Finite Group Databasebeta

← #16035070

Subgroups — #16035070

Order 3328.

2226 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120506C211yesmaximal, characteristic, complemented
2#13120497C212yesmaximal, complemented
3#13120059C214yesmaximal, complemented
4#13119846C214yesmaximal, complemented
5#13118498C214yesmaximal
6#13118111C214yesmaximal, complemented
7#13117370C214yesmaximal, complemented
8#13117366C214yesmaximal, complemented
9#13117216C211yesmaximal, characteristic
10C4×C22⋊C4×D13C212yesmaximal
11C13×#2608C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C2×#88151C2214yes—
14C2×#88150C2214yes—
15C2×#88141C2214yescomplemented
16C2×C22⋊C4×D13C2214yes—
17C2×#88131C2212yes—
18C2×C42×D13C2212yes—
19C2×C42×D13C2212yes—
20C13×#396C2214yes—
21C13×#389C2214yescomplemented
22C13×#387C2214yescomplemented
23C13×#381C2211yescharacteristic
24C4×C13×C22⋊C4C2212yes—
25#11718872C2211yescharacteristic
26C4×C22⋊Dic13C2212yes—
27#11718650C2214yes—
28#11718650C2214yes—
29#11718650C2214yes—
30#11718648C2214yes—
31#11718645C2214yescomplemented
32#11718644C2214yescomplemented
33#11718640C2214yescomplemented
34C4⋊C4×Dic13C2214yescomplemented
35C4⋊C4×Dic13C2214yescomplemented
36#11718616C2212yes—
37#11718610C2214yes—
38#11718609C2214yes—
39#11718608C2214yes—
40C22⋊C4×Dic13C2214yes—
41C4×#6103C2212yes—
42C4×#6103C2212yes—
43#11718594C2214yescomplemented
44#11718590C2214yescomplemented
45#11718329C2214yes—
46#11718328C2214yes—
47#11718328C2214yes—
48#11718327C2214yes—
49#11718327C2214yes—
50D13×#95C2214yes—
51#11718319C2214yescomplemented
52#11718315C2214yescomplemented
53#11718315C2214yescomplemented
54#11718310C2214yescomplemented
55#11718308C2214yescomplemented
56#11718307C2214yescomplemented
57C24×D13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×Dic13C2311yescharacteristic
60C22×C4×D13—44no—
61C22×C4×D13Q818yescomplemented
62C22×C4×D13C2314yes—
63C22×C4×D13C2314yes—
64C22×C4×D13C2312yes—
65C22×C4×D13C2312yes—
66C22×Dic26C2314yes—
67C2×C13×C4⋊C4C2314yes—
68C2×C13×C4⋊C4C2314yes—
69C2×C13×C4⋊C4C2314yes—
70C2×C13×C22⋊C4C2314yes—
71C2×C13×C22⋊C4C2312yes—
72C2×C42×C13C2312yes—
73C2×C42×C13C2312yes—
74C2×C22⋊Dic13C2314yes—
75C2×C22⋊Dic13C2312yes—
76C2×#6103C2314yes—
77C2×#6103C2314yes—
78C2×#6103C2314yes—
79C2×#6103C2314yes—
80C2×C4⋊Dic13C2314yes—
81C2×C4⋊Dic13C2314yes—
82C2×#6101C2314yes—
83C2×#6101C2314yes—
84C2×#6101C2314yes—
85C2×#6101C2314yes—
86C2×#6101C2314yes—
87C2×C4×Dic13C2314yes—
88C2×C4×Dic13C2314yes—
89C2×C4×Dic13C2314yes—
90C2×C4×Dic13C2312yes—
91C2×C4×Dic13C2312yes—
92#88151—216no—
93#88150—216no—
94#88141—48no—
95C22⋊C4×D13—216no—
96#88131—44no—
97C42×D13—44no—
98C42×D13—44no—
99C13×#95C2314yes—
100C13×#95C2314yes—
101C13×#95C2314yes—
