Finite Group Databasebeta

← #13131335

Subgroups — #13131335

Order 1664.

532 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×#123C211yesmaximal, characteristic
2#11719151C211yesmaximal, characteristic
3#11719150C211yesmaximal, characteristic
4#11719136C211yesmaximal, characteristic, complemented
5C4×C22⋊#261C211yesmaximal, characteristic, complemented
6#11719083C211yesmaximal, characteristic, complemented
7#11719082C211yesmaximal, characteristic, complemented
8#11719082C211yesmaximal, characteristic, complemented
9C4⋊C4×#261C211yesmaximal, characteristic, complemented
10#11719071C211yesmaximal, characteristic, complemented
11#11719071C211yesmaximal, characteristic, complemented
12#11719071C211yesmaximal, characteristic, complemented
13#11719071C211yesmaximal, characteristic, complemented
14#11719070C211yesmaximal, characteristic, complemented
15C22⋊C4×#261C211yesmaximal, characteristic, complemented
16C23×#261C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C2×C22⋊#261C2211yescharacteristic
20C2×C22⋊#261C2211yescharacteristic
21C2×C22⋊#261C2211yescharacteristic
22C2×C22⋊#261C2211yescharacteristic
23C2×C22⋊#261C2211yescharacteristic
24C2×C22⋊#261C2211yescharacteristic
25C2×C22⋊#261C2211yescharacteristic
26C2×C4⋊#261C2211yescharacteristic
27C2×C4⋊#261C2211yescharacteristic
28C2×C4⋊#261C2211yescharacteristic
29C2×C4⋊#261C2211yescharacteristic
30C2×C4⋊#261C2211yescharacteristic
31C2×C4×#261C2211yescharacteristic
32C2×C4×#261C2211yescharacteristic
33C2×C4×#261C2211yescharacteristic
34C2×C4×#261C2211yescharacteristic
35C2×C4×#261C2211yescharacteristic
36C13×#123C411yescharacteristic, complemented
37#88189C411yescharacteristic, complemented
38#88183C411yescharacteristic, complemented
39#88148C411yescharacteristic, complemented
40#88148C411yescharacteristic, complemented
41C4⋊C4×D13C2211yescharacteristic
42C4⋊C4×D13C2211yescharacteristic
43#88140C411yescharacteristic, complemented
44#88137C411yescharacteristic, complemented
45#88137C411yescharacteristic, complemented
46C22⋊C4×D13C2211yescharacteristic
47C22⋊C4×D13C2211yescharacteristic
48C22⋊C4×D13C2211yescharacteristic
49(C2×#261)⋊C4C2211yescharacteristic
50(C2×#261)⋊C4C2211yescharacteristic
51(C2×#261)⋊C4C2211yescharacteristic
52(C2×#261)⋊C4C2211yescharacteristic
53(C2×#261)⋊C4C2211yescharacteristic
54(C2×#261)⋊C4C2211yescharacteristic
55(C2×#261)⋊C4C2211yescharacteristic
56(C2×#261)⋊C4C2211yescharacteristic
57(C2×#261)⋊C4C2211yescharacteristic
58(C2×#261)⋊C4C2211yescharacteristic
59C23×D13C2311yescharacteristic
60C23×D13C2311yescharacteristic
61C22×#261—22no—
62C22×#261—41no—
63C22×#261—41no—
64C22×#261C2311yescharacteristic
65C22×#261C2311yescharacteristic
66C22×#261C2311yescharacteristic
67C22×#261C2311yescharacteristic
68C22×#261C2311yescharacteristic
69C22×#261C2311yescharacteristic
70C22×#261C2311yescharacteristic
71C22×#261C2311yescharacteristic
72C2×D4×C13C2×C411yescharacteristic
73C22×C4×C13C2×C411yescharacteristic, complemented
74C2×C22⋊D13C2×C411yescharacteristic
75C2×C22⋊D13C2×C411yescharacteristic
76C22×Dic13C2×C411yescharacteristic, complemented
77D4×D13—41no—
78D4×D13—41no—
79C2×D52C2×C411yescharacteristic
