Finite Group Databasebeta

← #13121217

Subgroups — #13121217

Order 1664.

688 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88136C211yesmaximal, characteristic
2C2×#88129C211yesmaximal, characteristic, complemented
3C13×#388C211yesmaximal, characteristic, complemented
4#11718654C211yesmaximal, characteristic, complemented
5#11718652C211yesmaximal, characteristic, complemented
6#11718620C211yesmaximal, characteristic, complemented
7#11718617C211yesmaximal, characteristic, complemented
8#11718616C211yesmaximal, characteristic, complemented
9#11718616C211yesmaximal, characteristic, complemented
10#11718608C211yesmaximal, characteristic, complemented
11#11718601C211yesmaximal, characteristic, complemented
12#11718336C211yesmaximal, characteristic, complemented
13#11718334C211yesmaximal, characteristic, complemented
14#11718326C211yesmaximal, characteristic, complemented
15#11718326C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×C22⋊D13C2211yescharacteristic
18C22×D52C2211yescharacteristic
19C22×D52C2211yescharacteristic
20C22×C4×D13C2211yescharacteristic, complemented
21C22×Dic26C2211yescharacteristic, complemented
22C2×C13×C4⋊C4C2211yescharacteristic, complemented
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C42×C13C2211yescharacteristic, complemented
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic
39C2×#6103C2211yescharacteristic, complemented
40C2×#6103C2211yescharacteristic, complemented
41C2×#6103C2211yescharacteristic, complemented
42C2×#6101C2211yescharacteristic, complemented
43#88136—24no—
44#88129—24no—
45C13×#95C2211yescharacteristic, complemented
46C13×#95C2211yescharacteristic, complemented
47#88071C2211yescharacteristic, complemented
48#88071C2211yescharacteristic, complemented
49#88071C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53C24×C13C2311yescharacteristic
54C23×D13—22no—
55C23×D13—22no—
56C23×D13—22no—
57C23×D13—41no—
58C23×D13—41no—
59C23×D13—41no—
60C23×D13—41no—
61C23×D13C2311yescharacteristic
62C23×D13C2311yescharacteristic
63C23×D13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C2×C22⋊D13—22no—
71C2×C22⋊D13—22no—
72C2×C22⋊D13—41no—
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C2×D52—22no—
79C2×D52—22no—
80C2×D52—41no—
81C2×D52—41no—
82C2×D52—41no—
83C2×D52D414yes—
84C2×C4×D13—41no—
85C2×C4×D13—41no—
86C2×C4×D13—41no—
87C2×Dic26—22no—
88C2×Dic26—41no—
89C2×Dic26—41no—
90C13×C4⋊C4—41no—
91C13×C22⋊C4—22no—
92C13×C22⋊C4—22no—
93C13×C22⋊C4—41no—
94C42×C13—22no—
95C22⋊Dic13—41no—
96C22⋊Dic13—41no—
97#6103—22no—
98#6103—22no—
99#6103—22no—
100#6103—22no—
101#6103—22no—
102#6103—22no—
103#6103—22no—
104#6103—41no—
105#6103—41no—
106#6103—41no—
107#6103—41no—
108#6103—41no—
109#6103—41no—
110#6101—41no—
111#2684—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13#4112yes—
119C23×C13C2411yescharacteristic
120C22×D13—21no—
121C22×D13—21no—
122C22×D13—21no—
123C22×D13—21no—
124C22×D13—21no—
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×D13—21no—
136C22×D13—21no—
137C22×D13—21no—
138C22×D13—44no—
139C22×D13—44no—
140C22×D13—44no—
141C22×D13—44no—
142C22×D13—44no—
143C22×D13—44no—
144C22×D13—44no—
