Finite Group Databasebeta

← #13121213

Subgroups — #13121213

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×#88191C211yesmaximal, characteristic
2C2×#88139C211yesmaximal, characteristic, complemented
3C13×#386C211yesmaximal, characteristic, complemented
4#11718883C211yesmaximal, characteristic, complemented
5#11718874C211yesmaximal, characteristic, complemented
6#11718874C211yesmaximal, characteristic, complemented
7#11718620C211yesmaximal, characteristic, complemented
8#11718616C211yesmaximal, characteristic, complemented
9#11718616C211yesmaximal, characteristic, complemented
10#11718608C211yesmaximal, characteristic, complemented
11#11718606C211yesmaximal, characteristic, complemented
12#11718336C211yesmaximal, characteristic, complemented
13#11718336C211yesmaximal, characteristic, complemented
14#11718334C211yesmaximal, characteristic, complemented
15#11718330C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C23×C4×C13C2211yescharacteristic, complemented
19C22×C22⋊D13C2211yescharacteristic
20C22×C22⋊D13C2211yescharacteristic
21C22×Dic26C2211yescharacteristic, complemented
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic, complemented
29C2×C22⋊Dic13C2211yescharacteristic, complemented
30#88191—24no—
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic
39C2×#6103C2211yescharacteristic
40C2×#6103C2211yescharacteristic
41C2×#6101C2211yescharacteristic, complemented
42C2×#6101C2211yescharacteristic, complemented
43C2×C4×Dic13C2211yescharacteristic, complemented
44#88139—24no—
45C13×#95C2211yescharacteristic, complemented
46C13×#95C2211yescharacteristic, complemented
47#88071C2211yescharacteristic, complemented
48#88071C2211yescharacteristic, complemented
49#88071C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53C24×C13C2311yescharacteristic
54C24×C13C2311yescharacteristic
55C23×D13—22no—
56C23×D13—22no—
57C23×D13—22no—
58C23×D13—41no—
59C23×D13—41no—
60C23×D13—41no—
61C23×D13—41no—
62C23×D13C2311yescharacteristic
63C23×D13C2311yescharacteristic
64C2×D4×C13—22no—
65C2×D4×C13—22no—
66C2×D4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13C2311yescharacteristic
71C22×C4×C13C2311yescharacteristic
72C22×C4×C13C2311yescharacteristic
73C22×C4×C13C2311yescharacteristic
74C22×C4×C13C2311yescharacteristic
75C2×C22⋊D13—22no—
76C2×C22⋊D13—22no—
77C2×C22⋊D13—41no—
78C2×C22⋊D13—41no—
79C2×C22⋊D13—41no—
80C2×C22⋊D13D414yes—
81C22×Dic13C2311yescharacteristic
82C22×Dic13C2311yescharacteristic
83C22×Dic13C2311yescharacteristic
84C22×Dic13C2311yescharacteristic
85C22×Dic13C2311yescharacteristic
86C22×Dic13C2311yescharacteristic
87C2×Dic26—22no—
88C2×Dic26—41no—
89C2×Dic26—41no—
90C13×C22⋊C4—22no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C22⋊Dic13—22no—
94C22⋊Dic13—22no—
95C22⋊Dic13—22no—
96C22⋊Dic13—41no—
97C22⋊Dic13—41no—
98#6103—22no—
99#6103—22no—
100#6103—22no—
101#6103—22no—
102#6103—22no—
103#6103—41no—
104#6103—41no—
105#6103—41no—
106#6103—41no—
107#6103—41no—
108#6101—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—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13C2×D412yes—
125C23×C13#4112yes—
126C23×C13C2411yescharacteristic
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—21no—
139C22×D13—44no—
140C22×D13—44no—
141C22×D13—44no—
142C22×D13—44no—
143C22×D13—44no—
144C22×D13—44no—
145C22×D13—44no—
146C22×D13C2×D412yes—
147C22×D13#4112yes—
148D4×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—44no—
165C22⋊D13—44no—
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—
182C2×Dic13—21no—
183C2×Dic13—21no—
184C2×Dic13C2×D412yes—
185Dic26—44no—
186C2×#124—131no—
187C2×#120—131no—
188#397—131no—
189#397—131no—
190#394—131no—
191#394—131no—
192#393—131no—
193#393—131no—
194#388—131no—
195#388—131no—
196#386—131no—
197#386—131no—
198#386D1311yescharacteristic, complemented
199#379—131no—
200#379—131no—
201C22×C13—22no—
202C22×C13—22no—
203C22×C13—22no—
204C22×C13—22no—
205C22×C13—22no—
206C22×C13—22no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13—41no—
214C22×C13—41no—
215C22×C13C22×D411yescharacteristic
216C22×C13C2×#4111yescharacteristic
217C22×C13C2×#4111yescharacteristic
218C22×C13H(5,𝔽2)11yescharacteristic
219C22×C13H(5,𝔽2)11yescharacteristic
