Finite Group Databasebeta

← #13118231

Subgroups — #13118231

Order 1664.

814 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88191C211yesmaximal, characteristic
2C22×#6103C211yesmaximal, characteristic, complemented
3C2×#88137C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D13C211yesmaximal, characteristic, complemented
5C13×#386C211yesmaximal, characteristic, complemented
6#11718881C211yesmaximal, characteristic, complemented
7#11718873C211yesmaximal, characteristic, complemented
8#11718622C211yesmaximal, characteristic, complemented
9#11718620C211yesmaximal, characteristic, complemented
10#11718617C211yesmaximal, characteristic, complemented
11#11718603C211yesmaximal, characteristic, complemented
12#11718336C211yesmaximal, characteristic, complemented
13#11718335C211yesmaximal, characteristic, complemented
14#11718329C211yesmaximal, characteristic, complemented
15#11718325C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C23×C4×C13C2211yescharacteristic
19C22×C22⋊D13C2211yescharacteristic
20C22×C22⋊D13C2211yescharacteristic
21C23×Dic13C2211yescharacteristic
22C22×C4×D13C2211yescharacteristic
23C22×C4×D13C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic, complemented
26C2×C13×C22⋊C4C2211yescharacteristic, complemented
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic, complemented
30C2×C22⋊Dic13C2211yescharacteristic, complemented
31#88191—24no—
32C2×#6103—24no—
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic
39C2×#6103C2211yescharacteristic
40C2×#6103C2211yescharacteristic
41C2×C4⋊Dic13C2211yescharacteristic, complemented
42C2×C4⋊Dic13C2211yescharacteristic, complemented
43C2×#6101C2211yescharacteristic, complemented
44C2×#6101C2211yescharacteristic, complemented
45#88137—24no—
46C22⋊C4×D13—24no—
47C13×#95C2211yescharacteristic, complemented
48C13×#95C2211yescharacteristic, complemented
49#88071C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53#88071C2211yescharacteristic, complemented
54#88071C2211yescharacteristic, complemented
55C24×C13C2311yescharacteristic
56C24×C13C2311yescharacteristic
57C23×D13—22no—
58C23×D13—22no—
59C23×D13—22no—
60C23×D13—22no—
61C23×D13—41no—
62C23×D13—41no—
63C23×D13D414yes—
64C23×D13C2311yescharacteristic
65C23×D13C2311yescharacteristic
66C2×D4×C13—22no—
67C2×D4×C13—22no—
68C2×D4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—41no—
72C22×C4×C13C2311yescharacteristic
73C22×C4×C13C2311yescharacteristic
74C22×C4×C13C2311yescharacteristic
75C22×C4×C13C2311yescharacteristic
76C22×C4×C13C2311yescharacteristic
77C2×C22⋊D13—22no—
78C2×C22⋊D13—22no—
79C2×C22⋊D13—22no—
80C2×C22⋊D13—22no—
81C2×C22⋊D13—41no—
82C2×C22⋊D13—41no—
83C22×Dic13—22no—
84C22×Dic13—22no—
85C22×Dic13—41no—
86C22×Dic13C2311yescharacteristic
87C22×Dic13C2311yescharacteristic
88C22×Dic13C2311yescharacteristic
89C22×Dic13C2311yescharacteristic
90C22×Dic13C2311yescharacteristic
91C22×Dic13C2311yescharacteristic
92C2×C4×D13—22no—
93C2×C4×D13—22no—
94C2×C4×D13—22no—
95C2×C4×D13—22no—
96C2×C4×D13—41no—
97C2×C4×D13—41no—
98C13×C22⋊C4—22no—
99C13×C22⋊C4—22no—
100C13×C22⋊C4—41no—
101C22⋊Dic13—22no—
102C22⋊Dic13—22no—
103C22⋊Dic13—22no—
104C22⋊Dic13—41no—
105#6103—22no—
106#6103—22no—
107#6103—22no—
108#6103—22no—
109#6103—22no—
110#6103—22no—
111#6103—22no—
112#6103D414yescomplemented
113C4⋊Dic13—22no—
114C4⋊Dic13—41no—
115#6101—22no—
116#6101—41no—
117#2412—131nomaximal, Sylow
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13C2×D412yes—
130C23×C13#4112yes—
131C23×C13#4112yes—
132C23×C13C2411yescharacteristic
133C22×D13—21no—
134C22×D13—21no—
135C22×D13—21no—
136C22×D13—21no—
137C22×D13—28no—
138C22×D13—21no—
139C22×D13—21no—
