Finite Group Databasebeta

← #15769227

Subgroups — #15769227

Order 3328.

1118 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88077C211yesmaximal, characteristic
2C2×M16×Dic13C211yesmaximal, characteristic, complemented
3#13117327C211yesmaximal, characteristic
4C2×#11718147C211yesmaximal, characteristic, complemented
5C2×#11718115C211yesmaximal, characteristic, complemented
6C4×#88071C211yesmaximal, characteristic, complemented
7C22×C13×#104C211yesmaximal, characteristic
8C22×C13×#41C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C22×C42×C13C2211yescharacteristic
11C2×#88180C2211yescharacteristic
12C22×C4×Dic13C2211yescharacteristic
13C22×C4×Dic13C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15C2×C13×#104—22no—
16C2×C13×#104—22no—
17C2×C13×#104C414yescomplemented
18C2×#88077—22no—
19C2×#88077—22no—
20C2×#88077C414yescomplemented
21#11718891C412yescomplemented
22#11718882C412yescomplemented
23#11718881—22no—
24C4×C22⋊Dic13—21no—
25C4×C22⋊Dic13—21no—
26C2×#88071—22no—
27M16×Dic13—22no—
28M16×Dic13—22no—
29C2×#88055—21no—
30C2×C8×Dic13—21no—
31#11718147—22no—
32#11718115—22no—
33C2×C13×#41—21no—
34C2×C13×#41—21no—
35C2×C13×#41—21no—
36C2×C13×#41—21no—
37C2×C13×#41—21no—
38C2×C13×#41—21no—
39C2×C13×#41—21no—
40C2×C13×#41—21no—
41C2×C13×#41—21no—
42C2×C13×#41—21no—
43C2×C13×#41C2×C412yes—
44C2×C13×#41C2×C412yes—
45C22×Q8×C13C2×C411yescharacteristic
46C22×D4×C13—21no—
47C22×D4×C13C2×C411yescharacteristic
48C23×C4×C13—21no—
49C23×C4×C13—21no—
50C23×C4×C13C2311yescharacteristic
51C23×Dic13—21no—
52C23×Dic13D412yes—
53C2×C13×M16—21no—
54C2×C13×M16—21no—
55C2×C13×M16—21no—
56C2×C13×M16C2×C412yes—
57C2×C13×M16D412yes—
58C2×C13×M16D412yes—
59C22×C8×C13—21no—
60C2×C42×C13—21no—
61C2×C42×C13—21no—
62C2×C42×C13—21no—
63C2×C42×C13—21no—
64C2×C42×C13—21no—
65C2×C42×C13C2×C412yes—
66C2×C22⋊Dic13—21no—
67C2×C22⋊Dic13—22no—
68C2×C22⋊Dic13—22no—
69#88180—21no—
70#88180—21no—
71#88180—21no—
72#88180—21no—
73C2×C4⋊Dic13C2×C412yes—
74C2×C4×Dic13—21no—
75C2×C4×Dic13—21no—
76C2×C4×Dic13—21no—
77C2×C4×Dic13—21no—
78C2×C4×Dic13—21no—
79C2×C4×Dic13—21no—
80C2×C4×Dic13—21no—
81C2×C4×Dic13—21no—
82C2×C4×Dic13—21no—
83C2×C4×Dic13—21no—
84C2×C4×Dic13C2×C412yes—
85C2×C4×Dic13C2×C412yes—
86C2×C4×Dic13D411yescharacteristic
87C2×C4×Dic13D411yescharacteristic
88C2×#6099—21no—
89C2×#6099—21no—
90C2×#6099—21no—
91C2×#6099C2×C412yes—
92C2×#6099D412yes—
93C2×#6099D412yes—
94C22×#1055—21no—
95C13×#104—28no—
96#88077—28no—
97#88071—28no—
98#88071—22no—
99#88071—22no—
100#88055—24no—
101C8×Dic13—24no—
102#10933—131nomaximal, Sylow
103C24×C13—21no—
104C24×C13C2×D411yescharacteristic
105C13×#41—22no—
106C13×#41—22no—
107C13×#41—22no—
108C13×#41—22no—
109C13×#41—22no—
110C13×#41—22no—
111C13×#41—22no—
112C13×#41—22no—
113C13×#41—41no—
114C13×#41—41no—
115C13×#41—41no—
116C13×#41—41no—
117C13×#41—41no—
118C13×#41—41no—
119C13×#41—41no—
120C13×#41—41no—
121C2×Q8×C13—21no—
122C2×Q8×C13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13—21no—
125C2×Q8×C13—21no—
126C2×Q8×C13C4212yes—
