Finite Group Databasebeta

← #15917088

Subgroups — #15917088

Order 3328.

1028 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718716C211yesmaximal, characteristic
2C2×#11718681C211yesmaximal, characteristic, complemented
3#13120041C211yesmaximal, characteristic, complemented
4#13116079C212yesmaximal, complemented
5#13116072C212yesmaximal
6#13115777C211yesmaximal, characteristic, complemented
7#13115769C211yesmaximal, characteristic
8#13115104C212yesmaximal, complemented
9#13115097C212yesmaximal
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×#88123C2211yescharacteristic
26#11718891—21no—
27C2×#88075C2212yes—
28C2×#88075C2212yes—
29C2×#88075C2212yes—
30C2×#88075C2212yes—
31C2×#88072C2212yes—
32C2×#88072C2212yes—
33#11718716—24no—
34#11718681—24no—
35#11718640—21no—
36#11718640—21no—
37#11718637—21no—
38C2×#88048C2212yes—
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
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13C2312yes—
91C2×C4⋊Dic13C2312yes—
92C2×#6101—22no—
93C2×#6101—22no—
94C2×C4×Dic13—21no—
95C22×#1055C2312yes—
96C22×#1055C2312yes—
97#88123—22no—
98#88123—22no—
99#88075—24no—
100#88075—24no—
101#88075—24no—
102#88075—24no—
103#88072—24no—
104#88072—24no—
105#88071—22no—
106#88071—22no—
107#88071—21no—
108#88048—24no—
109C4⋊#1055—22no—
110#88043—22no—
111#25662—131nomaximal, Sylow
112C24×C13—21no—
113C2×Q8×C13—22no—
114C2×Q8×C13—22no—
115C2×Q8×C13—21no—
116C2×Q8×C13—21no—
117C2×Q8×C13—22no—
118C2×Q8×C13—22no—
119C2×Q8×C13—22no—
120C2×Q8×C13—22no—
121C2×Q8×C13—41no—
122C2×Q8×C13C2×D412yes—
123C2×Q8×C13C2×D412yes—
124C2×D4×C13—21no—
125C2×D4×C13—22no—
126C2×D4×C13—22no—
127C2×D4×C13C2×D412yes—
128C22×C4×C13—24no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—42no—
133C22×C4×C13—42no—
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2411yescharacteristic
141C22×Dic13—22no—
142C22×Dic13—22no—
143C2×Dic26—42no—
144C2×Dic26—82no—
145C13×C4⋊C4—24no—
146C13×C4⋊C4—24no—
147C13×C4⋊C4—24no—
148C13×C4⋊C4—24no—
149C13×C4⋊C4—22no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4C2×D412yes—
154C13×C22⋊C4—24no—
155C13×C22⋊C4—24no—
156C13×C22⋊C4—24no—
157C13×C22⋊C4—24no—
158C13×C22⋊C4—24no—
159C42×C13—24no—
160C42×C13—24no—
161C42×C13—21no—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13C2×D412yes—
166C42×C13C2×D412yes—
167C4⋊Dic13—22no—
168C4⋊Dic13—22no—
169C4⋊Dic13—22no—
170C4⋊Dic13—42no—
171C4⋊Dic13#4114yes—
172#6101—82no—
173#6101—82no—
174C4×Dic13—42no—
175C2×#1055—22no—
176C2×#1055—22no—
177C2×#1055—22no—
178C2×#1055—22no—
179C2×#1055—22no—
180C2×#1055—22no—
181C2×#556D1311yescharacteristic
182C2×#489—131no—
183C2×#475—131no—
184#2567—131no—
185#2043—132no—
186#2042—132no—
187#1985—131no—
188#1983—131no—
189#1865—132no—
190#1864—132no—
191#1763—131no—
192C23×C13—22no—
193C23×C13—42no—
194C23×C13—41no—
195C23×C13—41no—
196C23×C13—42no—
197C23×C13C22×D411yescharacteristic
198Q8×C13—22no—
199Q8×C13—22no—
200Q8×C13—24no—
201Q8×C13—44no—
202Q8×C13—41no—
203Q8×C13—41no—
204Q8×C13—42no—
205D4×C13—24no—
206D4×C13—41no—
207D4×C13—41no—
