Finite Group Databasebeta

← #13131359

Subgroups — #13131359

Order 1664.

652 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#261C211yesmaximal, characteristic
2C2×#88237C211yesmaximal, characteristic, complemented
3D13×#123C211yesmaximal, characteristic
4#11719150C211yesmaximal, characteristic
5C2×(C2×#261)⋊C4C211yesmaximal, 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#11719070C211yesmaximal, characteristic, complemented
13#11719070C211yesmaximal, characteristic, complemented
14C22⋊C4×#261C211yesmaximal, characteristic, complemented
15C22⋊C4×#261C211yesmaximal, characteristic, complemented
16C23×#261C2211yescharacteristic
17C23×#261C2211yescharacteristic
18C23×#261C2211yescharacteristic
19C2×D4×D13C2211yescharacteristic
20C22×C4×D13C2211yescharacteristic
21C2×C22⋊#261C2211yescharacteristic
22C2×C22⋊#261C2211yescharacteristic
23C2×C22⋊#261C2211yescharacteristic
24C2×C22⋊#261C2211yescharacteristic
25C2×C22⋊#261C2211yescharacteristic
26D4×#261—24no—
27#88237—24no—
28C2×C4⋊#261C2211yescharacteristic
29C2×C4⋊#261C2211yescharacteristic
30C2×C4⋊#261C2211yescharacteristic
31C2×C4⋊#261C2211yescharacteristic
32C2×C4⋊#261C2211yescharacteristic
33C2×C4×#261C2211yescharacteristic
34C2×C4×#261C2211yescharacteristic
35C2×C4×#261C2211yescharacteristic
36C2×C4×#261C2211yescharacteristic
37C2×C4×#261C2211yescharacteristic
38C13×#123C411yescharacteristic, complemented
39#88189C411yescharacteristic, complemented
40#88183C411yescharacteristic, complemented
41#88148C411yescharacteristic, complemented
42#88148C411yescharacteristic, complemented
43C4⋊C4×D13C2211yescharacteristic
44C4⋊C4×D13C2211yescharacteristic
45#88140C411yescharacteristic, complemented
46#88137C411yescharacteristic, complemented
47#88137C411yescharacteristic, complemented
48C22⋊C4×D13C2211yescharacteristic
49C22⋊C4×D13C2211yescharacteristic
50C22⋊C4×D13C2211yescharacteristic
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
59(C2×#261)⋊C4C2211yescharacteristic
60(C2×#261)⋊C4C2211yescharacteristic
61C23×D13C2311yescharacteristic
62C23×D13C2311yescharacteristic
63C22×#261—22no—
64C22×#261—22no—
65C22×#261—22no—
66C22×#261—22no—
67C22×#261—22no—
68C22×#261—22no—
69C22×#261—41no—
70C22×#261—41no—
71C22×#261—41no—
72C22×#261C2311yescharacteristic
73C22×#261C2311yescharacteristic
74C22×#261C2311yescharacteristic
75C22×#261C2311yescharacteristic
76C22×#261C2311yescharacteristic
77C22×#261C2311yescharacteristic
78C22×#261C2311yescharacteristic
79C22×#261C2311yescharacteristic
80C2×D4×C13C2×C411yescharacteristic
81C22×C4×C13C2×C411yescharacteristic, complemented
82C2×C22⋊D13C2×C411yescharacteristic
83C2×C22⋊D13C2×C411yescharacteristic
84C22×Dic13C2×C411yescharacteristic, complemented
85D4×D13—22no—
86D4×D13—22no—
87C2×D52C2×C411yescharacteristic
88C2×C4×D13—22no—
89C2×C4×D13—22no—
90C2×C4×D13C2×C411yescharacteristic, complemented
91C2×C4×D13C2×C411yescharacteristic, complemented
92C2×C4×D13C2311yescharacteristic
93C2×C4×D13C2311yescharacteristic
94C2×C4×D13C2311yescharacteristic
95C2×C4×D13C2311yescharacteristic
96C2×C4×D13C2311yescharacteristic
97C22⋊#261—22no—
98C22⋊#261—22no—
99C22⋊#261—22no—
100C22⋊#261—41no—
101C22⋊#261D414yes—
102C4⋊#261—22no—
103C4⋊#261—22no—
104C4⋊#261—22no—
