Finite Group Databasebeta

← #13117813

Subgroups — #13117813

Order 1664.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 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×C4×C22⋊D13C211yesmaximal, characteristic, complemented
4C22×#6103C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D13C211yesmaximal, characteristic, complemented
6#11718881C211yesmaximal, characteristic, complemented
7#11718874C211yesmaximal, characteristic, complemented
8#11718871C211yesmaximal, characteristic, complemented
9#11718651C211yesmaximal, characteristic, complemented
10#11718650C211yesmaximal, characteristic, complemented
11#11718618C211yesmaximal, characteristic, complemented
12#11718617C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
14#11718601C211yesmaximal, characteristic, complemented
15C4×#6103C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C23×C4×C13C2211yescharacteristic
19C23×C4×C13C2211yescharacteristic, complemented
20C22×C22⋊D13C2211yescharacteristic
21C22×C22⋊D13C2211yescharacteristic
22C23×Dic13C2211yescharacteristic
23C22×C4×D13C2211yescharacteristic
24C22×C4×D13C2211yescharacteristic
25C4×D4×C13—24no—
26C2×C13×C4⋊C4C2211yescharacteristic, complemented
27C2×C13×C22⋊C4C2211yescharacteristic
28C2×C13×C22⋊C4C2211yescharacteristic, complemented
29C2×C42×C13C2211yescharacteristic, complemented
30C2×C22⋊Dic13C2211yescharacteristic
31C2×C22⋊Dic13C2211yescharacteristic
32C2×C22⋊Dic13C2211yescharacteristic, complemented
33C2×C22⋊Dic13C2211yescharacteristic, complemented
34#88191C418yescomplemented
35C4×C22⋊D13—24no—
36C2×#6103—24no—
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic
39C2×#6103C2211yescharacteristic
40C2×#6103C2211yescharacteristic
41C2×#6103C2211yescharacteristic
42C2×#6103C2211yescharacteristic
43C2×#6103C2211yescharacteristic
44C2×#6103C2211yescharacteristic
45C2×#6101C2211yescharacteristic, complemented
46C2×#6101C2211yescharacteristic, complemented
47C2×C4×Dic13C2211yescharacteristic, complemented
48C2×C4×Dic13C2211yescharacteristic, complemented
49C22⋊C4×D13—24no—
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53#88071C2211yescharacteristic, complemented
54#88071C2211yescharacteristic, complemented
55#88071C2211yescharacteristic, complemented
56C24×C13C2311yescharacteristic
57C24×C13C2311yescharacteristic
58C23×D13—22no—
59C23×D13—22no—
60C23×D13—22no—
61C23×D13—22no—
62C23×D13—41no—
63C23×D13—41no—
64C23×D13C2×C414yescomplemented
65C23×D13C2311yescharacteristic
66C23×D13C2311yescharacteristic
67C2×D4×C13—22no—
68C2×D4×C13—22no—
69C2×D4×C13C2×C414yescomplemented
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—22no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13C2311yescharacteristic
77C22×C4×C13C2311yescharacteristic
78C22×C4×C13C2311yescharacteristic
79C22×C4×C13C2311yescharacteristic
80C22×C4×C13C2311yescharacteristic
81C2×C22⋊D13—22no—
82C2×C22⋊D13—22no—
83C2×C22⋊D13—41no—
84C2×C22⋊D13—41no—
85C2×C22⋊D13C2×C414yescomplemented
86C2×C22⋊D13C2×C414yescomplemented
87C22×Dic13—22no—
