Finite Group Databasebeta

← #13119730

Subgroups — #13119730

Order 1664.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88148C211yesmaximal, characteristic, complemented
2C2×#88136C211yesmaximal, characteristic
3C2×C22⋊C4×D13C211yesmaximal, characteristic, complemented
4C2×C4×D52C211yesmaximal, characteristic, complemented
5C13×#388C211yesmaximal, characteristic, complemented
6#11718655C211yesmaximal, characteristic, complemented
7#11718620C211yesmaximal, characteristic, complemented
8#11718617C211yesmaximal, characteristic, complemented
9#11718616C211yesmaximal, characteristic, complemented
10#11718609C211yesmaximal, characteristic, complemented
11#11718601C211yesmaximal, characteristic, complemented
12#11718333C211yesmaximal, characteristic, complemented
13#11718328C211yesmaximal, characteristic, complemented
14#11718326C211yesmaximal, characteristic, complemented
15#11718325C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×C22⋊D13C2211yescharacteristic
18C22×D52C2211yescharacteristic
19C22×D52C2211yescharacteristic
20C22×C4×D13C2211yescharacteristic
21C22×C4×D13C2211yescharacteristic
22C22×C4×D13C2211yescharacteristic, complemented
23C2×C13×C4⋊C4C2211yescharacteristic, complemented
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C13×C22⋊C4C2211yescharacteristic
27C2×C42×C13C2211yescharacteristic, complemented
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×C4⋊Dic13C2211yescharacteristic, complemented
42C2×#6101C2211yescharacteristic, complemented
43C2×#6101C2211yescharacteristic, complemented
44C2×#6101C2211yescharacteristic, complemented
45#88148—24no—
46#88136—24no—
47C22⋊C4×D13—24no—
48C4×D52—24no—
49C13×#95C2211yescharacteristic, complemented
50C13×#95C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, 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—41no—
85C2×D52D414yes—
86C2×C4×D13—22no—
87C2×C4×D13—22no—
88C2×C4×D13—22no—
89C2×C4×D13—22no—
90C2×C4×D13—41no—
91C2×C4×D13—41no—
92C2×C4×D13—41no—
93C2×C4×D13—41no—
94C2×C4×D13D414yescomplemented
95C13×C4⋊C4—22no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4—22no—
98C13×C22⋊C4—22no—
99C42×C13—22no—
100C22⋊Dic13—22no—
101C22⋊Dic13—41no—
102#6103—22no—
103#6103—22no—
104#6103—22no—
105#6103—22no—
106#6103—22no—
107#6103—22no—
108#6103—22no—
109#6103—22no—
110#6103—22no—
111#6103—22no—
112#6103—41no—
113C4⋊Dic13—22no—
114#6101—22no—
115#6101—41no—
116#6101—41no—
117#2534—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—44no—
144C22×D13—44no—
145C22×D13—44no—
146C22×D13—44no—
147C22×D13—44no—
148C22×D13—44no—
149C22×D13C2×D412yes—
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×Dic13—21no—
187C2×Dic13C2×D412yes—
188D52—28no—
189D52—44no—
190C4×D13—44no—
191C4×D13—44no—
192C4×D13—44no—
193C2×#123—131no—
194C2×#120—131no—
195C2×C4×D4—131no—
196C22×C22⋊C4—131no—
197#396—131no—
198#396—131no—
199#394—131no—
200#394—131no—
201#388—131no—
202#388D1311yescharacteristic, complemented
203#386—131no—
204#386—131no—
205#381—131no—
206#380—131no—
207#379—131no—
208C22×C13—22no—
209C22×C13—22no—
210C22×C13—22no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13—41no—
214C22×C13—41no—
215C22×C13C22×D411yescharacteristic
216C22×C13C22×D411yescharacteristic
217C22×C13C2×#4111yescharacteristic
218C22×C13C2×#4111yescharacteristic
219C22×C13C2×#4111yescharacteristic
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—22no—
229C2×D13—22no—
230C2×D13—22no—
231C2×D13—22no—
232C2×D13—22no—
233C2×D13—22no—
234C2×D13—416no—
235C2×D13—41no—
236C2×D13—41no—
237C2×D13—41no—
238C2×D13—41no—
239C2×D13—41no—
240C2×D13—41no—
241C2×D13—41no—
242C2×D13—41no—
243C2×D13#12114yes—
244C4×C13—22no—
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—
255C25—131no—
256C22×D4—131no—
257C22×D4—131no—
258C22×D4—131no—
259C23×C4—131no—
260C23×C4—131no—
261C23×C4—131no—
262#123—264no—
263#120—264no—
264C4×D4—264no—
265C2×C4⋊C4—131no—
266C2×C4⋊C4—131no—
267C2×C4⋊C4—131no—
268C2×C4⋊C4—131no—
269C2×C4⋊C4C2×D1311yescharacteristic, complemented
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×C42C2×D1311yescharacteristic, complemented
288#95—131no—
289#95—131no—
290#95—131no—
291#95—131no—
292#95C2×D1311yescharacteristic, complemented
