Finite Group Databasebeta

← #13131334

Subgroups — #13131334

Order 1664.

476 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×#126C211yesmaximal, characteristic
2#11719083C211yesmaximal, characteristic, complemented
3#11719083C211yesmaximal, characteristic, complemented
4#11719082C211yesmaximal, characteristic, complemented
5#11719082C211yesmaximal, characteristic, complemented
6#11719082C211yesmaximal, characteristic, complemented
7C4⋊C4×#261C211yesmaximal, characteristic, complemented
8#11719071C211yesmaximal, characteristic
9#11719071C211yesmaximal, characteristic
10#11719071C211yesmaximal, characteristic
11#11719070C211yesmaximal, characteristic
12#11719070C211yesmaximal, characteristic
13C22⋊C4×#261C211yesmaximal, characteristic
14#11719060C211yesmaximal, characteristic, complemented
15C4×C4⋊#261C211yesmaximal, characteristic, complemented
16C23×#261C2211yescharacteristic
17C2×C22⋊#261C2211yescharacteristic
18C2×C22⋊#261C2211yescharacteristic
19C2×C22⋊#261C2211yescharacteristic
20C2×C4⋊#261C2211yescharacteristic
21C2×C4⋊#261C2211yescharacteristic
22C2×C4⋊#261C2211yescharacteristic
23C2×C4⋊#261C2211yescharacteristic
24C2×C4⋊#261C2211yescharacteristic
25C2×C4⋊#261C2211yescharacteristic
26C2×C4⋊#261C2211yescharacteristic
27C2×C4×#261C2211yescharacteristic
28C2×C4×#261C2211yescharacteristic
29C2×C4×#261C2211yescharacteristic
30C2×C4×#261C2211yescharacteristic
31C2×C4×#261C2211yescharacteristic
32C13×#126C411yescharacteristic, complemented
33#88152C411yescharacteristic, complemented
34#88152C411yescharacteristic, complemented
35#88152C411yescharacteristic, complemented
36C4⋊C4×D13C2211yescharacteristic
37C4⋊C4×D13C2211yescharacteristic
38C4⋊C4×D13C2211yescharacteristic
39C22⋊C4×D13C2211yescharacteristic
40C22⋊C4×D13C2211yescharacteristic
41C22⋊C4×D13C2211yescharacteristic
42#88133C411yescharacteristic, complemented
43#88133C411yescharacteristic, complemented
44#88133C411yescharacteristic, complemented
45#88130C411yescharacteristic, complemented
46C42×D13C2211yescharacteristic
47(C2×#261)⋊C4C2211yescharacteristic
48(C2×#261)⋊C4C2211yescharacteristic
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
60C22×#261—22no—
61C22×#261—41no—
62C22×#261—41no—
63C22×#261C2311yescharacteristic
64C22×#261C2311yescharacteristic
65C22×#261C2311yescharacteristic
66C22×#261C2311yescharacteristic
67C22×#261C2311yescharacteristic
68C22×#261C2311yescharacteristic
69C22×#261C2311yescharacteristic
70C22×#261C2311yescharacteristic
71C2×C4×D13C2311yescharacteristic
72C2×C4×D13C2311yescharacteristic
73C2×C4×D13C2311yescharacteristic
74C2×C4×D13C2311yescharacteristic
75C2×C4×D13C2311yescharacteristic
76C2×C4×D13C2311yescharacteristic
77C22⋊#261—22no—
78C22⋊#261—41no—
79C22⋊#261—41no—
80C4⋊#261—22no—
81C4⋊#261—22no—
82C4⋊#261—22no—
83C4⋊#261—41no—
84C4⋊#261—41no—
85C4⋊#261—41no—
86C4⋊#261—41no—
87C4×#261—22no—
88C4×#261—41no—
89C4×#261—41no—
