Finite Group Databasebeta

← #13117853

Subgroups — #13117853

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×D4×C13C211yesmaximal, characteristic, complemented
2C2×#88193C211yesmaximal, characteristic
3C2×C4×C22⋊D13C211yesmaximal, characteristic, complemented
4C22×#6101C211yesmaximal, characteristic, complemented
5C2×#88135C211yesmaximal, characteristic, complemented
6#11718881C211yesmaximal, characteristic, complemented
7#11718874C211yesmaximal, characteristic, complemented
8#11718871C211yesmaximal, characteristic, complemented
9#11718650C211yesmaximal, characteristic, complemented
10#11718633C211yesmaximal, characteristic, complemented
11#11718618C211yesmaximal, characteristic, complemented
12#11718605C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
14#11718601C211yesmaximal, characteristic, complemented
15C4×#6101C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C23×C4×C13C2211yescharacteristic
18C23×C4×C13C2211yescharacteristic
19C22×C22⋊D13C2211yescharacteristic
20C22×C22⋊D13C2211yescharacteristic
21C23×Dic13C2211yescharacteristic
22C23×Dic13C2211yescharacteristic
23C22×C4×D13C2211yescharacteristic
24C4×D4×C13—24no—
25C2×C13×C4⋊C4C2211yescharacteristic
26C2×C13×C22⋊C4C2211yescharacteristic
27C2×C13×C22⋊C4C2211yescharacteristic
28C2×C42×C13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊Dic13C2211yescharacteristic
31C2×C22⋊Dic13C2211yescharacteristic
32C2×C22⋊Dic13C2211yescharacteristic
33#88193C418yescomplemented
34C4×C22⋊D13—24no—
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic
39C2×#6101—24no—
40C2×#6101C2211yescharacteristic
41C2×#6101C2211yescharacteristic
42C2×#6101C2211yescharacteristic
43C2×#6101C2211yescharacteristic
44C2×#6101C2211yescharacteristic
45C2×#6101C2211yescharacteristic
46C2×C4×Dic13C2211yescharacteristic
47C2×C4×Dic13C2211yescharacteristic
48C2×C4×Dic13C2211yescharacteristic
49#88135—24no—
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53#88071C2211yescharacteristic
54#88071C2211yescharacteristic
55#88071C2211yescharacteristic
56C24×C13C2311yescharacteristic
57C24×C13C2311yescharacteristic
58C23×D13C2311yescharacteristic
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13C2×C414yescomplemented
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C22×C4×C13C2311yescharacteristic
71C22×C4×C13C2311yescharacteristic
72C22×C4×C13C2311yescharacteristic
73C2×C22⋊D13—22no—
74C2×C22⋊D13—22no—
75C2×C22⋊D13—22no—
76C2×C22⋊D13—22no—
77C2×C22⋊D13C2×C414yescomplemented
78C2×C22⋊D13C2×C414yescomplemented
79C22×Dic13—22no—
80C22×Dic13—22no—
81C22×Dic13—22no—
82C22×Dic13—22no—
83C22×Dic13—41no—
84C22×Dic13C2×C414yescomplemented
85C22×Dic13C2311yescharacteristic
86C22×Dic13C2311yescharacteristic
87C22×Dic13C2311yescharacteristic
88C22×Dic13C2311yescharacteristic
89C22×Dic13C2311yescharacteristic
90C22×Dic13C2311yescharacteristic
91C22×Dic13C2311yescharacteristic
92C2×C4×D13—22no—
93C2×C4×D13—22no—
94C2×C4×D13—41no—
95C13×C4⋊C4—22no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4D414yescomplemented
98C42×C13—22no—
99C22⋊Dic13—22no—
100C22⋊Dic13—22no—
101C22⋊Dic13—41no—
102C22⋊Dic13C2×C414yescomplemented
103#6103—22no—
104#6103—22no—
105#6103—41no—
106#6103C2×C414yescomplemented
107#6101—22no—
108#6101—22no—
109#6101—22no—
110#6101—22no—
111#6101C2×C414yescomplemented
112#6101D414yescomplemented
