Finite Group Databasebeta

← #15925942

Subgroups — #15925942

Order 3328.

864 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718755C211yesmaximal, characteristic, complemented
2C2×C4×#6105C211yesmaximal, characteristic
3C4⋊C4×Dic26C211yesmaximal, characteristic, complemented
4#13116369C211yesmaximal, characteristic
5#13116312C211yesmaximal, characteristic, complemented
6#13116210C211yesmaximal, characteristic
7#13116166C211yesmaximal, characteristic, complemented
8#13115561C211yesmaximal, characteristic, complemented
9#13115395C211yesmaximal, characteristic, complemented
10#13115194C211yesmaximal, characteristic
11#13115194C211yesmaximal, characteristic
12#13115103C211yesmaximal, characteristic, complemented
13#13115103C211yesmaximal, characteristic, complemented
14#13115097C211yesmaximal, characteristic
15C13×#2452C211yesmaximal, characteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8—21no—
18C2×C4×D4×C13C2211yescharacteristic
19C22×#6105C2211yescharacteristic
20C2×C4×Dic26C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C13×#396—21no—
24C13×#393—21no—
25C13×#390C2211yescharacteristic
26C13×#390C2211yescharacteristic
27C13×#389C2211yescharacteristic
28C13×#389C2211yescharacteristic
29C13×#385—21no—
30C4×C13×C4⋊C4C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34#11718755—24no—
35C4×#6105—24no—
36#11718637—21no—
37C4⋊C4×Dic13—21no—
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88048C2211yescharacteristic
46#11718596C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718308—21no—
52#11718308—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13—21no—
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C22×Dic26C2311yescharacteristic
65C13×C4⋊Q8—22no—
66C13×C4⋊Q8—41no—
67C13×C22⋊Q8—44no—
68C4×D4×C13—22no—
69C4×D4×C13—41no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4D411yescharacteristic
74C2×C13×C4⋊C4D411yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×#6105—22no—
87C2×#6105—22no—
88C2×#6105Q814yescomplemented
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C4×Dic26—22no—
107C4×Dic26—22no—
108C4×Dic26—22no—
109C4×Dic26—22no—
110C4×Dic26—41no—
111C4×Dic26—41no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95D411yescharacteristic
115C13×#95D411yescharacteristic
116#88072—22no—
117#88072—22no—
118#88072—41no—
119#88071—21no—
120#88071—21no—
121#88050—22no—
122#88050—22no—
123#88050D414yes—
124#88048—22no—
125#88048—22no—
126#88048—22no—
127#88048—22no—
128#88048—41no—
129C4⋊#1055—22no—
130C4×#1055—22no—
131#26373—131nomaximal, Sylow
132C24×C13—21no—
133C2×Q8×C13—42no—
134C2×Q8×C13—42no—
135C2×Q8×C13—81no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13—21no—
140C2×D4×C13—21no—
141C2×D4×C13C2×Q812yes—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—42no—
146C22×C4×C13—42no—
147C22×C4×C13—81no—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2411yescharacteristic
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C2×Dic26—21no—
160C2×Dic26—21no—
161C2×Dic26—21no—
162C2×Dic26C2×D412yes—
163C2×Dic26C2×Q812yes—
164C2×Dic26#4112yes—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—41no—
171C13×C4⋊C4—42no—
172C13×C4⋊C4—42no—
173C13×C4⋊C4—42no—
174C13×C4⋊C4SD1614yescomplemented
175C13×C4⋊C4C2×D412yes—
176C13×C22⋊C4—42no—
177C13×C22⋊C4—42no—
178C13×C22⋊C4—42no—
179C13×C22⋊C4—42no—
180C13×C22⋊C4—81no—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—21no—
186C42×C13—21no—
187#6105—28no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—42no—
194C4⋊Dic13—81no—
195C4⋊Dic13#4112yes—
196#6101—24no—
197#6101—42no—
198#6101—42no—
199#6101—81no—
200#6101—81no—
201C4×Dic13—24no—
202C4×Dic13—42no—
203C4×Dic13—42no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055C2×D412yes—
215C2×#1055C2×Q812yes—
216C2×#475—131no—
217C2×C4×SD16—131no—
218#2452D1311yescharacteristic
219Q8×C4⋊C4—131no—
220#2094—131no—
221#2084—131no—
222#2065—131no—
223#2058—131no—
224#1941—131no—
