Finite Group Databasebeta

← #15920610

Subgroups — #15920610

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#13118538C211yesmaximal, characteristic
2#13117711C211yesmaximal, characteristic
3#13116400C211yesmaximal, characteristic, complemented
4#13116329C211yesmaximal, characteristic, complemented
5#13116329C211yesmaximal, characteristic, complemented
6#13116165C211yesmaximal, characteristic, complemented
7#13115783C211yesmaximal, characteristic, complemented
8#13115595C211yesmaximal, characteristic, complemented
9#13115429C211yesmaximal, characteristic, complemented
10#13115429C211yesmaximal, characteristic, complemented
11#13115026C211yesmaximal, characteristic
12#13114927C211yesmaximal, characteristic
13#13114865C211yesmaximal, characteristic
14C2×#11718143C211yesmaximal, characteristic
15C13×#1850C211yesmaximal, characteristic
16C23×C8×C13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C2×#88132—21no—
20C2×#88123C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C4×C13×C22⋊C4C2211yescharacteristic
25#11718873C2211yescharacteristic
26#11718873C2211yescharacteristic
27C2×#88058C2211yescharacteristic
28C2×#88058C2211yescharacteristic
29C2×#88058C2211yescharacteristic
30C2×#88058C2211yescharacteristic
31#11718611—21no—
32#11718603—21no—
33C22⋊C4×Dic13—21no—
34#11718596C2211yescharacteristic
35C4×C4⋊Dic13C2211yescharacteristic
36C4×C4⋊Dic13C2211yescharacteristic
37#11718589C2211yescharacteristic
38#11718589C2211yescharacteristic
39#11718589C2211yescharacteristic
40#11718589C2211yescharacteristic
41#11718322—21no—
42#11718317—21no—
43#11718315—21no—
44#11718315—21no—
45C13×#336C2211yescharacteristic
46C13×#336C2211yescharacteristic
47#11718143C2211yescharacteristic
48#11718143C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×Dic13—21no—
61C23×Dic13—21no—
62C22×Dic26—21no—
63C22×C8×C13—22no—
64C22×C8×C13—22no—
65C22×C8×C13—41no—
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C2×C13×C22⋊C4D411yescharacteristic
71C2×C13×C22⋊C4D411yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—22no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—41no—
84C2×C4⋊Dic13Q814yescomplemented
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99#88132—44no—
100#88123—22no—
101#88123—41no—
102C13×C4⋊C8—22no—
103C13×C4⋊C8—41no—
104C13×C22⋊C8—22no—
105C13×#95D411yescharacteristic
106C13×#95D411yescharacteristic
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88058—22no—
116#88058—22no—
117#88058—41no—
118#88058—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×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×Q812yes—
131C22×C4×C13#4112yes—
132C22×C4×C13C2411yescharacteristic
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—24no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—42no—
143C22×Dic13—42no—
144C22×Dic13—81no—
145C22×Dic13—81no—
146C22×Dic13—81no—
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—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—44no—
162C2×C8×C13#4112yes—
163C13×C22⋊C4—22no—
164C13×C22⋊C4Q1614yes—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13—21no—
168C42×C13—21no—
169C22⋊Dic13—42no—
170C22⋊Dic13—42no—
171C4⋊Dic13—24no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—42no—
186C4⋊Dic13—42no—
187C4⋊Dic13—42no—
188C4⋊Dic13—81no—
189C4⋊Dic13C2×Q812yes—
190C4⋊Dic13C2×Q812yes—
191C4⋊Dic13#4112yes—
192#6101—42no—
193#6101—42no—
194#6101—81no—
195#6101—81no—
196C4×Dic13—81no—
197C4×Dic13—81no—
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#1850D1311yescharacteristic
210#1824—131no—
211#1808—131no—
212C2×#340—131no—
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—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13C22⋊Q812yes—
238C2×C4×C13C2×Q1612yes—
239C2×C4×C13C2×Q1612yes—
240C2×C4×C13C22×Q811yescharacteristic
241C2×C4×C13C2×#4111yescharacteristic
242C2×C4×C13C2×#4111yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13H(5,𝔽2)11yescharacteristic
245C2×C4×C132−1+411yescharacteristic
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
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×Dic13—84no—
271C2×Dic13—84no—
272Dic26—84no—
273C8×C13—22no—
274C8×C13—41no—
275C8×C13—41no—
276C8×C13—41no—
277C23×C8C2×D1311yescharacteristic
278C2×C4⋊Q8—131no—
279C2×C22⋊Q8—261no—
280C22×C4⋊C4—131no—
281C22×C4⋊C4—131no—
282C2×#107—131no—
283C2×#107—131no—
284C2×#107—131no—
285C2×#107—131no—
286C2×C4⋊C8C2×D1311yescharacteristic
287C2×C4⋊C8C2×D1311yescharacteristic
288C2×C22⋊C8C2×D1311yescharacteristic
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—261no—
305C4×C22⋊C4C2×D1311yescharacteristic
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#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#336C2×D1311yescharacteristic
319#336C2×D1311yescharacteristic
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—22no—
336C4×C13—22no—
337C4×C13—41no—
338C4×C13—41no—
339C4×C13#53311yescharacteristic