145C22×D13C2×D412yes—
146C22×D13C2×D412yes—
147C22×D13#4112yes—
148C2×C4×C13—21no—
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—
164C2×C4×C13—21no—
165C2×C4×C13C2×D412yes—
166C22⋊D13—44no—
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—
182D52—44no—
183D52—44no—
184C4×D13—44no—
185Dic26—44no—
186C2×#124—131no—
187C2×#120—131no—
188#397—131no—
189#397—131no—
190#394—131no—
191#394—131no—
192#393—131no—
193#393—131no—
194#388—131no—
195#388D1311yescharacteristic, complemented
196#386—131no—
197#386—131no—
198#386—131no—
199#379—131no—
200#379—131no—
201C22×C13—22no—
202C22×C13—22no—
203C22×C13—22no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13C22×D411yescharacteristic
209C22×C13C2×#4111yescharacteristic
210C22×C13C2×#4111yescharacteristic
211C22×C13H(5,𝔽2)11yescharacteristic
212C22×C13H(5,𝔽2)11yescharacteristic
213C22×C13H(5,𝔽2)11yescharacteristic
214C22×C13H(5,𝔽2)11yescharacteristic
215C2×D13—22no—
216C2×D13—22no—
217C2×D13—22no—
218C2×D13—22no—
219C2×D13—22no—
220C2×D13—22no—
221C2×D13—22no—
222C2×D13—22no—
223C2×D13—22no—
224C2×D13—416no—
225C2×D13—41no—
226C2×D13—41no—
227C2×D13—41no—
228C2×D13—41no—
229C2×D13—41no—
230C2×D13—41no—
231C2×D13—41no—
232C2×D13—41no—
233C2×D13—41no—
234C2×D13—41no—
235C2×D13—41no—
236C2×D13—41no—
237C4×C13—22no—
238C4×C13—41no—
239C4×C13—41no—
240C4×C13—41no—
241C4×C13—41no—
242C4×C13—41no—
243Dic13—41no—
244Dic13—41no—
245Dic13—41no—
246Dic13—41no—
247Dic13—41no—
248C25—131no—
249C22×Q8—131no—
250C22×D4—131no—
251C22×D4—131no—
252C22×D4—131no—
253C23×C4—131no—
254#124—264no—
255#120—264no—
256C2×C4⋊C4—131no—
257C2×C4⋊C4C2×D1311yescharacteristic, complemented
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⋊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
276C2×C42C2×D1311yescharacteristic, complemented
277#95—131no—
278#95—131no—
279#95—131no—
280#95—131no—
281#95—131no—
282#95—131no—
283#95C2×D1311yescharacteristic, complemented
284#95C2×D1311yescharacteristic, complemented
285C2×C13—42no—
286C2×C13#53411yescharacteristic
287C2×C13#53811yescharacteristic
288C2×C13#53811yescharacteristic
289C2×C13#54611yescharacteristic
290C2×C13#54611yescharacteristic
291C2×C13#55111yescharacteristic
292C2×C13H(3,𝔽4)11yescharacteristic
293D13—42no—
294D13—42no—
295D13—42no—
296C24—131no—
297C24—131no—
298C24—131no—
299C24—262no—
300C24—262no—
301C24—262no—
302C24—521no—
303C24—521no—
304C24—521no—
305C24—521no—
306C24C22×D1311yescharacteristic
307C2×Q8—262no—
308C2×Q8—521no—
309C2×Q8—521no—
310C2×D4—134no—
311C2×D4—262no—
312C2×D4—262no—
313C2×D4—262no—
314C2×D4—262no—
315C2×D4—521no—
316C2×D4—521no—
317C2×D4—521no—
318C2×D4—521no—
319C22×C4—131no—
320C22×C4—131no—
321C22×C4—131no—
322C22×C4—131no—
323C22×C4—131no—
324C22×C4—521no—
325C22×C4—521no—
326C22×C4—521no—
327C22×C4C22×D1311yescharacteristic
328C22×C4C22×D1311yescharacteristic
329C22×C4C22×D1311yescharacteristic
330C22×C4C22×D1311yescharacteristic
331C22×C4C22×D1311yescharacteristic
332C22×C4C22×D1311yescharacteristic
333C4⋊C4—41no—
334C4⋊C4—521no—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—41no—
338C22⋊C4—262no—
339C22⋊C4—262no—
340C22⋊C4—262no—
341C22⋊C4—262no—
