C4×C11C2312yes—
68C23×Dic11—24no—
69C23×Dic11—24no—
70C23×Dic11C2×C418yescomplemented
71C23×Dic11C2312yes—
72C23×Dic11C2312yes—
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2314yes—
76C23×Dic11C2312yes—
77C23×Dic11C2312yes—
78C23×Dic11C2312yes—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—24no—
81C2×C11×C22⋊C4C2312yes—
82C2×C11×C22⋊C4C2312yes—
83C2×C11×C22⋊C4C2312yes—
84C2×C11×C22⋊C4C2312yes—
85C2×C11×C22⋊C4C2318yes—
86C2×C22⋊Dic11—24no—
87C2×C22⋊Dic11—28no—
88C2×C22⋊Dic11C2×C4116yescomplemented
89C2×C22⋊Dic11C2×C418yescomplemented
90C2×C22⋊Dic11D418yes—
91C2×C22⋊Dic11C2312yes—
92C2×C22⋊Dic11C2312yes—
93C2×C22⋊Dic11C2314yes—
94C2×C22⋊Dic11C2314yes—
95C2×C22⋊Dic11C2312yes—
96C2×C22⋊Dic11C2314yes—
97C2×C22⋊Dic11C2312yes—
98C2×C22⋊Dic11C2312yes—
99C2×C22⋊Dic11C2312yes—
100#66988C2×C4116yescomplemented
101#66988C2×C4116yescomplemented
102#66988C2×C4132yescomplemented
103D4×Dic11—216no—
104D4×Dic11—216no—
105#66979—28no—
106C2×C4⋊Dic11C2314yes—
107C2×Dic11⋊C4—28no—
108C2×Dic11⋊C4C2×C4116yescomplemented
109C2×Dic11⋊C4C2318yes—
110C2×Dic11⋊C4C2318yes—
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2314yes—
113C2×C4×Dic11—28no—
114C2×C4×Dic11C2318yes—
115C2×C4×Dic11C2314yes—
116C2×C4×Dic11C2318yes—
117#66930—216no—
118#66930—216no—
119C11×#95C2318yes—
120C11⋊#95C2318yes—
121C11⋊#95C2318yes—
122C11⋊#95C2318yes—
123C11⋊#95C2318yes—
124#34199—111nomaximal, Sylow
125C24×C11—22no—
126C24×C11—22no—
127C24×C11—44no—
128C24×C11—44no—
129C24×C11C22×C414yes—
130C24×C11C22×C414yes—
131C24×C11C2×D414yes—
132C24×C11#4114yes—
133C24×C11C2412yes—
134C24×C11C2411yescharacteristic
135C24×C11C2411yescharacteristic
136C24×C11C2411yescharacteristic
137C2×D4×C11—232no—
138C2×D4×C11—24no—
139C2×D4×C11—24no—
140C2×D4×C11—24no—
141C2×D4×C11—24no—
142C2×D4×C11C22×C418yes—
143C2×D4×C11C22×C418yes—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—44no—
149C22×C4×C11—44no—
150C22×C4×C11C22×C414yes—
151C22×C4×C11C2414yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2412yes—
154C22×Dic11—28no—
155C22×Dic11—232no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—24no—
165C22×Dic11—44no—
166C22×Dic11—44no—
167C22×Dic11—44no—
168C22×Dic11—48no—
169C22×Dic11C22×C418yes—
170C22×Dic11C22×C418yes—
171C22×Dic11C22×C414yes—
172C22×Dic11C22×C414yes—
173C22×Dic11C22×C418yes—
174C22×Dic11C2×D418yes—
175C22×Dic11C2414yes—
176C22×Dic11C2412yes—
177C22×Dic11C2414yes—
178C22×Dic11C2412yes—
179C22×Dic11C2414yes—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—48no—
185C22⋊Dic11—28no—
186C22⋊Dic11—24no—
187C22⋊Dic11—24no—
188C22⋊Dic11C22×C4116yes—
189C22⋊Dic11C22×C4116yes—
190C22⋊Dic11C22×C418yes—
191C22⋊Dic11C22×C418yes—
192C22⋊Dic11C2×D418yes—
193C22⋊Dic11C2×D418yes—
194C4⋊Dic11—28no—
195Dic11⋊C4—216no—
196Dic11⋊C4—48no—
197Dic11⋊C4C22×C4116yes—
198Dic11⋊C4C22×C4116yes—
199C4×Dic11—216no—
200C4×Dic11—28no—
201C4×Dic11—48no—
202C22×#123—111no—
203C2×#518—111no—
