Finite Group Databasebeta

← #15916581

Subgroups — #15916581

Order 3328.

1116 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718721C211yesmaximal, characteristic, complemented
2C2×#11718754C211yesmaximal, characteristic, complemented
3#13120602C211yesmaximal, characteristic, complemented
4#13115844C212yesmaximal, complemented
5#13115839C212yesmaximal
6#13115810C211yesmaximal, characteristic, complemented
7#13115648C211yesmaximal, characteristic, complemented
8#13115177C212yesmaximal, complemented
9#13115170C212yesmaximal, complemented
10#13114602C211yesmaximal, characteristic, complemented
11C2×C13×#542C211yesmaximal, characteristic
12C13×#542—24no—
13C13×#542—24no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#126—21no—
16C2×C13×#124—21no—
17C2×C13×#124C2211yescharacteristic
18C2×C13×#123—21no—
19C2×C13×C22⋊Q8—21no—
20C2×C13×C22⋊Q8C2211yescharacteristic
21C2×C13×#121C2211yescharacteristic
22C2×C4×Q8×C13C2211yescharacteristic
23C2×C4×D4×C13C2211yescharacteristic
24C2×C13×#117C2211yescharacteristic
25C22×#6107C2212yes—
26C22×#6105C2212yes—
27C2×#88178C2212yes—
28C2×#88123C2211yescharacteristic
29C2×#88075C2212yes—
30C2×#88072C2212yes—
31C2×C22⋊#1055C2212yes—
32#11718754—24no—
33#11718721—24no—
34#11718644—21no—
35#11718644—21no—
36C2×#88050C2212yes—
37C2×#88050C2212yes—
38#11718614—21no—
39#11718614—21no—
40#11718597C2211yescharacteristic
41#11718590C2212yes—
42C2×#88043C2211yescharacteristic
43C2×C4×#1055C2211yescharacteristic
44#11718121C2212yes—
45#11718121C2212yes—
46#11718116C2212yes—
47C22×Q8×C13—21no—
48C22×Q8×C13C2311yescharacteristic
49C22×D4×C13—21no—
50C22×D4×C13C2311yescharacteristic
51C23×C4×C13—21no—
52C23×C4×C13C2311yescharacteristic
53C22×Dic26C2312yes—
54C13×C4⋊Q8—22no—
55C13×C4⋊Q8D414yes—
56C13×#126—28no—
57C13×#124—28no—
58C13×#124—22no—
59C13×#124D414yes—
60C13×#123—28no—
61C13×C22⋊Q8—28no—
62C13×C22⋊Q8—22no—
63C13×C22⋊Q8—22no—
64C13×#121—22no—
65C13×#121—22no—
66C4×Q8×C13—22no—
67C4×Q8×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C13×#117—22no—
71C13×#117—22no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C42×C13—21no—
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×C22⋊Dic13—22no—
90C2×#6107—24no—
91C2×#6107—24no—
92C2×#6107—42no—
93C2×#6105—24no—
94C2×#6105—24no—
95C2×#6105—42no—
96C2×C4⋊Dic13—21no—
97C2×C4⋊Dic13—21no—
98C2×C4⋊Dic13C2312yes—
99#88178—42no—
100#88178—42no—
101C2×#6101—22no—
102C22×#1055C2312yes—
103C22×#1055C2312yes—
104#88123—22no—
105#88123—22no—
106#88075—42no—
107#88072—42no—
108#88071—22no—
109#88071—22no—
110#88071—21no—
111#88071—21no—
112C22⋊#1055—24no—
113#88050—24no—
114#88050—24no—
115#88043—22no—
116C4×#1055—22no—
117#25613—131nomaximal, Sylow
118C24×C13—21no—
119C24×C13C2×D411yescharacteristic
120C2×Q8×C13—24no—
121C2×Q8×C13—21no—
122C2×Q8×C13—22no—
123C2×Q8×C13—22no—
124C2×Q8×C13—82no—
125C2×Q8×C13C2×D412yes—
126C2×D4×C13—24no—
127C2×D4×C13—21no—
128C2×D4×C13—22no—
129C2×D4×C13—22no—
130C2×D4×C13—82no—
131C2×D4×C13C2×D412yes—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—24no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—82no—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2411yescharacteristic
147C22×Dic13—22no—
148C22×Dic13—22no—
149C2×Dic26—22no—
150C2×Dic26—22no—
151C2×Dic26—22no—
152C2×Dic26—22no—
153C2×Dic26—22no—
154C2×Dic26—22no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—24no—
157C13×C4⋊C4—24no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4C2×D412yes—
163C13×C4⋊C4C2×D412yes—
164C13×C22⋊C4—24no—
165C13×C22⋊C4—24no—
166C13×C22⋊C4—24no—
167C13×C22⋊C4—24no—
168C13×C22⋊C4—24no—
169C13×C22⋊C4—22no—
170C13×C22⋊C4—22no—
