Finite Group Databasebeta

← #15925671

Subgroups — #15925671

Order 3328.

848 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718752C211yesmaximal, characteristic, complemented
2C2×#11718625C211yesmaximal, characteristic
3#13117861C211yesmaximal, characteristic
4#13116380C211yesmaximal, characteristic, complemented
5#13116338C211yesmaximal, characteristic, complemented
6#13116214C211yesmaximal, characteristic, complemented
7#13116166C211yesmaximal, characteristic, complemented
8#13115592C211yesmaximal, characteristic, complemented
9#13115404C211yesmaximal, characteristic, complemented
10#13115267C211yesmaximal, characteristic
11#13115143C211yesmaximal, characteristic
12#13115089C211yesmaximal, characteristic, complemented
13#13115033C211yesmaximal, characteristic
14#13115021C211yesmaximal, characteristic
15C13×#2440C211yesmaximal, characteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8—21no—
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C2×#88178C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C13×#398—21no—
24C13×#395—21no—
25C13×#389C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C13×#385—21no—
28C13×#384C2211yescharacteristic
29C13×#380C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32#11718752—24no—
33C2×#88050C2211yescharacteristic
34C2×#88050C2211yescharacteristic
35C2×#88050C2211yescharacteristic
36C2×#88050C2211yescharacteristic
37#11718625—24no—
38C2×#88048C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718606—21no—
45#11718605—21no—
46C4×C4⋊Dic13C2211yescharacteristic
47#11718590C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51#11718313—21no—
52#11718310—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13—21no—
62C23×C4×C13—21no—
63C23×C4×C13C2311yescharacteristic
64C22×Dic26C2311yescharacteristic
65C13×C4⋊Q8—22no—
66C13×C4⋊Q8—41no—
67C13×C22⋊Q8—44no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—41no—
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4D411yescharacteristic
82C2×C13×C22⋊C4D411yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C22⋊Dic13—21no—
86C2×C22⋊Dic13—21no—
87#88180—22no—
88#88180—41no—
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92#88178—22no—
93#88178Q814yescomplemented
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C2×#6099—22no—
101C2×#6099—22no—
102C2×#6099—22no—
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C4×Dic26—22no—
108C4×Dic26—41no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95—21no—
112C13×#95D411yescharacteristic
113C13×#95D411yescharacteristic
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118C22⋊#1055—22no—
119#88050—22no—
120#88050—22no—
121#88050—22no—
122#88050—41no—
123#88048—22no—
124#88048—22no—
125#88048—41no—
126#88047—22no—
127#88047—22no—
128#88047D414yes—
129C4⋊#1055—22no—
130C4⋊#1055—22no—
131#26355—131nomaximal, Sylow
132C24×C13C2×D411yescharacteristic
133C2×Q8×C13—42no—
134C2×Q8×C13—42no—
135C2×Q8×C13—81no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—42no—
145C22×C4×C13—42no—
146C22×C4×C13—81no—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×Q812yes—
153C22×C4×C13#4112yes—
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×Dic26—21no—
163C2×Dic26—21no—
164C2×Dic26C2×Q812yes—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—42no—
173C13×C4⋊C4—42no—
174C13×C4⋊C4—42no—
175C13×C4⋊C4—42no—
176C13×C4⋊C4—42no—
177C13×C4⋊C4—81no—
178C13×C4⋊C4C2×D412yes—
179C13×C22⋊C4—22no—
180C13×C22⋊C4—22no—
181C13×C22⋊C4—42no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—21no—
186C22⋊Dic13—24no—
187C22⋊Dic13—42no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13C2×D412yes—
193C4⋊Dic13C2×Q812yes—
194#6101—24no—
195#6101—42no—
196#6101—42no—
197C4×Dic13—42no—
198C4×Dic13—42no—
199C4×Dic13—42no—
