Finite Group Databasebeta

← #15832663

Subgroups — #15832663

Order 3328.

682 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123799C212yesmaximal, complemented
2C4×#88166C211yesmaximal, characteristic
3#13113734C211yesmaximal, characteristic, complemented
4#13113732C211yesmaximal, characteristic, complemented
5#13113729C212yesmaximal, complemented
6#13113724C212yesmaximal, complemented
7#13113721C211yesmaximal, characteristic, complemented
8#13113583C211yesmaximal, characteristic, complemented
9#13113215C212yesmaximal, complemented
10C82×D13C211yesmaximal, characteristic, complemented
11C13×#1589C211yesmaximal, characteristic, complemented
12C2×#88166C411yescharacteristic
13C4×#6129C2212yes—
14C4×C13×D8C2211yescharacteristic
15C13×#436C2212yes—
16D8×Dic13C411yescharacteristic
17#11718788—22no—
18M16×Dic13—22no—
19C4×#6105C2212yes—
20#11718673C2212yes—
21#11718541C411yescharacteristic
22#11718534C411yescharacteristic
23#11718494C2212yes—
24#11718492C2212yes—
25#11718433C412yes—
26#11718419C412yes—
27#11718389—22no—
28#11718379—22no—
29C4×Dic52C2211yescharacteristic
30C4×C8×D13C2211yescharacteristic
31C4×C8×D13C2211yescharacteristic
32C4×C8×D13C2211yescharacteristic
33#11718340C2212yes—
34C13×#335C2211yescharacteristic
35C13×D4⋊C8C2212yes—
36C82×C13C2211yescharacteristic
37D4⋊#1055C2212yes—
38#11718076C2212yes—
39#11718072C2212yes—
40#11718050C2211yescharacteristic
41#11718048C2212yes—
42C8×#1055C2211yescharacteristic
43C8×#1055C2211yescharacteristic
44C8×#1055C2211yescharacteristic
45C2×#6129C2×C412yes—
46C2×C13×D8C2×C411yescharacteristic
47C2×C13×M16—22no—
48C4×D4×C13C2312yes—
49D4×Dic13C2×C412yes—
50C2×#6105C2×C412yes—
51C4×C22⋊D13—22no—
52C2×C4×Dic13—22no—
53C2×#6099—22no—
54#88166—24no—
55C2×Dic52C2×C411yescharacteristic
56C2×C8×D13—21no—
57C2×C8×D13C2×C411yescharacteristic
58C2×C8×D13C2×C411yescharacteristic
59C2×C8×D13D411yescharacteristic
60C2×C8×D13D411yescharacteristic
61#88146C2×C412yes—
62#88141C2×C412yes—
63#88135—22no—
64#88131—22no—
65C42×D13C2311yescharacteristic
66C4×Dic26C2312yes—
67C13×#107C2×C411yescharacteristic
68C13×C4⋊C8C2312yes—
69C13×#102C2×C412yes—
70C13×C22⋊C8—22no—
71C4×C8×C13C2311yescharacteristic
72C4×C8×C13C2311yescharacteristic
73C4×C8×C13C2311yescharacteristic
74#88072C2×C412yes—
75C22⋊#1055—22no—
76#88060—22no—
77#88058C2×C411yescharacteristic
78#88056C2×C412yes—
79#88055—22no—
80#88055—22no—
81#88054—22no—
82#88054—22no—
83C8×Dic13—22no—
84C8×Dic13—21no—
85C8×Dic13C2×C411yescharacteristic
86C8×Dic13C2×C411yescharacteristic
87C8×Dic13D411yescharacteristic
88C8×Dic13D411yescharacteristic
89#88050C2×C412yes—
90#88048C2×C412yes—
91C4⋊#1055C2312yes—
92C4×#1055C2311yescharacteristic
93C4×#1055C2311yescharacteristic
94C4×#1055C2311yescharacteristic
95#17886—131nomaximal, Sylow
96C2×D4×C13C22×C412yes—
97C22×C4×C13—22no—
98C2×C22⋊D13—22no—
99C22×Dic13—22no—
100C22×Dic13—22no—
101#6129—24no—
102#6129—24no—
103C2×C4×D13C22×C411yescharacteristic
104C2×C4×D13C2×D411yescharacteristic
105C2×C4×D13#4111yescharacteristic
106C2×Dic26C22×C412yes—
107C13×D8—22no—
108C13×M16—44no—
109C2×C8×C13—21no—
110C2×C8×C13—22no—
111C2×C8×C13C22×C411yescharacteristic
112C2×C8×C13C22×C411yescharacteristic
113C2×C8×C13C2×D411yescharacteristic
114C2×C8×C13C2×D411yescharacteristic
115C13×C4⋊C4C22×C412yes—