204C22×#117—111no—
205#2359—118no—
206#2344—114no—
207#2342—114no—
208#2322—114no—
209#2315—111no—
210#2308D1111yescharacteristic
211C4×#123—114no—
212C2×#381—111no—
213#2273—111no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—28no—
220C23×C11—28no—
221C23×C11—48no—
222C23×C11—48no—
223C23×C11—48no—
224C23×C11—48no—
225C23×C11—84no—
226C23×C11—84no—
227C23×C11C4×D4116yes—
228C23×C11C23×C414yes—
229C23×C11C23×C412yes—
230C23×C11C23×C412yes—
231C23×C11C23×C412yes—
232C23×C11C22×D412yes—
233C23×C11C22×D412yes—
234C23×C11C22×D412yes—
235C23×C11C2×#4112yes—
236C23×C11C2×#4112yes—
237C23×C11C2×#4112yes—
238C23×C11C2511yescharacteristic
239D4×C11—216no—
240D4×C11—216no—
241C2×C4×C11—28no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—28no—
247C2×C4×C11—28no—
248C2×C4×C11—48no—
249C2×C4×C11—84no—
250C2×C4×C11C23×C414yes—
251C2×Dic11—216no—
252C2×Dic11—216no—
253C2×Dic11—28no—
254C2×Dic11—28no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—28no—
260C2×Dic11—28no—
261C2×Dic11—24no—
262C2×Dic11—28no—
263C2×Dic11—48no—
264C2×Dic11—48no—
265C2×Dic11—88no—
266C2×Dic11—84no—
267C2×Dic11C23×C418yes—
268C2×Dic11C23×C414yes—
269C2×Dic11C23×C414yes—
270C2×Dic11C22×D418yes—
271C23×D4C2×D1111yescharacteristic
272C24×C4—111no—
273C2×#123—112no—
274C2×#123—114no—
275C2×#123—112no—
276C2×#123—1116no—
277#518—228no—
278C2×C4×D4—114no—
279C2×C4×D4—114no—
280C2×#117—112no—
281C2×#117—114no—
282C2×#117—114no—
283C2×#117—228no—
284C22×C4⋊C4—112no—
285C22×C4⋊C4—112no—
286C22×C22⋊C4—111no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—111no—
289C22×C22⋊C4—111no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4C2×D1111yescharacteristic
292C22×C22⋊C4C2×D1111yescharacteristic
293C22×C42—112no—
294#389—118no—
295#388—118no—
296#388—118no—
297#387—118no—
298#387—118no—
299#386C2×D1114yes—
300#386C2×D1114yes—
301#385—114no—
302#385—114no—
303#385—118no—
304#381—112no—
305#381—114no—
306#381—112no—
307#381C2×D1112yes—
308#380—114no—
309#379C2×D1112yes—
310C4×C4⋊C4—118no—
311C4×C22⋊C4—114no—
312C4×C22⋊C4—114no—
313C4×C22⋊C4—114no—
314C4×C22⋊C4—118no—
315C2×#95—114no—
316C22×C11—24no—
317C22×C11—24no—
318C22×C11—24no—
319C22×C11—24no—
320C22×C11—24no—
321C22×C11—24no—
322C22×C11—24no—
323C22×C11—24no—
324C22×C11—24no—
325C22×C11—24no—
326C22×C11—28no—
327C22×C11—416no—
328C22×C11—44no—
329C22×C11—44no—
330C22×C11—88no—
331C22×C11C2×C4×D414yes—
332C22×C11C2×C4×D414yes—
333C22×C11C2×C4×D414yes—
334C22×C11C24×C411yescharacteristic
335C22×C11C23×D411yescharacteristic
336C22×C11C22×#4111yescharacteristic
337C22×C11#58514yes—
338C4×C11—24no—
339C4×C11—44no—
340C4×C11—44no—
341Dic11—24no—
342Dic11—24no—
343Dic11—28no—
344Dic11—28no—
345Dic11—44no—
346C25C22×D1111yescharacteristic
347C25C22×D1111yescharacteristic
348C22×D4—24no—
349C22×D4—24no—
350C22×D4C4×D1118yes—
351C22×D4C22×D1112yes—
352C22×D4C22×D1112yes—
353C23×C4—118no—
354C23×C4—112no—
355C23×C4—111no—
356C23×C4—112no—
