Finite Group Databasebeta

← #13117818

Subgroups — #13117818

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
1C22×#6103C211yesmaximal, characteristic, complemented
2C2×#88136C211yesmaximal, characteristic
3C2×#88135C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D13C211yesmaximal, characteristic, complemented
5C2×C4×D52C211yesmaximal, characteristic, complemented
6C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
7#11718874C211yesmaximal, characteristic, complemented
8#11718611C211yesmaximal, characteristic, complemented
9#11718601C211yesmaximal, characteristic, complemented
10#11718600C211yesmaximal, characteristic, complemented
11C4×#6103C211yesmaximal, characteristic, complemented
12#11718331C211yesmaximal, characteristic, complemented
13#11718329C211yesmaximal, characteristic, complemented
14#11718326C211yesmaximal, characteristic, complemented
15#11718326C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C23×C4×C13C2211yescharacteristic
18C22×C22⋊D13C2211yescharacteristic
19C23×Dic13C2211yescharacteristic
20C22×D52C2211yescharacteristic
21C22×D52C2211yescharacteristic
22C22×C4×D13C2211yescharacteristic
23C22×C4×D13C2211yescharacteristic
24C22×C4×D13C2211yescharacteristic, complemented
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C13×C22⋊C4C2211yescharacteristic
27C2×C42×C13C2211yescharacteristic, complemented
28C2×C42×C13C2211yescharacteristic, complemented
29C2×C22⋊Dic13C2211yescharacteristic
30C2×#6103—24no—
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic
39C2×#6103C2211yescharacteristic, complemented
40C2×#6103C2211yescharacteristic, complemented
41C2×#6103C2211yescharacteristic, complemented
42C2×C4⋊Dic13C2211yescharacteristic, complemented
43C2×C4⋊Dic13C2211yescharacteristic, complemented
44C2×#6101C2211yescharacteristic, complemented
45C2×C4×Dic13C2211yescharacteristic, complemented
46#88136C418yescomplemented
47#88135—24no—
48C22⋊C4×D13—24no—
49C4×D52—24no—
50C13×#95C2211yescharacteristic, complemented
51C13×#95C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53#88071C2211yescharacteristic, complemented
54#88071C2211yescharacteristic, complemented
55#88071C2211yescharacteristic, complemented
56C24×C13C2311yescharacteristic
57C23×D13—22no—
58C23×D13—22no—
59C23×D13—22no—
60C23×D13—22no—
61C23×D13—41no—
62C23×D13—41no—
63C23×D13C2×C414yescomplemented
64C23×D13C2311yescharacteristic
65C23×D13C2311yescharacteristic
66C23×D13C2311yescharacteristic
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—41no—
70C22×C4×C13C2311yescharacteristic
71C22×C4×C13C2311yescharacteristic
72C22×C4×C13C2311yescharacteristic
73C22×C4×C13C2311yescharacteristic
74C22×C4×C13C2311yescharacteristic
75C22×C4×C13C2311yescharacteristic
76C2×C22⋊D13—22no—
77C2×C22⋊D13—22no—
78C2×C22⋊D13C2×C414yescomplemented
79C22×Dic13—22no—
80C22×Dic13—22no—
81C22×Dic13—41no—
82C22×Dic13C2311yescharacteristic
83C22×Dic13C2311yescharacteristic
84C22×Dic13C2311yescharacteristic
85C22×Dic13C2311yescharacteristic
86C22×Dic13C2311yescharacteristic
87C2×D52—22no—
88C2×D52—22no—
89C2×D52—41no—
90C2×D52—41no—
91C2×D52C2×C414yescomplemented
92C2×D52C2×C414yescomplemented
93C2×C4×D13—22no—
94C2×C4×D13—22no—
95C2×C4×D13—22no—
96C2×C4×D13—22no—
97C2×C4×D13—22no—
98C2×C4×D13—22no—
99C2×C4×D13—41no—
100C2×C4×D13—41no—
101C2×C4×D13—41no—
102C13×C22⋊C4C2×C414yescomplemented
103C13×C22⋊C4D414yescomplemented
104C42×C13—22no—
105C42×C13—41no—
106C22⋊Dic13—22no—
107#6103—22no—
108#6103—22no—
109#6103—22no—
110#6103—22no—
111#6103—22no—
112#6103—22no—
113#6103—22no—
114#6103—41no—
115#6103C2×C414yescomplemented
116#6103C2×C414yescomplemented
117#6103D414yescomplemented
118C4⋊Dic13—22no—
119C4⋊Dic13—41no—
120#6101—22no—
121C4×Dic13—22no—
122#2358—131nomaximal, Sylow
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13C22×C412yes—