102#88071C2314yes—
103#88071C2314yes—
104#88071C2314yes—
105#88071C2314yes—
106#88071C2314yes—
107#88071C2314yes—
108#88071C2314yes—
109#88071C2314yes—
110#88071C2314yes—
111#34958—131nomaximal, Sylow
112C24×C13C2411yescharacteristic
113C23×D13—28no—
114C23×D13—42no—
115C23×D13C2×Q814yes—
116C23×D13C2412yes—
117C22×C4×C13—42no—
118C22×C4×C13C2×Q814yes—
119C22×C4×C13C2414yes—
120C22×C4×C13C2414yes—
121C22×C4×C13C2412yes—
122C22×C4×C13C2414yes—
123C22×Dic13—24no—
124C22×Dic13C2×Q814yes—
125C22×Dic13C2414yes—
126C22×Dic13C2414yes—
127C22×Dic13C2411yescharacteristic
128C22×Dic13C2414yes—
129C22×Dic13C2411yescharacteristic
130C2×C4×D13—24no—
131C2×C4×D13—24no—
132C2×C4×D13—28no—
133C2×C4×D13—28no—
134C2×C4×D13—28no—
135C2×C4×D13—28no—
136C2×C4×D13—416no—
137C2×C4×D13—44no—
138C2×C4×D13—44no—
139C2×C4×D13—42no—
140C2×C4×D13—42no—
141C2×C4×D13C2×Q818yes—
142C2×C4×D13C2×Q818yes—
143C2×Dic26—28no—
144C2×Dic26—28no—
145C2×Dic26—44no—
146C13×C4⋊C4—28no—
147C13×C4⋊C4—28no—
148C13×C4⋊C4—44no—
149C13×C22⋊C4—28no—
150C13×C22⋊C4—42no—
151C42×C13—42no—
152C42×C13—42no—
153C22⋊Dic13—28no—
154C22⋊Dic13—42no—
155#6103—28no—
156#6103—28no—
157#6103—28no—
158#6103#41116yes—
159C4⋊Dic13—28no—
160C4⋊Dic13—28no—
161#6101—28no—
162#6101—28no—
163#6101—44no—
164#6101—44no—
165#6101—44no—
166C4×Dic13—28no—
167C4×Dic13—28no—
168C4×Dic13—28no—
169C4×Dic13—42no—
170C4×Dic13—42no—
171#2608—131no—
172#2608D1311yescharacteristic, complemented
173#2607—132no—
174#2569—134no—
175#2549—134no—
176#2437—134no—
177#2396—134no—
178C4×C22⋊Q8—134no—
179C4×C22⋊Q8—134no—
180#2280—131no—
181C2×C4×C22⋊C4—132no—
182C23×C13—24no—
183C23×C13—22no—
184C23×C13C22×Q812yes—
185C23×C13C2511yescharacteristic
186C22×D13—24no—
187C22×D13—22no—
188C22×D13—22no—
189C22×D13—216no—
190C22×D13—44no—
191C22×D13—416no—
192C22×D13C22×Q814yes—
193C22×D13C2×#4118yes—
194C2×C4×C13—24no—
195C2×C4×C13—24no—
196C2×C4×C13—22no—
197C2×C4×C13—22no—
198C2×C4×C13—24no—
199C2×C4×C13—24no—
200C2×C4×C13—24no—
201C2×C4×C13—24no—
202C2×C4×C13—24no—
203C2×C4×C13—24no—
204C2×C4×C13—44no—
205C2×C4×C13C22×Q814yes—
206C2×C4×C13C2×#4118yes—
207C2×Dic13—24no—
208C2×Dic13—24no—
209C2×Dic13—22no—
210C2×Dic13—28no—
211C2×Dic13—24no—
212C2×Dic13—24no—
213C2×Dic13—24no—
214C2×Dic13—24no—
215C2×Dic13—24no—
216C2×Dic13—24no—
217C2×Dic13C22×Q812yes—
218C2×Dic13C22×Q812yes—
219C2×Dic13C2×#4118yes—
220C2×Dic13H(5,𝔽2)14yes—
221C4×D13—216no—
222C4×D13—48no—
223C4×D13—416no—
224C4×D13—416no—
225Dic26—416no—
226C24×C4—131no—
227C2×C22⋊Q8—134no—
228C2×C22⋊Q8—134no—
229C2×C4×Q8—134no—
230C2×#117—132no—
231C22×C22⋊C4—134no—
232C22×C42—132no—
233C22×C42—132no—
234#400—134no—
235#399—134no—
236#398—134no—
237#398—134no—
238#396—134no—
239#396C2×D1314yes—
