Finite Group Databasebeta

← #13121400

Subgroups — #13121400

Order 1664.

680 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88191C211yesmaximal, characteristic
2C2×#88183C211yesmaximal, characteristic, complemented
3C13×#386C211yesmaximal, characteristic, complemented
4#11718883C211yesmaximal, characteristic, complemented
5#11718874C211yesmaximal, characteristic, complemented
6#11718622C211yesmaximal, characteristic, complemented
7#11718618C211yesmaximal, characteristic, complemented
8#11718616C211yesmaximal, characteristic, complemented
9#11718616C211yesmaximal, characteristic, complemented
10#11718609C211yesmaximal, characteristic, complemented
11#11718605C211yesmaximal, characteristic, complemented
12#11718337C211yesmaximal, characteristic, complemented
13#11718336C211yesmaximal, characteristic, complemented
14#11718335C211yesmaximal, characteristic, complemented
15#11718330C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C23×C4×C13C2211yescharacteristic, complemented
19C22×C22⋊D13C2211yescharacteristic
20C22×C22⋊D13C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic, complemented
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic, complemented
28C2×C22⋊Dic13C2211yescharacteristic, complemented
29#88191—24no—
30#88183—24no—
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic
39C2×#6103C2211yescharacteristic
40C2×#6103C2211yescharacteristic
41C2×C4⋊Dic13C2211yescharacteristic, complemented
42C2×#6101C2211yescharacteristic, complemented
43C2×#6101C2211yescharacteristic, complemented
44C2×#6101C2211yescharacteristic, complemented
45C2×#6101C2211yescharacteristic, complemented
46C2×C4×Dic13C2211yescharacteristic, complemented
47C13×#95C2211yescharacteristic, complemented
48C13×#95C2211yescharacteristic, 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—22no—
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
87C13×C22⋊C4—41no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C22⋊Dic13—22no—
91C22⋊Dic13—22no—
92C22⋊Dic13—22no—
93C22⋊Dic13—41no—
94C22⋊Dic13—41no—
95#6103—22no—
96#6103—22no—
97#6103—22no—
98#6103—22no—
99#6103—22no—
100#6103—41no—
101#6103—41no—
102#6103—41no—
103#6103—41no—
104#6103—41no—
105C4⋊Dic13—41no—
106#6101—22no—
107#6101—22no—
108#6101—41no—
109#6101—41no—
110C4×Dic13—41no—
111#2697—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—
185C2×#123—131no—
186C2×#120—131no—
187#397—131no—
188#397—131no—
189#396—131no—
190#396—131no—
191#394—131no—
192#394—131no—
193#390—131no—
194#388—131no—
195#388—131no—
196#386—131no—
197#386D1311yescharacteristic, complemented
198#379—131no—
199#379—131no—
200C22×C13—22no—
201C22×C13—22no—
202C22×C13—22no—
203C22×C13—22no—
204C22×C13—22no—
205C22×C13—22no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13—41no—
214C22×C13C22×D411yescharacteristic
215C22×C13C2×#4111yescharacteristic
216C22×C13C2×#4111yescharacteristic
217C22×C13H(5,𝔽2)11yescharacteristic
218C22×C13H(5,𝔽2)11yescharacteristic
219C22×C13H(5,𝔽2)11yescharacteristic
220C22×C13H(5,𝔽2)11yescharacteristic
221C2×D13—22no—
222C2×D13—22no—
223C2×D13—22no—
224C2×D13—22no—
225C2×D13—22no—
226C2×D13—22no—
227C2×D13—416no—
228C2×D13—41no—
229C2×D13—41no—
230C2×D13—41no—
231C2×D13—41no—
232C2×D13—41no—
233C2×D13—41no—
234C2×D13—41no—
235C2×D13—41no—
236C4×C13—41no—
237C4×C13—41no—
238C4×C13—41no—
239C4×C13—41no—
240C4×C13—41no—
241Dic13—22no—
242Dic13—41no—
243Dic13—41no—
244Dic13—41no—
245Dic13—41no—
246Dic13—41no—
247C25—131no—
248C22×D4—131no—
249C22×D4—131no—
250C22×D4C2×D1311yescharacteristic
251C23×C4C2×D1311yescharacteristic, complemented
252#123—264no—
253#120—264no—
254C2×C4⋊C4—131no—
255C2×C4⋊C4—131no—
256C2×C4⋊C4—131no—
257C2×C4⋊C4—131no—
258C2×C4⋊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⋊C4—131no—
274C2×C22⋊C4C2×D1311yescharacteristic
275C2×C22⋊C4C2×D1311yescharacteristic
276C2×C22⋊C4C2×D1311yescharacteristic, complemented
277C2×C42—131no—
278#95—131no—
279#95—131no—
280#95—131no—
281#95—131no—
282#95C2×D1311yescharacteristic, complemented
283#95C2×D1311yescharacteristic, complemented
284C2×C13—42no—
285C2×C13—42no—
