Finite Group Databasebeta

← #13118969

Subgroups — #13118969

Order 1664.

786 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#88201C211yesmaximal, characteristic, complemented
3C22×#6103C211yesmaximal, characteristic, complemented
4C2×#88136C211yesmaximal, characteristic
5#11718892C211yesmaximal, characteristic, complemented
6#11718874C211yesmaximal, characteristic, complemented
7#11718654C211yesmaximal, characteristic, complemented
8#11718652C211yesmaximal, characteristic, complemented
9#11718652C211yesmaximal, characteristic, complemented
10#11718651C211yesmaximal, characteristic, complemented
11#11718651C211yesmaximal, characteristic, complemented
12#11718649C211yesmaximal, characteristic, complemented
13#11718619C211yesmaximal, characteristic, complemented
14#11718616C211yesmaximal, characteristic, complemented
15C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic, complemented
18C23×C4×C13C2211yescharacteristic
19C22×C22⋊D13C2211yescharacteristic
20C23×Dic13C2211yescharacteristic
21C22×D52C2211yescharacteristic
22C22×D52C2211yescharacteristic
23C13×C22⋊Q8—24no—
24C2×C13×C4⋊C4C2211yescharacteristic, complemented
25C2×C13×C4⋊C4C2211yescharacteristic, complemented
26C2×C13×C4⋊C4C2211yescharacteristic, complemented
27C2×C13×C22⋊C4C2211yescharacteristic
28C2×C13×C22⋊C4C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30#88201—24no—
31C2×#6103—24no—
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic
39C2×#6103C2211yescharacteristic
40C2×#6103C2211yescharacteristic
41C2×#6103C2211yescharacteristic
42C2×#6103C2211yescharacteristic, complemented
43C2×#6103C2211yescharacteristic, complemented
44C2×#6103C2211yescharacteristic, complemented
45C2×#6103C2211yescharacteristic, complemented
46C2×C4×Dic13C2211yescharacteristic, complemented
47C2×C4×Dic13C2211yescharacteristic, complemented
48#88136—24no—
49#88071C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53#88071C2211yescharacteristic, complemented
54#88071C2211yescharacteristic, complemented
55C24×C13C2311yescharacteristic
56C23×D13—22no—
57C23×D13—22no—
58C23×D13—22no—
59C23×D13—22no—
60C23×D13—22no—
61C23×D13—41no—
62C23×D13—41no—
63C23×D13C2311yescharacteristic
64C23×D13C2311yescharacteristic
65C23×D13C2311yescharacteristic
66C2×Q8×C13—22no—
67C2×Q8×C13—22no—
68C2×Q8×C13—41no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—41no—
72C22×C4×C13C2311yescharacteristic
73C22×C4×C13C2311yescharacteristic
74C22×C4×C13C2311yescharacteristic
75C22×C4×C13C2311yescharacteristic
76C22×C4×C13C2311yescharacteristic
77C22×C4×C13C2311yescharacteristic
78C2×C22⋊D13—22no—
79C2×C22⋊D13—22no—
80C2×C22⋊D13—22no—
81C22×Dic13—22no—
82C22×Dic13—22no—
83C22×Dic13—41no—
84C22×Dic13C2311yescharacteristic
85C22×Dic13C2311yescharacteristic
86C22×Dic13C2311yescharacteristic
87C22×Dic13C2311yescharacteristic
88C22×Dic13C2311yescharacteristic