88C22×Dic13—22no—
89C22×Dic13—41no—
90C22×Dic13C2311yescharacteristic
91C22×Dic13C2311yescharacteristic
92C22×Dic13C2311yescharacteristic
93C22×Dic13C2311yescharacteristic
94C22×Dic13C2311yescharacteristic
95C22×Dic13C2311yescharacteristic
96C2×C4×D13—22no—
97C2×C4×D13—22no—
98C2×C4×D13—22no—
99C2×C4×D13—22no—
100C2×C4×D13—41no—
101C2×C4×D13—41no—
102C13×C4⋊C4—22no—
103C13×C22⋊C4—22no—
104C13×C22⋊C4D414yescomplemented
105C42×C13—22no—
106C22⋊Dic13—22no—
107C22⋊Dic13—22no—
108C22⋊Dic13—41no—
109C22⋊Dic13C2×C414yescomplemented
110#6103—22no—
111#6103—22no—
112#6103—22no—
113#6103—22no—
114#6103—22no—
115#6103C2×C414yescomplemented
116#6103C2×C414yescomplemented
117#6103D414yescomplemented
118#6101—22no—
119#6101—41no—
120C4×Dic13—22no—
121C4×Dic13—41no—
122#2358—131nomaximal, Sylow
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×C13C22×C412yes—
134C23×C13C22×C412yes—
135C23×C13C2×D412yes—
136C23×C13#4112yes—
137C23×C13C2411yescharacteristic
138C22×D13—21no—
139C22×D13—21no—
140C22×D13—21no—
141C22×D13—21no—
142C22×D13—28no—
143C22×D13—21no—
144C22×D13—21no—
145C22×D13—21no—
146C22×D13—21no—
147C22×D13—21no—
148C22×D13—21no—
149C22×D13—28no—
150C22×D13—44no—
151C22×D13—44no—
152C22×D13—44no—
153C22×D13—44no—
154C22×D13—44no—
155C22×D13C22×C412yes—
156C22×D13C22×C412yes—
157C22×D13C2×D412yes—
158C22×D13#4112yes—
159D4×C13—28no—
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—21no—
171C2×C4×C13—44no—
172C2×C4×C13—44no—
173C2×C4×C13C22×C412yes—
174C2×C4×C13C2×D412yes—
175C2×C4×C13C2×D412yes—
176C2×C4×C13C2×D412yes—
177C22⋊D13—28no—
178C22⋊D13—44no—
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—21no—
192C2×Dic13—21no—
193C2×Dic13—21no—
194C2×Dic13—44no—
195C2×Dic13C22×C412yes—
196C2×Dic13C22×C412yes—
197C2×Dic13C2×D412yes—
198C4×D13—44no—
199C4×D13—44no—
200C2×#120—131no—
201C2×C4×D4—131no—
202C2×C4×D4D1311yescharacteristic, complemented
203C22×C22⋊C4—131no—
204C22×C22⋊C4—131no—
205#390—131no—
206#388—131no—
207#388—131no—
208#386—131no—
209#386—131no—
210#386—131no—
211#385—131no—
212#385—131no—
213C4×C22⋊C4—131no—
214C4×C22⋊C4—131no—
215C22×C13—22no—
216C22×C13—22no—
217C22×C13—22no—
218C22×C13—22no—
219C22×C13—22no—
220C22×C13—22no—
221C22×C13—22no—
222C22×C13—22no—
223C22×C13—22no—
224C22×C13—41no—
225C22×C13—41no—
226C22×C13—41no—
227C22×C13—41no—
228C22×C13C4×D414yescomplemented
229C22×C13C23×C411yescharacteristic
230C22×C13C22×D411yescharacteristic
231C22×C13C22×D411yescharacteristic
232C22×C13C2×#4111yescharacteristic
233C22×C13C2×#4111yescharacteristic
234C22×C13H(5,𝔽2)11yescharacteristic
235C22×C13H(5,𝔽2)11yescharacteristic
236C2×D13—22no—
237C2×D13—22no—
238C2×D13—22no—
239C2×D13—22no—
240C2×D13—22no—
241C2×D13—22no—
242C2×D13—22no—
243C2×D13—22no—
244C2×D13—22no—
245C2×D13—416no—
246C2×D13—41no—
247C2×D13—41no—
248C2×D13—41no—
249C2×D13—41no—
250C2×D13C4×D414yescomplemented
251C4×C13—22no—
252C4×C13—22no—
253C4×C13—22no—
254C4×C13—22no—
255C4×C13—41no—
256Dic13—22no—
257Dic13—22no—
258Dic13—22no—
259Dic13—41no—