105C4⋊#261—22no—
106C4⋊#261—41no—
107C4×#261—22no—
108C4×#261—22no—
109C4×#261—22no—
110C4×#261—22no—
111C4×#261—41no—
112C13×C4⋊C4C2×C411yescharacteristic, complemented
113C13×C4⋊C4C2×C411yescharacteristic, complemented
114C13×C22⋊C4C2×C411yescharacteristic, complemented
115C13×C22⋊C4C2×C411yescharacteristic, complemented
116C13×C22⋊C4C2×C411yescharacteristic, complemented
117C22⋊Dic13C2×C411yescharacteristic, complemented
118C22⋊Dic13C2×C411yescharacteristic, complemented
119C22⋊Dic13C2×C411yescharacteristic, complemented
120#6103C2×C411yescharacteristic, complemented
121#6103C2×C411yescharacteristic, complemented
122#6103C2×C411yescharacteristic, complemented
123#6103C2×C411yescharacteristic, complemented
124#6103C2×C411yescharacteristic, complemented
125#6103C2×C411yescharacteristic, complemented
126C4⋊Dic13C2×C411yescharacteristic, complemented
127C4⋊Dic13C2×C411yescharacteristic, complemented
128#6101C2×C411yescharacteristic, complemented
129#6101C2×C411yescharacteristic, complemented
130#6101C2×C411yescharacteristic, complemented
131#6101C2×C411yescharacteristic, complemented
132#2359—131nomaximal, Sylow
133C23×C13C22×C411yescharacteristic
134C23×C13C22×C411yescharacteristic
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—21no—
145C22×D13C22×C411yescharacteristic
146C22×D13C22×C411yescharacteristic
147C22×D13C2×D412yes—
148C22×D13#4112yes—
149C22×D13C2411yescharacteristic
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—21no—
167C2×#261—21no—
168C2×#261—21no—
169C2×#261—21no—
170C2×#261—44no—
171C2×#261—44no—
172C2×#261—44no—
173C2×#261C2×D412yes—
174C2×#261C2×D412yes—
175C2×#261#4112yes—
176C2×#261#4112yes—
177D4×C13—22no—
178C2×C4×C13—22no—
179C2×C4×C13C22×C411yescharacteristic
180C2×C4×C13C22×C411yescharacteristic
181C2×C4×C13C22×C411yescharacteristic
182C2×C4×C13C22×C411yescharacteristic
183C2×C4×C13C22×C411yescharacteristic
184C22⋊D13—22no—
185C22⋊D13—22no—
186C2×Dic13—22no—
187C2×Dic13C22×C411yescharacteristic
188C2×Dic13C22×C411yescharacteristic
189C2×Dic13C22×C411yescharacteristic
190C2×Dic13C22×C411yescharacteristic
191C2×Dic13C22×C411yescharacteristic
192D52—22no—
193C4×D13—22no—
194C4×D13—22no—
195C4×D13—21no—
196C4×D13—21no—
197C4×D13—21no—
198C4×D13—21no—
199C4×D13—21no—
200C4×D13—21no—
201C4×D13—21no—
202C4×D13—21no—
203C4×D13—21no—
204C4×D13—21no—
205C2×#123—131no—
206C2×C4×D4—131no—
207C2×#117—131no—
208#389—131no—
209#388—131no—
210#388—131no—
211#387—131no—
212#387—131no—
213#386—131no—
214#385—131no—
215#385—131no—
216C4×C4⋊C4—131no—
217C4×C22⋊C4—131no—
218C4×C22⋊C4—131no—
219C2×#95—131no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13C4×D412yes—
226C22×C13C23×C411yescharacteristic
227C2×D13—21no—
228C2×D13—21no—
229C2×D13—22no—
230C2×D13—22no—
231C2×D13—22no—
232C2×D13—22no—
233C2×D13—21no—
234C2×D13—21no—
235C2×D13—21no—
236C2×D13—41no—
237C2×D13—41no—
238C2×D13—41no—
239C2×D13—41no—
240C2×D13C4×D412yes—
241C2×D13C22×D411yescharacteristic
242C2×D13C2×#4111yescharacteristic
243C2×D13C2×#4111yescharacteristic
244C2×D13C2×#4111yescharacteristic
245C2×D13H(5,𝔽2)11yescharacteristic
246C2×D132−1+411yescharacteristic
247#261—22no—
248#261—22no—
249#261—22no—
250#261—22no—
251#261—41no—
252#261—41no—
253#261—41no—
