Finite Group Databasebeta

← #14769088

Subgroups — #14769088

Order 2816.

1512 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C212yesmaximal, complemented
2C2×#10622847C212yesmaximal, complemented
3#13069415C212yesmaximal, complemented
4#13068914C212yesmaximal, complemented
5#13068909C212yesmaximal, complemented
6#13068596C211yesmaximal, characteristic, complemented
7#13068528C212yesmaximal, complemented
8#13068378C211yesmaximal, characteristic, complemented
9C2×C11×#532C211yesmaximal, characteristic
10C22×C11×#41C2212yes—
11C11×#532—28no—
12C2×C11×C4⋊Q8C411yescharacteristic
13C2×C11×#127C411yescharacteristic
14C2×C11×#124C412yes—
15C2×C11×#121C411yescharacteristic
16C2×C11×#121C411yescharacteristic
17C2×C11×#121C412yes—
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×#4318C2212yes—
23C23×C11⋊C8C2212yes—
24#10622847—28no—
25C2×C22⋊(C11⋊C8)C2212yes—
26C2×C22⋊(C11⋊C8)C2212yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28C2×C22⋊(C11⋊C8)C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2212yes—
32C2×C22⋊(C11⋊C8)C2212yes—
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34#10622624—28no—
35C2×C4⋊(C11⋊C8)C2212yes—
36C2×#66867C2212yes—
37#10622162C2211yescharacteristic
38#10622162C2211yescharacteristic
39#10622162C2212yes—
40C2×C11×#41—24no—
41C2×C11×#41—24no—
42C2×C11×#41—24no—
43C2×C11×#41—24no—
44C2×C11×#41—42no—
45C2×C11×#41—42no—
46C22×Q8×C11C2×C412yes—
47C22×D4×C11C2×C412yes—
48C22×D4×C11C2×C412yes—
49C22×D4×C11C2×C412yes—
50C22×D4×C11C2×C412yes—
51C22×D4×C11C2×C411yescharacteristic
52C22×D4×C11C2×C411yescharacteristic
53C23×C4×C11C2×C411yescharacteristic
54C23×C4×C11C2×C411yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C11×C4⋊Q8—24no—
59C11×#127—24no—
60C11×#124—28no—
61C11×#121—24no—
62C11×#121—24no—
63C11×#121—28no—
64C4×D4×C11—24no—
65C4×D4×C11—24no—
66C4×D4×C11—24no—
67C4×D4×C11D418yes—
68C2×C11×C4⋊C4C2×C411yescharacteristic
69C2×C11×C4⋊C4C2×C412yes—
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C22⋊C4C2×C412yes—
72C2×C11×C22⋊C4C2×C412yes—
73C2×C11×C22⋊C4C2×C412yes—
74C2×C11×C22⋊C4C2×C412yes—
75C2×C42×C11—24no—
76C2×C42×C11C2×C411yescharacteristic
77C2×C42×C11C2×C411yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×#4318—24no—
81C2×#4318—24no—
82C2×#4318—42no—
83C22×C11⋊C8—24no—
84C22×C11⋊C8—24no—
85C22×C11⋊C8—42no—
86C22×C11⋊C8C2312yes—
87C22×C11⋊C8C2312yes—
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2312yes—
90C22⋊(C11⋊C8)—24no—
91C22⋊(C11⋊C8)—24no—
92C22⋊(C11⋊C8)—24no—
93C22⋊(C11⋊C8)—22no—
94C22⋊(C11⋊C8)—24no—
95C22⋊(C11⋊C8)—24no—
96C22⋊(C11⋊C8)—42no—
97C22⋊(C11⋊C8)—42no—
98C22⋊(C11⋊C8)D414yescomplemented
99C4⋊(C11⋊C8)—24no—
100#66867—24no—
101#22403—111nomaximal, Sylow
102C24×C11C22×C412yes—
103C24×C11C22×C412yes—
104C24×C11C22×C411yescharacteristic
105C11×#41—48no—
106C11×#41—48no—
107C11×#41—48no—
108C11×#41—48no—
109C2×Q8×C11—24no—
110C2×Q8×C11—24no—
111C2×Q8×C11—42no—
112C2×D4×C11—24no—
113C2×D4×C11—24no—
114C2×D4×C11—24no—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—22no—
118C2×D4×C11—24no—
119C2×D4×C11—24no—
120C2×D4×C11—24no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—42no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—42no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11C22⋊C414yes—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C412yes—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C412yes—
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4C22⋊C414yes—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4C22⋊C418yes—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11C2×D414yes—
171#4318—48no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—48no—
184C2×C11⋊C8C2×D414yes—
