Finite Group Databasebeta

← #13117855

Subgroups — #13117855

Order 1664.

788 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D13C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D13C211yesmaximal, characteristic, complemented
3C2×#88147C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×D13C211yesmaximal, characteristic, complemented
5C2×#88138C211yesmaximal, characteristic
6C13×#385C211yesmaximal, characteristic, complemented
7#11718651C211yesmaximal, characteristic, complemented
8#11718633C211yesmaximal, characteristic, complemented
9#11718618C211yesmaximal, characteristic, complemented
10#11718617C211yesmaximal, characteristic, complemented
11#11718612C211yesmaximal, characteristic, complemented
12#11718329C211yesmaximal, characteristic, complemented
13#11718327C211yesmaximal, characteristic, complemented
14#11718326C211yesmaximal, characteristic, complemented
15#11718310C211yesmaximal, characteristic, complemented
16C23×C4×C13C2211yescharacteristic
17C22×C22⋊D13C2211yescharacteristic
18C22×C22⋊D13C2211yescharacteristic
19C22×D52C2211yescharacteristic
20C22×C4×D13C2211yescharacteristic
21C22×C4×D13C2211yescharacteristic
22C22×C4×D13C2211yescharacteristic
23C22×C4×D13C2211yescharacteristic
24C2×C13×C4⋊C4C2211yescharacteristic
25C2×C13×C4⋊C4C2211yescharacteristic
26C2×C13×C22⋊C4C2211yescharacteristic
27C2×C13×C22⋊C4C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30C4×C22⋊D13—24no—
31C4×C22⋊D13—24no—
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×C4⋊Dic13C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×#6101C2211yescharacteristic
41C2×#6101C2211yescharacteristic
42C2×#6101C2211yescharacteristic
43C2×C4×Dic13C2211yescharacteristic
44C2×C4×Dic13C2211yescharacteristic
45C2×C4×Dic13C2211yescharacteristic
46C2×C4×Dic13C2211yescharacteristic
47#88147—24no—
48C4⋊C4×D13—24no—
49#88138C418yescomplemented
50C13×#95C2211yescharacteristic
51C13×#95C2211yescharacteristic
52#88071C2211yescharacteristic
53#88071C2211yescharacteristic
54#88071C2211yescharacteristic
55#88071C2211yescharacteristic
56C24×C13C2311yescharacteristic
57C23×D13C2311yescharacteristic
58C23×D13C2311yescharacteristic
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—41no—
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C2×C22⋊D13—22no—
69C2×C22⋊D13—22no—
70C2×C22⋊D13—22no—
71C2×C22⋊D13—22no—
72C2×C22⋊D13C2×C414yescomplemented
73C2×C22⋊D13C2×C414yescomplemented
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C22×Dic13C2311yescharacteristic
80C2×D52—22no—
81C2×D52—22no—
82C2×D52C2×C414yescomplemented
83C2×C4×D13—22no—
84C2×C4×D13—22no—
85C2×C4×D13—22no—
86C2×C4×D13—22no—
87C2×C4×D13—22no—
88C2×C4×D13—22no—
89C2×C4×D13—22no—
90C2×C4×D13—22no—
91C2×C4×D13—41no—
92C2×C4×D13—41no—
93C2×C4×D13—41no—
94C2×C4×D13C2×C414yescomplemented
95C13×C4⋊C4—22no—
96C13×C4⋊C4—22no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4C2×C414yescomplemented
99C22⋊Dic13—22no—
100C22⋊Dic13—22no—
101#6103—22no—
102#6103—22no—
103#6103—22no—
104#6103—41no—
105#6103C2×C414yescomplemented
106#6103D414yescomplemented
107C4⋊Dic13—22no—
108#6101—22no—
109#6101—22no—
110#6101C2×C414yescomplemented
111#6101D414yescomplemented
112C4×Dic13—22no—
113C4×Dic13—22no—
114C4×Dic13—22no—
115C4×Dic13—22no—
116#2361—131nomaximal, Sylow
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13C22×C412yes—
124C23×C13C2411yescharacteristic
125C22×D13—21no—
126C22×D13—21no—
127C22×D13—21no—
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—21no—
131C22×D13—21no—
132C22×D13—21no—
133C22×D13—21no—
