Finite Group Databasebeta

← #13118366

Subgroups — #13118366

Order 1664.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×C13C211yesmaximal, characteristic, complemented
2C2×#88193C211yesmaximal, characteristic, complemented
3C2×#88191C211yesmaximal, characteristic, complemented
4C2×#88184C211yesmaximal, characteristic, complemented
5C22×#6103C211yesmaximal, characteristic, complemented
6C2×#88136C211yesmaximal, characteristic, complemented
7#11718874C211yesmaximal, characteristic, complemented
8#11718874C211yesmaximal, characteristic, complemented
9#11718655C211yesmaximal, characteristic, complemented
10#11718652C211yesmaximal, characteristic, complemented
11#11718622C211yesmaximal, characteristic, complemented
12#11718621C211yesmaximal, characteristic, complemented
13#11718611C211yesmaximal, characteristic, complemented
14#11718601C211yesmaximal, characteristic, complemented
15#11718600C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C23×C4×C13C2211yescharacteristic
19C23×C4×C13C2211yescharacteristic, complemented
20C22×C22⋊D13C2211yescharacteristic
21C22×C22⋊D13C2211yescharacteristic
22C22×C22⋊D13C2211yescharacteristic
23C22×C22⋊D13C2211yescharacteristic, complemented
24C23×Dic13C2211yescharacteristic
25C22×D52C2211yescharacteristic
26C22×D52C2211yescharacteristic
27C4×D4×C13—24no—
28C2×C13×C4⋊C4C2211yescharacteristic, complemented
29C2×C13×C22⋊C4C2211yescharacteristic
30C2×C13×C22⋊C4C2211yescharacteristic, complemented
31C2×C42×C13C2211yescharacteristic, complemented
32C2×C22⋊Dic13C2211yescharacteristic
33C2×C22⋊Dic13C2211yescharacteristic, complemented
34#88193—24no—
35#88191—24no—
36#88184—24no—
37C2×#6103—24no—
38C2×#6103C2211yescharacteristic
39C2×#6103C2211yescharacteristic
40C2×#6103C2211yescharacteristic
41C2×#6103C2211yescharacteristic
42C2×#6103C2211yescharacteristic
43C2×#6103C2211yescharacteristic
44C2×#6103C2211yescharacteristic
45C2×#6103C2211yescharacteristic
46C2×#6103C2211yescharacteristic, complemented
47C2×#6103C2211yescharacteristic, complemented
48C2×#6103C2211yescharacteristic, complemented
49C2×C4⋊Dic13C2211yescharacteristic, complemented
50C2×C4⋊Dic13C2211yescharacteristic, complemented
51C2×#6101C2211yescharacteristic, complemented
52#88136—24no—
53#88071C2211yescharacteristic, complemented
54#88071C2211yescharacteristic, complemented
55#88071C2211yescharacteristic, complemented
56#88071C2211yescharacteristic, complemented
57C24×C13C2311yescharacteristic
58C24×C13C2311yescharacteristic
59C23×D13—22no—
60C23×D13—22no—
61C23×D13—22no—
62C23×D13—22no—
63C23×D13—22no—
64C23×D13—41no—
65C23×D13—41no—
66C23×D13C2311yescharacteristic
67C23×D13C2311yescharacteristic
68C23×D13C2311yescharacteristic
69C2×D4×C13—22no—
70C2×D4×C13—22no—
71C2×D4×C13D414yescomplemented
72C22×C4×C13—22no—
73C22×C4×C13—22no—
74C22×C4×C13—22no—
75C22×C4×C13—22no—
76C22×C4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13C2311yescharacteristic
79C22×C4×C13C2311yescharacteristic
80C22×C4×C13C2311yescharacteristic
81C22×C4×C13C2311yescharacteristic
82C22×C4×C13C2311yescharacteristic
83C2×C22⋊D13—22no—
84C2×C22⋊D13—22no—
85C2×C22⋊D13—22no—
86C2×C22⋊D13—22no—
87C2×C22⋊D13—22no—
88C2×C22⋊D13—22no—
89C2×C22⋊D13—22no—
