Finite Group Databasebeta

← #16023366

Subgroups — #16023366

Order 3328.

2310 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719393C211yesmaximal, characteristic
2#13117844C214yesmaximal
3#13117838C214yesmaximal
4#13117790C214yesmaximal, complemented
5#13117750C214yesmaximal, complemented
6#13117578C211yesmaximal, characteristic, complemented
7#13117577C211yesmaximal, characteristic, complemented
8#13117575C211yesmaximal, characteristic, complemented
9#13117458C212yesmaximal
10#13117407C212yesmaximal, complemented
11C4×#88142C212yesmaximal, complemented
12D13×#384C211yesmaximal, characteristic
13#13117190C212yesmaximal
14#13117175C211yesmaximal, characteristic
15C13×#2330C211yesmaximal, characteristic, complemented
16C2×C13×#125C2211yescharacteristic
17#11719393C4116yescomplemented
18C2×#88150C2214yes—
19C2×#88146C2212yes—
20C2×C4⋊C4×D13C2212yes—
21C2×C4⋊C4×D13C2214yes—
22C2×#88142C2212yes—
23C2×#88141C2214yes—
24C2×#88141C2214yes—
25C2×#88126C2211yescharacteristic
26C2×#88126C2211yescharacteristic
27C2×C42×D13C2211yescharacteristic
28C2×#88124C2211yescharacteristic
29C2×C4×Dic26C2214yes—
30C13×#389C2212yes—
31C13×#389C2214yes—
32C13×#387C2214yes—
33C13×#384C2211yescharacteristic
34C4×C13×C4⋊C4C2212yes—
35C13×#376C2211yescharacteristic
36#11718650C2214yes—
37#11718646C2212yes—
38#11718646C2214yes—
39#11718642C2214yes—
40#11718639C2214yes—
41#11718637C2214yes—
42#11718637C2214yes—
43#11718637C2212yes—
44C4⋊C4×Dic13C2212yes—
45C4⋊C4×Dic13C2212yes—
46#11718634C2212yes—
47#11718633C2214yes—
48#11718633C2214yes—
49C4×#6103C2214yes—
50#11718596C2211yescharacteristic
51C4×C4⋊Dic13C2212yes—
52#11718593C2211yescharacteristic
53C4×#6101C2214yes—
54C4×#6101C2214yes—
55C42×Dic13C2211yescharacteristic
56C42×Dic13C2211yescharacteristic
57#11718589C2212yes—
58#11718329C2214yes—
59#11718327C2214yes—
60#11718327C2212yes—
61#11718327C2212yes—
62#11718316C2214yes—
63#11718311C2214yes—
64#11718310C2214yes—
65#11718310C2212yes—
66#11718310C2212yes—
67#11718310C2214yes—
68#11718308C2214yes—
69#11718308C2214yes—
70#11718307C2214yes—
71#11718307C2214yes—
72C22×C4×D13C2312yes—
73C22×C4×D13C2314yes—
74C22×C4×D13C2311yescharacteristic
75C22×Dic26C2314yes—
76C13×#125C2×C418yescomplemented
77C2×C13×C4⋊C4C2312yes—
78C2×C13×C4⋊C4C2314yes—
79C2×C13×C4⋊C4C2314yes—
80C2×C13×C4⋊C4C2312yes—
81C2×C13×C4⋊C4C2314yes—
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2314yes—
84C2×C42×C13C2311yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×#6103C2311yescharacteristic
87C2×#6103C2311yescharacteristic
88C2×#6103C2314yes—
89C2×#6103C2312yes—
90C2×C4⋊Dic13C2312yes—