357C23×C4—111no—
358C23×C4—112no—
359C23×C4—112no—
360C23×C4—112no—
361C23×C4—114no—
362C23×C4—224no—
363C23×C4—224no—
364C23×C4C22×D1111yescharacteristic
365C23×C4C22×D1112yes—
366C23×C4C22×D1112yes—
367#123—1116no—
368#123—1132no—
369#123—1116no—
370C4×D4—2216no—
371C4×D4—2216no—
372#117—2216no—
373#117—2216no—
374#117—228no—
375C2×C4⋊C4—1116no—
376C2×C4⋊C4—114no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—118no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—118no—
381C2×C4⋊C4—228no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—1116no—
385C2×C22⋊C4—118no—
386C2×C22⋊C4—118no—
387C2×C22⋊C4—112no—
388C2×C22⋊C4—112no—
389C2×C22⋊C4—112no—
390C2×C22⋊C4—112no—
391C2×C22⋊C4—114no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—112no—
394C2×C22⋊C4—112no—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—228no—
397C2×C22⋊C4—224no—
398C2×C22⋊C4C22×D1112yes—
399C2×C22⋊C4C22×D1112yes—
400C2×C22⋊C4C22×D1112yes—
401C2×C22⋊C4C22×D1112yes—
402C2×C22⋊C4C22×D1118yes—
403C2×C42—118no—
404C2×C42—114no—
405C2×C42—118no—
406C2×C42—228no—
407#95—118no—
408#95—118no—
409#95—118no—
410#95—118no—
411#95C22×D1118yes—
412C2×C11—24no—
413C2×C11—24no—
414C2×C11—24no—
415C2×C11—44no—
416C2×C11C22×C4×D411yescharacteristic
417C2×C11#342812yes—
418C2×C11#348512yes—
419C2×C11#349112yes—
420C24—22no—
421C24—22no—
422C24—44no—
423C24—44no—
424C24C2×C4×D1114yes—
425C24C2×C4×D1114yes—
426C24D4×D1114yes—
427C24#434114yes—
428C24C23×D1112yes—
429C24C23×D1111yescharacteristic
430C24C23×D1111yescharacteristic
431C24C23×D1111yescharacteristic
432C2×D4—232no—
433C2×D4—24no—
434C2×D4—24no—
435C2×D4—24no—
436C2×D4—24no—
437C2×D4C2×C4×D1118yes—
438C2×D4C2×C4×D1118yes—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—44no—
444C22×C4—44no—
445C22×C4—118no—
446C22×C4—114no—
447C22×C4—118no—
448C22×C4—114no—
449C22×C4—112no—
450C22×C4—114no—
451C22×C4—112no—
452C22×C4—114no—
453C22×C4—118no—
454C22×C4—118no—
455C22×C4—114no—
456C22×C4—228no—
457C22×C4—2232no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—224no—
461C22×C4—224no—
462C22×C4—224no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—224no—
466C22×C4—224no—
467C22×C4—444no—
468C22×C4—444no—
469C22×C4—448no—
470C22×C4—444no—
471C22×C4C2×C4×D1114yes—
472C22×C4C23×D1114yes—
473C22×C4C23×D1114yes—
474C22×C4C23×D1112yes—
475C4⋊C4—1116no—
476C4⋊C4—1116no—
477C4⋊C4—2216no—
478C4⋊C4—228no—
479C4⋊C4—448no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—48no—
485C22⋊C4—118no—
486C22⋊C4—118no—
487C22⋊C4—1116no—
488C22⋊C4—1116no—
489C22⋊C4—118no—
490C22⋊C4—118no—
491C22⋊C4—228no—
492C22⋊C4—224no—
493C22⋊C4—224no—
494C42—2216no—
495C42—228no—
496C42—448no—
497C11#3419911yescharacteristic, complemented, Sylow
498C23—24no—
499C23—24no—
500C23—24no—
501C23—22no—
502C23—22no—
503C23—28no—
504C23—28no—
505C23—48no—
506C23—48no—
507C23—48no—
508C23—48no—
509C23—84no—
510C23—84no—
511C23(C22⋊D11)⋊C4116yes—
