Finite Group Databasebeta

← #15881273

Subgroups — #15881273

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718679C211yesmaximal, characteristic
2C2×#11718418C211yesmaximal, characteristic
3C2×#11718419C211yesmaximal, characteristic
4#13117753C211yesmaximal, characteristic, complemented
5D4×C4⋊Dic13C211yesmaximal, characteristic
6#13115573C211yesmaximal, characteristic, complemented
7#13115568C211yesmaximal, characteristic, complemented
8#13115105C211yesmaximal, characteristic, complemented
9#13115095C211yesmaximal, characteristic
10#13115091C211yesmaximal, characteristic, complemented
11#13115081C211yesmaximal, characteristic
12#13115005C211yesmaximal, characteristic, complemented
13#13114842C211yesmaximal, characteristic, complemented
14#13114713C211yesmaximal, characteristic, complemented
15C13×#1804C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×D4×Dic13C2211yescharacteristic
18C2×D4×Dic13C2211yescharacteristic
19C22×#6105C2211yescharacteristic
20C22×C4⋊Dic13—21no—
21C2×#88141C2211yescharacteristic
22C2×#88141C2211yescharacteristic
23C2×C4×Dic26C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×#102C2211yescharacteristic
26C2×C13×#102C2211yescharacteristic
27C13×#382C2211yescharacteristic
28C2×#88072C2211yescharacteristic
29#11718873—21no—
30C2×#88056C2211yescharacteristic
31C2×#88056C2211yescharacteristic
32C2×#88055C2211yescharacteristic
33C2×C8×Dic13C2211yescharacteristic
34#11718679C418yescomplemented
35#11718646C2211yescharacteristic
36#11718646C2211yescharacteristic
37#11718634C2211yescharacteristic
38#11718634C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45#11718611—21no—
46#11718611—21no—
47#11718596C2211yescharacteristic
48C4×C4⋊Dic13C2211yescharacteristic
49C2×#88043C2211yescharacteristic
50#11718419—24no—
51#11718418—24no—
52#11718311—21no—
53#11718310—21no—
54#11718308—21no—
55#11718308—21no—
56C13×#340C2211yescharacteristic
57C13×#340C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60#11718142C2211yescharacteristic
61#11718142C2211yescharacteristic
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C23×Dic13—21no—
65C23×Dic13—21no—
66C22×Dic26C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C4×D4×C13—22no—
70C4×D4×C13C2×C414yes—
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C22⋊C4—21no—
75C2×C42×C13C2311yescharacteristic
76C2×C22⋊Dic13—21no—
77C2×C22⋊Dic13—21no—
78D4×Dic13—22no—
79D4×Dic13—22no—
80D4×Dic13—41no—
81D4×Dic13—41no—
82C2×#6105C2×C414yes—
83C2×#6105D414yes—
84C2×#6105Q814yes—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—44no—
90C2×C4⋊Dic13D411yescharacteristic
91C2×C4⋊Dic13D411yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102C2×C4×Dic13—21no—
103C2×C4×Dic13C2311yescharacteristic
104C2×C4×Dic13C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107#88141—22no—
108#88141—22no—
109#88141—41no—
110#88141—41no—
111C4×Dic26—22no—
112C4×Dic26C2×C414yescomplemented
113C13×C4⋊C8—22no—
114C13×#102—22no—
115C13×#102—22no—
116C13×#95—21no—
117C13×#95—21no—
118#88072C2×C414yes—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88071—21no—
123#88071D411yescharacteristic
124#88071D411yescharacteristic
125#88056—22no—
126#88056—22no—
127#88055—22no—
128C8×Dic13—22no—
129#88050C2×C414yescomplemented
130#88048—22no—
131#88048—41no—
132#88047—22no—
133#88047—41no—
134#88047C2×C414yescomplemented
135#88043C2×C414yescomplemented
136#22677—131nomaximal, Sylow