91C2×C4⋊Dic13C2314yes—
92C2×C4⋊Dic13C2314yes—
93C2×C4⋊Dic13C2312yes—
94C2×#6101C2314yes—
95C2×#6101C2311yescharacteristic
96C2×#6101C2311yescharacteristic
97C2×#6101C2314yes—
98C2×#6101C2314yes—
99C2×#6101C2314yes—
100C2×#6101C2314yes—
101C2×#6101C2314yes—
102C2×#6101C2314yes—
103C2×#6101C2312yes—
104C2×C4×Dic13C2312yes—
105C2×C4×Dic13C2311yescharacteristic
106C2×C4×Dic13C2312yes—
107C2×C4×Dic13C2312yes—
108C2×C4×Dic13C2312yes—
109C2×C4×Dic13C2314yes—
110C2×C4×Dic13C2314yes—
111C2×C4×Dic13C2314yes—
112C2×C4×Dic13C2312yes—
113C2×C4×Dic13C2311yescharacteristic
114C2×C4×Dic13C2314yes—
115C2×C4×Dic13C2311yescharacteristic
116#88150C2×C4132yes—
117#88146C2×C4116yes—
118C4⋊C4×D13—28no—
119C4⋊C4×D13—48no—
120#88142C2×C4116yescomplemented
121#88141—48no—
122#88141C2×C4132yescomplemented
123#88126—24no—
124#88126Q818yescomplemented
125C42×D13C2×C418yes—
126#88124C2×C418yescomplemented
127C4×Dic26—48no—
128C13×#95C2314yes—
129C13×#95C2314yes—
130C13×#95C2312yes—
131C13×#95C2312yes—
132#88071C2314yes—
133#88071C2314yes—
134#88071C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2312yes—
139#88071C2312yes—
140#34214—131nomaximal, Sylow
141C23×D13C2411yescharacteristic
142C22×C4×C13C2411yescharacteristic
143C22×C4×C13C2414yes—
144C22×C4×C13C2411yescharacteristic
145C22×C4×C13C2414yes—
146C22×C4×C13C2412yes—
147C22×C4×C13C2412yes—
148C22×C4×C13C2411yescharacteristic
149C22×Dic13C2411yescharacteristic
150C22×Dic13C2414yes—
151C22×Dic13C2411yescharacteristic
152C22×Dic13C2414yes—
153C22×Dic13C2412yes—
154C22×Dic13C2411yescharacteristic
155C22×Dic13C2412yes—
156C2×C4×D13—24no—
157C2×C4×D13—24no—
158C2×C4×D13—28no—
159C2×C4×D13—44no—
160C2×C4×D13—44no—
161C2×C4×D13C22×C418yes—
162C2×C4×D13C22×C414yes—
163C2×C4×D13C2×Q814yes—
164C2×C4×D13#4114yes—
165C2×Dic26—28no—
166C2×Dic26—28no—
167C2×Dic26C22×C4116yes—
168C13×C4⋊C4—24no—
169C13×C4⋊C4—44no—
170C13×C4⋊C4—44no—
171C13×C4⋊C4C22×C4116yes—
172C13×C4⋊C4C22×C418yes—
173C42×C13—22no—
174C42×C13—44no—
175C42×C13C22×C414yes—
176C42×C13C2×Q814yes—
177#6103—22no—
178#6103—22no—
179#6103C22×C4116yes—
180#6103C2×Q818yes—
181C4⋊Dic13—24no—
182C4⋊Dic13—44no—
183C4⋊Dic13—44no—
184C4⋊Dic13C22×C418yes—
185#6101—22no—
186#6101—22no—
187#6101—28no—
188#6101—28no—
189#6101—28no—
190#6101—44no—
191#6101—44no—
192#6101C22×C4116yes—
193#6101C22×C4116yes—
194#6101C2×Q818yes—
195C4×Dic13—22no—
196C4×Dic13—24no—
197C4×Dic13—24no—
198C4×Dic13—24no—
199C4×Dic13—24no—
200C4×Dic13—44no—
201C4×Dic13—44no—
202C4×Dic13—44no—
203C4×Dic13C22×C418yes—
204C4×Dic13C22×C414yes—
205C4×Dic13C22×C4116yes—
206C4×Dic13C2×Q814yes—