140C22×D13—21no—
141C22×D13—21no—
142C22×D13—21no—
143C22×D13—21no—
144C22×D13—28no—
145C22×D13—44no—
146C22×D13—44no—
147C22×D13—44no—
148C22×D13—44no—
149C22×D13—44no—
150C22×D13C2×D412yes—
151C22×D13C2×D412yes—
152C22×D13C2×D412yes—
153C22×D13#4112yes—
154D4×C13—44no—
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×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—44no—
170C2×C4×C13C2×D412yes—
171C22⋊D13—44no—
172C22⋊D13—44no—
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×Dic13—21no—
185C2×Dic13—21no—
186C2×Dic13—21no—
187C2×Dic13—21no—
188C2×Dic13—21no—
189C2×Dic13—21no—
190C2×Dic13—44no—
191C2×Dic13C2×D412yes—
192C4×D13—44no—
193C4×D13—44no—
194C2×#123—131no—
195C2×#120—131no—
196C22×C22⋊C4—131no—
197C22×C22⋊C4—131no—
198#397—131no—
199#397—131no—
200#394—131no—
201#394—131no—
202#386—131no—
203#386—131no—
204#386D1311yescharacteristic, complemented
205#385—131no—
206#381—131no—
207#380—131no—
208#380—131no—
209C22×C13—22no—
210C22×C13—22no—
211C22×C13—22no—
212C22×C13—22no—
213C22×C13—22no—
214C22×C13—22no—
215C22×C13—41no—
216C22×C13—41no—
217C22×C13—41no—
218C22×C13—41no—
219C22×C13—41no—
220C22×C13—41no—
221C22×C13—41no—
222C22×C13#12314yescomplemented
223C22×C13C22×D411yescharacteristic
224C22×C13C22×D411yescharacteristic
225C22×C13C2×#4111yescharacteristic
226C22×C13C2×#4111yescharacteristic
227C22×C13C2×#4111yescharacteristic
228C22×C13H(5,𝔽2)11yescharacteristic
229C22×C13H(5,𝔽2)11yescharacteristic
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—416no—
240C2×D13—41no—
241C2×D13—41no—
242C2×D13—41no—
243C2×D13—41no—
244C2×D13#12114yes—
245C4×C13—22no—
246C4×C13—41no—
247C4×C13—41no—
248C4×C13—41no—
249C4×C13—41no—
250Dic13—22no—
251Dic13—41no—
252Dic13—41no—
253Dic13—41no—
254Dic13—41no—
255Dic13—41no—
256C25—131no—
257C22×D4—131no—
258C22×D4—131no—
259C22×D4C2×D1311yescharacteristic
260C23×C4—131no—
261C23×C4—131no—
262C23×C4—131no—
263C23×C4C2×D1311yescharacteristic
264#123—264no—
265#120—264no—
266C2×C4⋊C4—131no—
267C2×C4⋊C4—131no—
268C2×C4⋊C4—131no—
269C2×C4⋊C4—131no—
270C2×C22⋊C4—131no—
271C2×C22⋊C4—131no—
272C2×C22⋊C4—131no—
273C2×C22⋊C4—131no—
274C2×C22⋊C4—131no—
275C2×C22⋊C4—131no—
276C2×C22⋊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—264no—
283C2×C22⋊C4—264no—
284C2×C22⋊C4C2×D1311yescharacteristic
285C2×C22⋊C4C2×D1311yescharacteristic, complemented
286C2×C22⋊C4C2×D1311yescharacteristic, complemented
287#95—131no—
288#95—131no—
289#95—131no—
290#95—131no—
291#95—131no—
292#95—131no—
293#95C2×D1311yescharacteristic, complemented
294#95C2×D1311yescharacteristic, complemented
295C2×C13—24no—
296C2×C13—81no—
297C2×C13C2×#12111yescharacteristic
298C2×C13C2×#12311yescharacteristic
299C2×C13#53411yescharacteristic
300C2×C13#54611yescharacteristic
301C2×C13#54611yescharacteristic
302C2×C13#55111yescharacteristic
303C2×C13#55111yescharacteristic
304D13—24no—
305D13—42no—
306C24—131no—
307C24—131no—
308C24—134no—
309C24—262no—
310C24—262no—
311C24—262no—
312C24—262no—
313C24—521no—
314C24—521no—
315C24C22×D1311yescharacteristic
316C24C22×D1311yescharacteristic
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—22no—
320C2×D4—262no—
321C2×D4—262no—
322C2×D4—262no—
323C2×D4—262no—
324C2×D4—521no—
325C2×D4—521no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—41no—
329C22×C4—131no—
330C22×C4—131no—
331C22×C4—131no—
332C22×C4—131no—
333C22×C4—131no—
334C22×C4—131no—
335C22×C4—262no—
336C22×C4—262no—
337C22×C4—262no—
338C22×C4—262no—
339C22×C4—262no—
340C22×C4—262no—
341C22×C4—521no—
342C22×C4—521no—
343C22×C4—521no—
344C22×C4C22×D1311yescharacteristic
345C22×C4C22×D1311yescharacteristic
346C22×C4C22×D1311yescharacteristic
