Finite Group Databasebeta

← #14682197

Subgroups — #14682197

Order 2816.

1390 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622598C212yesmaximal
2C2×#10622594C212yesmaximal
3#13066881C212yesmaximal
4#13066869C212yesmaximal
5#13066869C212yesmaximal
6#13066850C212yesmaximal
7#13066846C211yesmaximal, characteristic
8#13066846C211yesmaximal, characteristic
9C2×C11×#389C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2212yes—
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2212yes—
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4×Dic11C2212yes—
21C11×#389C418yescomplemented
22C2×C11×#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32#10622598—28no—
33#10622594—28no—
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C2×C11×C4⋊C4—24no—
44C2×C11×C4⋊C4—24no—
45C2×C11×C4⋊C4—41no—
46C2×C11×C4⋊C4—41no—
47C2×C11×C4⋊C4C2×C418yes—
48C2×C11×C4⋊C4C2×C414yes—
49C2×C11×C4⋊C4C2×C414yes—
50C2×C11×C4⋊C4D414yes—
51C2×C11×C4⋊C4Q814yes—
52C2×C42×C11—41no—
53C2×C42×C11—41no—
54C2×C42×C11C2×C414yes—
55C2×C4⋊Dic11—24no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—24no—
59C2×C4⋊Dic11—24no—
60C2×C4⋊Dic11—41no—
61C2×C4⋊Dic11—41no—
62C2×C4⋊Dic11—41no—
63C2×C4⋊Dic11—41no—
64C2×C4⋊Dic11—42no—
65C2×C4⋊Dic11—41no—
66C2×C4⋊Dic11—41no—
67C2×C4⋊Dic11—41no—
68C2×C4⋊Dic11—41no—
69C2×C4⋊Dic11—42no—
70C2×C4⋊Dic11—42no—
71C2×C4⋊Dic11D414yes—
72C2×C4⋊Dic11Q814yes—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—42no—
76C11×#95C2×C418yes—
77C11⋊#95—24no—
78C11⋊#95—24no—
79C11⋊#95—24no—
80C11⋊#95—24no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86#14441—111nomaximal, Sylow
87C24×C11C2411yescharacteristic
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11C22×C414yes—
111C22×C4×C11C22×C414yes—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D414yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×Q812yes—
119C22×C4×C11C2×Q814yes—
120C22×C4×C11C2×Q812yes—
121C22×C4×C11#4112yes—
122C22×C4×C11#4112yes—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
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—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
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×Dic11C2×D414yes—
150C22×Dic11C2×Q814yes—
151C11×C4⋊C4—216no—
152C11×C4⋊C4—44no—
153C11×C4⋊C4C4⋊C4116yescomplemented
154C42×C11—44no—
155C4⋊Dic11—44no—
156C4⋊Dic11—44no—
157C4⋊Dic11—48no—
158C4⋊Dic11—44no—
159C4⋊Dic11—44no—
160C4⋊Dic11—48no—
161C4×Dic11—48no—
162C2×#389—112no—
163C2×#389D1111yescharacteristic
164C2×#387—112no—
165#1444—112no—
166#1441—112no—
167#1441—112no—
168#1436—112no—
169C4⋊#95—111no—
170C4⋊#95—111no—
171C23×C11C23×C411yescharacteristic
172C23×C11C22×D411yescharacteristic
173C23×C11C22×D411yescharacteristic
174C23×C11C22×Q811yescharacteristic
175C23×C11C22×Q811yescharacteristic
176C23×C11C2×#4111yescharacteristic
177C23×C11C2×#4111yescharacteristic
178C23×C11H(5,𝔽2)11yescharacteristic
179C23×C11H(5,𝔽2)11yescharacteristic
180C23×C11H(5,𝔽2)11yescharacteristic
181C23×C11H(5,𝔽2)11yescharacteristic
182C23×C112−1+411yescharacteristic
183C23×C112−1+411yescharacteristic
184C23×C112−1+411yescharacteristic
185C23×C112−1+411yescharacteristic
186C2×C4×C11—24no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
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—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11C2×C4⋊C414yes—
218C2×C4×C11C2×C4⋊C418yes—
219C2×C4×C11C4×D414yes—
220C2×C4×C11C4×Q814yes—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
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—
248C2×Dic11—42no—
249C22×C4⋊C4—111no—
250C22×C4⋊C4—111no—
