Finite Group Databasebeta

← #15879834

Subgroups — #15879834

Order 3328.

1280 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718379C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Dic13C211yesmaximal, characteristic
3#13115445C212yesmaximal, complemented
4#13115439C212yesmaximal, complemented
5#13115014C212yesmaximal, complemented
6#13114902C211yesmaximal, characteristic, complemented
7#13114814C211yesmaximal, characteristic, complemented
8#13114746C211yesmaximal, characteristic
9C8×C22⋊Dic13C212yesmaximal, complemented
10C22⋊C8×Dic13C211yesmaximal, characteristic, complemented
11C22×C13×C22⋊C8C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C23×C8×C13C2212yes—
14C22×C22⋊Dic13C411yescharacteristic
15C22×C22⋊Dic13C411yescharacteristic
16C22×C4×Dic13C2211yescharacteristic
17C22×C4×Dic13C2211yescharacteristic
18C2×C13×C22⋊C8—24no—
19C2×C13×C22⋊C8C2211yescharacteristic
20C2×C13×C22⋊C8C2212yes—
21C2×C13×C22⋊C8C2211yescharacteristic
22C4×C22⋊Dic13C411yescharacteristic
23C4×C22⋊Dic13C411yescharacteristic
24C4×C22⋊Dic13C411yescharacteristic
25C4×C22⋊Dic13C411yescharacteristic
26C4×C22⋊Dic13C2211yescharacteristic
27C4×C22⋊Dic13C2211yescharacteristic
28C4×C22⋊Dic13C2211yescharacteristic
29C4×C22⋊Dic13C2211yescharacteristic
30C2×#88071C411yescharacteristic
31C2×#88071C411yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2212yes—
35C2×C22⋊#1055C2212yes—
36C2×#88054C2212yescomplemented
37C2×#88054C2212yescomplemented
38C2×C8×Dic13C2212yescomplemented
39C2×C8×Dic13C2212yescomplemented
40#11718379—24no—
41#11718142C2212yescomplemented
42#11718142C2212yescomplemented
43#11718142C2212yescomplemented
44#11718142C2212yescomplemented
45C25×C13C2×C411yescharacteristic
46C23×C4×C13—22no—
47C23×C4×C13—22no—
48C23×C4×C13—24no—
49C23×C4×C13—42no—
50C23×C4×C13C2×C411yescharacteristic
51C23×C4×C13C2×C411yescharacteristic
52C23×C4×C13C2×C411yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×Dic13C2×C411yescharacteristic
57C23×Dic13C2×C411yescharacteristic
58C23×Dic13C2×C411yescharacteristic
59C23×Dic13C2×C411yescharacteristic
60C22×C8×C13—24no—
61C22×C8×C13—24no—
62C22×C8×C13—42no—
63C22×C8×C13C2312yes—
64C22×C8×C13C2312yes—
65C2×C22⋊Dic13—24no—
66C2×C22⋊Dic13C818yescomplemented
67C2×C22⋊Dic13C2×C411yescharacteristic
68C2×C22⋊Dic13C2×C411yescharacteristic
69C2×C22⋊Dic13C2×C411yescharacteristic
70C2×C22⋊Dic13C2×C411yescharacteristic
71C2×C22⋊Dic13C2×C411yescharacteristic
72C2×C22⋊Dic13C2×C411yescharacteristic
73C2×C22⋊Dic13C2×C411yescharacteristic
74C2×C22⋊Dic13C2×C411yescharacteristic
75C2×C4×Dic13—22no—
76C2×C4×Dic13—22no—
77C2×C4×Dic13—42no—
78C2×C4×Dic13C2×C411yescharacteristic
79C2×C4×Dic13C2×C411yescharacteristic
80C2×C4×Dic13C2×C411yescharacteristic
81C2×C4×Dic13C2×C411yescharacteristic
82C2×C4×Dic13C2311yescharacteristic