90C2×C22⋊D13—22no—
91C2×C22⋊D13—22no—
92C2×C22⋊D13—41no—
93C2×C22⋊D13—41no—
94C2×C22⋊D13—41no—
95C22×Dic13—22no—
96C22×Dic13—22no—
97C22×Dic13—41no—
98C22×Dic13C2311yescharacteristic
99C22×Dic13C2311yescharacteristic
100C22×Dic13C2311yescharacteristic
101C22×Dic13C2311yescharacteristic
102C22×Dic13C2311yescharacteristic
103C2×D52—22no—
104C2×D52—22no—
105C2×D52—22no—
106C2×D52—22no—
107C2×D52—41no—
108C2×D52—41no—
109C13×C4⋊C4—22no—
110C13×C22⋊C4—22no—
111C13×C22⋊C4D414yescomplemented
112C42×C13—22no—
113C22⋊Dic13—22no—
114C22⋊Dic13—22no—
115#6103—22no—
116#6103—22no—
117#6103—22no—
118#6103—22no—
119#6103—22no—
120#6103—22no—
121#6103—22no—
122#6103—22no—
123#6103—22no—
124#6103—41no—
125#6103D414yescomplemented
126C4⋊Dic13—22no—
127C4⋊Dic13—41no—
128#6101—22no—
129#2424—131nomaximal, Sylow
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×C13C2×D412yes—
141C23×C13C2×D412yes—
142C23×C13C2×D412yes—
143C23×C13#4112yes—
144C23×C13C2411yescharacteristic
145C22×D13—28no—
146C22×D13—21no—
147C22×D13—21no—
148C22×D13—21no—
149C22×D13—21no—
150C22×D13—21no—
151C22×D13—21no—
152C22×D13—21no—
153C22×D13—21no—
154C22×D13—21no—
155C22×D13—21no—
156C22×D13—21no—
157C22×D13—21no—
158C22×D13—21no—
159C22×D13—21no—
160C22×D13—21no—
161C22×D13—21no—
162C22×D13—21no—
163C22×D13—21no—
164C22×D13—21no—
165C22×D13—44no—
166C22×D13—44no—
167C22×D13—44no—
168C22×D13—44no—
169C22×D13—44no—
170C22×D13—44no—
171C22×D13C2×D412yes—
172C22×D13#4112yes—
173D4×C13—28no—
174C2×C4×C13—21no—
175C2×C4×C13—21no—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—21no—
180C2×C4×C13—21no—
181C2×C4×C13—21no—
182C2×C4×C13—21no—
183C2×C4×C13—21no—
184C2×C4×C13—21no—
185C2×C4×C13—44no—
186C2×C4×C13—44no—
187C2×C4×C13C2×D412yes—
188C2×C4×C13C2×D412yes—
189C2×C4×C13C2×D412yes—
190C2×C4×C13C2×D412yes—
191C22⋊D13—44no—
192C22⋊D13—44no—
193C22⋊D13—44no—
194C22⋊D13—44no—
195C2×Dic13—21no—
196C2×Dic13—21no—
197C2×Dic13—21no—
198C2×Dic13—21no—
199C2×Dic13—21no—
200C2×Dic13—21no—
201C2×Dic13—21no—
202C2×Dic13—21no—
203C2×Dic13—21no—
204C2×Dic13—21no—
205C2×Dic13—21no—
206C2×Dic13—21no—
207C2×Dic13—21no—
208C2×Dic13—21no—
209C2×Dic13—44no—
210C2×Dic13C2×D412yes—
211D52—44no—
212D52—44no—
213C2×#121—131no—
214C2×#121—131no—
215C2×#120—131no—
216C2×#120—131no—
217C2×C4×D4D1311yescharacteristic, complemented
218C22×C22⋊C4—131no—
219#396—131no—
220#394—131no—
221#394—131no—
222#392—131no—
223#390—131no—
224#388—131no—
225#386—131no—
226#386—131no—
227#385—131no—
228C22×C13—22no—
229C22×C13—22no—
230C22×C13—22no—
231C22×C13—22no—
232C22×C13—22no—
233C22×C13—22no—
234C22×C13—22no—
235C22×C13—22no—
236C22×C13—22no—
237C22×C13—41no—
238C22×C13—41no—
239C22×C13—41no—
240C22×C13—41no—
241C22×C13#12114yescomplemented
242C22×C13C22×D411yescharacteristic
243C22×C13C22×D411yescharacteristic
244C22×C13C22×D411yescharacteristic
245C22×C13C2×#4111yescharacteristic
246C22×C13C2×#4111yescharacteristic
247C22×C13H(5,𝔽2)11yescharacteristic
248C22×C13H(5,𝔽2)11yescharacteristic
249C2×D13—22no—
250C2×D13—22no—
251C2×D13—22no—
252C2×D13—22no—
253C2×D13—22no—
254C2×D13—22no—
255C2×D13—416no—
256C2×D13—41no—
257C2×D13—41no—
258C2×D13—41no—
259C2×D13—41no—
260C2×D13—41no—
261C2×D13—41no—
262C2×D13—41no—
