Finite Group Databasebeta

← #15828739

Subgroups — #15828739

Order 3328.

1278 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×#11719209C211yesmaximal, characteristic
2#13123858C212yesmaximal, complemented
3#13113158C212yesmaximal, complemented
4#13113153C212yesmaximal, complemented
5#13113152C212yesmaximal, complemented
6#13113149C212yesmaximal, complemented
7C2×#11718120C211yesmaximal, characteristic, complemented
8D13×#324C212yesmaximal, complemented
9C2×C13×#324C211yesmaximal, characteristic, complemented
10C22×#6127C411yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C2×C4×C22⋊D13C411yescharacteristic
13C2×C4×C22⋊D13C411yescharacteristic
14C2×C4×C22⋊D13C2211yescharacteristic
15C2×C4×C22⋊D13C2211yescharacteristic
16C2×#88180C411yescharacteristic
17#11719209—24no—
18#11719209—24no—
19C2×#88147C411yescharacteristic
20C2×#88147C2211yescharacteristic
21C2×#88146C411yescharacteristic
22C2×#88146C2211yescharacteristic
23C2×C4⋊C4×D13C411yescharacteristic
24C2×C4⋊C4×D13C2211yescharacteristic
25C2×#88141C411yescharacteristic
26C2×#88141C2211yescharacteristic
27C2×C13×C22⋊C8C2212yes—
28C2×C22⋊#1055C2212yes—
29C8×C22⋊D13—24no—
30#11718386—24no—
31D13×C22⋊C8C2214yes—
32#11718379C2214yes—
33C13×#324C2212yes—
34C13×#324C2212yes—
35#11718120C2212yes—
36#11718120C2212yes—
37#11718061C2214yes—
38#11718060C2214yes—
39C23×C4×C13C2×C411yescharacteristic
40C23×C4×C13C2×C411yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C22×C22⋊D13C2×C411yescharacteristic
43C22×C22⋊D13C2×C411yescharacteristic
44C2×#6127—22no—
45C2×#6127—22no—
46C2×#6127—24no—
47C2×#6127C818yescomplemented
48C22×D52C2×C411yescharacteristic
49C22×C4×D13C2×C411yescharacteristic
50C22×C4×D13C2×C411yescharacteristic
51C22×C4×D13C2×C411yescharacteristic
52C22×C4×D13C2×C411yescharacteristic
53C22×C4×D13C2×C411yescharacteristic
54C22×C4×D13C2311yescharacteristic
55C22×Dic26C2×C411yescharacteristic
56C22×C8×C13—22no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4C2×C411yescharacteristic
60C2×C13×C4⋊C4C2×C411yescharacteristic
61C2×C13×C4⋊C4C2311yescharacteristic
62C2×C13×C4⋊C4C2311yescharacteristic
63C2×C22⋊Dic13C2×C411yescharacteristic
64C2×C22⋊Dic13C2×C411yescharacteristic
65C4×C22⋊D13—22no—
66C4×C22⋊D13—22no—
67C4×C22⋊D13—22no—
68C4×C22⋊D13—22no—
69C4×C22⋊D13—22no—
70C4×C22⋊D13—22no—
71C4×C22⋊D13D414yes—
72C4×C22⋊D13D414yes—
73C2×#6103C2×C411yescharacteristic
74C2×#6103C2×C411yescharacteristic
75C2×#6103C2×C411yescharacteristic
76C2×#6103C2311yescharacteristic
77#88180—22no—
78#88180—22no—
79C2×C4⋊Dic13C2×C411yescharacteristic
80C2×C4⋊Dic13C2×C411yescharacteristic
81C2×#6101C2×C411yescharacteristic
82C2×#6101C2×C411yescharacteristic
83C2×#6101C2×C411yescharacteristic
84C2×#6101C2311yescharacteristic
85C2×C4×Dic13C2×C411yescharacteristic
86C2×C4×Dic13C2×C411yescharacteristic
87C2×C4×Dic13C2×C411yescharacteristic
88C2×C4×Dic13C2×C411yescharacteristic
89C2×C4×Dic13C2×C411yescharacteristic
90C2×C4×Dic13C2311yescharacteristic
91C22×#1055—22no—
92C2×C8×D13—24no—
93#88147—24no—
94#88147—24no—
95#88146—24no—
96#88146—24no—
97C4⋊C4×D13—24no—
98C4⋊C4×D13—24no—
99#88141—24no—
100#88141—24no—
101C13×C22⋊C8—22no—
102C13×C22⋊C8C2314yes—
103C22⋊#1055—22no—
104C22⋊#1055C2314yes—
105#88060—24no—
106#88054—24no—
107C8×Dic13—24no—
108#17351—131nomaximal, Sylow