254#261—41no—
255C4×C13—21no—
256C4×C13—21no—
257C4×C13—21no—
258C4×C13—21no—
259C4×C13—21no—
260Dic13—21no—
261Dic13—21no—
262Dic13—21no—
263Dic13—21no—
264Dic13—21no—
265C22×D4—131no—
266C23×C4—131no—
267C23×C4—131no—
268C23×C4—131no—
269C23×C4—131no—
270#123—131no—
271#123—131no—
272#123—131no—
273#123—131no—
274#123—131no—
275#123—131no—
276#123—131no—
277#123#26111yescharacteristic, complemented
278C4×D4—264no—
279#117—264no—
280C2×C4⋊C4—131no—
281C2×C4⋊C4—131no—
282C2×C4⋊C4—131no—
283C2×C4⋊C4—131no—
284C2×C4⋊C4—131no—
285C2×C4⋊C4—131no—
286C2×C4⋊C4—131no—
287C2×C22⋊C4—131no—
288C2×C22⋊C4—131no—
289C2×C22⋊C4—131no—
290C2×C22⋊C4—131no—
291C2×C22⋊C4—131no—
292C2×C22⋊C4—131no—
293C2×C22⋊C4—131no—
294C2×C22⋊C4—131no—
295C2×C42—131no—
296C2×C42—131no—
297C2×C42—131no—
298C2×C42—131no—
299C2×C42—131no—
300#95—131no—
301#95—131no—
302#95—131no—
303#95—131no—
304#95—131no—
305#95—131no—
306#95—131no—
307#95—131no—
308#95—131no—
309#95—131no—
310C2×C13—22no—
311C2×C13—41no—
312C2×C13C2×C4×D411yescharacteristic
313C2×C13C4×#4111yescharacteristic
314C2×C13#52011yescharacteristic
315D13—22no—
316D13—41no—
317D13#54611yescharacteristic
318D13#54711yescharacteristic
319D13#55111yescharacteristic
320D13#55211yescharacteristic
321C24—131no—
322C24—131no—
323C2×D4—131no—
324C2×D4—131no—
325C2×D4—131no—
326C2×D4—262no—
327C2×D4—262no—
328C2×D4C2×#26111yescharacteristic
329C22×C4—131no—
330C22×C4—131no—
331C22×C4—131no—
332C22×C4—131no—
333C22×C4—131no—
334C22×C4—131no—
335C22×C4—131no—
336C22×C4—131no—
337C22×C4—131no—
338C22×C4—131no—
339C22×C4—131no—
340C22×C4—131no—
341C22×C4—131no—
342C22×C4—131no—
343C22×C4—131no—
344C22×C4—131no—
345C22×C4—262no—
346C22×C4—262no—
347C22×C4—262no—
348C22×C4—262no—
349C22×C4—262no—
350C22×C4—262no—
351C22×C4—262no—
352C22×C4—262no—
353C22×C4—521no—
354C22×C4—521no—
355C22×C4—521no—
356C22×C4C2×#26111yescharacteristic, complemented
357C4⋊C4—131no—
358C4⋊C4—131no—
359C4⋊C4—131no—
360C4⋊C4—131no—
361C4⋊C4—131no—
362C4⋊C4—131no—
363C4⋊C4—262no—
364C4⋊C4—262no—
365C4⋊C4—262no—
366C4⋊C4—262no—
367C4⋊C4—521no—
368C4⋊C4C2×#26111yescharacteristic, complemented
369C4⋊C4C2×#26111yescharacteristic, complemented
370C22⋊C4—134no—
371C22⋊C4—131no—
372C22⋊C4—131no—
373C22⋊C4—131no—
374C22⋊C4—131no—
375C22⋊C4—131no—
376C22⋊C4—131no—
377C22⋊C4—131no—
378C22⋊C4—131no—
379C22⋊C4—131no—
380C22⋊C4—262no—
381C22⋊C4—262no—
382C22⋊C4—262no—
383C22⋊C4—521no—
384C22⋊C4C2×#26111yescharacteristic, complemented
385C22⋊C4C2×#26111yescharacteristic, complemented
386C22⋊C4C2×#26111yescharacteristic, complemented
387C42—262no—
388C42—262no—
389C42—262no—
390C42—262no—
391C42—521no—
392C13#235911yescharacteristic, complemented, Sylow
393C23—131no—
394C23—132no—
395C23—132no—
396C23—131no—
397C23—131no—
398C23—261no—
399C23—261no—
400C23—261no—
401C23—261no—
402C23—261no—
403C23—261no—
404C23—261no—
405C23—261no—
406C23—261no—
407C23—261no—
408C23C22×#26111yescharacteristic
409C23C22×#26111yescharacteristic
410D4—22no—
411D4—262no—
412D4—262no—
413D4—262no—
414C2×C4—22no—
415C2×C4—132no—
416C2×C4—132no—
417C2×C4—132no—
418C2×C4—132no—
419C2×C4—131no—
420C2×C4—131no—
421C2×C4—131no—
422C2×C4—131no—
423C2×C4—131no—
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—262no—
