Finite Group Databasebeta

← #15917077

Subgroups — #15917077

Order 3328.

1048 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×#11718716C211yesmaximal, characteristic
2C2×#11718682C211yesmaximal, characteristic, complemented
3#13119821C211yesmaximal, characteristic, complemented
4#13116079C212yesmaximal, complemented
5#13116072C212yesmaximal
6#13115777C211yesmaximal, characteristic, complemented
7#13115769C211yesmaximal, characteristic
8#13115090C212yesmaximal, complemented
9#13115083C212yesmaximal
10#13114666C211yesmaximal, characteristic, complemented
11C2×C13×#556C211yesmaximal, characteristic
12C13×#556—24no—
13C13×#556—24no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#126—21no—
16C2×C13×#126—21no—
17C2×C13×#124C2211yescharacteristic
18C2×C13×#124C2211yescharacteristic
19C2×C13×C22⋊Q8—21no—
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×Q8×C13C2211yescharacteristic
22C2×C4×Q8×C13C2211yescharacteristic
23C2×C4×D4×C13C2211yescharacteristic
24C2×C13×#117—21no—
25C2×#88198—21no—
26C2×#88123C2211yescharacteristic
27C2×#88075C2212yes—
28C2×#88075C2212yes—
29C2×#88075C2212yes—
30C2×#88075C2212yes—
31C2×#88072C2212yes—
32C2×#88072C2212yes—
33#11718716—24no—
34#11718682—24no—
35#11718644—21no—
36#11718644—21no—
37#11718635—21no—
38C2×#88047C2212yes—
39C4×C4⋊Dic13C2211yescharacteristic
40#11718589C2212yes—
41#11718589C2212yes—
42C2×C4⋊#1055C2211yescharacteristic
43C2×#88043C2211yescharacteristic
44#11718121C2212yes—
45#11718116C2212yes—
46#11718116C2212yes—
47C22×Q8×C13D411yescharacteristic
48C22×Q8×C13C2311yescharacteristic
49C22×Q8×C13C2311yescharacteristic
50C22×D4×C13C2311yescharacteristic
51C23×C4×C13—21no—
52C22×Dic26—21no—
53C13×C4⋊Q8—22no—
54C13×C4⋊Q8—22no—
55C13×#126—28no—
56C13×#126—28no—
57C13×#124—22no—
58C13×#124—22no—
59C13×#124—22no—
60C13×#124D414yes—
61C13×C22⋊Q8—28no—
62C4×Q8×C13—22no—
63C4×Q8×C13—22no—
64C4×Q8×C13—22no—
65C4×Q8×C13—22no—
66C4×Q8×C13—22no—
67C4×Q8×C13D414yes—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C13×#117—28no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C42×C13—21no—
85C2×C42×C13—21no—
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89#88198—44no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13C2312yes—
92C2×C4⋊Dic13C2312yes—
93C2×#6101—22no—
94C2×#6101—22no—
95C2×C4×Dic13—21no—
96C22×#1055C2312yes—
97C22×#1055C2312yes—
98#88123—22no—
99#88123—22no—
100#88075—24no—
101#88075—24no—
102#88075—24no—
103#88075—24no—
104#88072—24no—
105#88072—24no—
106#88071—22no—
107#88071—22no—
108#88071—21no—
109#88047—24no—
110C4⋊#1055—22no—
111#88043—22no—
112#25661—131nomaximal, Sylow
113C24×C13—21no—
114C2×Q8×C13—22no—
115C2×Q8×C13—22no—
116C2×Q8×C13—21no—
117C2×Q8×C13—21no—
118C2×Q8×C13—22no—
119C2×Q8×C13—22no—
120C2×Q8×C13—22no—
121C2×Q8×C13—22no—
122C2×Q8×C13—41no—
123C2×Q8×C13C2×D412yes—
124C2×Q8×C13C2×D412yes—
125C2×D4×C13—21no—
126C2×D4×C13—22no—
127C2×D4×C13—22no—
128C2×D4×C13C2×D412yes—
129C22×C4×C13—24no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—42no—
134C22×C4×C13—42no—
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2411yescharacteristic
142C22×Dic13—22no—
143C22×Dic13—22no—
144C2×Dic26—42no—
145C2×Dic26—42no—
146C2×Dic26—42no—
147C13×C4⋊C4—24no—
148C13×C4⋊C4—24no—
149C13×C4⋊C4—24no—
150C13×C4⋊C4—24no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4C2×D412yes—
156C13×C22⋊C4—24no—
157C13×C22⋊C4—24no—
158C13×C22⋊C4—24no—
159C13×C22⋊C4—24no—
160C13×C22⋊C4—24no—
161C42×C13—24no—
162C42×C13—24no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13C2×D412yes—