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×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13C22×C412yes—
128C23×C13C22×C412yes—
129C23×C13C2×D412yes—
130C23×C13#4112yes—
131C23×C13C2411yescharacteristic
132C22×D13—21no—
133C22×D13—21no—
134C22×D13—21no—
135C22×D13—21no—
136C22×D13—21no—
137C22×D13—21no—
138C22×D13C22×C412yes—
139D4×C13—28no—
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—44no—
152C2×C4×C13—44no—
153C2×C4×C13C22×C412yes—
154C2×C4×C13C2×D412yes—
155C2×C4×C13C2×D412yes—
156C2×C4×C13C2×D412yes—
157C22⋊D13—28no—
158C22⋊D13—28no—
159C2×Dic13—21no—
160C2×Dic13—21no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163C2×Dic13—21no—
164C2×Dic13—21no—
165C2×Dic13—28no—
166C2×Dic13—21no—
167C2×Dic13—21no—
168C2×Dic13—21no—
169C2×Dic13—21no—
170C2×Dic13—21no—
171C2×Dic13—21no—
172C2×Dic13—21no—
173C2×Dic13—21no—
174C2×Dic13—21no—
175C2×Dic13—44no—
176C2×Dic13C22×C412yes—
177C2×Dic13C22×C412yes—
178C2×Dic13C22×C412yes—
179C2×Dic13C2×D412yes—
180C2×Dic13C2×D412yes—
181C2×Dic13#4112yes—
182C4×D13—44no—
183C2×#121—131no—
184C2×C4×D4—131no—
185C2×C4×D4—131no—
186C2×C4×D4D1311yescharacteristic, complemented
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#385—131no—
196C4×C4⋊C4—131no—
197C4×C22⋊C4—131no—
198C22×C13—22no—
199C22×C13—22no—
200C22×C13—22no—
201C22×C13—22no—
202C22×C13—22no—
203C22×C13—22no—
204C22×C13—22no—
205C22×C13—22no—
206C22×C13—22no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13C4×D414yescomplemented
212C22×C13C23×C411yescharacteristic
213C22×C13C22×D411yescharacteristic
214C22×C13C22×D411yescharacteristic
215C22×C13C2×#4111yescharacteristic
216C22×C13C2×#4111yescharacteristic
217C22×C13H(5,𝔽2)11yescharacteristic
218C22×C132−1+411yescharacteristic
219C2×D13—22no—
220C2×D13—22no—
221C2×D13—22no—
222C2×D13—41no—
223C2×D13—41no—
224C2×D13—41no—
225C2×D13—41no—
226C4×C13—22no—
227C4×C13—22no—
228C4×C13—22no—
229C4×C13—22no—
230C4×C13—41no—
231Dic13—22no—
232Dic13—22no—
233Dic13—22no—
234Dic13—41no—
235Dic13—41no—
236Dic13—41no—
237Dic13C4×D414yescomplemented
238C22×D4—131no—
239C22×D4—131no—
240C22×D4C2×D1311yescharacteristic
241C23×C4—131no—
242C23×C4—131no—
243C23×C4—131no—
244C23×C4C2×D1311yescharacteristic
245C23×C4C2×D1311yescharacteristic
246#121—138no—
247C4×D4—24no—
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—131no—
256C2×C4⋊C4—264no—
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×C42C2×D1311yescharacteristic
272#95—131no—
273#95—131no—
274#95—131no—
275#95—131no—
276#95—131no—
277#95—131no—
278C2×C13—24no—
279C2×C13—42no—
280C2×C13C2×C4×D411yescharacteristic
281C2×C13C2×C4×D411yescharacteristic
282C2×C13#52011yescharacteristic
283C2×C13D4211yescharacteristic
284C2×C13#54711yescharacteristic
285C2×C13#54811yescharacteristic
286C2×C13#55311yescharacteristic
287D13—42no—
288C24—131no—
289C24C22×D1311yescharacteristic
290C24C22×D1311yescharacteristic
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—134no—
294C2×D4—134no—
295C2×D4—262no—
296C2×D4—262no—
297C2×D4—262no—
298C2×D4—262no—
299C2×D4C4×D1314yescomplemented
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—131no—
307C22×C4—134no—
308C22×C4—131no—
309C22×C4—131no—
310C22×C4—131no—
311C22×C4—131no—
312C22×C4—131no—
313C22×C4—131no—
314C22×C4—262no—
315C22×C4—262no—
316C22×C4—262no—
317C22×C4—262no—
318C22×C4—262no—
319C22×C4—262no—
320C22×C4—521no—
321C22×C4—521no—
