Finite Group Databasebeta

← #13118958

Subgroups — #13118958

Order 1664.

786 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×C13×#124C211yesmaximal, characteristic, complemented
2C2×#88200C211yesmaximal, characteristic, complemented
3C2×#88191C211yesmaximal, characteristic
4C2×C22⋊C4×D13C211yesmaximal, characteristic, complemented
5#11718892C211yesmaximal, characteristic, complemented
6#11718883C211yesmaximal, characteristic, complemented
7#11718622C211yesmaximal, characteristic, complemented
8#11718618C211yesmaximal, characteristic, complemented
9#11718617C211yesmaximal, characteristic, complemented
10#11718617C211yesmaximal, characteristic, complemented
11#11718616C211yesmaximal, characteristic, complemented
12#11718613C211yesmaximal, characteristic, complemented
13#11718612C211yesmaximal, characteristic, complemented
14#11718601C211yesmaximal, characteristic, complemented
15C4×#6103C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic, complemented
18C22×D4×C13C2211yescharacteristic
19C22×C22⋊D13C2211yescharacteristic
20C22×C22⋊D13C2211yescharacteristic
21C22×C4×D13C2211yescharacteristic
22C22×C4×D13C2211yescharacteristic
23C13×#124—24no—
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C13×C22⋊C4C2211yescharacteristic, complemented
27C2×C13×C22⋊C4C2211yescharacteristic, complemented
28C2×C42×C13C2211yescharacteristic, complemented
29C2×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊Dic13C2211yescharacteristic
31C2×C22⋊Dic13C2211yescharacteristic
32C2×C22⋊Dic13C2211yescharacteristic, complemented
33C2×C22⋊Dic13C2211yescharacteristic, complemented
34#88200—24no—
35#88191—24no—
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic
39C2×#6103C2211yescharacteristic
40C2×#6103C2211yescharacteristic
41C2×#6103C2211yescharacteristic
42C2×#6103C2211yescharacteristic
43C2×#6103C2211yescharacteristic
44C2×C4⋊Dic13C2211yescharacteristic, complemented
45C2×#6101C2211yescharacteristic, complemented
46C2×#6101C2211yescharacteristic, complemented
47C2×C4×Dic13C2211yescharacteristic, complemented
48C22⋊C4×D13—24no—
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—22no—
62C23×D13—41no—
63C23×D13—41no—
64C23×D13C2311yescharacteristic
65C23×D13C2311yescharacteristic
66C2×Q8×C13—22no—
67C2×Q8×C13—22no—
68C2×Q8×C13—41no—
69C2×D4×C13—22no—
70C2×D4×C13—22no—
71C2×D4×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—22no—
82C2×C22⋊D13—41no—
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—22no—
93C2×C4×D13—41no—
94C2×C4×D13—41no—
95C13×C22⋊C4—22no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4—22no—
98C13×C22⋊C4D414yescomplemented
99C42×C13—22no—
100C22⋊Dic13—22no—
101C22⋊Dic13—22no—
102C22⋊Dic13—41no—
103C22⋊Dic13—41no—
104C22⋊Dic13—41no—
105#6103—22no—
106#6103—22no—
107#6103—22no—
108#6103—22no—
109#6103—22no—
110#6103—22no—
111#6103—41no—
112#6103D414yes—
113C4⋊Dic13—22no—
114#6101—22no—
115#6101—22no—
116C4×Dic13—41no—
117#2472—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×C13C2×D412yes—
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×D13#4112yes—
152C22×D13#4112yes—
153C22×D13#4112yes—
154Q8×C13—44no—
155D4×C13—44no—
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—
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×Dic13C2×D412yes—
191C4×D13—44no—
192C4×D13—44no—
193C2×#124D1311yescharacteristic, complemented
194C2×C22⋊Q8—131no—
195C2×#120—131no—
196C22×C22⋊C4—131no—
197#397—131no—
198#394—131no—
199#394—131no—
200#393—131no—
201#390—131no—
202#388—131no—
203#388—131no—
204#386—131no—
205#386—131no—
206#379—131no—
207C4×C22⋊C4—131no—
208C22×C13—22no—
209C22×C13—22no—
210C22×C13—22no—
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×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#12414yescomplemented
244C4×C13—22no—
245C4×C13—22no—
246C4×C13—22no—
247C4×C13—41no—
248C4×C13—41no—
249Dic13—22no—
250Dic13—41no—
251Dic13—41no—
252Dic13—41no—
253Dic13—41no—
254Dic13—41no—
255C25—131no—
256C22×Q8C2×D1311yescharacteristic, complemented
257C22×D4—131no—
258C22×D4—131no—
259C22×D4C2×D1311yescharacteristic