127C2×D4×C13—22no—
128C2×D4×C13—22no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—41no—
135C2×D4×C13—41no—
136C2×D4×C13—41no—
137C2×D4×C13—41no—
138C2×D4×C13C4212yes—
139C22×C4×C13—24no—
140C22×C4×C13—21no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—42no—
145C22×C4×C13—41no—
146C22×C4×C13—41no—
147C22×C4×C13—41no—
148C22×C4×C13—41no—
149C22×C4×C13—41no—
150C22×C4×C13—41no—
151C22×C4×C13C22×C411yescharacteristic
152C22×C4×C13C22×C411yescharacteristic
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13#4111yescharacteristic
160C22×C4×C13#4111yescharacteristic
161C22×C4×C13#4111yescharacteristic
162C22×C4×C13#4111yescharacteristic
163C22×C4×C13#4111yescharacteristic
164C22×C4×C13#4111yescharacteristic
165C22×Dic13—24no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—24no—
170C22×Dic13—22no—
171C22×Dic13—42no—
172C22×Dic13—42no—
173C22×Dic13—41no—
174C22×Dic13—41no—
175C22×Dic13C22⋊C412yes—
176C22×Dic13C22⋊C412yes—
177C13×M16—22no—
178C13×M16—22no—
179C13×M16—22no—
180C13×M16C22⋊C414yescomplemented
181C2×C8×C13—22no—
182C2×C8×C13—22no—
183C2×C8×C13—22no—
184C42×C13—22no—
185C42×C13—22no—
186C42×C13—41no—
187C42×C13—41no—
188C22⋊Dic13—44no—
189C22⋊Dic13—41no—
190C22⋊Dic13—41no—
191C22⋊Dic13—44no—
192C4⋊Dic13—22no—
193C4⋊Dic13—22no—
194C4×Dic13—22no—
195C4×Dic13—22no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—22no—
201C4×Dic13—22no—
202C4×Dic13—41no—
203C4×Dic13—41no—
204C4×Dic13—41no—
205C4×Dic13—41no—
206#6099—22no—
207#6099—22no—
208#6099—22no—
209#6099C22⋊C414yescomplemented
210C2×#1055—22no—
211C2×#1055—22no—
212C2×#1055—22no—
213C22×#104—131no—
214C22×#104D1311yescharacteristic
215C2×C4×M16—131no—
216#2297—131no—
217C2×#339—131no—
218C2×#339—131no—
219C4×#95—131no—
220C23×C13—22no—
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13—42no—
226C23×C13—42no—
227C23×C13C2×C22⋊C411yescharacteristic
228C23×C13C4×D411yescharacteristic
229C23×C13C4×D411yescharacteristic
230C23×C13#12111yescharacteristic
231C23×C13#12111yescharacteristic
232C23×C13#12411yescharacteristic
233C23×C13#12711yescharacteristic
234Q8×C13—22no—
235Q8×C13—22no—
236Q8×C13—41no—
237Q8×C13—41no—
238D4×C13—22no—
239D4×C13—22no—
240D4×C13—42no—
241D4×C13—42no—
242D4×C13—42no—
243D4×C13—42no—
244D4×C13—41no—
245D4×C13—41no—
246C2×C4×C13—24no—
247C2×C4×C13—22no—
248C2×C4×C13—44no—
249C2×C4×C13—44no—
250C2×C4×C13—42no—
251C2×C4×C13—41no—
252C2×C4×C13—42no—
253C2×C4×C13—41no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13C2×C4211yescharacteristic
259C2×C4×C13C2×C22⋊C411yescharacteristic
260C2×C4×C13C2×C22⋊C411yescharacteristic
261C2×C4×C13#11711yescharacteristic
262C2×C4×C13#11711yescharacteristic
263C2×C4×C13#11711yescharacteristic
264C2×C4×C13C4×D411yescharacteristic
265C2×C4×C13C4×D411yescharacteristic
266C2×C4×C13C4×D411yescharacteristic
267C2×C4×C13C4×D411yescharacteristic
268C2×C4×C13C4×D411yescharacteristic
269C2×C4×C13C4×D411yescharacteristic
270C2×C4×C13C4×D411yescharacteristic
271C2×C4×C13C4×D411yescharacteristic
272C2×C4×C13C4×D411yescharacteristic
