Finite Group Databasebeta

← #16792485

Subgroups — #16792485

Order 3328.

1074 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130024C212yesmaximal
2#13130024C212yesmaximal
3#13130023C212yesmaximal
4#13130022C212yesmaximal
5#13130021C211yesmaximal, characteristic
6#13130021C212yesmaximal
7#13130013C211yesmaximal, characteristic
8#13130011C212yesmaximal
9D13×#400C211yesmaximal, characteristic
10C22×C4⋊#261C2211yescharacteristic
11C22×C4⋊#261C2211yescharacteristic
12C22×C4⋊#261C2212yes—
13C22×C4⋊#261C2212yes—
14C22×C4×#261C2211yescharacteristic
15C2×C4⋊C4×D13C2211yescharacteristic
16C2×C4⋊C4×D13C2211yescharacteristic
17C2×(C2×#261)⋊C4C2212yes—
18C2×(C2×#261)⋊C4C2212yes—
19C2×(C2×#261)⋊C4C2212yes—
20C2×(C2×#261)⋊C4C2212yes—
21C2×(C2×#261)⋊C4C2212yes—
22C2×(C2×#261)⋊C4C2212yes—
23C2×(C2×#261)⋊C4C2212yes—
24C2×(C2×#261)⋊C4C2212yes—
25C2×(C2×#261)⋊C4C2211yescharacteristic
26C2×(C2×#261)⋊C4C2212yes—
27C2×(C2×#261)⋊C4C2212yes—
28C13×#400C411yescharacteristic, complemented
29#11718647C411yescharacteristic, complemented
30#11718643C411yescharacteristic, complemented
31D13×#95C2212yes—
32D13×#95C2211yescharacteristic
33D13×#95C2212yes—
34#11718321C412yescomplemented
35#11718320C411yescharacteristic, complemented
36#11718319C412yescomplemented
37C23×#261C2312yes—
38C23×#261C2312yes—
39C23×#261C2312yes—
40C23×#261C2312yes—
41C22×C4×D13C2311yescharacteristic
42C22×C4×D13C2311yescharacteristic
43C22×C4×D13C2312yes—
44C22×C4×D13C2312yes—
45C22×C4×D13C2311yescharacteristic
46C2×C4⋊#261—22no—
47C2×C4⋊#261—41no—
48C2×C4⋊#261—41no—
49C2×C4⋊#261—42no—
50C2×C4⋊#261—42no—
51C2×C4⋊#261—42no—
52C2×C4⋊#261—42no—
53C2×C4⋊#261—42no—
54C2×C4⋊#261—42no—
55C2×C4⋊#261—41no—
56C2×C4⋊#261—42no—
57C2×C4×#261—41no—
58C2×C4×#261—41no—
59C2×C4×#261Q814yes—
60C2×C13×C4⋊C4C2×C411yescharacteristic
61C2×C13×C4⋊C4C2×C411yescharacteristic
62C2×C4⋊Dic13C2×C411yescharacteristic
63C2×C4⋊Dic13C2×C411yescharacteristic
64C2×#6101C2×C411yescharacteristic
65C2×#6101C2×C412yes—
66C2×#6101C2×C411yescharacteristic
67C4⋊C4×D13—41no—
68C4⋊C4×D13—41no—
69C4⋊C4×D13—41no—
70C4⋊C4×D13—41no—
71(C2×#261)⋊C4—24no—
72(C2×#261)⋊C4—42no—
73(C2×#261)⋊C4—42no—
74(C2×#261)⋊C4—42no—
75(C2×#261)⋊C4—41no—
76(C2×#261)⋊C4—42no—
77(C2×#261)⋊C4—42no—
78(C2×#261)⋊C4—42no—
79(C2×#261)⋊C4—42no—
80(C2×#261)⋊C4—42no—
81(C2×#261)⋊C4—42no—
82C13×#95C2×C412yes—
83C13×#95C2×C411yescharacteristic
84C13×#95C2×C412yes—
85#88071C2×C412yes—
86#88071C2×C412yes—
87#88071C2×C412yes—
88#88071C2×C412yes—
89#88071C2×C412yes—
90#88071C2×C412yes—
91#88071C2×C412yes—
92#88071C2×C411yescharacteristic
93#14639—131nomaximal, Sylow
94C23×D13C2411yescharacteristic
95C22×#261—22no—
96C22×#261—22no—
97C22×#261—22no—
98C22×#261—22no—
99C22×#261—22no—
100C22×#261—22no—
101C22×#261—22no—
102C22×#261—22no—
103C22×#261—22no—
104C22×#261—22no—
105C22×#261—22no—
106C22×#261—22no—
107C22×#261—22no—
108C22×#261—22no—
109C22×#261—22no—
110C22×#261—22no—
111C22×#261—22no—
112C22×#261—22no—
113C22×#261—22no—
114C22×#261—22no—
115C22×#261—22no—
116C22×#261—22no—
117C22×#261—22no—
118C22×#261—22no—
119C22×#261—22no—
