Finite Group Databasebeta

← #13118216

Subgroups — #13118216

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×#88148C211yesmaximal, characteristic, complemented
2C2×#88146C211yesmaximal, characteristic, complemented
3C2×#88136C211yesmaximal, characteristic
4C2×C22⋊C4×D13C211yesmaximal, characteristic, complemented
5C13×#396C211yesmaximal, characteristic, complemented
6#11718655C211yesmaximal, characteristic, complemented
7#11718652C211yesmaximal, characteristic, complemented
8#11718650C211yesmaximal, characteristic, complemented
9#11718649C211yesmaximal, characteristic, complemented
10#11718622C211yesmaximal, characteristic, complemented
11#11718618C211yesmaximal, characteristic, complemented
12#11718616C211yesmaximal, characteristic, complemented
13#11718605C211yesmaximal, characteristic, complemented
14#11718330C211yesmaximal, characteristic, complemented
15#11718326C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×C22⋊D13C2211yescharacteristic
18C22×D52C2211yescharacteristic
19C22×D52C2211yescharacteristic
20C22×C4×D13C2211yescharacteristic
21C22×C4×D13C2211yescharacteristic
22C2×C13×C4⋊C4C2211yescharacteristic, complemented
23C2×C13×C4⋊C4C2211yescharacteristic, complemented
24C2×C13×C4⋊C4C2211yescharacteristic, complemented
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C13×C22⋊C4C2211yescharacteristic
27C2×C13×C22⋊C4C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
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×#6103C2211yescharacteristic, complemented
42C2×C4⋊Dic13C2211yescharacteristic, complemented
43C2×#6101C2211yescharacteristic, complemented
44C2×#6101C2211yescharacteristic, complemented
45C2×C4×Dic13C2211yescharacteristic, complemented
46C2×C4×Dic13C2211yescharacteristic, complemented
47#88148—24no—
48#88146—24no—
49#88136—24no—
50C22⋊C4×D13—24no—
51C13×#95C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53#88071C2211yescharacteristic, complemented
54#88071C2211yescharacteristic, complemented
55C24×C13C2311yescharacteristic
56C23×D13—22no—
57C23×D13—22no—
58C23×D13—22no—
59C23×D13—22no—
60C23×D13—22no—
61C23×D13—41no—
62C23×D13—41no—
63C23×D13C2311yescharacteristic
64C23×D13C2311yescharacteristic
65C23×D13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C22×C4×C13C2311yescharacteristic
71C22×C4×C13C2311yescharacteristic
72C2×C22⋊D13—22no—
73C2×C22⋊D13—22no—
74C2×C22⋊D13—41no—
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C22×Dic13C2311yescharacteristic
80C2×D52—22no—
81C2×D52—22no—
82C2×D52—22no—
83C2×D52—22no—
84C2×D52—22no—
85C2×D52—41no—
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×C4⋊C4—22no—
94C13×C4⋊C4—41no—
95C13×C22⋊C4—22no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4—41no—
98C22⋊Dic13—22no—
99C22⋊Dic13—22no—
100#6103—22no—
101#6103—22no—
102#6103—22no—
103#6103—22no—
104#6103—22no—
105#6103—22no—
106#6103—22no—
107#6103—22no—
108#6103—41no—
109#6103—41no—
110#6103—41no—
111#6103D414yes—
112C4⋊Dic13—22no—
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#4112yes—
125C23×C13C2411yescharacteristic
126C22×D13—21no—
127C22×D13—21no—
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—28no—
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—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—
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×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13C2×D412yes—
171C2×C4×C13C2×D412yes—
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×Dic13C2×D412yes—
187C2×Dic13C2×D412yes—
188D52—44no—
189D52—44no—
190C4×D13—28no—
191C4×D13—44no—
192C2×#123—131no—
193C2×#120—131no—
194C2×#117—131no—
195C22×C22⋊C4—131no—
196#396—131no—
197#396D1311yescharacteristic, complemented
198#394—131no—
199#394—131no—
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×C13C22×D411yescharacteristic
215C22×C13C22×D411yescharacteristic
216C22×C13C2×#4111yescharacteristic
217C22×C13C2×#4111yescharacteristic
218C22×C13C2×#4111yescharacteristic
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—22no—
228C2×D13—22no—
229C2×D13—22no—
230C2×D13—416no—
231C2×D13—41no—
232C2×D13—41no—
233C2×D13—41no—
234C2×D13—41no—
235C2×D13—41no—
236C2×D13—41no—
237C2×D13—41no—
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—
248C4×C13—41no—
249Dic13—22no—
250Dic13—22no—
251Dic13—41no—
252Dic13—41no—
253Dic13—41no—
254C25—131no—
255C22×D4—131no—
256C22×D4—131no—
257C22×D4—131no—
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⋊C4C2×D1311yescharacteristic, complemented
