Finite Group Databasebeta

← #15906851

Subgroups — #15906851

Order 3328.

940 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718711C211yesmaximal, characteristic
2C2×C4×#6107C211yesmaximal, characteristic, complemented
3C22⋊C4×Dic26C211yesmaximal, characteristic
4#13116375C211yesmaximal, characteristic, complemented
5#13116267C211yesmaximal, characteristic
6#13116158C211yesmaximal, characteristic, complemented
7#13116036C211yesmaximal, characteristic
8#13115511C211yesmaximal, characteristic, complemented
9#13115444C211yesmaximal, characteristic
10#13115180C211yesmaximal, characteristic, complemented
11#13115177C211yesmaximal, characteristic, complemented
12#13115089C211yesmaximal, characteristic, complemented
13#13114838C211yesmaximal, characteristic, complemented
14#13114770C211yesmaximal, characteristic
15C13×#2423C211yesmaximal, characteristic
16C23×Dic26C2211yescharacteristic
17C2×C13×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C22×#6107C2211yescharacteristic
20C22×#6107C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C13×#399—21no—
24C13×#398—21no—
25C13×#391C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C13×#388—21no—
28C13×#387—21no—
29C13×#384C2211yescharacteristic
30C13×#380C2211yescharacteristic
31C4×C13×C22⋊C4C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34#11718873C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36C2×C22⋊#1055C2211yescharacteristic
37#11718711—24no—
38C4×#6107—24no—
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88050C2211yescharacteristic
44C2×#88050C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47#11718603—21no—
48C22⋊C4×Dic13—21no—
49#11718590C2211yescharacteristic
50#11718590C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53#11718307—21no—
54#11718307—21no—
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×Dic13—21no—
64C22×Dic26—21no—
65C22×Dic26—22no—
66C22×Dic26—22no—
67C22×Dic26—22no—
68C22×Dic26—22no—
69C22×Dic26—41no—
70C22×Dic26—41no—
71C22×Dic26C2311yescharacteristic
72C22×Dic26C2311yescharacteristic
73C13×C22⋊Q8—22no—
74C13×C22⋊Q8—41no—
75C4×Q8×C13—22no—
76C4×Q8×C13—41no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4D411yescharacteristic
88C2×C13×C22⋊C4D411yescharacteristic
89C2×C42×C13—21no—
90C2×C42×C13C2311yescharacteristic
91C2×C42×C13C2311yescharacteristic
92C2×C22⋊Dic13—21no—
93C2×#6107—22no—
94C2×#6107—22no—
95C2×#6107—22no—
96C2×#6107—22no—
97C2×#6107—41no—
98C2×#6107D414yes—
99C2×C4⋊Dic13C2311yescharacteristic
100C2×C4⋊Dic13C2311yescharacteristic
101C2×#6101—21no—
102C2×#6101—21no—
103C2×C4×Dic13—21no—
104C2×C4×Dic13—21no—
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109C4×Dic26—22no—
110C4×Dic26—22no—
111C4×Dic26—41no—
112C4×Dic26—41no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95—21no—
116C13×#95—21no—
117C13×#95D411yescharacteristic
118C13×#95D411yescharacteristic
119#88075—22no—
120#88075—41no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126C22⋊#1055—22no—
127C22⋊#1055—41no—
128#88050—22no—
129#88050—22no—
130#88050—22no—
131#88050—22no—
132#88050—22no—
133#88050—41no—
134#88047—22no—
135#88047—41no—
136C4⋊#1055—41no—
137C4×#1055—22no—
138#24906—131nomaximal, Sylow
139C24×C13C2×D411yescharacteristic
140C2×Q8×C13—21no—