251C22×C4⋊C4—112no—
252C22×C4⋊C4—111no—
253C22×C4⋊C4—111no—
254C22×C4⋊C4—112no—
255C22×C4⋊C4C2×D1112yes—
256C22×C4⋊C4C2×D1111yescharacteristic
257C22×C4⋊C4C2×D1111yescharacteristic
258C22×C42—112no—
259C22×C42C2×D1111yescharacteristic
260#389—228no—
261#389Dic1118yescomplemented
262#387—228no—
263C2×#95—112no—
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—
273C22×C11C22×C4⋊C411yescharacteristic
274C22×C11C2×C4×D411yescharacteristic
275C22×C11C2×C4×Q811yescharacteristic
276C22×C11#51811yescharacteristic
277C22×C11#51911yescharacteristic
278C22×C11#52011yescharacteristic
279C22×C11#52011yescharacteristic
280C22×C11#53411yescharacteristic
281C22×C11#53711yescharacteristic
282C22×C11#53711yescharacteristic
283C22×C11#53711yescharacteristic
284C22×C11#53811yescharacteristic
285C22×C11#53811yescharacteristic
286C22×C11#53911yescharacteristic
287C22×C11#53911yescharacteristic
288C22×C11#54311yescharacteristic
289C22×C11#54411yescharacteristic
290C22×C11#54411yescharacteristic
291C22×C11#54411yescharacteristic
292C22×C11D4211yescharacteristic
293C22×C11#54711yescharacteristic
294C22×C11#54711yescharacteristic
295C22×C11D4×Q811yescharacteristic
296C22×C11D4×Q811yescharacteristic
297C22×C11D4×Q811yescharacteristic
298C22×C11#55011yescharacteristic
299C22×C11#55411yescharacteristic
300C22×C11#55611yescharacteristic
301C22×C11#55711yescharacteristic
302C22×C11#55711yescharacteristic
303C22×C11Q8211yescharacteristic
304C22×C11#56211yescharacteristic
305C22×C11#56311yescharacteristic
306C22×C11#56311yescharacteristic
307C22×C11#56411yescharacteristic
308C4×C11—24no—
309C4×C11—24no—
310C4×C11—24no—
311C4×C11—28no—
312C4×C11—44no—
313Dic11—44no—
314Dic11—44no—
315Dic11—82no—
316Dic11—82no—
317C23×C4—112no—
318C23×C4—112no—
319C23×C4—112no—
320C23×C4—112no—
321C23×C4C22×D1112yes—
322C23×C4C22×D1112yes—
323C23×C4C22×D1111yescharacteristic
324C23×C4C22×D1111yescharacteristic
325C23×C4C22×D1111yescharacteristic
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—41no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4—114no—
331C2×C4⋊C4—114no—
332C2×C4⋊C4—224no—
333C2×C4⋊C4—224no—
334C2×C4⋊C4—224no—
335C2×C4⋊C4—222no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—441no—
338C2×C4⋊C4—441no—
339C2×C4⋊C4—441no—
340C2×C4⋊C4—441no—
341C2×C4⋊C4—442no—
342C2×C4⋊C4—441no—
343C2×C4⋊C4—441no—
344C2×C4⋊C4—441no—
345C2×C4⋊C4—441no—
346C2×C4⋊C4—442no—
347C2×C4⋊C4—442no—
348C2×C4⋊C4Dic2214yes—
349C2×C4⋊C4D4414yes—
350C2×C4⋊C4C2×Dic1118yes—
351C2×C4⋊C4C2×Dic1114yes—
352C2×C4⋊C4C2×Dic1114yes—
353C2×C42—41no—
354C2×C42—41no—
355C2×C42—224no—
356C2×C42—224no—
357C2×C42—442no—
358C2×C42C2×Dic1114yes—
359#95—224no—
360#95—224no—
361#95—224no—
362#95—224no—
363#95—224no—
364#95—224no—
365#95—224no—
366#95—442no—
367#95—442no—
368#95C2×Dic1118yes—
369C2×C11#231611yescharacteristic
370C2×C11#232511yescharacteristic
371C2×C11#232911yescharacteristic
372C2×C11D4×C4⋊C411yescharacteristic
373C2×C11Q8×C4⋊C411yescharacteristic
374C2×C11#236511yescharacteristic
375C2×C11#238211yescharacteristic
376C2×C11#268211yescharacteristic
377C2×C11#268311yescharacteristic
378C2×C11#272611yescharacteristic
379C2×C11#272611yescharacteristic
380C2×C11#272711yescharacteristic
381C2×C11#273411yescharacteristic
382C2×C11#280511yescharacteristic
383C2×C11#280611yescharacteristic
384C24C23×D1111yescharacteristic
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—114no—
408C22×C4—114no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
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—222no—
434C22×C4—222no—
435C22×C4C2×Dic2212yes—
