Finite Group Databasebeta

← #14770304

Subgroups — #14770304

Order 2816.

1292 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
1C22×C4×Dic22C211yesmaximal, characteristic
2C2×#10622314C212yesmaximal, complemented
3#13069556C212yesmaximal, complemented
4#13069554C212yesmaximal, complemented
5#13069550C212yesmaximal, complemented
6#13068596C211yesmaximal, characteristic
7#13068594C211yesmaximal, characteristic
8#13068594C211yesmaximal, characteristic
9#13068380C211yesmaximal, characteristic
10C22⋊C8×Dic11C211yesmaximal, characteristic
11C11×#1749C211yesmaximal, characteristic
12C23×Dic22C411yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C411yescharacteristic
15C22×Dic11⋊C4C411yescharacteristic
16C22×Dic11⋊C4C411yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C2×C4×Dic22—28no—
20C2×C4×Dic22C411yescharacteristic
21C2×C4×Dic22C411yescharacteristic
22C2×C4×Dic22C411yescharacteristic
23C2×C4×Dic22C411yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27C2×C4×Dic22C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C11×#97C2212yes—
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66879C2212yes—
34C2×Dic11⋊C8C2212yes—
35C2×Dic11⋊C8C2212yes—
36C2×C8×Dic11C2212yes—
37C2×C4⋊(C11⋊C8)C2212yes—
38#10622314—28no—
39C11×#336C2212yes—
40#10622188C2212yes—
41#10622188C2212yes—
42#10622188C2212yes—
43#10622188C2212yes—
44#10622162C2212yes—
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2×C411yescharacteristic
49C23×Dic11C2×C411yescharacteristic
50C23×Dic11C2×C411yescharacteristic
51C23×Dic11C2×C411yescharacteristic
52C22×Dic22—24no—
53C22×Dic22—24no—
54C22×Dic22—24no—
55C22×Dic22C2×C411yescharacteristic
56C22×Dic22C2×C411yescharacteristic
57C22×Dic22C2×C411yescharacteristic
58C22×Dic22C2×C411yescharacteristic
59C22×C8×C11C2312yes—
60C22×C8×C11C2312yes—
61C2×C42×C11—24no—
62C2×C42×C11C2×C411yescharacteristic
63C2×C42×C11C2×C411yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C4⋊Dic11—24no—
67C2×C4⋊Dic11C2×C411yescharacteristic
68C2×C4⋊Dic11C2×C411yescharacteristic
69C2×C4⋊Dic11C2×C411yescharacteristic
70C2×C4⋊Dic11C2×C411yescharacteristic
71C2×Dic11⋊C4—24no—
72C2×Dic11⋊C4—24no—
73C2×Dic11⋊C4C2×C411yescharacteristic
74C2×Dic11⋊C4C2×C411yescharacteristic
75C2×Dic11⋊C4C2×C411yescharacteristic
76C2×Dic11⋊C4C2×C411yescharacteristic
77C2×Dic11⋊C4C2×C411yescharacteristic
78C2×Dic11⋊C4C2×C411yescharacteristic
79C2×Dic11⋊C4C2×C411yescharacteristic
80C2×Dic11⋊C4C2×C411yescharacteristic
81C2×C4×Dic11—24no—
82C2×C4×Dic11—24no—
83C2×C4×Dic11C2×C411yescharacteristic
84C2×C4×Dic11C2×C411yescharacteristic
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2312yes—
92C22×C11⋊C8C2312yes—
93C4×Dic22—24no—
94C4×Dic22—24no—
95C4×Dic22—24no—
96C4×Dic22—24no—
97C4×Dic22—24no—
98C4×Dic22—24no—
99C4×Dic22—24no—
100C4×Dic22D418yes—
101C11×C22⋊C8—22no—
102C11×C22⋊C8Q814yescomplemented
103C11×#97—24no—
104C22⋊(C11⋊C8)—22no—
105C22⋊(C11⋊C8)—22no—
106#66879—24no—
107Dic11⋊C8—24no—
108Dic11⋊C8—24no—
109C8×Dic11—24no—
110C4⋊(C11⋊C8)—24no—
111#22510—111nomaximal, Sylow
112C24×C11C22×C411yescharacteristic
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—41no—
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C2×Q812yes—
127C22×C4×C11#4112yes—
128C22×C4×C11C2411yescharacteristic
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—41no—
139C22×Dic11—41no—
140C22×Dic11M1614yes—
141C22×Dic11C22×C411yescharacteristic
142C22×Dic11C22×C411yescharacteristic
143C22×Dic11C22×C411yescharacteristic
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C22×Dic11C22×C411yescharacteristic
147C22×Dic11C22×C411yescharacteristic
148C22×Dic11C22×C411yescharacteristic
149C2×Dic22—232no—
150C2×Dic22—22no—
151C2×Dic22—22no—
152C2×Dic22—22no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—22no—
158C2×Dic22—22no—
159C2×Dic22—22no—
160C2×Dic22C22⋊C414yes—
161C2×Dic22M1614yes—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11C2×Q814yescomplemented
