Finite Group Databasebeta

← #15895351

Subgroups — #15895351

Order 3328.

1228 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718711C211yesmaximal, characteristic, complemented
2C2×#11718665C211yesmaximal, characteristic, complemented
3#13118201C211yesmaximal, characteristic
4#13115984C212yesmaximal, complemented
5#13115844C212yesmaximal, complemented
6#13115270C211yesmaximal, characteristic, complemented
7#13115177C212yesmaximal, complemented
8#13115143C212yesmaximal, complemented
9#13115134C211yesmaximal, characteristic
10#13114931C211yesmaximal, characteristic, complemented
11C2×C13×#552C211yesmaximal, characteristic
12C23×Dic26C2211yescharacteristic
13C13×#552—24no—
14C13×#552—24no—
15C2×C13×#126—21no—
16C2×C13×#125—21no—
17C2×C13×#125C2211yescharacteristic
18C2×C13×#123—21no—
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×C22⋊Q8C2211yescharacteristic
21C2×C4×Q8×C13C2211yescharacteristic
22C2×C4×D4×C13C2211yescharacteristic
23C2×C13×#117—21no—
24C2×C13×#117C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×#6107C2212yes—
27C2×#88178C2212yes—
28C22×#6099C2211yescharacteristic
29C2×#88075C2212yes—
30#11718881—21no—
31#11718873C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2212yes—
34#11718711—24no—
35#11718665—24no—
36#11718640—21no—
37C2×#88050C2212yes—
38C2×#88050C2212yes—
39C2×#88050C2212yes—
40#11718608—21no—
41#11718607—21no—
42#11718590C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45#11718121C2212yes—
46#11718116C2212yes—
47C22×Q8×C13C2311yescharacteristic
48C22×D4×C13D411yescharacteristic
49C23×C4×C13—21no—
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C23×Dic13—21no—
53C22×Dic26—22no—
54C22×Dic26—24no—
55C22×Dic26—22no—
56C22×Dic26—21no—
57C22×Dic26—42no—
58C22×Dic26C2312yes—
59C13×#126—28no—
60C13×#125—28no—
61C13×#125—22no—
62C13×#125—22no—
63C13×#123—28no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—22no—
67C13×C22⋊Q8D414yes—
68C4×Q8×C13—22no—
69C4×Q8×C13—22no—
70C4×D4×C13—22no—
71C4×D4×C13—22no—
72C13×#117—28no—
73C13×#117—22no—
74C13×#117D414yes—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4D411yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C4⋊C4C2311yescharacteristic
86C2×C13×C4⋊C4C2311yescharacteristic
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4—21no—
89C2×C13×C22⋊C4—21no—
90C2×C13×C22⋊C4D411yescharacteristic
91C2×C13×C22⋊C4D411yescharacteristic
92C2×C42×C13—21no—
93C2×C42×C13—21no—
94C2×C42×C13C2311yescharacteristic
95C2×C22⋊Dic13—22no—
96C2×C22⋊Dic13—21no—
97C2×#6107—24no—
98C2×#6107—24no—
99C2×#6107—42no—
100C2×C4⋊Dic13C2312yes—
101#88178—24no—
102#88178—42no—
103C2×#6101—22no—
104C2×#6099—22no—
105C2×#6099—42no—
106C22×#1055C2312yes—
107C22×#1055C2312yes—
108#88075—42no—
109#88071—22no—
110#88071—22no—
111#88071—21no—
112C22⋊#1055—22no—
113C22⋊#1055—42no—
114#88050—24no—
115#88050—24no—
116#88050—24no—
117#23983—131nomaximal, Sylow
118C24×C13C2×D411yescharacteristic
119C24×C13C2×D411yescharacteristic
120C2×Q8×C13—21no—
121C2×Q8×C13—22no—
122C2×Q8×C13—22no—
123C2×Q8×C13C2×D412yes—
124C2×D4×C13—22no—
125C2×D4×C13—22no—
126C2×D4×C13—41no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—24no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—42no—
139C22×C4×C13—42no—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D412yes—
145C22×C4×C13C2×D412yes—
146C22×C4×C13C2411yescharacteristic
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—44no—
150C22×Dic13—42no—
151C2×Dic26—28no—
152C2×Dic26—22no—
153C2×Dic26—22no—
154C2×Dic26—22no—
155C2×Dic26—22no—
156C2×Dic26—22no—
157C2×Dic26—48no—
158C2×Dic26—44no—
159C2×Dic26—44no—
160C2×Dic26—42no—
161C2×Dic26#4114yes—
162C13×C4⋊C4—24no—
163C13×C4⋊C4—24no—
164C13×C4⋊C4—24no—
165C13×C4⋊C4—24no—
166C13×C4⋊C4—24no—