286C2×C13#53411yescharacteristic
287C2×C13#53811yescharacteristic
288C2×C13#53811yescharacteristic
289C2×C13#54611yescharacteristic
290C2×C13#54611yescharacteristic
291C2×C13#55111yescharacteristic
292C2×C13#56011yescharacteristic
293D13—42no—
294D13—42no—
295C24—131no—
296C24—131no—
297C24—262no—
298C24—262no—
299C24—262no—
300C24—521no—
301C24—521no—
302C24—521no—
303C24—521no—
304C24C22×D1311yescharacteristic
305C24C22×D1311yescharacteristic
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—41no—
309C2×D4—134no—
310C2×D4—262no—
311C2×D4—262no—
312C2×D4—521no—
313C2×D4—521no—
314C2×D4—521no—
315C22×C4—22no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—131no—
319C22×C4—131no—
320C22×C4—131no—
321C22×C4—131no—
322C22×C4—131no—
323C22×C4—131no—
324C22×C4C22×D1311yescharacteristic
325C22×C4C22×D1311yescharacteristic
326C22×C4C22×D1311yescharacteristic
327C22×C4C22×D1311yescharacteristic
328C22×C4C22×D1311yescharacteristic
329C4⋊C4—262no—
330C4⋊C4—262no—
331C4⋊C4—521no—
332C4⋊C4—521no—
333C4⋊C4—521no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—262no—
338C22⋊C4—262no—
339C22⋊C4—262no—
340C22⋊C4—262no—
341C22⋊C4—262no—
342C22⋊C4—262no—
343C22⋊C4—262no—
344C22⋊C4—262no—
345C22⋊C4—521no—
346C22⋊C4—521no—
347C22⋊C4—521no—
348C22⋊C4—521no—
349C22⋊C4—521no—
350C22⋊C4—521no—
351C22⋊C4—521no—
352C42—521no—
353C13#269711yescharacteristic, complemented, Sylow
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—132no—
367C23—132no—
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—524no—
381C23—524no—
382C23—524no—
383C23—524no—
384C23—524no—
385C23—524no—
386C23—524no—
387C23#612712yes—
388C23D4×D1312yes—
389C23C23×D1311yescharacteristic
390D4—44no—
391D4—524no—
392D4—524no—
393C2×C4—21no—
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—44no—
409C2×C4—132no—
410C2×C4—261no—
411C2×C4—261no—
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—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—262no—
442C22—262no—
443C22—262no—
444C22—262no—
445C22—262no—
446C22—262no—
447C22—5216no—
448C22—521no—
449C22—521no—
450C22—521no—
451C22—521no—
452C22—521no—
453C22—521no—
454C22—521no—
455C22—521no—
456C22C2×#612711yescharacteristic
457C22C2×D4×D1311yescharacteristic
458C22#8825111yescharacteristic
459C22#8825111yescharacteristic
460C22#8825111yescharacteristic
461C22#41×D1311yescharacteristic
462C22#8825611yescharacteristic
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—41no—
468C4—262no—
469C4—521no—
470C4—521no—
471C4—521no—
472C4—521no—
473C4—521no—
474C2—42no—
475C2—42no—
476C2—522no—
477C2—522no—
478C2#1171919511yescharacteristic
479C2#1171926111yescharacteristic
480C2#1171926511yescharacteristic
481C2#1171929411yescharacteristic
482C2#1171931811yescharacteristic
483C2#1171932511yescharacteristic
484C2#1171935911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#386C2
prime radicalC2×#88191C2
hypercenter#386D13
hypocenterC13#2697
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×#88183C2semidirect
3. C13×#386C2semidirect
4. #11718883C2semidirect
5. #11718874C2semidirect
6. #11718622C2semidirect
7. #11718618C2semidirect
8. #11718616C2semidirect
9. #11718616C2semidirect
10. #11718609C2semidirect
11. #11718605C2semidirect
12. #11718337C2semidirect
13. #11718336C2semidirect
14. #11718335C2semidirect
15. #11718330C2semidirect
18. C23×C4×C13C22semidirect
23. C2×C13×C22⋊C4C22semidirect
27. C2×C22⋊Dic13C22semidirect
28. C2×C22⋊Dic13C22semidirect
41. C2×C4⋊Dic13C22semidirect
42. C2×#6101C22semidirect
43. C2×#6101C22semidirect
44. C2×#6101C22semidirect
45. C2×#6101C22semidirect
46. C2×C4×Dic13C22semidirect
47. C13×#95C22semidirect
48. C13×#95C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
197. #386D13semidirect
251. C23×C4C2×D13semidirect
276. C2×C22⋊C4C2×D13semidirect
282. #95C2×D13semidirect
283. #95C2×D13semidirect
353. C13#2697semidirect

Maximal subgroups

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

subgroupindex
C2×#881912
C2×#881832
C13×#3862
#117188832
#117188742
#117186222
#117186182
#117186162
#117186092
#117186052
#117183372
#117183362
#117183352
#117183302
#269713