128C23×C13C2×D412yes—
129C23×C13#4112yes—
130C23×C13C2411yescharacteristic
131C22×D13—21no—
132C22×D13—21no—
133C22×D13—21no—
134C22×D13—21no—
135C22×D13—28no—
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—21no—
147C22×D13—21no—
148C22×D13—28no—
149C22×D13—44no—
150C22×D13—44no—
151C22×D13—44no—
152C22×D13—44no—
153C22×D13—44no—
154C22×D13C22×C412yes—
155C22×D13C22×C412yes—
156C22×D13C22×C412yes—
157C22×D13C2×D412yes—
158C22×D13#4112yes—
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—21no—
171C2×C4×C13—21no—
172C2×C4×C13—44no—
173C2×C4×C13C22×C412yes—
174C2×C4×C13C22×C412yes—
175C2×C4×C13C2×D412yes—
176C2×C4×C13C2×D412yes—
177C2×C4×C13C2×D412yes—
178C22⋊D13—28no—
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—44no—
193C2×Dic13C22×C412yes—
194C2×Dic13C2×D412yes—
195D52—28no—
196D52—44no—
197C4×D13—44no—
198C4×D13—44no—
199C4×D13—44no—
200C2×#120—131no—
201C2×C4×D4—131no—
202C2×C4×D4—131no—
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⋊C4D1311yescharacteristic, complemented
215C22×C13—22no—
216C22×C13—22no—
217C22×C13—22no—
218C22×C13—22no—
219C22×C13—22no—
220C22×C13—22no—
221C22×C13C4×D414yescomplemented
222C22×C13C23×C411yescharacteristic
223C22×C13C22×D411yescharacteristic
224C22×C13C22×D411yescharacteristic
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—22no—
236C2×D13—22no—
237C2×D13—22no—
238C2×D13—22no—
239C2×D13—22no—
240C2×D13—22no—
241C2×D13—416no—
242C2×D13—41no—
243C2×D13—41no—
244C2×D13—41no—
245C2×D13—41no—
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—22no—
256C4×C13—41no—
257Dic13—22no—
258Dic13—22no—
259Dic13—41no—
260Dic13—41no—
261Dic13—41no—
262C25—131no—
263C22×D4—131no—
264C22×D4—131no—
265C22×D4—131no—
266C23×C4—131no—
267C23×C4—131no—
268C23×C4—131no—
269C23×C4—131no—
270C23×C4C2×D1311yescharacteristic
271#120—138no—
272C4×D4—264no—
273C4×D4—264no—
274C2×C4⋊C4—131no—
275C2×C4⋊C4—131no—
276C2×C4⋊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—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
293C2×C42—131no—
294C2×C42C2×D1311yescharacteristic, complemented
295C2×C42C2×D1311yescharacteristic, complemented
296#95—131no—
297#95—131no—
298#95—131no—
299#95—131no—
300#95C2×D1311yescharacteristic, complemented
301#95C2×D1311yescharacteristic, complemented
302C2×C13—24no—
303C2×C13C2×C4×D411yescharacteristic
304C2×C13C2×C4×D411yescharacteristic
305C2×C13#51811yescharacteristic
306C2×C13D4211yescharacteristic
307C2×C13#54611yescharacteristic
308C2×C13#54611yescharacteristic
309C2×C13#55111yescharacteristic
310D13—24no—
311D13—42no—
312D13—42no—
313C24—131no—
314C24—131no—
315C24—131no—
316C24—134no—
317C24—262no—
318C24—262no—
319C24—262no—
320C24—262no—
321C24—521no—
322C24—521no—
323C24C22×D1311yescharacteristic
324C2×D4—134no—
325C2×D4—134no—
326C2×D4—134no—
327C2×D4—262no—
328C2×D4—262no—
329C2×D4—262no—
330C2×D4—262no—
331C2×D4—521no—
332C2×D4—521no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—41no—
336C22×C4—131no—
337C22×C4—131no—
338C22×C4—131no—
339C22×C4—131no—
340C22×C4—131no—
341C22×C4—262no—
342C22×C4—262no—
343C22×C4—262no—
344C22×C4—262no—
345C22×C4—262no—
346C22×C4—262no—
347C22×C4—262no—
348C22×C4—262no—
349C22×C4—521no—
350C22×C4—521no—
351C22×C4—521no—
352C22×C4—521no—
353C22×C4C22×D1311yescharacteristic
354C22×C4C22×D1311yescharacteristic
355C22×C4C22×D1311yescharacteristic
356C22×C4C22×D1311yescharacteristic
357C22×C4C22×D1311yescharacteristic
358C22×C4C22×D1311yescharacteristic
359C4⋊C4—262no—
360C4⋊C4—262no—
361C4⋊C4—521no—
362C22⋊C4—134no—
363C22⋊C4—134no—
364C22⋊C4—134no—
365C22⋊C4—262no—
366C22⋊C4—262no—
367C22⋊C4—262no—
368C22⋊C4—262no—
369C22⋊C4—262no—
370C22⋊C4—262no—
371C22⋊C4—262no—
372C22⋊C4—262no—
373C22⋊C4—521no—
374C22⋊C4C4×D1314yescomplemented
375C22⋊C4D5214yescomplemented
