Finite Group Databasebeta

← #13121219

Subgroups — #13121219

Order 1664.

688 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×#88201C211yesmaximal, characteristic, complemented
2C2×#88136C211yesmaximal, characteristic
3C13×#393C211yesmaximal, characteristic, complemented
4#11718892C211yesmaximal, characteristic, complemented
5#11718622C211yesmaximal, characteristic, complemented
6#11718617C211yesmaximal, characteristic, complemented
7#11718616C211yesmaximal, characteristic, complemented
8#11718616C211yesmaximal, characteristic, complemented
9#11718605C211yesmaximal, characteristic, complemented
10#11718336C211yesmaximal, characteristic, complemented
11#11718335C211yesmaximal, characteristic, complemented
12#11718333C211yesmaximal, characteristic, complemented
13#11718331C211yesmaximal, characteristic, complemented
14#11718326C211yesmaximal, characteristic, complemented
15#11718326C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic, complemented
18C22×C22⋊D13C2211yescharacteristic
19C22×D52C2211yescharacteristic
20C22×D52C2211yescharacteristic
21C22×C4×D13C2211yescharacteristic, complemented
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27#88201—24no—
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic, complemented
39C2×#6103C2211yescharacteristic, complemented
40C2×#6103C2211yescharacteristic, complemented
41C2×C4⋊Dic13C2211yescharacteristic, complemented
42C2×#6101C2211yescharacteristic, complemented
43C2×C4×Dic13C2211yescharacteristic, complemented
44#88136—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—22no—
57C23×D13—41no—
58C23×D13—41no—
59C23×D13—41no—
60C23×D13—41no—
61C23×D13C2311yescharacteristic
62C23×D13C2311yescharacteristic
63C23×D13C2311yescharacteristic
64C2×Q8×C13—22no—
65C2×Q8×C13—41no—
66C2×Q8×C13—41no—
67C22×C4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C22×C4×C13C2311yescharacteristic
71C22×C4×C13C2311yescharacteristic
72C22×C4×C13C2311yescharacteristic
73C2×C22⋊D13—22no—
74C2×C22⋊D13—22no—
75C2×C22⋊D13—41no—
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C22×Dic13C2311yescharacteristic
80C22×Dic13C2311yescharacteristic
81C2×D52—22no—
82C2×D52—22no—
83C2×D52—41no—
84C2×D52—41no—
85C2×D52—41no—
86C2×D52D414yes—
87C2×C4×D13—41no—
88C2×C4×D13—41no—
89C2×C4×D13—41no—
90C13×C22⋊C4—22no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C22⋊Dic13—22no—
94C22⋊Dic13—41no—
95#6103—22no—
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—
110C4×Dic13—22no—
111#2684—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13#4112yes—
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—21no—
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×D13—44no—
145C22×D13C2×D412yes—
146C22×D13C2×D412yes—
147C22×D13#4112yes—
148Q8×C13—44no—
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—
166C2×C4×C13C2×D412yes—
167C22⋊D13—44no—
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—
182C2×Dic13—21no—
183D52—44no—
184D52—44no—
185C4×D13—44no—
186C2×#124—131no—
187C2×#120—131no—
188#397—131no—
189#397—131no—
190#394—131no—
191#394—131no—
192#393—131no—
193#393D1311yescharacteristic, complemented
194#388—131no—
195#388—131no—
196#386—131no—
197#386—131no—
198#386—131no—
199#379—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—41no—
237C4×C13—22no—
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×Q8C2×D1311yescharacteristic, complemented
250C22×D4—131no—
251C22×D4—131no—
252C22×D4—131no—
253C23×C4—131no—
254#124—264no—
255#120—264no—
256C2×C4⋊C4—131no—
257C2×C4⋊C4—131no—
258C2×C22⋊C4—131no—
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⋊C4C2×D1311yescharacteristic
274C2×C22⋊C4C2×D1311yescharacteristic
275C2×C22⋊C4C2×D1311yescharacteristic
276C2×C42—131no—
