Finite Group Databasebeta

← #13118961

Subgroups — #13118961

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×#120C211yesmaximal, characteristic
2C22×C22⋊Dic13C211yesmaximal, characteristic, complemented
3C2×#88190C211yesmaximal, characteristic, complemented
4C2×#88132C211yesmaximal, characteristic, complemented
5#11718908C211yesmaximal, characteristic, complemented
6#11718883C211yesmaximal, characteristic, complemented
7#11718883C211yesmaximal, characteristic, complemented
8#11718882C211yesmaximal, characteristic, complemented
9#11718881C211yesmaximal, characteristic, complemented
10#11718881C211yesmaximal, characteristic, complemented
11#11718614C211yesmaximal, characteristic, complemented
12#11718608C211yesmaximal, characteristic, complemented
13#11718606C211yesmaximal, characteristic, complemented
14#11718606C211yesmaximal, characteristic, complemented
15C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
16C25×C13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C22×D4×C13C2211yescharacteristic
19C22×D4×C13C2211yescharacteristic
20C23×Dic13C2211yescharacteristic
21C23×Dic13C2211yescharacteristic
22C22×Dic26C2211yescharacteristic, complemented
23C13×#120—24no—
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C13×C22⋊C4C2211yescharacteristic
27C2×C22⋊Dic13—24no—
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊Dic13C2211yescharacteristic
31C2×C22⋊Dic13C2211yescharacteristic
32C2×C22⋊Dic13C2211yescharacteristic
33C2×C22⋊Dic13C2211yescharacteristic
34C2×C22⋊Dic13C2211yescharacteristic
35C2×C22⋊Dic13C2211yescharacteristic
36C2×C22⋊Dic13C2211yescharacteristic
37C2×C22⋊Dic13C2211yescharacteristic
38C2×C22⋊Dic13C2211yescharacteristic, complemented
39C2×C22⋊Dic13C2211yescharacteristic, complemented
40C2×C22⋊Dic13C2211yescharacteristic, complemented
41C2×C22⋊Dic13C2211yescharacteristic, complemented
42#88190—24no—
43C2×C4⋊Dic13C2211yescharacteristic, complemented
44C2×#6101C2211yescharacteristic, complemented
45C2×#6101C2211yescharacteristic, complemented
46C2×C4×Dic13C2211yescharacteristic, complemented
47C2×C4×Dic13C2211yescharacteristic, complemented
48#88132—24no—
49#88071C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53#88071C2211yescharacteristic, complemented
54#88071C2211yescharacteristic, complemented
55C24×C13—22no—
56C24×C13—22no—
57C24×C13—22no—
58C24×C13—22no—
59C24×C13—22no—
60C24×C13—41no—
61C24×C13—41no—
62C24×C13C2311yescharacteristic
63C24×C13C2311yescharacteristic
64C24×C13C2311yescharacteristic
65C24×C13C2311yescharacteristic
66C2×D4×C13—22no—
67C2×D4×C13—22no—
68C2×D4×C13—22no—
69C2×D4×C13—22no—
70C2×D4×C13—22no—
71C2×D4×C13—22no—
72C2×D4×C13—22no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C22×C4×C13C2311yescharacteristic
76C22×C4×C13C2311yescharacteristic
77C22×C4×C13C2311yescharacteristic
78C22×Dic13—22no—
79C22×Dic13—22no—
80C22×Dic13—22no—
81C22×Dic13—22no—
82C22×Dic13—41no—
83C22×Dic13—41no—
84C22×Dic13C2311yescharacteristic
85C22×Dic13C2311yescharacteristic
86C22×Dic13C2311yescharacteristic
87C22×Dic13C2311yescharacteristic
88C22×Dic13C2311yescharacteristic
89C22×Dic13C2311yescharacteristic
90C22×Dic13C2311yescharacteristic
91C22×Dic13C2311yescharacteristic
92C2×Dic26—22no—
93C2×Dic26—22no—
94C2×Dic26—41no—
95C13×C22⋊C4—22no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4D414yes—
