Finite Group Databasebeta

← #13121402

Subgroups — #13121402

Order 1664.

680 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88191C211yesmaximal, characteristic
2C2×#88140C211yesmaximal, characteristic, complemented
3C13×#394C211yesmaximal, characteristic, complemented
4#11718881C211yesmaximal, characteristic, complemented
5#11718655C211yesmaximal, characteristic, complemented
6#11718654C211yesmaximal, characteristic, complemented
7#11718620C211yesmaximal, characteristic, complemented
8#11718619C211yesmaximal, characteristic, complemented
9#11718618C211yesmaximal, characteristic, complemented
10#11718616C211yesmaximal, characteristic, complemented
11#11718616C211yesmaximal, characteristic, complemented
12#11718612C211yesmaximal, characteristic, complemented
13#11718609C211yesmaximal, characteristic, complemented
14#11718336C211yesmaximal, characteristic, complemented
15#11718331C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C22×C22⋊D13C2211yescharacteristic
19C22×C22⋊D13C2211yescharacteristic
20C23×Dic13C2211yescharacteristic, complemented
21C2×C13×C4⋊C4C2211yescharacteristic, complemented
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic, complemented
25C2×C13×C22⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic, complemented
30#88191—24no—
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic
39C2×#6103C2211yescharacteristic
40C2×#6103C2211yescharacteristic
41C2×C4⋊Dic13C2211yescharacteristic, complemented
42C2×C4⋊Dic13C2211yescharacteristic, complemented
43C2×#6101C2211yescharacteristic, complemented
44C2×#6101C2211yescharacteristic, complemented
45C2×C4×Dic13C2211yescharacteristic, complemented
46#88140—24no—
47C13×#95C2211yescharacteristic, complemented
48#88071C2211yescharacteristic, complemented
49#88071C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53C24×C13C2311yescharacteristic
54C24×C13C2311yescharacteristic
55C23×D13—22no—
56C23×D13—22no—
57C23×D13—22no—
58C23×D13—41no—
59C23×D13—41no—
60C23×D13—41no—
61C23×D13—41no—
62C23×D13C2311yescharacteristic
63C23×D13C2311yescharacteristic
64C2×D4×C13—22no—
65C2×D4×C13—22no—
66C2×D4×C13—41no—
67C22×C4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C22×C4×C13C2311yescharacteristic
71C22×C4×C13C2311yescharacteristic
72C2×C22⋊D13—22no—
73C2×C22⋊D13—22no—
74C2×C22⋊D13—41no—
75C2×C22⋊D13—41no—
76C2×C22⋊D13—41no—
77C2×C22⋊D13D414yes—
78C22×Dic13—22no—
79C22×Dic13—41no—
80C22×Dic13—41no—
81C22×Dic13C2311yescharacteristic
82C22×Dic13C2311yescharacteristic
83C22×Dic13C2311yescharacteristic
84C22×Dic13C2311yescharacteristic
85C22×Dic13C2311yescharacteristic
86C22×Dic13C2311yescharacteristic
87C13×C4⋊C4—41no—
88C13×C22⋊C4—22no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C22⋊Dic13—22no—
93C22⋊Dic13—41no—
94C22⋊Dic13—41no—
95C22⋊Dic13—41no—
96#6103—22no—
97#6103—22no—
98#6103—22no—
99#6103—22no—
100#6103—22no—
101#6103—41no—
102#6103—41no—
103#6103—41no—
104#6103—41no—
105#6103—41no—
106C4⋊Dic13—22no—
107C4⋊Dic13—22no—
108#6101—41no—
109#6101—41no—
110C4×Dic13—41no—
111#2697—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13C2×D412yes—
125C23×C13#4112yes—
126C23×C13C2411yescharacteristic
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×D13—21no—
136C22×D13—21no—
137C22×D13—21no—
138C22×D13—21no—