342C22⋊C4—262no—
343C22⋊C4—262no—
344C22⋊C4—262no—
345C22⋊C4—521no—
346C22⋊C4—521no—
347C22⋊C4—521no—
348C22⋊C4—521no—
349C22⋊C4—521no—
350C22⋊C4—521no—
351C22⋊C4—521no—
352C22⋊C4—521no—
353C42—22no—
354C13#268411yescharacteristic, complemented, Sylow
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—132no—
362C23—132no—
363C23—132no—
364C23—261no—
365C23—261no—
366C23—261no—
367C23—261no—
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—261no—
381C23—261no—
382C23—524no—
383C23—524no—
384C23—524no—
385C23—524no—
386C23—524no—
387C23—524no—
388C23—524no—
389C23#612712yes—
390C23C23×D1311yescharacteristic
391Q8—524no—
392D4—524no—
393D4—524no—
394D4—524no—
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—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
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—261no—
427C2×C4—524no—
428C2×C4D4×D1312yes—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—262no—
437C22—262no—
438C22—262no—
439C22—262no—
440C22—262no—
441C22—262no—
442C22—262no—
443C22—262no—
444C22—262no—
445C22—5216no—
446C22—521no—
447C22—521no—
448C22—521no—
449C22—521no—
450C22—521no—
451C22—521no—
452C22—521no—
453C22—521no—
454C22—521no—
455C22—521no—
456C22—521no—
457C22—521no—
458C22C2×#612711yescharacteristic
459C22C2×D4×D1311yescharacteristic
460C22#8825111yescharacteristic
461C22#41×D1311yescharacteristic
462C22#8825611yescharacteristic
463C22#8825611yescharacteristic
464C22#8825611yescharacteristic
465C4—22no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—521no—
472C4—521no—
473C4—521no—
474C4—521no—
475C4—521no—
476C2—42no—
477C2—522no—
478C2—522no—
479C2—522no—
480C2#1171923211yescharacteristic
481C2#1171925511yescharacteristic
482C2#1171926511yescharacteristic
483C2#1171931711yescharacteristic
484C2#1171935811yescharacteristic
485C2#1171938811yescharacteristic
486C2#1171940911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#388C2
prime radicalC2×#88136C2
hypercenter#388D13
hypocenterC13#2684
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#88129C2semidirect
3. C13×#388C2semidirect
4. #11718654C2semidirect
5. #11718652C2semidirect
6. #11718620C2semidirect
7. #11718617C2semidirect
8. #11718616C2semidirect
9. #11718616C2semidirect
10. #11718608C2semidirect
11. #11718601C2semidirect
12. #11718336C2semidirect
13. #11718334C2semidirect
14. #11718326C2semidirect
15. #11718326C2semidirect
20. C22×C4×D13C22semidirect
21. C22×Dic26C22semidirect
22. C2×C13×C4⋊C4C22semidirect
26. C2×C42×C13C22semidirect
39. C2×#6103C22semidirect
40. C2×#6103C22semidirect
41. C2×#6103C22semidirect
42. C2×#6101C22semidirect
45. C13×#95C22semidirect
46. C13×#95C22semidirect
47. #88071C22semidirect
48. #88071C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
195. #388D13semidirect
257. C2×C4⋊C4C2×D13semidirect
276. C2×C42C2×D13semidirect
283. #95C2×D13semidirect
284. #95C2×D13semidirect
354. C13#2684semidirect

Maximal subgroups

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

subgroupindex
C2×#881362
C2×#881292
C13×#3882
#117186542
#117186522
#117186202
#117186172
#117186162
#117186082
#117186012
#117183362
#117183342
#117183262
#268413