83C2×C4×Dic13C2311yescharacteristic
84C2×C4×Dic13C2311yescharacteristic
85C2×C4×Dic13C2311yescharacteristic
86C22×#1055C2312yes—
87C22×#1055C2312yes—
88C13×C22⋊C8—22no—
89C13×C22⋊C8—24no—
90C13×C22⋊C8D414yes—
91#88071C2×C411yescharacteristic
92#88071C2×C411yescharacteristic
93#88071C2×C411yescharacteristic
94#88071C2×C411yescharacteristic
95#88071C2×C411yescharacteristic
96#88071C2×C411yescharacteristic
97#88071C2×C411yescharacteristic
98#88071C2×C411yescharacteristic
99C22⋊#1055—22no—
100C22⋊#1055—22no—
101C22⋊#1055—24no—
102C22⋊#1055—42no—
103#88054—24no—
104#88054—42no—
105C8×Dic13—24no—
106C8×Dic13—42no—
107#22552—131nomaximal, Sylow
108C24×C13—22no—
109C24×C13—22no—
110C24×C13—22no—
111C24×C13—22no—
112C24×C13—41no—
113C24×C13—41no—
114C24×C13C2×C814yes—
115C24×C13C22×C411yescharacteristic
116C24×C13C22×C411yescharacteristic
117C24×C13C22×C411yescharacteristic
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—41no—
134C22×C4×C13—41no—
135C22×C4×C13—41no—
136C22×C4×C13—48no—
137C22×C4×C13—48no—
138C22×C4×C13C22×C411yescharacteristic
139C22×C4×C13C22×C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×C4×C13C2×D412yes—
142C22×C4×C13#4112yes—
143C22×C4×C13#4114yes—
144C22×C4×C13C2411yescharacteristic
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—41no—
152C22×Dic13—41no—
153C22×Dic13—41no—
154C22×Dic13—41no—
155C22×Dic13C2×C814yescomplemented
156C22×Dic13C2×C814yescomplemented
157C22×Dic13C22×C411yescharacteristic
158C22×Dic13C22×C411yescharacteristic
159C22×Dic13C22×C411yescharacteristic
160C22×Dic13C22×C411yescharacteristic
161C22×Dic13C22×C411yescharacteristic
162C22×Dic13C22×C411yescharacteristic
163C22×Dic13C22×C411yescharacteristic
164C22×Dic13C22×C411yescharacteristic
165C2×C8×C13—22no—
166C2×C8×C13—22no—
167C2×C8×C13—22no—
168C2×C8×C13—22no—
169C2×C8×C13—22no—
170C2×C8×C13—48no—
171C2×C8×C13C2×D414yes—
172C22⋊Dic13—22no—
173C22⋊Dic13—22no—
174C22⋊Dic13—22no—
175C22⋊Dic13C2×C814yes—
176C22⋊Dic13C2×C814yes—
177C22⋊Dic13C2×C814yescomplemented
178C22⋊Dic13C2×C814yescomplemented
179C22⋊Dic13M1614yes—
180C4×Dic13—22no—
181C4×Dic13—22no—
182C4×Dic13—21no—
183C4×Dic13—21no—
184C4×Dic13—21no—
185C4×Dic13—21no—
186C4×Dic13—22no—
187C4×Dic13—22no—
188C4×Dic13—41no—
189C4×Dic13—41no—
190C2×#1055—22no—
191C2×#1055—22no—
192C2×#1055—22no—
193C2×#1055—22no—
194C2×#1055—22no—
195C2×#1055—22no—
196C2×#431—131no—
197C22×C22⋊C8D1311yescharacteristic
198C2×C4×C22⋊C4—131no—
199#1923—132no—
200#1923—132no—
201#1850—132no—
202#1817—131no—
203#1797—131no—
204#1779—131no—
205C8×C22⋊C4—132no—
206C4×C22⋊C8—131no—
207C23×C13—21no—
208C23×C13—21no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13—21no—
218C23×C13—21no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—28no—
222C23×C13—28no—
223C23×C13—44no—