208C2×C4×C13—21no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—22no—
213C2×C4×C13—21no—
214C2×C4×C13—22no—
215C2×C4×C13—21no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—48no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13#12012yes—
229C2×C4×C13#12012yes—
230C2×C4×C13#13712yes—
231C2×C4×C13C22×D411yescharacteristic
232C2×C4×C13C22×D411yescharacteristic
233C2×C4×C13C2×#4112yes—
234C2×C4×C132−1+412yes—
235C2×Dic13—24no—
236C2×Dic13—42no—
237C2×Dic13—42no—
238C2×Dic13—42no—
239C2×Dic13—42no—
240C2×Dic13—42no—
241Dic26—84no—
242#1055—42no—
243#1055—42no—
244#556—24no—
245#556—24no—
246C2×C4⋊Q8—131no—
247C2×C4⋊Q8C2×D1311yescharacteristic
248C2×#126—21no—
249C2×#126—21no—
250C2×#124C2×D1311yescharacteristic
251C2×#124C2×D1311yescharacteristic
252C2×C22⋊Q8—21no—
253C2×C4×Q8C2×D1311yescharacteristic
254C2×C4×Q8C2×D1311yescharacteristic
255C2×C4×Q8C2×D1311yescharacteristic
256C2×C4×D4C2×D1311yescharacteristic
257C2×#117—21no—
258#489—264no—
259#475—264no—
260C2×#106—132no—
261C2×C4⋊C8—131no—
262C2×#103—132no—
263C2×#103—132no—
264C2×#103—132no—
265C2×#103—132no—
266C2×#102—132no—
267C2×#102—132no—
268C2×#97—131no—
269#395—261no—
270#395—261no—
271#391—261no—
272#389—132no—
273#389—132no—
274#384—261no—
275C4×C4⋊C4—131no—
276#340—132no—
277#336—132no—
278#336—132no—
279C22×C13—42no—
280C22×C13—42no—
281C22×C13—42no—
282C22×C13—82no—
283C22×C13—82no—
284C22×C13C2×#12011yescharacteristic
285C22×C13#54812yes—
286C22×C13C2×#13711yescharacteristic
287C22×C13#57511yescharacteristic
288C22×C13#57712yes—
289C4×C13—22no—
290C4×C13—22no—
291C4×C13—22no—
292C4×C13—42no—
293C4×C13—42no—
294C4×C13—41no—
295C4×C13—42no—
296C4×C13—41no—
297C4×C13—41no—
298C4×C13#53211yescharacteristic
299C4×C13#53611yescharacteristic
300C4×C13#54712yes—
301Dic13—44no—
302Dic13—82no—
303C22×Q8—261no—
304C22×Q8C22⋊D1311yescharacteristic
305C22×Q8C22×D1311yescharacteristic
306C22×Q8C22×D1311yescharacteristic
307C22×D4C22×D1311yescharacteristic
308C23×C4—21no—
309C22×C8—132no—
310C22×C8—132no—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8—262no—
314C4⋊Q8—262no—
315#126—28no—
316#126—28no—
317#124—22no—
318#124—22no—
319#124—22no—
320#124C22⋊D1314yes—
321C22⋊Q8—28no—
322C4×Q8—22no—
323C4×Q8—22no—
324C4×Q8—22no—
325C4×Q8—22no—
326C4×Q8—22no—
327C4×Q8C22⋊D1314yes—
328C4×D4—22no—
329C4×D4—22no—
330#117—28no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—132no—
336C2×C4⋊C4—132no—
337C2×C4⋊C4—261no—
338C2×C4⋊C4—262no—
339C2×C4⋊C4—262no—
340C2×C4⋊C4C22⋊D1311yescharacteristic
341C2×C4⋊C4C22⋊D1311yescharacteristic
342C2×C4⋊C4C22⋊D1311yescharacteristic
343C2×C4⋊C4C22×D1311yescharacteristic
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—261no—
352C2×C42C22×D1311yescharacteristic
353C2×C42C22×D1311yescharacteristic
354C2×C42C22×D1311yescharacteristic
355#106—264no—
356C4⋊C8—262no—
357#103—264no—
358#103—264no—
359#103—264no—
360#103—264no—
361#102—264no—
362#102—264no—
363#97—262no—
364#95—261no—
365#95—262no—
366#95—262no—
367C2×C13—82no—
368C2×C13#243211yescharacteristic
369C2×C13#300711yescharacteristic
