Finite Group Databasebeta

← #13119724

Subgroups — #13119724

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×#88191C211yesmaximal, characteristic
2C2×C4×C22⋊D13C211yesmaximal, characteristic, complemented
3C2×#88137C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D13C211yesmaximal, characteristic, complemented
5C13×#386C211yesmaximal, characteristic, complemented
6#11718883C211yesmaximal, characteristic, complemented
7#11718874C211yesmaximal, characteristic, complemented
8#11718620C211yesmaximal, characteristic, complemented
9#11718616C211yesmaximal, characteristic, complemented
10#11718609C211yesmaximal, characteristic, complemented
11#11718605C211yesmaximal, characteristic, complemented
12#11718337C211yesmaximal, characteristic, complemented
13#11718331C211yesmaximal, characteristic, complemented
14#11718328C211yesmaximal, characteristic, complemented
15#11718325C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C23×C4×C13C2211yescharacteristic, complemented
19C22×C22⋊D13C2211yescharacteristic
20C22×C22⋊D13C2211yescharacteristic
21C22×C4×D13C2211yescharacteristic
22C22×C4×D13C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic, complemented
30C2×C22⋊Dic13C2211yescharacteristic, complemented
31#88191—24no—
32C4×C22⋊D13—24no—
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
47#88137—24no—
48C22⋊C4×D13—24no—
49C13×#95C2211yescharacteristic, complemented
50C13×#95C2211yescharacteristic, 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—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×C13—22no—
70C22×C4×C13—41no—
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⋊D13D414yes—
83C22×Dic13C2311yescharacteristic
84C22×Dic13C2311yescharacteristic
85C22×Dic13C2311yescharacteristic
86C22×Dic13C2311yescharacteristic
87C22×Dic13C2311yescharacteristic
88C22×Dic13C2311yescharacteristic
89C2×C4×D13—22no—
90C2×C4×D13—22no—
91C2×C4×D13—22no—
92C2×C4×D13—41no—
93C2×C4×D13—41no—
94C2×C4×D13D414yescomplemented
95C13×C22⋊C4—22no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4—41no—
98C22⋊Dic13—22no—
99C22⋊Dic13—22no—
100C22⋊Dic13—22no—
101C22⋊Dic13—22no—
102C22⋊Dic13—22no—
103#6103—22no—
104#6103—22no—
105#6103—22no—
106#6103—22no—
107#6103—22no—
108#6103—22no—
109#6103—22no—
110#6103—41no—
111C4⋊Dic13—22no—
112#6101—22no—
113#6101—22no—
114#6101—41no—
115#6101—41no—
116C4×Dic13—22no—
117#2534—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×C13C2×D412yes—
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×C13—21no—
169C2×C4×C13—44no—
170C2×C4×C13C2×D412yes—
171C22⋊D13—28no—
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×Dic13C2×D412yes—
190C2×Dic13C2×D412yes—
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#388—131no—
203#386—131no—
204#386D1311yescharacteristic, complemented
205#381—131no—
206#380—131no—
207#379—131no—
208C22×C13—22no—
209C22×C13—22no—
210C22×C13—22no—
211C22×C13—22no—
212C22×C13—22no—
213C22×C13—22no—
214C22×C13—41no—
215C22×C13—41no—
216C22×C13—41no—
217C22×C13—41no—
218C22×C13—41no—
219C22×C13—41no—
220C22×C13—41no—
221C22×C13—41no—
222C22×C13C22×D411yescharacteristic
223C22×C13C22×D411yescharacteristic
224C22×C13C2×#4111yescharacteristic
225C22×C13C2×#4111yescharacteristic
226C22×C13C2×#4111yescharacteristic
227C22×C13H(5,𝔽2)11yescharacteristic
228C22×C13H(5,𝔽2)11yescharacteristic
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—22no—
238C2×D13—416no—
239C2×D13—41no—
240C2×D13—41no—
241C2×D13—41no—
242C2×D13—41no—
243C2×D13#12114yes—
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—
254Dic13—41no—
255C25—131no—
256C22×D4—131no—
257C22×D4—131no—
258C22×D4C2×D1311yescharacteristic
259C23×C4—131no—
260C23×C4—131no—
261C23×C4C2×D1311yescharacteristic, complemented
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⋊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, complemented
287C2×C42—131no—
288#95—131no—
289#95—131no—
290#95—131no—
291#95—131no—
