Finite Group Databasebeta

← #15914709

Subgroups — #15914709

Order 3328.

812 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718727C211yesmaximal, characteristic
2#13119790C211yesmaximal, characteristic
3#13117936C211yesmaximal, characteristic, complemented
4#13116315C211yesmaximal, characteristic, complemented
5#13116310C211yesmaximal, characteristic, complemented
6#13116219C211yesmaximal, characteristic
7#13116205C211yesmaximal, characteristic
8#13115785C211yesmaximal, characteristic, complemented
9#13115596C211yesmaximal, characteristic, complemented
10#13115591C211yesmaximal, characteristic, complemented
11#13115559C211yesmaximal, characteristic, complemented
12#13115462C211yesmaximal, characteristic
13#13115455C211yesmaximal, characteristic
14#13114662C211yesmaximal, characteristic
15C2×C13×#501C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×#125C2211yescharacteristic
18C2×#88200—21no—
19C2×#88200—21no—
20C2×C4×D52C2211yescharacteristic
21C13×#501—24no—
22C2×C13×#107C2211yescharacteristic
23C2×C13×#107C2211yescharacteristic
24C2×C13×#106C2211yescharacteristic
25C2×C13×#106C2211yescharacteristic
26C2×C13×#97C2211yescharacteristic
27C2×#88061C2211yescharacteristic
28C2×#88061C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31#11718727—24no—
32#11718653—21no—
33#11718653—21no—
34#11718649C2211yescharacteristic
35#11718649C2211yescharacteristic
36#11718646—21no—
37#11718646C2211yescharacteristic
38#11718646C2211yescharacteristic
39#11718642—21no—
40#11718642—21no—
41#11718637C2211yescharacteristic
42#11718637C2211yescharacteristic
43C4⋊C4×Dic13—21no—
44C4⋊C4×Dic13C2211yescharacteristic
45C4⋊C4×Dic13C2211yescharacteristic
46C2×#88049C2211yescharacteristic
47C2×#88049C2211yescharacteristic
48C2×#88048C2211yescharacteristic
49C2×#88047C2211yescharacteristic
50C4×C4⋊Dic13C2211yescharacteristic
51C4×C4⋊Dic13C2211yescharacteristic
52C2×C4⋊#1055C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C22×Q8×C13—21no—
62C22×D52C2311yescharacteristic
63C22×C4×D13—21no—
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C13×C4⋊Q8—22no—
67C13×C4⋊Q8—22no—
68C13×#125—22no—
69C13×#125D414yes—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C42×C13C2311yescharacteristic
78#88200—44no—
79#88200—44no—
80C2×#6103—21no—
81C2×#6103—21no—
82C2×#6103—21no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13D411yescharacteristic
88C2×C4⋊Dic13D411yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×C4×Dic13—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13C2311yescharacteristic
100C2×C4×Dic13C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C4×D52—22no—
104C4×D52—22no—
105C13×#107—22no—
106C13×#107—22no—
107C13×#106—22no—
108C13×#106—22no—
109C13×#97—22no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071D411yescharacteristic
116#88071D411yescharacteristic
117#88061—22no—
118#88061Q814yescomplemented
119#88054—22no—
120#88054—22no—
121#88049—22no—
122#88049—22no—
123#88048—22no—
124#88047—22no—
125C4⋊#1055—22no—
126#25465—131nomaximal, Sylow
127C23×D13—21no—
128C2×Q8×C13—42no—
129C2×Q8×C13—42no—
130C2×Q8×C13—42no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2411yescharacteristic
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13C2×D411yescharacteristic
142C22×Dic13C2×D411yescharacteristic
143C22×Dic13C2×D411yescharacteristic
144C22×Dic13C2×D411yescharacteristic
145C2×D52—21no—
146C2×D52—21no—
147C2×D52—21no—
148C2×D52—21no—
149C2×D52—21no—
150C2×D52C2×Q812yes—
151C2×C4×D13—42no—
152C2×C4×D13—42no—
153C2×C4×D13—42no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13C2×Q812yes—
159C2×C8×C13#4112yes—
160C13×C4⋊C4—24no—
161C13×C4⋊C4—24no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—42no—
169C13×C4⋊C4C2×D412yes—
170C13×C4⋊C4C2×D412yes—
171C42×C13C2×D412yes—
172C42×C13#4112yes—
173#6103—42no—
174#6103—42no—
175#6103—42no—