98C22⋊Dic13—22no—
99C22⋊Dic13—22no—
100C22⋊Dic13—22no—
101C22⋊Dic13—22no—
102C22⋊Dic13—22no—
103C22⋊Dic13—22no—
104C22⋊Dic13—22no—
105C22⋊Dic13—22no—
106C22⋊Dic13—22no—
107C22⋊Dic13—41no—
108C22⋊Dic13—41no—
109C22⋊Dic13—41no—
110C22⋊Dic13—41no—
111C22⋊Dic13D414yescomplemented
112C4⋊Dic13—22no—
113#6101—22no—
114#6101—22no—
115C4×Dic13—22no—
116C4×Dic13—41no—
117#2472—131nomaximal, Sylow
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—28no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—21no—
130C23×C13—21no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—21no—
134C23×C13—21no—
135C23×C13—21no—
136C23×C13—21no—
137C23×C13—21no—
138C23×C13—21no—
139C23×C13—21no—
140C23×C13—21no—
141C23×C13—21no—
142C23×C13—44no—
143C23×C13—44no—
144C23×C13—44no—
145C23×C13—44no—
146C23×C13—44no—
147C23×C13—44no—
148C23×C13C2×D412yes—
149C23×C13C2×D412yes—
150C23×C13#4112yes—
151C23×C13#4112yes—
152C23×C13#4112yes—
153C23×C13C2411yescharacteristic
154D4×C13—44no—
155D4×C13—44no—
156D4×C13—44no—
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×C13C2×D412yes—
165C2×C4×C13C2×D412yes—
166C2×Dic13—21no—
167C2×Dic13—21no—
168C2×Dic13—21no—
169C2×Dic13—21no—
170C2×Dic13—21no—
171C2×Dic13—21no—
172C2×Dic13—21no—
173C2×Dic13—21no—
174C2×Dic13—21no—
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—44no—
189C2×Dic13—44no—
190C2×Dic13C2×D412yes—
191C2×Dic13C2×D412yes—
192Dic26—44no—
193C2×#124—131no—
194C2×C22⋊Q8—131no—
195C2×#120D1311yescharacteristic
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—22no—
215C22×C13—22no—
216C22×C13—22no—
217C22×C13—22no—
218C22×C13—22no—
219C22×C13—22no—
220C22×C13—416no—
221C22×C13—41no—
222C22×C13—41no—
223C22×C13—41no—
224C22×C13—41no—
225C22×C13—41no—
226C22×C13—41no—
227C22×C13—41no—
228C22×C13—41no—
229C22×C13—41no—
230C22×C13—41no—
231C22×C13—41no—
232C22×C13—41no—
233C22×C13—41no—
234C22×C13—41no—
235C22×C13—41no—
236C22×C13#12414yescomplemented
237C22×C13C22×D411yescharacteristic
238C22×C13C22×D411yescharacteristic
239C22×C13C2×#4111yescharacteristic
240C22×C13C2×#4111yescharacteristic
241C22×C13C2×#4111yescharacteristic
242C22×C13H(5,𝔽2)11yescharacteristic
243C22×C13H(5,𝔽2)11yescharacteristic
244C4×C13—22no—
245C4×C13—22no—
246C4×C13—41no—
247Dic13—22no—
248Dic13—22no—
249Dic13—41no—
250Dic13—41no—
251Dic13—41no—
252Dic13—41no—
253Dic13—41no—
254Dic13—41no—
255C25C2×D1311yescharacteristic
256C22×Q8—131no—
257C22×D4C2×D1311yescharacteristic
258C22×D4C2×D1311yescharacteristic
259C22×D4C2×D1311yescharacteristic
260C23×C4—131no—
261C23×C4—131no—
262#124—264no—
263C22⋊Q8—264no—
264#120—24no—
265C2×C4⋊C4—131no—
266C2×C4⋊C4—131no—
267C2×C4⋊C4—131no—
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—264no—
283C2×C22⋊C4C2×D1311yescharacteristic
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—42no—
296C2×C13—42no—
297C2×C13—81no—
298C2×C13#52511yescharacteristic
299C2×C13C2×#12411yescharacteristic
300C2×C13#53811yescharacteristic
301C2×C13D4211yescharacteristic
302C2×C13#54611yescharacteristic
303C2×C13#54611yescharacteristic
304C2×C13#55111yescharacteristic
305C24—22no—
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—41no—
311C24—41no—
312C24C22×D1311yescharacteristic
313C24C22×D1311yescharacteristic
