Finite Group Databasebeta

← #15905546

Subgroups — #15905546

Order 3328.

942 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718669C211yesmaximal, characteristic, complemented
2C2×C4×#6104C211yesmaximal, characteristic
3#13120005C211yesmaximal, characteristic, complemented
4#13116317C212yesmaximal, complemented
5#13116207C212yesmaximal, complemented
6#13115796C211yesmaximal, characteristic, complemented
7#13115555C211yesmaximal, characteristic, complemented
8#13115184C212yesmaximal
9#13114846C212yesmaximal, complemented
10#13114833C211yesmaximal, characteristic, complemented
11D4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×D4×C13C2212yes—
13C2×C4×D4×C13C2211yescharacteristic
14C22×C13×C4⋊C4—21no—
15C22×#6104C2211yescharacteristic
16C2×C4×D52C2211yescharacteristic
17C2×#88123C2211yescharacteristic
18C13×#389C2212yes—
19C13×#385—22no—
20C13×#384C2211yescharacteristic
21C13×#380—21no—
22C4×C13×C4⋊C4C2211yescharacteristic
23C2×#88072C2211yescharacteristic
24C2×#88072C2212yes—
25C4×#6104—24no—
26#11718669—24no—
27#11718648—21no—
28#11718648—21no—
29C2×#88049C2211yescharacteristic
30C2×#88049C2212yes—
31C2×#88048C2212yes—
32C2×#88047C2211yescharacteristic
33#11718600C2212yes—
34#11718597C2212yes—
35C2×C4⋊#1055C2211yescharacteristic
36C2×C4⋊#1055C2212yes—
37C2×C4×#1055C2211yescharacteristic
38#11718334—22no—
39#11718121C2212yes—
40#11718121C2212yes—
41#11718121C2212yes—
42#11718116C2212yes—
43C22×D4×C13C2311yescharacteristic
44C23×C4×C13—21no—
45C23×C4×C13—22no—
46C22×D52C2311yescharacteristic
47C22×C4×D13—21no—
48C22×Dic26—21no—
49C4×D4×C13—24no—
50C4×D4×C13—22no—
51C4×D4×C13—42no—
52C4×D4×C13D414yes—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—44no—
57C2×C13×C4⋊C4D411yescharacteristic
58C2×C13×C4⋊C4D411yescharacteristic
59C2×C13×C4⋊C4C2312yes—
60C2×C13×C4⋊C4C2311yescharacteristic
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—22no—
63C2×C42×C13C2312yes—
64C2×C42×C13C2311yescharacteristic
65C2×#6104—22no—
66C2×#6104—22no—
67C2×#6104Q814yescomplemented
68C2×#6103—21no—
69C2×#6103—22no—
70C2×#6103—22no—
71C2×C4⋊Dic13—21no—
72C2×C4⋊Dic13C2312yes—
73C2×C4⋊Dic13C2311yescharacteristic
74C22×#1055C2311yescharacteristic
75C22×#1055C2312yes—
76C22×#1055C2311yescharacteristic
77C4×D52—22no—
78C4×D52—22no—
79#88123—22no—
80#88123—22no—
81C13×#95—22no—
82C13×#95D412yes—
83#88072—24no—
84#88072—22no—
85#88071—22no—
86#88071—22no—
87#88049—22no—
88#88049—42no—
89#88048—24no—
90#88047—22no—
91C4⋊#1055—22no—
92C4⋊#1055—42no—
93C4×#1055—22no—
94#24812—131nomaximal, Sylow
95C24×C13—21no—
96C23×D13—21no—
97C2×D4×C13—21no—
98C2×D4×C13—21no—
99C2×D4×C13—21no—
100C2×D4×C13C2×D412yes—
101C2×D4×C13C2×Q812yes—
102C2×D4×C13#4112yes—
103C22×C4×C13—21no—
104C22×C4×C13—24no—
105C22×C4×C13—22no—
106C22×C4×C13—44no—
107C22×C4×C13—44no—
108C22×C4×C13—42no—
109C22×C4×C13—42no—
110C22×C4×C13—82no—
111C22×C4×C13C2×D412yes—
112C22×C4×C13C2×D412yes—