168C42×C13C2×D412yes—
169C4⋊Dic13—22no—
170C4⋊Dic13—22no—
171C4⋊Dic13—22no—
172C4⋊Dic13—42no—
173C4⋊Dic13#4114yes—
174#6101—44no—
175#6101—44no—
176C4×Dic13—42no—
177C2×#1055—22no—
178C2×#1055—22no—
179C2×#1055—22no—
180C2×#1055—22no—
181C2×#1055—22no—
182C2×#1055—22no—
183C2×#556D1311yescharacteristic
184C2×#489—131no—
185C2×#477—131no—
186#2546—131no—
187#2043—132no—
188#2042—132no—
189#1985—131no—
190#1983—131no—
191#1863—132no—
192#1862—132no—
193#1763—131no—
194C23×C13—22no—
195C23×C13—42no—
196C23×C13—41no—
197C23×C13—41no—
198C23×C13—42no—
199C23×C13C22×D411yescharacteristic
200Q8×C13—22no—
201Q8×C13—22no—
202Q8×C13—24no—
203Q8×C13—44no—
204Q8×C13—41no—
205Q8×C13—41no—
206Q8×C13—42no—
207D4×C13—24no—
208D4×C13—41no—
209D4×C13—41no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—22no—
215C2×C4×C13—21no—
216C2×C4×C13—22no—
217C2×C4×C13—21no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—48no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13#12012yes—
231C2×C4×C13#12012yes—
232C2×C4×C13AGL(1,ℤ/8)12yes—
233C2×C4×C13C22×D411yescharacteristic
234C2×C4×C13C22×D411yescharacteristic
235C2×C4×C13C2×#4112yes—
236C2×C4×C132−1+412yes—
237C2×Dic13—24no—
238C2×Dic13—42no—
239C2×Dic13—42no—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—42no—
243Dic26—84no—
244#1055—42no—
245#1055—42no—
246#556—24no—
247#556—24no—
248C2×C4⋊Q8—131no—
249C2×C4⋊Q8—261no—
250C2×C4⋊Q8C2×D1311yescharacteristic
251C2×#126—21no—
252C2×#126—21no—
253C2×#124C2×D1311yescharacteristic
254C2×#124C2×D1311yescharacteristic
255C2×C22⋊Q8—21no—
256C2×C4×Q8C2×D1311yescharacteristic
257C2×C4×Q8C2×D1311yescharacteristic
258C2×C4×Q8C2×D1311yescharacteristic
259C2×C4×D4C2×D1311yescharacteristic
260C2×#117—21no—
261#489—264no—
262#477—264no—
263C2×#107—132no—
264C2×C4⋊C8—131no—
265C2×#103—132no—
266C2×#103—132no—
267C2×#103—132no—
268C2×#103—132no—
269C2×#102—132no—
270C2×#102—132no—
271C2×#97—131no—
272#398—261no—
273#398—261no—
274#391—261no—
275#389—132no—
276#389—132no—
277C4×C4⋊C4—131no—
278#340—132no—
279#336—132no—
280#336—132no—
281C22×C13—42no—
282C22×C13—42no—
283C22×C13—42no—
284C22×C13—82no—
285C22×C13—82no—
286C22×C13C2×#12011yescharacteristic
287C22×C13#54812yes—
288C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C13#57511yescharacteristic
290C22×C13#57812yes—
291C4×C13—22no—
292C4×C13—22no—
293C4×C13—22no—
294C4×C13—42no—
295C4×C13—42no—
296C4×C13—41no—
297C4×C13—42no—
298C4×C13—41no—
299C4×C13—41no—
300C4×C13#53211yescharacteristic
301C4×C13#53611yescharacteristic
302C4×C13#54712yes—
303Dic13—44no—
304Dic13—82no—
305C22×Q8—261no—
306C22×Q8C22⋊D1311yescharacteristic
307C22×Q8C22×D1311yescharacteristic
308C22×Q8C22×D1311yescharacteristic
309C22×D4C22×D1311yescharacteristic
310C23×C4—21no—
311C22×C8—132no—
312C22×C8—132no—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8—262no—
316C4⋊Q8—262no—
317C4⋊Q8—524no—
318#126—28no—
319#126—28no—
320#124—22no—
321#124—22no—
322#124—22no—
323#124C22⋊D1314yes—
324C22⋊Q8—28no—
325C4×Q8—22no—
326C4×Q8—22no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8C22⋊D1314yes—
331C4×D4—22no—
332C4×D4—22no—
333#117—28no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—132no—
339C2×C4⋊C4—132no—
340C2×C4⋊C4—261no—
341C2×C4⋊C4—262no—
342C2×C4⋊C4—262no—
343C2×C4⋊C4C22⋊D1311yescharacteristic
344C2×C4⋊C4C22⋊D1311yescharacteristic
345C2×C4⋊C4C22⋊D1311yescharacteristic
346C2×C4⋊C4C22×D1311yescharacteristic
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—261no—