314C24C22×D1311yescharacteristic
315C24C22×D1311yescharacteristic
316C2×Q8—262no—
317C2×Q8—262no—
318C2×Q8—521no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—41no—
327C2×D4—41no—
328C22×C4—131no—
329C22×C4—131no—
330C22×C4—131no—
331C22×C4—131no—
332C22×C4—131no—
333C22×C4—131no—
334C22×C4—131no—
335C22×C4—131no—
336C22×C4—262no—
337C22×C4—262no—
338C22×C4—262no—
339C22×C4—262no—
340C22×C4—521no—
341C22×C4—521no—
342C22×C4C22×D1311yescharacteristic
343C22×C4C22×D1311yescharacteristic
344C22×C4C22×D1311yescharacteristic
345C4⋊C4—262no—
346C4⋊C4—262no—
347C4⋊C4—262no—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—134no—
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—28no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—44no—
393C23—44no—
394C23—44no—
395C23—44no—
396C23—44no—
397C23—44no—
398C23D4×D1312yes—
399C23#612912yes—
400C23#612912yes—
401C23#612912yes—
402C23C2×C22⋊D1312yes—
403C23C23×D1311yescharacteristic
404Q8—524no—
405D4—44no—
406D4—44no—
407D4—44no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—132no—
416C2×C4—132no—
417C2×C4—261no—
418C2×C4—261no—
419C2×C4—261no—
420C2×C4—261no—
421C2×C4—261no—
422C2×C4—261no—
423C2×C4—261no—
424C2×C4—261no—
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×C4—524no—
441C2×C4C2×C22⋊D1312yes—
442C2×C4C2×C22⋊D1312yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—416no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22#8819014yescomplemented
472C22C2×D4×D1311yescharacteristic
473C22C2×#612911yescharacteristic
474C22C2×#612911yescharacteristic
475C22C2×#612911yescharacteristic
476C22#8825111yescharacteristic
477C22#8825111yescharacteristic
478C22C22×C22⋊D1311yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—262no—
483C4—262no—
484C4—521no—
485C4—521no—
486C4—521no—
487C4—521no—
488C4—521no—
489C4—521no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—81no—
494C2#1171929111yescharacteristic
495C2#1171929211yescharacteristic
496C2#1171929611yescharacteristic
497C2#1171929811yescharacteristic
498C2C2×#8819011yescharacteristic
499C2D4×C22⋊D1311yescharacteristic
500C2#1171951111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC2×C13×#120C2
hypercenterC2×#120D13
hypocenterC13#2472
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊Dic13C2semidirect
3. C2×#88190C2semidirect
4. C2×#88132C2semidirect
5. #11718908C2semidirect
6. #11718883C2semidirect
7. #11718883C2semidirect
8. #11718882C2semidirect
9. #11718881C2semidirect
10. #11718881C2semidirect
11. #11718614C2semidirect
12. #11718608C2semidirect
13. #11718606C2semidirect
14. #11718606C2semidirect
15. C22⋊C4×Dic13C2semidirect
22. C22×Dic26C22semidirect
38. C2×C22⋊Dic13C22semidirect
39. C2×C22⋊Dic13C22semidirect
40. C2×C22⋊Dic13C22semidirect
41. C2×C22⋊Dic13C22semidirect
43. C2×C4⋊Dic13C22semidirect
44. C2×#6101C22semidirect
45. C2×#6101C22semidirect
46. C2×C4×Dic13C22semidirect
47. C2×C4×Dic13C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
53. #88071C22semidirect
54. #88071C22semidirect
111. C22⋊Dic13D4semidirect
236. C22×C13#124semidirect
367. C13#2472semidirect
471. C22#88190semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1202
C22×C22⋊Dic132
C2×#881902
C2×#881322
#117189082
#117188832
#117188822
#117188812
#117186142
#117186082
#117186062
C22⋊C4×Dic132
#247213