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×D411yescharacteristic
115C22×C4×C13C2411yescharacteristic
116C22×Dic13—21no—
117C22×Dic13—22no—
118C2×D52—21no—
119C2×D52—21no—
120C2×D52—21no—
121C2×D52—21no—
122C2×D52—21no—
123C2×D52C2×Q812yes—
124C2×C4×D13—42no—
125C2×C4×D13—42no—
126C2×C4×D13—42no—
127C2×Dic26—42no—
128C2×Dic26—81no—
129C2×Dic26—81no—
130C13×C4⋊C4—22no—
131C13×C4⋊C4—22no—
132C13×C4⋊C4—21no—
133C13×C4⋊C4—22no—
134C13×C4⋊C4—22no—
135C13×C4⋊C4—44no—
136C13×C4⋊C4—42no—
137C13×C4⋊C4—81no—
138C13×C4⋊C4C2×D412yes—
139C13×C22⋊C4—24no—
140C13×C22⋊C4—44no—
141C42×C13—22no—
142C42×C13—22no—
143C42×C13C2×D412yes—
144C42×C13#4112yes—
145#6104—28no—
146#6103—42no—
147#6103—82no—
148#6103—82no—
149C4⋊Dic13—22no—
150C4⋊Dic13—21no—
151C4⋊Dic13—22no—
152C4⋊Dic13—21no—
153C4⋊Dic13—42no—
154C2×#1055—21no—
155C2×#1055—21no—
156C2×#1055—21no—
157C2×#1055—22no—
158C2×#1055—21no—
159C2×#1055—22no—
160C2×#1055—21no—
161C2×#1055—22no—
162C2×#1055C2×Q812yes—
163C2×#476—131no—
164C2×C4×D8—131no—
165#2563—131no—
166D4×C4⋊C4D1311yescharacteristic, complemented
167#2085—132no—
168#2065—132no—
169#1990—131no—
170#1939—131no—
171#1879—132no—
172#1804—132no—
173#1802—131no—
174C23×C13—22no—
175C23×C13—22no—
176C23×C13—22no—
177C23×C13—41no—
178C23×C13—41no—
179C23×C13—41no—
180C23×C13—41no—
181C23×C13C22×D411yescharacteristic
182C22×D13—22no—
183C22×D13—41no—
184C22×D13—41no—
185C22×D13—41no—
186C22×D13—41no—
187C22×D13—41no—
188C22×D13—41no—
189D4×C13—22no—
190D4×C13—22no—
191D4×C13—22no—
192D4×C13C22⋊Q814yes—
193C2×C4×C13—21no—
194C2×C4×C13—21no—
195C2×C4×C13—22no—
196C2×C4×C13—22no—
197C2×C4×C13—22no—
198C2×C4×C13—22no—
199C2×C4×C13—22no—
200C2×C4×C13—22no—
201C2×C4×C13—22no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—48no—
205C2×C4×C13—42no—
206C2×C4×C13—42no—
207C2×C4×C13—42no—
208C2×C4×C13—88no—
209C2×C4×C13#12112yes—
210C2×C4×C13#12112yes—
211C2×C4×C13#13512yes—
212C2×C4×C13AGL(1,ℤ/8)12yes—
213C2×C4×C13C22×D411yescharacteristic
214C2×C4×C13C22×Q811yescharacteristic
215C2×C4×C13C2×#4111yescharacteristic
216C2×C4×C13C2×#4111yescharacteristic
217C2×C4×C13H(5,𝔽2)11yescharacteristic
218C2×C4×C132−1+411yescharacteristic
219C2×Dic13—42no—
220C2×Dic13—41no—
221C2×Dic13—41no—
222C2×Dic13—41no—
223C2×Dic13—42no—
224C2×Dic13—42no—
225D52—22no—
226D52—22no—
227D52—41no—
228D52—41no—
229C4×D13—84no—
230Dic26—84no—
231#1055—22no—
232#1055—41no—
233#1055—42no—
234C22×D8—131no—
235C2×C4⋊Q8—131no—
236C2×C4×D4—131no—
237C2×C4×D4C2×D1312yes—
238C2×C4×D4C2×D1311yescharacteristic
239C22×C4⋊C4—21no—
240#476—264no—
241C4×D8—264no—
242C2×#107—131no—
243C2×#106—132no—
244C2×C4⋊C8—131no—
245C2×C4⋊C8—132no—
246C2×#102—131no—
247C2×#102—132no—
248C2×#102—131no—
249C2×#102—132no—
250C2×C4×C8—131no—
251#393—262no—
252#390—132no—
253#389C2×D1312yes—
254#385—22no—
255#384C2×D1311yescharacteristic
256#382—132no—
257#380—21no—
258#380—261no—
259#380—261no—
260C4×C4⋊C4C2×D1311yescharacteristic