89C2×D52—22no—
90C2×D52—22no—
91C2×D52—22no—
92C2×D52—22no—
93C2×D52—41no—
94C2×D52—41no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—22no—
98C13×C22⋊C4—22no—
99C13×C22⋊C4D414yes—
100C22⋊Dic13—22no—
101#6103—22no—
102#6103—22no—
103#6103—22no—
104#6103—22no—
105#6103—22no—
106#6103—22no—
107#6103—22no—
108#6103—22no—
109#6103—22no—
110#6103—41no—
111#6103—41no—
112#6103—41no—
113#6103—41no—
114#6103D414yescomplemented
115C4×Dic13—22no—
116C4×Dic13—41no—
117#2472—131nomaximal, Sylow
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13C2×D412yes—
123C23×C13#4112yes—
124C23×C13#4112yes—
125C23×C13C2411yescharacteristic
126C22×D13—28no—
127C22×D13—21no—
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—21no—
131C22×D13—21no—
132C22×D13—21no—
133C22×D13—21no—
134C22×D13—21no—
135C22×D13—21no—
136C22×D13—21no—
137C22×D13—21no—
138C22×D13—21no—
139C22×D13—21no—
140C22×D13—21no—
141C22×D13—21no—
142C22×D13—21no—
143C22×D13—21no—
144C22×D13—21no—
145C22×D13—21no—
146C22×D13—44no—
147C22×D13—44no—
148C22×D13—44no—
149C22×D13—44no—
150C22×D13—44no—
151C22×D13—44no—
152C22×D13C2×D412yes—
153C22×D13#4112yes—
154Q8×C13—44no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—44no—
171C2×C4×C13C2×D412yes—
172C2×C4×C13C2×D412yes—
173C2×C4×C13C2×D412yes—
174C22⋊D13—44no—
175C2×Dic13—21no—
176C2×Dic13—21no—
177C2×Dic13—21no—
178C2×Dic13—21no—
179C2×Dic13—21no—
180C2×Dic13—21no—
181C2×Dic13—21no—
182C2×Dic13—21no—
183C2×Dic13—21no—
184C2×Dic13—21no—
185C2×Dic13—21no—
186C2×Dic13—21no—
187C2×Dic13—21no—
188C2×Dic13—21no—
189C2×Dic13—44no—
190C2×Dic13C2×D412yes—
191D52—44no—
192D52—44no—
193C2×#124—131no—
194C2×C22⋊Q8D1311yescharacteristic, complemented
195C2×#120—131no—
196C22×C22⋊C4—131no—
197#397—131no—
198#394—131no—
199#394—131no—
200#393—131no—
201#390—131no—
202#388—131no—
203#388—131no—
204#386—131no—
205#386—131no—
206#379—131no—
207C4×C22⋊C4—131no—
208C22×C13—22no—
209C22×C13—22no—
210C22×C13—22no—
211C22×C13—22no—
212C22×C13—22no—
213C22×C13—22no—
214C22×C13#12414yescomplemented
215C22×C13C22×D411yescharacteristic
216C22×C13C22×D411yescharacteristic
217C22×C13C2×#4111yescharacteristic
218C22×C13C2×#4111yescharacteristic
219C22×C13C2×#4111yescharacteristic
220C22×C13H(5,𝔽2)11yescharacteristic
221C22×C13H(5,𝔽2)11yescharacteristic
222C2×D13—22no—
223C2×D13—22no—
224C2×D13—22no—
225C2×D13—22no—
226C2×D13—22no—
227C2×D13—22no—
228C2×D13—416no—
229C2×D13—41no—
230C2×D13—41no—
231C2×D13—41no—
232C2×D13—41no—
233C2×D13—41no—
234C2×D13—41no—
235C2×D13—41no—
236C2×D13—41no—
237C2×D13—41no—
238C2×D13—41no—
239C2×D13—41no—
240C2×D13—41no—
241C2×D13—41no—
242C2×D13—41no—
243C2×D13—41no—
244C4×C13—22no—
245C4×C13—22no—
246C4×C13—22no—
247C4×C13—41no—
248C4×C13—41no—
249C4×C13—41no—
250Dic13—22no—
251Dic13—41no—
252Dic13—41no—
253Dic13—41no—
254Dic13—41no—
255C25—131no—