90C4×#261—41no—
91C4×#261—41no—
92C13×C4⋊C4C2×C411yescharacteristic, complemented
93C13×C4⋊C4C2×C411yescharacteristic, complemented
94C13×C4⋊C4C2×C411yescharacteristic, complemented
95C13×C22⋊C4C2×C411yescharacteristic
96C13×C22⋊C4C2×C411yescharacteristic
97C13×C22⋊C4C2×C411yescharacteristic
98C42×C13C2×C411yescharacteristic, complemented
99C22⋊Dic13C2×C411yescharacteristic
100C22⋊Dic13C2×C411yescharacteristic
101C22⋊Dic13C2×C411yescharacteristic
102#6103C2×C411yescharacteristic
103#6103C2×C411yescharacteristic
104#6103C2×C411yescharacteristic
105#6103C2×C411yescharacteristic
106#6103C2×C411yescharacteristic
107#6103C2×C411yescharacteristic
108C4⋊Dic13C2×C411yescharacteristic, complemented
109C4⋊Dic13C2×C411yescharacteristic, complemented
110C4⋊Dic13C2×C411yescharacteristic, complemented
111#6101C2×C411yescharacteristic, complemented
112#6101C2×C411yescharacteristic, complemented
113#6101C2×C411yescharacteristic, complemented
114#6101C2×C411yescharacteristic, complemented
115#6101C2×C411yescharacteristic, complemented
116#6101C2×C411yescharacteristic, complemented
117C4×Dic13C2×C411yescharacteristic, complemented
118C4×Dic13C2×C411yescharacteristic, complemented
119C4×Dic13C2×C411yescharacteristic, complemented
120#2334—131nomaximal, Sylow
121C23×C13C22×C411yescharacteristic
122C22×D13—21no—
123C22×D13—21no—
124C22×D13—21no—
125C22×D13—21no—
126C22×D13—21no—
127C22×D13—21no—
128C22×D13C22×C411yescharacteristic
129C22×D13C2411yescharacteristic
130C2×#261—21no—
131C2×#261—21no—
132C2×#261—21no—
133C2×#261—21no—
134C2×#261—21no—
135C2×#261—21no—
136C2×#261—21no—
137C2×#261—21no—
138C2×#261—21no—
139C2×#261—21no—
140C2×#261—21no—
141C2×#261—21no—
142C2×#261—21no—
143C2×#261—21no—
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—44no—
153C2×#261#4112yes—
154C2×#261#4112yes—
155C2×C4×C13C22×C411yescharacteristic
156C2×C4×C13C22×C411yescharacteristic
157C2×C4×C13C22×C411yescharacteristic
158C2×C4×C13C22×C411yescharacteristic
159C2×C4×C13C22×C411yescharacteristic
160C2×C4×C13C22×C411yescharacteristic
161C2×Dic13C22×C411yescharacteristic
162C2×Dic13C22×C411yescharacteristic
163C2×Dic13C22×C411yescharacteristic
164C2×Dic13C22×C411yescharacteristic
165C2×Dic13C22×C411yescharacteristic
166C2×Dic13C22×C411yescharacteristic
167C4×D13—21no—
168C4×D13—21no—
169C4×D13—21no—
170C4×D13—21no—
171C4×D13—21no—
172C4×D13—21no—
173C4×D13—21no—
174C4×D13—21no—
175C4×D13—21no—
176C4×D13—21no—
177C4×D13—21no—
178C4×D13—21no—
179C2×#126—131no—
180#389—131no—
181#389—131no—
182#388—131no—
183#388—131no—
184#388—131no—
185#387—131no—
186#387—131no—
187#387—131no—
188#385—131no—
189#385—131no—
190#382—131no—
191C4×C4⋊C4—131no—
192C4×C4⋊C4—131no—
193C4×C22⋊C4—131no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13C23×C411yescharacteristic
198C2×D13—21no—
199C2×D13—21no—
200C2×D13—21no—
201C2×D13—41no—
202C2×D13—41no—
203C2×D13—41no—
204C2×D13—41no—