376C42—22no—
377C42—41no—
378C42—262no—
379C13#235811yescharacteristic, complemented, Sylow
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—132no—
385C23—132no—
386C23—132no—
387C23—132no—
388C23—132no—
389C23—268no—
390C23—261no—
391C23—261no—
392C23—261no—
393C23—261no—
394C23—268no—
395C23—261no—
396C23—261no—
397C23—261no—
398C23—261no—
399C23—261no—
400C23—261no—
401C23—261no—
402C23—261no—
403C23—261no—
404C23—261no—
405C23—261no—
406C23—261no—
407C23—524no—
408C23—524no—
409C23—524no—
410C23—524no—
411C23—524no—
412C23C2×C4×D1312yes—
413C23C2×D5212yes—
414C23#612712yes—
415C23C23×D1311yescharacteristic
416D4—268no—
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—21no—
431C2×C4—21no—
432C2×C4—44no—
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—524no—
449C2×C4—524no—
450C2×C4—524no—
451C2×C4—524no—
452C2×C4C2×C4×D1312yes—
453C2×C4C2×C4×D1312yes—
454C2×C4C2×D5212yes—
455C2×C4C2×D5212yes—
456C2×C4D4×D1312yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—134no—
464C22—262no—
465C22—262no—
466C22—262no—
467C22—262no—
468C22—262no—
469C22—262no—
470C22—262no—
471C22—262no—
472C22—262no—
473C22—262no—
474C22—262no—
475C22—262no—
476C22—5216no—
477C22—521no—
478C22—521no—
479C22—521no—
480C22—521no—
481C22—521no—
482C22—521no—
483C22—521no—
484C22—521no—
485C22C4×D5214yescomplemented
486C22C22×C4×D1311yescharacteristic
487C22C22×D5211yescharacteristic
488C22C2×#612711yescharacteristic
489C22C2×D4×D1311yescharacteristic
490C22#8825111yescharacteristic
491C22#41×D1311yescharacteristic
492C22#8825611yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—22no—
498C4—41no—
499C4—262no—
500C4—262no—
501C4—521no—
502C4—521no—
503C4—521no—
504C2—24no—
505C2—264no—
506C2—522no—
507C2—522no—
508C2C2×C4×D5211yescharacteristic
509C2#1171919511yescharacteristic
510C2#1171923211yescharacteristic
511C2C4×D4×D1311yescharacteristic
512C2#1171925011yescharacteristic
513C2D4×D5211yescharacteristic
514C2#1171925911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC4×C13×C22⋊C4C2
socle, cosocleC23×C13C24
prime radicalC2×#88136C2
hypercenterC4×C22⋊C4D13
hypocenterC13#2358
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6103C2semidirect
3. C2×#88135C2semidirect
4. C2×C22⋊C4×D13C2semidirect
5. C2×C4×D52C2semidirect
6. C4×C13×C22⋊C4C2semidirect
7. #11718874C2semidirect
8. #11718611C2semidirect
9. #11718601C2semidirect
10. #11718600C2semidirect
11. C4×#6103C2semidirect
12. #11718331C2semidirect
13. #11718329C2semidirect
14. #11718326C2semidirect
15. #11718326C2semidirect
24. C22×C4×D13C22semidirect
27. C2×C42×C13C22semidirect
28. C2×C42×C13C22semidirect
39. C2×#6103C22semidirect
40. C2×#6103C22semidirect
41. C2×#6103C22semidirect
42. C2×C4⋊Dic13C22semidirect
43. C2×C4⋊Dic13C22semidirect
44. C2×#6101C22semidirect
45. C2×C4×Dic13C22semidirect
46. #88136C4semidirect
50. C13×#95C22semidirect
51. C13×#95C22semidirect
52. #88071C22semidirect
53. #88071C22semidirect
54. #88071C22semidirect
55. #88071C22semidirect
63. C23×D13C2×C4semidirect
78. C2×C22⋊D13C2×C4semidirect
91. C2×D52C2×C4semidirect
92. C2×D52C2×C4semidirect
102. C13×C22⋊C4C2×C4semidirect
103. C13×C22⋊C4D4semidirect
115. #6103C2×C4semidirect
116. #6103C2×C4semidirect
117. #6103D4semidirect
214. C4×C22⋊C4D13semidirect
221. C22×C13C4×D4semidirect
250. C2×D13C4×D4semidirect
294. C2×C42C2×D13semidirect
295. C2×C42C2×D13semidirect
300. #95C2×D13semidirect
301. #95C2×D13semidirect
374. C22⋊C4C4×D13semidirect
375. C22⋊C4D52semidirect
379. C13#2358semidirect
485. C22C4×D52semidirect

Maximal subgroups

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

subgroupindex
C22×#61032
C2×#881362
C2×#881352
C2×C22⋊C4×D132
C2×C4×D522
C4×C13×C22⋊C42
#117188742
#117186112
#117186012
#117186002
C4×#61032
#117183312
#117183292
#117183262
#235813