Finite Group Databasebeta

← #13120610

Subgroups — #13120610

Order 1664.

702 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88136C211yesmaximal, characteristic
2C2×C22⋊C4×D13C211yesmaximal, characteristic, complemented
3C13×#397C211yesmaximal, characteristic, complemented
4#11718652C211yesmaximal, characteristic, complemented
5#11718650C211yesmaximal, characteristic, complemented
6#11718622C211yesmaximal, characteristic, complemented
7#11718620C211yesmaximal, characteristic, complemented
8#11718616C211yesmaximal, characteristic, complemented
9#11718613C211yesmaximal, characteristic, complemented
10#11718336C211yesmaximal, characteristic, complemented
11#11718335C211yesmaximal, characteristic, complemented
12#11718333C211yesmaximal, characteristic, complemented
13#11718329C211yesmaximal, characteristic, complemented
14#11718326C211yesmaximal, characteristic, complemented
15#11718326C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×C22⋊D13C2211yescharacteristic
18C22×D52C2211yescharacteristic
19C22×D52C2211yescharacteristic
20C22×C4×D13C2211yescharacteristic
21C22×C4×D13C2211yescharacteristic
22C2×C13×C4⋊C4C2211yescharacteristic, complemented
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic, complemented
37C2×#6103C2211yescharacteristic, complemented
38C2×#6103C2211yescharacteristic, complemented
39C2×#6103C2211yescharacteristic, complemented
40C2×C4⋊Dic13C2211yescharacteristic, complemented
41C2×#6101C2211yescharacteristic, complemented
42C2×#6101C2211yescharacteristic, complemented
43#88136—24no—
44C22⋊C4×D13—24no—
45C13×#95C2211yescharacteristic, complemented
46C13×#95C2211yescharacteristic, complemented
47C13×#95C2211yescharacteristic, complemented
48#88071C2211yescharacteristic, complemented
49#88071C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53C24×C13C2311yescharacteristic
54C23×D13—22no—
55C23×D13—22no—
56C23×D13—41no—
57C23×D13—41no—
58C23×D13—41no—
59C23×D13—41no—
60C23×D13D414yes—
61C23×D13C2311yescharacteristic
62C23×D13C2311yescharacteristic
63C23×D13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C2×C22⋊D13—22no—
71C2×C22⋊D13—41no—
72C2×C22⋊D13—41no—
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C2×D52—22no—
79C2×D52—22no—
80C2×D52—22no—
81C2×D52—22no—
82C2×D52—41no—
83C2×D52—41no—
84C2×C4×D13—22no—
85C2×C4×D13—22no—
86C2×C4×D13—41no—
87C2×C4×D13—41no—
88C2×C4×D13—41no—
89C2×C4×D13—41no—
90C13×C4⋊C4—41no—
91C13×C22⋊C4—22no—
92C13×C22⋊C4—22no—
93C13×C22⋊C4—41no—
94C22⋊Dic13—22no—
95C22⋊Dic13—41no—
96#6103—22no—
97#6103—22no—
98#6103—22no—
99#6103—22no—
100#6103—22no—
101#6103—22no—
102#6103—41no—
103#6103—41no—
104#6103—41no—
105#6103—41no—
106#6103—41no—
107#6103—41no—
108C4⋊Dic13—41no—
109#6101—41no—
110#6101—41no—
111#2622—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13C2×D412yes—
119C23×C13C2411yescharacteristic
120C22×D13—21no—
121C22×D13—21no—
122C22×D13—21no—
123C22×D13—21no—
124C22×D13—21no—
125C22×D13—21no—
126C22×D13—21no—
127C22×D13—21no—
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—28no—
131C22×D13—21no—
132C22×D13—21no—
133C22×D13—21no—
134C22×D13—21no—
135C22×D13—21no—
136C22×D13—21no—
137C22×D13—21no—
138C22×D13—44no—
139C22×D13—44no—
140C22×D13—44no—
141C22×D13—44no—
142C22×D13—44no—
143C22×D13—44no—
144C22×D13C2×D412yes—
145C22×D13C2×D412yes—