171C42×C13—24no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13C2×D412yes—
175C42×C13C2×D412yes—
176C22⋊Dic13—44no—
177#6107—48no—
178#6105—48no—
179C4⋊Dic13—22no—
180C4⋊Dic13—22no—
181C4⋊Dic13—42no—
182C4⋊Dic13—42no—
183#6101—44no—
184C2×#1055—22no—
185C2×#1055—22no—
186C2×#1055—22no—
187C2×#1055—22no—
188C2×#1055—22no—
189C2×#1055#4114yes—
190C2×#542D1311yescharacteristic
191C2×#497—131no—
192C2×#487—131no—
193#2621—131no—
194#2001—132no—
195#2000—132no—
196#1993—131no—
197#1958—131no—
198#1878—132no—
199#1877—132no—
200#1750—131no—
201C23×C13—21no—
202C23×C13—22no—
203C23×C13—21no—
204C23×C13—21no—
205C23×C13—22no—
206C23×C13—22no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13C22×D411yescharacteristic
212Q8×C13—24no—
213Q8×C13—42no—
214Q8×C13—84no—
215D4×C13—24no—
216D4×C13—42no—
217D4×C13—84no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—21no—
221C2×C4×C13—22no—
222C2×C4×C13—21no—
223C2×C4×C13—22no—
224C2×C4×C13—21no—
225C2×C4×C13—22no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—84no—
237C2×C4×C13#12012yes—
238C2×C4×C13#12012yes—
239C2×C4×C13C22×D411yescharacteristic
240C2×C4×C13C22×D411yescharacteristic
241C2×C4×C13C2×#4112yes—
242C2×C4×C13H(5,𝔽2)12yes—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13—42no—
249Dic26—42no—
250Dic26—42no—
251Dic26—42no—
252Dic26—42no—
253#1055—24no—
254#1055—42no—
255C22×Q16—132no—
256C22×SD16—132no—
257#542—24no—
258#542—24no—
259C2×C4⋊Q8—131no—
260C2×C4⋊Q8C2×D1311yescharacteristic
261C2×#126—21no—
262C2×#124—21no—
263C2×#124C2×D1311yescharacteristic
264C2×#123—21no—
265C2×C22⋊Q8—21no—
266C2×C22⋊Q8—132no—
267C2×C22⋊Q8C2×D1311yescharacteristic
268C2×#121C2×D1311yescharacteristic
269C2×C4×Q8C2×D1311yescharacteristic
270C2×C4×D4C2×D1311yescharacteristic
271C2×#117C2×D1311yescharacteristic
272#497—264no—
273#487—264no—
274C2×#103—132no—
275C2×#103—132no—
276C2×#103—132no—
277C2×#102—132no—
278C2×C22⋊C8—132no—
279C2×#97—131no—
280C2×C4×C8—131no—
281#398—261no—
282#398—261no—
283#397—261no—
284#397—261no—
285#391—132no—
286#382—131no—
287#340—132no—
288#340—132no—
289#336—132no—
290C22×C13—42no—
291C22×C13—41no—
292C22×C13—42no—
293C22×C13—42no—
294C22×C13—42no—
295C22×C13—41no—
296C22×C13—41no—
297C22×C13—42no—
298C22×C13—82no—
299C22×C13—82no—
300C22×C13C2×#12011yescharacteristic
301C22×C13#53211yescharacteristic
302C22×C13#53511yescharacteristic
303C22×C13#57712yes—
304C22×C13#57812yes—
305C4×C13—22no—
306C4×C13—22no—
307C4×C13—41no—
308C4×C13—42no—
309C4×C13—41no—
310C4×C13—42no—
311C4×C13—42no—
312C4×C13—41no—
313C4×C13#54612yes—
314C4×C13#55012yes—
315Dic13—82no—
316Dic13—82no—
317C22×Q8—21no—
318C22×Q8—132no—
319C22×Q8C22×D1311yescharacteristic
320C22×D4—21no—
321C22×D4C22×D1311yescharacteristic
322C23×C4—21no—
323C23×C4C22×D1311yescharacteristic
324C2×Q16—264no—
325C2×Q16—264no—
326C2×Q16—522no—
327C2×SD16—264no—
328C2×SD16—264no—
329C2×SD16—522no—
330C22×C8—132no—
331C22×C8—132no—
332C4⋊Q8—22no—
333C4⋊Q8—262no—
334C4⋊Q8—262no—
335C4⋊Q8C22⋊D1314yes—
336#126—28no—
337#124—28no—
338#124—22no—
339#124C22⋊D1314yes—
340#123—28no—
341C22⋊Q8—28no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—522no—
345C22⋊Q8—522no—
346#121—22no—
347#121—22no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×D4—22no—
351C4×D4—22no—
352#117—22no—
353#117—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—132no—
358C2×C4⋊C4—262no—
359C2×C4⋊C4—261no—
360C2×C4⋊C4—261no—
361C2×C4⋊C4C22⋊D1311yescharacteristic
362C2×C4⋊C4C22⋊D1311yescharacteristic
363C2×C4⋊C4C22×D1311yescharacteristic
364C2×C4⋊C4C22×D1311yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—262no—
371C2×C22⋊C4C22⋊D1311yescharacteristic