347C22×C4C22×D1311yescharacteristic
348C22×C4C22×D1311yescharacteristic
349C4⋊C4—262no—
350C4⋊C4—262no—
351C4⋊C4—521no—
352C4⋊C4—521no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—41no—
356C22⋊C4—134no—
357C22⋊C4—262no—
358C22⋊C4—262no—
359C22⋊C4—262no—
360C22⋊C4—262no—
361C22⋊C4—262no—
362C22⋊C4—262no—
363C22⋊C4—262no—
364C22⋊C4—262no—
365C22⋊C4—262no—
366C22⋊C4—262no—
367C22⋊C4—521no—
368C13#241211yescharacteristic, complemented, Sylow
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—132no—
381C23—132no—
382C23—132no—
383C23—132no—
384C23—268no—
385C23—261no—
386C23—261no—
387C23—261no—
388C23—261no—
389C23—268no—
390C23—261no—
391C23—261no—
392C23—261no—
393C23—261no—
394C23—261no—
395C23—261no—
396C23—524no—
397C23—524no—
398C23—524no—
399C23—524no—
400C23—524no—
401C23#612712yes—
402C23D4×D1312yes—
403C23#612912yes—
404C23C23×D1311yescharacteristic
405D4—44no—
406D4—524no—
407D4—524no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—44no—
423C2×C4—132no—
424C2×C4—261no—
425C2×C4—261no—
426C2×C4—261no—
427C2×C4—261no—
428C2×C4—261no—
429C2×C4—261no—
430C2×C4—261no—
431C2×C4—261no—
432C2×C4—261no—
433C2×C4—261no—
434C2×C4—261no—
435C2×C4—261no—
436C2×C4—261no—
437C2×C4—261no—
438C2×C4—261no—
439C2×C4—261no—
440C2×C4—261no—
441C2×C4—524no—
442C2×C4—524no—
443C2×C4—524no—
444C2×C4D4×D1312yes—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—134no—
459C22—262no—
460C22—262no—
461C22—262no—
462C22—262no—
463C22—262no—
464C22—262no—
465C22—262no—
466C22—262no—
467C22—262no—
468C22—5216no—
469C22—521no—
470C22—521no—
471C22—521no—
472C22—521no—
473C22#8813714yescomplemented
474C22C2×#612711yescharacteristic
475C22C2×D4×D1311yescharacteristic
476C22C2×D4×D1311yescharacteristic
477C22C2×#612911yescharacteristic
478C22#8825111yescharacteristic
479C22#41×D1311yescharacteristic
480C22#8825611yescharacteristic
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—262no—
487C4—521no—
488C4—521no—
489C4—521no—
490C4—521no—
491C4—521no—
492C2—24no—
493C2—81no—
494C2—264no—
495C2—522no—
496C2C2×#8813711yescharacteristic
497C2#1171925511yescharacteristic
498C2#1171926111yescharacteristic
499C2#1171929611yescharacteristic
500C2D13×#12111yescharacteristic
501C2#1171931011yescharacteristic
502C2#1171936311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#386C2
prime radicalC2×#88191C2
hypercenter#386D13
hypocenterC13#2412
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×#6103C2semidirect
3. C2×#88137C2semidirect
4. C2×C22⋊C4×D13C2semidirect
5. C13×#386C2semidirect
6. #11718881C2semidirect
7. #11718873C2semidirect
8. #11718622C2semidirect
9. #11718620C2semidirect
10. #11718617C2semidirect
11. #11718603C2semidirect
12. #11718336C2semidirect
13. #11718335C2semidirect
14. #11718329C2semidirect
15. #11718325C2semidirect
25. C2×C13×C22⋊C4C22semidirect
26. C2×C13×C22⋊C4C22semidirect
29. C2×C22⋊Dic13C22semidirect
30. C2×C22⋊Dic13C22semidirect
41. C2×C4⋊Dic13C22semidirect
42. C2×C4⋊Dic13C22semidirect
43. C2×#6101C22semidirect
44. C2×#6101C22semidirect
47. C13×#95C22semidirect
48. C13×#95C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
53. #88071C22semidirect
54. #88071C22semidirect
112. #6103D4semidirect
204. #386D13semidirect
222. C22×C13#123semidirect
285. C2×C22⋊C4C2×D13semidirect
286. C2×C22⋊C4C2×D13semidirect
293. #95C2×D13semidirect
294. #95C2×D13semidirect
368. C13#2412semidirect
473. C22#88137semidirect

Maximal subgroups

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

subgroupindex
C2×#881912
C22×#61032
C2×#881372
C2×C22⋊C4×D132
C13×#3862
#117188812
#117188732
#117186222
#117186202
#117186172
#117186032
#117183362
#117183352
#117183292
#117183252
#241213