261#340—132no—
262#340—132no—
263#340—132no—
264#336—132no—
265C22×C13—24no—
266C22×C13—42no—
267C22×C13—42no—
268C22×C13—42no—
269C22×C13—42no—
270C22×C13—42no—
271C22×C13—42no—
272C22×C13C2×#12111yescharacteristic
273C22×C13#54611yescharacteristic
274C22×C13D4×Q811yescharacteristic
275C22×C13C2×#13511yescharacteristic
276C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C13#57611yescharacteristic
278C22×C13#57711yescharacteristic
279C2×D13—42no—
280C2×D13—42no—
281C2×D13—42no—
282C2×D13—81no—
283C2×D13—81no—
284C2×D13—81no—
285C2×D13—81no—
286C4×C13—22no—
287C4×C13—42no—
288C4×C13—42no—
289C4×C13—42no—
290C4×C13—82no—
291C4×C13#46314yes—
292C4×C13C2×C22⋊Q811yescharacteristic
293C4×C13#53711yescharacteristic
294C4×C13#55211yescharacteristic
295C4×C13#55411yescharacteristic
296Dic13—81no—
297Dic13—82no—
298C22×Q8—261no—
299C22×D4—131no—
300C22×D4C22×D1311yescharacteristic
301C23×C4—21no—
302C23×C4—22no—
303C23×C4—261no—
304C2×D8—134no—
305C2×D8—262no—
306C2×D8—262no—
307C22×C8—131no—
308C22×C8—132no—
309C22×C8—131no—
310C4⋊Q8—262no—
311C4⋊Q8—262no—
312C4×D4—24no—
313C4×D4—22no—
314C4×D4—42no—
315C4×D4—262no—
316C4×D4—262no—
317C4×D4D5214yes—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—131no—
323C2×C4⋊C4—132no—
324C2×C4⋊C4—261no—
325C2×C4⋊C4C22⋊D1311yescharacteristic
326C2×C4⋊C4C22⋊D1311yescharacteristic
327C2×C4⋊C4C22×D1312yes—
328C2×C4⋊C4C22×D1311yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—261no—
332C2×C22⋊C4—262no—
333C2×C22⋊C4—262no—
334C2×C42C22×D1312yes—
335C2×C42C22×D1311yescharacteristic
336#107—262no—
337#106—264no—
338C4⋊C8—262no—
339C4⋊C8—522no—
340#102—262no—
341#102—264no—
342#102—262no—
343#102—522no—
344C4×C8—262no—
345#95—22no—
346#95—262no—
347#95—262no—
348#95C22⋊D1312yes—
349C2×C13—44no—
350C2×C13#241711yescharacteristic
351C2×C13C2×#46311yescharacteristic
352C2×C13#304511yescharacteristic
353C2×C13#330311yescharacteristic
354C2×C13#332511yescharacteristic
355C2×C13#338011yescharacteristic
356C2×C13#338411yescharacteristic
357D13—82no—
358C24—21no—
359C24—261no—
360C2×Q8—522no—
361C2×Q8—1041no—
362C2×Q8—1041no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—132no—
367C2×D4—261no—
368C2×D4—261no—
369C2×D4—261no—
370C2×D4—261no—
371C2×D4—261no—
372C2×D4C2×D5212yes—
373C2×D4#612912yes—
374C2×D4Q8×D1312yes—
375C22×C4—21no—
376C22×C4—24no—
377C22×C4—22no—
378C22×C4—44no—
379C22×C4—44no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—82no—
383C22×C4—261no—
384C22×C4—262no—
385C22×C4—522no—
386C22×C4—522no—
387C22×C4—522no—
388C22×C4C2×C22⋊D1312yes—
389C22×C4C2×C22⋊D1312yes—
390C22×C4C2×C22⋊D1311yescharacteristic
391C22×C4C2×C22⋊D1311yescharacteristic
392C22×C4C23×D1311yescharacteristic
393D8—268no—
394C2×C8—132no—
395C2×C8—261no—
396C2×C8—261no—
397C2×C8—261no—
398C2×C8—262no—
399C2×C8—262no—
400C2×C8—261no—
401C2×C8—262no—
402C2×C8—261no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—44no—