139C22×D13—44no—
140C22×D13—44no—
141C22×D13—44no—
142C22×D13—44no—
143C22×D13—44no—
144C22×D13—44no—
145C22×D13—44no—
146C22×D13C2×D412yes—
147C22×D13#4112yes—
148D4×C13—44no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C22⋊D13—44no—
165C22⋊D13—44no—
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—21no—
176C2×Dic13—21no—
177C2×Dic13—21no—
178C2×Dic13—21no—
179C2×Dic13—21no—
180C2×Dic13—21no—
181C2×Dic13—21no—
182C2×Dic13—21no—
183C2×Dic13—44no—
184C2×Dic13C2×D412yes—
185C2×#123—131no—
186C2×#120—131no—
187#397—131no—
188#397—131no—
189#396—131no—
190#396—131no—
191#394—131no—
192#394D1311yescharacteristic, complemented
193#390—131no—
194#388—131no—
195#388—131no—
196#386—131no—
197#386—131no—
198#379—131no—
199#379—131no—
200C22×C13—22no—
201C22×C13—22no—
202C22×C13—22no—
203C22×C13—22no—
204C22×C13—22no—
205C22×C13—22no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13—41no—
214C22×C13C22×D411yescharacteristic
215C22×C13C2×#4111yescharacteristic
216C22×C13C2×#4111yescharacteristic
217C22×C13H(5,𝔽2)11yescharacteristic
218C22×C13H(5,𝔽2)11yescharacteristic
219C22×C13H(5,𝔽2)11yescharacteristic
220C22×C13H(5,𝔽2)11yescharacteristic
221C2×D13—22no—
222C2×D13—22no—
223C2×D13—22no—
224C2×D13—22no—
225C2×D13—22no—
226C2×D13—22no—
227C2×D13—416no—
228C2×D13—41no—
229C2×D13—41no—
230C2×D13—41no—
231C2×D13—41no—
232C2×D13—41no—
233C2×D13—41no—
234C2×D13—41no—
235C2×D13—41no—
236C4×C13—41no—
237C4×C13—41no—
238C4×C13—41no—
239C4×C13—41no—
240C4×C13—41no—
241Dic13—22no—
242Dic13—41no—
243Dic13—41no—
244Dic13—41no—
245Dic13—41no—
246Dic13—41no—
247C25—131no—
248C22×D4—131no—
249C22×D4—131no—
250C22×D4C2×D1311yescharacteristic
251C23×C4—131no—
252#123—264no—
253#120—264no—
254C2×C4⋊C4—131no—
255C2×C4⋊C4—131no—
256C2×C4⋊C4—131no—
257C2×C4⋊C4—131no—
258C2×C4⋊C4C2×D1311yescharacteristic, complemented
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⋊C4—131no—
267C2×C22⋊C4—131no—
268C2×C22⋊C4—131no—
269C2×C22⋊C4—131no—
270C2×C22⋊C4—131no—
271C2×C22⋊C4—131no—
272C2×C22⋊C4—131no—
273C2×C22⋊C4C2×D1311yescharacteristic
274C2×C22⋊C4C2×D1311yescharacteristic
275C2×C22⋊C4C2×D1311yescharacteristic, complemented
276C2×C22⋊C4C2×D1311yescharacteristic, complemented
277C2×C42—131no—
278#95—131no—
279#95—131no—
280#95—131no—
281#95—131no—
282#95—131no—
283#95C2×D1311yescharacteristic, complemented
284C2×C13—42no—
285C2×C13—42no—
286C2×C13#53411yescharacteristic
287C2×C13#53811yescharacteristic
288C2×C13#53811yescharacteristic
289C2×C13#54611yescharacteristic
290C2×C13#54611yescharacteristic
291C2×C13#55111yescharacteristic
292C2×C13#56011yescharacteristic
293D13—42no—
294D13—42no—
295C24—131no—
296C24—131no—
297C24—262no—
298C24—262no—
299C24—262no—
300C24—521no—
301C24—521no—
302C24—521no—
303C24—521no—
304C24C22×D1311yescharacteristic
305C24C22×D1311yescharacteristic
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—41no—
309C2×D4—134no—
310C2×D4—262no—
311C2×D4—262no—
312C2×D4—521no—
313C2×D4—521no—
314C2×D4—521no—
315C22×C4—131no—
316C22×C4—131no—
317C22×C4—131no—
318C22×C4—131no—
319C22×C4—131no—
320C22×C4—131no—
321C22×C4—262no—
322C22×C4—521no—
323C22×C4—521no—
324C22×C4C22×D1311yescharacteristic
325C22×C4C22×D1311yescharacteristic
326C22×C4C22×D1311yescharacteristic