205C2×D13C2×#4111yescharacteristic
206C2×D13C2×#4111yescharacteristic
207C2×D13H(5,𝔽2)11yescharacteristic
208C2×D13H(5,𝔽2)11yescharacteristic
209C2×D132−1+411yescharacteristic
210C2×D132−1+411yescharacteristic
211#261—22no—
212#261—22no—
213#261—41no—
214#261—41no—
215#261—41no—
216#261—41no—
217#261—41no—
218#261—41no—
219C4×C13—21no—
220C4×C13—21no—
221C4×C13—21no—
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—21no—
225Dic13—21no—
226Dic13—21no—
227Dic13—21no—
228Dic13—21no—
229Dic13—21no—
230Dic13—21no—
231C23×C4—131no—
232#126—131no—
233#126—131no—
234#126—131no—
235#126—131no—
236#126—131no—
237#126—131no—
238#126—131no—
239#126#26111yescharacteristic, complemented
240C2×C4⋊C4—131no—
241C2×C4⋊C4—131no—
242C2×C4⋊C4—131no—
243C2×C4⋊C4—131no—
244C2×C4⋊C4—131no—
245C2×C4⋊C4—131no—
246C2×C4⋊C4—131no—
247C2×C4⋊C4—131no—
248C2×C4⋊C4—131no—
249C2×C4⋊C4—131no—
250C2×C22⋊C4—131no—
251C2×C22⋊C4—131no—
252C2×C22⋊C4—131no—
253C2×C22⋊C4—131no—
254C2×C22⋊C4—131no—
255C2×C22⋊C4—131no—
256C2×C42—131no—
257C2×C42—131no—
258C2×C42—131no—
259C2×C42—131no—
260C2×C42—131no—
261C2×C42—131no—
262#95—131no—
263#95—131no—
264#95—131no—
265#95—131no—
266#95—131no—
267#95—131no—
268#95—131no—
269#95—131no—
270#95—131no—
271#95—131no—
272#95—131no—
273#95—131no—
274C2×C13—41no—
275C2×C13C4×#4111yescharacteristic
276C2×C13#52011yescharacteristic
277C2×C13#52011yescharacteristic
278D13—41no—
279D13#53811yescharacteristic
280D13#53911yescharacteristic
281D13#54111yescharacteristic
282D13#54211yescharacteristic
283C24—131no—
284C22×C4—131no—
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—131no—
288C22×C4—131no—
289C22×C4—131no—
290C22×C4—131no—
291C22×C4—131no—
292C22×C4—131no—
293C22×C4—131no—
294C22×C4—131no—
295C22×C4—131no—
296C22×C4—131no—
297C22×C4—131no—
298C22×C4—262no—
299C22×C4—521no—
300C22×C4—521no—
301C4⋊C4—131no—
302C4⋊C4—131no—
303C4⋊C4—131no—
304C4⋊C4—131no—
305C4⋊C4—131no—
306C4⋊C4—131no—
307C4⋊C4—131no—
308C4⋊C4—131no—
309C4⋊C4—131no—
310C4⋊C4—262no—
311C4⋊C4—262no—
312C4⋊C4—262no—
313C4⋊C4—521no—
314C4⋊C4—521no—
315C4⋊C4—521no—
316C4⋊C4—521no—
317C4⋊C4C2×#26111yescharacteristic, complemented
318C4⋊C4C2×#26111yescharacteristic, complemented
319C4⋊C4C2×#26111yescharacteristic, complemented
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—262no—
330C22⋊C4—521no—
331C22⋊C4—521no—
332C22⋊C4C2×#26111yescharacteristic
333C22⋊C4C2×#26111yescharacteristic
334C22⋊C4C2×#26111yescharacteristic
335C42—131no—
336C42—131no—
337C42—131no—
338C42—262no—
339C42—521no—
340C42—521no—
341C42—521no—
342C42—521no—
343C42C2×#26111yescharacteristic, complemented
344C13#233411yescharacteristic, complemented, Sylow
345C23—131no—
346C23—131no—
347C23—261no—
348C23—261no—
349C23—261no—
350C23—261no—
351C23—261no—
352C23—261no—
353C23C22×#26111yescharacteristic
354C2×C4—132no—
355C2×C4—132no—
356C2×C4—131no—
357C2×C4—131no—
358C2×C4—131no—