109C24×C13C22×C411yescharacteristic
110C23×D13C22×C411yescharacteristic
111C23×D13C22×C411yescharacteristic
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—22no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—81no—
118C22×C4×C13—81no—
119C22×C4×C13C2×C814yescomplemented
120C22×C4×C13C22×C411yescharacteristic
121C22×C4×C13C22×C411yescharacteristic
122C22×C4×C13C22×C411yescharacteristic
123C22×C4×C13C22×C411yescharacteristic
124C22×C4×C13C22×C411yescharacteristic
125C22×C4×C13C2×D412yes—
126C22×C4×C13C2×D412yes—
127C22×C4×C13C2411yescharacteristic
128C2×C22⋊D13—21no—
129C2×C22⋊D13—21no—
130C2×C22⋊D13—22no—
131C2×C22⋊D13C22⋊C412yes—
132C2×C22⋊D13C22⋊C412yes—
133C2×C22⋊D13C2×C814yes—
134C2×C22⋊D13C2×C814yescomplemented
135C2×C22⋊D13M1614yes—
136C22×Dic13C22×C411yescharacteristic
137C22×Dic13C22×C411yescharacteristic
138C22×Dic13C22×C411yescharacteristic
139C22×Dic13C22×C411yescharacteristic
140C22×Dic13C22×C411yescharacteristic
141C22×Dic13C22×C411yescharacteristic
142#6127—216no—
143#6127—216no—
144C2×D52—22no—
145C2×D52—22no—
146C2×D52C2×C814yescomplemented
147C2×C4×D13—22no—
148C2×C4×D13—22no—
149C2×C4×D13—22no—
150C2×C4×D13—22no—
151C2×C4×D13—22no—
152C2×C4×D13—22no—
153C2×C4×D13—22no—
154C2×C4×D13—81no—
155C2×C4×D13—81no—
156C2×C4×D13—81no—
157C2×C4×D13—81no—
158C2×C4×D13C2×C814yescomplemented
159C2×C4×D13C2×C814yescomplemented
160C2×C4×D13C2×D414yes—
161C2×Dic26—22no—
162C2×Dic26—22no—
163C2×Dic26C2×C814yescomplemented
164C2×C8×C13—24no—
165C2×C8×C13—82no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C22⋊Dic13—21no—
171C22⋊Dic13—21no—
172C22⋊Dic13C22⋊C412yes—
173C22⋊Dic13C22⋊C412yes—
174#6103—22no—
175#6103—22no—
176#6103—22no—
177#6103C22⋊C414yes—
178C4⋊Dic13—22no—
179C4⋊Dic13—22no—
180#6101—22no—
181#6101—22no—
182#6101—22no—
183#6101C22⋊C414yes—
184C4×Dic13—22no—
185C4×Dic13—22no—
186C4×Dic13—22no—
187C4×Dic13—22no—
188C4×Dic13—22no—
189C4×Dic13C2×D414yes—
190C2×#1055—24no—
191C2×#1055—82no—
192C8×D13—84no—
193C2×#520—131no—
194#2972—132no—
195#1461—132no—
196#1459—132no—
197#1459—132no—
198#1458—132no—
199C2×#324—132no—
200C2×#324—131no—
201C2×#324D1311yescharacteristic, complemented
202C23×C13—41no—
203C23×C13—41no—
204C23×C13C2×C22⋊C411yescharacteristic
205C23×C13C2×C22⋊C411yescharacteristic
206C23×C13C22×C812yes—
207C23×C13C2×M1612yes—
208C23×C13C23×C411yescharacteristic
209C22×D13—21no—
210C22×D13—21no—
211C22×D13—41no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—41no—
215C22×D13C2×C22⋊C412yes—
216C22×D13C22×C812yes—
217C22×D13C22×C812yes—
218C22×D13C2×M1612yes—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—24no—
224C2×C4×C13—24no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—81no—
234C2×C4×C13—81no—
235C2×C4×C13C2×C22⋊C412yes—
236C2×C4×C13C22×C812yes—
237C2×C4×C13C22×C812yes—
238C2×C4×C13C22×D412yes—
239C22⋊D13—24no—
240C22⋊D13—24no—
241C22⋊D13C22⋊C818yes—
242C22⋊D13C22⋊C818yes—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—41no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13C2×C22⋊C412yes—
252C2×Dic13C2×C22⋊C412yes—
253C2×Dic13C2×C22⋊C412yes—
254C2×Dic13C22×C812yes—
255C2×Dic13C22×C812yes—
256C2×Dic13C2×M1612yes—
257D52—28no—
258C4×D13—28no—
259C4×D13—28no—
260C4×D13—44no—
261C4×D13—82no—
262C4×D13—82no—
263C4×D13—82no—
