Finite Group Databasebeta

← #15920612

Subgroups — #15920612

Order 3328.

774 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118532C211yesmaximal, characteristic
2#13117713C211yesmaximal, characteristic
3#13116402C211yesmaximal, characteristic, complemented
4#13116333C211yesmaximal, characteristic, complemented
5#13116331C211yesmaximal, characteristic, complemented
6#13116163C211yesmaximal, characteristic, complemented
7#13115782C211yesmaximal, characteristic, complemented
8#13115593C211yesmaximal, characteristic, complemented
9#13115431C211yesmaximal, characteristic, complemented
10#13115427C211yesmaximal, characteristic, complemented
11#13115024C211yesmaximal, characteristic
12#13115014C211yesmaximal, characteristic
13#13114926C211yesmaximal, characteristic
14#13114865C211yesmaximal, characteristic
15C2×C13×#340C211yesmaximal, characteristic
16C23×C8×C13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88178—21no—
20C2×#88142C2211yescharacteristic
21#11718873—21no—
22#11718873C2211yescharacteristic
23#11718873C2211yescharacteristic
24#11718871—21no—
25C4×C22⋊Dic13—21no—
26C4×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊#1055C2211yescharacteristic
28C2×#88058C2211yescharacteristic
29C2×#88058C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32#11718646C2211yescharacteristic
33#11718646C2211yescharacteristic
34#11718646C2211yescharacteristic
35#11718645—21no—
36#11718642—21no—
37#11718642—21no—
38#11718640—21no—
39#11718637C2211yescharacteristic
40C4⋊C4×Dic13C2211yescharacteristic
41C4⋊C4×Dic13C2211yescharacteristic
42#11718634C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45C13×#340C2211yescharacteristic
46C13×#340C2211yescharacteristic
47C13×#340C2211yescharacteristic
48C13×#340C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C22×Dic26—21no—
63C22×C8×C13—22no—
64C22×C8×C13—22no—
65C22×C8×C13—41no—
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—41no—
73C2×C13×C4⋊C4Q814yescomplemented
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C22⋊Dic13—21no—
79C2×C22⋊Dic13—21no—
80C2×C22⋊Dic13D411yescharacteristic
81C2×C22⋊Dic13D411yescharacteristic
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89#88178—44no—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13C2311yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100#88142—22no—
101#88142—41no—
102#88071—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071D411yescharacteristic
111#88071D411yescharacteristic
112C22⋊#1055—22no—
113#88058—22no—
114#88058—41no—
115#88054—22no—
116#88054—41no—
117#88047—22no—
118#88047—41no—
119#25994—131nomaximal, Sylow
120C24×C13C2×D411yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—24no—
129C22×C4×C13—21no—
130C22×C4×C13—42no—
131C22×C4×C13—42no—
132C22×C4×C13—81no—
133C22×C4×C13—81no—
134C22×C4×C13—81no—
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×Q812yes—
137C22×C4×C13#4112yes—
138C22×C4×C13C2411yescharacteristic
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13C2×D411yescharacteristic
144C22×Dic13C2×D411yescharacteristic
145C22×Dic13C2×D411yescharacteristic
146C22×Dic13C2×D411yescharacteristic
147C2×Dic26—42no—
148C2×Dic26—42no—
149C2×Dic26—81no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—44no—
156C2×C8×C13#4112yes—
157C13×C4⋊C4—24no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—42no—
164C13×C4⋊C4C2×Q812yes—
165C13×C4⋊C4C2×Q812yes—
166C13×C4⋊C4#4112yes—
167C22⋊Dic13—22no—
168C22⋊Dic13—42no—
169C22⋊Dic13—42no—
170C22⋊Dic13Q1614yes—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—42no—
180C4⋊Dic13—81no—
181C4⋊Dic13—81no—