137C24×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13—21no—
140C2×D4×C13—21no—
141C2×D4×C13C22×C412yes—
142C2×D4×C13C2×D412yes—
143C2×D4×C13C2×Q812yes—
144C22×C4×C13—21no—
145C22×C4×C13—24no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—42no—
149C22×C4×C13—42no—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2411yescharacteristic
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—42no—
158C22×Dic13—42no—
159C22×Dic13—42no—
160C22×Dic13—42no—
161C22×Dic13—81no—
162C22×Dic13—81no—
163C22×Dic13C2×D411yescharacteristic
164C22×Dic13C2×D411yescharacteristic
165C22×Dic13C2×D411yescharacteristic
166C22×Dic13C2×D411yescharacteristic
167C2×Dic26—21no—
168C2×Dic26—21no—
169C2×Dic26—21no—
170C2×Dic26C22×C412yes—
171C2×Dic26C2×D412yes—
172C2×Dic26C2×Q812yes—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4C22×C412yes—
185C13×C22⋊C4—24no—
186C42×C13C22×C412yes—
187C42×C13#4112yes—
188C22⋊Dic13—42no—
189C22⋊Dic13—42no—
190#6105C4⋊C4116yescomplemented
191C4⋊Dic13—21no—
192C4⋊Dic13—22no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—41no—
198C4⋊Dic13—42no—
199C4⋊Dic13—42no—
200C4⋊Dic13—42no—
201C4⋊Dic13—81no—
202C4⋊Dic13C22×C412yes—
203#6101—24no—
204#6101—42no—
205#6101—42no—
206#6101—42no—
207#6101—42no—
208C4×Dic13—24no—
209C4×Dic13—21no—
210C4×Dic13—21no—
211C4×Dic13—21no—
212C4×Dic13—21no—
213C4×Dic13—42no—
214C4×Dic13—42no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055C22×C412yes—
218C2×#1055C22×C412yes—
219C2×#1055C2×D412yes—
220C2×#1055C2×Q812yes—
221C2×#440—131no—
222C2×#440—131no—
223C2×C4×SD16—131no—
224#2351—131no—
225D4×C4⋊C4—131no—
226#1943—131no—
227#1942—131no—
228#1865—131no—
229#1864—131no—
230#1863—131no—
231#1862—131no—
232#1847—131no—
233#1804D1311yescharacteristic
234#1803—131no—
235#1771—131no—
236C23×C13—22no—
237C23×C13—22no—
238C23×C13—22no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13C22×D411yescharacteristic
244D4×C13—22no—
245D4×C13—22no—
246D4×C13—22no—
247D4×C13C2×C4⋊C414yes—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—22no—
253C2×C4×C13—48no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13C4×D412yes—
263C2×C4×C13C4×D412yes—
264C2×C4×C13C23×C411yescharacteristic
265C2×C4×C13C22×D411yescharacteristic
266C2×C4×C13C22×Q811yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×C4×C13H(5,𝔽2)11yescharacteristic
269C2×C4×C132−1+411yescharacteristic
270C2×Dic13—22no—
271C2×Dic13—21no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—21no—
275C2×Dic13—22no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—21no—
280C2×Dic13—21no—
281C2×Dic13—21no—
282C2×Dic13—21no—
283C2×Dic13—21no—
284C2×Dic13—21no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—84no—
294C2×Dic13—84no—
295C2×Dic13AGL(1,ℤ/8)12yes—
296Dic26—22no—
297Dic26—22no—
298Dic26—22no—
299Dic26C2×C4⋊C414yescomplemented
300C8×C13—41no—
301C8×C13—41no—
302#1055—22no—
303#1055C2×C4⋊C414yescomplemented
304C22×SD16—131no—
305C2×C4×Q8—131no—
306C2×C4×Q8—131no—
307C2×C4×Q8—131no—
308C2×C4×D4—131no—
309C2×C4×D4—131no—
310C2×C4×D4C2×D1311yescharacteristic
311C22×C4⋊C4—261no—
312#440—138no—
313#440—264no—
314C4×SD16—264no—
315C2×#107—131no—
316C2×#107—131no—
317C2×#107—131no—
318C2×#106—131no—
319C2×#106—131no—
320C2×C4⋊C8C2×D1311yescharacteristic
321C2×#103—131no—
322C2×#103—131no—
323C2×#103—131no—
324C2×#102—131no—
325C2×#102C2×D1311yescharacteristic
326C2×#102C2×D1311yescharacteristic
327C2×#97—131no—
328C2×#97—131no—