260Dic13—41no—
261Dic13—41no—
262C25—131no—
263C22×D4—131no—
264C22×D4—131no—
265C22×D4C2×D1311yescharacteristic
266C23×C4—131no—
267C23×C4—131no—
268C23×C4—131no—
269C23×C4C2×D1311yescharacteristic
270C23×C4C2×D1311yescharacteristic, complemented
271#120—138no—
272C4×D4—24no—
273C4×D4—264no—
274C2×C4⋊C4—131no—
275C2×C4⋊C4—131no—
276C2×C4⋊C4C2×D1311yescharacteristic, complemented
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—131no—
285C2×C22⋊C4—131no—
286C2×C22⋊C4—131no—
287C2×C22⋊C4—131no—
288C2×C22⋊C4—131no—
289C2×C22⋊C4—264no—
290C2×C22⋊C4—264no—
291C2×C22⋊C4C2×D1311yescharacteristic
292C2×C22⋊C4C2×D1311yescharacteristic, complemented
293C2×C42—131no—
294C2×C42—131no—
295C2×C42C2×D1311yescharacteristic, complemented
296#95—131no—
297#95—131no—
298#95—131no—
299#95—131no—
300#95—131no—
301#95—131no—
302C2×C13—24no—
303C2×C13—42no—
304C2×C13C2×C4×D411yescharacteristic
305C2×C13C2×C4×D411yescharacteristic
306C2×C13#51811yescharacteristic
307C2×C13D4211yescharacteristic
308C2×C13#54611yescharacteristic
309C2×C13#54611yescharacteristic
310C2×C13#55111yescharacteristic
311D13—24no—
312D13—42no—
313C24—131no—
314C24—131no—
315C24—134no—
316C24—262no—
317C24—262no—
318C24—262no—
319C24—262no—
320C24—521no—
321C24—521no—
322C24C22×D1311yescharacteristic
323C24C22×D1311yescharacteristic
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—134no—
327C2×D4—134no—
328C2×D4—262no—
329C2×D4—262no—
330C2×D4—521no—
331C2×D4—521no—
332C2×D4C4×D1314yescomplemented
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—131no—
340C22×C4—131no—
341C22×C4—131no—
342C22×C4—131no—
343C22×C4—131no—
344C22×C4—131no—
345C22×C4—262no—
346C22×C4—262no—
347C22×C4—262no—
348C22×C4—262no—
349C22×C4—262no—
350C22×C4—262no—
351C22×C4—521no—
352C22×C4—521no—
353C22×C4—521no—
354C22×C4C22×D1311yescharacteristic
355C22×C4C22×D1311yescharacteristic
356C22×C4C22×D1311yescharacteristic
357C22×C4C22×D1311yescharacteristic
358C22×C4C22×D1311yescharacteristic
359C4⋊C4—22no—
360C4⋊C4—262no—
361C4⋊C4—521no—
362C22⋊C4—22no—
363C22⋊C4—134no—
364C22⋊C4—134no—
365C22⋊C4—134no—
366C22⋊C4—134no—
367C22⋊C4—262no—
368C22⋊C4—262no—
369C22⋊C4—262no—
370C22⋊C4—262no—
371C22⋊C4—262no—
372C22⋊C4—262no—
373C22⋊C4—262no—
374C22⋊C4—521no—
375C22⋊C4C22⋊D1314yescomplemented
376C42—22no—
377C42—262no—
378C42—521no—
379C13#235811yescharacteristic, complemented, Sylow
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—132no—
391C23—132no—
392C23—132no—
393C23—132no—
394C23—268no—
395C23—261no—
396C23—261no—
397C23—261no—
398C23—261no—
399C23—268no—
400C23—261no—
401C23—261no—
402C23—261no—
403C23—261no—
404C23—261no—
405C23—261no—
406C23—524no—
407C23—524no—
408C23—524no—
409C23—524no—
410C23—524no—
411C23C2×C4×D1312yes—
412C23C2×C4×D1312yes—
413C23#612712yes—
414C23C2×C22⋊D1312yes—
415C23C23×D1311yescharacteristic
416D4—28no—
417D4—268no—
418D4—524no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4—132no—
433C2×C4—132no—
434C2×C4—132no—
435C2×C4—261no—
436C2×C4—261no—
437C2×C4—261no—