263C2×D13—41no—
264C2×D13—41no—
265C2×D13—41no—
266C2×D13—41no—
267C2×D13—41no—
268C2×D13—41no—
269C2×D13—41no—
270C2×D13—41no—
271C4×C13—22no—
272C4×C13—22no—
273C4×C13—22no—
274C4×C13—22no—
275C4×C13—41no—
276Dic13—22no—
277Dic13—41no—
278Dic13—41no—
279Dic13—41no—
280Dic13—41no—
281C25—131no—
282C22×D4—131no—
283C22×D4—131no—
284C22×D4—131no—
285C22×D4—131no—
286C22×D4—131no—
287C22×D4—131no—
288C22×D4C2×D1311yescharacteristic
289C23×C4—131no—
290C23×C4C2×D1311yescharacteristic
291C23×C4C2×D1311yescharacteristic, complemented
292#121—264no—
293#121—264no—
294#120—264no—
295#120—264no—
296C4×D4—24no—
297C2×C4⋊C4—131no—
298C2×C4⋊C4—131no—
299C2×C4⋊C4—131no—
300C2×C4⋊C4C2×D1311yescharacteristic, complemented
301C2×C22⋊C4—131no—
302C2×C22⋊C4—131no—
303C2×C22⋊C4—131no—
304C2×C22⋊C4—131no—
305C2×C22⋊C4—131no—
306C2×C22⋊C4—131no—
307C2×C22⋊C4—131no—
308C2×C22⋊C4—131no—
309C2×C22⋊C4—131no—
310C2×C22⋊C4—131no—
311C2×C22⋊C4—131no—
312C2×C22⋊C4—131no—
313C2×C22⋊C4—131no—
314C2×C22⋊C4—264no—
315C2×C22⋊C4C2×D1311yescharacteristic
316C2×C22⋊C4C2×D1311yescharacteristic, complemented
317C2×C42C2×D1311yescharacteristic, complemented
318#95—131no—
319#95—131no—
320#95—131no—
321#95—131no—
322C2×C13—24no—
323C2×C13—42no—
324C2×C13C2×#12111yescharacteristic
325C2×C13#52511yescharacteristic
326C2×C13#53811yescharacteristic
327C2×C13D4211yescharacteristic
328C2×C13D4211yescharacteristic
329C2×C13#54611yescharacteristic
330C2×C13#54611yescharacteristic
331D13—42no—
332D13—42no—
333D13—81no—
334C24—131no—
335C24—131no—
336C24—131no—
337C24—262no—
338C24—262no—
339C24—262no—
340C24—262no—
341C24—262no—
342C24—521no—
343C24—521no—
344C24C22×D1311yescharacteristic
345C24C22×D1311yescharacteristic
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—262no—
349C2×D4—262no—
350C2×D4—262no—
351C2×D4—262no—
352C2×D4—262no—
353C2×D4—262no—
354C2×D4—262no—
355C2×D4—262no—
356C2×D4—262no—
357C2×D4—262no—
358C2×D4—262no—
359C2×D4—262no—
360C2×D4—262no—
361C2×D4—521no—
362C2×D4—521no—
363C2×D4—521no—
364C2×D4—521no—
365C2×D4—521no—
366C2×D4D5214yescomplemented
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—131no—
374C22×C4—131no—
375C22×C4—131no—
376C22×C4—131no—
377C22×C4—131no—
378C22×C4—262no—
379C22×C4—262no—
380C22×C4—521no—
381C22×C4C22×D1311yescharacteristic
382C22×C4C22×D1311yescharacteristic
383C22×C4C22×D1311yescharacteristic
384C22×C4C22×D1311yescharacteristic
385C22×C4C22×D1311yescharacteristic
386C4⋊C4—22no—
387C4⋊C4—262no—
388C4⋊C4—262no—
389C4⋊C4—521no—
390C22⋊C4—22no—
391C22⋊C4—134no—
392C22⋊C4—262no—
393C22⋊C4—262no—
394C22⋊C4—262no—
395C22⋊C4—262no—
396C22⋊C4—262no—
397C22⋊C4—262no—
398C22⋊C4—262no—
399C22⋊C4—262no—
400C22⋊C4—262no—
401C22⋊C4—262no—
402C22⋊C4—262no—
403C22⋊C4—521no—
404C22⋊C4C22⋊D1314yescomplemented
405C42—22no—
406C13#242411yescharacteristic, complemented, Sylow
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—132no—
418C23—132no—
419C23—268no—
420C23—261no—
421C23—261no—
422C23—261no—
423C23—261no—
424C23—261no—
425C23—261no—
426C23—261no—
427C23—261no—
428C23—261no—
429C23—261no—
430C23—261no—
431C23—261no—
432C23—261no—
433C23—261no—
434C23—261no—
435C23—261no—
436C23—261no—
437C23—261no—
438C23—261no—
439C23—524no—
