Finite Group Databasebeta

← #15914662

Subgroups — #15914662

Order 3328.

764 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718741C211yesmaximal, characteristic, complemented
2#13120032C211yesmaximal, characteristic
3#13117926C211yesmaximal, characteristic, complemented
4#13116320C211yesmaximal, characteristic, complemented
5#13116310C211yesmaximal, characteristic, complemented
6#13116220C211yesmaximal, characteristic
7#13116206C211yesmaximal, characteristic
8#13115791C211yesmaximal, characteristic, complemented
9#13115601C211yesmaximal, characteristic, complemented
10#13115591C211yesmaximal, characteristic, complemented
11#13115557C211yesmaximal, characteristic, complemented
12#13115466C211yesmaximal, characteristic
13#13115459C211yesmaximal, characteristic
14#13114661C211yesmaximal, characteristic
15C2×C13×#474C211yesmaximal, characteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×#88124C2211yescharacteristic
19C13×#474—24no—
20C2×C13×#107C2211yescharacteristic
21C2×C13×#107C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C2×C13×#102C2211yescharacteristic
24C2×C13×#102C2211yescharacteristic
25#11718891—21no—
26#11718891—21no—
27#11718882C2211yescharacteristic
28#11718882C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31#11718871—21no—
32#11718871—21no—
33C2×#88054C2211yescharacteristic
34C2×#88054C2211yescharacteristic
35#11718741—24no—
36#11718646—21no—
37#11718646C2211yescharacteristic
38#11718646C2211yescharacteristic
39#11718638C2211yescharacteristic
40#11718637C2211yescharacteristic
41C4⋊C4×Dic13—21no—
42C4⋊C4×Dic13C2211yescharacteristic
43C4⋊C4×Dic13C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88048C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47C2×#88047C2211yescharacteristic
48#11718609—21no—
49#11718609—21no—
50C4×C4⋊Dic13C2211yescharacteristic
51C4×C4⋊Dic13C2211yescharacteristic
52C2×#88043C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C22×Q8×C13—21no—
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C13×C4⋊Q8—22no—
67C13×C4⋊Q8D414yes—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C22⋊C4—21no—
75C2×C42×C13C2311yescharacteristic
76C2×C22⋊Dic13—21no—
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13—21no—
79C2×C22⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13D411yescharacteristic
83C2×C4⋊Dic13D411yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99#88124—22no—
100#88124—22no—
101C13×#107—22no—
102C13×#107—22no—
103C13×C4⋊C8—22no—
104C13×#102—22no—
105C13×#102—22no—
106#88072—22no—
107#88072Q814yescomplemented
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071D411yescharacteristic
116#88071D411yescharacteristic
117#88054—22no—
118#88054—22no—
119#88048—22no—
120#88048—22no—
121#88047—22no—
122#88047—22no—
123#88043—22no—
124#25462—131nomaximal, Sylow
125C24×C13—21no—
126C2×Q8×C13—24no—
127C2×Q8×C13—81no—
128C2×Q8×C13—81no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13C2×Q812yes—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—42no—
139C22×C4×C13—81no—
140C22×C4×C13—81no—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2411yescharacteristic
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13C2×D411yescharacteristic
149C22×Dic13C2×D411yescharacteristic
150C22×Dic13C2×D411yescharacteristic
151C22×Dic13C2×D411yescharacteristic
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C13×C4⋊C4—24no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4C2×D412yes—
164C13×C4⋊C4C2×D412yes—
165C13×C22⋊C4—42no—
166C42×C13C2×D412yes—
167C42×C13#4112yes—
168C22⋊Dic13—42no—
169C22⋊Dic13—42no—
170C22⋊Dic13—81no—
171C22⋊Dic13—81no—
172C4⋊Dic13—21no—
173C4⋊Dic13—22no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—41no—