273C2×C4×C13C4×D411yescharacteristic
274C2×C4×C13#12011yescharacteristic
275C2×C4×C13#12111yescharacteristic
276C2×C4×C13#12111yescharacteristic
277C2×C4×C13#12111yescharacteristic
278C2×C4×C13#12111yescharacteristic
279C2×C4×C13#12311yescharacteristic
280C2×C4×C13#12311yescharacteristic
281C2×C4×C13#12311yescharacteristic
282C2×C4×C13#12411yescharacteristic
283C2×C4×C13#12411yescharacteristic
284C2×C4×C13#12611yescharacteristic
285C2×C4×C13#12611yescharacteristic
286C2×Dic13—22no—
287C2×Dic13—22no—
288C2×Dic13—24no—
289C2×Dic13—22no—
290C2×Dic13—22no—
291C2×Dic13—22no—
292C2×Dic13—44no—
293C2×Dic13—44no—
294C2×Dic13—44no—
295C2×Dic13—44no—
296C2×Dic13—42no—
297C2×Dic13—42no—
298C2×Dic13—42no—
299C2×Dic13—42no—
300C2×Dic13—42no—
301C2×Dic13#10414yescomplemented
302C8×C13—24no—
303#1055—24no—
304C22×#41C2×D1311yescharacteristic
305C22×M16—131no—
306C22×M16C2×D1311yescharacteristic
307C2×#117—131no—
308C22×C42—131no—
309C22×C42—131no—
310C22×C42C2×D1311yescharacteristic
311C2×#104—22no—
312C2×#104—22no—
313C2×#104—134no—
314C2×#104—262no—
315C2×#104—262no—
316C2×#104Dic1314yescomplemented
317C4×M16—262no—
318C4×M16—262no—
319C2×#97—261no—
320C2×C4×C8—261no—
321#391—132no—
322#390—132no—
323#386—262no—
324C4×C22⋊C4—261no—
325C4×C22⋊C4—261no—
326C2×#95—262no—
327#339—262no—
328#339—262no—
329C22×C13—22no—
330C22×C13—22no—
331C22×C13—22no—
332C22×C13—22no—
333C22×C13—21no—
334C22×C13—21no—
335C22×C13—21no—
336C22×C13—21no—
337C22×C13—42no—
338C22×C13—42no—
339C22×C13—42no—
340C22×C13—82no—
341C22×C13—82no—
342C22×C13C4×C22⋊C411yescharacteristic
343C22×C13#38611yescharacteristic
344C22×C13#38811yescharacteristic
345C22×C13#38811yescharacteristic
346C22×C13#39011yescharacteristic
347C22×C13#39011yescharacteristic
348C22×C13#39011yescharacteristic
349C22×C13C2×#10412yes—
350C22×C13#42112yes—
351C4×C13—44no—
352C4×C13—42no—
353C4×C13C4×C22⋊C411yescharacteristic
354C4×C13C4×C22⋊C411yescharacteristic
355C4×C13#38611yescharacteristic
356C4×C13#38611yescharacteristic
357C4×C13#38811yescharacteristic
358C4×C13#38811yescharacteristic
359C4×C13#38811yescharacteristic
360C4×C13#38811yescharacteristic
361Dic13—24no—
362Dic13—44no—
363Dic13—42no—
364Dic13—82no—
365C2×#41—21no—
366C2×#41—21no—
367C2×#41—21no—
368C2×#41—21no—
369C2×#41—21no—
370C2×#41—21no—
371C2×#41—21no—
372C2×#41—21no—
373C2×#41—21no—
374C2×#41—21no—
375C2×#41C4×D1312yes—
376C2×#41C2×Dic1312yes—
377C22×Q8C4×D1311yescharacteristic
378C22×D4—21no—
379C22×D4C4×D1311yescharacteristic
380C23×C4—21no—
381C23×C4—21no—
382C23×C4—132no—
383C23×C4—261no—
384C23×C4C22×D1311yescharacteristic
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—132no—
389C2×M16—132no—
390C2×M16—132no—
391C2×M16—261no—
392C2×M16—261no—
393C2×M16—261no—
394C2×M16C2×Dic1312yes—
395C2×M16C22⋊D1312yes—
396C2×M16C22⋊D1312yes—
397C22×C8—21no—
398C22×C8—261no—
399#117—261no—
400#117—261no—
401#117—261no—
402#117—261no—
403C2×C4⋊C4—132no—
404C2×C22⋊C4—262no—
405C2×C22⋊C4—262no—
406C2×C22⋊C4—261no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—132no—