176#6103—42no—
177#6103—42no—
178C4⋊Dic13—21no—
179C4⋊Dic13—22no—
180C4⋊Dic13—22no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—42no—
186C4⋊Dic13—81no—
187C4⋊Dic13C2×Q812yes—
188#6101—42no—
189#6101—42no—
190#6101—42no—
191#6101—42no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13—42no—
197C4×Dic13—81no—
198C4×Dic13—81no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#501D1311yescharacteristic, complemented
206C2×#478—131no—
207#2542—131no—
208#2370—131no—
209#2084—131no—
210#2083—131no—
211#2067—131no—
212#2065—131no—
213#1987—131no—
214#1948—131no—
215#1947—131no—
216#1940—131no—
217#1926—131no—
218#1925—131no—
219#1762—131no—
220C23×C13C22×D411yescharacteristic
221C22×D13—22no—
222C22×D13—41no—
223C22×D13—41no—
224C22×D13—41no—
225C22×D13—41no—
226C22×D13—41no—
227C22×D13—41no—
228Q8×C13—84no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13#12112yes—
246C2×C4×C13#12112yes—
247C2×C4×C13C22×D411yescharacteristic
248C2×C4×C13C22×Q811yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C132−1+411yescharacteristic
252C2×C4×C132−1+411yescharacteristic
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—22no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13AGL(1,ℤ/8)12yes—
273C2×Dic13AGL(1,ℤ/8)12yes—
274D52—22no—
275D52—22no—
276D52—41no—
277D52—41no—
278C4×D13—84no—
279C8×C13—22no—
280C8×C13—22no—
281#1055—41no—
282#1055—41no—
283C2×C4⋊Q8C2×D1311yescharacteristic
284C2×#125C2×D1311yescharacteristic
285C2×C22⋊Q8—261no—
286C2×C22⋊Q8—261no—
287C2×C4×D4—131no—
288#501—24no—
289#478—264no—
290C2×#107—131no—
291C2×#107C2×D1311yescharacteristic
292C2×#107C2×D1311yescharacteristic
293C2×#106—131no—
294C2×#106C2×D1311yescharacteristic
295C2×#106C2×D1311yescharacteristic
296C2×C4⋊C8—131no—
297C2×C4⋊C8—131no—
298C2×C4⋊C8—131no—
299C2×#102—131no—
300C2×#102—131no—
301C2×#102—131no—
302C2×#102—131no—
303C2×#97C2×D1311yescharacteristic
304#399—261no—
305#399—261no—
306#390—131no—
307#390—131no—
308#389—131no—
309#389—131no—
310#389—261no—
311#387—261no—
312#387—261no—
313#384—131no—
314#384—131no—
315C4×C4⋊C4—131no—
316C4×C4⋊C4—131no—
317C4×C4⋊C4—131no—
318C4×C4⋊C4—131no—
319C4×C4⋊C4—261no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#336—131no—
327#336—131no—
328C22×C13C2×#12111yescharacteristic
329C22×C13#54711yescharacteristic
330C22×C13D4×Q811yescharacteristic
331C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C13#57711yescharacteristic
334C22×C13#57811yescharacteristic
335C2×D13—42no—
336C2×D13—42no—
337C2×D13—42no—
338C2×D13—81no—
339C2×D13—81no—
340C2×D13—81no—
341C2×D13—81no—
342C4×C13—22no—
343C4×C13—22no—
344C4×C13—42no—
345C4×C13—42no—
346C4×C13—81no—
347C4×C13—81no—
348C4×C13#53311yescharacteristic
349C4×C13#54111yescharacteristic
350C4×C13#54811yescharacteristic
351C4×C13D4×Q811yescharacteristic
352Dic13—22no—
353Dic13—22no—
354Dic13—41no—
355Dic13—41no—
356Dic13—42no—
357Dic13—81no—
358Dic13—81no—
359C22×Q8—21no—
360C22×D4—131no—
361C23×C4—261no—
362C22×C8—131no—
363C22×C8—131no—
364C22×C8C22×D1311yescharacteristic
365C22×C8C22×D1311yescharacteristic
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368#125—22no—
369#125C22⋊D1314yes—
370C22⋊Q8—524no—
371C22⋊Q8—524no—
372C4×D4—262no—
373C4×D4—262no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C4⋊C4C22×D1311yescharacteristic
390C2×C4⋊C4C22×D1311yescharacteristic
391C2×C4⋊C4C22×D1311yescharacteristic
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C22⋊C4—261no—
395C2×C22⋊C4—261no—
396C2×C22⋊C4—261no—
397C2×C42—131no—
398C2×C42—131no—
399C2×C42—261no—
400C2×C42—261no—
401C2×C42—261no—
402C2×C42C22×D1311yescharacteristic
403#107—22no—
404#107—22no—
405#107—262no—
406#106—22no—
407#106—22no—
408#106—262no—
409C4⋊C8—262no—
410C4⋊C8—262no—
411C4⋊C8—262no—
412#102—134no—
413#102—262no—
414#102—262no—
415#102—262no—
416#97—22no—
417#95—131no—
418#95—131no—