359C2×C4—131no—
360C2×C4—131no—
361C2×C4—131no—
362C2×C4—261no—
363C2×C4—261no—
364C2×C4—261no—
365C2×C4—261no—
366C2×C4—261no—
367C2×C4—261no—
368C2×C4—261no—
369C2×C4—261no—
370C2×C4—261no—
371C2×C4—261no—
372C2×C4—261no—
373C2×C4—261no—
374C2×C4—261no—
375C2×C4—261no—
376C2×C4—261no—
377C2×C4—261no—
378C2×C4—261no—
379C2×C4—261no—
380C2×C4—261no—
381C2×C4—261no—
382C2×C4—261no—
383C2×C4—261no—
384C2×C4—261no—
385C2×C4—261no—
386C2×C4—261no—
387C2×C4—261no—
388C2×C4—261no—
389C2×C4—261no—
390C2×C4—261no—
391C2×C4—261no—
392C2×C4—261no—
393C2×C4—261no—
394C2×C4—261no—
395C2×C4—261no—
396C2×C4—524no—
397C2×C4C22×#26111yescharacteristic
398C2×C4C22×#26111yescharacteristic
399C2×C4C22×#26111yescharacteristic
400C2×C4C22×#26111yescharacteristic
401C2×C4C22×#26111yescharacteristic
402C2×C4C22×#26111yescharacteristic
403C22—21no—
404C22—21no—
405C22—21no—
406C22—131no—
407C22—131no—
408C22—131no—
409C22—131no—
410C22—131no—
411C22—131no—
412C22—261no—
413C22—261no—
414C22—261no—
415C22—521no—
416C22—521no—
417C22—521no—
418C22—521no—
419C22C23×#26111yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—262no—
427C4—262no—
428C4—261no—
429C4—261no—
430C4—261no—
431C4—261no—
432C4—261no—
433C4—261no—
434C4—521no—
435C4—521no—
436C4—521no—
437C4—521no—
438C4—521no—
439C4—521no—
440C2—41no—
441C2—131no—
442C2—131no—
443C2—131no—
444C2—131no—
445C2—521no—
446C2#41×#26111yescharacteristic
447C2#1171963111yescharacteristic
448C2#1171963111yescharacteristic
subgroupG/H
center, FrattiniC22C23×#261
commutator, socleC22×C13C23×C4
FittingC13×#126C4
prime radicalC23×D13C23
cosocleC22×D13C24
hypercenter#126#261
hypocenterC13#2334
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
2. #11719083C2semidirect
3. #11719083C2semidirect
4. #11719082C2semidirect
5. #11719082C2semidirect
6. #11719082C2semidirect
7. C4⋊C4×#261C2semidirect
14. #11719060C2semidirect
15. C4×C4⋊#261C2semidirect
32. C13×#126C4semidirect
33. #88152C4semidirect
34. #88152C4semidirect
35. #88152C4semidirect
42. #88133C4semidirect
43. #88133C4semidirect
44. #88133C4semidirect
45. #88130C4semidirect
92. C13×C4⋊C4C2×C4semidirect
93. C13×C4⋊C4C2×C4semidirect
94. C13×C4⋊C4C2×C4semidirect
98. C42×C13C2×C4semidirect
108. C4⋊Dic13C2×C4semidirect
109. C4⋊Dic13C2×C4semidirect
110. C4⋊Dic13C2×C4semidirect
111. #6101C2×C4semidirect
112. #6101C2×C4semidirect
113. #6101C2×C4semidirect
114. #6101C2×C4semidirect
115. #6101C2×C4semidirect
116. #6101C2×C4semidirect
117. C4×Dic13C2×C4semidirect
118. C4×Dic13C2×C4semidirect
119. C4×Dic13C2×C4semidirect
239. #126#261semidirect
317. C4⋊C4C2×#261semidirect
318. C4⋊C4C2×#261semidirect
319. C4⋊C4C2×#261semidirect
343. C42C2×#261semidirect
344. C13#2334semidirect

Maximal subgroups

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

subgroupindex
D13×#1262
#117190832
#117190822
C4⋊C4×#2612
#117190712
#117190702
C22⋊C4×#2612
#117190602
C4×C4⋊#2612
#233413