413C2×C42—131no—
414C2×C42—131no—
415C2×C42—132no—
416C2×C42—261no—
417C2×C42—261no—
418C2×C42—261no—
419C2×C42—261no—
420C2×C42—261no—
421C2×C42—261no—
422C2×C42—261no—
423C2×C42—261no—
424C2×C42—261no—
425C2×C42—261no—
426C2×C42C2×Dic1312yes—
427#104—28no—
428#104—268no—
429#97—264no—
430C4×C8—264no—
431#95—262no—
432#95—262no—
433#95—268no—
434C2×C13—21no—
435C2×C13—21no—
436C2×C13—21no—
437C2×C13—21no—
438C2×C13—82no—
439C2×C13#143711yescharacteristic
440C2×C13C4×#10411yescharacteristic
441C2×C13#175911yescharacteristic
442C2×C13#187112yes—
443C2×C13#198012yes—
444C24—21no—
445C24D4×D1311yescharacteristic
446#41—22no—
447#41—22no—
448#41—22no—
449#41—22no—
450#41—22no—
451#41—22no—
452#41—22no—
453#41—22no—
454#41—41no—
455#41—41no—
456#41—41no—
457#41—41no—
458#41—41no—
459#41—41no—
460#41—41no—
461#41—41no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8C4×Dic1312yes—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4C4×Dic1312yes—
480C22×C4—24no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—42no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—132no—
493C22×C4—132no—
494C22×C4—264no—
495C22×C4—264no—
496C22×C4—262no—
497C22×C4—262no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—522no—
501C22×C4—522no—
502C22×C4—521no—
503C22×C4—521no—
504C22×C4C2×C4×D1311yescharacteristic
505C22×C4C2×C4×D1311yescharacteristic
506C22×C4#612711yescharacteristic
507C22×C4#612711yescharacteristic
508C22×C4D4×D1311yescharacteristic
509C22×C4D4×D1311yescharacteristic
510C22×C4D4×D1311yescharacteristic
511C22×C4#612911yescharacteristic
512C22×C4#612911yescharacteristic
513C22×C4#612911yescharacteristic
514C22×C4#612911yescharacteristic
515C22×C4C22×Dic1311yescharacteristic
516C22×C4C2×C22⋊D1311yescharacteristic
517C22×C4C2×C22⋊D1311yescharacteristic
518M16—22no—
519M16—22no—
520M16—22no—
521M16—134no—
522M16—262no—
523M16—262no—
524M16—262no—
525M16C22⋊Dic1314yescomplemented
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—262no—
530C2×C8—262no—
531C2×C8—262no—
532C4⋊C4—262no—
533C4⋊C4—262no—
534C22⋊C4—524no—
535C22⋊C4—524no—
536C22⋊C4—521no—
537C22⋊C4—521no—
538C42—22no—
539C42—22no—
540C42—41no—
541C42—41no—
542C42—262no—
543C42—261no—
544C42—261no—
545C42—262no—
546C42—261no—
547C42—261no—
548C42—262no—
549C42—262no—
550C42—521no—
551C42—521no—
552C42—521no—
553C42—521no—
554C13#1093311yescharacteristic, complemented, Sylow
555C23—22no—
556C23—22no—
557C23—22no—
558C23—42no—
559C23—42no—
560C23—41no—
561C23—41no—
562C23C22⋊C4×D1311yescharacteristic
563C23#8813511yescharacteristic
564C23#8813811yescharacteristic
565C23#8813911yescharacteristic
566C23D4×Dic1311yescharacteristic
567C23#8819211yescharacteristic
568C23#8819411yescharacteristic
569Q8—22no—
570Q8—22no—
571Q8—41no—
572Q8—41no—
573D4—22no—
574D4—22no—
575D4—42no—
576D4—42no—
577D4—42no—
578D4—42no—
579D4—41no—
580D4—41no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—42no—
584C2×C4—44no—
585C2×C4—44no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—134no—