340C4×C13#54411yescharacteristic
341C4×C13#55111yescharacteristic
342C4×C13#55211yescharacteristic
343Dic13—42no—
344Dic13—42no—
345Dic13—42no—
346Dic13—81no—
347Dic13—81no—
348Dic13—81no—
349Dic13—81no—
350Dic13—81no—
351C22×Q8—261no—
352C23×C4—261no—
353C23×C4—261no—
354C23×C4C22×D1311yescharacteristic
355C22×C8—22no—
356C22×C8—22no—
357C22×C8—41no—
358C22×C8C22×D1311yescharacteristic
359C22×C8C22×D1311yescharacteristic
360C22×C8C22×D1311yescharacteristic
361C22×C8C22×D1311yescharacteristic
362C4⋊Q8—262no—
363C4⋊Q8—521no—
364C22⋊Q8—524no—
365C2×C4⋊C4—134no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—262no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—521no—
386C2×C22⋊C4—261no—
387C2×C22⋊C4—261no—
388C2×C22⋊C4D5211yescharacteristic
389C2×C22⋊C4D5211yescharacteristic
390C2×C42—261no—
391C2×C42—261no—
392C2×C42C22×D1311yescharacteristic
393C2×C42C22×D1311yescharacteristic
394#107—262no—
395#107—262no—
396#107—521no—
397#107—521no—
398C4⋊C8—22no—
399C4⋊C8—41no—
400C22⋊C8—22no—
401#95—261no—
402#95—261no—
403#95—261no—
404#95—261no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95D5211yescharacteristic
410#95D5211yescharacteristic
411C2×C13—24no—
412C2×C13#243811yescharacteristic
413C2×C13C2×#47711yescharacteristic
414C2×C13#308111yescharacteristic
415C2×C13#329911yescharacteristic
416C2×C13#331811yescharacteristic
417C2×C13#333811yescharacteristic
418C2×C13#334511yescharacteristic
419C24C2×D5211yescharacteristic
420C2×Q8—522no—
421C2×Q8—522no—
422C2×Q8—1041no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—261no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—264no—
431C22×C4—261no—
432C22×C4—261no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—522no—
437C22×C4—522no—
438C22×C4—1041no—
439C22×C4—1041no—
440C22×C4—1041no—
441C22×C4C2×D5211yescharacteristic
442C22×C4C2×D5211yescharacteristic
443C22×C4C2×D5211yescharacteristic
444C22×C4C2×D5211yescharacteristic
445C22×C4C2×D5211yescharacteristic
446C22×C4#612912yes—
447C22×C4Q8×D1312yes—
448C22×C4C23×D1311yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—44no—
461C2×C8#612912yes—
462C4⋊C4—132no—
463C4⋊C4—132no—
464C4⋊C4—132no—
465C4⋊C4—264no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
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—261no—
478C4⋊C4—261no—
479C4⋊C4—522no—
480C4⋊C4—522no—
481C4⋊C4—522no—
482C4⋊C4—522no—
483C4⋊C4—522no—
484C4⋊C4—1041no—
485C4⋊C4—1041no—
486C4⋊C4—1041no—
487C22⋊C4—22no—
488C22⋊C4—522no—
489C22⋊C4—522no—
490C22⋊C4Dic5214yes—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—1041no—
496C42—1041no—
497C13#2599411yescharacteristic, complemented, Sylow
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23#8815112yes—
503C23C2×Dic5212yes—
504C23#8816212yes—
505C23C22×D5211yescharacteristic
506Q8—1044no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—262no—
524C2×C4—262no—
525C2×C4—262no—
526C2×C4—521no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
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—1044no—
548C2×C4—1044no—
549C2×C4#8815112yes—
550C2×C4C2×Dic5212yes—
551C2×C4C2×Dic5212yes—
552C2×C4C2×#612911yescharacteristic
553C2×C4C2×#612911yescharacteristic
554C2×C4#8825111yescharacteristic
555C2×C4C2×Q8×D1311yescharacteristic
556C2×C4#41×D1311yescharacteristic
557C2×C4#8825711yescharacteristic
558C8—22no—
559C8—41no—
560C8—41no—
561C8—41no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22#1171851114yes—
569C22C2×#8815111yescharacteristic
570C22#1171925911yescharacteristic
571C22#1171926011yescharacteristic
572C22C22×Dic5211yescharacteristic
573C22C2×#8816211yescharacteristic
574C22#1171945611yescharacteristic
575C22#1171945711yescharacteristic
576C4—22no—
577C4—22no—
578C4—22no—
579C4—41no—
580C4—41no—
581C4—522no—
582C4—522no—
583C4—522no—
584C4—1041no—
585C4—1041no—
586C4—1041no—
587C4—1041no—
588C4—1041no—
589C4#1171929211yescharacteristic
590C4#1171932711yescharacteristic
591C4#1171932811yescharacteristic
592C4#1171935511yescharacteristic
593C2—24no—
594C2#1311851011yescharacteristic
595C2C2×#1171851111yescharacteristic
596C2#1312466811yescharacteristic
597C2#1312671311yescharacteristic
598C2#1312697911yescharacteristic
599C2#1312722911yescharacteristic
600C2#1312730811yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1850C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1850D13
hypocenterC13#25994
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
3. #13116400C2semidirect
4. #13116329C2semidirect
5. #13116329C2semidirect
6. #13116165C2semidirect
7. #13115783C2semidirect
8. #13115595C2semidirect
9. #13115429C2semidirect
10. #13115429C2semidirect
84. C2×C4⋊Dic13Q8semidirect
497. C13#25994semidirect

Maximal subgroups

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

subgroupindex
#131185382
#131177112
#131164002
#131163292
#131161652
#131157832
#131155952
#131154292
#131150262
#131149272
#131148652
C2×#117181432
C13×#18502
#2599413