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×C13#53411yescharacteristic
287C2×C13#53811yescharacteristic
288C2×C13#53811yescharacteristic
289C2×C13#54611yescharacteristic
290C2×C13#54611yescharacteristic
291C2×C13#55111yescharacteristic
292C2×C13H(3,𝔽4)11yescharacteristic
293D13—42no—
294D13—42no—
295D13—42no—
296C24—131no—
297C24—131no—
298C24—131no—
299C24—262no—
300C24—262no—
301C24—262no—
302C24—521no—
303C24—521no—
304C24—521no—
305C24—521no—
306C24C22×D1311yescharacteristic
307C2×Q8—22no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×D4—134no—
311C2×D4—262no—
312C2×D4—262no—
313C2×D4—262no—
314C2×D4—262no—
315C2×D4—521no—
316C2×D4—521no—
317C2×D4—521no—
318C2×D4—521no—
319C22×C4—131no—
320C22×C4—131no—
321C22×C4—131no—
322C22×C4—131no—
323C22×C4—131no—
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—521no—
334C4⋊C4—521no—
335C22⋊C4—22no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—262no—
339C22⋊C4—262no—
340C22⋊C4—262no—
341C22⋊C4—262no—
342C22⋊C4—262no—
343C22⋊C4—262no—
344C22⋊C4—262no—
345C22⋊C4—262no—
346C22⋊C4—521no—
347C22⋊C4—521no—
348C22⋊C4—521no—
349C22⋊C4—521no—
350C22⋊C4—521no—
351C22⋊C4—521no—
352C22⋊C4—521no—
353C42—262no—
354C13#268411yescharacteristic, complemented, Sylow
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—132no—
362C23—132no—
363C23—132no—
364C23—261no—
365C23—261no—
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—524no—
383C23—524no—
384C23—524no—
385C23—524no—
386C23—524no—
387C23—524no—
388C23—524no—
389C23#613112yes—
390C23C23×D1311yescharacteristic
391Q8—44no—
392D4—524no—
393D4—524no—
394D4—524no—
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×C4D4×D1312yes—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—262no—
437C22—262no—
438C22—262no—
439C22—262no—
440C22—262no—
441C22—262no—
442C22—262no—
443C22—262no—
444C22—262no—
445C22—5216no—
446C22—521no—
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#8825111yescharacteristic
461C22C2×#613111yescharacteristic
462C22#41×D1311yescharacteristic
463C22#8825611yescharacteristic
464C22#8825611yescharacteristic
465C4—22no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—521no—
472C4—521no—
473C4—521no—
474C4—521no—
475C4—521no—
476C2—42no—
477C2—522no—
478C2—522no—
479C2—522no—
480C2#1171929411yescharacteristic
481C2#1171933511yescharacteristic
482C2#1171934211yescharacteristic
483C2#1171934911yescharacteristic
484C2#1171938111yescharacteristic
485C2#1171938311yescharacteristic
486C2#1171938811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#393C2
prime radicalC2×#88136C2
hypercenter#393D13
hypocenterC13#2684
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#88201C2semidirect
3. C13×#393C2semidirect
4. #11718892C2semidirect
5. #11718622C2semidirect
6. #11718617C2semidirect
7. #11718616C2semidirect
8. #11718616C2semidirect
9. #11718605C2semidirect
10. #11718336C2semidirect
11. #11718335C2semidirect
12. #11718333C2semidirect
13. #11718331C2semidirect
14. #11718326C2semidirect
15. #11718326C2semidirect
17. C22×Q8×C13C22semidirect
21. C22×C4×D13C22semidirect
38. C2×#6103C22semidirect
39. C2×#6103C22semidirect
40. C2×#6103C22semidirect
41. C2×C4⋊Dic13C22semidirect
42. C2×#6101C22semidirect
43. C2×C4×Dic13C22semidirect
45. C13×#95C22semidirect
46. C13×#95C22semidirect
47. C13×#95C22semidirect
48. #88071C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
193. #393D13semidirect
249. C22×Q8C2×D13semidirect
282. #95C2×D13semidirect
283. #95C2×D13semidirect
284. #95C2×D13semidirect
354. C13#2684semidirect

Maximal subgroups

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

subgroupindex
C2×#882012
C2×#881362
C13×#3932
#117188922
#117186222
#117186172
#117186162
#117186052
#117183362
#117183352
#117183332
#117183312
#117183262
#268413