207C2×#533—131no—
208#2360—134no—
209#2360—134no—
210#2355—134no—
211Q8×C4⋊C4—134no—
212#2330—131no—
213#2330—131no—
214#2330—131no—
215#2330D1311yescharacteristic, complemented
216#2317—132no—
217C4×C4⋊Q8—132no—
218C4×C4⋊Q8—132no—
219C2×#384—131no—
220#2274—132no—
221C4×#117—131no—
222C23×C13C2511yescharacteristic
223C22×D13—22no—
224C22×D13—22no—
225C22×D13C23×C412yes—
226C22×D13C22×Q812yes—
227C22×D13C2×#4112yes—
228C2×C4×C13—22no—
229C2×C4×C13—24no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—24no—
233C2×C4×C13—22no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—24no—
237C2×C4×C13—22no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—22no—
241C2×C4×C13C23×C414yes—
242C2×C4×C13C23×C418yes—
243C2×C4×C13C23×C412yes—
244C2×C4×C13C22×Q814yes—
245C2×C4×C13C22×Q812yes—
246C2×C4×C13C2×#4112yes—
247C2×Dic13—22no—
248C2×Dic13—24no—
249C2×Dic13—22no—
250C2×Dic13—24no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—24no—
254C2×Dic13—22no—
255C2×Dic13—24no—
256C2×Dic13—24no—
257C2×Dic13—22no—
258C2×Dic13C23×C418yes—
259C2×Dic13C23×C412yes—
260C2×Dic13C23×C414yes—
261C2×Dic13C22×Q814yes—
262C2×Dic13C22×Q812yes—
263C2×Dic13C2×#4112yes—
264C2×Dic13H(5,𝔽2)14yes—
265C2×Dic132−1+414yes—
266C4×D13—216no—
267C4×D13—88no—
268C4×D13C4×Q8116yescomplemented
269Dic26—232no—
270#533—1316no—
271C2×C4⋊Q8—132no—
272C2×#125—131no—
273C2×#125C2×D1311yescharacteristic
274C2×C22⋊Q8—134no—
275C2×C4×Q8—134no—
276C2×C4×Q8—134no—
277C2×C4×Q8—134no—
278C2×#117—132no—
279C2×#117—131no—
280C2×#117—131no—
281C22×C4⋊C4—132no—
282C22×C4⋊C4—134no—
283C22×C42—131no—
284#391—134no—
285#391—134no—
286#389—132no—
287#389—132no—
288#389—134no—
289#389—134no—
290#389—134no—
291#389—132no—
292#389—134no—
293#389—134no—
294#389C2×D1312yes—
295#389C2×D1314yes—
296#387—134no—
297#387—134no—
298#387—134no—
299#387C2×D1314yes—
300#385—134no—
301#385—134no—
302#384—132no—
303#384—134no—
304#384—134no—
305#384—131no—
306#384C2×D1311yescharacteristic
307#382—134no—
308C4×C4⋊C4—132no—
309C4×C4⋊C4—132no—
310C4×C4⋊C4—132no—
311C4×C4⋊C4—134no—
312C4×C4⋊C4—134no—
313C4×C4⋊C4—134no—
314C4×C4⋊C4—132no—
315C4×C4⋊C4—134no—
316C4×C4⋊C4—132no—
317C4×C4⋊C4C2×D1312yes—
318C4×C22⋊C4—134no—
319C4×C22⋊C4—132no—
320C4×C22⋊C4—132no—
321C4×C22⋊C4—134no—
322#376—131no—
323#376C2×D1311yescharacteristic
324C43—131no—
325C43—131no—
326C22×C13C24×C411yescharacteristic
327C22×C13C23×Q811yescharacteristic
328C22×C13C22×#4111yescharacteristic
329C22×C13C2×H(5,𝔽2)12yes—
330C22×C13C2×2−1+412yes—
331C2×D13—24no—
332C2×D13—24no—
333C2×D13—22no—
334C2×D13—22no—
335C2×D13C2×C4×Q814yes—
