Finite Group Databasebeta

← #16023852

Subgroups — #16023852

Order 3328.

2858 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719277C211yesmaximal, characteristic
2C2×#11719277C211yesmaximal, characteristic
3C2×C4×Q8×D13C211yesmaximal, characteristic
4#13117755C213yesmaximal, complemented
5#13117754C211yesmaximal, characteristic, complemented
6#13117753C213yesmaximal, complemented
7Q8×C4⋊Dic13C211yesmaximal, characteristic, complemented
8C4⋊C4×Dic26C213yesmaximal, complemented
9#13117750C213yesmaximal, complemented
10Q8×#6101C211yesmaximal, characteristic, complemented
11#13117461C213yesmaximal
12#13117458C213yesmaximal
13#13117317C213yesmaximal
14#13117316C213yesmaximal
15C13×#2351C211yesmaximal, characteristic, complemented
16C22×Q8×D13C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C2×C4×Q8×C13C2211yescharacteristic
20C2×Q8×Dic13C2211yescharacteristic
21C2×Q8×Dic13C2211yescharacteristic
22C2×Q8×Dic13C2211yescharacteristic
23#11719277—28no—
24#11719277C4116yescomplemented
25C4×Q8×D13—28no—
26C2×#88146C2213yes—
27C2×#88146C2213yes—
28C2×C4⋊C4×D13C2213yes—
29C2×#88141C2213yes—
30C2×#88141C2213yes—
31C2×#88141C2213yes—
32C2×#88126C2213yes—
33C2×#88126C2213yes—
34C2×C42×D13C2213yes—
35C2×C4×Dic26C2213yes—
36C2×C4×Dic26C2213yes—
37C2×C4×Dic26C2213yes—
38C13×#389C2213yes—
39C13×#389C2213yes—
40C13×#382C2213yes—
41C4×C13×C4⋊C4C2213yes—
42#11718650C2213yes—
43#11718650C2213yes—
44#11718646C2213yes—
45#11718646C2213yes—
46#11718638C2213yes—
47#11718637C2216yes—
48#11718637C2213yes—
49C4⋊C4×Dic13C2216yes—
50#11718634C2213yes—
51#11718634C2213yes—
52#11718633C2213yes—
53#11718633C2213yes—
54#11718596C2213yes—
55C4×C4⋊Dic13C2213yes—
56C4×#6101C2213yes—
57C4×#6101C2213yes—
58#11718589C2213yes—
59#11718589C2213yes—
60#11718329C2216yes—
61#11718329C2213yes—
62#11718329C2211yescharacteristic
63#11718311C2216yes—
64#11718310C2216yes—
65#11718308C2216yes—
66#11718308C2216yes—
67#11718308C2213yes—
68#11718308C2213yes—
69C22×Q8×C13C2311yescharacteristic
70C2×Q8×D13C2×C418yes—
71C2×Q8×D13D418yes—
72C2×Q8×D13Q818yes—
73C22×C4×D13C2311yescharacteristic
74C22×C4×D13C2313yes—
75C22×C4×D13C2313yes—
76C22×Dic26C2313yes—
77C4×Q8×C13—24no—
78C4×Q8×C13—24no—
79C4×Q8×C13C2×C418yescomplemented
80C2×C13×C4⋊C4C2313yes—
81C2×C13×C4⋊C4C2313yes—
82C2×C13×C4⋊C4C2313yes—
83C2×C13×C4⋊C4C2313yes—
84C2×C13×C4⋊C4C2313yes—
85C2×C42×C13C2313yes—
86C2×C42×C13C2313yes—
87C2×C42×C13C2313yes—
88Q8×Dic13—24no—
89Q8×Dic13—24no—
90Q8×Dic13C2×C418yescomplemented
91C2×#6103C2311yescharacteristic
92C2×#6103C2313yes—
93C2×#6103C2311yescharacteristic
94C2×#6103C2313yes—
95C2×C4⋊Dic13C2313yes—
96C2×C4⋊Dic13C2313yes—
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2313yes—
99C2×C4⋊Dic13C2316yes—
