Finite Group Databasebeta

← #15881265

Subgroups — #15881265

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×#11718679C211yesmaximal, characteristic
3C2×C4×#6105C211yesmaximal, characteristic
4#13117756C211yesmaximal, characteristic, complemented
5#13115571C211yesmaximal, characteristic, complemented
6#13115566C211yesmaximal, characteristic, complemented
7#13115103C211yesmaximal, characteristic, complemented
8#13115097C211yesmaximal, characteristic
9#13115089C211yesmaximal, characteristic, complemented
10#13115083C211yesmaximal, characteristic
11#13115002C211yesmaximal, characteristic, complemented
12#13114846C211yesmaximal, characteristic
13#13114838C211yesmaximal, characteristic, complemented
14#13114711C211yesmaximal, characteristic, complemented
15D4×C13×C4⋊C4C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C22×C13×C4⋊C4—21no—
20C22×#6105C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C2×C4×Dic26C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C13×#385—21no—
27C13×#385—21no—
28C13×#384C2211yescharacteristic
29C13×#380—21no—
30C4×C13×C4⋊C4C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34#11718679—24no—
35#11718679C418yescomplemented
36C4×#6105—24no—
37#11718633—21no—
38#11718633—21no—
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47#11718597C2211yescharacteristic
48#11718589C2211yescharacteristic
49#11718589C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51C2×#88043C2211yescharacteristic
52C2×#88043C2211yescharacteristic
53C2×C4×#1055C2211yescharacteristic
54#11718311—21no—
55#11718310—21no—
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718116C2211yescharacteristic
61#11718116C2211yescharacteristic
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C23×C4×C13—21no—
65C23×C4×C13—21no—
66C22×Dic26C2311yescharacteristic
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C4×D4×C13—41no—
71C4×D4×C13—41no—
72C4×D4×C13C2×C414yes—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—44no—
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4D411yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×#6105C2×C414yes—
90C2×#6105D414yes—
91C2×#6105Q814yes—
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—
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C4×Dic26—22no—
108C4×Dic26—22no—
109C4×Dic26—22no—
110C4×Dic26—41no—
111C4×Dic26—41no—
112C4×Dic26C2×C414yescomplemented
113C13×#95—21no—
114C13×#95—21no—
115C13×#95D411yescharacteristic
116C13×#95D411yescharacteristic
117#88072—22no—
118#88072—22no—
119#88072C2×C414yes—
120#88071—21no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124#88050—22no—
125#88050—22no—
126#88050C2×C414yescomplemented
127#88048—22no—
128#88048—41no—
129#88047—22no—
130#88047—41no—
131#88047C2×C414yescomplemented
132C4⋊#1055—22no—
133#88043—22no—
134#88043C2×C414yescomplemented
135C4×#1055—22no—
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×C13—42no—
151C22×C4×C13—42no—
152C22×C4×C13—42no—
153C22×C4×C13—42no—
154C22×C4×C13—81no—
155C22×C4×C13—81no—
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2411yescharacteristic
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C2×Dic26—21no—
168C2×Dic26—21no—
169C2×Dic26—21no—
170C2×Dic26C22×C412yes—
171C2×Dic26C2×D412yes—
172C2×Dic26C2×Q812yes—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—41no—
180C13×C4⋊C4—42no—
181C13×C4⋊C4—42no—
182C13×C4⋊C4—42no—
183C13×C4⋊C4—81no—
184C13×C4⋊C4C22×C412yes—
185C13×C22⋊C4—24no—
186C13×C22⋊C4—42no—
187C13×C22⋊C4—42no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—21no—
192C42×C13C22×C412yes—
193C42×C13#4112yes—