134C22×D13—21no—
135C22×D13C22×C412yes—
136C22×D13C22×C412yes—
137C22×D13C2×D412yes—
138C22×D13#4112yes—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—44no—
154C2×C4×C13C22×C412yes—
155C2×C4×C13C22×C412yes—
156C2×C4×C13C2×D412yes—
157C2×C4×C13C2×D412yes—
158C22⋊D13—28no—
159C22⋊D13—28no—
160C2×Dic13—21no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163C2×Dic13—21no—
164C2×Dic13—21no—
165C2×Dic13—21no—
166C2×Dic13—21no—
167C2×Dic13—21no—
168C2×Dic13—21no—
169C2×Dic13—21no—
170C2×Dic13—21no—
171C2×Dic13—21no—
172C2×Dic13C22×C412yes—
173C2×Dic13C22×C412yes—
174C2×Dic13C2×D412yes—
175C2×Dic13C2×D412yes—
176C2×Dic13C2×D412yes—
177C2×Dic13#4112yes—
178D52—28no—
179C4×D13—28no—
180C4×D13—44no—
181C4×D13—44no—
182C4×D13—44no—
183C2×#121—131no—
184C2×C4×D4—131no—
185C2×C4×D4—131no—
186C2×C4×D4—131no—
187C22×C4⋊C4—131no—
188#390—131no—
189#389—131no—
190#388—131no—
191#388—131no—
192#386—131no—
193#386—131no—
194#385—131no—
195#385D1311yescharacteristic, complemented
196C4×C4⋊C4—131no—
197C4×C22⋊C4—131no—
198C22×C13—22no—
199C22×C13—22no—
200C22×C13—22no—
201C22×C13—41no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13C23×C411yescharacteristic
206C22×C13C22×D411yescharacteristic
207C22×C13C22×D411yescharacteristic
208C22×C13C2×#4111yescharacteristic
209C22×C13C2×#4111yescharacteristic
210C22×C13H(5,𝔽2)11yescharacteristic
211C22×C132−1+411yescharacteristic
212C2×D13—22no—
213C2×D13—22no—
214C2×D13—22no—
215C2×D13—22no—
216C2×D13—22no—
217C2×D13—22no—
218C2×D13—22no—
219C2×D13—22no—
220C2×D13—22no—
221C2×D13—41no—
222C2×D13—41no—
223C2×D13—41no—
224C2×D13—41no—
225C2×D13C4×D414yescomplemented
226C4×C13—22no—
227C4×C13—22no—
228C4×C13—22no—
229C4×C13—22no—
230C4×C13—41no—
231C4×C13—41no—
232Dic13—22no—
233Dic13—22no—
234Dic13—22no—
235Dic13—41no—
236Dic13—41no—
237Dic13C4×D414yescomplemented
238C22×D4—131no—
239C22×D4—131no—
240C22×D4—131no—
241C23×C4—131no—
242C23×C4—131no—
243C23×C4—131no—
244C23×C4—131no—
245C23×C4C2×D1311yescharacteristic
246#121—138no—
247C4×D4—264no—
248C4×D4—264no—
249C4×D4—264no—
250C2×C4⋊C4—131no—
251C2×C4⋊C4—131no—
252C2×C4⋊C4—131no—
253C2×C4⋊C4—131no—
254C2×C4⋊C4—131no—
255C2×C4⋊C4—264no—
256C2×C4⋊C4C2×D1311yescharacteristic
257C2×C4⋊C4C2×D1311yescharacteristic
258C2×C22⋊C4—131no—
259C2×C22⋊C4—131no—
260C2×C22⋊C4—131no—
261C2×C22⋊C4—131no—
262C2×C22⋊C4—131no—
263C2×C22⋊C4—131no—
264C2×C22⋊C4—131no—
265C2×C22⋊C4—131no—
266C2×C22⋊C4C2×D1311yescharacteristic
267C2×C22⋊C4C2×D1311yescharacteristic
268C2×C42—131no—
269C2×C42—131no—
270C2×C42—131no—
271C2×C42—131no—
272#95—131no—
273#95—131no—
274#95—131no—
275#95—131no—
276#95C2×D1311yescharacteristic
277#95C2×D1311yescharacteristic
278C2×C13—42no—
279C2×C13C2×C4×D411yescharacteristic
280C2×C13C2×C4×D411yescharacteristic
281C2×C13#52011yescharacteristic
282C2×C13D4211yescharacteristic
283C2×C13#54711yescharacteristic
284C2×C13#54811yescharacteristic
285C2×C13#55311yescharacteristic
286D13—24no—
287D13—42no—
288C24—131no—
289C24—131no—
290C24C22×D1311yescharacteristic
291C2×D4—134no—
292C2×D4—134no—
293C2×D4—134no—
294C2×D4—262no—
295C2×D4—262no—
296C2×D4—262no—
297C2×D4—262no—
298C2×D4—262no—
299C2×D4—262no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—41no—
303C22×C4—131no—
304C22×C4—131no—
305C22×C4—131no—
306C22×C4—131no—
307C22×C4—134no—
308C22×C4—131no—
309C22×C4—131no—
310C22×C4—262no—
311C22×C4—262no—
312C22×C4—262no—
313C22×C4—262no—
314C22×C4—262no—
315C22×C4—262no—
316C22×C4—262no—
317C22×C4—262no—
318C22×C4—521no—
319C22×C4—521no—
320C22×C4—521no—
