Finite Group Databasebeta

← #13118292

Subgroups — #13118292

Order 1664.

800 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×C4×D4×C13C211yesmaximal, characteristic, complemented
2C2×#88191C211yesmaximal, characteristic
3C2×#88183C211yesmaximal, characteristic, complemented
4C22×#6103C211yesmaximal, characteristic, complemented
5#11718881C211yesmaximal, characteristic, complemented
6#11718874C211yesmaximal, characteristic, complemented
7#11718871C211yesmaximal, characteristic, complemented
8#11718654C211yesmaximal, characteristic, complemented
9#11718653C211yesmaximal, characteristic, complemented
10#11718620C211yesmaximal, characteristic, complemented
11#11718620C211yesmaximal, characteristic, complemented
12#11718616C211yesmaximal, characteristic, complemented
13#11718603C211yesmaximal, characteristic, complemented
14#11718601C211yesmaximal, characteristic, complemented
15#11718601C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C23×C4×C13C2211yescharacteristic
19C23×C4×C13C2211yescharacteristic, complemented
20C22×C22⋊D13C2211yescharacteristic
21C22×C22⋊D13C2211yescharacteristic
22C23×Dic13C2211yescharacteristic
23C4×D4×C13—24no—
24C2×C13×C4⋊C4C2211yescharacteristic, complemented
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C13×C22⋊C4C2211yescharacteristic, complemented
27C2×C42×C13C2211yescharacteristic, complemented
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊Dic13C2211yescharacteristic, complemented
31C2×C22⋊Dic13C2211yescharacteristic, complemented
32#88191—24no—
33#88183—24no—
34C2×#6103—24no—
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic
39C2×#6103C2211yescharacteristic
40C2×#6103C2211yescharacteristic
41C2×#6103C2211yescharacteristic
42C2×#6103C2211yescharacteristic
43C2×#6103C2211yescharacteristic
44C2×#6103C2211yescharacteristic
45C2×#6101C2211yescharacteristic, complemented
46C2×#6101C2211yescharacteristic, complemented
47C2×#6101C2211yescharacteristic, complemented
48C2×#6101C2211yescharacteristic, complemented
49#88071C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53#88071C2211yescharacteristic, complemented
54#88071C2211yescharacteristic, complemented
55C24×C13C2311yescharacteristic
56C24×C13C2311yescharacteristic
57C23×D13—22no—
58C23×D13—22no—
59C23×D13—22no—
60C23×D13—22no—
61C23×D13—22no—
62C23×D13—41no—
63C23×D13—41no—
64C23×D13C2311yescharacteristic
65C23×D13C2311yescharacteristic
66C2×D4×C13—22no—
67C2×D4×C13—22no—
68C2×D4×C13D414yes—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13C2311yescharacteristic
76C22×C4×C13C2311yescharacteristic
77C22×C4×C13C2311yescharacteristic
78C22×C4×C13C2311yescharacteristic
79C22×C4×C13C2311yescharacteristic
80C2×C22⋊D13—22no—
81C2×C22⋊D13—22no—
82C2×C22⋊D13—22no—
83C2×C22⋊D13—22no—
84C2×C22⋊D13—41no—
85C2×C22⋊D13—41no—
86C22×Dic13—22no—
87C22×Dic13—22no—
88C22×Dic13—41no—
89C22×Dic13C2311yescharacteristic
90C22×Dic13C2311yescharacteristic
91C22×Dic13C2311yescharacteristic
92C22×Dic13C2311yescharacteristic
93C22×Dic13C2311yescharacteristic
94C22×Dic13C2311yescharacteristic
95C13×C4⋊C4—22no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4—22no—
98C42×C13—22no—
99C22⋊Dic13—22no—
100C22⋊Dic13—22no—
101C22⋊Dic13—22no—
102C22⋊Dic13—41no—