436C22×C4C2×Dic2214yes—
437C22×C4C2×D4412yes—
438C22×C4C2×D4414yes—
439C22×C4D4×D1112yes—
440C22×C4#434112yes—
441C22×C4Q8×D1112yes—
442C22×C4#434312yes—
443C22×C4C22×Dic1114yes—
444C22×C4C22×Dic1114yes—
445C22×C4C22×Dic1112yes—
446C22×C4C22×Dic1112yes—
447C22×C4C22×Dic1112yes—
448C4⋊C4—216no—
449C4⋊C4—44no—
450C4⋊C4—444no—
451C4⋊C4—444no—
452C4⋊C4—448no—
453C4⋊C4—444no—
454C4⋊C4—444no—
455C4⋊C4—448no—
456C4⋊C4C4⋊Dic11116yescomplemented
457C42—44no—
458C42—448no—
459C11#1444111yescharacteristic, complemented, Sylow
460C23C22×Dic2211yescharacteristic
461C23C22×D4411yescharacteristic
462C23C2×D4×D1111yescharacteristic
463C23C2×#434111yescharacteristic
464C23#6703711yescharacteristic
465C23#6703711yescharacteristic
466C23C2×Q8×D1111yescharacteristic
467C23C2×#434311yescharacteristic
468C23#6704011yescharacteristic
469C23#6704011yescharacteristic
470C23#6704211yescharacteristic
471C23#6704211yescharacteristic
472C23#6704311yescharacteristic
473C23#6704311yescharacteristic
474C23C23×Dic1111yescharacteristic
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—442no—
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×C4C2×C4⋊Dic1114yes—
535C2×C4C2×C4⋊Dic1118yes—
536C2×C4D4×Dic1114yes—
537C2×C4Q8×Dic1114yes—
538C22#1062303111yescharacteristic
539C22#1062303111yescharacteristic
540C22#1062304111yescharacteristic
541C22#1062304111yescharacteristic
542C22D4×Dic2211yescharacteristic
543C22#1062307411yescharacteristic
544C22D4×D4411yescharacteristic
545C22#1062308611yescharacteristic
546C22Q8×Dic2211yescharacteristic
547C22#1062310111yescharacteristic
548C22Q8×D4411yescharacteristic
549C22#1062310811yescharacteristic
550C22#1062312811yescharacteristic
551C22#1062313311yescharacteristic
552C22#1062313611yescharacteristic
553C22#1062314811yescharacteristic
554C22#1062315411yescharacteristic
555C22#1062316511yescharacteristic
556C22#1062317511yescharacteristic
557C22#1062317611yescharacteristic
558C22C11⋊#56411yescharacteristic
559C22#1062323011yescharacteristic
560C22#1062323011yescharacteristic
561C22#1062323111yescharacteristic
562C22#1062325211yescharacteristic
563C22#1062325711yescharacteristic
564C22#1062325811yescharacteristic
565C22#1062326311yescharacteristic
566C22C22×C4⋊Dic1111yescharacteristic
567C22C2×D4×Dic1111yescharacteristic
568C22#1062332911yescharacteristic
569C22C2×Q8×Dic1111yescharacteristic
570C22#1062334311yescharacteristic
571C22#1062335811yescharacteristic
572C22#1062335811yescharacteristic
573C4—24no—
574C4—28no—
575C4—24no—
576C4—24no—
577C4—44no—
578C4—444no—
579C4—444no—
580C4—882no—
581C4—882no—
582C2#1307123411yescharacteristic
583C2#1307132111yescharacteristic
584C2#1307135111yescharacteristic
585C2D4×C4⋊Dic1111yescharacteristic
586C2Q8×C4⋊Dic1111yescharacteristic
587C2#1307167611yescharacteristic
588C2#1307180211yescharacteristic
589C2#1307497811yescharacteristic
590C2#1307498711yescharacteristic
591C2#1307556711yescharacteristic
592C2#1307556811yescharacteristic
593C2#1307557711yescharacteristic
594C2#1307564711yescharacteristic
595C2#1307656911yescharacteristic
596C2#1307657811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#389C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#389D11
hypocenterC11#14441
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
21. C11×#389C4semidirect
153. C11×C4⋊C4C4⋊C4semidirect
261. #389Dic11semidirect
456. C4⋊C4C4⋊Dic11semidirect
459. C11#14441semidirect

Maximal subgroups

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

subgroupindex
C2×#106225982
C2×#106225942
#130668812
#130668692
#130668502
#130668462
C2×C11×#3892
#1444111