80C2×C4×D13—41no—
81C2×C4×D13—41no—
82C2×C4×D13C2×C411yescharacteristic, complemented
83C2×C4×D13C2×C411yescharacteristic, complemented
84C2×C4×D13C2311yescharacteristic
85C2×C4×D13C2311yescharacteristic
86C2×C4×D13C2311yescharacteristic
87C2×C4×D13C2311yescharacteristic
88C2×C4×D13C2311yescharacteristic
89C22⋊#261—22no—
90C22⋊#261—22no—
91C22⋊#261—22no—
92C22⋊#261—41no—
93C22⋊#261—41no—
94C22⋊#261—41no—
95C22⋊#261—41no—
96C4⋊#261—22no—
97C4⋊#261—41no—
98C4⋊#261—41no—
99C4⋊#261—41no—
100C4⋊#261—41no—
101C4×#261—22no—
102C4×#261—41no—
103C4×#261—41no—
104C4×#261—41no—
105C4×#261—41no—
106C13×C4⋊C4C2×C411yescharacteristic, complemented
107C13×C4⋊C4C2×C411yescharacteristic, complemented
108C13×C22⋊C4C2×C411yescharacteristic
109C13×C22⋊C4C2×C411yescharacteristic
110C13×C22⋊C4C2×C411yescharacteristic, complemented
111C22⋊Dic13C2×C411yescharacteristic
112C22⋊Dic13C2×C411yescharacteristic
113C22⋊Dic13C2×C411yescharacteristic, complemented
114#6103C2×C411yescharacteristic
115#6103C2×C411yescharacteristic
116#6103C2×C411yescharacteristic
117#6103C2×C411yescharacteristic
118#6103C2×C411yescharacteristic, complemented
119#6103C2×C411yescharacteristic, complemented
120C4⋊Dic13C2×C411yescharacteristic, complemented
121C4⋊Dic13C2×C411yescharacteristic, complemented
122#6101C2×C411yescharacteristic, complemented
123#6101C2×C411yescharacteristic, complemented
124#6101C2×C411yescharacteristic, complemented
125#6101C2×C411yescharacteristic, complemented
126#2335—131nomaximal, Sylow
127C23×C13C22×C411yescharacteristic
128C23×C13C22×C411yescharacteristic
129C22×D13—21no—
130C22×D13—21no—
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×D13C22×C411yescharacteristic
142C22×D13C22×C411yescharacteristic
143C22×D13C2411yescharacteristic
144C2×#261—21no—
145C2×#261—21no—
146C2×#261—21no—
147C2×#261—21no—
148C2×#261—21no—
149C2×#261—21no—
150C2×#261—21no—
151C2×#261—21no—
152C2×#261—21no—
153C2×#261—21no—
154C2×#261—21no—
155C2×#261—21no—
156C2×#261—21no—
157C2×#261—21no—
158C2×#261—21no—
159C2×#261—21no—
160C2×#261—21no—
161C2×#261—21no—
162C2×#261—21no—
163C2×#261—21no—
164C2×#261—21no—
165C2×#261—21no—
166C2×#261—44no—
167C2×#261#4112yes—
168C2×#261#4112yes—
169D4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13C22×C411yescharacteristic
172C2×C4×C13C22×C411yescharacteristic
173C2×C4×C13C22×C411yescharacteristic
174C2×C4×C13C22×C411yescharacteristic
175C2×C4×C13C22×C411yescharacteristic
176C22⋊D13—41no—
177C22⋊D13—41no—
178C2×Dic13—41no—
179C2×Dic13C22×C411yescharacteristic
180C2×Dic13C22×C411yescharacteristic
181C2×Dic13C22×C411yescharacteristic
182C2×Dic13C22×C411yescharacteristic
183C2×Dic13C22×C411yescharacteristic
184D52—41no—
185C4×D13—21no—
186C4×D13—21no—
187C4×D13—21no—
188C4×D13—21no—
189C4×D13—21no—
190C4×D13—21no—
191C4×D13—21no—
192C4×D13—21no—
193C4×D13—21no—
194C4×D13—21no—
195C4×D13—41no—
196C4×D13—41no—
197C2×#123—131no—
198#390—131no—
199#389—131no—
200#388—131no—
201#388—131no—
202#388—131no—
203#388—131no—
204#387—131no—
205#387—131no—
206#386—131no—
207#385—131no—
208#380—131no—
209C4×C4⋊C4—131no—
210C4×C22⋊C4—131no—
211C4×C22⋊C4—131no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13C23×C411yescharacteristic