194#6105C4⋊C4116yescomplemented
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13C22×C412yes—
201#6101—24no—
202#6101—42no—
203#6101—42no—
204#6101—42no—
205#6101—42no—
206C4×Dic13—24no—
207C4×Dic13—42no—
208C4×Dic13—42no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
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⋊C4D1311yescharacteristic
226#1943—131no—
227#1942—131no—
228#1865—131no—
229#1864—131no—
230#1863—131no—
231#1862—131no—
232#1847—131no—
233#1804—131no—
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—21no—
253C2×C4×C13—21no—
254C2×C4×C13—22no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—48no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—84no—
274C2×C4×C13—84no—
275C2×C4×C13C4×D412yes—
276C2×C4×C13C4×D412yes—
277C2×C4×C13AGL(1,ℤ/8)12yes—
278C2×C4×C13C23×C411yescharacteristic
279C2×C4×C13C22×D411yescharacteristic
280C2×C4×C13C22×Q811yescharacteristic
281C2×C4×C13C2×#4111yescharacteristic
282C2×C4×C13H(5,𝔽2)11yescharacteristic
283C2×C4×C132−1+411yescharacteristic
284C2×Dic13—22no—
285C2×Dic13—22no—
286C2×Dic13—22no—
287C2×Dic13—22no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296Dic26—22no—
297Dic26—22no—
298Dic26—22no—
299Dic26C2×C4⋊C414yescomplemented
300#1055—22no—
301#1055—41no—
302#1055—41no—
303#1055C2×C4⋊C414yescomplemented
304C22×SD16—131no—
305C2×C4×Q8—131no—
306C2×C4×Q8—131no—
307C2×C4×Q8—131no—
308C2×C4×D4C2×D1311yescharacteristic
309C2×C4×D4C2×D1311yescharacteristic
310C2×C4×D4C2×D1311yescharacteristic
311C22×C4⋊C4—21no—
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⋊C8—131no—
321C2×#103—131no—
322C2×#103—131no—
323C2×#103—131no—
324C2×#102—131no—
325C2×#102—131no—
326C2×#102—131no—
327C2×#97—131no—
328C2×#97—131no—
329C2×C4×C8—131no—
330#389—131no—
331#389—131no—
332#389—261no—
333#389—261no—
334#389C2×D1311yescharacteristic
335#389C2×D1311yescharacteristic
336#385—21no—
337#385—21no—
338#384C2×D1311yescharacteristic
339#382—131no—
340#382—261no—
341#380—21no—
342C4×C4⋊C4—261no—
343C4×C4⋊C4C2×D1311yescharacteristic
344#340—131no—
345#340—131no—
346#340—131no—
347#340—131no—
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—22no—
367C4×C13—42no—
368C4×C13—41no—
369C4×C13—41no—
370C4×C13—41no—
371C4×C13—81no—
372C4×C13—81no—
373C4×C13C22×C4⋊C411yescharacteristic
374C4×C13#52011yescharacteristic
375C4×C13#54711yescharacteristic
376C4×C13#55411yescharacteristic
377Dic13—24no—
378Dic13—42no—
379Dic13—81no—
380Dic13—81no—
381C22×Q8—131no—
382C22×D4C22×D1311yescharacteristic
383C23×C4—21no—
384C23×C4—21no—
385C23×C4—21no—
386C2×SD16—134no—
387C2×SD16—134no—
388C2×SD16—134no—
389C22×C8—131no—
390C22×C8—131no—
391C22×C8—131no—
392C22×C8—131no—
393C4×Q8—134no—
394C4×Q8—262no—
395C4×Q8—262no—
396C4×Q8—262no—
397C4×Q8—521no—
398C4×Q8—521no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—41no—
403C4×D4—41no—
404C4×D4C4×D1314yes—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4—131no—
411C2×C4⋊C4—131no—
412C2×C4⋊C4—131no—
413C2×C4⋊C4—261no—
414C2×C4⋊C4—261no—
415C2×C4⋊C4—261no—
416C2×C4⋊C4—261no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4C22⋊D1311yescharacteristic
419C2×C4⋊C4C22⋊D1311yescharacteristic
420C2×C4⋊C4C22×D1311yescharacteristic
421C2×C4⋊C4C22×D1311yescharacteristic
422C2×C4⋊C4C22×D1311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C42—261no—
427C2×C42—261no—
428C2×C42—261no—
429C2×C42C22×D1311yescharacteristic
430C2×C42C22×D1311yescharacteristic
431C2×C42C22×D1311yescharacteristic
432#107—134no—
433#107—262no—
434#107—521no—
435#106—262no—
436#106—521no—
437C4⋊C8—262no—
438#103—134no—
439#103—262no—
440#103—262no—
441#102—134no—