329C2×C4×C8—131no—
330#389—131no—
331#389—131no—
332#389—131no—
333#389—131no—
334#389—261no—
335#389—261no—
336#385—261no—
337#385—261no—
338#384—131no—
339#382—261no—
340#382C2×D1311yescharacteristic
341#380—261no—
342C4×C4⋊C4—131no—
343C4×C4⋊C4—261no—
344#340—131no—
345#340—131no—
346#340C2×D1311yescharacteristic
347#340C2×D1311yescharacteristic
348#336—131no—
349#336—131no—
350C22×C13—24no—
351C22×C13—42no—
352C22×C13—42no—
353C22×C13—42no—
354C22×C13—42no—
355C22×C13—42no—
356C22×C13—42no—
357C22×C13C2×C4×D411yescharacteristic
358C22×C13D4211yescharacteristic
359C22×C13D4×Q811yescharacteristic
360C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
361C22×C13#57511yescharacteristic
362C22×C13#57711yescharacteristic
363C22×C13#57811yescharacteristic
364C4×C13—22no—
365C4×C13—22no—
366C4×C13—42no—
367C4×C13—81no—
368C4×C13—81no—
369C4×C13C22×C4⋊C411yescharacteristic
370C4×C13#52011yescharacteristic
371C4×C13#54711yescharacteristic
372C4×C13#55411yescharacteristic
373Dic13—24no—
374Dic13—22no—
375Dic13—42no—
376Dic13—41no—
377Dic13—41no—
378Dic13—41no—
379Dic13—81no—
380Dic13—81no—
381C22×Q8—131no—
382C22×D4C22×D1311yescharacteristic
383C23×C4—21no—
384C23×C4—261no—
385C23×C4—261no—
386C2×SD16—134no—
387C2×SD16—134no—
388C2×SD16—134no—
389C22×C8—131no—
390C22×C8—131no—
391C22×C8C22×D1311yescharacteristic
392C22×C8C22×D1311yescharacteristic
393C4×Q8—134no—
394C4×Q8—262no—
395C4×Q8—262no—
396C4×Q8—262no—
397C4×Q8—521no—
398C4×Q8—521no—
399C4×D4—22no—
400C4×D4—262no—
401C4×D4—262no—
402C4×D4—521no—
403C4×D4—521no—
404C4×D4C4×D1314yes—
405C2×C4⋊C4—131no—
406C2×C4⋊C4—131no—
407C2×C4⋊C4—131no—
408C2×C4⋊C4—131no—
409C2×C4⋊C4—131no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4—261no—
412C2×C4⋊C4—261no—
413C2×C4⋊C4—261no—
414C2×C4⋊C4—261no—
415C2×C4⋊C4—261no—
416C2×C4⋊C4—261no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4—261no—
419C2×C4⋊C4—524no—
420C2×C4⋊C4C22×D1311yescharacteristic
421C2×C4⋊C4C22×D1311yescharacteristic
422C2×C4⋊C4C22×D1311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—261no—
425C2×C22⋊C4—261no—
426C2×C42—131no—
427C2×C42—131no—
428C2×C42—261no—
429C2×C42—261no—
430C2×C42—261no—
431C2×C42C22×D1311yescharacteristic
432#107—134no—
433#107—262no—
434#107—521no—
435#106—262no—
436#106—521no—
437C4⋊C8—22no—
438#103—134no—
439#103—262no—
440#103—262no—
441#102—22no—
442#102—22no—
443#102—134no—
444#97—134no—
445#97—262no—
446C4×C8—262no—
447#95—21no—
448#95—21no—
449#95—131no—
450#95—131no—
451#95—261no—
452#95—261no—
453#95—261no—
454#95—261no—
455C2×C13—44no—
456C2×C13D4×C4⋊C411yescharacteristic
457C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
458C2×C13#294711yescharacteristic
459C2×C13#326511yescharacteristic
460C2×C13#326911yescharacteristic
461C2×C13#338611yescharacteristic
462C2×C13#338811yescharacteristic
463C24—21no—
464C2×Q8—132no—
465C2×Q8—132no—
466C2×Q8—132no—
467C2×Q8—261no—
468C2×Q8—261no—
469C2×Q8—261no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4C2×C4×D1312yes—
474C2×D4D4×D1312yes—
475C2×D4Q8×D1312yes—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—131no—
485C22×C4—131no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—522no—
491C22×C4—522no—
492C22×C4—522no—
493C22×C4—522no—
494C22×C4—1041no—
495C22×C4—1041no—
496C22×C4D4×D1311yescharacteristic
497C22×C4D4×D1311yescharacteristic
498C22×C4C23×D1311yescharacteristic
499SD16—1316no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—132no—