200#6099—28no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055C2×D412yes—
212C2×#1055#4112yes—
213C2×#477—131no—
214C2×#428—131no—
215#2440D1311yescharacteristic
216#2362—131no—
217#2096—131no—
218#2088—131no—
219#2066—131no—
220#2058—131no—
221#1947—131no—
222#1918—131no—
223#1894—131no—
224#1872—131no—
225#1863—131no—
226#1854—131no—
227#1851—131no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13C22⋊Q812yes—
235C23×C13C22×D411yescharacteristic
236Q8×C13—84no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—21no—
248C2×C4×C13—22no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
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×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—84no—
266C2×C4×C13C22⋊Q812yes—
267C2×C4×C13AGL(1,ℤ/8)12yes—
268C2×C4×C13#13712yes—
269C2×C4×C13C22×D411yescharacteristic
270C2×C4×C13C22×Q811yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13H(5,𝔽2)11yescharacteristic
274C2×C4×C132−1+411yescharacteristic
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—22no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287Dic26—22no—
288Dic26—22no—
289Dic26—41no—
290Dic26—41no—
291#1055—22no—
292#1055—22no—
293#1055—41no—
294#1055—41no—
295C22×M16—131no—
296C2×C4⋊Q8C2×D1311yescharacteristic
297C2×C22⋊Q8—21no—
298C2×C22⋊Q8—131no—
299C2×C4×Q8—131no—
300C2×#117—131no—
301C22×C4⋊C4C2×D1311yescharacteristic
302#477—264no—
303#428—264no—
304C2×#107—131no—
305C2×#107—131no—
306C2×#107—131no—
307C2×#106—131no—
308C2×#106—131no—
309C2×#106—131no—
310C2×C4⋊C8—131no—
311C2×C4⋊C8—131no—
312C2×#103—131no—
313C2×#103—131no—
314C2×#103—131no—
315C2×#103—131no—
316C2×C22⋊C8—131no—
317#398—21no—
318#395—21no—
319#391—131no—
320#389—131no—
321#389C2×D1311yescharacteristic
322#389C2×D1311yescharacteristic
323#388—261no—
324#388—261no—
325#387—261no—
326#385—21no—
327#384C2×D1311yescharacteristic
328#380C2×D1311yescharacteristic
329C4×C4⋊C4—131no—
330C4×C4⋊C4—261no—
331C4×C22⋊C4C2×D1311yescharacteristic
332#340—131no—
333#340—131no—
334#340—131no—
335#340—131no—
336#340—131no—
337#340—131no—
338#336—131no—
339#336—131no—
340C22×C13—22no—
341C22×C13—22no—
342C22×C13—22no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13—41no—
347C22×C13C2×C22⋊Q811yescharacteristic
348C22×C13D4211yescharacteristic
349C22×C13#54711yescharacteristic
350C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C13C2×#13711yescharacteristic
352C22×C13#57711yescharacteristic
353C22×C13#57811yescharacteristic
354C4×C13—22no—
355C4×C13—22no—
356C4×C13—22no—
357C4×C13—41no—
358C4×C13—41no—
359C4×C13—42no—
360C4×C13—81no—
361C4×C13—81no—
362C4×C13—81no—
363C4×C13#52511yescharacteristic
364C4×C13#53911yescharacteristic
365C4×C13D4×Q811yescharacteristic
366C4×C13#55411yescharacteristic
367Dic13—42no—
368Dic13—42no—
369Dic13—42no—
370Dic13—81no—
371C22×Q8—21no—
372C22×Q8—131no—
373C23×C4—21no—
374C23×C4C22×D1311yescharacteristic
375C2×M16—262no—
376C2×M16—262no—
377C2×M16—262no—
378C22×C8—131no—
379C22×C8—131no—
380C22×C8—131no—
381C22×C8—131no—
382C4⋊Q8—22no—
383C4⋊Q8—41no—
384C22⋊Q8—44no—
385C22⋊Q8—134no—
386C22⋊Q8—262no—
387C4×Q8—262no—
388C4×Q8—521no—
389#117—262no—
390#117—521no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—41no—
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⋊C4C22×D1311yescharacteristic
406C2×C4⋊C4C22×D1311yescharacteristic
407C2×C4⋊C4C22×D1311yescharacteristic
408C2×C4⋊C4C22×D1311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—261no—
411C2×C22⋊C4—261no—
412C2×C22⋊C4C22⋊D1311yescharacteristic
413C2×C22⋊C4C22⋊D1311yescharacteristic
414C2×C42—261no—
415C2×C42—261no—
416C2×C42—261no—
417C2×C42C22×D1311yescharacteristic
418C2×C42C22×D1311yescharacteristic
419#107—134no—
420#107—262no—
421#107—262no—
422#106—262no—
423#106—262no—
424#106—521no—
425C4⋊C8—262no—