419#95—261no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95—261no—
424C2×C13#242911yescharacteristic
425C2×C13#303811yescharacteristic
426C2×C13#304611yescharacteristic
427C2×C13#334311yescharacteristic
428C2×C13#334511yescharacteristic
429C2×C13#338411yescharacteristic
430C2×C13#338611yescharacteristic
431D13—82no—
432C24—261no—
433C2×Q8—42no—
434C2×Q8—42no—
435C2×Q8—42no—
436C2×D4—132no—
437C2×D4—261no—
438C2×D4—261no—
439C2×D4—261no—
440C2×D4—261no—
441C2×D4—261no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—131no—
447C22×C4—131no—
448C22×C4—131no—
449C22×C4—131no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—522no—
454C22×C4—522no—
455C22×C4—522no—
456C22×C4D4×D1311yescharacteristic
457C22×C4D4×D1311yescharacteristic
458C22×C4C23×D1311yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8Q8×D1312yes—
470C2×C8#613112yes—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—42no—
480C4⋊C4—132no—
481C4⋊C4—262no—
482C4⋊C4—262no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—522no—
489C4⋊C4—522no—
490C4⋊C4—522no—
491C4⋊C4—522no—
492C4⋊C4—522no—
493C4⋊C4—1041no—
494C4⋊C4C2×C22⋊D1312yes—
495C4⋊C4C2×C22⋊D1312yes—
496C22⋊C4—522no—
497C22⋊C4—522no—
498C22⋊C4—522no—
499C22⋊C4—522no—
500C22⋊C4—522no—
501C42—261no—
502C42—261no—
503C42—261no—
504C42—261no—
505C42—522no—
506C42—1041no—
507C42—1041no—
508C42#612912yes—
509C42C2×C22⋊D1312yes—
510C13#2546511yescharacteristic, complemented, Sylow
511C23—262no—
512C23—521no—
513C23—521no—
514C23—521no—
515C23—521no—
516C23—521no—
517C23—521no—
518C23C2×D4×D1311yescharacteristic
519Q8—84no—
520D4—262no—
521D4—262no—
522D4—521no—
523D4—521no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—132no—
541C2×C4—132no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—262no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—261no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—1044no—
562C2×C4#8819312yes—
563C2×C4#8819312yes—
564C2×C4C2×#612911yescharacteristic
565C2×C4C2×Q8×D1311yescharacteristic
566C2×C4C2×#613111yescharacteristic
567C2×C4#8825411yescharacteristic
568C2×C4#8825411yescharacteristic
569C2×C4C22×C22⋊D1311yescharacteristic
570C8—22no—
571C8—22no—
572C8—521no—
573C8—521no—
574C22—522no—
575C22—522no—
576C22—522no—
577C22—1041no—
578C22—1041no—
579C22—1041no—
580C22—1041no—
581C22#1171943111yescharacteristic
582C22#1171943211yescharacteristic
583C22D13×AGL(1,ℤ/8)11yescharacteristic
584C22D13×AGL(1,ℤ/8)11yescharacteristic
585C22#1171948311yescharacteristic
586C22#1171948411yescharacteristic
587C22C2×#8819311yescharacteristic
588C4—22no—
589C4—22no—
590C4—42no—
591C4—42no—
592C4—81no—
593C4—81no—
594C4—262no—
595C4—262no—
596C4—522no—
597C4—521no—
598C4—521no—
599C4—1041no—
600C4—1041no—
601C4#1171943311yescharacteristic
602C4#1171943611yescharacteristic
603C4Q8×C22⋊D1311yescharacteristic
604C4#1171952211yescharacteristic
605C2—1042no—
606C2#1311843811yescharacteristic
607C2#1312431411yescharacteristic
608C2#1312439011yescharacteristic
609C2#1312727511yescharacteristic
610C2#1312730511yescharacteristic
611C2#1312773211yescharacteristic
612C2#1312775411yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#501C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenterC2×#501D13
hypocenterC13#25465
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #13117936C2semidirect
4. #13116315C2semidirect
5. #13116310C2semidirect
8. #13115785C2semidirect
9. #13115596C2semidirect
10. #13115591C2semidirect
11. #13115559C2semidirect
15. C2×C13×#501C2semidirect
118. #88061Q8semidirect
205. C2×#501D13semidirect
510. C13#25465semidirect

Maximal subgroups

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

subgroupindex
C2×#117187272
#131197902
#131179362
#131163152
#131163102
#131162192
#131162052
#131157852
#131155962
#131155912
#131155592
#131154622
#131154552
#131146622
C2×C13×#5012
#2546513