Finite Group Databasebeta

← #13118214

Subgroups — #13118214

Order 1664.

786 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88191C211yesmaximal, characteristic
2C2×#88146C211yesmaximal, characteristic, complemented
3C2×#88137C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D13C211yesmaximal, characteristic, complemented
5C13×#394C211yesmaximal, characteristic, complemented
6#11718882C211yesmaximal, characteristic, complemented
7#11718655C211yesmaximal, characteristic, complemented
8#11718622C211yesmaximal, characteristic, complemented
9#11718618C211yesmaximal, characteristic, complemented
10#11718617C211yesmaximal, characteristic, complemented
11#11718616C211yesmaximal, characteristic, complemented
12#11718612C211yesmaximal, characteristic, complemented
13#11718609C211yesmaximal, characteristic, complemented
14#11718331C211yesmaximal, characteristic, complemented
15#11718329C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C22×C22⋊D13C2211yescharacteristic
19C22×C22⋊D13C2211yescharacteristic
20C22×C4×D13C2211yescharacteristic
21C22×C4×D13C2211yescharacteristic
22C2×C13×C4⋊C4C2211yescharacteristic, complemented
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic, complemented
26C2×C13×C22⋊C4C2211yescharacteristic, complemented
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊Dic13C2211yescharacteristic, complemented
31C2×C22⋊Dic13C2211yescharacteristic, complemented
32#88191—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×C4⋊Dic13C2211yescharacteristic, complemented
44C2×#6101C2211yescharacteristic, complemented
45C2×#6101C2211yescharacteristic, complemented
46C2×C4×Dic13C2211yescharacteristic, complemented
47C2×C4×Dic13C2211yescharacteristic, complemented
48#88146—24no—
49#88137—24no—
50C22⋊C4×D13—24no—
51C13×#95C2211yescharacteristic, 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—22no—
62C23×D13—41no—
63C23×D13—41no—
64C23×D13C2311yescharacteristic
65C23×D13C2311yescharacteristic
66C2×D4×C13—22no—
67C2×D4×C13—22no—
68C2×D4×C13—41no—
69C22×C4×C13C2311yescharacteristic
70C22×C4×C13C2311yescharacteristic
71C22×C4×C13C2311yescharacteristic
72C22×C4×C13C2311yescharacteristic
73C22×C4×C13C2311yescharacteristic
74C2×C22⋊D13—22no—
75C2×C22⋊D13—22no—
76C2×C22⋊D13—22no—
77C2×C22⋊D13—22no—
78C2×C22⋊D13—22no—
79C2×C22⋊D13—41no—
80C22×Dic13C2311yescharacteristic
81C22×Dic13C2311yescharacteristic
82C22×Dic13C2311yescharacteristic
83C22×Dic13C2311yescharacteristic
84C22×Dic13C2311yescharacteristic
85C22×Dic13C2311yescharacteristic
86C2×C4×D13—22no—
87C2×C4×D13—22no—
88C2×C4×D13—22no—
89C2×C4×D13—41no—
90C2×C4×D13—41no—
91C2×C4×D13D414yescomplemented
92C13×C4⋊C4—22no—
93C13×C22⋊C4—22no—
94C13×C22⋊C4—22no—
95C13×C22⋊C4—22no—
96C13×C22⋊C4—41no—
97C22⋊Dic13—22no—
98C22⋊Dic13—22no—
99C22⋊Dic13—22no—
100C22⋊Dic13—41no—
101C22⋊Dic13—41no—
102#6103—22no—
103#6103—22no—
104#6103—22no—
105#6103—22no—
106#6103—22no—
107#6103—22no—
108#6103—41no—
109#6103D414yes—
110C4⋊Dic13—22no—
111C4⋊Dic13—22no—
112C4⋊Dic13—41no—
113#6101—22no—
114#6101—41no—
115C4×Dic13—22no—
116C4×Dic13—22no—
117#2411—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×C13—21no—
130C23×C13—21no—
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—44no—
145C22×D13—44no—
146C22×D13—44no—
147C22×D13—44no—
148C22×D13—44no—
149C22×D13—44no—
150C22×D13C2×D412yes—