260C23×C4—131no—
261C23×C4—131no—
262#124—24no—
263C22⋊Q8—264no—
264#120—264no—
265C2×C4⋊C4—131no—
266C2×C4⋊C4—131no—
267C2×C4⋊C4—131no—
268C2×C22⋊C4—131no—
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—264no—
282C2×C22⋊C4C2×D1311yescharacteristic
283C2×C22⋊C4C2×D1311yescharacteristic
284C2×C22⋊C4C2×D1311yescharacteristic, complemented
285C2×C22⋊C4C2×D1311yescharacteristic, complemented
286C2×C42—131no—
287C2×C42C2×D1311yescharacteristic, complemented
288#95—131no—
289#95—131no—
290#95—131no—
291#95—131no—
292#95—131no—
293#95—131no—
294C2×C13—42no—
295C2×C13—81no—
296C2×C13#52511yescharacteristic
297C2×C13C2×#12411yescharacteristic
298C2×C13#53811yescharacteristic
299C2×C13D4211yescharacteristic
300C2×C13#54611yescharacteristic
301C2×C13#54611yescharacteristic
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×Q8—22no—
317C2×Q8—22no—
318C2×Q8—41no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—41no—
322C2×D4—262no—
323C2×D4—262no—
324C2×D4—262no—
325C2×D4—262no—
326C2×D4—262no—
327C2×D4—521no—
328C22×C4—131no—
329C22×C4—131no—
330C22×C4—131no—
331C22×C4—131no—
332C22×C4—131no—
333C22×C4—131no—
334C22×C4—262no—
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—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—22no—
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—521no—
361C22⋊C4—521no—
362C22⋊C4—521no—
363C22⋊C4—521no—
364C22⋊C4C22⋊D1314yescomplemented
365C42—22no—
366C42—521no—
367C13#247211yescharacteristic, 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—21no—
381C23—132no—
382C23—132no—
383C23—132no—
384C23—132no—
385C23—268no—
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—
402C23C2×C22⋊D1312yes—
403C23C23×D1311yescharacteristic
404Q8—44no—
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—132no—
421C2×C4—261no—
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×C4—524no—
440C2×C4D4×D1312yes—
441C2×C4C2×C22⋊D1312yes—
442C2×C4C2×C22⋊D1312yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—41no—
447C22—41no—
448C22—41no—
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×D4×D1311yescharacteristic
473C22#8825111yescharacteristic
474C22#41×D1311yescharacteristic
475C22#41×D1311yescharacteristic
476C22#41×D1311yescharacteristic
477C22#8825611yescharacteristic
478C22C22×C22⋊D1311yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—262no—
485C4—521no—
486C4—521no—
487C4—521no—
488C4—521no—
489C4—521no—
490C2—42no—
491C2—81no—
492C2—264no—
493C2—522no—
494C2D13×#12411yescharacteristic
495C2#1171938111yescharacteristic
496C2#1171938311yescharacteristic
497C2#1171938411yescharacteristic
498C2D4×C22⋊D1311yescharacteristic
499C2#1171953311yescharacteristic
500C2#1171953411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#124C2
prime radicalC2×#88191C2
hypercenterC2×#124D13
hypocenterC13#2472
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×C13×#124C2semidirect
2. C2×#88200C2semidirect
4. C2×C22⋊C4×D13C2semidirect
5. #11718892C2semidirect
6. #11718883C2semidirect
7. #11718622C2semidirect
8. #11718618C2semidirect
9. #11718617C2semidirect
10. #11718617C2semidirect
11. #11718616C2semidirect
12. #11718613C2semidirect
13. #11718612C2semidirect
14. #11718601C2semidirect
15. C4×#6103C2semidirect
17. C22×Q8×C13C22semidirect
26. C2×C13×C22⋊C4C22semidirect
27. C2×C13×C22⋊C4C22semidirect
28. C2×C42×C13C22semidirect
32. C2×C22⋊Dic13C22semidirect
33. C2×C22⋊Dic13C22semidirect
44. C2×C4⋊Dic13C22semidirect
45. C2×#6101C22semidirect
46. C2×#6101C22semidirect
47. C2×C4×Dic13C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
53. #88071C22semidirect
54. #88071C22semidirect
98. C13×C22⋊C4D4semidirect
193. C2×#124D13semidirect
243. C2×D13#124semidirect
256. C22×Q8C2×D13semidirect
284. C2×C22⋊C4C2×D13semidirect
285. C2×C22⋊C4C2×D13semidirect
287. C2×C42C2×D13semidirect
364. C22⋊C4C22⋊D13semidirect
367. C13#2472semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1242
C2×#882002
C2×#881912
C2×C22⋊C4×D132
#117188922
#117188832
#117186222
#117186182
#117186172
#117186162
#117186132
#117186122
#117186012
C4×#61032
#247213