512C23C22×C4×D1114yes—
513C23C22×C4×D1112yes—
514C23C22×C4×D1112yes—
515C23C22×C4×D1112yes—
516C23C2×D4×D1112yes—
517C23C2×D4×D1112yes—
518C23C2×D4×D1112yes—
519C23C2×#434112yes—
520C23C2×#434112yes—
521C23C2×#434112yes—
522C23C24×D1111yescharacteristic
523D4—216no—
524D4—216no—
525C2×C4—28no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—28no—
531C2×C4—28no—
532C2×C4—48no—
533C2×C4—84no—
534C2×C4—118no—
535C2×C4—114no—
536C2×C4—114no—
537C2×C4—118no—
538C2×C4—2216no—
539C2×C4—228no—
540C2×C4—228no—
541C2×C4—2216no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—228no—
547C2×C4—228no—
548C2×C4—224no—
549C2×C4—228no—
550C2×C4—448no—
551C2×C4—448no—
552C2×C4—888no—
553C2×C4—884no—
554C2×C4C22×C4×D1114yes—
555C22—24no—
556C22—24no—
557C22—24no—
558C22—24no—
559C22—24no—
560C22—24no—
561C22—24no—
562C22—24no—
563C22—24no—
564C22—24no—
565C22—28no—
566C22—416no—
567C22—44no—
568C22—44no—
569C22—88no—
570C22C2×(C22⋊D11)⋊C414yes—
571C22C2×(C22⋊D11)⋊C414yes—
572C22C2×(C22⋊D11)⋊C414yes—
573C22C23×C4×D1111yescharacteristic
574C22C22×D4×D1111yescharacteristic
575C22C22×#434111yescharacteristic
576C22#1062345514yes—
577C4—24no—
578C4—44no—
579C4—44no—
580C4—228no—
581C4—224no—
582C4—224no—
583C4—228no—
584C4—444no—
585C2—24no—
586C2—24no—
587C2—24no—
588C2—44no—
589C2C22×(C22⋊D11)⋊C411yescharacteristic
590C2#1308181412yes—
591C2#1308225712yes—
592C2#1308231312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2308C2
socle, cosocleC23×C11C25
prime radicalC23×D4×C11C22
hypercenter#2308D11
hypocenterC11#34199
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2308

Complements

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

NH ≅ G/Ntype
3. C22×#66930C2semidirect
4. #13071614C2semidirect
5. #13071480C2semidirect
6. #13071467C2semidirect
7. #13071290C2semidirect
8. #13071228C2semidirect
9. #13071141C2semidirect
10. C2×#10622556C2semidirect
11. #13070969C2semidirect
23. C2×#66988C4semidirect
31. C22×Dic11⋊C4C22semidirect
32. C22×C4×Dic11C22semidirect
35. C2×#66930C22semidirect
40. #10622823C22semidirect
41. C4×C22⋊Dic11C22semidirect
42. C2×C11⋊#95C22semidirect
43. #10622559C22semidirect
44. #10622559C22semidirect
45. #10622558C22semidirect
46. #10622557C22semidirect
48. #10622556C22semidirect
49. #10622556C22semidirect
52. C22⋊C4×Dic11C22semidirect
53. C22⋊C4×Dic11C22semidirect
54. #10622268C22semidirect
55. #10622265C22semidirect
56. #10622262C22semidirect
57. #10622260C22semidirect
70. C23×Dic11C2×C4semidirect
88. C2×C22⋊Dic11C2×C4semidirect
89. C2×C22⋊Dic11C2×C4semidirect
100. #66988C2×C4semidirect
101. #66988C2×C4semidirect
102. #66988C2×C4semidirect
108. C2×Dic11⋊C4C2×C4semidirect
497. C11#34199semidirect

Maximal subgroups

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

subgroupindex
C22×#669882
C2×#106233292
C22×#669302
#130716142
#130714802
#130714672
#130712902
#130712282
#130711412
C2×#106225562
#130709692
C11×#23082
#3419911