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#6103D414yescomplemented
113#6101—22no—
114#6101—22no—
115#6101—41no—
116#6101—41no—
117#2418—131nomaximal, Sylow
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13C2×D412yes—
129C23×C13C2×D412yes—
130C23×C13#4112yes—
131C23×C13#4112yes—
132C23×C13C2411yescharacteristic
133C22×D13—28no—
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—
154D4×C13—28no—
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—44no—
169C2×C4×C13—44no—
170C2×C4×C13C2×D412yes—
171C2×C4×C13C2×D412yes—
172C22⋊D13—44no—
173C22⋊D13—44no—
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—21no—
189C2×Dic13—21no—
190C2×Dic13—21no—
191C2×Dic13—44no—
192C2×Dic13C2×D412yes—
193C2×#123—131no—
194C2×#120—131no—
195C2×C4×D4D1311yescharacteristic, complemented
196C22×C22⋊C4—131no—
197#399—131no—
198#397—131no—
199#394—131no—
200#394—131no—
201#388—131no—
202#388—131no—
203#386—131no—
204#386—131no—
205#385—131no—
206#380—131no—
207#379—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—41no—
218C22×C13—41no—
219C22×C13—41no—
220C22×C13—41no—
221C22×C13#12314yescomplemented
222C22×C13C22×D411yescharacteristic
223C22×C13C22×D411yescharacteristic
224C22×C13C2×#4111yescharacteristic
225C22×C13C2×#4111yescharacteristic
226C22×C13C2×#4111yescharacteristic
227C22×C13H(5,𝔽2)11yescharacteristic
228C22×C13H(5,𝔽2)11yescharacteristic
229C2×D13—22no—
230C2×D13—22no—
231C2×D13—22no—
232C2×D13—22no—
233C2×D13—22no—
234C2×D13—22no—
235C2×D13—416no—
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—41no—
247C4×C13—41no—
248C4×C13—41no—
249Dic13—22no—
250Dic13—41no—
251Dic13—41no—
252Dic13—41no—
253Dic13—41no—
254Dic13—41no—
255C25—131no—
256C22×D4—131no—
257C22×D4—131no—
258C22×D4C2×D1311yescharacteristic
259C23×C4—131no—
260C23×C4C2×D1311yescharacteristic
261C23×C4C2×D1311yescharacteristic, complemented
262#123—264no—
263#120—264no—
264C4×D4—24no—
265C2×C4⋊C4—131no—
266C2×C4⋊C4—131no—
267C2×C4⋊C4—131no—
268C2×C4⋊C4—131no—
269C2×C4⋊C4C2×D1311yescharacteristic, complemented
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—131no—
284C2×C22⋊C4—264no—
285C2×C22⋊C4C2×D1311yescharacteristic
286C2×C22⋊C4C2×D1311yescharacteristic, complemented
287C2×C42C2×D1311yescharacteristic, complemented
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×C13C2×#12311yescharacteristic
297C2×C13#52511yescharacteristic
298C2×C13#53811yescharacteristic
299C2×C13D4211yescharacteristic
300C2×C13#54611yescharacteristic
301C2×C13#54611yescharacteristic
302C2×C13#55111yescharacteristic
303D13—42no—
304D13—42no—
305C24—131no—
306C24—131no—
307C24—262no—
308C24—262no—
309C24—262no—
310C24—262no—
311C24—262no—
312C24—521no—
313C24—521no—
314C24C22×D1311yescharacteristic
315C24C22×D1311yescharacteristic
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—262no—
319C2×D4—262no—
320C2×D4—262no—
321C2×D4—262no—
322C2×D4—521no—
323C2×D4—521no—
324C2×D4C22⋊D1314yes—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—131no—
332C22×C4—131no—
333C22×C4—131no—
334C22×C4—131no—
335C22×C4—131no—
336C22×C4—131no—
337C22×C4—262no—
338C22×C4—262no—
339C22×C4—521no—
340C22×C4C22×D1311yescharacteristic
341C22×C4C22×D1311yescharacteristic
342C22×C4C22×D1311yescharacteristic
343C22×C4C22×D1311yescharacteristic
344C22×C4C22×D1311yescharacteristic