219C2×D13—21no—
220C2×D13—21no—
221C2×D13—21no—
222C2×D13—21no—
223C2×D13—21no—
224C2×D13—21no—
225C2×D13—41no—
226C2×D13—41no—
227C2×D13—41no—
228C2×D13—41no—
229C2×D13—41no—
230C2×D13—41no—
231C2×D13—41no—
232C2×D13—41no—
233C2×D13C2×#4111yescharacteristic
234C2×D13C2×#4111yescharacteristic
235C2×D13H(5,𝔽2)11yescharacteristic
236C2×D13H(5,𝔽2)11yescharacteristic
237C2×D13H(5,𝔽2)11yescharacteristic
238C2×D132−1+411yescharacteristic
239#261—22no—
240#261—22no—
241#261—41no—
242#261—41no—
243#261—41no—
244#261—41no—
245#261—41no—
246#261—41no—
247C4×C13—21no—
248C4×C13—21no—
249C4×C13—21no—
250C4×C13—21no—
251C4×C13—21no—
252Dic13—21no—
253Dic13—21no—
254Dic13—21no—
255Dic13—21no—
256Dic13—21no—
257C22×D4—131no—
258C23×C4—131no—
259C23×C4—131no—
260#123—131no—
261#123—131no—
262#123—131no—
263#123—131no—
264#123—131no—
265#123—131no—
266#123—131no—
267#123#26111yescharacteristic, complemented
268C2×C4⋊C4—131no—
269C2×C4⋊C4—131no—
270C2×C4⋊C4—131no—
271C2×C4⋊C4—131no—
272C2×C4⋊C4—131no—
273C2×C4⋊C4—131no—
274C2×C4⋊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—131no—
284C2×C22⋊C4—131no—
285C2×C42—131no—
286C2×C42—131no—
287C2×C42—131no—
288C2×C42—131no—
289C2×C42—131no—
290#95—131no—
291#95—131no—
292#95—131no—
293#95—131no—
294#95—131no—
295#95—131no—
296#95—131no—
297#95—131no—
298#95—131no—
299#95—131no—
300C2×C13—41no—
301C2×C13—41no—
302C2×C13C4×#4111yescharacteristic
303C2×C13#51811yescharacteristic
304C2×C13#52011yescharacteristic
305D13—41no—
306D13—41no—
307D13#53811yescharacteristic
308D13#53911yescharacteristic
309D13#54011yescharacteristic
310D13#54211yescharacteristic
311C24—131no—
312C24—131no—
313C2×D4—131no—
314C2×D4—131no—
315C2×D4—131no—
316C2×D4—521no—
317C2×D4—521no—
318C2×D4C2×#26111yescharacteristic
319C22×C4—131no—
320C22×C4—131no—
321C22×C4—131no—
322C22×C4—131no—
323C22×C4—131no—
324C22×C4—131no—
325C22×C4—131no—
326C22×C4—131no—
327C22×C4—131no—
328C22×C4—131no—
329C22×C4—131no—
330C22×C4—131no—
331C22×C4—131no—
332C22×C4—131no—
333C22×C4—131no—
334C22×C4—131no—
335C22×C4—262no—
336C22×C4—521no—
337C22×C4—521no—
338C22×C4—521no—
339C22×C4—521no—
340C22×C4C2×#26111yescharacteristic, complemented
341C4⋊C4—131no—
342C4⋊C4—131no—
343C4⋊C4—131no—
344C4⋊C4—131no—
345C4⋊C4—131no—
346C4⋊C4—131no—
347C4⋊C4—262no—
348C4⋊C4—521no—
349C4⋊C4—521no—
350C4⋊C4—521no—
351C4⋊C4—521no—
352C4⋊C4C2×#26111yescharacteristic, complemented
353C4⋊C4C2×#26111yescharacteristic, complemented
354C22⋊C4—131no—
355C22⋊C4—131no—
356C22⋊C4—131no—
357C22⋊C4—131no—
358C22⋊C4—131no—
359C22⋊C4—131no—
360C22⋊C4—131no—
361C22⋊C4—131no—
362C22⋊C4—131no—
363C22⋊C4—262no—
364C22⋊C4—262no—
365C22⋊C4—262no—
366C22⋊C4—521no—
367C22⋊C4—521no—
368C22⋊C4—521no—
369C22⋊C4—521no—
370C22⋊C4C2×#26111yescharacteristic
371C22⋊C4C2×#26111yescharacteristic
372C22⋊C4C2×#26111yescharacteristic, complemented
373C42—262no—
374C42—521no—
375C42—521no—
376C42—521no—
377C42—521no—
378C13#233511yescharacteristic, complemented, Sylow
379C23—131no—
380C23—131no—
381C23—131no—
382C23—261no—
383C23—261no—
384C23—261no—
385C23—261no—
386C23—261no—
387C23—261no—
388C23—261no—
389C23—261no—
390C23—261no—