426C4⋊C8—262no—
427#103—262no—
428#103—262no—
429#103—262no—
430#103—521no—
431C22⋊C8—262no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—261no—
436#95—261no—
437#95—261no—
438#95—261no—
439#95C22⋊D1311yescharacteristic
440#95C22⋊D1311yescharacteristic
441C2×C13—42no—
442C2×C13#244911yescharacteristic
443C2×C13#307911yescharacteristic
444C2×C13#308211yescharacteristic
445C2×C13#327011yescharacteristic
446C2×C13#327211yescharacteristic
447C2×C13#334311yescharacteristic
448C2×C13#335611yescharacteristic
449C24C2×C22⋊D1311yescharacteristic
450C2×Q8—42no—
451C2×Q8—42no—
452C2×Q8—81no—
453C2×Q8—132no—
454C2×Q8—261no—
455C2×Q8—261no—
456C2×Q8—261no—
457C2×Q8—261no—
458C2×Q8—261no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—81no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4Q8×D1312yes—
475C22×C4#613112yes—
476C22×C4C2×C22⋊D1311yescharacteristic
477C22×C4C2×C22⋊D1311yescharacteristic
478C22×C4C2×C22⋊D1311yescharacteristic
479C22×C4C2×C22⋊D1311yescharacteristic
480C22×C4C2×C22⋊D1311yescharacteristic
481C22×C4C23×D1311yescharacteristic
482M16—268no—
483C2×C8—132no—
484C2×C8—132no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—81no—
508C4⋊C4—132no—
509C4⋊C4—132no—
510C4⋊C4—264no—
511C4⋊C4—261no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—522no—
516C4⋊C4—522no—
517C4⋊C4D4×D1312yes—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—42no—
521C22⋊C4—264no—
522C22⋊C4—522no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—522no—
528C42—522no—
529C42—522no—
530C13#2635511yescharacteristic, complemented, Sylow
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23#8820012yes—
538C23C22×C22⋊D1311yescharacteristic
539Q8—84no—
540Q8—262no—
541Q8—262no—
542Q8—521no—
543Q8—521no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—84no—
573C2×C4—262no—
574C2×C4—262no—
575C2×C4—262no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4#8818612yes—
586C2×C4#8819612yes—
587C2×C4#8820012yes—
588C2×C4C2×D4×D1311yescharacteristic
589C2×C4#8825111yescharacteristic
590C2×C4C2×Q8×D1311yescharacteristic
591C2×C4C2×#613111yescharacteristic
592C2×C4#41×D1311yescharacteristic
593C2×C4#8825711yescharacteristic
594C8—262no—
595C8—262no—
596C8—521no—
597C8—521no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22C2×#8818611yescharacteristic
606C22D4×C22⋊D1311yescharacteristic
607C22C2×#8819611yescharacteristic
608C22C2×#8820011yescharacteristic
609C22#1171952911yescharacteristic
610C22#1171954111yescharacteristic
611C22#1171954311yescharacteristic
612C4—22no—
613C4—22no—
614C4—22no—
615C4—41no—
616C4—41no—
617C4—42no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4—522no—
622C4—522no—
623C4—522no—
624C4—1041no—
625C4#1171933211yescharacteristic
626C4#1171933711yescharacteristic
627C4#1171934111yescharacteristic
628C4#1171935011yescharacteristic
629C2—42no—
630C2#1311864111yescharacteristic
631C2#1312464511yescharacteristic
632C2#1312467211yescharacteristic
633C2#1312640711yescharacteristic
634C2#1312643211yescharacteristic
635C2#1312727011yescharacteristic
636C2#1312745111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2440C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2440D13
hypocenterC13#26355
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
1. C2×#11718752C2semidirect
4. #13116380C2semidirect
5. #13116338C2semidirect
6. #13116214C2semidirect
7. #13116166C2semidirect
8. #13115592C2semidirect
9. #13115404C2semidirect
12. #13115089C2semidirect
93. #88178Q8semidirect
530. C13#26355semidirect

Maximal subgroups

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

subgroupindex
C2×#117187522
C2×#117186252
#131178612
#131163802
#131163382
#131162142
#131161662
#131155922
#131154042
#131152672
#131151432
#131150892
#131150332
#131150212
C13×#24402
#2635513