434C2×C4—262no—
435C2×C4—261no—
436C2×C4—261no—
437C2×C4—261no—
438C2×C4—261no—
439C2×C4—261no—
440C2×C4—261no—
441C2×C4—261no—
442C2×C4—261no—
443C2×C4—261no—
444C2×C4—262no—
445C2×C4—261no—
446C2×C4—261no—
447C2×C4—261no—
448C2×C4—261no—
449C2×C4—261no—
450C2×C4—261no—
451C2×C4—261no—
452C2×C4—261no—
453C2×C4—261no—
454C2×C4—261no—
455C2×C4—261no—
456C2×C4—261no—
457C2×C4—524no—
458C2×C4—524no—
459C2×C4—524no—
460C2×C4C22×#26111yescharacteristic
461C2×C4C22×#26111yescharacteristic
462C2×C4C22×#26111yescharacteristic
463C2×C4C22×#26111yescharacteristic
464C2×C4C22×#26111yescharacteristic
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—131no—
471C22—131no—
472C22—131no—
473C22—131no—
474C22—131no—
475C22—131no—
476C22—132no—
477C22—262no—
478C22—262no—
479C22—262no—
480C22—262no—
481C22—261no—
482C22—261no—
483C22—261no—
484C22—261no—
485C22—261no—
486C22—521no—
487C22—521no—
488C22—521no—
489C22—521no—
490C22D4×#26112yes—
491C22C23×#26111yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—262no—
498C4—262no—
499C4—262no—
500C4—262no—
501C4—261no—
502C4—261no—
503C4—261no—
504C4—261no—
505C4—261no—
506C4—521no—
507C4—521no—
508C4—521no—
509C4—521no—
510C2—22no—
511C2—41no—
512C2—131no—
513C2—131no—
514C2—131no—
515C2—131no—
516C2—262no—
517C2—521no—
518C2C2×D4×#26111yescharacteristic
519C2#41×#26111yescharacteristic
520C2#1171963111yescharacteristic
subgroupG/H
center, FrattiniC22C23×#261
commutator, socleC22×C13C23×C4
FittingC13×#123C4
prime radicalC2×D4×D13C22
cosocleC22×D13C24
hypercenter#123#261
hypocenterC13#2359
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
2. C2×#88237C2semidirect
5. C2×(C2×#261)⋊C4C2semidirect
6. #11719083C2semidirect
7. #11719082C2semidirect
8. #11719082C2semidirect
9. C4⋊C4×#261C2semidirect
10. #11719071C2semidirect
11. #11719071C2semidirect
12. #11719070C2semidirect
13. #11719070C2semidirect
14. C22⋊C4×#261C2semidirect
15. C22⋊C4×#261C2semidirect
38. C13×#123C4semidirect
39. #88189C4semidirect
40. #88183C4semidirect
41. #88148C4semidirect
42. #88148C4semidirect
45. #88140C4semidirect
46. #88137C4semidirect
47. #88137C4semidirect
81. C22×C4×C13C2×C4semidirect
84. C22×Dic13C2×C4semidirect
90. C2×C4×D13C2×C4semidirect
91. C2×C4×D13C2×C4semidirect
112. C13×C4⋊C4C2×C4semidirect
113. C13×C4⋊C4C2×C4semidirect
114. C13×C22⋊C4C2×C4semidirect
115. C13×C22⋊C4C2×C4semidirect
116. C13×C22⋊C4C2×C4semidirect
117. C22⋊Dic13C2×C4semidirect
118. C22⋊Dic13C2×C4semidirect
119. C22⋊Dic13C2×C4semidirect
120. #6103C2×C4semidirect
121. #6103C2×C4semidirect
122. #6103C2×C4semidirect
123. #6103C2×C4semidirect
124. #6103C2×C4semidirect
125. #6103C2×C4semidirect
126. C4⋊Dic13C2×C4semidirect
127. C4⋊Dic13C2×C4semidirect
128. #6101C2×C4semidirect
129. #6101C2×C4semidirect
130. #6101C2×C4semidirect
131. #6101C2×C4semidirect
277. #123#261semidirect
356. C22×C4C2×#261semidirect
368. C4⋊C4C2×#261semidirect
369. C4⋊C4C2×#261semidirect
384. C22⋊C4C2×#261semidirect
385. C22⋊C4C2×#261semidirect
386. C22⋊C4C2×#261semidirect
392. C13#2359semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#2612
C2×#882372
D13×#1232
#117191502
C2×(C2×#261)⋊C42
#117190832
#117190822
C4⋊C4×#2612
#117190712
#117190702
C22⋊C4×#2612
#235913