120C22×#261—22no—
121C22×#261—22no—
122C22×#261C2×Q814yes—
123C22×C4×C13C22×C412yes—
124C22×C4×C13C22×C412yes—
125C22×C4×C13C22×C411yescharacteristic
126C22×C4×C13C22×C411yescharacteristic
127C22×C4×C13C22×C411yescharacteristic
128C22×Dic13C22×C412yes—
129C22×Dic13C22×C412yes—
130C22×Dic13C22×C411yescharacteristic
131C22×Dic13C22×C411yescharacteristic
132C22×Dic13C22×C411yescharacteristic
133C2×C4×D13—21no—
134C2×C4×D13—21no—
135C2×C4×D13—21no—
136C2×C4×D13—21no—
137C2×C4×D13—22no—
138C2×C4×D13—21no—
139C2×C4×D13—22no—
140C2×C4×D13—22no—
141C2×C4×D13—22no—
142C2×C4×D13—22no—
143C2×C4×D13—22no—
144C2×C4×D13—22no—
145C2×C4×D13—22no—
146C2×C4×D13—21no—
147C2×C4×D13—21no—
148C2×C4×D13—21no—
149C2×C4×D13—22no—
150C2×C4×D13—22no—
151C2×C4×D13—22no—
152C2×C4×D13—22no—
153C2×C4×D13—22no—
154C2×C4×D13—22no—
155C2×C4×D13—22no—
156C2×C4×D13—22no—
157C2×C4×D13C2×Q812yes—
158C2×C4×D13#4112yes—
159C4⋊#261—44no—
160C4⋊#261—44no—
161C4⋊#261—48no—
162C4⋊#261—48no—
163C4×#261—44no—
164C13×C4⋊C4—41no—
165C13×C4⋊C4—41no—
166C4⋊Dic13—41no—
167C4⋊Dic13—41no—
168#6101—41no—
169#6101—41no—
170#6101—42no—
171C2×#400—131no—
172#1444—132no—
173#1444—132no—
174#1443—132no—
175#1442—132no—
176#1441—131no—
177#1441—132no—
178C4⋊#95—131no—
179#1434—132no—
180C23×C13C23×C411yescharacteristic
181C22×D13C22×Q811yescharacteristic
182C22×D13C2×#4111yescharacteristic
183C22×D13H(5,𝔽2)11yescharacteristic
184C22×D13H(5,𝔽2)11yescharacteristic
185C22×D13H(5,𝔽2)11yescharacteristic
186C22×D13H(5,𝔽2)12yes—
187C22×D13H(5,𝔽2)12yes—
188C22×D132−1+411yescharacteristic
189C22×D132−1+412yes—
190C22×D132−1+412yes—
191C2×#261—24no—
192C2×#261—24no—
193C2×#261—24no—
194C2×#261—42no—
195C2×#261—42no—
196C2×#261—42no—
197C2×#261—42no—
198C2×#261—42no—
199C2×#261—42no—
200C2×#261—42no—
201C2×#261—42no—
202C2×#261—42no—
203C2×#261—42no—
204C2×#261—42no—
205C2×#261—42no—
206C2×#261—42no—
207C2×#261—42no—
208C2×#261—42no—
209C2×#261—42no—
210C2×#261—42no—
211C2×#261—42no—
212C2×#261—42no—
213C2×#261—42no—
214C2×#261—42no—
215C2×#261—42no—
216C2×#261—42no—
217C2×#261—42no—
218C2×#261—42no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
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—22no—
231C2×C4×C13C4×Q812yes—
232C2×Dic13—21no—
233C2×Dic13—21no—
234C2×Dic13—21no—
235C2×Dic13—21no—
236C2×Dic13—22no—
237C2×Dic13—22no—
238C2×Dic13—22no—
239C2×Dic13—22no—
240C2×Dic13—22no—
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—22no—
244C2×Dic13C4×Q812yes—
245C4×D13—22no—
246C4×D13—22no—
247C4×D13—22no—
248C4×D13—22no—
249C4×D13—41no—
250C4×D13—42no—
251C4×D13—41no—
252C4×D13—42no—
253C4×D13—42no—
254C4×D13—42no—
255C4×D13—42no—
256C4×D13—42no—
257C4×D13—41no—
258C4×D13—41no—
259C4×D13—42no—
260C4×D13—42no—
261C4×D13—42no—
262C4×D13—42no—
263C22×C4⋊C4—131no—
264C22×C4⋊C4—131no—
265C22×C4⋊C4—131no—
266C22×C4⋊C4—131no—
267C22×C4⋊C4—132no—
268C22×C4⋊C4—132no—
269C22×C42—131no—
270#400—131no—
271#400—131no—
272#400—132no—
273#400—131no—
274#400—132no—
275#400#26111yescharacteristic, complemented
276C2×#95—132no—
277C2×#95—131no—
278C2×#95—132no—