224C23×C13—44no—
225C23×C13—44no—
226C23×C13—44no—
227C23×C13—44no—
228C23×C13#11712yes—
229C23×C13C4×D412yes—
230C23×C13C22×C812yes—
231C23×C13C22×C812yes—
232C23×C13C22×C812yes—
233C23×C13C2×M1612yes—
234C23×C13#13112yes—
235C23×C13C23×C411yescharacteristic
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—44no—
248C2×C4×C13—44no—
249C2×C4×C13—44no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13#11712yes—
253C2×C4×C13C4×D412yes—
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C2×#4112yes—
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13H(5,𝔽2)12yes—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—28no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—44no—
278C2×Dic13—44no—
279C2×Dic13—44no—
280C2×Dic13C22×C812yes—
281C2×Dic13C22×C812yes—
282C2×Dic13C22×C812yes—
283C2×Dic13C22×C812yes—
284C2×Dic13C2×M1612yes—
285C2×Dic13C2×M1612yes—
286C8×C13—24no—
287C8×C13—42no—
288#1055—42no—
289#1055—42no—
290C24×C4C2×D1311yescharacteristic
291C23×C8C2×D1312yes—
292C22×C22⋊C4—131no—
293C22×C22⋊C4—131no—
294C22×C42—131no—
295C22×C42—131no—
296#431—264no—
297C2×C4⋊C8—132no—
298C2×C4⋊C8—132no—
299C2×C22⋊C8—24no—
300C2×C22⋊C8—131no—
301C2×C22⋊C8—131no—
302C2×C22⋊C8—132no—
303C2×C22⋊C8—132no—
304C2×C22⋊C8C2×D1311yescharacteristic
305C2×C22⋊C8C2×D1312yes—
306C2×C22⋊C8C2×D1311yescharacteristic
307C2×C4×C8—132no—
308C2×C4×C8—132no—
309C4×C22⋊C4—131no—
310C4×C22⋊C4—131no—
311C4×C22⋊C4—131no—
312C4×C22⋊C4—131no—
313C4×C22⋊C4—131no—
314C4×C22⋊C4—131no—
315C4×C22⋊C4—131no—
316C4×C22⋊C4—131no—
317C2×#95—131no—
318C2×#95—131no—
319#336—132no—
320#336—132no—
321#336—132no—
322#336—132no—
323C22×C13—22no—
324C22×C13—22no—
325C22×C13—22no—
326C22×C13—22no—
327C22×C13—22no—
328C22×C13—22no—
329C22×C13—22no—
330C22×C13—22no—
331C22×C13—22no—
332C22×C13—22no—
333C22×C13—22no—
334C22×C13—22no—
335C22×C13—22no—
336C22×C13—22no—
337C22×C13—22no—
338C22×C13—416no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13#43114yescomplemented
344C22×C13C8×D414yes—
345C22×C13C2×#11711yescharacteristic
346C22×C13C2×C4×D411yescharacteristic
347C22×C13#51811yescharacteristic
348C22×C13C23×C811yescharacteristic
349C22×C13C22×M1611yescharacteristic
350C22×C13C2×#13111yescharacteristic
351C22×C13#56811yescharacteristic
352C4×C13—22no—
353C4×C13—22no—
354C4×C13—41no—
355C4×C13#54612yes—
356C4×C13#55112yes—
357Dic13—22no—
358Dic13—22no—
359Dic13—22no—
360Dic13—22no—
361Dic13—22no—
362Dic13—22no—
363Dic13—41no—
364Dic13—41no—
365C25C4×D1311yescharacteristic
366C23×C4—22no—
367C23×C4—24no—
368C23×C4—22no—
369C23×C4—42no—
370C23×C4—131no—
371C23×C4—131no—
372C23×C4—131no—
373C23×C4—131no—
374C23×C4C4×D1311yescharacteristic
375C23×C4C4×D1311yescharacteristic
376C23×C4C4×D1311yescharacteristic
377C23×C4C22×D1311yescharacteristic