146C22×D13#4112yes—
147C22×D13#4112yes—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
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—
166C22⋊D13—44no—
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—
182D52—44no—
183D52—44no—
184C4×D13—44no—
185C4×D13—44no—
186C2×#120—131no—
187C22×C22⋊C4—131no—
188#397—131no—
189#397—131no—
190#397—131no—
191#397D1311yescharacteristic, complemented
192#394—131no—
193#394—131no—
194#394—131no—
195#394—131no—
196#386—131no—
197#386—131no—
198#385—131no—
199#385—131no—
200#379—131no—
201C22×C13—22no—
202C22×C13—22no—
203C22×C13—22no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13C22×D411yescharacteristic
209C22×C13C2×#4111yescharacteristic
210C22×C13C2×#4111yescharacteristic
211C22×C13H(5,𝔽2)11yescharacteristic
212C22×C13H(5,𝔽2)11yescharacteristic
213C22×C13H(5,𝔽2)11yescharacteristic
214C22×C13H(5,𝔽2)11yescharacteristic
215C2×D13—22no—
216C2×D13—22no—
217C2×D13—22no—
218C2×D13—22no—
219C2×D13—22no—
220C2×D13—22no—
221C2×D13—22no—
222C2×D13—22no—
223C2×D13—22no—
224C2×D13—416no—
225C2×D13—41no—
226C2×D13—41no—
227C2×D13—41no—
228C2×D13—41no—
229C2×D13—41no—
230C2×D13—41no—
231C2×D13—41no—
232C2×D13—41no—
233C2×D13—41no—
234C2×D13—41no—
235C2×D13—41no—
236C2×D13#12314yes—
237C4×C13—41no—
238C4×C13—41no—
239C4×C13—41no—
240C4×C13—41no—
241C4×C13—41no—
242C4×C13—41no—
243Dic13—41no—
244Dic13—41no—
245Dic13—41no—
246Dic13—41no—
247Dic13—41no—
248C25—131no—
249C22×D4—131no—
250C22×D4—131no—
251C22×D4—131no—
252C23×C4—131no—
253C23×C4—131no—
254#120—264no—
255C2×C4⋊C4—131no—
256C2×C4⋊C4—131no—
257C2×C4⋊C4—131no—
258C2×C4⋊C4C2×D1311yescharacteristic, complemented
259C2×C22⋊C4—131no—
260C2×C22⋊C4—131no—
261C2×C22⋊C4—131no—
262C2×C22⋊C4—131no—
263C2×C22⋊C4—131no—
264C2×C22⋊C4—131no—
265C2×C22⋊C4—131no—
266C2×C22⋊C4—131no—
267C2×C22⋊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—264no—
274C2×C22⋊C4C2×D1311yescharacteristic
275C2×C22⋊C4C2×D1311yescharacteristic
276C2×C22⋊C4C2×D1311yescharacteristic
277#95—131no—
278#95—131no—
279#95—131no—
280#95—131no—
281#95—131no—
282#95C2×D1311yescharacteristic, complemented
283#95C2×D1311yescharacteristic, complemented
284#95C2×D1311yescharacteristic, complemented
285C2×C13—42no—
286C2×C13C2×#12311yescharacteristic
287C2×C13#53411yescharacteristic
288C2×C13#53411yescharacteristic
289C2×C13#53811yescharacteristic
290C2×C13#53811yescharacteristic
291C2×C13#53811yescharacteristic
292C2×C13#53811yescharacteristic
293D13—24no—
294D13—42no—
295D13—81no—
296C24—131no—
297C24—131no—
298C24—134no—
299C24—131no—
300C24—262no—
301C24—262no—
302C24—521no—
303C24—521no—
304C24—521no—
305C24—521no—
306C24C22×D1311yescharacteristic
307C2×D4—262no—
308C2×D4—262no—
309C2×D4—262no—
310C2×D4—262no—
311C2×D4—262no—
312C2×D4—521no—
313C2×D4—521no—
314C2×D4—521no—
315C2×D4—521no—
316C22×C4—131no—
317C22×C4—131no—
318C22×C4—131no—
319C22×C4—131no—
320C22×C4—131no—
321C22×C4—262no—
322C22×C4—262no—
323C22×C4—521no—
324C22×C4—521no—
325C22×C4—521no—
326C22×C4—521no—
327C22×C4C22×D1311yescharacteristic
328C22×C4C22×D1311yescharacteristic
329C22×C4C22×D1311yescharacteristic
330C22×C4C22×D1311yescharacteristic
331C22×C4C22×D1311yescharacteristic
332C22×C4C22×D1311yescharacteristic
333C4⋊C4—41no—
334C4⋊C4—521no—
335C4⋊C4—521no—
336C4⋊C4—521no—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—41no—