292#95C2×D1311yescharacteristic, complemented
293#95C2×D1311yescharacteristic, complemented
294C2×C13—42no—
295C2×C13—42no—
296C2×C13C2×#12111yescharacteristic
297C2×C13#52511yescharacteristic
298C2×C13#53411yescharacteristic
299C2×C13#54611yescharacteristic
300C2×C13#54611yescharacteristic
301C2×C13#55111yescharacteristic
302C2×C13#55111yescharacteristic
303D13—24no—
304D13—42no—
305C24—131no—
306C24—131no—
307C24—262no—
308C24—262no—
309C24—262no—
310C24—262no—
311C24—262no—
312C24—521no—
313C24—521no—
314C24C22×D1311yescharacteristic
315C24C22×D1311yescharacteristic
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—41no—
319C2×D4—134no—
320C2×D4—262no—
321C2×D4—262no—
322C2×D4—262no—
323C2×D4—262no—
324C2×D4—521no—
325C22×C4—22no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—131no—
329C22×C4—131no—
330C22×C4—134no—
331C22×C4—131no—
332C22×C4—131no—
333C22×C4—131no—
334C22×C4—131no—
335C22×C4—262no—
336C22×C4—262no—
337C22×C4—262no—
338C22×C4—521no—
339C22×C4—521no—
340C22×C4C22×D1311yescharacteristic
341C22×C4C22×D1311yescharacteristic
342C22×C4C22×D1311yescharacteristic
343C22×C4C22×D1311yescharacteristic
344C22×C4C22×D1311yescharacteristic
345C4⋊C4—262no—
346C4⋊C4—262no—
347C4⋊C4—262no—
348C4⋊C4—521no—
349C4⋊C4—521no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—41no—
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—262no—
365C22⋊C4—521no—
366C42—262no—
367C13#253411yescharacteristic, complemented, Sylow
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#612712yes—
402C23D4×D1312yes—
403C23C23×D1311yescharacteristic
404D4—44no—
405D4—268no—
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—44no—
422C2×C4—132no—
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—524no—
441C2×C4—524no—
442C2×C4D4×D1312yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—134no—
458C22—262no—
459C22—262no—
460C22—262no—
461C22—262no—
462C22—262no—
463C22—262no—
464C22—262no—
465C22—262no—
466C22—262no—
467C22—5216no—
468C22—521no—
469C22—521no—
470C22—521no—
471C22—521no—
472C22C2×#612711yescharacteristic
473C22C2×D4×D1311yescharacteristic
474C22C2×D4×D1311yescharacteristic
475C22#8825111yescharacteristic
476C22#8825111yescharacteristic
477C22#41×D1311yescharacteristic
478C22#41×D1311yescharacteristic
479C4—22no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—262no—
485C4—262no—
486C4—521no—
487C4—521no—
488C4—521no—
489C4—521no—
490C2—42no—
491C2—42no—
492C2—264no—
493C2—522no—
494C2#1171919511yescharacteristic
495C2#1171925211yescharacteristic
496C2#1171926111yescharacteristic
497C2#1171929411yescharacteristic
498C2D13×#12111yescharacteristic
499C2#1171931511yescharacteristic
500C2#1171936411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#386C2
prime radicalC2×#88191C2
hypercenter#386D13
hypocenterC13#2534
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D13C2semidirect
3. C2×#88137C2semidirect
4. C2×C22⋊C4×D13C2semidirect
5. C13×#386C2semidirect
6. #11718883C2semidirect
7. #11718874C2semidirect
8. #11718620C2semidirect
9. #11718616C2semidirect
10. #11718609C2semidirect
11. #11718605C2semidirect
12. #11718337C2semidirect
13. #11718331C2semidirect
14. #11718328C2semidirect
15. #11718325C2semidirect
18. C23×C4×C13C22semidirect
25. C2×C13×C22⋊C4C22semidirect
29. C2×C22⋊Dic13C22semidirect
30. C2×C22⋊Dic13C22semidirect
41. C2×C4⋊Dic13C22semidirect
42. C2×#6101C22semidirect
43. C2×#6101C22semidirect
44. C2×#6101C22semidirect
45. C2×#6101C22semidirect
46. C2×C4×Dic13C22semidirect
49. C13×#95C22semidirect
50. C13×#95C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
53. #88071C22semidirect
54. #88071C22semidirect
94. C2×C4×D13D4semidirect
204. #386D13semidirect
261. C23×C4C2×D13semidirect
286. C2×C22⋊C4C2×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×#881912
C2×C4×C22⋊D132
C2×#881372
C2×C22⋊C4×D132
C13×#3862
#117188832
#117188742
#117186202
#117186162
#117186092
#117186052
#117183372
#117183312
#117183282
#117183252
#253413