225#1916—131no—
226#1880—131no—
227#1880—131no—
228#1865—131no—
229#1865—131no—
230#1864—131no—
231C23×C13—22no—
232C23×C13—41no—
233C23×C13—41no—
234C23×C13—41no—
235C23×C13—41no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13C22×D411yescharacteristic
239Q8×C13—84no—
240D4×C13—22no—
241D4×C13—22no—
242D4×C13—41no—
243D4×C13—41no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—22no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—84no—
269C2×C4×C13C2×SD1612yes—
270C2×C4×C13C2×SD1612yes—
271C2×C4×C13C2×SD1612yes—
272C2×C4×C13C22×D411yescharacteristic
273C2×C4×C13C22×Q811yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
275C2×C4×C13C2×#4111yescharacteristic
276C2×C4×C13H(5,𝔽2)11yescharacteristic
277C2×C4×C132−1+411yescharacteristic
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290Dic26—22no—
291Dic26—22no—
292Dic26—22no—
293Dic26C22⋊Q814yescomplemented
294#1055—22no—
295#1055—22no—
296#1055—41no—
297#1055—41no—
298C22×SD16—131no—
299C2×C4⋊Q8C2×D1311yescharacteristic
300C2×C22⋊Q8—21no—
301C2×C4×Q8—131no—
302C2×C4×Q8—131no—
303C2×C4×Q8—131no—
304C2×C4×D4C2×D1311yescharacteristic
305#475—264no—
306C4×SD16—264no—
307C2×#106—131no—
308C2×#106—131no—
309C2×#106—131no—
310C2×#106—131no—
311C2×#106—131no—
312C2×C4⋊C8—131no—
313C2×#103—131no—
314C2×#103—131no—
315C2×#103—131no—
316C2×#102—131no—
317C2×#102—131no—
318C2×#102—131no—
319C2×C4×C8—131no—
320#396—21no—
321#393—21no—
322#390C2×D1311yescharacteristic
323#390C2×D1311yescharacteristic
324#389—131no—
325#389—131no—
326#389—261no—
327#389—261no—
328#389C2×D1311yescharacteristic
329#389C2×D1311yescharacteristic
330#385—21no—
331#384—131no—
332#384—261no—
333C4×C4⋊C4—261no—
334C4×C4⋊C4C2×D1311yescharacteristic
335#340—131no—
336#340—131no—
337#340—131no—
338#340—131no—
339#336—131no—
340#336—131no—
341#336—131no—
342#336—131no—
343C22×C13—42no—
344C22×C13—42no—
345C22×C13—42no—
346C22×C13—81no—
347C22×C13—81no—
348C22×C13—81no—
349C22×C13—81no—
350C22×C13#52511yescharacteristic
351C22×C13D4211yescharacteristic
352C22×C13D4×Q811yescharacteristic
353C22×C13C22×SD1611yescharacteristic
354C22×C13#57511yescharacteristic
355C22×C13#57711yescharacteristic
356C22×C13#57711yescharacteristic
357C4×C13—22no—
358C4×C13—22no—
359C4×C13—22no—
360C4×C13—41no—
361C4×C13—41no—
362C4×C13—41no—
363C4×C13—42no—
364C4×C13—81no—
365C4×C13—81no—
366C4×C13C2×C22⋊Q811yescharacteristic
367C4×C13#53911yescharacteristic
368C4×C13#54711yescharacteristic
369C4×C13#55411yescharacteristic
370Dic13—24no—
371Dic13—42no—
372Dic13—81no—
373Dic13—81no—
374C22×Q8—21no—
375C22×Q8—131no—
376C22×D4C22×D1311yescharacteristic
377C23×C4—21no—
378C2×SD16—134no—
379C2×SD16—262no—
380C2×SD16—262no—
381C22×C8—131no—
382C22×C8—131no—
383C22×C8—131no—
384C22×C8—131no—
385C4⋊Q8—22no—
386C4⋊Q8—41no—
387C22⋊Q8—44no—
388C4×Q8—262no—
389C4×Q8—262no—
390C4×Q8—262no—
391C4×Q8—262no—
392C4×Q8—521no—
393C4×Q8—521no—
394C4×D4—22no—
395C4×D4—41no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—131no—
400C2×C4⋊C4—131no—
401C2×C4⋊C4—131no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4—261no—
406C2×C4⋊C4—261no—
407C2×C4⋊C4—261no—
408C2×C4⋊C4—261no—
409C2×C4⋊C4C22⋊D1311yescharacteristic
410C2×C4⋊C4C22⋊D1311yescharacteristic
411C2×C4⋊C4C22×D1311yescharacteristic
412C2×C4⋊C4C22×D1311yescharacteristic
413C2×C4⋊C4C22×D1311yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C42—261no—
420C2×C42—261no—
421C2×C42—261no—
422C2×C42C22×D1311yescharacteristic
423C2×C42C22×D1311yescharacteristic
424C2×C42C22×D1311yescharacteristic
425#106—262no—
426#106—262no—
427#106—262no—
428#106—262no—
429#106—521no—
430C4⋊C8—262no—
431#103—134no—
432#103—262no—
433#103—262no—
434#102—262no—
435#102—262no—
436#102—521no—
437C4×C8—262no—
438#95—21no—
439#95—21no—
440#95—261no—
441#95—261no—
442#95C22⋊D1311yescharacteristic
443#95C22⋊D1311yescharacteristic
444C2×C13—82no—
445C2×C13#244911yescharacteristic
446C2×C13#310311yescharacteristic