336C4×C13—28no—
337C4×C13—24no—
338C4×C13—24no—
339C4×C13—44no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13C2×C4×Q814yes—
343Dic13—28no—
344Dic13—24no—
345Dic13—44no—
346Dic13—41no—
347Dic13—41no—
348Dic13C2×C4×Q814yes—
349Dic13#52018yes—
350C22×Q8—134no—
351C23×C4—131no—
352C23×C4—132no—
353C23×C4—134no—
354C4⋊Q8—1316no—
355#125—138no—
356#125C4×D1318yescomplemented
357C22⋊Q8—1332no—
358C4×Q8—1332no—
359C4×Q8—528no—
360C4×Q8—528no—
361#117—1316no—
362#117—138no—
363#117—264no—
364C2×C4⋊C4—132no—
365C2×C4⋊C4—132no—
366C2×C4⋊C4—134no—
367C2×C4⋊C4—134no—
368C2×C4⋊C4—134no—
369C2×C4⋊C4—134no—
370C2×C4⋊C4—134no—
371C2×C4⋊C4—132no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—134no—
375C2×C4⋊C4—134no—
376C2×C4⋊C4—134no—
377C2×C4⋊C4—134no—
378C2×C4⋊C4—268no—
379C2×C4⋊C4—528no—
380C2×C4⋊C4C22×D1312yes—
381C2×C4⋊C4C22×D1314yes—
382C2×C4⋊C4C22×D1314yes—
383C2×C4⋊C4C22×D1312yes—
384C2×C4⋊C4C22×D1314yes—
385C2×C22⋊C4—134no—
386C2×C22⋊C4—132no—
387C2×C22⋊C4—131no—
388C2×C22⋊C4—131no—
389C2×C42—134no—
390C2×C42—131no—
391C2×C42—132no—
392C2×C42—131no—
393C2×C42—138no—
394C2×C42—131no—
395C2×C42—132no—
396C2×C42—132no—
397C2×C42—132no—
398C2×C42—132no—
399C2×C42—134no—
400C2×C42—134no—
401C2×C42—134no—
402C2×C42C22×D1311yescharacteristic
403C2×C42C22×D1314yes—
404C2×C42C22×D1311yescharacteristic
405C2×C42C22×D1311yescharacteristic
406#95—132no—
407#95—132no—
408#95—134no—
409#95—134no—
410#95—134no—
411#95—134no—
412#95—134no—
413#95—134no—
414#95C22×D1312yes—
415#95C22×D1312yes—
416#95C22×D1314yes—
417#95C22×D1314yes—
418C2×C13C22×C4×Q811yescharacteristic
419C2×C13C2×#52012yes—
420C2×C13#350312yes—
421C2×C13#350811yescharacteristic
422C2×C13#350911yescharacteristic
423D13—24no—
424C24—131no—
425C2×Q8—1316no—
426C2×Q8—268no—
427C2×Q8—268no—
428C22×C4—131no—
429C22×C4—132no—
430C22×C4—134no—
431C22×C4—134no—
432C22×C4—134no—
433C22×C4—132no—
434C22×C4—134no—
435C22×C4—138no—
436C22×C4—131no—
437C22×C4—134no—
438C22×C4—131no—
439C22×C4—264no—
440C22×C4—264no—
441C22×C4—268no—
442C22×C4—524no—
443C22×C4—524no—
444C22×C4C23×D1311yescharacteristic
445C22×C4C23×D1314yes—
446C22×C4C23×D1311yescharacteristic
447C22×C4C23×D1314yes—
448C22×C4C23×D1312yes—
449C22×C4C23×D1312yes—
450C22×C4C23×D1311yescharacteristic
451C4⋊C4—24no—
452C4⋊C4—44no—
453C4⋊C4—44no—
454C4⋊C4—138no—
455C4⋊C4—1316no—
456C4⋊C4—1316no—
457C4⋊C4—138no—
458C4⋊C4—268no—
459C4⋊C4—268no—
460C4⋊C4—268no—
461C4⋊C4—262no—
462C4⋊C4—262no—
463C4⋊C4—264no—
464C4⋊C4—524no—
465C4⋊C4—524no—
466C4⋊C4—524no—
467C4⋊C4—524no—
468C4⋊C4C2×C4×D1318yes—
469C4⋊C4C2×C4×D13116yes—
470C22⋊C4—1316no—