293#95C2×D1311yescharacteristic, complemented
294C2×C13—42no—
295C2×C13C2×#12111yescharacteristic
296C2×C13#52511yescharacteristic
297C2×C13#53411yescharacteristic
298C2×C13#54611yescharacteristic
299C2×C13#54611yescharacteristic
300C2×C13#55111yescharacteristic
301C2×C13#55111yescharacteristic
302D13—24no—
303D13—42no—
304D13—42no—
305C24—131no—
306C24—131no—
307C24—131no—
308C24—262no—
309C24—262no—
310C24—262no—
311C24—262no—
312C24—262no—
313C24—521no—
314C24—521no—
315C24C22×D1311yescharacteristic
316C2×D4—134no—
317C2×D4—262no—
318C2×D4—262no—
319C2×D4—262no—
320C2×D4—262no—
321C2×D4—262no—
322C2×D4—262no—
323C2×D4—521no—
324C2×D4—521no—
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—262no—
335C22×C4—521no—
336C22×C4—521no—
337C22×C4—521no—
338C22×C4—521no—
339C22×C4C22×D1311yescharacteristic
340C22×C4C22×D1311yescharacteristic
341C22×C4C22×D1311yescharacteristic
342C22×C4C22×D1311yescharacteristic
343C22×C4C22×D1311yescharacteristic
344C22×C4C22×D1311yescharacteristic
345C4⋊C4—22no—
346C4⋊C4—262no—
347C4⋊C4—262no—
348C4⋊C4—521no—
349C4⋊C4—521no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—22no—
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—262no—
362C22⋊C4—262no—
363C22⋊C4—262no—
364C22⋊C4—521no—
365C22⋊C4—521no—
366C42—22no—
367C13#253411yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—132no—
375C23—132no—
376C23—132no—
377C23—132no—
378C23—132no—
379C23—268no—
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—261no—
396C23—524no—
397C23—524no—
398C23—524no—
399C23—524no—
400C23—524no—
401C23—524no—
402C23#612712yes—
403C23C23×D1311yescharacteristic
404D4—268no—
405D4—524no—
406D4—524no—
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—21no—
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—524no—
439C2×C4—524no—
440C2×C4—524no—
441C2×C4D4×D1312yes—
442C2×C4D4×D1312yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—134no—
451C22—262no—
452C22—262no—
453C22—262no—
454C22—262no—
455C22—262no—
456C22—262no—
457C22—262no—
458C22—262no—
459C22—262no—
460C22—262no—
461C22—262no—
462C22—262no—
463C22—5216no—
464C22—521no—
465C22—521no—
466C22—521no—
467C22—521no—
468C22—521no—
469C22—521no—
470C22—521no—
471C22—521no—
472C22C2×#612711yescharacteristic
473C22C2×D4×D1311yescharacteristic
474C22C2×D4×D1311yescharacteristic
475C22#41×D1311yescharacteristic
476C22#41×D1311yescharacteristic
477C22#8825611yescharacteristic
478C22#8825611yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—262no—
486C4—521no—
487C4—521no—
488C4—521no—
489C4—521no—
490C2—42no—
491C2—264no—
492C2—522no—
493C2—522no—
494C2#1171923211yescharacteristic
495C2#1171925211yescharacteristic
496C2#1171925511yescharacteristic
497C2D13×#12111yescharacteristic
498C2#1171935811yescharacteristic
499C2#1171938111yescharacteristic
500C2#1171941011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#388C2
prime radicalC2×#88136C2
hypercenter#388D13
hypocenterC13#2534
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#88148C2semidirect
3. C2×C22⋊C4×D13C2semidirect
4. C2×C4×D52C2semidirect
5. C13×#388C2semidirect
6. #11718655C2semidirect
7. #11718620C2semidirect
8. #11718617C2semidirect
9. #11718616C2semidirect
10. #11718609C2semidirect
11. #11718601C2semidirect
12. #11718333C2semidirect
13. #11718328C2semidirect
14. #11718326C2semidirect
15. #11718325C2semidirect
22. C22×C4×D13C22semidirect
23. C2×C13×C4⋊C4C22semidirect
27. C2×C42×C13C22semidirect
38. C2×#6103C22semidirect
39. C2×#6103C22semidirect
40. C2×#6103C22semidirect
41. C2×C4⋊Dic13C22semidirect
42. C2×#6101C22semidirect
43. C2×#6101C22semidirect
44. C2×#6101C22semidirect
49. C13×#95C22semidirect
50. C13×#95C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
53. #88071C22semidirect
54. #88071C22semidirect
94. C2×C4×D13D4semidirect
202. #388D13semidirect
269. C2×C4⋊C4C2×D13semidirect
287. C2×C42C2×D13semidirect
292. #95C2×D13semidirect
293. #95C2×D13semidirect
367. C13#2534semidirect

Maximal subgroups

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

subgroupindex
C2×#881482
C2×#881362
C2×C22⋊C4×D132
C2×C4×D522
C13×#3882
#117186552
#117186202
#117186172
#117186162
#117186092
#117186012
#117183332
#117183282
#117183262
#117183252
#253413