264Dic26—28no—
265C8×C13—44no—
266#1055—44no—
267C22×#41—131no—
268#520—264no—
269#520—264no—
270C2×C4×Q8—131no—
271C2×C4×Q8—131no—
272C2×C4×D4—131no—
273C2×C4×D4—131no—
274C2×C4×D4—131no—
275C2×C4×D4—131no—
276C2×C4×D4—131no—
277C2×C4×D4—131no—
278C2×#117—131no—
279C2×#117—131no—
280C2×#117—131no—
281C22×C4⋊C4—131no—
282C22×C4⋊C4—131no—
283C22×C4⋊C4C2×D1311yescharacteristic
284C8×D4—264no—
285C8×D4—264no—
286#431—134no—
287C2×C22⋊C8—132no—
288C2×C22⋊C8—134no—
289C2×C22⋊C8C2×D1312yes—
290#324—132no—
291#324—132no—
292#324—134no—
293#324C2×D1312yes—
294#324C2×D1312yes—
295#323—134no—
296C22×C13—21no—
297C22×C13—21no—
298C22×C13—21no—
299C22×C13—21no—
300C22×C13—21no—
301C22×C13—21no—
302C22×C13—42no—
303C22×C13—42no—
304C22×C13C2×C22⋊C812yes—
305C22×C13C2×C22⋊C812yes—
306C22×C13C22×C22⋊C411yescharacteristic
307C22×C13C23×C811yescharacteristic
308C22×C13C22×M1611yescharacteristic
309C2×D13—22no—
310C2×D13—22no—
311C2×D13—22no—
312C2×D13—42no—
313C2×D13—42no—
314C2×D13—42no—
315C2×D13—41no—
316C2×D13—41no—
317C2×D13—42no—
318C2×D13C2×C22⋊C814yes—
319C4×C13—22no—
320C4×C13—22no—
321C4×C13—22no—
322C4×C13—22no—
323C4×C13—41no—
324C4×C13—41no—
325Dic13—22no—
326Dic13—22no—
327Dic13—22no—
328Dic13—41no—
329Dic13—41no—
330Dic13C2×C22⋊C814yes—
331C2×#41—138no—
332C2×#41—262no—
333C2×#41—262no—
334C2×#41—264no—
335C22×Q8—131no—
336C22×D4—131no—
337C22×D4—131no—
338C22×D4—131no—
339C23×C4—131no—
340C23×C4—131no—
341C23×C4—131no—
342C23×C4—131no—
343C23×C4—131no—
344C23×C4—131no—
345C23×C4C4×D1311yescharacteristic
346C23×C4C4×D1311yescharacteristic
347C23×C4C22×D1311yescharacteristic
348C22×C8—22no—
349C22×C8—264no—
350C22×C8—262no—
351C4×Q8—264no—
352C4×Q8—264no—
353C4×D4—134no—
354C4×D4—134no—
355C4×D4—264no—
356C4×D4—262no—
357C4×D4—262no—
358C4×D4—264no—
359C4×D4—262no—
360C4×D4—262no—
361C4×D4—262no—
362C4×D4—262no—
363#117—264no—
364#117—264no—
365#117—262no—
366#117—262no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—264no—
376C2×C4⋊C4—264no—
377C2×C4⋊C4C4×D1311yescharacteristic
378C2×C4⋊C4C4×D1311yescharacteristic
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C22⋊C4—131no—
382C2×C22⋊C4—131no—
383C2×C22⋊C4—131no—
384C2×C22⋊C4—131no—
385C2×C22⋊C4—131no—
386C2×C22⋊C4—131no—
387C2×C42—131no—
388C2×C42—131no—
389C2×C42—131no—
390C2×C42—131no—
391C2×C42—131no—
392C2×C42—131no—
393C4⋊C8—264no—
394C22⋊C8—22no—
395C22⋊C8—134no—
396C22⋊C8—264no—
397C22⋊C8—262no—
398C22⋊C8C22×D1314yes—
399C4×C8—264no—
400C2×C13—21no—
401C2×C13—21no—
402C2×C13—22no—
403C2×C13—22no—
404C2×C13C22×C22⋊C811yescharacteristic
405C2×C13#288311yescharacteristic
406C2×C13#288911yescharacteristic
407D13—24no—
408D13—42no—
409C24—131no—
410C24—131no—
411C24C2×C4×D1311yescharacteristic
412#41—2616no—
413#41—2616no—
414C2×Q8—134no—
415C2×Q8—262no—
416C2×Q8—262no—
417C2×D4—132no—
418C2×D4—132no—
419C2×D4—134no—
420C2×D4—134no—
421C2×D4—134no—
422C2×D4—134no—
423C2×D4—262no—
424C2×D4—262no—
425C2×D4—261no—
426C2×D4—261no—
427C2×D4—262no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—81no—
434C22×C4—81no—
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—134no—
440C22×C4—134no—
441C22×C4—134no—
442C22×C4—131no—
443C22×C4—131no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—1041no—
452C22×C4—1041no—
453C22×C4—1041no—