141C2×Q8×C13—21no—
142C2×Q8×C13—21no—
143C2×Q8×C13—21no—
144C2×Q8×C13—21no—
145C2×Q8×C13C2×D412yes—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2411yescharacteristic
162C22×Dic13—21no—
163C22×Dic13—24no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—42no—
168C22×Dic13—42no—
169C2×Dic26—21no—
170C2×Dic26—21no—
171C2×Dic26—21no—
172C2×Dic26—21no—
173C2×Dic26—21no—
174C2×Dic26—21no—
175C2×Dic26—21no—
176C2×Dic26—24no—
177C2×Dic26—21no—
178C2×Dic26—44no—
179C2×Dic26—44no—
180C2×Dic26—44no—
181C2×Dic26—42no—
182C2×Dic26—42no—
183C2×Dic26—44no—
184C2×Dic26C2×D412yes—
185C2×Dic26#4112yes—
186C2×Dic26#4112yes—
187C2×Dic26#4112yes—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—42no—
195C13×C4⋊C4—42no—
196C13×C4⋊C4—42no—
197C13×C4⋊C4—81no—
198C13×C4⋊C4—81no—
199C13×C22⋊C4—41no—
200C13×C22⋊C4—42no—
201C13×C22⋊C4—81no—
202C13×C22⋊C4Q1614yescomplemented
203C42×C13—21no—
204C42×C13—21no—
205C42×C13—21no—
206C42×C13—21no—
207C42×C13—42no—
208C22⋊Dic13—42no—
209#6107—28no—
210#6107—44no—
211C4⋊Dic13—21no—
212C4⋊Dic13—21no—
213C4⋊Dic13—21no—
214C4⋊Dic13—21no—
215#6101—42no—
216#6101—42no—
217C4×Dic13—42no—
218C4×Dic13—42no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#1055—21no—
228C2×#1055—21no—
229C2×#1055—21no—
230C2×#1055C2×D412yes—
231C2×#451—131no—
232C2×C4×Q16—131no—
233#2423D1311yescharacteristic
234Q8×C22⋊C4—131no—
235#2095—131no—
236#2076—131no—
237#2056—131no—
238#2036—131no—
239#1933—131no—
240#1923—131no—
241#1878—131no—
242#1878—131no—
243#1863—131no—
244#1803—131no—
245#1787—131no—
246C23×C13—21no—
247C23×C13—21no—
248C23×C13—21no—
249C23×C13—21no—
250C23×C13—21no—
251C23×C13—21no—
252C23×C13C2×Q1612yes—
253C23×C13C22×D411yescharacteristic
254Q8×C13—22no—
255Q8×C13—22no—
256Q8×C13—41no—
257Q8×C13—41no—
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—22no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13C2×Q1612yes—
288C2×C4×C13C2×Q1612yes—
289C2×C4×C13C22×D411yescharacteristic
290C2×C4×C13C2×#4111yescharacteristic
291C2×C4×C13C2×#4111yescharacteristic
292C2×C4×C13C2×#4111yescharacteristic
293C2×C4×C13H(5,𝔽2)11yescharacteristic
294C2×C4×C13H(5,𝔽2)11yescharacteristic
295C2×Dic13—22no—
296C2×Dic13—22no—
297C2×Dic13—22no—
298C2×Dic13—22no—
299C2×Dic13—48no—
300C2×Dic13—41no—
301C2×Dic13—41no—
302C2×Dic13—41no—
303C2×Dic13—41no—
304C2×Dic13—41no—
305C2×Dic13—41no—
306C2×Dic13—41no—
307C2×Dic13—41no—
308Dic26—22no—
309Dic26—22no—
310Dic26—22no—
311Dic26—22no—
312Dic26—22no—
313Dic26—48no—
314Dic26—41no—
315Dic26—41no—
316Dic26#12314yes—
317#1055—22no—
318#1055—41no—
319#1055—41no—
320#1055—41no—
321C23×Q8—131no—
322C22×Q16—131no—
323C22×Q16—131no—
324C2×C22⋊Q8C2×D1311yescharacteristic
325C2×C4×Q8—131no—
326C2×C4×Q8—131no—
327C2×C4×Q8C2×D1311yescharacteristic
328#451—264no—
329C4×Q16—264no—
330C2×#107—131no—
331C2×#107—131no—
332C2×C4⋊C8—131no—
333C2×#103—131no—
334C2×#103—131no—
335C2×#103—131no—
336C2×#103—131no—
337C2×#103—131no—
338C2×#103—131no—
339C2×#103—131no—
340C2×#103—131no—
341C2×C22⋊C8—131no—
342C2×C22⋊C8—131no—
343C2×C4×C8—131no—
344#399—21no—
345#398—21no—
346#391—131no—
347#391—131no—
348#391—261no—
349#391—261no—
350#391C2×D1311yescharacteristic
351#389C2×D1311yescharacteristic
352#388—21no—
353#387—21no—
354#384C2×D1311yescharacteristic