378C23×C4C22×D1311yescharacteristic
379C23×C4C22×D1311yescharacteristic
380C22×C8—24no—
381C22×C8—24no—
382C22×C8—42no—
383C22×C8—132no—
384C22×C8—132no—
385C22×C8C22×D1312yes—
386C22×C8C22×D1312yes—
387C2×C22⋊C4—138no—
388C2×C22⋊C4—131no—
389C2×C22⋊C4—131no—
390C2×C22⋊C4—131no—
391C2×C22⋊C4—131no—
392C2×C22⋊C4—131no—
393C2×C22⋊C4—131no—
394C2×C22⋊C4—131no—
395C2×C22⋊C4—131no—
396C2×C22⋊C4—264no—
397C2×C42—131no—
398C2×C42—131no—
399C2×C42—131no—
400C2×C42—131no—
401C2×C42—131no—
402C2×C42—131no—
403C2×C42—131no—
404C2×C42—131no—
405C2×C42—262no—
406C2×C42—262no—
407C2×C42—522no—
408C4⋊C8—264no—
409C4⋊C8—522no—
410C22⋊C8—22no—
411C22⋊C8—24no—
412C22⋊C8—262no—
413C22⋊C8—264no—
414C22⋊C8—262no—
415C22⋊C8—522no—
416C22⋊C8C22⋊D1314yes—
417C4×C8—264no—
418C4×C8—522no—
419#95—131no—
420#95—131no—
421#95—131no—
422#95—131no—
423#95—131no—
424#95—131no—
425#95—131no—
426#95—131no—
427C2×C13—24no—
428C2×C13—24no—
429C2×C13—42no—
430C2×C13#234211yescharacteristic
431C2×C13C2×#43111yescharacteristic
432C2×C13#292411yescharacteristic
433C2×C13C2×C8×D411yescharacteristic
434C2×C13D4×M1611yescharacteristic
435C2×C13#297211yescharacteristic
436C2×C13#297411yescharacteristic
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—41no—
442C24—41no—
443C24C8×D1314yes—
444C24C2×C4×D1311yescharacteristic
445C24C2×C4×D1311yescharacteristic
446C24C2×C4×D1311yescharacteristic
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—48no—
466C22×C4—48no—
467C22×C4—134no—
468C22×C4—131no—
469C22×C4—131no—
470C22×C4—131no—
471C22×C4—131no—
472C22×C4—131no—
473C22×C4—131no—
474C22×C4—134no—
475C22×C4—131no—
476C22×C4—131no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—521no—
484C22×C4—521no—
485C22×C4—521no—
486C22×C4—521no—
487C22×C4C2×C4×D1311yescharacteristic
488C22×C4C2×C4×D1311yescharacteristic
489C22×C4C2×C4×D1311yescharacteristic
490C22×C4#612712yes—
491C22×C4#612914yes—
492C22×C4C2×C22⋊D1312yes—
493C22×C4C23×D1311yescharacteristic
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—48no—
500C2×C8—262no—
501C2×C8—262no—
502C2×C8—262no—
503C2×C8—262no—
504C2×C8—262no—
505C2×C8—262no—
506C2×C8C2×C22⋊D1314yes—
507C22⋊C4—134no—
508C22⋊C4—134no—
509C22⋊C4—134no—
510C22⋊C4—134no—
511C22⋊C4—134no—
512C22⋊C4—262no—
513C22⋊C4—262no—
514C22⋊C4—262no—
515C42—262no—
516C42—262no—
517C42—261no—
518C42—261no—
519C42—262no—
520C42—262no—
521C42—261no—
522C42—261no—
523C42—521no—
524C42—521no—
525C13#2255211yescharacteristic, complemented, Sylow
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—28no—
541C23—28no—
542C23—44no—
543C23—44no—
544C23—44no—
545C23—44no—
546C23—44no—
547C23#8813112yes—
548C23C2×C8×D1312yes—
549C23C2×C8×D1312yes—
550C23C2×C8×D1312yes—
551C23#8815512yes—
552C23M16×D1312yes—
553C23C4×C22⋊D1312yes—
554C23C22×C4×D1311yescharacteristic