279C2×#95—132no—
280C2×#95—132no—
281C2×#95—132no—
282C2×#95—132no—
283C2×#95—132no—
284C2×#95—132no—
285C2×#95—132no—
286C2×#95—132no—
287C2×#95—131no—
288C2×#95—132no—
289C2×#95—132no—
290C22×C13C2×C4×Q811yescharacteristic
291C22×C13#51811yescharacteristic
292C22×C13#52011yescharacteristic
293C22×C13#52012yes—
294C22×C13#52012yes—
295C2×D13#53811yescharacteristic
296C2×D13#53911yescharacteristic
297C2×D13#54012yes—
298C2×D13#54112yes—
299C2×D13#54311yescharacteristic
300C2×D13#54412yes—
301C2×D13#54412yes—
302C2×D13#54411yescharacteristic
303C2×D13#56012yes—
304C2×D13#56011yescharacteristic
305C2×D13H(3,𝔽4)11yescharacteristic
306C2×D13#56212yes—
307C2×D13#56212yes—
308C2×D13#56312yes—
309C2×D13#56311yescharacteristic
310C2×D13#56311yescharacteristic
311C2×D13#56312yes—
312C2×D13#56312yes—
313#261—44no—
314#261—82no—
315#261—82no—
316#261—82no—
317C4×C13—22no—
318C4×C13—41no—
319C4×C13—41no—
320C4×C13—42no—
321C4×C13—42no—
322Dic13—22no—
323Dic13—41no—
324Dic13—41no—
325Dic13—42no—
326Dic13—42no—
327C23×C4—131no—
328C23×C4—132no—
329C23×C4—131no—
330C23×C4—132no—
331C23×C4—131no—
332C23×C4—132no—
333C23×C4—132no—
334C23×C4—132no—
335C23×C4—132no—
336C2×C4⋊C4—131no—
337C2×C4⋊C4—131no—
338C2×C4⋊C4—132no—
339C2×C4⋊C4—131no—
340C2×C4⋊C4—131no—
341C2×C4⋊C4—262no—
342C2×C4⋊C4—521no—
343C2×C4⋊C4—521no—
344C2×C4⋊C4—521no—
345C2×C4⋊C4—521no—
346C2×C4⋊C4—521no—
347C2×C4⋊C4—521no—
348C2×C4⋊C4—522no—
349C2×C4⋊C4—522no—
350C2×C4⋊C4—522no—
351C2×C4⋊C4—522no—
352C2×C4⋊C4—522no—
353C2×C4⋊C4—522no—
354C2×C4⋊C4—521no—
355C2×C4⋊C4—522no—
356C2×C4⋊C4C2×#26111yescharacteristic
357C2×C4⋊C4C2×#26111yescharacteristic
358C2×C42—134no—
359C2×C42—521no—
360C2×C42—521no—
361#95—132no—
362#95—132no—
363#95—131no—
364#95—132no—
365#95—132no—
366#95—132no—
367#95—132no—
368#95—132no—
369#95—264no—
370#95—522no—
371#95—522no—
372#95—522no—
373#95—522no—
374#95—522no—
375#95—522no—
376#95—522no—
377#95—521no—
378#95—522no—
379#95—522no—
380#95C2×#26111yescharacteristic
381#95C2×#26112yes—
382#95C2×#26112yes—
383C2×C13#232911yescharacteristic
384C2×C13#233012yes—
385C2×C13#237611yescharacteristic
386C2×C13#237911yescharacteristic
387C2×C13#238312yes—
388D13#282811yescharacteristic
389D13#283311yescharacteristic
390D13#283612yes—
391D13#284112yes—
392D13#284311yescharacteristic
393D13#284411yescharacteristic
394C24—131no—
395C22×C4—131no—
396C22×C4—132no—
397C22×C4—132no—
398C22×C4—134no—
399C22×C4—132no—
400C22×C4—131no—
401C22×C4—132no—
402C22×C4—131no—
403C22×C4—261no—
404C22×C4—261no—
405C22×C4—261no—
406C22×C4—261no—
407C22×C4—262no—
408C22×C4—261no—
409C22×C4—262no—
410C22×C4—262no—
411C22×C4—262no—
412C22×C4—262no—
413C22×C4—262no—
414C22×C4—262no—
415C22×C4—262no—
416C22×C4—261no—
417C22×C4—261no—
418C22×C4—261no—
419C22×C4—262no—
420C22×C4—262no—
421C22×C4—262no—
422C22×C4—262no—
423C22×C4—262no—
424C22×C4—262no—
425C22×C4—262no—
426C22×C4—262no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—262no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—262no—