151C22×D13C2×D412yes—
152C22×D13#4112yes—
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×C13C2×D412yes—
169C2×C4×C13C2×D412yes—
170C22⋊D13—44no—
171C22⋊D13—44no—
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×Dic13—21no—
185C2×Dic13—21no—
186C2×Dic13—21no—
187C2×Dic13—21no—
188C2×Dic13C2×D412yes—
189C2×Dic13C2×D412yes—
190C4×D13—28no—
191C4×D13—44no—
192C2×#123—131no—
193C2×#120—131no—
194C2×#117—131no—
195C22×C22⋊C4—131no—
196#396—131no—
197#396—131no—
198#394—131no—
199#394D1311yescharacteristic, complemented
200#390—131no—
201#390—131no—
202#388—131no—
203#388—131no—
204#386—131no—
205#385—131no—
206#379—131no—
207C22×C13—22no—
208C22×C13—22no—
209C22×C13—22no—
210C22×C13—41no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13—41no—
214C22×C13—41no—
215C22×C13—41no—
216C22×C13—41no—
217C22×C13—41no—
218C22×C13—41no—
219C22×C13—41no—
220C22×C13—41no—
221C22×C13C22×D411yescharacteristic
222C22×C13C22×D411yescharacteristic
223C22×C13C2×#4111yescharacteristic
224C22×C13C2×#4111yescharacteristic
225C22×C13C2×#4111yescharacteristic
226C22×C13H(5,𝔽2)11yescharacteristic
227C22×C13H(5,𝔽2)11yescharacteristic
228C2×D13—22no—
229C2×D13—22no—
230C2×D13—22no—
231C2×D13—22no—
232C2×D13—22no—
233C2×D13—22no—
234C2×D13—22no—
235C2×D13—22no—
236C2×D13—22no—
237C2×D13—416no—
238C2×D13—41no—
239C2×D13—41no—
240C2×D13—41no—
241C2×D13—41no—
242C2×D13#12114yes—
243C4×C13—22no—
244C4×C13—22no—
245C4×C13—41no—
246C4×C13—41no—
247C4×C13—41no—
248Dic13—22no—
249Dic13—22no—
250Dic13—41no—
251Dic13—41no—
252Dic13—41no—
253Dic13—41no—
254C25—131no—
255C22×D4—131no—
256C22×D4—131no—
257C22×D4C2×D1311yescharacteristic
258C23×C4—131no—
259C23×C4—131no—
260#123—264no—
261#120—264no—
262#117—264no—
263C2×C4⋊C4—131no—
264C2×C4⋊C4—131no—
265C2×C4⋊C4—131no—
266C2×C4⋊C4—131no—
267C2×C4⋊C4—131no—
268C2×C4⋊C4C2×D1311yescharacteristic, complemented
269C2×C22⋊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⋊C4C2×D1311yescharacteristic
284C2×C22⋊C4C2×D1311yescharacteristic
285C2×C22⋊C4C2×D1311yescharacteristic, complemented
286C2×C22⋊C4C2×D1311yescharacteristic, complemented
287C2×C42—131no—
288C2×C42—131no—
289#95—131no—
290#95—131no—
291#95—131no—
292#95C2×D1311yescharacteristic, complemented
293C2×C13—42no—
294C2×C13—81no—
295C2×C13C2×#12111yescharacteristic
296C2×C13#52511yescharacteristic
297C2×C13#53511yescharacteristic
298C2×C13#54611yescharacteristic
299C2×C13#54611yescharacteristic
300C2×C13#55111yescharacteristic
301C2×C13#55111yescharacteristic
302D13—24no—
303D13—42no—
304C24—131no—
305C24—131no—
306C24—262no—
307C24—262no—
308C24—262no—
309C24—262no—
310C24—262no—
311C24—521no—
312C24—521no—
313C24C22×D1311yescharacteristic
314C24C22×D1311yescharacteristic
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—41no—
318C2×D4—262no—
319C2×D4—262no—
320C2×D4—262no—
321C2×D4—262no—
322C2×D4—262no—
323C2×D4—521no—
324C22×C4—131no—
325C22×C4—131no—
326C22×C4—134no—
327C22×C4—131no—
328C22×C4—131no—
329C22×C4—131no—
330C22×C4—131no—
331C22×C4—262no—
332C22×C4—262no—
333C22×C4—262no—
334C22×C4—521no—
335C22×C4—521no—
336C22×C4C22×D1311yescharacteristic
337C22×C4C22×D1311yescharacteristic
338C22×C4C22×D1311yescharacteristic
339C22×C4C22×D1311yescharacteristic
340C22×C4C22×D1311yescharacteristic
341C4⋊C4—22no—
342C4⋊C4—262no—
343C4⋊C4—262no—