340C22⋊C4—262no—
341C22⋊C4—262no—
342C22⋊C4—262no—
343C22⋊C4—262no—
344C22⋊C4—262no—
345C22⋊C4—262no—
346C22⋊C4—262no—
347C22⋊C4—521no—
348C22⋊C4—521no—
349C22⋊C4—521no—
350C22⋊C4—521no—
351C22⋊C4—521no—
352C22⋊C4—521no—
353C22⋊C4—521no—
354C13#262211yescharacteristic, complemented, Sylow
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—132no—
362C23—132no—
363C23—132no—
364C23—132no—
365C23—268no—
366C23—261no—
367C23—261no—
368C23—261no—
369C23—261no—
370C23—261no—
371C23—261no—
372C23—261no—
373C23—261no—
374C23—261no—
375C23—261no—
376C23—261no—
377C23—261no—
378C23—261no—
379C23—261no—
380C23—261no—
381C23—261no—
382C23—261no—
383C23—524no—
384C23—524no—
385C23—524no—
386C23—524no—
387C23—524no—
388C23—524no—
389C23D4×D1312yes—
390C23C23×D1311yescharacteristic
391D4—524no—
392D4—524no—
393D4—524no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—261no—
413C2×C4—261no—
414C2×C4—261no—
415C2×C4—261no—
416C2×C4—261no—
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—524no—
428C2×C4—524no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—134no—
437C22—262no—
438C22—262no—
439C22—262no—
440C22—262no—
441C22—262no—
442C22—262no—
443C22—262no—
444C22—262no—
445C22—262no—
446C22—5216no—
447C22—521no—
448C22—521no—
449C22—521no—
450C22—521no—
451C22—521no—
452C22—521no—
453C22—521no—
454C22—521no—
455C22—521no—
456C22—521no—
457C22—521no—
458C22C2×D4×D1311yescharacteristic
459C22#8825111yescharacteristic
460C22#41×D1311yescharacteristic
461C22#41×D1311yescharacteristic
462C22#8825611yescharacteristic
463C22#8825611yescharacteristic
464C22#8825611yescharacteristic
465C4—41no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—521no—
472C4—521no—
473C4—521no—
474C4—521no—
475C4—521no—
476C2—42no—
477C2—264no—
478C2—522no—
479C2—1041no—
480C2#1171931011yescharacteristic
481C2D13×#12311yescharacteristic
482C2#1171935811yescharacteristic
483C2#1171936211yescharacteristic
484C2#1171938311yescharacteristic
485C2#1171940911yescharacteristic
486C2#1171940911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#397C2
prime radicalC2×#88136C2
hypercenter#397D13
hypocenterC13#2622
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D13C2semidirect
3. C13×#397C2semidirect
4. #11718652C2semidirect
5. #11718650C2semidirect
6. #11718622C2semidirect
7. #11718620C2semidirect
8. #11718616C2semidirect
9. #11718613C2semidirect
10. #11718336C2semidirect
11. #11718335C2semidirect
12. #11718333C2semidirect
13. #11718329C2semidirect
14. #11718326C2semidirect
15. #11718326C2semidirect
22. C2×C13×C4⋊C4C22semidirect
36. C2×#6103C22semidirect
37. C2×#6103C22semidirect
38. C2×#6103C22semidirect
39. C2×#6103C22semidirect
40. C2×C4⋊Dic13C22semidirect
41. C2×#6101C22semidirect
42. C2×#6101C22semidirect
45. C13×#95C22semidirect
46. C13×#95C22semidirect
47. C13×#95C22semidirect
48. #88071C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
191. #397D13semidirect
258. C2×C4⋊C4C2×D13semidirect
282. #95C2×D13semidirect
283. #95C2×D13semidirect
284. #95C2×D13semidirect
354. C13#2622semidirect

Maximal subgroups

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

subgroupindex
C2×#881362
C2×C22⋊C4×D132
C13×#3972
#117186522
#117186502
#117186222
#117186202
#117186162
#117186132
#117183362
#117183352
#117183332
#117183292
#117183262
#262213