185C2×#532D1111yescharacteristic
186C2×#435—112no—
187C2×#408—112no—
188#1955—112no—
189#1870—112no—
190#1869—112no—
191#1797—111no—
192#1780—112no—
193#1749—111no—
194C23×C11—21no—
195C23×C11—22no—
196C23×C11—21no—
197C23×C11—22no—
198C23×C11—21no—
199C23×C11—22no—
200C23×C11—21no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11C2×C22⋊C414yes—
214C23×C11C4×D412yes—
215C23×C11C23×C411yescharacteristic
216Q8×C11—48no—
217D4×C11—44no—
218D4×C11—48no—
219D4×C11—48no—
220D4×C11—48no—
221D4×C11—44no—
222D4×C11—48no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—44no—
246C2×C4×C11—44no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11C2×C22⋊C412yes—
252C2×C4×C11C2×C22⋊C412yes—
253C2×C4×C11C2×C22⋊C414yes—
254C2×C4×C11C4×D412yes—
255C2×C4×C11#13112yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D412yes—
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)12yes—
260C11⋊C8—24no—
261C11⋊C8—42no—
262C11⋊C8—42no—
263C11⋊C8—42no—
264C22×#41C2×D1112yes—
265C22×M16—112no—
266C23×C8—112no—
267#532—28no—
268C2×C4⋊Q8Dic1111yescharacteristic
269C2×#127Dic1111yescharacteristic
270C2×#124Dic1112yes—
271C2×#121Dic1111yescharacteristic
272C2×#121Dic1111yescharacteristic
273C2×#121Dic1112yes—
274C2×C4×D4C2×D1112yes—
275C2×C4×D4C2×D1111yescharacteristic
276C2×C4×D4C2×D1111yescharacteristic
277C22×C42C2×D1111yescharacteristic
278#435—228no—
279C2×C4⋊C8—112no—
280#408—228no—
281C2×C22⋊C8—111no—
282C2×C22⋊C8—112no—
283C2×C22⋊C8—112no—
284C2×C22⋊C8—112no—
285C2×C22⋊C8—112no—
286C2×C22⋊C8—112no—
287C2×C22⋊C8—111no—
288C2×C22⋊C8—112no—
289C2×C22⋊C8—112no—
290C2×#97—112no—
291#336—111no—
292#336—111no—
293#336—112no—
294C22×C11—22no—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—41no—
305C22×C11—42no—
306C22×C11—41no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11C22×C22⋊C411yescharacteristic
316C22×C11C2×C4×D411yescharacteristic
317C22×C11#51811yescharacteristic
318C22×C11C2×#13111yescharacteristic
319C22×C11#56811yescharacteristic
320C22×C11#56811yescharacteristic
321C22×C11#56811yescharacteristic
322C4×C11—24no—
323C4×C11—22no—
324C4×C11—22no—
325C4×C11—22no—
326C4×C11—22no—
327C4×C11—42no—
328C4×C11—41no—
329C4×C11D4212yes—
330C4×C11#54612yes—
331C2×#41—24no—
332C2×#41—24no—
333C2×#41—24no—
334C2×#41—24no—
335C2×#41—42no—
336C2×#41—42no—
337C22×Q8C2×Dic1112yes—
338C22×D4C2×Dic1112yes—
339C22×D4C2×Dic1112yes—
340C22×D4C2×Dic1112yes—
341C22×D4C2×Dic1112yes—
342C22×D4C2×Dic1111yescharacteristic
343C22×D4C2×Dic1111yescharacteristic
344C23×C4C2×Dic1111yescharacteristic
345C23×C4C2×Dic1111yescharacteristic
346C23×C4C22×D1112yes—
347C23×C4C22×D1111yescharacteristic
348C23×C4C22×D1112yes—
349C2×M16—224no—
350C2×M16—224no—
351C2×M16—442no—
352C22×C8—112no—
353C22×C8—112no—
354C22×C8—112no—
355C22×C8—112no—
356C22×C8—224no—
357C22×C8—224no—
358C22×C8—442no—
359C4⋊Q8—24no—
360#127—24no—
361#124—28no—
362#121—24no—
363#121—24no—
364#121—28no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—24no—
368C4×D4C22⋊D1118yes—
369C2×C4⋊C4C2×Dic1111yescharacteristic
370C2×C4⋊C4C2×Dic1112yes—
371C2×C4⋊C4C2×Dic1111yescharacteristic
372C2×C22⋊C4C2×Dic1112yes—
373C2×C22⋊C4C2×Dic1112yes—
374C2×C22⋊C4C2×Dic1112yes—
375C2×C22⋊C4C2×Dic1112yes—
376C2×C42—24no—
377C2×C42C2×Dic1111yescharacteristic
378C2×C42C2×Dic1111yescharacteristic
379C2×C42C22×D1111yescharacteristic
380C2×C42C22×D1111yescharacteristic
381C4⋊C8—224no—
382C22⋊C8—114no—
383C22⋊C8—224no—
384C22⋊C8—224no—
385C22⋊C8—224no—
386C22⋊C8—222no—
387C22⋊C8—224no—
388C22⋊C8—224no—
389C22⋊C8—442no—
390C22⋊C8—442no—
391#97—224no—
392C2×C11—42no—
393C2×C11—44no—
394C2×C11—82no—
395C2×C11D4×C22⋊C411yescharacteristic
396C2×C11#287911yescharacteristic