321C22×C4C22×D1311yescharacteristic
322C22×C4C22×D1311yescharacteristic
323C22×C4C22×D1311yescharacteristic
324C22×C4C22×D1311yescharacteristic
325C22×C4C22×D1311yescharacteristic
326C22×C4C22×D1311yescharacteristic
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—134no—
330C4⋊C4—134no—
331C4⋊C4—262no—
332C4⋊C4—262no—
333C4⋊C4—262no—
334C22⋊C4—41no—
335C22⋊C4—134no—
336C22⋊C4—134no—
337C22⋊C4—262no—
338C22⋊C4—262no—
339C22⋊C4—262no—
340C22⋊C4—262no—
341C22⋊C4—262no—
342C22⋊C4—521no—
343C22⋊C4C4×D1314yescomplemented
344C42—262no—
345C42—262no—
346C42—262no—
347C42—262no—
348C13#236111yescharacteristic, complemented, Sylow
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—132no—
356C23—132no—
357C23—132no—
358C23—132no—
359C23—261no—
360C23—261no—
361C23—261no—
362C23—261no—
363C23—261no—
364C23—261no—
365C23—261no—
366C23—261no—
367C23—261no—
368C23—261no—
369C23C2×C4×D1312yes—
370C23C23×D1311yescharacteristic
371D4—268no—
372D4—268no—
373D4—268no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—44no—
389C2×C4—132no—
390C2×C4—132no—
391C2×C4—132no—
392C2×C4—132no—
393C2×C4—132no—
394C2×C4—132no—
395C2×C4—268no—
396C2×C4—261no—
397C2×C4—261no—
398C2×C4—261no—
399C2×C4—261no—
400C2×C4—261no—
401C2×C4—261no—
402C2×C4—261no—
403C2×C4—261no—
404C2×C4—261no—
405C2×C4—261no—
406C2×C4—261no—
407C2×C4—261no—
408C2×C4—524no—
409C2×C4—524no—
410C2×C4—524no—
411C2×C4C2×C4×D1312yes—
412C2×C4C2×C4×D1312yes—
413C2×C4D4×D1312yes—
414C2×C4D4×D1312yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—134no—
423C22—262no—
424C22—262no—
425C22—262no—
426C22—262no—
427C22—262no—
428C22—262no—
429C22—262no—
430C22—262no—
431C22—262no—
432C22—521no—
433C22—521no—
434C22—521no—
435C22—521no—
436C22C22×C4×D1311yescharacteristic
437C22C2×D4×D1311yescharacteristic
438C22C2×D4×D1311yescharacteristic
439C22#8825111yescharacteristic
440C22#8825411yescharacteristic
441C22#41×D1311yescharacteristic
442C22#41×D1311yescharacteristic
443C4—22no—
444C4—22no—
445C4—22no—
446C4—22no—
447C4—41no—
448C4—41no—
449C4—134no—
450C4—262no—
451C4—262no—
452C4—262no—
453C4—521no—
454C4—521no—
455C2—42no—
456C2—264no—
457C2—522no—
458C2#1171920911yescharacteristic
459C2C4×D4×D1311yescharacteristic
460C2C4×D4×D1311yescharacteristic
461C2#1171929511yescharacteristic
462C2#1171933611yescharacteristic
463C2#1171933811yescharacteristic
464C2#1171936611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC13×#385C2
socle, cosocleC23×C13C24
prime radicalC2×#88138C2
hypercenter#385D13
hypocenterC13#2361
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊D13C2semidirect
2. C2×C4×C22⋊D13C2semidirect
3. C2×#88147C2semidirect
4. C2×C4⋊C4×D13C2semidirect
6. C13×#385C2semidirect
7. #11718651C2semidirect
8. #11718633C2semidirect
9. #11718618C2semidirect
10. #11718617C2semidirect
11. #11718612C2semidirect
12. #11718329C2semidirect
13. #11718327C2semidirect
14. #11718326C2semidirect
15. #11718310C2semidirect
49. #88138C4semidirect
72. C2×C22⋊D13C2×C4semidirect
73. C2×C22⋊D13C2×C4semidirect
82. C2×D52C2×C4semidirect
94. C2×C4×D13C2×C4semidirect
98. C13×C22⋊C4C2×C4semidirect
105. #6103C2×C4semidirect
106. #6103D4semidirect
110. #6101C2×C4semidirect
111. #6101D4semidirect
195. #385D13semidirect
225. C2×D13C4×D4semidirect
237. Dic13C4×D4semidirect
343. C22⋊C4C4×D13semidirect
348. C13#2361semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D132
C2×#881472
C2×C4⋊C4×D132
C2×#881382
C13×#3852
#117186512
#117186332
#117186182
#117186172
#117186122
#117183292
#117183272
#117183262
#117183102
#236113