168C42×C11—22no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11C2×D414yes—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11C22⋊C414yes—
176Dic11⋊C4—22no—
177Dic11⋊C4—22no—
178Dic11⋊C4—22no—
179Dic11⋊C4—22no—
180Dic11⋊C4—22no—
181Dic11⋊C4—22no—
182Dic11⋊C4C22⋊C414yes—
183Dic11⋊C4C22⋊C414yes—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11—22no—
189C4×Dic11—22no—
190C4×Dic11C2×D414yes—
191C4×Dic11C2×D414yes—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C22×C4×Q8—111no—
199C2×#446—112no—
200#1985—112no—
201#1985—112no—
202#1984—112no—
203#1797—111no—
204#1797—111no—
205#1797—111no—
206#1749—111no—
207#1749D1111yescharacteristic
208C4×C22⋊C8—111no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11C4×Q812yes—
214C23×C11C2×M1612yes—
215C23×C11#13112yes—
216C23×C11C23×C411yescharacteristic
217C2×C4×C11—28no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—44no—
232C2×C4×C11C2×C22⋊C412yes—
233C2×C4×C11C2×C22⋊C412yes—
234C2×C4×C11C4×Q812yes—
235C2×C4×C11C2×M1612yes—
236C2×C4×C11C22×D412yes—
237C2×C4×C11C22×Q811yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C112−1+412yes—
240C2×Dic11—28no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—28no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—44no—
259C2×Dic11—44no—
260C2×Dic11C2×C22⋊C412yes—
261C2×Dic11C2×C22⋊C412yes—
262C2×Dic11C2×C22⋊C412yes—
263C2×Dic11C2×C22⋊C412yes—
264C2×Dic11C2×M1612yes—
265C2×Dic11C2×M1612yes—
266C2×Dic11C2×M1612yes—
267C2×Dic11C2×M1612yes—
268Dic22—28no—
269Dic22—28no—
270Dic22—28no—
271Dic22—28no—
272C8×C11—24no—
273C8×C11—42no—
274C11⋊C8—42no—
275C11⋊C8—42no—
276C23×Q8—111no—
277C2×C4×Q8—111no—
278C2×C4×Q8—111no—
279C2×C4×Q8—111no—
280C2×C4×Q8—111no—
281C2×C4×Q8—111no—
282C2×C4×Q8—111no—
283C2×C4×Q8—111no—
284C2×C4×Q8—111no—
285C2×C4×Q8—228no—
286C22×C4⋊C4—111no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4—111no—
289C22×C42—111no—
290C22×C42—111no—
291C22×C42C2×D1111yescharacteristic
292#446—228no—
293C2×C4⋊C8—112no—
294C2×C4⋊C8—112no—
295C2×C4⋊C8—112no—
296C2×C22⋊C8—111no—
297C2×C22⋊C8—111no—
298C2×C22⋊C8C2×D1111yescharacteristic
299C2×C22⋊C8C2×D1111yescharacteristic
300C2×#97—112no—
301C2×#97C2×D1112yes—
302C2×C4×C8—112no—
303#336—112no—
304#336—112no—
305#336—112no—
306#336—112no—
307#336—112no—
308#336C2×D1112yes—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11#44614yescomplemented
316C22×C11C22×C22⋊C411yescharacteristic
317C22×C11C2×C4×Q811yescharacteristic
318C22×C11#51911yescharacteristic
319C22×C11C22×M1611yescharacteristic
320C22×C11C22×M1611yescharacteristic
321C22×C11C2×#13111yescharacteristic
322C22×C11#56811yescharacteristic
323C4×C11—22no—
324C4×C11—22no—
325C4×C11—22no—
326C4×C11—22no—
327C4×C11—41no—
328C4×C11#54812yes—
329C4×C11D4×Q812yes—
330Dic11—22no—
331Dic11—22no—
332Dic11—22no—
333Dic11—22no—
334Dic11—22no—
335Dic11—41no—
336Dic11—41no—
337Dic11#40714yes—
338C22×Q8—111no—
339C22×Q8—111no—
340C22×Q8—111no—
341C22×Q8—111no—
342C22×Q8—224no—
343C22×Q8—224no—
344C22×Q8—224no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—111no—
348C23×C4—111no—
349C23×C4C4×D1111yescharacteristic
350C23×C4C4×D1111yescharacteristic
351C23×C4C22×D1111yescharacteristic
352C22×C8—112no—
353C22×C8—112no—
354C22×C8C22×D1112yes—
355C22×C8C22×D1112yes—
356C4×Q8—118no—
357C4×Q8—224no—
358C4×Q8—224no—
359C4×Q8—224no—
360C4×Q8—224no—
361C4×Q8—224no—
362C4×Q8—224no—
363C4×Q8—224no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—224no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—224no—
379C2×C42—24no—
380C2×C42—111no—
381C2×C42—111no—
382C2×C42—111no—
383C2×C42—111no—
384C2×C42—111no—
385C2×C42—111no—
386C2×C42—111no—
387C2×C42—111no—
388C2×C42—224no—
389C2×C42—224no—
390C2×C42C4×D1111yescharacteristic
391C2×C42C4×D1111yescharacteristic
392C2×C42C22×D1111yescharacteristic
393C2×C42C22×D1111yescharacteristic
394C4⋊C8—224no—