267C2×C4⋊C4C2×D1311yescharacteristic, complemented
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—131no—
283C2×C22⋊C4—264no—
284C2×C22⋊C4C2×D1311yescharacteristic
285C2×C22⋊C4C2×D1311yescharacteristic
286C2×C22⋊C4C2×D1311yescharacteristic
287C2×C42—131no—
288C2×C42—131no—
289#95—131no—
290#95—131no—
291#95—131no—
292#95C2×D1311yescharacteristic, complemented
293C2×C13—42no—
294C2×C13C2×#12111yescharacteristic
295C2×C13#52511yescharacteristic
296C2×C13#53511yescharacteristic
297C2×C13#54611yescharacteristic
298C2×C13#54611yescharacteristic
299C2×C13#55111yescharacteristic
300C2×C13#55111yescharacteristic
301D13—24no—
302D13—42no—
303D13—81no—
304C24—131no—
305C24—131no—
306C24—131no—
307C24—262no—
308C24—262no—
309C24—262no—
310C24—262no—
311C24—262no—
312C24—521no—
313C24—521no—
314C24C22×D1311yescharacteristic
315C2×D4—262no—
316C2×D4—262no—
317C2×D4—262no—
318C2×D4—262no—
319C2×D4—262no—
320C2×D4—262no—
321C2×D4—262no—
322C2×D4—521no—
323C2×D4—521no—
324C22×C4—131no—
325C22×C4—131no—
326C22×C4—134no—
327C22×C4—131no—
328C22×C4—131no—
329C22×C4—131no—
330C22×C4—262no—
331C22×C4—262no—
332C22×C4—262no—
333C22×C4—521no—
334C22×C4—521no—
335C22×C4C22×D1311yescharacteristic
336C22×C4C22×D1311yescharacteristic
337C22×C4C22×D1311yescharacteristic
338C22×C4C22×D1311yescharacteristic
339C22×C4C22×D1311yescharacteristic
340C22×C4C22×D1311yescharacteristic
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—41no—
344C4⋊C4—262no—
345C4⋊C4—262no—
346C4⋊C4—521no—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—41no—
350C22⋊C4—134no—
351C22⋊C4—262no—
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—132no—
374C23—132no—
375C23—132no—
376C23—132no—
377C23—268no—
378C23—261no—
379C23—261no—
380C23—261no—
381C23—261no—
382C23—261no—
383C23—261no—
384C23—261no—
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#613112yes—
402C23C23×D1311yescharacteristic
403D4—524no—
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—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—132no—
423C2×C4—132no—
424C2×C4—268no—
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—134no—
449C22—262no—
450C22—262no—
451C22—262no—
452C22—262no—
453C22—262no—
454C22—262no—
455C22—262no—
456C22—262no—
457C22—262no—
458C22—5216no—
459C22—521no—
460C22—521no—
461C22—521no—
462C22—521no—
463C22—521no—
464C22—521no—
465C22—521no—
466C22—521no—
467C22—521no—
468C22—521no—
469C22—521no—
470C22C2×D4×D1311yescharacteristic
471C22C2×D4×D1311yescharacteristic
472C22#8825111yescharacteristic
473C22C2×#613111yescharacteristic
474C22#41×D1311yescharacteristic
475C22#41×D1311yescharacteristic
476C22#8825611yescharacteristic
477C4—22no—
478C4—22no—
479C4—41no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—262no—
484C4—262no—
485C4—521no—
486C4—521no—
487C4—521no—
488C2—42no—
489C2—264no—
490C2—522no—
491C2—1041no—
492C2D13×#12111yescharacteristic
493C2#1171931211yescharacteristic
494C2#1171931511yescharacteristic
495C2#1171933211yescharacteristic
496C2#1171933511yescharacteristic
497C2#1171934211yescharacteristic
498C2#1171941011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#396C2
prime radicalC2×#88136C2
hypercenter#396D13
hypocenterC13#2411
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#88148C2semidirect
2. C2×#88146C2semidirect
4. C2×C22⋊C4×D13C2semidirect
5. C13×#396C2semidirect
6. #11718655C2semidirect
7. #11718652C2semidirect
8. #11718650C2semidirect
9. #11718649C2semidirect
10. #11718622C2semidirect
11. #11718618C2semidirect
12. #11718616C2semidirect
13. #11718605C2semidirect
14. #11718330C2semidirect
15. #11718326C2semidirect
22. C2×C13×C4⋊C4C22semidirect
23. C2×C13×C4⋊C4C22semidirect
24. C2×C13×C4⋊C4C22semidirect
38. C2×#6103C22semidirect
39. C2×#6103C22semidirect
40. C2×#6103C22semidirect
41. C2×#6103C22semidirect
42. C2×C4⋊Dic13C22semidirect
43. C2×#6101C22semidirect
44. C2×#6101C22semidirect
45. C2×C4×Dic13C22semidirect
46. C2×C4×Dic13C22semidirect
51. C13×#95C22semidirect
52. #88071C22semidirect
53. #88071C22semidirect
54. #88071C22semidirect
91. C2×C4×D13D4semidirect
197. #396D13semidirect
266. C2×C4⋊C4C2×D13semidirect
267. C2×C4⋊C4C2×D13semidirect
268. C2×C4⋊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×#881482
C2×#881462
C2×#881362
C2×C22⋊C4×D132
C13×#3962
#117186552
#117186522
#117186502
#117186492
#117186222
#117186182
#117186162
#117186052
#117183302
#117183262
#241113