322C22×C4C22×D1311yescharacteristic
323C22×C4C22×D1311yescharacteristic
324C22×C4C22×D1311yescharacteristic
325C22×C4C22×D1311yescharacteristic
326C22×C4C22×D1311yescharacteristic
327C4⋊C4—22no—
328C4⋊C4—134no—
329C4⋊C4—134no—
330C4⋊C4—262no—
331C4⋊C4—262no—
332C4⋊C4—262no—
333C4⋊C4—262no—
334C22⋊C4—22no—
335C22⋊C4—134no—
336C22⋊C4—134no—
337C22⋊C4—262no—
338C22⋊C4—262no—
339C22⋊C4—262no—
340C22⋊C4—262no—
341C22⋊C4—521no—
342C22⋊C4—521no—
343C22⋊C4C22⋊D1314yescomplemented
344C42—22no—
345C42—262no—
346C42—262no—
347C42—262no—
348C13#236111yescharacteristic, complemented, Sylow
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—132no—
360C23—261no—
361C23—261no—
362C23—261no—
363C23—261no—
364C23—261no—
365C23—261no—
366C23C2×C4×D1312yes—
367C23C2×C4×D1312yes—
368C23#612712yes—
369C23C2×C22⋊D1312yes—
370C23C23×D1311yescharacteristic
371D4—28no—
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—44no—
386C2×C4—44no—
387C2×C4—132no—
388C2×C4—132no—
389C2×C4—132no—
390C2×C4—132no—
391C2×C4—132no—
392C2×C4—132no—
393C2×C4—268no—
394C2×C4—261no—
395C2×C4—261no—
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—261no—
409C2×C4—524no—
410C2×C4—524no—
411C2×C4C2×C4×D1312yes—
412C2×C4D4×D1312yes—
413C2×C4C2×C22⋊D1312yes—
414C2×C4C2×C22⋊D1312yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—262no—
429C22—262no—
430C22—262no—
431C22—521no—
432C22—521no—
433C22—521no—
434C22—521no—
435C22C4×C22⋊D1314yescomplemented
436C22C22×C4×D1311yescharacteristic
437C22C2×#612711yescharacteristic
438C22C2×D4×D1311yescharacteristic
439C22#8825111yescharacteristic
440C22#41×D1311yescharacteristic
441C22#8825711yescharacteristic
442C22C22×C22⋊D1311yescharacteristic
443C4—22no—
444C4—22no—
445C4—22no—
446C4—22no—
447C4—41no—
448C4—134no—
449C4—262no—
450C4—262no—
451C4—262no—
452C4—521no—
453C4—521no—
454C4—521no—
455C2—24no—
456C2—42no—
457C2—522no—
458C2#1171924511yescharacteristic
459C2C4×D4×D1311yescharacteristic
460C2#1171925111yescharacteristic
461C2#1171925711yescharacteristic
462C2C2×C4×C22⋊D1311yescharacteristic
463C2D4×C22⋊D1311yescharacteristic
464C2#1171952911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC2×C4×D4×C13C2
socle, cosocleC23×C13C24
prime radicalC2×#88193C2
hypercenterC2×C4×D4D13
hypocenterC13#2361
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×C13C2semidirect
3. C2×C4×C22⋊D13C2semidirect
4. C22×#6101C2semidirect
5. C2×#88135C2semidirect
6. #11718881C2semidirect
7. #11718874C2semidirect
8. #11718871C2semidirect
9. #11718650C2semidirect
10. #11718633C2semidirect
11. #11718618C2semidirect
12. #11718605C2semidirect
13. C22⋊C4×Dic13C2semidirect
14. #11718601C2semidirect
15. C4×#6101C2semidirect
33. #88193C4semidirect
61. C2×D4×C13C2×C4semidirect
77. C2×C22⋊D13C2×C4semidirect
78. C2×C22⋊D13C2×C4semidirect
84. C22×Dic13C2×C4semidirect
97. C13×C22⋊C4D4semidirect
102. C22⋊Dic13C2×C4semidirect
106. #6103C2×C4semidirect
111. #6101C2×C4semidirect
112. #6101D4semidirect
186. C2×C4×D4D13semidirect
211. C22×C13C4×D4semidirect
237. Dic13C4×D4semidirect
299. C2×D4C4×D13semidirect
343. C22⋊C4C22⋊D13semidirect
348. C13#2361semidirect
435. C22C4×C22⋊D13semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C132
C2×#881932
C2×C4×C22⋊D132
C22×#61012
C2×#881352
#117188812
#117188742
#117188712
#117186502
#117186332
#117186182
#117186052
C22⋊C4×Dic132
#117186012
C4×#61012
#236113