370C2×C13#301011yescharacteristic
371C2×C13#336912yes—
372C2×C13#337612yes—
373C24—21no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—41no—
383C2×Q8—522no—
384C2×Q8—1042no—
385C2×Q8C2×C22⋊D1312yes—
386C2×Q8C2×C22⋊D1312yes—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4C2×C22⋊D1312yes—
391C22×C4—24no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—262no—
398C22×C4—262no—
399C22×C4C2×C22⋊D1311yescharacteristic
400C22×C4C2×C22⋊D1311yescharacteristic
401C22×C4C2×C22⋊D1311yescharacteristic
402C22×C4C2×C22⋊D1311yescharacteristic
403C22×C4C2×C22⋊D1311yescharacteristic
404C22×C4C2×C22⋊D1311yescharacteristic
405C22×C4C23×D1311yescharacteristic
406C2×C8—262no—
407C2×C8—262no—
408C2×C8—262no—
409C2×C8—262no—
410C2×C8—262no—
411C2×C8—262no—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4—24no—
415C4⋊C4—24no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—21no—
420C4⋊C4—134no—
421C4⋊C4—262no—
422C4⋊C4—262no—
423C4⋊C4—262no—
424C4⋊C4—522no—
425C4⋊C4—1042no—
426C4⋊C4—1042no—
427C4⋊C4C2×C22⋊D1312yes—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C42—24no—
434C42—24no—
435C42—21no—
436C42—21no—
437C42—21no—
438C42—21no—
439C42—522no—
440C42C2×C22⋊D1312yes—
441C42C2×C22⋊D1312yes—
442C13#2566211yescharacteristic, complemented, Sylow
443C23—22no—
444C23—41no—
445C23—41no—
446C23—42no—
447C23—42no—
448C23C22×C22⋊D1311yescharacteristic
449Q8—24no—
450Q8—22no—
451Q8—22no—
452Q8—44no—
453Q8—42no—
454Q8—41no—
455Q8—41no—
456Q8—1044no—
457D4—24no—
458D4—41no—
459D4—41no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—48no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—264no—
481C2×C4—522no—
482C2×C4—522no—
483C2×C4—522no—
484C2×C4—522no—
485C2×C4—522no—
486C2×C4#8820512yes—
487C2×C4#8820712yes—
488C2×C4#8820712yes—
489C2×C4#41×D1312yes—
490C2×C4#8825712yes—
491C2×C4C22×C22⋊D1311yescharacteristic
492C2×C4C22×C22⋊D1311yescharacteristic
493C8—522no—
494C8—522no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—82no—
499C22—82no—
500C22#1171952711yescharacteristic
501C22C2×#8820511yescharacteristic
502C22#1171953612yes—
503C22#1171954212yes—
504C22C2×#8820711yescharacteristic
505C4—22no—
506C4—22no—
507C4—22no—
508C4—41no—
509C4—42no—
510C4—41no—
511C4—41no—
512C4—42no—
513C4—42no—
514C4—524no—
515C4—1042no—
516C4#1171952912yes—
517C4#1171953011yescharacteristic
518C4#1171953711yescharacteristic
519C2—82no—
520C2#1311846011yescharacteristic
521C2#1312409611yescharacteristic
522C2#1312412211yescharacteristic
523C2#1312757212yes—
524C2#1312765712yes—
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#25662
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×#11718681C2semidirect
3. #13120041C2semidirect
4. #13116079C2semidirect
6. #13115777C2semidirect
8. #13115104C2semidirect
10. #13114666C2semidirect
442. C13#25662semidirect

Maximal subgroups

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

subgroupindex
C2×#117187162
C2×#117186812
#131200412
#131160792
#131160722
#131157772
#131157692
#131151042
#131150972
#131146662
C2×C13×#5562
#2566213