167C13×C4⋊C4—24no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4C2×D412yes—
173C13×C4⋊C4C2×D412yes—
174C13×C4⋊C4C2×D412yes—
175C13×C22⋊C4—24no—
176C13×C22⋊C4—24no—
177C13×C22⋊C4—24no—
178C13×C22⋊C4—22no—
179C13×C22⋊C4—22no—
180C42×C13—24no—
181C42×C13—24no—
182C42×C13—21no—
183C42×C13—21no—
184C22⋊Dic13—44no—
185C22⋊Dic13—42no—
186#6107—48no—
187C4⋊Dic13—22no—
188C4⋊Dic13—22no—
189#6101—44no—
190#6099—44no—
191C2×#1055—22no—
192C2×#1055—22no—
193C2×#1055—22no—
194C2×#1055—22no—
195C2×#1055—22no—
196C2×#1055—22no—
197C2×#552D1311yescharacteristic
198C2×#451—131no—
199C2×#419—131no—
200#2409—131no—
201#2026—132no—
202#2001—132no—
203#1894—131no—
204#1878—132no—
205#1872—132no—
206#1870—131no—
207#1825—131no—
208C23×C13—21no—
209C23×C13—22no—
210C23×C13—22no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13—22no—
215C23×C13—22no—
216C23×C13#12012yes—
217C23×C13#13712yes—
218C23×C13C22×D411yescharacteristic
219Q8×C13—24no—
220Q8×C13—41no—
221Q8×C13—41no—
222D4×C13—44no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—24no—
227C2×C4×C13—21no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—22no—
238C2×C4×C13—48no—
239C2×C4×C13—42no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—42no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—42no—
248C2×C4×C13#12012yes—
249C2×C4×C13C22×D411yescharacteristic
250C2×C4×C13C22×D411yescharacteristic
251C2×C4×C13C2×#4112yes—
252C2×C4×C13H(5,𝔽2)12yes—
253C2×Dic13—24no—
254C2×Dic13—48no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260Dic26—24no—
261Dic26—24no—
262Dic26—48no—
263Dic26—42no—
264Dic26—42no—
265#1055—42no—
266#1055—42no—
267C23×Q8—131no—
268C22×Q16—132no—
269C22×M16—131no—
270#552—24no—
271#552—24no—
272C2×#126—21no—
273C2×#125—21no—
274C2×#125C2×D1311yescharacteristic
275C2×#123—21no—
276C2×C22⋊Q8—132no—
277C2×C22⋊Q8C2×D1311yescharacteristic
278C2×C22⋊Q8C2×D1311yescharacteristic
279C2×C4×Q8C2×D1311yescharacteristic
280C2×C4×D4C2×D1311yescharacteristic
281C2×#117—21no—
282C2×#117C2×D1311yescharacteristic
283C22×C4⋊C4C2×D1311yescharacteristic
284#451—264no—
285#419—264no—
286C2×#103—132no—
287C2×#103—132no—
288C2×#103—132no—
289C2×#103—132no—
290C2×C22⋊C8—131no—
291C2×C22⋊C8—132no—
292#395—261no—
293#393—261no—
294#391—132no—
295#386—261no—
296#385—261no—
297#380—131no—
298#340—132no—
299#340—132no—
300#340—132no—
301#336—132no—
302C22×C13—22no—
303C22×C13—22no—
304C22×C13—22no—
305C22×C13—22no—
306C22×C13—24no—
307C22×C13—41no—
308C22×C13—41no—
309C22×C13—42no—
310C22×C13—42no—
311C22×C13—42no—
312C22×C13C2×#12011yescharacteristic
313C22×C13#54612yes—
314C22×C13C2×#13711yescharacteristic
315C22×C13#57511yescharacteristic
316C22×C13#57812yes—
317C4×C13—22no—
318C4×C13—41no—
319C4×C13—42no—
320C4×C13—41no—
321C4×C13—42no—
322C4×C13—42no—
323C4×C13—41no—
324C4×C13—42no—
325C4×C13#52511yescharacteristic
326C4×C13#53511yescharacteristic
327C4×C13#54612yes—
328Dic13—44no—
329Dic13—82no—
330C22×Q8—132no—
331C22×Q8—264no—
332C22×Q8—261no—
333C22×Q8—262no—
334C22×Q8—262no—
335C22×Q8—522no—
336C22×Q8C22×D1311yescharacteristic
337C22×D4C22⋊D1311yescharacteristic
338C23×C4—21no—
339C23×C4—261no—
340C23×C4C22×D1311yescharacteristic
341C23×C4C22×D1311yescharacteristic
342C2×Q16—264no—
343C2×Q16—264no—
344C2×Q16—522no—
345C2×M16—262no—
346C2×M16—522no—
347C22×C8—132no—
348C22×C8—132no—
349#126—28no—
350#125—28no—
351#125—22no—
352#125—22no—
353#123—28no—
354C22⋊Q8—22no—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357C22⋊Q8—264no—
358C22⋊Q8—522no—
359C22⋊Q8C22⋊D1314yes—
360C4×Q8—22no—
361C4×Q8—22no—
362C4×D4—22no—
363C4×D4—22no—
364#117—28no—
365#117—22no—
366#117C22⋊D1314yes—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—132no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4C22⋊D1311yescharacteristic