372C2×C22⋊C4C22⋊D1311yescharacteristic
373C2×C42—21no—
374C2×C42C22×D1311yescharacteristic
375C2×C42C22×D1311yescharacteristic
376#103—264no—
377#103—264no—
378#103—522no—
379#102—522no—
380C22⋊C8—264no—
381#97—262no—
382C4×C8—262no—
383#95—261no—
384#95—261no—
385#95—262no—
386#95—262no—
387C2×C13—81no—
388C2×C13—82no—
389C2×C13#243111yescharacteristic
390C2×C13#300911yescharacteristic
391C2×C13#301111yescharacteristic
392C2×C13#317812yes—
393C2×C13#322512yes—
394C24—21no—
395C24C2×C22⋊D1311yescharacteristic
396C2×Q8—24no—
397C2×Q8—21no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—82no—
401C2×Q8—262no—
402C2×Q8—262no—
403C2×Q8—262no—
404C2×Q8—262no—
405C2×Q8—262no—
406C2×Q8—262no—
407C2×Q8C2×C22⋊D1312yes—
408C2×D4—24no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—21no—
412C2×D4—82no—
413C2×D4C2×C22⋊D1312yes—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—82no—
423C22×C4—262no—
424C22×C4—262no—
425C22×C4C2×C22⋊D1311yescharacteristic
426C22×C4C2×C22⋊D1311yescharacteristic
427C22×C4C2×C22⋊D1311yescharacteristic
428C22×C4C2×C22⋊D1311yescharacteristic
429C22×C4C2×C22⋊D1311yescharacteristic
430C22×C4C23×D1311yescharacteristic
431Q16—528no—
432SD16—528no—
433C2×C8—134no—
434C2×C8—262no—
435C2×C8—262no—
436C2×C8—262no—
437C2×C8—262no—
438C2×C8—262no—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—24no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—262no—
447C4⋊C4—262no—
448C4⋊C4—524no—
449C4⋊C4—522no—
450C4⋊C4—522no—
451C4⋊C4C2×C22⋊D1312yes—
452C4⋊C4C2×C22⋊D1312yes—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—524no—
461C42—24no—
462C42—21no—
463C42—21no—
464C42C2×C22⋊D1312yes—
465C42C2×C22⋊D1312yes—
466C13#2561311yescharacteristic, complemented, Sylow
467C23—21no—
468C23—21no—
469C23—22no—
470C23—22no—
471C23—21no—
472C23—22no—
473C23—41no—
474C23—41no—
475C23—42no—
476C23—42no—
477C23C22×C22⋊D1311yescharacteristic
478Q8—24no—
479Q8—42no—
480Q8—84no—
481Q8—522no—
482Q8—522no—
483Q8—522no—
484Q8—522no—
485D4—24no—
486D4—42no—
487D4—84no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—84no—
507C2×C4—522no—
508C2×C4—522no—
509C2×C4—522no—
510C2×C4—522no—
511C2×C4—522no—
512C2×C4—522no—
513C2×C4#8820712yes—
514C2×C4#8820712yes—
515C2×C4#41×D1312yes—
516C2×C4#8825612yes—
517C2×C4C22×C22⋊D1311yescharacteristic
518C2×C4C22×C22⋊D1311yescharacteristic
519C8—264no—
520C8—522no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—41no—
528C22—42no—
529C22—82no—
530C22—82no—
531C22#1171953511yescharacteristic
532C22#1171953711yescharacteristic
533C22#1171954112yes—
534C22#1171954312yes—
535C22C2×#8820711yescharacteristic
536C4—22no—
537C4—22no—
538C4—41no—
539C4—42no—
540C4—42no—
541C4—41no—
542C4—41no—
543C4—42no—
544C4—1042no—
545C4—1042no—
546C4#1171953412yes—
547C4#1171953912yes—
548C2—81no—
549C2—82no—
550C2#1311845111yescharacteristic
551C2#1312411311yescharacteristic
552C2#1312413111yescharacteristic
553C2#1312549812yes—
554C2#1312593912yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#542C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenterC2×#542D13
hypocenterC13#25613
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#11718721C2semidirect
2. C2×#11718754C2semidirect
3. #13120602C2semidirect
4. #13115844C2semidirect
6. #13115810C2semidirect
7. #13115648C2semidirect
8. #13115177C2semidirect
9. #13115170C2semidirect
10. #13114602C2semidirect
466. C13#25613semidirect

Maximal subgroups

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

subgroupindex
C2×#117187212
C2×#117187542
#131206022
#131158442
#131158392
#131158102
#131156482
#131151772
#131151702
#131146022
C2×C13×#5422
#2561313