256C22×Q8C2×D1311yescharacteristic, complemented
257C22×D4—131no—
258C22×D4—131no—
259C22×D4—131no—
260C23×C4—131no—
261C23×C4C2×D1311yescharacteristic
262#124—264no—
263C22⋊Q8—24no—
264#120—264no—
265C2×C4⋊C4C2×D1311yescharacteristic, complemented
266C2×C4⋊C4C2×D1311yescharacteristic, complemented
267C2×C4⋊C4C2×D1311yescharacteristic, complemented
268C2×C22⋊C4—131no—
269C2×C22⋊C4—131no—
270C2×C22⋊C4—131no—
271C2×C22⋊C4—131no—
272C2×C22⋊C4—131no—
273C2×C22⋊C4—131no—
274C2×C22⋊C4—131no—
275C2×C22⋊C4—131no—
276C2×C22⋊C4—131no—
277C2×C22⋊C4—131no—
278C2×C22⋊C4—131no—
279C2×C22⋊C4—131no—
280C2×C22⋊C4—131no—
281C2×C22⋊C4—131no—
282C2×C22⋊C4—131no—
283C2×C22⋊C4—264no—
284C2×C22⋊C4C2×D1311yescharacteristic
285C2×C22⋊C4C2×D1311yescharacteristic
286C2×C42—131no—
287C2×C42—131no—
288#95—131no—
289#95—131no—
290#95—131no—
291#95—131no—
292#95—131no—
293#95—131no—
294C2×C13—24no—
295C2×C13#52511yescharacteristic
296C2×C13C2×#12411yescharacteristic
297C2×C13#53811yescharacteristic
298C2×C13D4211yescharacteristic
299C2×C13#54611yescharacteristic
300C2×C13#54611yescharacteristic
301C2×C13#55111yescharacteristic
302D13—42no—
303D13—42no—
304D13—81no—
305C24—131no—
306C24—131no—
307C24—131no—
308C24—262no—
309C24—262no—
310C24—262no—
311C24—262no—
312C24—262no—
313C24—521no—
314C24—521no—
315C24C22×D1311yescharacteristic
316C2×Q8—22no—
317C2×Q8—22no—
318C2×Q8—41no—
319C2×D4—262no—
320C2×D4—262no—
321C2×D4—262no—
322C2×D4—262no—
323C2×D4—262no—
324C2×D4—262no—
325C2×D4—262no—
326C2×D4—521no—
327C2×D4—521no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—41no—
331C22×C4—131no—
332C22×C4—131no—
333C22×C4—131no—
334C22×C4—131no—
335C22×C4—131no—
336C22×C4—262no—
337C22×C4—262no—
338C22×C4—521no—
339C22×C4C22×D1311yescharacteristic
340C22×C4C22×D1311yescharacteristic
341C22×C4C22×D1311yescharacteristic
342C22×C4C22×D1311yescharacteristic
343C22×C4C22×D1311yescharacteristic
344C22×C4C22×D1311yescharacteristic
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—134no—
350C22⋊C4—262no—
351C22⋊C4—262no—
352C22⋊C4—262no—
353C22⋊C4—262no—
354C22⋊C4—262no—
355C22⋊C4—262no—
356C22⋊C4—262no—
357C22⋊C4—262no—
358C22⋊C4—262no—
359C22⋊C4—262no—
360C22⋊C4—521no—
361C22⋊C4—521no—
362C22⋊C4—521no—
363C22⋊C4—521no—
364C22⋊C4C22⋊D1314yes—
365C42—262no—
366C42—521no—
367C13#247211yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—132no—
373C23—132no—
374C23—268no—
375C23—261no—
376C23—261no—
377C23—261no—
378C23—261no—
379C23—261no—
380C23—261no—
381C23—261no—
382C23—261no—
383C23—261no—
384C23—261no—
385C23—261no—
386C23—261no—
387C23—261no—
388C23—261no—
389C23—261no—
390C23—261no—
391C23—261no—
392C23—261no—
393C23—261no—
394C23—524no—
395C23—524no—
396C23—524no—
397C23—524no—
398C23—524no—
399C23—524no—
400C23#613112yes—
401C23#613112yes—
402C23C2×C22⋊D1312yes—
403C23C23×D1311yescharacteristic