471C22⋊C4—138no—
472C22⋊C4—262no—
473C22⋊C4—262no—
474C42—22no—
475C42—44no—
476C42—138no—
477C42—134no—
478C42—1316no—
479C42—134no—
480C42—264no—
481C42—264no—
482C42—264no—
483C42—264no—
484C42—262no—
485C42—524no—
486C42—524no—
487C42—524no—
488C42C2×C4×D1314yes—
489C42Q8×D1314yes—
490C13#3421411yescharacteristic, complemented, Sylow
491C23—132no—
492C23—132no—
493C23—132no—
494C23—262no—
495C23—262no—
496C23C24×D1311yescharacteristic
497Q8—2632no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—132no—
512C2×C4—134no—
513C2×C4—132no—
514C2×C4—132no—
515C2×C4—134no—
516C2×C4—134no—
517C2×C4—1316no—
518C2×C4—138no—
519C2×C4—134no—
520C2×C4—2616no—
521C2×C4—262no—
522C2×C4—264no—
523C2×C4—262no—
524C2×C4—264no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—264no—
528C2×C4—262no—
529C2×C4—264no—
530C2×C4—264no—
531C2×C4—262no—
532C2×C4—1048no—
533C2×C4C22×C4×D1314yes—
534C2×C4C22×C4×D1318yes—
535C2×C4C22×C4×D1312yes—
536C2×C4C2×Q8×D1314yes—
537C2×C4C2×Q8×D1312yes—
538C2×C4#41×D1312yes—
539C22—134no—
540C22—262no—
541C22—262no—
542C22—264no—
543C22—264no—
544C22C23×C4×D1311yescharacteristic
545C22C22×Q8×D1311yescharacteristic
546C22C2×#41×D1311yescharacteristic
547C22D13×H(5,𝔽2)12yes—
548C22D13×2−1+412yes—
549C4—24no—
550C4—28no—
551C4—24no—
552C4—41no—
553C4—44no—
554C4—41no—
555C4—134no—
556C4—138no—
557C4—268no—
558C4—264no—
559C4—521no—
560C4—524no—
561C4—521no—
562C4C4×Q8×D1314yes—
563C2—264no—
564C2C2×C4×Q8×D1311yescharacteristic
565C2D13×#52012yes—
566C2#1312865112yes—
567C2#1312870811yescharacteristic
568C2#1312871811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2330C2
socle, cosocleC23×C13C25
prime radicalC23×D13C24
hypercenter#2330D13
hypocenterC13#34214
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2330

Complements

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

NH ≅ G/Ntype
4. #13117790C2semidirect
5. #13117750C2semidirect
6. #13117578C2semidirect
7. #13117577C2semidirect
8. #13117575C2semidirect
10. #13117407C2semidirect
11. C4×#88142C2semidirect
15. C13×#2330C2semidirect
17. #11719393C4semidirect
76. C13×#125C2×C4semidirect
120. #88142C2×C4semidirect
122. #88141C2×C4semidirect
124. #88126Q8semidirect
126. #88124C2×C4semidirect
215. #2330D13semidirect
268. C4×D13C4×Q8semidirect
356. #125C4×D13semidirect
490. C13#34214semidirect

Maximal subgroups

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

subgroupindex
C2×#117193932
#131178442
#131178382
#131177902
#131177502
#131175782
#131175772
#131175752
#131174582
#131174072
C4×#881422
D13×#3842
#131171902
#131171752
C13×#23302
#3421413