181C4⋊Dic13—81no—
182C4⋊Dic13—81no—
183C4⋊Dic13C2×Q812yes—
184#6101—42no—
185#6101—42no—
186#6101—81no—
187#6101—81no—
188C4×Dic13—21no—
189C4×Dic13—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—42no—
193C4×Dic13—81no—
194C4×Dic13—81no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055C2×Q812yes—
200C2×#1055#4112yes—
201C2×#501—131no—
202C2×#474D1311yescharacteristic
203#2566—131no—
204#2369—131no—
205#2085—131no—
206#2083—131no—
207#2067—131no—
208#2065—131no—
209#1989—131no—
210#1949—131no—
211#1947—131no—
212#1940—131no—
213#1926—131no—
214#1925—131no—
215#1762—131no—
216C23×C13—22no—
217C23×C13—41no—
218C23×C13—41no—
219C23×C13—41no—
220C23×C13—41no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13C22×D411yescharacteristic
224Q8×C13—84no—
225D4×C13—22no—
226D4×C13—22no—
227D4×C13—41no—
228D4×C13—41no—
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—84no—
243C2×C4×C13#12112yes—
244C2×C4×C13#12112yes—
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C22×Q811yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C132−1+411yescharacteristic
250C2×C4×C132−1+411yescharacteristic
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—22no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—41no—
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×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13#13712yes—
275C8×C13—41no—
276C8×C13—41no—
277#1055—22no—
278#1055—22no—
279C2×C4⋊Q8C2×D1311yescharacteristic
280C2×#125—131no—
281C2×C4×D4C2×D1311yescharacteristic
282#501—264no—
283#474—24no—
284C2×#107—131no—
285C2×#107—131no—
286C2×#107C2×D1311yescharacteristic
287C2×#107C2×D1311yescharacteristic
288C2×#106—131no—
289C2×#106—131no—
290C2×C4⋊C8—131no—
291C2×C4⋊C8—131no—
292C2×C4⋊C8C2×D1311yescharacteristic
293C2×#102—131no—
294C2×#102—131no—
295C2×#102C2×D1311yescharacteristic
296C2×#102C2×D1311yescharacteristic
297C2×#97—131no—
298#396—261no—
299#396—261no—
300#391—261no—
301#391—261no—
302#390—131no—
303#390—131no—
304#389—131no—
305#389—131no—
306#389—261no—
307#385—261no—
308#385—261no—
309#384—131no—
310#382—131no—
311C4×C4⋊C4—131no—
312C4×C4⋊C4—131no—
313C4×C4⋊C4—131no—
314C4×C4⋊C4—131no—
315C4×C4⋊C4—261no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#336—131no—
323#336—131no—
324C22×C13—42no—
325C22×C13—42no—
326C22×C13—42no—
327C22×C13—81no—
328C22×C13—81no—
329C22×C13—81no—
330C22×C13—81no—
331C22×C13C2×#12111yescharacteristic
332C22×C13#54711yescharacteristic
333C22×C13D4×Q811yescharacteristic
334C22×C13C2×#13711yescharacteristic
335C22×C13#57511yescharacteristic
336C22×C13#57611yescharacteristic
337C22×C13#57611yescharacteristic
338C4×C13—22no—
339C4×C13—22no—
340C4×C13—42no—
341C4×C13—42no—
342C4×C13—81no—
343C4×C13#53311yescharacteristic
344C4×C13#54111yescharacteristic
345C4×C13#54811yescharacteristic
346C4×C13D4×Q811yescharacteristic
347Dic13—22no—
348Dic13—41no—
349Dic13—41no—
350Dic13—41no—
351Dic13—42no—
352Dic13—81no—
353Dic13—81no—
354Dic13—81no—
355C22×Q8—21no—
356C22×D4C22×D1311yescharacteristic
357C23×C4—21no—
358C22×C8—131no—
359C22×C8—131no—
360C22×C8C22×D1311yescharacteristic
361C22×C8C22×D1311yescharacteristic
362C4⋊Q8—22no—
363C4⋊Q8C22⋊D1314yes—
364#125—262no—
365#125—262no—
366C4×D4—22no—
367C4×D4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C4⋊C4C22×D1311yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—261no—
386C2×C22⋊C4—261no—
387C2×C22⋊C4—261no—
388C2×C22⋊C4—261no—
389C2×C42—131no—
390C2×C42—131no—
391C2×C42—261no—
392C2×C42—261no—
393C2×C42—261no—
394C2×C42C22×D1311yescharacteristic
395#107—22no—
396#107—22no—
397#107—262no—
398#107—262no—
399#106—262no—
400#106—262no—
401C4⋊C8—22no—
402C4⋊C8—262no—
403C4⋊C8—262no—
404#102—22no—
405#102—22no—