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—44no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—132no—
572C2×C4—132no—
573C2×C4—132no—
574C2×C4—132no—
575C2×C4—132no—
576C2×C4—132no—
577C2×C4—261no—
578C2×C4—261no—
579C2×C4—261no—
580C2×C4—261no—
581C2×C4—261no—
582C2×C4—261no—
583C2×C4—261no—
584C2×C4—261no—
585C2×C4—261no—
586C2×C4—261no—
587C2×C4—261no—
588C2×C4—261no—
589C2×C4—268no—
590C2×C4—261no—
591C2×C4—261no—
592C2×C4—261no—
593C2×C4—261no—
594C2×C4—261no—
595C2×C4—261no—
596C2×C4—524no—
597C2×C4—524no—
598C2×C4—524no—
599C2×C4#8813112yes—
600C2×C4C4×C22⋊D1312yes—
601C2×C4C2×#612711yescharacteristic
602C2×C4C2×#612912yes—
603C2×C4#8825112yes—
604C2×C4C22×C22⋊D1311yescharacteristic
605C8—24no—
606C8—42no—
607C8—522no—
608C8—522no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—416no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22#1171837914yescomplemented
630C22C8×C22⋊D1314yes—
631C22C2×#8813111yescharacteristic
632C22#1171919111yescharacteristic
633C22C22×C8×D1311yescharacteristic
634C22C2×#8815511yescharacteristic
635C22C2×M16×D1311yescharacteristic
636C22#1171945011yescharacteristic
637C22C2×C4×C22⋊D1311yescharacteristic
638C4—22no—
639C4—22no—
640C4—41no—
641C4—262no—
642C4—262no—
643C4—262no—
644C4—262no—
645C4—262no—
646C4—262no—
647C4—521no—
648C4—521no—
649C4#1171920012yes—
650C4#1171951112yes—
651C2—24no—
652C2—24no—
653C2—42no—
654C2#1311768111yescharacteristic
655C2C2×#1171837911yescharacteristic
656C2#1312349011yescharacteristic
657C2C2×C8×C22⋊D1311yescharacteristic
658C2M16×C22⋊D1311yescharacteristic
659C2#1312385811yescharacteristic
660C2#1312386711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C23×C8
FittingC22×C13×C22⋊C8C2
socleC23×C13C23×C4
prime radicalC25×C13C2×C4
cosocleC22×C4×C13C24
hypercenterC22×C22⋊C8D13
hypocenterC13#22552
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#11718379C2semidirect
3. #13115445C2semidirect
4. #13115439C2semidirect
5. #13115014C2semidirect
6. #13114902C2semidirect
7. #13114814C2semidirect
9. C8×C22⋊Dic13C2semidirect
10. C22⋊C8×Dic13C2semidirect
36. C2×#88054C22semidirect
37. C2×#88054C22semidirect
38. C2×C8×Dic13C22semidirect
39. C2×C8×Dic13C22semidirect
41. #11718142C22semidirect
42. #11718142C22semidirect
43. #11718142C22semidirect
44. #11718142C22semidirect
66. C2×C22⋊Dic13C8semidirect
155. C22×Dic13C2×C8semidirect
156. C22×Dic13C2×C8semidirect
177. C22⋊Dic13C2×C8semidirect
178. C22⋊Dic13C2×C8semidirect
343. C22×C13#431semidirect
525. C13#22552semidirect
629. C22#11718379semidirect

Maximal subgroups

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

subgroupindex
C2×#117183792
C2×C4×C22⋊Dic132
#131154452
#131154392
#131150142
#131149022
#131148142
#131147462
C8×C22⋊Dic132
C22⋊C8×Dic132
C22×C13×C22⋊C82
#2255213