100C2×C4⋊Dic13C2313yes—
101C2×#6101C2313yes—
102C2×#6101C2316yes—
103C2×#6101C2313yes—
104C2×#6101C2313yes—
105C2×#6101C2311yescharacteristic
106C2×#6101C2313yes—
107C2×#6101C2316yes—
108C2×#6101C2313yes—
109C2×#6101C2313yes—
110C2×#6101C2313yes—
111C2×C4×Dic13C2313yes—
112C2×C4×Dic13C2316yes—
113C2×C4×Dic13C2313yes—
114C2×C4×Dic13C2313yes—
115C2×C4×Dic13C2313yes—
116C2×C4×Dic13C2316yes—
117C2×C4×Dic13C2313yes—
118#88146—212no—
119#88146C2×C4124yes—
120C4⋊C4×D13—212no—
121#88141—212no—
122#88141—212no—
123#88141C2×C4124yescomplemented
124#88126—212no—
125#88126C2×C4124yes—
126C42×D13—212no—
127C4×Dic26—212no—
128C4×Dic26—212no—
129C4×Dic26C2×C4124yescomplemented
130C13×#95C2311yescharacteristic
131C13×#95C2313yes—
132C13×#95C2316yes—
133#88071C2313yes—
134#88071C2313yes—
135#88071C2316yes—
136#88071C2313yes—
137#88071C2313yes—
138#88071C2313yes—
139#88071C2311yescharacteristic
140#34249—131nomaximal, Sylow
141C23×D13C2411yescharacteristic
142C2×Q8×C13C22×C414yes—
143C2×Q8×C13C2×D414yes—
144C2×Q8×C13C2×Q814yes—
145C22×C4×C13C2413yes—
146C22×C4×C13C2413yes—
147C22×C4×C13C2411yescharacteristic
148C22×C4×C13C2413yes—
149C22×C4×C13C2411yescharacteristic
150C22×C4×C13C2411yescharacteristic
151C22×C4×C13C2413yes—
152C22×Dic13C2411yescharacteristic
153C22×Dic13C2413yes—
154C22×Dic13C2413yes—
155C22×Dic13C2411yescharacteristic
156C22×Dic13C2413yes—
157C22×Dic13C2411yescharacteristic
158C22×Dic13C2413yes—
159Q8×D13C4⋊C4164yescomplemented
160C2×C4×D13—22no—
161C2×C4×D13—22no—
162C2×C4×D13—22no—
163C2×C4×D13—26no—
164C2×C4×D13—43no—
165C2×C4×D13—43no—
166C2×C4×D13C22×C4112yes—
167C2×C4×D13C2×D4112yes—
168C2×C4×D13C2×Q8112yes—
169C2×Dic26C22×C4112yes—
170C2×Dic26C2×D4112yes—
171C2×Dic26C2×Q8112yes—
172C13×C4⋊C4—26no—
173C13×C4⋊C4—26no—
174C13×C4⋊C4—26no—
175C13×C4⋊C4—43no—
176C13×C4⋊C4C22×C4112yes—
177C42×C13—26no—
178C42×C13—26no—
179C42×C13C22×C4112yes—
180#6103—22no—
181#6103—26no—
182#6103C22×C414yes—
183#6103C22×C4112yes—
184C4⋊Dic13—26no—
185C4⋊Dic13—26no—
186C4⋊Dic13—22no—
187C4⋊Dic13—43no—
188C4⋊Dic13—46no—
189C4⋊Dic13C22×C4112yes—
190#6101—22no—
191#6101—26no—
192#6101—212no—
193#6101—26no—
194#6101—26no—
195#6101—46no—
196#6101—43no—
197#6101—43no—
198#6101C22×C4112yes—
199#6101C22×C4112yes—
200C4×Dic13—26no—
201C4×Dic13—26no—
202C4×Dic13—26no—
203C4×Dic13—212no—
204C4×Dic13—26no—
205C4×Dic13C22×C4124yes—
206C4×Dic13C22×C4112yes—
207C2×#519—131no—
208C2×#519—131no—
209C22×C4×Q8—131no—
210#2351—133no—
211#2351—133no—
212#2351—131no—
213#2351D1311yescharacteristic, complemented
214Q8×C4⋊C4—133no—
215Q8×C4⋊C4—133no—
216Q8×C4⋊C4—131no—
217Q8×C4⋊C4—131no—
218#2317—133no—
219#2317—133no—
220#2296—133no—
221#2296—133no—
222C23×C13C2511yescharacteristic
223C22×D13—21no—
224C22×D13—21no—