182#6101—42no—
183#6101—42no—
184#6101—42no—
185#6101—81no—
186C4×Dic13—21no—
187C4×Dic13—21no—
188C4×Dic13—21no—
189C4×Dic13—21no—
190C4×Dic13—81no—
191C4×Dic13—81no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198#2440—131no—
199#2345—131no—
200#2100—131no—
201#2087—131no—
202#2087—131no—
203#2057—131no—
204#1987—131no—
205#1947—131no—
206#1921—131no—
207#1921—131no—
208#1852—131no—
209#1850—131no—
210#1824—131no—
211#1808—131no—
212C2×#340D1311yescharacteristic
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13C22⋊Q812yes—
218C23×C13C2×Q1612yes—
219C23×C13AGL(1,ℤ/8)12yes—
220C23×C13C22×D411yescharacteristic
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—84no—
240C2×C4×C13—84no—
241C2×C4×C13C22⋊Q812yes—
242C2×C4×C13C22×Q811yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C13H(5,𝔽2)11yescharacteristic
247C2×C4×C132−1+411yescharacteristic
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13C2×Q1612yes—
271C2×Dic13C2×Q1612yes—
272Dic26—84no—
273C8×C13—22no—
274C8×C13—41no—
275#1055—41no—
276#1055—41no—
277C23×C8C2×D1311yescharacteristic
278C2×C4⋊Q8—131no—
279C2×C22⋊Q8—261no—
280C22×C4⋊C4C2×D1311yescharacteristic
281C22×C4⋊C4C2×D1311yescharacteristic
282C2×#107—131no—
283C2×#107—131no—
284C2×#107—131no—
285C2×#107—131no—
286C2×C4⋊C8—131no—
287C2×C4⋊C8—131no—
288C2×C22⋊C8—131no—
289#398—261no—
290#395—261no—
291#389—131no—
292#389—131no—
293#389—131no—
294#389—131no—
295#387—261no—
296#387—261no—
297#385—261no—
298#384—131no—
299#380—131no—
300#380—131no—
301#380—261no—
302C4×C4⋊C4—131no—
303C4×C4⋊C4—131no—
304C4×C22⋊C4—131no—
305C4×C22⋊C4—261no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340C2×D1311yescharacteristic
315#340C2×D1311yescharacteristic
316#340C2×D1311yescharacteristic
317#340C2×D1311yescharacteristic
318#336—131no—
319#336—131no—
320C22×C13—22no—
321C22×C13—22no—
322C22×C13—22no—
323C22×C13—22no—
324C22×C13—22no—
325C22×C13—22no—
326C22×C13#47714yes—
327C22×C13C2×C22⋊Q811yescharacteristic
328C22×C13#54611yescharacteristic
329C22×C13#54711yescharacteristic
330C22×C13C22×Q1611yescharacteristic
331C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C13#57611yescharacteristic
333C22×C13#57711yescharacteristic
334C4×C13—22no—
335C4×C13—42no—
336C4×C13—42no—
337C4×C13—42no—
338C4×C13—81no—
339C4×C13#53311yescharacteristic
340C4×C13#54411yescharacteristic
341C4×C13#55111yescharacteristic
342C4×C13#55211yescharacteristic
343Dic13—22no—
344Dic13—22no—
345Dic13—41no—
346Dic13—41no—
347Dic13—81no—
348Dic13—81no—
349Dic13—81no—
350Dic13—81no—
351C22×Q8—261no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4C22×D1311yescharacteristic
355C22×C8—22no—
356C22×C8—22no—
357C22×C8—41no—
358C22×C8—131no—
359C22×C8—131no—
360C22×C8C22×D1311yescharacteristic
361C22×C8C22×D1311yescharacteristic
362C4⋊Q8—262no—
363C4⋊Q8—521no—
364C22⋊Q8—524no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—41no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—261no—
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⋊C4Dic2614yescomplemented
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C4⋊C4C22×D1311yescharacteristic
384C2×C4⋊C4C22×D1311yescharacteristic
385C2×C4⋊C4C22×D1311yescharacteristic
386C2×C22⋊C4—131no—
387C2×C22⋊C4—131no—
388C2×C22⋊C4—261no—
389C2×C22⋊C4—261no—
390C2×C42—131no—
391C2×C42—131no—
392C2×C42—261no—
393C2×C42—261no—
394#107—262no—
395#107—262no—
396#107—521no—
397#107—521no—
398C4⋊C8—262no—
399C4⋊C8—521no—
400C22⋊C8—262no—
401#95—131no—
402#95—131no—
403#95—261no—
404#95—261no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95—261no—
411C2×C13—24no—