437C22×C4—262no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—262no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—262no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4C22×#26112yes—
455C22×C4C22×#26111yescharacteristic
456C22×C4C22×#26112yes—
457C22×C4C22×#26111yescharacteristic
458C22×C4C22×#26111yescharacteristic
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—521no—
462C4⋊C4—521no—
463C4⋊C4—522no—
464C4⋊C4—521no—
465C4⋊C4—521no—
466C4⋊C4—524no—
467C4⋊C4—524no—
468C4⋊C4—528no—
469C4⋊C4—528no—
470C42—524no—
471C13#1463911yescharacteristic, complemented, Sylow
472C23—131no—
473C23—131no—
474C23—131no—
475C23—131no—
476C23—131no—
477C23—132no—
478C23—132no—
479C23—131no—
480C23—132no—
481C23—132no—
482C23C23×#26111yescharacteristic
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—132no—
496C2×C4—262no—
497C2×C4—262no—
498C2×C4—262no—
499C2×C4—262no—
500C2×C4—261no—
501C2×C4—261no—
502C2×C4—264no—
503C2×C4—264no—
504C2×C4—264no—
505C2×C4—261no—
506C2×C4—261no—
507C2×C4—262no—
508C2×C4—262no—
509C2×C4—262no—
510C2×C4—262no—
511C2×C4—262no—
512C2×C4—262no—
513C2×C4—262no—
514C2×C4—262no—
515C2×C4—521no—
516C2×C4—522no—
517C2×C4—522no—
518C2×C4—521no—
519C2×C4—522no—
520C2×C4—522no—
521C2×C4—521no—
522C2×C4—521no—
523C2×C4—522no—
524C2×C4—522no—
525C2×C4—522no—
526C2×C4—522no—
527C2×C4—522no—
528C2×C4—522no—
529C2×C4—522no—
530C2×C4—522no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4—522no—
538C2×C4—522no—
539C2×C4—522no—
540C2×C4—522no—
541C2×C4—522no—
542C2×C4—522no—
543C2×C4—522no—
544C2×C4—522no—
545C2×C4—522no—
546C2×C4—522no—
547C2×C4—522no—
548C2×C4—522no—
549C2×C4—522no—
550C2×C4—522no—
551C2×C4—522no—
552C2×C4—522no—
553C2×C4—522no—
554C2×C4Q8×#26112yes—
555C22—131no—
556C22—131no—
557C22—131no—
558C22—131no—
559C22—132no—
560C22—132no—
561C22—132no—
562C22—132no—
563C22—131no—
564C22—132no—
565C22—131no—
566C22—131no—
567C22—132no—
568C22—131no—
569C22—132no—
570C22—132no—
571C22—132no—
572C22—132no—
573C22#1171962311yescharacteristic
574C22C2×Q8×#26111yescharacteristic
575C22#1171963111yescharacteristic
576C22#1171963112yes—
577C22#1171963112yes—
578C4—22no—
579C4—41no—
580C4—41no—
581C4—42no—
582C4—42no—
583C4—262no—
584C4—524no—
585C4—521no—
586C4—521no—
587C4—522no—
588C4—522no—
589C4—1042no—
590C4—1042no—
591C4—1042no—
592C2—132no—
593C2—131no—
594C2—132no—
595C2—131no—
596C2—131no—
597C2—131no—
598C2#1313132911yescharacteristic
599C2#1313133012yes—
600C2#1313137611yescharacteristic
601C2#1313137911yescharacteristic
602C2#1313138312yes—
subgroupG/H
center, FrattiniC23C23×#261
commutator, socleC23×C13C23×C4
FittingC13×#400C4
prime radical, cosocleC23×D13C24
hypercenter#400#261
hypocenterC13#14639
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
28. C13×#400C4semidirect
29. #11718647C4semidirect
30. #11718643C4semidirect
34. #11718321C4semidirect
35. #11718320C4semidirect
36. #11718319C4semidirect
275. #400#261semidirect
471. C13#14639semidirect

Maximal subgroups

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

subgroupindex
#131300242
#131300232
#131300222
#131300212
#131300132
#131300112
D13×#4002
#1463913