225C22×D13—21no—
226C22×D13—21no—
227C22×D13C23×C412yes—
228C22×D13C22×D412yes—
229C22×D13C22×Q812yes—
230Q8×C13C2×C4⋊C4116yes—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—23no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—23no—
237C2×C4×C13—23no—
238C2×C4×C13—23no—
239C2×C4×C13—21no—
240C2×C4×C13—23no—
241C2×C4×C13—23no—
242C2×C4×C13—21no—
243C2×C4×C13—23no—
244C2×C4×C13—23no—
245C2×C4×C13—21no—
246C2×C4×C13C23×C416yes—
247C2×C4×C13C23×C412yes—
248C2×C4×C13C23×C416yes—
249C2×C4×C13C22×D416yes—
250C2×C4×C13C22×Q816yes—
251C2×C4×C132−1+412yes—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—23no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—23no—
258C2×Dic13—21no—
259C2×Dic13—23no—
260C2×Dic13—23no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—23no—
264C2×Dic13—23no—
265C2×Dic13—23no—
266C2×Dic13—23no—
267C2×Dic13C23×C412yes—
268C2×Dic13C23×C416yes—
269C2×Dic13C23×C416yes—
270C2×Dic13C22×D416yes—
271C2×Dic13C22×Q816yes—
272C2×Dic132−1+412yes—
273C4×D13—28no—
274C4×D13—412no—
275C4×D13C2×C4⋊C4148yes—
276Dic26C2×C4⋊C4148yes—
277C23×Q8—131no—
278#519—1316no—
279#519—268no—
280C2×C4×Q8—131no—
281C2×C4×Q8—131no—
282C2×C4×Q8—131no—
283C2×C4×Q8—133no—
284C2×C4×Q8—133no—
285C2×C4×Q8—133no—
286C2×C4×Q8—133no—
287C2×C4×Q8—133no—
288C2×C4×Q8—133no—
289C2×C4×Q8—268no—
290C2×C4×Q8C2×D1311yescharacteristic
291C2×C4×Q8C2×D1311yescharacteristic
292C2×C4×Q8C2×D1311yescharacteristic
293C2×#117—133no—
294C2×#117—133no—
295C2×#117—133no—
296C2×#117—133no—
297C22×C4⋊C4—133no—
298C22×C42—133no—
299#389—133no—
300#389—133no—
301#389—133no—
302#389—133no—
303#389—133no—
304#389—133no—
305#389—133no—
306#389—133no—
307#389—136no—
308#389—136no—
309#389—133no—
310#389—133no—
311#389C2×D1313yes—
312#389C2×D1313yes—
313#385—133no—
314#385—133no—
315#385—136no—
316#385—133no—
317#385—131no—
318#384—136no—
319#384—133no—
320#384—133no—
321#382—133no—
322#382—136no—
323#382C2×D1313yes—
324C4×C4⋊C4—136no—
325C4×C4⋊C4—133no—
326C4×C4⋊C4—133no—
327C4×C4⋊C4—133no—
328C4×C4⋊C4—136no—
329C4×C4⋊C4C2×D1313yes—
330C22×C13C24×C411yescharacteristic
331C22×C13C23×D411yescharacteristic
332C22×C13C23×Q811yescharacteristic
333C22×C13C2×2−1+411yescharacteristic
334C22×C13C2×2−1+411yescharacteristic
335C22×C13#58511yescharacteristic
336C22×C13#58511yescharacteristic
337C2×D13—22no—
338C2×D13—22no—
339C2×D13—22no—
340C2×D13—22no—
341C2×D13—22no—
342C2×D13—22no—
343C2×D13C22×C4⋊C414yes—
344C4×C13—22no—
345C4×C13—26no—
346C4×C13—22no—
347C4×C13—43no—
348C4×C13—43no—
349C4×C13—41no—
350C4×C13C22×C4⋊C4112yes—
351Dic13—26no—
352Dic13—22no—
353Dic13—22no—
354Dic13—41no—
355Dic13—43no—
356Dic13—43no—
357Dic13C22×C4⋊C4112yes—
358C22×Q8—138no—
359C22×Q8—138no—
360C22×Q8—138no—
361C22×Q8—133no—