404Q8—44no—
405D4—524no—
406D4—524no—
407D4—524no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—44no—
424C2×C4—132no—
425C2×C4—261no—
426C2×C4—261no—
427C2×C4—261no—
428C2×C4—261no—
429C2×C4—261no—
430C2×C4—261no—
431C2×C4—261no—
432C2×C4—261no—
433C2×C4—261no—
434C2×C4—261no—
435C2×C4—261no—
436C2×C4—261no—
437C2×C4—261no—
438C2×C4—261no—
439C2×C4—524no—
440C2×C4D4×D1312yes—
441C2×C4C2×C22⋊D1312yes—
442C2×C4C2×C22⋊D1312yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—262no—
450C22—262no—
451C22—262no—
452C22—262no—
453C22—262no—
454C22—262no—
455C22—5216no—
456C22—521no—
457C22—521no—
458C22—521no—
459C22—521no—
460C22—521no—
461C22—521no—
462C22—521no—
463C22—521no—
464C22—521no—
465C22—521no—
466C22—521no—
467C22—521no—
468C22—521no—
469C22—521no—
470C22—521no—
471C22#8820114yescomplemented
472C22C2×D4×D1311yescharacteristic
473C22#8825111yescharacteristic
474C22C2×#613111yescharacteristic
475C22C2×#613111yescharacteristic
476C22#41×D1311yescharacteristic
477C22#8825611yescharacteristic
478C22C22×C22⋊D1311yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—262no—
486C4—521no—
487C4—521no—
488C4—521no—
489C4—521no—
490C2—24no—
491C2—522no—
492C2—522no—
493C2—1041no—
494C2#1171933211yescharacteristic
495C2#1171933511yescharacteristic
496C2#1171934211yescharacteristic
497C2#1171934911yescharacteristic
498C2D4×C22⋊D1311yescharacteristic
499C2C2×#8820111yescharacteristic
500C2#1171953411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×C22⋊Q8C2
prime radicalC2×#88136C2
hypercenterC2×C22⋊Q8D13
hypocenterC13#2472
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C13×C22⋊Q8C2semidirect
2. C2×#88201C2semidirect
3. C22×#6103C2semidirect
5. #11718892C2semidirect
6. #11718874C2semidirect
7. #11718654C2semidirect
8. #11718652C2semidirect
9. #11718652C2semidirect
10. #11718651C2semidirect
11. #11718651C2semidirect
12. #11718649C2semidirect
13. #11718619C2semidirect
14. #11718616C2semidirect
15. C22⋊C4×Dic13C2semidirect
17. C22×Q8×C13C22semidirect
24. C2×C13×C4⋊C4C22semidirect
25. C2×C13×C4⋊C4C22semidirect
26. C2×C13×C4⋊C4C22semidirect
42. C2×#6103C22semidirect
43. C2×#6103C22semidirect
44. C2×#6103C22semidirect
45. C2×#6103C22semidirect
46. C2×C4×Dic13C22semidirect
47. C2×C4×Dic13C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
53. #88071C22semidirect
54. #88071C22semidirect
114. #6103D4semidirect
194. C2×C22⋊Q8D13semidirect
214. C22×C13#124semidirect
256. C22×Q8C2×D13semidirect
265. C2×C4⋊C4C2×D13semidirect
266. C2×C4⋊C4C2×D13semidirect
267. C2×C4⋊C4C2×D13semidirect
367. C13#2472semidirect
471. C22#88201semidirect

Maximal subgroups

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

subgroupindex
C2×C13×C22⋊Q82
C2×#882012
C22×#61032
C2×#881362
#117188922
#117188742
#117186542
#117186522
#117186512
#117186492
#117186192
#117186162
C22⋊C4×Dic132
#247213