378C2×C4⋊C4C22×D1311yescharacteristic
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—262no—
385C2×C22⋊C4—261no—
386C2×C22⋊C4C22⋊D1311yescharacteristic
387C2×C22⋊C4C22⋊D1311yescharacteristic
388C2×C42—21no—
389C2×C42—21no—
390C2×C42C22×D1311yescharacteristic
391#103—264no—
392#103—264no—
393#103—264no—
394#103—522no—
395C22⋊C8—262no—
396C22⋊C8—522no—
397#95—261no—
398#95—262no—
399#95—262no—
400C2×C13—42no—
401C2×C13—42no—
402C2×C13#240411yescharacteristic
403C2×C13#300711yescharacteristic
404C2×C13#301111yescharacteristic
405C2×C13#331212yes—
406C2×C13#332712yes—
407C24C2×C22⋊D1311yescharacteristic
408C24C2×C22⋊D1311yescharacteristic
409C2×Q8—21no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—134no—
413C2×Q8—268no—
414C2×Q8—262no—
415C2×Q8—262no—
416C2×Q8—262no—
417C2×Q8—262no—
418C2×Q8—262no—
419C2×Q8—524no—
420C2×Q8—528no—
421C2×Q8—524no—
422C2×Q8—522no—
423C2×Q8C2×C22⋊D1312yes—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—41no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—524no—
443C22×C4—522no—
444C22×C4C2×C22⋊D1311yescharacteristic
445C22×C4C2×C22⋊D1311yescharacteristic
446C22×C4C2×C22⋊D1311yescharacteristic
447C22×C4C2×C22⋊D1311yescharacteristic
448C22×C4C2×C22⋊D1312yes—
449C22×C4C2×C22⋊D1312yes—
450C22×C4C23×D1311yescharacteristic
451Q16—528no—
452M16—524no—
453C2×C8—262no—
454C2×C8—262no—
455C2×C8—262no—
456C2×C8—262no—
457C2×C8—262no—
458C2×C8—262no—
459C4⋊C4—24no—
460C4⋊C4—24no—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—262no—
470C4⋊C4—262no—
471C4⋊C4—524no—
472C4⋊C4C2×C22⋊D1312yes—
473C4⋊C4C2×C22⋊D1312yes—
474C4⋊C4C2×C22⋊D1312yes—
475C22⋊C4—24no—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—524no—
481C22⋊C4—522no—
482C42—24no—
483C42—24no—
484C42—21no—
485C42—21no—
486C13#2398311yescharacteristic, complemented, Sylow
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—21no—
495C23#8820512yes—
496C23#8820712yes—
497C23C22×C22⋊D1311yescharacteristic
498Q8—24no—
499Q8—41no—
500Q8—41no—
501Q8—264no—
502Q8—264no—
503Q8—528no—
504Q8—522no—
505Q8—522no—
506D4—44no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—48no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—264no—
533C2×C4—528no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4—522no—
538C2×C4—522no—
539C2×C4#8820712yes—
540C2×C4#41×D1312yes—
541C2×C4#8825612yes—
542C2×C4C22×C22⋊D1311yescharacteristic
543C2×C4C22×C22⋊D1311yescharacteristic
544C8—522no—
545C8—522no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—24no—
551C22—41no—
552C22—42no—
553C22—42no—
554C22—41no—
555C22—42no—
556C22#1171952711yescharacteristic
557C22C2×#8820511yescharacteristic
558C22#1171953412yes—
559C22#1171954312yes—
560C22C2×#8820711yescharacteristic
561C4—22no—
562C4—41no—
563C4—42no—
564C4—42no—
565C4—41no—
566C4—42no—
567C4—41no—
568C4—42no—
569C4—524no—
570C4—1042no—
571C4#1171953311yescharacteristic
572C4#1171953412yes—
573C4#1171953511yescharacteristic
574C2—42no—
575C2—42no—
576C2#1311815111yescharacteristic
577C2#1312409611yescharacteristic
578C2#1312413111yescharacteristic
579C2#1312688112yes—
580C2#1312709812yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#552C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenterC2×#552D13
hypocenterC13#23983
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#11718711C2semidirect
2. C2×#11718665C2semidirect
4. #13115984C2semidirect
5. #13115844C2semidirect
6. #13115270C2semidirect
7. #13115177C2semidirect
8. #13115143C2semidirect
10. #13114931C2semidirect
486. C13#23983semidirect

Maximal subgroups

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

subgroupindex
C2×#117187112
C2×#117186652
#131182012
#131159842
#131158442
#131152702
#131151772
#131151432
#131151342
#131149312
C2×C13×#5522
#2398313