362C22×Q8C22×D1311yescharacteristic
363C23×C4—133no—
364C23×C4—131no—
365C23×C4—133no—
366C4×Q8—24no—
367C4×Q8—24no—
368C4×Q8—138no—
369C4×Q8—1324no—
370C4×Q8—1324no—
371C4×Q8—2612no—
372C4×Q8—2612no—
373C4×Q8—2612no—
374C4×Q8—2612no—
375C4×Q8—264no—
376C4×Q8—264no—
377C4×Q8C4×D1318yescomplemented
378#117—1324no—
379#117—1324no—
380#117—2612no—
381#117—2612no—
382C2×C4⋊C4—133no—
383C2×C4⋊C4—133no—
384C2×C4⋊C4—133no—
385C2×C4⋊C4—136no—
386C2×C4⋊C4—133no—
387C2×C4⋊C4—133no—
388C2×C4⋊C4—133no—
389C2×C4⋊C4—133no—
390C2×C4⋊C4—133no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—133no—
394C2×C4⋊C4—133no—
395C2×C4⋊C4—136no—
396C2×C4⋊C4—136no—
397C2×C4⋊C4—133no—
398C2×C4⋊C4—2612no—
399C2×C4⋊C4C22×D1313yes—
400C2×C4⋊C4C22×D1313yes—
401C2×C4⋊C4C22×D1313yes—
402C2×C4⋊C4C22×D1313yes—
403C2×C4⋊C4C22×D1313yes—
404C2×C22⋊C4—133no—
405C2×C22⋊C4—131no—
406C2×C22⋊C4—131no—
407C2×C22⋊C4—133no—
408C2×C42—136no—
409C2×C42—133no—
410C2×C42—136no—
411C2×C42—133no—
412C2×C42—133no—
413C2×C42—133no—
414C2×C42—133no—
415C2×C42—2612no—
416C2×C42C22×D1313yes—
417C2×C42C22×D1313yes—
418C2×C42C22×D1313yes—
419#95—131no—
420#95—133no—
421#95—133no—
422#95—133no—
423#95—133no—
424#95—136no—
425#95—133no—
426#95C22×D1316yes—
427#95C22×D1311yescharacteristic
428#95C22×D1313yes—
429C2×C13C23×C4⋊C411yescharacteristic
430C2×C13C4×2−1+411yescharacteristic
431C2×C13C4×2−1+411yescharacteristic
432C2×C13#348611yescharacteristic
433C2×C13#348711yescharacteristic
434C2×C13#350211yescharacteristic
435C2×C13#350211yescharacteristic
436D13—24no—
437C24—131no—
438C2×Q8—1364no—
439C2×Q8—1312no—
440C2×Q8—1312no—
441C2×Q8—1312no—
442C2×Q8C2×C4×D1314yes—
443C2×Q8D4×D1314yes—
444C2×Q8Q8×D1314yes—
445C22×C4—133no—
446C22×C4—1312no—
447C22×C4—1312no—
448C22×C4—1312no—
449C22×C4—131no—
450C22×C4—131no—
451C22×C4—133no—
452C22×C4—131no—
453C22×C4—133no—
454C22×C4—133no—
455C22×C4—262no—
456C22×C4—262no—
457C22×C4—266no—
458C22×C4—262no—
459C22×C4—523no—
460C22×C4—523no—
461C22×C4C23×D1313yes—
462C22×C4C23×D1313yes—
463C22×C4C23×D1311yescharacteristic
464C22×C4C23×D1313yes—
465C22×C4C23×D1311yescharacteristic
466C22×C4C23×D1311yescharacteristic
467C22×C4C23×D1313yes—
468C4⋊C4—26no—
469C4⋊C4—26no—
470C4⋊C4—26no—
471C4⋊C4—43no—
472C4⋊C4—1312no—
473C4⋊C4—1312no—
474C4⋊C4—1312no—
475C4⋊C4—2612no—
476C4⋊C4—266no—
477C4⋊C4—266no—
478C4⋊C4—266no—
479C4⋊C4—262no—
480C4⋊C4—266no—
481C4⋊C4—266no—
482C4⋊C4—262no—
483C4⋊C4—523no—
484C4⋊C4—523no—
485C4⋊C4—526no—
486C4⋊C4—526no—
487C4⋊C4—523no—
488C4⋊C4C2×C4×D13112yes—
489C22⋊C4—1312no—
490C22⋊C4—134no—
491C22⋊C4—262no—
492C22⋊C4—266no—
493C42—26no—
494C42—26no—
495C42—1324no—
496C42—1312no—
497C42—266no—
498C42—266no—
499C42—2612no—
500C42—266no—
501C42—266no—
502C42C2×C4×D13112yes—