412C2×C13#243811yescharacteristic
413C2×C13C2×#47711yescharacteristic
414C2×C13#308111yescharacteristic
415C2×C13#329911yescharacteristic
416C2×C13#331811yescharacteristic
417C2×C13#333811yescharacteristic
418C2×C13#334511yescharacteristic
419C24D4×D1311yescharacteristic
420C2×Q8—522no—
421C2×Q8—522no—
422C2×Q8—1041no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—21no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—81no—
435C22×C4—81no—
436C22×C4—81no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4—131no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4C2×Dic2612yes—
446C22×C4D4×D1311yescharacteristic
447C22×C4#612912yes—
448C22×C4C23×D1311yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—44no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8#612712yes—
462C4⋊C4—24no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—522no—
478C4⋊C4—522no—
479C4⋊C4—522no—
480C4⋊C4—522no—
481C4⋊C4—1041no—
482C4⋊C4—1041no—
483C4⋊C4—1041no—
484C4⋊C4C2×Dic2612yes—
485C4⋊C4C2×Dic2612yes—
486C4⋊C4#612712yes—
487C22⋊C4—134no—
488C22⋊C4—262no—
489C22⋊C4—522no—
490C22⋊C4—522no—
491C42—261no—
492C42—261no—
493C42—261no—
494C42—261no—
495C42—1041no—
496C42—1041no—
497C13#2599411yescharacteristic, complemented, Sylow
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23#8813212yes—
503C23#8816812yes—
504C23Q16×D1312yes—
505C23C2×D4×D1311yescharacteristic
506Q8—1044no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—84no—
526C2×C4—84no—
527C2×C4—132no—
528C2×C4—132no—
529C2×C4—261no—
530C2×C4—261no—
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—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—521no—
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#8813212yes—
552C2×C4C22×Dic2611yescharacteristic
553C2×C4C2×#612711yescharacteristic
554C2×C4C2×#612711yescharacteristic
555C2×C4C2×#612911yescharacteristic
556C2×C4#8825111yescharacteristic
557C2×C4#8825411yescharacteristic
558C8—22no—
559C8—41no—
560C8—521no—
561C8—521no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22#1171845514yes—
569C22C2×#8813211yescharacteristic
570C22#1171919511yescharacteristic
571C22#1171921211yescharacteristic
572C22#1171946211yescharacteristic
573C22C2×#8816811yescharacteristic
574C22#1171946711yescharacteristic
575C22C2×Q16×D1311yescharacteristic
576C4—22no—
577C4—42no—
578C4—42no—
579C4—42no—
580C4—81no—
581C4—262no—
582C4—262no—
583C4—521no—
584C4—521no—
585C4—1041no—
586C4—1041no—
587C4—1041no—
588C4—1041no—
589C4#1171917511yescharacteristic
590C4#1171920011yescharacteristic
591C4#1171920511yescharacteristic
592C4#1171921811yescharacteristic
593C2—24no—
594C2#1311851211yescharacteristic
595C2C2×#1171845511yescharacteristic
596C2#1312466311yescharacteristic
597C2#1312670811yescharacteristic
598C2#1312697311yescharacteristic
599C2#1312722611yescharacteristic
600C2#1312730211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#340C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC2×#340D13
hypocenterC13#25994
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
3. #13116402C2semidirect
4. #13116333C2semidirect
5. #13116331C2semidirect
6. #13116163C2semidirect
7. #13115782C2semidirect
8. #13115593C2semidirect
9. #13115431C2semidirect
10. #13115427C2semidirect
73. C2×C13×C4⋊C4Q8semidirect
381. C2×C4⋊C4Dic26semidirect
497. C13#25994semidirect

Maximal subgroups

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

subgroupindex
#131185322
#131177132
#131164022
#131163332
#131163312
#131161632
#131157822
#131155932
#131154312
#131154272
#131150242
#131150142
#131149262
#131148652
C2×C13×#3402
#2599413