507C2×C8—132no—
508C2×C8—132no—
509C2×C8—132no—
510C2×C8—261no—
511C2×C8—261no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—132no—
518C4⋊C4—262no—
519C4⋊C4—264no—
520C4⋊C4—261no—
521C4⋊C4—261no—
522C4⋊C4—261no—
523C4⋊C4—261no—
524C4⋊C4—261no—
525C4⋊C4—521no—
526C4⋊C4—522no—
527C4⋊C4—522no—
528C4⋊C4—522no—
529C4⋊C4—522no—
530C4⋊C4—522no—
531C4⋊C4—522no—
532C4⋊C4—522no—
533C4⋊C4—1041no—
534C4⋊C4C2×C4×D1312yes—
535C22⋊C4—24no—
536C22⋊C4—522no—
537C22⋊C4—522no—
538C42—264no—
539C42—261no—
540C42—261no—
541C42—261no—
542C42—261no—
543C42—522no—
544C42—522no—
545C42C2×C4×D1312yes—
546C42#612912yes—
547C13#2267711yescharacteristic, complemented, Sylow
548C23—22no—
549C23—22no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23C2×D4×D1311yescharacteristic
556Q8—134no—
557Q8—262no—
558Q8—262no—
559Q8—262no—
560D4—22no—
561D4—22no—
562D4—22no—
563D4C4⋊C4×D1314yes—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—48no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—132no—
579C2×C4—262no—
580C2×C4—261no—
581C2×C4—261no—
582C2×C4—262no—
583C2×C4—262no—
584C2×C4—262no—
585C2×C4—261no—
586C2×C4—261no—
587C2×C4—261no—
588C2×C4—261no—
589C2×C4—261no—
590C2×C4—261no—
591C2×C4—261no—
592C2×C4—261no—
593C2×C4—261no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—1044no—
603C2×C4—1044no—
604C2×C4#8813512yes—
605C2×C4#8813512yes—
606C2×C4C22×C4×D1311yescharacteristic
607C2×C4C2×D4×D1311yescharacteristic
608C2×C4C2×#612911yescharacteristic
609C2×C4C2×Q8×D1311yescharacteristic
610C2×C4#8825611yescharacteristic
611C2×C4#8825711yescharacteristic
612C8—41no—
613C8—41no—
614C8—134no—
615C8—262no—
616C22—24no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22C2×#8813511yescharacteristic
624C22#1171931411yescharacteristic
625C22#1171933711yescharacteristic
626C22#1171947511yescharacteristic
627C22#1171947611yescharacteristic
628C22D13×AGL(1,ℤ/8)11yescharacteristic
629C22#1171947811yescharacteristic
630C4—22no—
631C4—22no—
632C4—42no—
633C4—81no—
634C4—81no—
635C4—264no—
636C4—262no—
637C4—522no—
638C4—521no—
639C4—521no—
640C4—521no—
641C4—1041no—
642C4—1041no—
643C4C2×C4⋊C4×D1311yescharacteristic
644C4#1171922811yescharacteristic
645C4#1171931611yescharacteristic
646C4#1171934011yescharacteristic
647C2—44no—
648C2#1311773211yescharacteristic
649C2#1312364011yescharacteristic
650C2#1312368211yescharacteristic
651C2#1312633711yescharacteristic
652C2#1312639711yescharacteristic
653C2#1312775211yescharacteristic
654C2#1312777811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1804C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#1804D13
hypocenterC13#22677
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
4. #13117753C2semidirect
6. #13115573C2semidirect
7. #13115568C2semidirect
8. #13115105C2semidirect
10. #13115091C2semidirect
12. #13115005C2semidirect
13. #13114842C2semidirect
14. #13114713C2semidirect
34. #11718679C4semidirect
112. C4×Dic26C2×C4semidirect
129. #88050C2×C4semidirect
134. #88047C2×C4semidirect
135. #88043C2×C4semidirect
190. #6105C4⋊C4semidirect
299. Dic26C2×C4⋊C4semidirect
303. #1055C2×C4⋊C4semidirect
547. C13#22677semidirect

Maximal subgroups

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

subgroupindex
C2×#117186792
C2×#117184182
C2×#117184192
#131177532
D4×C4⋊Dic132
#131155732
#131155682
#131151052
#131150952
#131150912
#131150812
#131150052
#131148422
#131147132
C13×#18042
#2267713