440C23—524no—
441C23—524no—
442C23—524no—
443C23—524no—
444C23—524no—
445C23C2×D5212yes—
446C23C2×D5212yes—
447C23#612712yes—
448C23C2×C22⋊D1312yes—
449C23C23×D1311yescharacteristic
450D4—28no—
451D4—524no—
452D4—524no—
453D4—524no—
454D4—524no—
455D4—524no—
456D4—524no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—132no—
471C2×C4—261no—
472C2×C4—261no—
473C2×C4—261no—
474C2×C4—261no—
475C2×C4—261no—
476C2×C4—261no—
477C2×C4—261no—
478C2×C4—261no—
479C2×C4—261no—
480C2×C4—261no—
481C2×C4—261no—
482C2×C4—261no—
483C2×C4—261no—
484C2×C4—261no—
485C2×C4—524no—
486C2×C4C2×D5212yes—
487C2×C4D4×D1312yes—
488C2×C4C2×C22⋊D1312yes—
489C2×C4C2×C22⋊D1312yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—262no—
504C22—262no—
505C22—262no—
506C22—262no—
507C22—262no—
508C22—262no—
509C22—5216no—
510C22—521no—
511C22—521no—
512C22—521no—
513C22—521no—
514C22—521no—
515C22—521no—
516C22—521no—
517C22—521no—
518C22—521no—
519C22—521no—
520C22—521no—
521C22—521no—
522C22—521no—
523C22—521no—
524C22—521no—
525C22#8818414yescomplemented
526C22C22×D5211yescharacteristic
527C22C2×#612711yescharacteristic
528C22C2×D4×D1311yescharacteristic
529C22#8825111yescharacteristic
530C22#41×D1311yescharacteristic
531C22#8825611yescharacteristic
532C22C22×C22⋊D1311yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—22no—
537C4—41no—
538C4—262no—
539C4—521no—
540C4—521no—
541C4—521no—
542C4—521no—
543C2—24no—
544C2—42no—
545C2—522no—
546C2—522no—
547C2—1041no—
548C2#1171925211yescharacteristic
549C2D4×D5211yescharacteristic
550C2#1171925911yescharacteristic
551C2#1171926511yescharacteristic
552C2C2×#8818411yescharacteristic
553C2D4×C22⋊D1311yescharacteristic
554C2#1171953411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C4×D4×C13C2
hypercenterC2×C4×D4D13
hypocenterC13#2424
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
2. C2×#88193C2semidirect
3. C2×#88191C2semidirect
4. C2×#88184C2semidirect
5. C22×#6103C2semidirect
6. C2×#88136C2semidirect
7. #11718874C2semidirect
8. #11718874C2semidirect
9. #11718655C2semidirect
10. #11718652C2semidirect
11. #11718622C2semidirect
12. #11718621C2semidirect
13. #11718611C2semidirect
14. #11718601C2semidirect
15. #11718600C2semidirect
19. C23×C4×C13C22semidirect
23. C22×C22⋊D13C22semidirect
28. C2×C13×C4⋊C4C22semidirect
30. C2×C13×C22⋊C4C22semidirect
31. C2×C42×C13C22semidirect
33. C2×C22⋊Dic13C22semidirect
46. C2×#6103C22semidirect
47. C2×#6103C22semidirect
48. C2×#6103C22semidirect
49. C2×C4⋊Dic13C22semidirect
50. C2×C4⋊Dic13C22semidirect
51. C2×#6101C22semidirect
53. #88071C22semidirect
54. #88071C22semidirect
55. #88071C22semidirect
56. #88071C22semidirect
71. C2×D4×C13D4semidirect
111. C13×C22⋊C4D4semidirect
125. #6103D4semidirect
217. C2×C4×D4D13semidirect
241. C22×C13#121semidirect
291. C23×C4C2×D13semidirect
300. C2×C4⋊C4C2×D13semidirect
316. C2×C22⋊C4C2×D13semidirect
317. C2×C42C2×D13semidirect
366. C2×D4D52semidirect
404. C22⋊C4C22⋊D13semidirect
406. C13#2424semidirect
525. C22#88184semidirect

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×#881932
C2×#881912
C2×#881842
C22×#61032
C2×#881362
#117188742
#117186552
#117186522
#117186222
#117186212
#117186112
#117186012
#117186002
#242413