344C4⋊C4—262no—
345C4⋊C4—521no—
346C4⋊C4—521no—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—41no—
351C22⋊C4—134no—
352C22⋊C4—262no—
353C22⋊C4—262no—
354C22⋊C4—262no—
355C22⋊C4—262no—
356C22⋊C4—262no—
357C22⋊C4—262no—
358C22⋊C4—262no—
359C22⋊C4—262no—
360C22⋊C4—262no—
361C22⋊C4—521no—
362C22⋊C4—521no—
363C22⋊C4—521no—
364C42—262no—
365C42—262no—
366C13#241111yescharacteristic, complemented, Sylow
367C23—21no—
368C23—21no—
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—261no—
390C23—261no—
391C23—261no—
392C23—261no—
393C23—261no—
394C23—261no—
395C23—524no—
396C23—524no—
397C23—524no—
398C23—524no—
399C23—524no—
400C23—524no—
401C23#612912yes—
402C23C23×D1311yescharacteristic
403D4—44no—
404D4—524no—
405D4—524no—
406C2×C4—21no—
407C2×C4—21no—
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—132no—
420C2×C4—132no—
421C2×C4—268no—
422C2×C4—261no—
423C2×C4—261no—
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—524no—
439C2×C4D4×D1312yes—
440C2×C4D4×D1312yes—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—134no—
456C22—262no—
457C22—262no—
458C22—262no—
459C22—262no—
460C22—262no—
461C22—262no—
462C22—262no—
463C22—262no—
464C22—262no—
465C22—5216no—
466C22—521no—
467C22—521no—
468C22—521no—
469C22—521no—
470C22C2×D4×D1311yescharacteristic
471C22C2×D4×D1311yescharacteristic
472C22C2×#612911yescharacteristic
473C22#8825111yescharacteristic
474C22#41×D1311yescharacteristic
475C22#41×D1311yescharacteristic
476C22#8825611yescharacteristic
477C4—22no—
478C4—22no—
479C4—41no—
480C4—41no—
481C4—41no—
482C4—262no—
483C4—262no—
484C4—521no—
485C4—521no—
486C4—521no—
487C4—521no—
488C2—42no—
489C2—81no—
490C2—264no—
491C2—522no—
492C2#1171929611yescharacteristic
493C2D13×#12111yescharacteristic
494C2#1171931111yescharacteristic
495C2#1171931211yescharacteristic
496C2#1171936311yescharacteristic
497C2#1171936411yescharacteristic
498C2#1171938111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC2×#88191C2
hypercenter#394D13
hypocenterC13#2411
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#88146C2semidirect
3. C2×#88137C2semidirect
4. C2×C22⋊C4×D13C2semidirect
5. C13×#394C2semidirect
6. #11718882C2semidirect
7. #11718655C2semidirect
8. #11718622C2semidirect
9. #11718618C2semidirect
10. #11718617C2semidirect
11. #11718616C2semidirect
12. #11718612C2semidirect
13. #11718609C2semidirect
14. #11718331C2semidirect
15. #11718329C2semidirect
22. C2×C13×C4⋊C4C22semidirect
25. C2×C13×C22⋊C4C22semidirect
26. C2×C13×C22⋊C4C22semidirect
30. C2×C22⋊Dic13C22semidirect
31. C2×C22⋊Dic13C22semidirect
41. C2×C4⋊Dic13C22semidirect
42. C2×C4⋊Dic13C22semidirect
43. C2×C4⋊Dic13C22semidirect
44. C2×#6101C22semidirect
45. C2×#6101C22semidirect
46. C2×C4×Dic13C22semidirect
47. C2×C4×Dic13C22semidirect
51. C13×#95C22semidirect
52. #88071C22semidirect
53. #88071C22semidirect
54. #88071C22semidirect
91. C2×C4×D13D4semidirect
199. #394D13semidirect
268. C2×C4⋊C4C2×D13semidirect
285. C2×C22⋊C4C2×D13semidirect
286. C2×C22⋊C4C2×D13semidirect
292. #95C2×D13semidirect
366. C13#2411semidirect

Maximal subgroups

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

subgroupindex
C2×#881912
C2×#881462
C2×#881372
C2×C22⋊C4×D132
C13×#3942
#117188822
#117186552
#117186222
#117186182
#117186172
#117186162
#117186122
#117186092
#117183312
#117183292
#241113