406#102—134no—
407#102—262no—
408#97—262no—
409#95—131no—
410#95—131no—
411#95—261no—
412#95—261no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95—261no—
418C2×C13—82no—
419C2×C13#242911yescharacteristic
420C2×C13#303711yescharacteristic
421C2×C13#304111yescharacteristic
422C2×C13#334611yescharacteristic
423C2×C13#334711yescharacteristic
424C2×C13#338511yescharacteristic
425C2×C13#338911yescharacteristic
426C24—21no—
427C2×Q8—24no—
428C2×Q8—81no—
429C2×Q8—81no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4Q8×D1312yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—42no—
440C22×C4—81no—
441C22×C4—81no—
442C22×C4—131no—
443C22×C4—131no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4D4×D1311yescharacteristic
451C22×C4D4×D1311yescharacteristic
452C22×C4C23×D1311yescharacteristic
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—132no—
460C2×C8—132no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C4⋊C4—24no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—132no—
471C4⋊C4—262no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—521no—
480C4⋊C4—522no—
481C4⋊C4—522no—
482C4⋊C4—1041no—
483C4⋊C4—1041no—
484C4⋊C4—1041no—
485C4⋊C4—1041no—
486C4⋊C4C2×C22⋊D1312yes—
487C4⋊C4C2×C22⋊D1312yes—
488C22⋊C4—42no—
489C22⋊C4—522no—
490C22⋊C4—522no—
491C22⋊C4—1041no—
492C22⋊C4—1041no—
493C42—261no—
494C42—261no—
495C42—261no—
496C42—261no—
497C42—522no—
498C42—1041no—
499C42—1041no—
500C42#612912yes—
501C42C2×C22⋊D1312yes—
502C13#2546211yescharacteristic, complemented, Sylow
503C23—22no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23C2×D4×D1311yescharacteristic
511Q8—84no—
512D4—22no—
513D4—22no—
514D4—41no—
515D4—41no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—84no—
530C2×C4—132no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—262no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4#8819312yes—
555C2×C4#8819312yes—
556C2×C4C2×#612911yescharacteristic
557C2×C4C2×Q8×D1311yescharacteristic
558C2×C4#8825411yescharacteristic
559C2×C4#41×D1311yescharacteristic
560C2×C4#8825711yescharacteristic
561C2×C4C22×C22⋊D1311yescharacteristic
562C8—41no—
563C8—41no—
564C8—262no—
565C8—262no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22#1171933611yescharacteristic
574C22#1171933711yescharacteristic
575C22#1171946211yescharacteristic
576C22#1171946211yescharacteristic
577C22D13×#13711yescharacteristic
578C22#1171948211yescharacteristic
579C22C2×#8819311yescharacteristic
580C4—22no—
581C4—22no—
582C4—42no—
583C4—42no—
584C4—81no—
585C4—262no—
586C4—522no—
587C4—521no—
588C4—521no—
589C4—521no—
590C4—1041no—
591C4—1041no—
592C4—1041no—
593C4#1171932711yescharacteristic
594C4#1171933011yescharacteristic
595C4Q8×C22⋊D1311yescharacteristic
596C4#1171953611yescharacteristic
597C2—82no—
598C2#1311843711yescharacteristic
599C2#1312430511yescharacteristic
600C2#1312433611yescharacteristic
601C2#1312731811yescharacteristic
602C2#1312734311yescharacteristic
603C2#1312774111yescharacteristic
604C2#1312778911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#474C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenterC2×#474D13
hypocenterC13#25462
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#11718741C2semidirect
3. #13117926C2semidirect
4. #13116320C2semidirect
5. #13116310C2semidirect
8. #13115791C2semidirect
9. #13115601C2semidirect
10. #13115591C2semidirect
11. #13115557C2semidirect
107. #88072Q8semidirect
502. C13#25462semidirect

Maximal subgroups

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

subgroupindex
C2×#117187412
#131200322
#131179262
#131163202
#131163102
#131162202
#131162062
#131157912
#131156012
#131155912
#131155572
#131154662
#131154592
#131146612
C2×C13×#4742
#2546213