438C2×C4—261no—
439C2×C4—261no—
440C2×C4—261no—
441C2×C4—261no—
442C2×C4—261no—
443C2×C4—261no—
444C2×C4—261no—
445C2×C4—261no—
446C2×C4—261no—
447C2×C4—261no—
448C2×C4—261no—
449C2×C4—261no—
450C2×C4—524no—
451C2×C4—524no—
452C2×C4—524no—
453C2×C4C2×C4×D1312yes—
454C2×C4D4×D1312yes—
455C2×C4C2×C22⋊D1312yes—
456C2×C4C2×C22⋊D1312yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—134no—
471C22—262no—
472C22—262no—
473C22—262no—
474C22—262no—
475C22—262no—
476C22—262no—
477C22—262no—
478C22—262no—
479C22—262no—
480C22—5216no—
481C22—521no—
482C22—521no—
483C22—521no—
484C22—521no—
485C22C4×C22⋊D1314yescomplemented
486C22C22×C4×D1311yescharacteristic
487C22C2×#612711yescharacteristic
488C22C2×D4×D1311yescharacteristic
489C22#8825111yescharacteristic
490C22#41×D1311yescharacteristic
491C22#8825611yescharacteristic
492C22C22×C22⋊D1311yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—262no—
499C4—262no—
500C4—262no—
501C4—521no—
502C4—521no—
503C4—521no—
504C2—24no—
505C2—42no—
506C2—264no—
507C2—522no—
508C2C4×D4×D1311yescharacteristic
509C2#1171925011yescharacteristic
510C2#1171925511yescharacteristic
511C2#1171926111yescharacteristic
512C2C2×C4×C22⋊D1311yescharacteristic
513C2D4×C22⋊D1311yescharacteristic
514C2#1171953411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC2×C4×D4×C13C2
socle, cosocleC23×C13C24
prime radicalC2×#88191C2
hypercenterC2×C4×D4D13
hypocenterC13#2358
LCSG ▷ C22×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×C4×C22⋊D13C2semidirect
4. C22×#6103C2semidirect
5. C2×C22⋊C4×D13C2semidirect
6. #11718881C2semidirect
7. #11718874C2semidirect
8. #11718871C2semidirect
9. #11718651C2semidirect
10. #11718650C2semidirect
11. #11718618C2semidirect
12. #11718617C2semidirect
13. C22⋊C4×Dic13C2semidirect
14. #11718601C2semidirect
15. C4×#6103C2semidirect
19. C23×C4×C13C22semidirect
26. C2×C13×C4⋊C4C22semidirect
28. C2×C13×C22⋊C4C22semidirect
29. C2×C42×C13C22semidirect
32. C2×C22⋊Dic13C22semidirect
33. C2×C22⋊Dic13C22semidirect
34. #88191C4semidirect
45. C2×#6101C22semidirect
46. C2×#6101C22semidirect
47. C2×C4×Dic13C22semidirect
48. C2×C4×Dic13C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
53. #88071C22semidirect
54. #88071C22semidirect
55. #88071C22semidirect
64. C23×D13C2×C4semidirect
69. C2×D4×C13C2×C4semidirect
85. C2×C22⋊D13C2×C4semidirect
86. C2×C22⋊D13C2×C4semidirect
104. C13×C22⋊C4D4semidirect
109. C22⋊Dic13C2×C4semidirect
115. #6103C2×C4semidirect
116. #6103C2×C4semidirect
117. #6103D4semidirect
202. C2×C4×D4D13semidirect
228. C22×C13C4×D4semidirect
250. C2×D13C4×D4semidirect
270. C23×C4C2×D13semidirect
276. C2×C4⋊C4C2×D13semidirect
292. C2×C22⋊C4C2×D13semidirect
295. C2×C42C2×D13semidirect
332. C2×D4C4×D13semidirect
375. C22⋊C4C22⋊D13semidirect
379. C13#2358semidirect
485. C22C4×C22⋊D13semidirect

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×C4×C22⋊D132
C22×#61032
C2×C22⋊C4×D132
#117188812
#117188742
#117188712
#117186512
#117186502
#117186182
#117186172
C22⋊C4×Dic132
#117186012
C4×#61032
#235813