345C4⋊C4—22no—
346C4⋊C4—262no—
347C4⋊C4—262no—
348C4⋊C4—521no—
349C4⋊C4—521no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—134no—
353C22⋊C4—262no—
354C22⋊C4—262no—
355C22⋊C4—262no—
356C22⋊C4—262no—
357C22⋊C4—262no—
358C22⋊C4—262no—
359C22⋊C4—262no—
360C22⋊C4—262no—
361C22⋊C4—262no—
362C22⋊C4—262no—
363C22⋊C4—521no—
364C22⋊C4—521no—
365C22⋊C4—521no—
366C42—22no—
367C13#241811yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—132no—
379C23—132no—
380C23—268no—
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—524no—
394C23—524no—
395C23—524no—
396C23—524no—
397C23—524no—
398C23—524no—
399C23#612712yes—
400C23#612712yes—
401C23C2×C22⋊D1312yes—
402C23C2×C22⋊D1312yes—
403C23C23×D1311yescharacteristic
404D4—28no—
405D4—524no—
406D4—524no—
407C2×C4—21no—
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—44no—
421C2×C4—44no—
422C2×C4—132no—
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—261no—
440C2×C4—524no—
441C2×C4D4×D1312yes—
442C2×C4C2×C22⋊D1312yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—262no—
457C22—262no—
458C22—262no—
459C22—262no—
460C22—262no—
461C22—262no—
462C22—5216no—
463C22—521no—
464C22—521no—
465C22—521no—
466C22—521no—
467C22—521no—
468C22—521no—
469C22—521no—
470C22—521no—
471C22#8818314yescomplemented
472C22C2×#612711yescharacteristic
473C22C2×#612711yescharacteristic
474C22C2×D4×D1311yescharacteristic
475C22#8825111yescharacteristic
476C22#41×D1311yescharacteristic
477C22#8825611yescharacteristic
478C22C22×C22⋊D1311yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—262no—
485C4—521no—
486C4—521no—
487C4—521no—
488C4—521no—
489C4—521no—
490C2—24no—
491C2—42no—
492C2—522no—
493C2—522no—
494C2#1171925211yescharacteristic
495C2#1171925511yescharacteristic
496C2#1171926111yescharacteristic
497C2#1171926511yescharacteristic
498C2C2×#8818311yescharacteristic
499C2D4×C22⋊D1311yescharacteristic
500C2#1171953411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C4×D4×C13C2
prime radicalC2×#88191C2
hypercenterC2×C4×D4D13
hypocenterC13#2418
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×C13C2semidirect
3. C2×#88183C2semidirect
4. C22×#6103C2semidirect
5. #11718881C2semidirect
6. #11718874C2semidirect
7. #11718871C2semidirect
8. #11718654C2semidirect
9. #11718653C2semidirect
10. #11718620C2semidirect
11. #11718620C2semidirect
12. #11718616C2semidirect
13. #11718603C2semidirect
14. #11718601C2semidirect
15. #11718601C2semidirect
19. C23×C4×C13C22semidirect
24. C2×C13×C4⋊C4C22semidirect
26. C2×C13×C22⋊C4C22semidirect
27. C2×C42×C13C22semidirect
30. C2×C22⋊Dic13C22semidirect
31. C2×C22⋊Dic13C22semidirect
45. C2×#6101C22semidirect
46. C2×#6101C22semidirect
47. C2×#6101C22semidirect
48. C2×#6101C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
53. #88071C22semidirect
54. #88071C22semidirect
112. #6103D4semidirect
195. C2×C4×D4D13semidirect
221. C22×C13#123semidirect
261. C23×C4C2×D13semidirect
269. C2×C4⋊C4C2×D13semidirect
286. C2×C22⋊C4C2×D13semidirect
287. C2×C42C2×D13semidirect
367. C13#2418semidirect
471. C22#88183semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C132
C2×#881912
C2×#881832
C22×#61032
#117188812
#117188742
#117188712
#117186542
#117186532
#117186202
#117186162
#117186032
#117186012
#241813