Finite Group Databasebeta

← #14675313

Subgroups — #14675313

Order 2816.

1970 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic22C211yesmaximal, characteristic
2C2×#10622259C212yesmaximal
3C2×C4×Dic11⋊C4C212yesmaximal
4#13066850C212yesmaximal
5#13066849C212yesmaximal
6Dic11⋊#95C211yesmaximal, characteristic
7#13066843C211yesmaximal, characteristic
8#13066842C211yesmaximal, characteristic
9#95×Dic11C211yesmaximal, characteristic
10#95×Dic11C211yesmaximal, characteristic
11C4×C11×#95C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C22×C42×C11C2212yes—
14C22×C42×C11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×Dic11⋊C4C2212yes—
17C22×Dic11⋊C4C2211yescharacteristic
18C22×Dic11⋊C4C2211yescharacteristic
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2212yes—
23C2×C4×Dic22—28no—
24C2×C4×Dic22C418yescomplemented
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2212yes—
27C2×C11×#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C4×Dic11⋊C4—28no—
38#10622259C4116yescomplemented
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C22×Dic22—24no—
51C22×Dic22—22no—
52C22×Dic22—22no—
53C22×Dic22C2×C414yes—
54C22×Dic22C2×C418yes—
55C2×C42×C11—24no—
56C2×C42×C11—24no—
57C2×C42×C11—24no—
58C2×C42×C11—42no—
59C2×C42×C11C2×C414yes—
60C2×C4⋊Dic11—24no—
61C2×C4⋊Dic11C2×C414yes—
62C2×Dic11⋊C4—24no—
63C2×Dic11⋊C4—24no—
64C2×Dic11⋊C4—24no—
65C2×Dic11⋊C4C2×C414yes—
66C2×Dic11⋊C4C2×C418yes—
67C2×Dic11⋊C4C2×C414yes—
68C2×Dic11⋊C4D418yes—
69C2×C4×Dic11—24no—
70C2×C4×Dic11—24no—
71C2×C4×Dic11—24no—
72C2×C4×Dic11—24no—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—42no—
76C2×C4×Dic11C2×C414yes—
77C2×C4×Dic11C2×C414yes—
78C2×C4×Dic11C2×C418yes—
79C4×Dic22—232no—
80C11×#95—22no—
81C11×#95C2×C418yes—
82C11×#95Q814yescomplemented
83C11⋊#95—24no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—42no—
89C11⋊#95C2×C418yes—
90C11⋊#95C2×C418yes—
91C11⋊#95C2×C418yes—
92#13817—111nomaximal, Sylow
93C24×C11C2411yescharacteristic
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
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×C11C22×C414yes—
113C22×C4×C11C22×C414yes—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C22×C414yes—
118C22×C4×C11C2×D414yes—
119C22×C4×C11C2×Q812yes—
120C22×C4×C11C2×Q814yes—
121C22×C4×C11#4112yes—
122C22×C4×C11#4114yes—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11C22×C414yes—
146C22×Dic11C22×C414yes—
147C22×Dic11C22×C412yes—
148C22×Dic11C22×C414yes—
149C22×Dic11C22×C412yes—
150C22×Dic11C22×C412yes—
151C22×Dic11C22×C412yes—
152C22×Dic11C22×C414yes—
153C22×Dic11C2×D414yes—
154C22×Dic11C2×D414yes—
155C22×Dic11#4112yes—
156C22×Dic11#4112yes—
157C2×Dic22—28no—
158C2×Dic22—28no—
159C2×Dic22—216no—
160C2×Dic22—216no—
161C2×Dic22C42116yescomplemented
162C42×C11—28no—
163C42×C11—48no—
164C4⋊Dic11—28no—
165Dic11⋊C4—216no—
166Dic11⋊C4—28no—
167Dic11⋊C4C22⋊C4116yes—
168C4×Dic11—28no—
169C4×Dic11—28no—
170C4×Dic11—216no—
171C4×Dic11—48no—
172C22×C4×Q8—111no—
173C2×#391—112no—
174C2×C4×C4⋊C4—112no—
175#1436—112no—
176#1436—112no—
177C4⋊#95—111no—
178#1434—111no—
179#1434—111no—
180C4×#95—111no—
181C4×#95—111no—
182C4×#95D1111yescharacteristic
183C23×C11C23×C411yescharacteristic
184C23×C11C23×C412yes—
185C23×C11C22×D412yes—
186C23×C11C22×Q811yescharacteristic
187C23×C11C2×#4112yes—
188C23×C11C2×#4111yescharacteristic
189C23×C11C2×#4111yescharacteristic
190C23×C11C2×#4111yescharacteristic