220C22×C13H(5,𝔽2)11yescharacteristic
221C22×C13H(5,𝔽2)11yescharacteristic
222C2×D13—22no—
223C2×D13—22no—
224C2×D13—22no—
225C2×D13—22no—
226C2×D13—22no—
227C2×D13—22no—
228C2×D13—416no—
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—41no—
238C4×C13—41no—
239C4×C13—41no—
240C4×C13—41no—
241C4×C13—41no—
242Dic13—22no—
243Dic13—41no—
244Dic13—41no—
245Dic13—41no—
246Dic13—41no—
247Dic13—41no—
248C25—131no—
249C22×Q8—131no—
250C22×D4—131no—
251C22×D4—131no—
252C22×D4C2×D1311yescharacteristic
253C23×C4C2×D1311yescharacteristic, complemented
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, complemented
276C2×C42—131no—
277#95—131no—
278#95—131no—
279#95—131no—
280#95—131no—
281#95—131no—
282#95—131no—
283#95C2×D1311yescharacteristic, complemented
284#95C2×D1311yescharacteristic, complemented
285C2×C13—42no—
286C2×C13—42no—
287C2×C13#53411yescharacteristic
288C2×C13#53811yescharacteristic
289C2×C13#53811yescharacteristic
290C2×C13#54611yescharacteristic
291C2×C13#54611yescharacteristic
292C2×C13#55111yescharacteristic
293C2×C13H(3,𝔽4)11yescharacteristic
294D13—42no—
295D13—42no—
296C24—131no—
297C24—131no—
298C24—262no—
299C24—262no—
300C24—262no—
301C24—521no—
302C24—521no—
303C24—521no—
304C24—521no—
305C24C22×D1311yescharacteristic
306C24C22×D1311yescharacteristic
307C2×Q8—262no—
308C2×Q8—521no—
309C2×Q8—521no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—41no—
313C2×D4—134no—
314C2×D4—262no—
315C2×D4—262no—
316C2×D4—521no—
317C2×D4—521no—
318C2×D4—521no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—131no—
323C22×C4—131no—
324C22×C4—131no—
325C22×C4—131no—
326C22×C4—131no—
327C22×C4—131no—
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—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—132no—
368C23—132no—
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—524no—
382C23—524no—
383C23—524no—
384C23—524no—
385C23—524no—
386C23—524no—
387C23—524no—
388C23#612712yes—
389C23D4×D1312yes—
390C23C23×D1311yescharacteristic
391Q8—524no—
392D4—44no—
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—44no—
411C2×C4—132no—
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—261no—
428C2×C4—261no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—262no—
444C22—262no—
445C22—262no—
446C22—262no—
447C22—262no—
448C22—262no—
449C22—5216no—
450C22—521no—
451C22—521no—
452C22—521no—
453C22—521no—
454C22—521no—
455C22—521no—
456C22—521no—
457C22—521no—
458C22C2×#612711yescharacteristic
459C22C2×D4×D1311yescharacteristic
460C22#8825111yescharacteristic
461C22#8825111yescharacteristic
462C22#8825111yescharacteristic
463C22#41×D1311yescharacteristic
464C22#8825611yescharacteristic
465C4—41no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—41no—
470C4—262no—
471C4—521no—
472C4—521no—
473C4—521no—
474C4—521no—
475C4—521no—
476C2—42no—
477C2—42no—
478C2—522no—
479C2—522no—
480C2#1171919511yescharacteristic
481C2#1171926111yescharacteristic
482C2#1171926511yescharacteristic
483C2#1171929911yescharacteristic
484C2#1171931011yescharacteristic
485C2#1171931511yescharacteristic
486C2#1171936211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#386C2
prime radicalC2×#88191C2
hypercenter#386D13
hypocenterC13#2684
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×#88139C2semidirect
3. C13×#386C2semidirect
4. #11718883C2semidirect
5. #11718874C2semidirect
6. #11718874C2semidirect
7. #11718620C2semidirect
8. #11718616C2semidirect
9. #11718616C2semidirect
10. #11718608C2semidirect
11. #11718606C2semidirect
12. #11718336C2semidirect
13. #11718336C2semidirect
14. #11718334C2semidirect
15. #11718330C2semidirect
18. C23×C4×C13C22semidirect
21. C22×Dic26C22semidirect
24. C2×C13×C22⋊C4C22semidirect
28. C2×C22⋊Dic13C22semidirect
29. C2×C22⋊Dic13C22semidirect
41. C2×#6101C22semidirect
42. C2×#6101C22semidirect
43. C2×C4×Dic13C22semidirect
45. C13×#95C22semidirect
46. C13×#95C22semidirect
47. #88071C22semidirect
48. #88071C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
198. #386D13semidirect
253. C23×C4C2×D13semidirect
275. C2×C22⋊C4C2×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×#881912
C2×#881392
C13×#3862
#117188832
#117188742
#117186202
#117186162
#117186082
#117186062
#117183362
#117183342
#117183302
#268413