355C2×C42C22×D1311yescharacteristic
356C2×C42C22×D1311yescharacteristic
357C2×C42C22×D1311yescharacteristic
358#107—264no—
359C4⋊C8—262no—
360#103—264no—
361#103—264no—
362#103—264no—
363#103—264no—
364#102—264no—
365#102—264no—
366#97—262no—
367#95—261no—
368#95—262no—
369#95—262no—
370C2×C13—82no—
371C2×C13#243211yescharacteristic
372C2×C13#300611yescharacteristic
373C2×C13#301111yescharacteristic
374C2×C13#336712yes—
375C2×C13#337712yes—
376C24—21no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—41no—
386C2×Q8—522no—
387C2×Q8—522no—
388C2×Q8—522no—
389C2×Q8C2×C22⋊D1312yes—
390C2×Q8C2×C22⋊D1312yes—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4C2×C22⋊D1312yes—
395C22×C4—24no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—262no—
402C22×C4—262no—
403C22×C4C2×C22⋊D1311yescharacteristic
404C22×C4C2×C22⋊D1311yescharacteristic
405C22×C4C2×C22⋊D1311yescharacteristic
406C22×C4C2×C22⋊D1311yescharacteristic
407C22×C4C2×C22⋊D1311yescharacteristic
408C22×C4C2×C22⋊D1311yescharacteristic
409C22×C4C23×D1311yescharacteristic
410C2×C8—262no—
411C2×C8—262no—
412C2×C8—262no—
413C2×C8—262no—
414C2×C8—262no—
415C2×C8—262no—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—24no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—21no—
424C4⋊C4—134no—
425C4⋊C4—262no—
426C4⋊C4—262no—
427C4⋊C4—262no—
428C4⋊C4—524no—
429C4⋊C4—524no—
430C4⋊C4—522no—
431C4⋊C4C2×C22⋊D1312yes—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—24no—
437C42—24no—
438C42—24no—
439C42—21no—
440C42—21no—
441C42—21no—
442C42—21no—
443C42—522no—
444C42C2×C22⋊D1312yes—
445C42C2×C22⋊D1312yes—
446C13#2566111yescharacteristic, complemented, Sylow
447C23—22no—
448C23—41no—
449C23—41no—
450C23—42no—
451C23—42no—
452C23C22×C22⋊D1311yescharacteristic
453Q8—24no—
454Q8—22no—
455Q8—22no—
456Q8—44no—
457Q8—42no—
458Q8—41no—
459Q8—41no—
460Q8—1044no—
461D4—24no—
462D4—41no—
463D4—41no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—48no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—264no—
485C2×C4—522no—
486C2×C4—522no—
487C2×C4—522no—
488C2×C4—522no—
489C2×C4—522no—
490C2×C4#8820312yes—
491C2×C4#8820712yes—
492C2×C4#8820712yes—
493C2×C4#41×D1312yes—
494C2×C4#8825712yes—
495C2×C4C22×C22⋊D1311yescharacteristic
496C2×C4C22×C22⋊D1311yescharacteristic
497C8—522no—
498C8—522no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—82no—
503C22—82no—
504C22C2×#8820311yescharacteristic
505C22#1171952711yescharacteristic
506C22#1171953612yes—
507C22#1171954312yes—
508C22C2×#8820711yescharacteristic
509C4—22no—
510C4—22no—
511C4—22no—
512C4—41no—
513C4—41no—
514C4—41no—
515C4—42no—
516C4—42no—
517C4—42no—
518C4—524no—
519C4—1042no—
520C4#1171952912yes—
521C4#1171953011yescharacteristic
522C4#1171953711yescharacteristic
523C2—82no—
524C2#1311846011yescharacteristic
525C2#1312408811yescharacteristic
526C2#1312413111yescharacteristic
527C2#1312755012yes—
528C2#1312767212yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#556C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenterC2×#556D13
hypocenterC13#25661
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. C2×#11718682C2semidirect
3. #13119821C2semidirect
4. #13116079C2semidirect
6. #13115777C2semidirect
8. #13115090C2semidirect
10. #13114666C2semidirect
446. C13#25661semidirect

Maximal subgroups

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

subgroupindex
C2×#117187162
C2×#117186822
#131198212
#131160792
#131160722
#131157772
#131157692
#131150902
#131150832
#131146662
C2×C13×#5562
#2566113