355#380—131no—
356#380—261no—
357#380C2×D1311yescharacteristic
358C4×C22⋊C4—261no—
359C4×C22⋊C4C2×D1311yescharacteristic
360#340—131no—
361#340—131no—
362#340—131no—
363#340—131no—
364#336—131no—
365#336—131no—
366C22×C13—22no—
367C22×C13—22no—
368C22×C13—22no—
369C22×C13—41no—
370C22×C13—41no—
371C22×C13—41no—
372C22×C13—41no—
373C22×C13#52511yescharacteristic
374C22×C13D4211yescharacteristic
375C22×C13#54611yescharacteristic
376C22×C13C22×Q1611yescharacteristic
377C22×C13#57511yescharacteristic
378C22×C13#57711yescharacteristic
379C22×C13#57811yescharacteristic
380C4×C13—22no—
381C4×C13—22no—
382C4×C13—41no—
383C4×C13—42no—
384C4×C13—41no—
385C4×C13—41no—
386C4×C13—81no—
387C4×C13—81no—
388C4×C13—81no—
389C4×C13C2×#12311yescharacteristic
390C4×C13#53811yescharacteristic
391C4×C13#54611yescharacteristic
392C4×C13#55111yescharacteristic
393Dic13—24no—
394Dic13—42no—
395Dic13—81no—
396Dic13—81no—
397C22×Q8—131no—
398C22×Q8—131no—
399C22×Q8—262no—
400C22×Q8—262no—
401C22×Q8—262no—
402C22×Q8—262no—
403C22×Q8—261no—
404C22×Q8—521no—
405C22×Q8—521no—
406C22×Q8C22×D1311yescharacteristic
407C23×C4—261no—
408C23×C4C22×D1311yescharacteristic
409C2×Q16—134no—
410C2×Q16—262no—
411C2×Q16—262no—
412C2×Q16—262no—
413C2×Q16—262no—
414C2×Q16—521no—
415C22×C8—131no—
416C22×C8—131no—
417C22×C8—131no—
418C22×C8—131no—
419C22⋊Q8—22no—
420C22⋊Q8—41no—
421C4×Q8—22no—
422C4×Q8—41no—
423C4×Q8—262no—
424C4×Q8—262no—
425C4×Q8—521no—
426C4×Q8—521no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—131no—
433C2×C4⋊C4—131no—
434C2×C4⋊C4—261no—
435C2×C4⋊C4—261no—
436C2×C4⋊C4C22×D1311yescharacteristic
437C2×C4⋊C4C22×D1311yescharacteristic
438C2×C4⋊C4C22×D1311yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—261no—
442C2×C22⋊C4C22⋊D1311yescharacteristic
443C2×C22⋊C4C22⋊D1311yescharacteristic
444C2×C42—21no—
445C2×C42—261no—
446C2×C42—261no—
447C2×C42C22×D1311yescharacteristic
448C2×C42C22×D1311yescharacteristic
449#107—262no—
450#107—521no—
451C4⋊C8—521no—
452#103—262no—
453#103—262no—
454#103—262no—
455#103—262no—
456#103—262no—
457#103—262no—
458#103—521no—
459#103—521no—
460C22⋊C8—262no—
461C22⋊C8—521no—
462C4×C8—262no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—261no—
468#95—261no—
469#95—261no—
470#95—261no—
471#95—261no—
472#95C22⋊D1311yescharacteristic
473#95C22⋊D1311yescharacteristic
474C2×C13—42no—
475C2×C13#241811yescharacteristic
476C2×C13#310411yescharacteristic
477C2×C13#312111yescharacteristic
478C2×C13#327111yescharacteristic
479C2×C13D4×Q1611yescharacteristic
480C2×C13#329911yescharacteristic
481C2×C13#332711yescharacteristic
482C24C2×C22⋊D1311yescharacteristic
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—132no—
489C2×Q8—132no—
490C2×Q8—132no—
491C2×Q8—132no—
492C2×Q8—264no—
493C2×Q8—261no—
494C2×Q8—261no—
495C2×Q8—261no—
496C2×Q8—261no—
497C2×Q8—261no—
498C2×Q8—261no—
499C2×Q8—261no—
500C2×Q8—261no—
501C2×Q8—522no—
502C2×Q8—522no—
503C2×Q8—524no—
504C2×Q8—524no—
505C2×Q8—524no—
506C2×Q8—524no—
507C2×Q8D4×D1312yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—261no—
519C22×C4—264no—
520C22×C4—261no—
521C22×C4—261no—
522C22×C4—261no—
523C22×C4—522no—
524C22×C4—522no—
525C22×C4C2×C22⋊D1311yescharacteristic
526C22×C4C2×C22⋊D1311yescharacteristic