503C13#3424911yescharacteristic, complemented, Sylow
504C23—132no—
505C23—132no—
506C23—132no—
507C23—261no—
508C23—261no—
509C23—261no—
510C23—261no—
511C23C24×D1311yescharacteristic
512Q8—1348no—
513Q8C4⋊C4×D13116yes—
514C2×C4—21no—
515C2×C4—23no—
516C2×C4—23no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—23no—
522C2×C4—23no—
523C2×C4—23no—
524C2×C4—21no—
525C2×C4—23no—
526C2×C4—23no—
527C2×C4—21no—
528C2×C4—23no—
529C2×C4—136no—
530C2×C4—136no—
531C2×C4—136no—
532C2×C4—1348no—
533C2×C4—136no—
534C2×C4—132no—
535C2×C4—132no—
536C2×C4—268no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—263no—
542C2×C4—263no—
543C2×C4—261no—
544C2×C4—263no—
545C2×C4—263no—
546C2×C4—261no—
547C2×C4—263no—
548C2×C4—263no—
549C2×C4—261no—
550C2×C4—263no—
551C2×C4—263no—
552C2×C4—5212no—
553C2×C4C22×C4×D1316yes—
554C2×C4C22×C4×D1312yes—
555C2×C4C22×C4×D1316yes—
556C2×C4C2×D4×D1316yes—
557C2×C4C2×Q8×D1316yes—
558C2×C4#8825712yes—
559C22—134no—
560C22—262no—
561C22—262no—
562C22—262no—
563C22—262no—
564C22—262no—
565C22—262no—
566C22C23×C4×D1311yescharacteristic
567C22C22×D4×D1311yescharacteristic
568C22C22×Q8×D1311yescharacteristic
569C22C2×#8825711yescharacteristic
570C22#1171964811yescharacteristic
571C22D13×2−1+411yescharacteristic
572C22#1171965211yescharacteristic
573C4—22no—
574C4—22no—
575C4—26no—
576C4—43no—
577C4—41no—
578C4—43no—
579C4—1312no—
580C4—262no—
581C4—266no—
582C4—262no—
583C4—521no—
584C4—523no—
585C4—523no—
586C4C2×C4⋊C4×D13112yes—
587C2—264no—
588C2C22×C4⋊C4×D1311yescharacteristic
589C2#1312804511yescharacteristic
590C2C4×#8825711yescharacteristic
591C2#1312848211yescharacteristic
592C2#1312849311yescharacteristic
593C2#1312864011yescharacteristic
594C2#1312864311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2351C2
socle, cosocleC23×C13C25
prime radicalC23×D13C24
hypercenter#2351D13
hypocenterC13#34249
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2351

Complements

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

NH ≅ G/Ntype
4. #13117755C2semidirect
5. #13117754C2semidirect
6. #13117753C2semidirect
7. Q8×C4⋊Dic13C2semidirect
8. C4⋊C4×Dic26C2semidirect
9. #13117750C2semidirect
10. Q8×#6101C2semidirect
15. C13×#2351C2semidirect
24. #11719277C4semidirect
79. C4×Q8×C13C2×C4semidirect
90. Q8×Dic13C2×C4semidirect
123. #88141C2×C4semidirect
129. C4×Dic26C2×C4semidirect
159. Q8×D13C4⋊C4semidirect
213. #2351D13semidirect
377. C4×Q8C4×D13semidirect
503. C13#34249semidirect

Maximal subgroups

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

subgroupindex
C2×#117192772
C2×C4×Q8×D132
#131177552
#131177542
#131177532
Q8×C4⋊Dic132
C4⋊C4×Dic262
#131177502
Q8×#61012
#131174612
#131174582
#131173172
#131173162
C13×#23512
#3424913