409C4⋊C4—42no—
410C4⋊C4—81no—
411C4⋊C4—262no—
412C4⋊C4—261no—
413C4⋊C4—261no—
414C4⋊C4—262no—
415C4⋊C4—522no—
416C4⋊C4C2×D5212yes—
417C22⋊C4—24no—
418C22⋊C4—44no—
419C22⋊C4—522no—
420C22⋊C4—1042no—
421C22⋊C4—1042no—
422C42—22no—
423C42—22no—
424C42C2×D5212yes—
425C42#612712yes—
426C13#2481211yescharacteristic, complemented, Sylow
427C23—22no—
428C23—22no—
429C23—22no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—262no—
435C23—521no—
436C23—521no—
437C23—521no—
438C23—521no—
439C23—521no—
440C23—521no—
441C23C22×C22⋊D1311yescharacteristic
442Q8—1044no—
443D4—22no—
444D4—22no—
445D4—22no—
446D4—262no—
447D4—262no—
448D4—521no—
449D4—521no—
450D4#8815114yes—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—48no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—88no—
467C2×C4—521no—
468C2×C4—522no—
469C2×C4—521no—
470C2×C4—521no—
471C2×C4—522no—
472C2×C4—522no—
473C2×C4—1044no—
474C2×C4#8818412yes—
475C2×C4#8818412yes—
476C2×C4#8818612yes—
477C2×C4#8820412yes—
478C2×C4C22×D5211yescharacteristic
479C2×C4C2×#612711yescharacteristic
480C2×C4C2×#612911yescharacteristic
481C2×C4#8825111yescharacteristic
482C2×C4C2×Q8×D1311yescharacteristic
483C2×C4#8825411yescharacteristic
484C8—262no—
485C8—521no—
486C8—522no—
487C22—24no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—522no—
495C22—522no—
496C22—522no—
497C22—1041no—
498C22—1041no—
499C22—1041no—
500C22—1041no—
501C22C2×#8818411yescharacteristic
502C22C2×#8818611yescharacteristic
503C22#1171951111yescharacteristic
504C22Q8×C22⋊D1311yescharacteristic
505C22C2×#8820411yescharacteristic
506C22#1171954011yescharacteristic
507C22#1171954211yescharacteristic
508C4—22no—
509C4—42no—
510C4—42no—
511C4—42no—
512C4—82no—
513C4—1042no—
514C4—1041no—
515C4#1171867714yes—
516C4C2×#8815111yescharacteristic
517C4#1171921511yescharacteristic
518C4#1171921611yescharacteristic
519C4#1171921811yescharacteristic
520C2—44no—
521C2—1042no—
522C2#1311828111yescharacteristic
523C2C2×#1171867711yescharacteristic
524C2#1312437511yescharacteristic
525C2#1312676411yescharacteristic
526C2#1312707811yescharacteristic
527C2#1312769911yescharacteristic
528C2#1312773111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingD4×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radicalC22×#6104C22
hypercenterD4×C4⋊C4D13
hypocenterC13#24812
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11718669C2semidirect
3. #13120005C2semidirect
4. #13116317C2semidirect
5. #13116207C2semidirect
6. #13115796C2semidirect
7. #13115555C2semidirect
9. #13114846C2semidirect
10. #13114833C2semidirect
11. D4×C13×C4⋊C4C2semidirect
67. C2×#6104Q8semidirect
166. D4×C4⋊C4D13semidirect
426. C13#24812semidirect

Maximal subgroups

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

subgroupindex
C2×#117186692
C2×C4×#61042
#131200052
#131163172
#131162072
#131157962
#131155552
#131151842
#131148462
#131148332
D4×C13×C4⋊C42
#2481213