116C13×C22⋊C4—22no—
117C42×C13C2411yescharacteristic
118C22⋊Dic13—22no—
119#6105—24no—
120#6103—22no—
121C4⋊Dic13C22×C412yes—
122#6101—22no—
123#6101—22no—
124C4×Dic13—22no—
125C4×Dic13—22no—
126C4×Dic13—22no—
127C4×Dic13C22×C411yescharacteristic
128C4×Dic13C2×D411yescharacteristic
129C4×Dic13#4111yescharacteristic
130#6099—44no—
131C2×#1055—21no—
132C2×#1055—22no—
133C2×#1055C22×C411yescharacteristic
134C2×#1055C22×C411yescharacteristic
135C2×#1055C2×D411yescharacteristic
136C2×#1055C2×D411yescharacteristic
137Dic52—22no—
138C8×D13—24no—
139C8×D13—22no—
140C8×D13—22no—
141C8×D13—22no—
142C8×D13M1614yescomplemented
143#2965—132no—
144C4×#135—131no—
145#1591—131no—
146#1591—131no—
147#1590—132no—
148#1590—132no—
149#1589—131no—
150#1589D1311yescharacteristic, complemented
151#1564—131no—
152#1476—132no—
153C2×C82—131no—
154C23×C13—22no—
155C22×D13C4×D411yescharacteristic
156D4×C13—22no—
157D4×C13—22no—
158C2×C4×C13—22no—
159C2×C4×C13—42no—
160C2×C4×C13—42no—
161C2×C4×C13C23×C411yescharacteristic
162C2×C4×C13C22×D411yescharacteristic
163C2×C4×C13C2×#4111yescharacteristic
164C22⋊D13—44no—
165C2×Dic13—22no—
166C2×Dic13—22no—
167C2×Dic13—44no—
168C2×Dic13—44no—
169C2×Dic13C4×D411yescharacteristic
170C2×Dic13C4×D411yescharacteristic
171C2×Dic13C4×D411yescharacteristic
172C4×D13—21no—
173C4×D13—21no—
174C4×D13—22no—
175C4×D13C2×M1612yes—
176C4×D13#13112yes—
177Dic26—22no—
178Dic26—22no—
179C8×C13—22no—
180C8×C13—21no—
181C8×C13—21no—
182C8×C13—42no—
183C8×C13C2×M1612yes—
184C8×C13#13512yescomplemented
185#1055—22no—
186#1055—21no—
187#1055—21no—
188#1055—42no—
189#1055C2×M1612yes—
190#1055#13512yescomplemented
191C2×#135—131no—
192C4×#41—132no—
193#446—132no—
194#446—132no—
195C4×Q16—131no—
196C4×Q16—131no—
197C4×SD16—132no—
198C4×SD16—132no—
199C4×D8—131no—
200C4×D8C2×D1311yescharacteristic
201#436—132no—
202#436C2×D1312yes—
203#435—262no—
204#435—262no—
205#431—132no—
206#431—262no—
207#427—131no—
208#416—132no—
209C4×M16—262no—
210C2×C4×C8—131no—
211C2×C4×C8—131no—
212C2×C4×C8—131no—
213#335—131no—
214#335C2×D1311yescharacteristic
215#334—132no—
216Q8⋊C8—132no—
217Q8⋊C8—132no—
218D4⋊C8—132no—
219D4⋊C8C2×D1312yes—
220C82—131no—
221C82—131no—
222C82—131no—
223C82C2×D1311yescharacteristic
224C22×C13—42no—
225C22×C13—42no—
226C22×C13—42no—
227C22×C13C2×C4×D411yescharacteristic
228C2×D13—21no—
229C2×D13—21no—
230C2×D13#43612yes—
231C4×C13—21no—
232C4×C13—42no—
233C4×C13C22×M1611yescharacteristic
234C4×C13C2×#13111yescharacteristic
235C4×C13C2×#13511yescharacteristic
236C4×C13C2×#13511yescharacteristic
237Dic13—21no—
238Dic13—42no—
239Dic13—42no—
240Dic13#43612yes—
241Dic13#44312yes—
242C2×#41—132no—
243#135—264no—
244C2×Q16—131no—
245C2×SD16—132no—
246C2×D8C4×D1311yescharacteristic
247C2×M16—22no—
248C2×M16—262no—
249C22×C8—131no—
250C22×C8—131no—
251C22×C8—131no—
252C22×C8—131no—
253C22×C8—261no—
254C4×Q8—132no—
255C4×Q8—132no—
256C4×D4—132no—
257C4×D4—262no—
258C4×D4—262no—
259C4×D4C22×D1312yes—
260#117—132no—
261#117—262no—
262C2×C42—131no—
263C2×C42—262no—
264#107—131no—
265#107C4×D1311yescharacteristic
266#106—132no—
267C4⋊C8—132no—
268C4⋊C8—262no—
269C4⋊C8—262no—
270C4⋊C8C22×D1312yes—
271#103—132no—
272#103—132no—
273#102—132no—
274#102C4×D1312yes—
275C22⋊C8—22no—
276C22⋊C8—262no—
277C22⋊C8—262no—
278#97—262no—
279#97—262no—