527C22×C4C2×C22⋊D1311yescharacteristic
528C22×C4C2×C22⋊D1311yescharacteristic
529C22×C4C2×C22⋊D1311yescharacteristic
530C22×C4C23×D1311yescharacteristic
531Q16—268no—
532Q16—524no—
533C2×C8—132no—
534C2×C8—261no—
535C2×C8—261no—
536C2×C8—261no—
537C2×C8—261no—
538C2×C8—261no—
539C2×C8—261no—
540C2×C8—261no—
541C2×C8—261no—
542C2×C8—261no—
543C2×C8—261no—
544C2×C8—261no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—81no—
555C4⋊C4—81no—
556C4⋊C4—261no—
557C4⋊C4—261no—
558C4⋊C4—261no—
559C4⋊C4—261no—
560C4⋊C4—522no—
561C4⋊C4—522no—
562C22⋊C4—41no—
563C22⋊C4—42no—
564C22⋊C4—81no—
565C22⋊C4—522no—
566C22⋊C4#610714yescomplemented
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C42—522no—
573C42—522no—
574C13#2490611yescharacteristic, complemented, Sylow
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23C2×#610712yes—
582C23C22×C22⋊D1311yescharacteristic
583Q8—22no—
584Q8—22no—
585Q8—41no—
586Q8—41no—
587Q8—134no—
588Q8—262no—
589Q8—262no—
590Q8—262no—
591Q8—262no—
592Q8—262no—
593Q8—528no—
594Q8—521no—
595Q8—521no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—262no—
626C2×C4—262no—
627C2×C4—262no—
628C2×C4—262no—
629C2×C4—528no—
630C2×C4—521no—
631C2×C4—521no—
632C2×C4—521no—
633C2×C4—521no—
634C2×C4—521no—
635C2×C4—521no—
636C2×C4—521no—
637C2×C4—521no—
638C2×C4C2×#610712yes—
639C2×C4C2×#610712yes—
640C2×C4C2×D4×D1311yescharacteristic
641C2×C4#8825111yescharacteristic
642C2×C4#41×D1311yescharacteristic
643C2×C4#41×D1311yescharacteristic
644C2×C4#41×D1311yescharacteristic
645C2×C4#8825611yescharacteristic
646C8—262no—
647C8—521no—
648C8—521no—
649C8—521no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22D4×C22⋊D1311yescharacteristic
658C22C22×#610711yescharacteristic
659C22#1171952711yescharacteristic
660C22#1171953311yescharacteristic
661C22#1171953411yescharacteristic
662C22#1171954111yescharacteristic
663C22#1171954311yescharacteristic
664C4—22no—
665C4—22no—
666C4—41no—
667C4—41no—
668C4—42no—
669C4—41no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4—264no—
674C4—522no—
675C4—1041no—
676C4—1041no—
677C4D13×#12311yescharacteristic
678C4#1171935911yescharacteristic
679C4#1171936211yescharacteristic
680C4#1171936411yescharacteristic
681C2—42no—
682C2#1311829511yescharacteristic
683C2#1312487111yescharacteristic
684C2#1312505911yescharacteristic
685C2#1312641711yescharacteristic
686C2D4×#610711yescharacteristic
687C2#1312670611yescharacteristic
688C2#1312709811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2423C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2423D13
hypocenterC13#24906
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2423

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6107C2semidirect
4. #13116375C2semidirect
6. #13116158C2semidirect
8. #13115511C2semidirect
10. #13115180C2semidirect
11. #13115177C2semidirect
12. #13115089C2semidirect
13. #13114838C2semidirect
202. C13×C22⋊C4Q16semidirect
566. C22⋊C4#6107semidirect
574. C13#24906semidirect

Maximal subgroups

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

subgroupindex
C2×#117187112
C2×C4×#61072
C22⋊C4×Dic262
#131163752
#131162672
#131161582
#131160362
#131155112
#131154442
#131151802
#131151772
#131150892
#131148382
#131147702
C13×#24232
#2490613