191C23×C11H(5,𝔽2)11yescharacteristic
192C23×C112−1+411yescharacteristic
193C23×C112−1+412yes—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11C2×C4214yes—
220C2×C4×C11C2×C22⋊C414yes—
221C2×C4×C11C4×Q814yes—
222C2×C4×C11C4×Q818yescomplemented
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—22no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—22no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11C2×C4214yes—
251C2×Dic11C2×C4214yes—
252C2×Dic11C2×C22⋊C414yes—
253C2×Dic11C2×C22⋊C414yes—
254C2×Dic11#11714yes—
255C2×Dic11C4×D418yes—
256C2×Dic11C4×D418yes—
257Dic22—232no—
258C23×Q8—111no—
259C2×C4×Q8—118no—
260C2×C4×Q8—228no—
261C22×C4⋊C4—111no—
262C22×C4⋊C4—111no—
263C22×C4⋊C4—112no—
264C22×C4⋊C4—111no—
265C22×C42—111no—
266C22×C42—111no—
267C22×C42—112no—
268C22×C42—112no—
269C22×C42C2×D1112yes—
270C22×C42C2×D1111yescharacteristic
271#391—1116no—
272C4×C4⋊C4—228no—
273C2×#95—112no—
274C2×#95—112no—
275C2×#95—112no—
276C2×#95—111no—
277C2×#95—111no—
278C2×#95—112no—
279C2×#95—112no—
280C2×#95—112no—
281C2×#95—112no—
282C2×#95C2×D1111yescharacteristic
283C2×#95C2×D1111yescharacteristic
284C2×#95C2×D1112yes—
285C22×C11C22×C4211yescharacteristic
286C22×C11C22×C22⋊C411yescharacteristic
287C22×C11C2×#11711yescharacteristic
288C22×C11C2×C4×D412yes—
289C22×C11C2×C4×D412yes—
290C22×C11C2×C4×Q811yescharacteristic
291C22×C11C2×C4×Q812yes—
292C22×C11C4×#4111yescharacteristic
293C22×C11C4×#4112yes—
294C22×C11#51911yescharacteristic
295C22×C11#51912yes—
296C22×C11#52011yescharacteristic
297C22×C11#52012yes—
298C22×C11#54612yes—
299C22×C11#54712yes—
300C22×C11#54812yes—
301C22×C11D4×Q812yes—
302C22×C11#55212yes—
303C22×C11#55411yescharacteristic
304C22×C11#55612yes—
305C22×C11#55611yescharacteristic
306C22×C11#55711yescharacteristic
307C22×C11#55911yescharacteristic
308C4×C11—24no—
309C4×C11—24no—
310C4×C11—28no—
311C4×C11—24no—
312C4×C11—44no—
313Dic11—24no—
314Dic11—24no—
315Dic11—42no—
316Dic11—44no—
317Dic11—44no—
318Dic11C4×C22⋊C418yes—
319C22×Q8—114no—
320C22×Q8—118no—
321C22×Q8—224no—
322C22×Q8—222no—
323C22×Q8—222no—
324C23×C4—111no—
325C23×C4—111no—
326C23×C4—111no—
327C23×C4—111no—
328C23×C4—112no—
329C23×C4—112no—
330C23×C4C22×D1112yes—
331C23×C4C22×D1111yescharacteristic
332C23×C4C22×D1112yes—
333C23×C4C22×D1111yescharacteristic
334C23×C4C22×D1111yescharacteristic
335C4×Q8—2232no—
336C2×C4⋊C4—114no—
337C2×C4⋊C4—118no—
338C2×C4⋊C4—114no—
339C2×C4⋊C4—114no—
340C2×C4⋊C4—118no—
341C2×C4⋊C4—224no—
342C2×C4⋊C4—224no—
343C2×C4⋊C4—224no—
344C2×C4⋊C4—224no—
345C2×C42—24no—
346C2×C42—24no—
347C2×C42—24no—
348C2×C42—42no—
349C2×C42—114no—
350C2×C42—114no—
351C2×C42—118no—
352C2×C42—224no—
353C2×C42—224no—
354C2×C42—224no—
355C2×C42—224no—
356C2×C42—224no—
357C2×C42—224no—
358C2×C42—442no—
359C2×C42C4×D1114yes—
360#95—22no—
361#95—118no—
362#95—118no—
363#95—118no—
364#95—224no—
365#95—222no—
366#95—222no—
367#95—224no—
368#95—224no—
369#95—442no—
370#95Dic2214yescomplemented
371#95C4×D1118yes—
372C2×C11C2×C4×C22⋊C411yescharacteristic
373C2×C11C42×Q811yescharacteristic
374C2×C11#227611yescharacteristic
375C2×C11#233911yescharacteristic
376C2×C11Q8×C22⋊C411yescharacteristic
377C2×C11#235511yescharacteristic
378C2×C11#235611yescharacteristic
379C2×C11#236012yes—
380C2×C11#236212yes—
381C2×C11#236512yes—
382C2×C11#236712yes—
383C24C23×D1111yescharacteristic
384C2×Q8—1116no—
385C2×Q8—228no—
386C2×Q8—228no—