397C2×C11#288011yescharacteristic
398C2×C11#293211yescharacteristic
399C2×C11#293511yescharacteristic
400C2×C11#298011yescharacteristic
401C2×C11#298111yescharacteristic
402C24C22×Dic1112yes—
403C24C22×Dic1111yescharacteristic
404C24C22×Dic1112yes—
405#41—48no—
406#41—48no—
407#41—48no—
408#41—48no—
409C2×Q8—24no—
410C2×Q8—24no—
411C2×Q8—42no—
412C2×D4—24no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—24no—
419C2×D4—22no—
420C2×D4—24no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—42no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4C22⋊Dic1114yes—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4D4×D1112yes—
449C22×C4#434112yes—
450C22×C4C22×Dic1111yescharacteristic
451C22×C4C22×Dic1112yes—
452C22×C4C22×Dic1111yescharacteristic
453C22×C4C22×Dic1111yescharacteristic
454C22×C4C22×Dic1111yescharacteristic
455C22×C4C22×Dic1111yescharacteristic
456C22×C4C22×Dic1112yes—
457C22×C4C2×C22⋊D1114yes—
458C22×C4C2×C22⋊D1114yes—
459C22×C4C23×D1111yescharacteristic
460M16—448no—
461C2×C8—114no—
462C2×C8—222no—
463C2×C8—222no—
464C2×C8—222no—
465C2×C8—222no—
466C2×C8—222no—
467C2×C8—222no—
468C2×C8—222no—
469C2×C8—222no—
470C2×C8—222no—
471C2×C8—222no—
472C2×C8—222no—
473C2×C8—448no—
474C4⋊C4—24no—
475C4⋊C4—22no—
476C4⋊C4C22⋊Dic1114yes—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4C22⋊Dic1118yes—
481C42—22no—
482C42—22no—
483C42—22no—
484C42C2×C22⋊D1114yes—
485C11#2240311yescharacteristic, complemented, Sylow
486C23—22no—
487C23—21no—
488C23—22no—
489C23—21no—
490C23—22no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—21no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23D4×Dic1112yes—
506C23C2×C22⋊Dic1114yes—
507C23C23×Dic1111yescharacteristic
508Q8—48no—
509D4—44no—
510D4—48no—
511D4—48no—
512D4—48no—
513D4—44no—
514D4—48no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—44no—
538C2×C4—44no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4D4×Dic1112yes—
544C2×C4#6700112yes—
545C2×C4C2×C22⋊Dic1112yes—
546C2×C4C2×C22⋊Dic1112yes—
547C2×C4C2×C22⋊Dic1114yes—
548C2×C4C2×D4×D1111yescharacteristic
549C2×C4C2×#434111yescharacteristic
550C2×C4#6703712yes—
551C2×C4C22×C22⋊D1112yes—
552C8—224no—
553C8—442no—
554C8—442no—
555C8—442no—
556C22—24no—
557C22—24no—
558C22—22no—
559C22—24no—
560C22—22no—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—42no—
565C22—42no—
566C22—41no—
567C22—42no—
568C22—41no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22C2×D4×Dic1111yescharacteristic
578C22#1062332911yescharacteristic
579C22C2×#6700111yescharacteristic
580C22#1062335011yescharacteristic
581C22#1062335011yescharacteristic
582C22#1062335011yescharacteristic
583C22C22×C22⋊Dic1111yescharacteristic
584C4—22no—
585C4—22no—
586C4—22no—
587C4—22no—
588C4—24no—
589C4—41no—
590C4—42no—
591C4D4×C22⋊D1112yes—
592C4#1062333712yes—
593C2—44no—
594C2—42no—
595C2—82no—
596C2D4×C22⋊Dic1111yescharacteristic
597C2#1307706111yescharacteristic
598C2#1307706511yescharacteristic
599C2#1307733411yescharacteristic
600C2#1307736011yescharacteristic
601C2#1307768711yescharacteristic
602C2#1307769211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
Fitting, prime radicalC2×C11×#532C2
cosocleC22×C4×C11C24
hypercenterC2×#532D11
hypocenterC11#22403
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×#10622624C2semidirect
2. C2×#10622847C2semidirect
3. #13069415C2semidirect
4. #13068914C2semidirect
5. #13068909C2semidirect
6. #13068596C2semidirect
7. #13068528C2semidirect
8. #13068378C2semidirect
98. C22⋊(C11⋊C8)D4semidirect
485. C11#22403semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
C2×#106228472
#130694152
#130689142
#130689092
#130685962
#130685282
#130683782
C2×C11×#5322
#2240311