395C4⋊C8—224no—
396C4⋊C8—224no—
397C22⋊C8—22no—
398C22⋊C8—222no—
399C22⋊C8—222no—
400C22⋊C8Dic2214yescomplemented
401#97—24no—
402#97—224no—
403C4×C8—224no—
404C2×C11—24no—
405C2×C11Q8×C22⋊C411yescharacteristic
406C2×C11C2×#40711yescharacteristic
407C2×C11#288011yescharacteristic
408C2×C11C2×#44611yescharacteristic
409C2×C11Q8×M1611yescharacteristic
410C2×C11#298311yescharacteristic
411C2×C11#298411yescharacteristic
412C24C2×C4×D1111yescharacteristic
413C2×Q8—114no—
414C2×Q8—114no—
415C2×Q8—222no—
416C2×Q8—222no—
417C2×Q8—222no—
418C2×Q8—222no—
419C2×Q8—222no—
420C2×Q8—222no—
421C2×Q8—222no—
422C2×Q8—222no—
423C2×Q8—2232no—
424C2×Q8—222no—
425C2×Q8—222no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—41no—
434C22×C4—111no—
435C22×C4—114no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—441no—
453C22×C4—441no—
454C22×C4C2×Dic2212yes—
455C22×C4C2×C4×D1111yescharacteristic
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4C2×C4×D1111yescharacteristic
458C22×C4C2×C4×D1111yescharacteristic
459C22×C4C2×C4×D1111yescharacteristic
460C22×C4#433912yes—
461C22×C4C23×D1111yescharacteristic
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—222no—
468C2×C8—222no—
469C2×C8—222no—
470C2×C8—222no—
471C2×C8—222no—
472C2×C8—222no—
473C2×C8C2×Dic2214yescomplemented
474C4⋊C4—114no—
475C4⋊C4—114no—
476C4⋊C4—114no—
477C4⋊C4—222no—
478C4⋊C4—222no—
479C4⋊C4—222no—
480C4⋊C4—222no—
481C4⋊C4—222no—
482C4⋊C4—222no—
483C4⋊C4—222no—
484C4⋊C4—222no—
485C4⋊C4—222no—
486C42—22no—
487C42—22no—
488C42—22no—
489C42—114no—
490C42—114no—
491C42—222no—
492C42—222no—
493C42—222no—
494C42—222no—
495C42—222no—
496C42—222no—
497C42D4×D1114yes—
498C11#2251011yescharacteristic, complemented, Sylow
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23C4×Dic2212yes—
504C23M16×D1112yes—
505C23#6696012yes—
506C23C22×C4×D1111yescharacteristic
507Q8—228no—
508Q8—228no—
509Q8—228no—
510Q8—228no—
511C2×C4—28no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—44no—
526C2×C4—112no—
527C2×C4—112no—
528C2×C4—112no—
529C2×C4—112no—
530C2×C4—112no—
531C2×C4—112no—
532C2×C4—112no—
533C2×C4—112no—
534C2×C4—228no—
535C2×C4—228no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—444no—
553C2×C4—444no—
554C2×C4C4×Dic2212yes—
555C2×C4C22⋊C4×D1112yes—
556C2×C4C22⋊C4×D1112yes—
557C2×C4M16×D1112yes—
558C2×C4C22×Dic2211yescharacteristic
559C2×C4C2×#433911yescharacteristic
560C2×C4C2×D4×D1112yes—
561C2×C4#6704312yes—
562C8—24no—
563C8—42no—
564C8—442no—
565C8—442no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22#1062231414yescomplemented
573C22C2×C4×Dic2211yescharacteristic
574C22C2×C22⋊C4×D1111yescharacteristic
575C22#1062304711yescharacteristic
576C22C2×M16×D1111yescharacteristic
577C22C2×M16×D1111yescharacteristic
578C22C2×#6696011yescharacteristic
579C22#1062327611yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—114no—
586C4—222no—
587C4—222no—
588C4—222no—
589C4—222no—
590C4—222no—
591C4—441no—
592C4—441no—
593C4D4×Dic2212yes—
594C4#1062308312yes—
595C2—24no—
596C2C22⋊C4×Dic2211yescharacteristic
597C2D11×#40711yescharacteristic
598C2#1307706611yescharacteristic
599C2C2×#1062231411yescharacteristic
600C2M16×Dic2211yescharacteristic
601C2#1307770011yescharacteristic
602C2#1307770611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1749C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1749D11
hypocenterC11#22510
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. C2×#10622314C2semidirect
3. #13069556C2semidirect
4. #13069554C2semidirect
5. #13069550C2semidirect
102. C11×C22⋊C8Q8semidirect
167. C2×C8×C11C2×Q8semidirect
315. C22×C11#446semidirect
400. C22⋊C8Dic22semidirect
473. C2×C8C2×Dic22semidirect
498. C11#22510semidirect
572. C22#10622314semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic222
C2×#106223142
#130695562
#130695542
#130695502
#130685962
#130685942
#130683802
C22⋊C8×Dic112
C11×#17492
#2251011