454C22×C4—1041no—
455C22×C4C8×D1314yescomplemented
456C22×C4C2×C4×D1311yescharacteristic
457C22×C4C2×C4×D1311yescharacteristic
458C22×C4C2×C4×D1311yescharacteristic
459C22×C4C2×C4×D1311yescharacteristic
460C22×C4C2×C4×D1311yescharacteristic
461C22×C4D4×D1312yes—
462C22×C4D4×D1312yes—
463C22×C4C23×D1311yescharacteristic
464C2×C8—24no—
465C2×C8—82no—
466C2×C8—264no—
467C2×C8—1044no—
468C2×C8—1042no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—134no—
474C4⋊C4—262no—
475C4⋊C4—262no—
476C4⋊C4—262no—
477C4⋊C4—262no—
478C4⋊C4—262no—
479C22⋊C4—132no—
480C22⋊C4—132no—
481C22⋊C4—134no—
482C22⋊C4—262no—
483C22⋊C4—262no—
484C22⋊C4—261no—
485C22⋊C4—261no—
486C22⋊C4—262no—
487C42—134no—
488C42—262no—
489C42—262no—
490C42—262no—
491C42—262no—
492C42—262no—
493C13#1735111yescharacteristic, complemented, Sylow
494C23—41no—
495C23—41no—
496C23—132no—
497C23—132no—
498C23—132no—
499C23—132no—
500C23—261no—
501C23—261no—
502C23—521no—
503C23—521no—
504C23—521no—
505C23—521no—
506C23C22⋊C4×D1311yescharacteristic
507C23C22⋊C4×D1311yescharacteristic
508C23C2×C8×D1312yes—
509C23M16×D1312yes—
510C23C22×C4×D1311yescharacteristic
511Q8—268no—
512D4—138no—
513D4—138no—
514D4—268no—
515D4—264no—
516D4—264no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—132no—
534C2×C4—132no—
535C2×C4—132no—
536C2×C4—132no—
537C2×C4—132no—
538C2×C4—132no—
539C2×C4—268no—
540C2×C4—268no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—524no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—1042no—
551C2×C4—1042no—
552C2×C4—1042no—
553C2×C4C22⋊C4×D1312yes—
554C2×C4C2×C8×D1312yes—
555C2×C4C2×C8×D1312yes—
556C2×C4C2×D4×D1312yes—
557C8—44no—
558C8—524no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—42no—
566C22—42no—
567C22—134no—
568C22—262no—
569C22—262no—
570C22—262no—
571C22—522no—
572C22—522no—
573C22—522no—
574C22—522no—
575C22—521no—
576C22—521no—
577C22D13×C22⋊C812yes—
578C22D13×C22⋊C812yes—
579C22C2×C22⋊C4×D1311yescharacteristic
580C22C22×C8×D1311yescharacteristic
581C22C2×M16×D1311yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—134no—
589C4—262no—
590C4—262no—
591C4—262no—
592C4—521no—
593C4—521no—
594C2—21no—
595C2—21no—
596C2—22no—
597C2—22no—
598C2—264no—
599C2—522no—
600C2C2×D13×C22⋊C811yescharacteristic
601C2#1312329411yescharacteristic
602C2#1312331611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC22×C13C23×C8
FrattiniC22×C4C23×D13
FittingC2×C13×#324C2
socleC22×C13C22×C22⋊C4
prime radicalC22×#6127C4
cosocleC22×C4×C13C24
hypercenterC2×#324D13
hypocenterC13#17351
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #13123858C2semidirect
3. #13113158C2semidirect
4. #13113153C2semidirect
5. #13113152C2semidirect
6. #13113149C2semidirect
7. C2×#11718120C2semidirect
8. D13×#324C2semidirect
9. C2×C13×#324C2semidirect
47. C2×#6127C8semidirect
119. C22×C4×C13C2×C8semidirect
134. C2×C22⋊D13C2×C8semidirect
146. C2×D52C2×C8semidirect
158. C2×C4×D13C2×C8semidirect
159. C2×C4×D13C2×C8semidirect
163. C2×Dic26C2×C8semidirect
201. C2×#324D13semidirect
455. C22×C4C8×D13semidirect
493. C13#17351semidirect

Maximal subgroups

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

subgroupindex
C2×#117192092
#131238582
#131131582
#131131532
#131131522
#131131492
C2×#117181202
D13×#3242
C2×C13×#3242
#1735113