327C22×C4C22×D1311yescharacteristic
328C22×C4C22×D1311yescharacteristic
329C4⋊C4—41no—
330C4⋊C4—262no—
331C4⋊C4—262no—
332C4⋊C4—521no—
333C4⋊C4—521no—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—262no—
339C22⋊C4—262no—
340C22⋊C4—262no—
341C22⋊C4—262no—
342C22⋊C4—262no—
343C22⋊C4—262no—
344C22⋊C4—521no—
345C22⋊C4—521no—
346C22⋊C4—521no—
347C22⋊C4—521no—
348C22⋊C4—521no—
349C22⋊C4—521no—
350C22⋊C4—521no—
351C22⋊C4—521no—
352C42—521no—
353C13#269711yescharacteristic, complemented, Sylow
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—132no—
367C23—132no—
368C23—261no—
369C23—261no—
370C23—261no—
371C23—261no—
372C23—261no—
373C23—261no—
374C23—261no—
375C23—261no—
376C23—261no—
377C23—261no—
378C23—261no—
379C23—261no—
380C23—524no—
381C23—524no—
382C23—524no—
383C23—524no—
384C23—524no—
385C23—524no—
386C23—524no—
387C23D4×D1312yes—
388C23#612912yes—
389C23C23×D1311yescharacteristic
390D4—44no—
391D4—524no—
392D4—524no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—132no—
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—524no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—262no—
442C22—262no—
443C22—262no—
444C22—262no—
445C22—262no—
446C22—262no—
447C22—5216no—
448C22—521no—
449C22—521no—
450C22—521no—
451C22—521no—
452C22—521no—
453C22—521no—
454C22—521no—
455C22—521no—
456C22C2×D4×D1311yescharacteristic
457C22C2×#612911yescharacteristic
458C22#8825111yescharacteristic
459C22#8825111yescharacteristic
460C22#41×D1311yescharacteristic
461C22#8825611yescharacteristic
462C22#8825611yescharacteristic
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—41no—
468C4—262no—
469C4—521no—
470C4—521no—
471C4—521no—
472C4—521no—
473C4—521no—
474C2—42no—
475C2—42no—
476C2—522no—
477C2—522no—
478C2#1171929611yescharacteristic
479C2#1171931511yescharacteristic
480C2#1171932211yescharacteristic
481C2#1171932511yescharacteristic
482C2#1171935811yescharacteristic
483C2#1171936311yescharacteristic
484C2#1171938311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC2×#88191C2
hypercenter#394D13
hypocenterC13#2697
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#88140C2semidirect
3. C13×#394C2semidirect
4. #11718881C2semidirect
5. #11718655C2semidirect
6. #11718654C2semidirect
7. #11718620C2semidirect
8. #11718619C2semidirect
9. #11718618C2semidirect
10. #11718616C2semidirect
11. #11718616C2semidirect
12. #11718612C2semidirect
13. #11718609C2semidirect
14. #11718336C2semidirect
15. #11718331C2semidirect
20. C23×Dic13C22semidirect
21. C2×C13×C4⋊C4C22semidirect
24. C2×C13×C22⋊C4C22semidirect
25. C2×C13×C22⋊C4C22semidirect
29. C2×C22⋊Dic13C22semidirect
41. C2×C4⋊Dic13C22semidirect
42. C2×C4⋊Dic13C22semidirect
43. C2×#6101C22semidirect
44. C2×#6101C22semidirect
45. C2×C4×Dic13C22semidirect
47. C13×#95C22semidirect
48. #88071C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
192. #394D13semidirect
258. C2×C4⋊C4C2×D13semidirect
275. C2×C22⋊C4C2×D13semidirect
276. C2×C22⋊C4C2×D13semidirect
283. #95C2×D13semidirect
353. C13#2697semidirect

Maximal subgroups

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

subgroupindex
C2×#881912
C2×#881402
C13×#3942
#117188812
#117186552
#117186542
#117186202
#117186192
#117186182
#117186162
#117186122
#117186092
#117183362
#117183312
#269713