240#395—134no—
241#393—134no—
242#391—134no—
243#391—134no—
244#389—134no—
245#389C2×D1314yescomplemented
246#387—134no—
247#387—134no—
248#387—134no—
249#387C2×D1314yescomplemented
250#385—134no—
251#385—134no—
252#385—134no—
253#385—134no—
254#381—131no—
255#381C2×D1311yescharacteristic
256#380—134no—
257#380—134no—
258#380—134no—
259#379—132no—
260C4×C4⋊C4—134no—
261C4×C4⋊C4—134no—
262C4×C4⋊C4—134no—
263C4×C22⋊C4—132no—
264C4×C22⋊C4—134no—
265C4×C22⋊C4—132no—
266C4×C22⋊C4—132no—
267C4×C22⋊C4—134no—
268C4×C22⋊C4—134no—
269C4×C22⋊C4C2×D1312yes—
270C2×#95—134no—
271C22×C13—24no—
272C22×C13—22no—
273C22×C13—44no—
274C22×C13C23×Q811yescharacteristic
275C22×C13C22×#4114yes—
276C22×C13C2×H(5,𝔽2)12yes—
277C2×D13—24no—
278C2×D13—24no—
279C2×D13—28no—
280C2×D13—28no—
281C2×D13—416no—
282C2×D13#53318yes—
283C4×C13—24no—
284C4×C13—28no—
285C4×C13—44no—
286C4×C13—44no—
287Dic13—22no—
288Dic13—28no—
289Dic13—44no—
290Dic13—44no—
291Dic13#54314yes—
292C25—131no—
293C22×Q8—134no—
294C23×C4—131no—
295C23×C4—132no—
296C23×C4—138no—
297C23×C4—132no—
298C23×C4—134no—
299C23×C4—134no—
300C23×C4—524no—
301C23×C4C22×D1311yescharacteristic
302C22⋊Q8—2616no—
303C22⋊Q8—2616no—
304C4×Q8—528no—
305#117—524no—
306C2×C4⋊C4—134no—
307C2×C4⋊C4—134no—
308C2×C4⋊C4—134no—
309C2×C4⋊C4—134no—
310C2×C4⋊C4—134no—
311C2×C4⋊C4—134no—
312C2×C4⋊C4—134no—
313C2×C4⋊C4C22×D1314yes—
314C2×C4⋊C4C22×D1314yes—
315C2×C4⋊C4C22×D1314yes—
316C2×C22⋊C4—134no—
317C2×C22⋊C4—134no—
318C2×C22⋊C4—134no—
319C2×C22⋊C4—134no—
320C2×C22⋊C4—134no—
321C2×C22⋊C4—132no—
322C2×C22⋊C4—2616no—
323C2×C22⋊C4C22×D1314yes—
324C2×C22⋊C4C22×D1312yes—
325C2×C42—134no—
326C2×C42—134no—
327C2×C42—134no—
328C2×C42—132no—
329C2×C42—132no—
330C2×C42—524no—
331C2×C42—524no—
332C2×C42C22×D1312yes—
333C2×C42C22×D1312yes—
334#95—134no—
335#95—134no—
336#95—134no—
337#95—134no—
338#95—134no—
339#95—134no—
340#95—134no—
341#95—134no—
342#95—134no—
343#95C22×D1314yes—
344#95C22×D1314yes—
345#95C22×D1314yes—
346C2×C13—42no—
347C2×C13C2×#53312yes—
348C2×C13C2×#54311yescharacteristic
349C2×C13#348114yes—
350D13—28no—
351C24—132no—
352C24—134no—
353C24—268no—
354C24—522no—
355C24C23×D1311yescharacteristic
356C2×Q8—268no—
357C2×Q8—268no—
358C2×Q8—524no—
359C22×C4—42no—
360C22×C4—131no—
361C22×C4—134no—
362C22×C4—131no—
363C22×C4—134no—
364C22×C4—138no—
365C22×C4—138no—
366C22×C4—134no—
367C22×C4—134no—
368C22×C4—264no—
369C22×C4—264no—
370C22×C4—268no—
371C22×C4—268no—
372C22×C4—268no—
373C22×C4—264no—
374C22×C4—268no—
375C22×C4—524no—
376C22×C4—524no—
377C22×C4—522no—
378C22×C4—522no—
379C22×C4—5216no—
380C22×C4Q8×D1314yes—
381C22×C4C23×D1314yes—
382C22×C4C23×D1314yes—
383C22×C4C23×D1312yes—
384C22×C4C23×D1314yes—
385C4⋊C4—28no—