280C4×C8—131no—
281C4×C8—131no—
282C4×C8—131no—
283C4×C8—131no—
284C4×C8—131no—
285C4×C8—131no—
286C4×C8—131no—
287C4×C8—261no—
288C4×C8—262no—
289C4×C8C22×D1311yescharacteristic
290C4×C8C22×D1311yescharacteristic
291C4×C8C22×D1311yescharacteristic
292C2×C13—82no—
293C2×C13C2×#43611yescharacteristic
294C2×C13C4×#13511yescharacteristic
295C2×C13C2×#44311yescharacteristic
296D13—22no—
297#41—264no—
298#41—264no—
299C2×Q8—132no—
300C2×D4—262no—
301C2×D4C2×C4×D1312yes—
302C22×C4—22no—
303C22×C4—131no—
304C22×C4—131no—
305C22×C4—131no—
306C22×C4—262no—
307C22×C4—262no—
308Q16—262no—
309SD16—264no—
310D8—22no—
311M16—44no—
312M16—524no—
313C2×C8—21no—
314C2×C8—22no—
315C2×C8—131no—
316C2×C8—131no—
317C2×C8—134no—
318C2×C8—131no—
319C2×C8—131no—
320C2×C8—262no—
321C2×C8—262no—
322C2×C8—264no—
323C2×C8—261no—
324C2×C8—262no—
325C2×C8—262no—
326C2×C8C2×C4×D1311yescharacteristic
327C2×C8C2×C4×D1311yescharacteristic
328C2×C8D4×D1311yescharacteristic
329C2×C8D4×D1311yescharacteristic
330C4⋊C4—132no—
331C4⋊C4—262no—
332C4⋊C4—262no—
333C4⋊C4C2×C4×D1312yes—
334C22⋊C4—22no—
335C22⋊C4—262no—
336C22⋊C4—262no—
337C42—131no—
338C42—131no—
339C42—131no—
340C42—262no—
341C42—262no—
342C42—262no—
343C42C23×D1311yescharacteristic
344C13#1788611yescharacteristic, complemented, Sylow
345C23—22no—
346C23—131no—
347Q8—262no—
348Q8—262no—
349D4—22no—
350D4—22no—
351D4—524no—
352C2×C4—22no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—131no—
356C2×C4—131no—
357C2×C4—132no—
358C2×C4—132no—
359C2×C4—131no—
360C2×C4—262no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—262no—
364C2×C4—262no—
365C2×C4—524no—
366C2×C4—524no—
367C2×C4C22×C4×D1311yescharacteristic
368C2×C4C2×D4×D1311yescharacteristic
369C2×C4#41×D1311yescharacteristic
370C8—22no—
371C8—21no—
372C8—21no—
373C8—42no—
374C8—132no—
375C8—132no—
376C8—262no—
377C8—261no—
378C8—261no—
379C8—522no—
380C8M16×D1312yes—
381C8#8816612yescomplemented
382C22—42no—
383C22—42no—
384C22—42no—
385C22—132no—
386C22—261no—
387C22—261no—
388C22C4×D4×D1311yescharacteristic
389C4—21no—
390C4—42no—
391C4—132no—
392C4—132no—
393C4—261no—
394C4—522no—
395C4—522no—
396C4C2×M16×D1311yescharacteristic
397C4D13×#13111yescharacteristic
398C4C2×#8816611yescharacteristic
399C4D13×#13511yescharacteristic
400C2—82no—
401C2—262no—
402C2D13×#43611yescharacteristic
403C2C4×#8816611yescharacteristic
404C2D13×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1589C2
socleC22×C13C2×C4×D4
prime radicalC2×#88166C4
cosocleC42×C13C24
hypercenter#1589D13
hypocenterC13#17886
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1589

Complements

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

NH ≅ G/Ntype
1. #13123799C2semidirect
3. #13113734C2semidirect
4. #13113732C2semidirect
5. #13113729C2semidirect
6. #13113724C2semidirect
7. #13113721C2semidirect
8. #13113583C2semidirect
9. #13113215C2semidirect
10. C82×D13C2semidirect
11. C13×#1589C2semidirect
142. C8×D13M16semidirect
150. #1589D13semidirect
184. C8×C13#135semidirect
190. #1055#135semidirect
344. C13#17886semidirect
381. C8#88166semidirect

Maximal subgroups

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

subgroupindex
#131237992
C4×#881662
#131137342
#131137322
#131137292
#131137242
#131137212
#131135832
#131132152
C82×D132
C13×#15892
#1788613