391C23—261no—
392C23—261no—
393C23—261no—
394C23C22×#26111yescharacteristic
395C23C22×#26111yescharacteristic
396D4—41no—
397D4—521no—
398D4—521no—
399D4—521no—
400C2×C4—41no—
401C2×C4—132no—
402C2×C4—132no—
403C2×C4—131no—
404C2×C4—131no—
405C2×C4—131no—
406C2×C4—131no—
407C2×C4—131no—
408C2×C4—261no—
409C2×C4—261no—
410C2×C4—261no—
411C2×C4—261no—
412C2×C4—261no—
413C2×C4—261no—
414C2×C4—261no—
415C2×C4—261no—
416C2×C4—261no—
417C2×C4—261no—
418C2×C4—261no—
419C2×C4—261no—
420C2×C4—261no—
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—261no—
439C2×C4—261no—
440C2×C4—521no—
441C2×C4—521no—
442C2×C4—521no—
443C2×C4—524no—
444C2×C4C22×#26111yescharacteristic
445C2×C4C22×#26111yescharacteristic
446C2×C4C22×#26111yescharacteristic
447C2×C4C22×#26111yescharacteristic
448C2×C4C22×#26111yescharacteristic
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—131no—
456C22—131no—
457C22—131no—
458C22—131no—
459C22—131no—
460C22—131no—
461C22—261no—
462C22—261no—
463C22—261no—
464C22—261no—
465C22—261no—
466C22—261no—
467C22—521no—
468C22—521no—
469C22—521no—
470C22—521no—
471C22—521no—
472C22—521no—
473C22—521no—
474C22—521no—
475C22C23×#26111yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—262no—
482C4—262no—
483C4—261no—
484C4—261no—
485C4—261no—
486C4—261no—
487C4—261no—
488C4—521no—
489C4—521no—
490C4—521no—
491C4—521no—
492C4—521no—
493C4—521no—
494C2—41no—
495C2—41no—
496C2—131no—
497C2—131no—
498C2—131no—
499C2—131no—
500C2—521no—
501C2—521no—
502C2#1171962311yescharacteristic
503C2#41×#26111yescharacteristic
504C2#1171963111yescharacteristic
subgroupG/H
center, FrattiniC22C23×#261
commutator, socleC22×C13C23×C4
FittingC13×#123C4
prime radicalC2×D4×D13C22
cosocleC22×D13C24
hypercenter#123#261
hypocenterC13#2335
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
4. #11719136C2semidirect
5. C4×C22⋊#261C2semidirect
6. #11719083C2semidirect
7. #11719082C2semidirect
8. #11719082C2semidirect
9. C4⋊C4×#261C2semidirect
10. #11719071C2semidirect
11. #11719071C2semidirect
12. #11719071C2semidirect
13. #11719071C2semidirect
14. #11719070C2semidirect
15. C22⋊C4×#261C2semidirect
36. C13×#123C4semidirect
37. #88189C4semidirect
38. #88183C4semidirect
39. #88148C4semidirect
40. #88148C4semidirect
43. #88140C4semidirect
44. #88137C4semidirect
45. #88137C4semidirect
73. C22×C4×C13C2×C4semidirect
76. C22×Dic13C2×C4semidirect
82. C2×C4×D13C2×C4semidirect
83. C2×C4×D13C2×C4semidirect
106. C13×C4⋊C4C2×C4semidirect
107. C13×C4⋊C4C2×C4semidirect
110. C13×C22⋊C4C2×C4semidirect
113. C22⋊Dic13C2×C4semidirect
118. #6103C2×C4semidirect
119. #6103C2×C4semidirect
120. C4⋊Dic13C2×C4semidirect
121. C4⋊Dic13C2×C4semidirect
122. #6101C2×C4semidirect
123. #6101C2×C4semidirect
124. #6101C2×C4semidirect
125. #6101C2×C4semidirect
267. #123#261semidirect
340. C22×C4C2×#261semidirect
352. C4⋊C4C2×#261semidirect
353. C4⋊C4C2×#261semidirect
372. C22⋊C4C2×#261semidirect
378. C13#2335semidirect

Maximal subgroups

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

subgroupindex
D13×#1232
#117191512
#117191502
#117191362
C4×C22⋊#2612
#117190832
#117190822
C4⋊C4×#2612
#117190712
#117190702
C22⋊C4×#2612
#233513