594C2×C4—262no—
595C2×C4—262no—
596C2×C4—264no—
597C2×C4—262no—
598C2×C4—262no—
599C2×C4—262no—
600C2×C4—524no—
601C2×C4—524no—
602C2×C4—522no—
603C2×C4—524no—
604C2×C4—524no—
605C2×C4—522no—
606C2×C4—522no—
607C2×C4—522no—
608C2×C4—522no—
609C2×C4#8813111yescharacteristic
610C2×C4#8813111yescharacteristic
611C2×C4#8813311yescharacteristic
612C2×C4#8813311yescharacteristic
613C2×C4C22⋊C4×D1311yescharacteristic
614C2×C4#8813511yescharacteristic
615C2×C4#8813511yescharacteristic
616C2×C4#8813511yescharacteristic
617C2×C4#8813711yescharacteristic
618C2×C4#8813711yescharacteristic
619C2×C4#8813811yescharacteristic
620C2×C4#8813911yescharacteristic
621C2×C4C2×C4×Dic1311yescharacteristic
622C2×C4#8818011yescharacteristic
623C2×C4C4×C22⋊D1311yescharacteristic
624C2×C4C4×C22⋊D1311yescharacteristic
625C2×C4C4×C22⋊D1311yescharacteristic
626C2×C4C4×C22⋊D1311yescharacteristic
627C2×C4D4×Dic1311yescharacteristic
628C2×C4D4×Dic1311yescharacteristic
629C2×C4D4×Dic1311yescharacteristic
630C2×C4#8818911yescharacteristic
631C2×C4#8819011yescharacteristic
632C2×C4#8819111yescharacteristic
633C2×C4#8819211yescharacteristic
634C2×C4#8819311yescharacteristic
635C2×C4#8819311yescharacteristic
636C2×C4C2×C22⋊Dic1311yescharacteristic
637C8—24no—
638C8—264no—
639C22—21no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—82no—
651C22—82no—
652C22D13×#10412yes—
653C22#1171848212yes—
654C22C22⋊C4×Dic1311yescharacteristic
655C22#1171860511yescharacteristic
656C22#1171861211yescharacteristic
657C22#1171861711yescharacteristic
658C22#1171861811yescharacteristic
659C22#1171861811yescharacteristic
660C22#1171888211yescharacteristic
661C4—44no—
662C4—42no—
663C4—264no—
664C4—524no—
665C4—522no—
666C4—1042no—
667C4C22⋊C4×Dic1311yescharacteristic
668C4#1171860511yescharacteristic
669C4#1171860611yescharacteristic
670C4#1171860611yescharacteristic
671C4#1171861211yescharacteristic
672C4#1171861711yescharacteristic
673C4C4×C22⋊Dic1311yescharacteristic
674C4#1171888111yescharacteristic
675C2—21no—
676C2—21no—
677C2—21no—
678C2—21no—
679C2—82no—
680C2#1311307311yescharacteristic
681C2#104×Dic1311yescharacteristic
682C2#1311464811yescharacteristic
683C2#1311513512yes—
684C2#1311575312yes—
subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC22×C13×#104C2
socleC23×C13C2×C22⋊C4
prime radicalC22×C13×#41C22
cosocleC23×C4×C13C23
hypercenterC22×#104D13
hypocenterC13#10933
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C2×M16×Dic13C2semidirect
4. C2×#11718147C2semidirect
5. C2×#11718115C2semidirect
6. C4×#88071C2semidirect
17. C2×C13×#104C4semidirect
20. C2×#88077C4semidirect
21. #11718891C4semidirect
22. #11718882C4semidirect
180. C13×M16C22⋊C4semidirect
209. #6099C22⋊C4semidirect
301. C2×Dic13#104semidirect
316. C2×#104Dic13semidirect
525. M16C22⋊Dic13semidirect
554. C13#10933semidirect

Maximal subgroups

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

subgroupindex
C22×#880772
C2×M16×Dic132
#131173272
C2×#117181472
C2×#117181152
C4×#880712
C22×C13×#1042
#1093313