386C4⋊C4—28no—
387C4⋊C4—44no—
388C4⋊C4—268no—
389C4⋊C4—268no—
390C4⋊C4—268no—
391C4⋊C4—268no—
392C4⋊C4—524no—
393C4⋊C4—524no—
394C4⋊C4—524no—
395C22⋊C4—28no—
396C22⋊C4—42no—
397C22⋊C4—1316no—
398C22⋊C4—268no—
399C22⋊C4—268no—
400C22⋊C4—268no—
401C22⋊C4—268no—
402C22⋊C4—522no—
403C42—42no—
404C42—42no—
405C42—268no—
406C42—268no—
407C42—268no—
408C42—522no—
409C42—522no—
410C13#3495811yescharacteristic, complemented, Sylow
411C23—24no—
412C23—22no—
413C23—134no—
414C23—138no—
415C23—2616no—
416C23—264no—
417C23—262no—
418C23—262no—
419C23—524no—
420C23—5216no—
421C23C2×Q8×D1312yes—
422C23C24×D1311yescharacteristic
423Q8—5216no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—44no—
435C2×C4—132no—
436C2×C4—134no—
437C2×C4—132no—
438C2×C4—138no—
439C2×C4—2616no—
440C2×C4—268no—
441C2×C4—264no—
442C2×C4—264no—
443C2×C4—262no—
444C2×C4—264no—
445C2×C4—264no—
446C2×C4—264no—
447C2×C4—264no—
448C2×C4—264no—
449C2×C4—264no—
450C2×C4—528no—
451C2×C4—5216no—
452C2×C4—5216no—
453C2×C4C2×Q8×D1314yes—
454C2×C4#41×D1318yes—
455C22—22no—
456C22—24no—
457C22—44no—
458C22—138no—
459C22—264no—
460C22—264no—
461C22—268no—
462C22—268no—
463C22—5216no—
464C22C22×Q8×D1311yescharacteristic
465C22C2×#41×D1314yes—
466C22D13×H(5,𝔽2)12yes—
467C4—24no—
468C4—28no—
469C4—44no—
470C4—44no—
471C4—134no—
472C4—262no—
473C4—268no—
474C4—524no—
475C4—524no—
476C2—42no—
477C2—268no—
478C2D13×#53312yes—
479C2D13×#54311yescharacteristic
480C2#1312844314yes—
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC13×#2608C2
prime radicalC24×D13C23
hypercenter#2608D13
hypocenterC13#34958
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2608

Complements

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

NH ≅ G/Ntype
1. #13120506C2semidirect
2. #13120497C2semidirect
3. #13120059C2semidirect
4. #13119846C2semidirect
6. #13118111C2semidirect
7. #13117370C2semidirect
8. #13117366C2semidirect
11. C13×#2608C2semidirect
15. C2×#88141C22semidirect
21. C13×#389C22semidirect
22. C13×#387C22semidirect
31. #11718645C22semidirect
32. #11718644C22semidirect
33. #11718640C22semidirect
34. C4⋊C4×Dic13C22semidirect
35. C4⋊C4×Dic13C22semidirect
43. #11718594C22semidirect
44. #11718590C22semidirect
51. #11718319C22semidirect
52. #11718315C22semidirect
53. #11718315C22semidirect
54. #11718310C22semidirect
55. #11718308C22semidirect
56. #11718307C22semidirect
61. C22×C4×D13Q8semidirect
172. #2608D13semidirect
245. #389C2×D13semidirect
249. #387C2×D13semidirect
410. C13#34958semidirect

Maximal subgroups

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

subgroupindex
#131205062
#131204972
#131200592
#131198462
#131184982
#131181112
#131173702
#131173662
#131172162
C4×C22⋊C4×D132
C13×#26082
#3495813