442#102—262no—
443#102—262no—
444#97—134no—
445#97—262no—
446C4×C8—262no—
447#95—21no—
448#95—21no—
449#95—261no—
450#95—261no—
451#95—261no—
452#95—261no—
453#95C22⋊D1311yescharacteristic
454#95C22⋊D1311yescharacteristic
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—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4C2×C22⋊D1311yescharacteristic
493C22×C4C2×C22⋊D1311yescharacteristic
494C22×C4C2×C22⋊D1311yescharacteristic
495C22×C4C2×C22⋊D1311yescharacteristic
496C22×C4C2×C22⋊D1311yescharacteristic
497C22×C4C2×C22⋊D1311yescharacteristic
498C22×C4C23×D1311yescharacteristic
499SD16—1316no—
500C2×C8—132no—
501C2×C8—132no—
502C2×C8—132no—
503C2×C8—132no—
504C2×C8—261no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—41no—
519C4⋊C4—42no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—81no—
523C4⋊C4—132no—
524C4⋊C4—264no—
525C4⋊C4—261no—
526C4⋊C4—261no—
527C4⋊C4—261no—
528C4⋊C4—261no—
529C4⋊C4—261no—
530C4⋊C4—522no—
531C4⋊C4—522no—
532C4⋊C4—522no—
533C4⋊C4—522no—
534C4⋊C4C2×C4×D1312yes—
535C22⋊C4—24no—
536C22⋊C4—42no—
537C22⋊C4—42no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—264no—
543C42—522no—
544C42—522no—
545C42C2×C4×D1312yes—
546C42#612712yes—
547C13#2267711yescharacteristic, complemented, Sylow
548C23—22no—
549C23—22no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23C22×C22⋊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—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—48no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—84no—
590C2×C4—84no—
591C2×C4—262no—
592C2×C4—262no—
593C2×C4—262no—
594C2×C4—262no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4C4×C22⋊D1312yes—
604C2×C4C4×C22⋊D1312yes—
605C2×C4#8818612yes—
606C2×C4C22×C4×D1311yescharacteristic
607C2×C4C2×#612711yescharacteristic
608C2×C4C2×D4×D1311yescharacteristic
609C2×C4#8825111yescharacteristic
610C2×C4C2×Q8×D1311yescharacteristic
611C2×C4#8825411yescharacteristic
612C8—134no—
613C8—262no—
614C8—521no—
615C8—521no—
616C22—24no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22C2×C4×C22⋊D1311yescharacteristic
624C22C2×#8818611yescharacteristic
625C22D4×C22⋊D1311yescharacteristic
626C22Q8×C22⋊D1311yescharacteristic
627C22#1171952711yescharacteristic
628C22#1171954111yescharacteristic
629C22#1171954311yescharacteristic
630C4—22no—
631C4—22no—
632C4—22no—
633C4—42no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—81no—
638C4—81no—
639C4—264no—
640C4—522no—
641C4—1041no—
642C4—1041no—
643C4C2×C4⋊C4×D1311yescharacteristic
644C4#1171920911yescharacteristic
645C4#1171921211yescharacteristic
646C4#1171921611yescharacteristic
647C2—44no—
648C2C4⋊C4×C22⋊D1311yescharacteristic
649C2C4×#8818611yescharacteristic
650C2#1312367511yescharacteristic
651C2#1312632711yescharacteristic
652C2#1312638711yescharacteristic
653C2#1312775711yescharacteristic
654C2#1312778111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingD4×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenterD4×C4⋊C4D13
hypocenterC13#22677
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #13117756C2semidirect
5. #13115571C2semidirect
6. #13115566C2semidirect
7. #13115103C2semidirect
9. #13115089C2semidirect
11. #13115002C2semidirect
13. #13114838C2semidirect
14. #13114711C2semidirect
35. #11718679C4semidirect
112. C4×Dic26C2×C4semidirect
126. #88050C2×C4semidirect
131. #88047C2×C4semidirect
134. #88043C2×C4semidirect
194. #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×C4×#61052
#131177562
#131155712
#131155662
#131151032
#131150972
#131150892
#131150832
#131150022
#131148462
#131148382
#131147112
D4×C13×C4⋊C42
#2267713