387C2×Q8—2216no—
388C2×Q8—2216no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—112no—
408C22×C4—114no—
409C22×C4—114no—
410C22×C4—112no—
411C22×C4—112no—
412C22×C4—114no—
413C22×C4—112no—
414C22×C4—112no—
415C22×C4—114no—
416C22×C4—114no—
417C22×C4—114no—
418C22×C4—112no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—221no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—221no—
434C22×C4—222no—
435C22×C4—221no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4C2×Dic2212yes—
442C22×C4C2×Dic2214yes—
443C22×C4C2×C4×D1114yes—
444C22×C4C2×C4×D1112yes—
445C22×C4C2×C4×D1114yes—
446C22×C4C2×C4×D1114yes—
447C22×C4C2×C4×D1112yes—
448C22×C4C2×C4×D1112yes—
449C22×C4#433912yes—
450C22×C4#433914yes—
451C22×C4D4×D1114yes—
452C4⋊C4—1116no—
453C4⋊C4—228no—
454C4⋊C4—2216no—
455C4⋊C4—228no—
456C42—28no—
457C42—48no—
458C42—228no—
459C42—228no—
460C42—2216no—
461C42—448no—
462C11#1381711yescharacteristic, complemented, Sylow
463C23C22×Dic2211yescharacteristic
464C23C22×C4×D1111yescharacteristic
465C23C22×C4×D1112yes—
466C23C2×#433912yes—
467C23C2×#433911yescharacteristic
468C23C2×D4×D1112yes—
469C23#6703711yescharacteristic
470C23#6704011yescharacteristic
471C23#41×D1111yescharacteristic
472C23#41×D1111yescharacteristic
473C23#6704312yes—
474Q8—2232no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—114no—
501C2×C4—114no—
502C2×C4—114no—
503C2×C4—118no—
504C2×C4—118no—
505C2×C4—114no—
506C2×C4—114no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—224no—
510C2×C4—222no—
511C2×C4—224no—
512C2×C4—222no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4C4×Dic2214yes—
535C2×C4C4×Dic2218yescomplemented
536C2×C4C42×D1114yes—
537C2×C4C22⋊C4×D1114yes—
538C22C2×C4×Dic2212yes—
539C22C2×C4×Dic2211yescharacteristic
540C22C2×C42×D1111yescharacteristic
541C22C4×#433912yes—
542C22C4×#433911yescharacteristic
543C22C2×C22⋊C4×D1111yescharacteristic
544C22#1062302112yes—
545C22#1062303511yescharacteristic
546C22#1062303812yes—
547C22#1062304711yescharacteristic
548C22D11×#11711yescharacteristic
549C22#1062306212yes—
550C22#1062306412yes—
551C22D4×Dic2212yes—
552C22#1062307011yescharacteristic
553C22C4×D4×D1112yes—
554C22C4×D4×D1112yes—
555C22#1062307712yes—
556C22#1062308312yes—
557C22#1062309011yescharacteristic
558C22#1062309911yescharacteristic
559C22#1062310011yescharacteristic
560C22#1062310312yes—
561C4—28no—
562C4—24no—
563C4—24no—
564C4—24no—
565C4—44no—
566C4—118no—
567C4—224no—
568C4—224no—
569C4—444no—
570C4—444no—
571C4—442no—
572C2C4×C22⋊C4×D1111yescharacteristic
573C2C42×Dic2211yescharacteristic
574C2#1307098011yescharacteristic
575C2#1307144311yescharacteristic
576C2C22⋊C4×Dic2211yescharacteristic
577C2#1307157411yescharacteristic
578C2#1307158211yescharacteristic
579C2#1307162212yes—
580C2#1307164412yes—
581C2#1307167512yes—
582C2#1307168812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC4×C11×#95C2
socle, prime radical, cosocleC24×C11C24
hypercenterC4×#95D11
hypocenterC11#13817
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
24. C2×C4×Dic22C4semidirect
38. #10622259C4semidirect
82. C11×#95Q8semidirect
161. C2×Dic22C42semidirect
222. C2×C4×C11C4×Q8semidirect
370. #95Dic22semidirect
462. C11#13817semidirect
535. C2×C4C4×Dic22semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic222
C2×#106222592
C2×C4×Dic11⋊C42
#130668502
#130668492
Dic11⋊#952
#130668432
#130668422
#95×Dic112
C4×C11×#952
#1381711