447C2×C13#312511yescharacteristic
448C2×C13#327111yescharacteristic
449C2×C13D4×SD1611yescharacteristic
450C2×C13Q8×SD1611yescharacteristic
451C2×C13#338811yescharacteristic
452C24—21no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×Q8—81no—
456C2×Q8—132no—
457C2×Q8—132no—
458C2×Q8—132no—
459C2×Q8—261no—
460C2×Q8—261no—
461C2×Q8—261no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4Q8×D1312yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—81no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4C2×C22⋊D1311yescharacteristic
479C22×C4C2×C22⋊D1311yescharacteristic
480C22×C4C2×C22⋊D1311yescharacteristic
481C22×C4C2×C22⋊D1311yescharacteristic
482C22×C4C2×C22⋊D1311yescharacteristic
483C22×C4C2×C22⋊D1311yescharacteristic
484C22×C4C23×D1311yescharacteristic
485SD16—268no—
486C2×C8—132no—
487C2×C8—132no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—41no—
504C4⋊C4—42no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—132no—
508C4⋊C4—264no—
509C4⋊C4—261no—
510C4⋊C4—261no—
511C4⋊C4—261no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—522no—
515C4⋊C4—522no—
516C4⋊C4—522no—
517C4⋊C4—1041no—
518C4⋊C4—1041no—
519C4⋊C4—1041no—
520C4⋊C4#610514yescomplemented
521C4⋊C4D4×D1312yes—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—42no—
525C22⋊C4—42no—
526C22⋊C4—81no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—264no—
534C42—522no—
535C42—522no—
536C13#2637311yescharacteristic, complemented, Sylow
537C23—22no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23C22×C22⋊D1311yescharacteristic
545Q8—84no—
546Q8—134no—
547Q8—262no—
548Q8—262no—
549Q8—262no—
550D4—22no—
551D4—22no—
552D4—41no—
553D4—41no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
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—84no—
579C2×C4—262no—
580C2×C4—262no—
581C2×C4—262no—
582C2×C4—262no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4C2×#610512yes—
592C2×C4C2×#610512yes—
593C2×C4C2×#610512yes—
594C2×C4C2×D4×D1311yescharacteristic
595C2×C4#8825111yescharacteristic
596C2×C4C2×Q8×D1311yescharacteristic
597C2×C4#8825411yescharacteristic
598C2×C4#41×D1311yescharacteristic
599C2×C4#41×D1311yescharacteristic
600C8—262no—
601C8—262no—
602C8—521no—
603C8—521no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22C22×#610511yescharacteristic
612C22D4×C22⋊D1311yescharacteristic
613C22Q8×C22⋊D1311yescharacteristic
614C22#1171952711yescharacteristic
615C22#1171953311yescharacteristic
616C22#1171954111yescharacteristic
617C22#1171954211yescharacteristic
618C4—22no—
619C4—22no—
620C4—22no—
621C4—41no—
622C4—41no—
623C4—42no—
624C4—41no—
625C4—81no—
626C4—81no—
627C4—264no—
628C4—522no—
629C4—1041no—
630C4—1041no—
631C4D13×C22⋊Q811yescharacteristic
632C4#1171933611yescharacteristic
633C4#1171934111yescharacteristic
634C4#1171934311yescharacteristic
635C2—82no—
636C2#1311864211yescharacteristic
637C2#1312486311yescharacteristic
638C2#1312510711yescharacteristic
639C2#1312642211yescharacteristic
640C2D4×#610511yescharacteristic
641C2Q8×#610511yescharacteristic
642C2#1312778111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2452C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenter#2452D13
hypocenterC13#26373
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2452

Complements

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

NH ≅ G/Ntype
1. C2×#11718755C2semidirect
3. C4⋊C4×Dic26C2semidirect
5. #13116312C2semidirect
7. #13116166C2semidirect
8. #13115561C2semidirect
9. #13115395C2semidirect
12. #13115103C2semidirect
13. #13115103C2semidirect
88. C2×#6105Q8semidirect
174. C13×C4⋊C4SD16semidirect
293. Dic26C22⋊Q8semidirect
520. C4⋊C4#6105semidirect
536. C13#26373semidirect

Maximal subgroups

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

subgroupindex
C2×#117187552
C2×C4×#61052
C4⋊C4×Dic262
#131163692
#131163122
#131162102
#131161662
#131155612
#131153952
#131151942
#131151032
#131150972
C13×#24522
#2637313