Finite Group Databasebeta

← #15750934

Subgroups — #15750934

Order 3328.

568 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117319C211yesmaximal, characteristic
2#13114904C211yesmaximal, characteristic
3#13112660C212yesmaximal, complemented
4#13112658C212yesmaximal, complemented
5C2×C13×#336C211yesmaximal, characteristic
6C23×C8×C13—21no—
7C22×C42×C13C2211yescharacteristic
8C2×#88180C411yescharacteristic
9C2×#88180C411yescharacteristic
10#11718871—21no—
11#11718871—21no—
12C2×C22⋊#1055—21no—
13C4×#6101—21no—
14C4×#6101—21no—
15#11718589C411yescharacteristic
16#11718589C411yescharacteristic
17#11718589C2211yescharacteristic
18#11718589C2211yescharacteristic
19C13×#336—21no—
20C13×#336C2212yes—
21#11718116—21no—
22#11718116C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×C8×C13—24no—
27C22×C8×C13—22no—
28C22×C8×C13—42no—
29C22×C8×C13—42no—
30C2×C42×C13—42no—
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37#88180—22no—
38#88180—42no—
39#88180C814yescomplemented
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×C4⋊Dic13C2×C411yescharacteristic
42C2×C4⋊Dic13C2×C411yescharacteristic
43C2×C4⋊Dic13C2×C411yescharacteristic
44C2×#6101—21no—
45C2×#6101—21no—
46C2×#6101—21no—
47C2×#6101—21no—
48C2×C4×Dic13—21no—
49C2×C4×Dic13—21no—
50C22×#1055—22no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55C22⋊#1055—42no—
56#7579—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—41no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C2×C812yes—
71C22×C4×C13M1612yes—
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C2×C8×C13—24no—
80C2×C8×C13—48no—
81C2×C8×C13—42no—
82C2×C8×C13—42no—
83C42×C13—41no—
84C42×C13—41no—
85C42×C13—41no—
86C42×C13—41no—
87C22⋊Dic13—24no—
88C22⋊Dic13—42no—
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13—41no—
92C4⋊Dic13—41no—
93C4⋊Dic13C2×C812yescomplemented
94C4⋊Dic13C2×C812yescomplemented
95#6101—42no—
96#6101—42no—
97#6101—42no—
98#6101—41no—
99#6101—41no—
100C4×Dic13—24no—
101C4×Dic13—42no—
102C2×#1055—42no—
103C2×#1055—42no—
104C2×#1055—42no—
105#2296—131no—
106#1817—131no—
107C2×#336D1311yescharacteristic
108#1271—132no—
109#1271—132no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13C22⋊C812yes—
115C23×C13#9912yes—
116C23×C13#10112yes—
117C23×C13C2×C22⋊C411yescharacteristic
118C2×C4×C13—24no—
119C2×C4×C13—24no—
120C2×C4×C13—24no—
121C2×C4×C13—24no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—44no—
136C2×C4×C13C22⋊C812yes—
137C2×C4×C13#10412yes—
138C2×C4×C13C22×C811yescharacteristic
139C2×C4×C13C2×M1611yescharacteristic
140C2×C4×C13#13512yes—
141C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C13#13711yescharacteristic
143C2×Dic13—22no—
144C2×Dic13—22no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C8×C13—44no—
156#1055—82no—
157C23×C8—21no—
158C2×#117—131no—
159C2×#117—131no—
160C22×C42C2×D1311yescharacteristic
161C2×C22⋊C8—261no—
162#389—131no—
163#389—131no—
164#389—131no—
165#389—131no—
166#385—261no—
167#385—261no—
168C4×C4⋊C4—261no—
169C4×C4⋊C4—261no—
170#336—21no—
171#336—132no—
172#336—261no—
173#336C2×D1312yes—
174C22×C13—22no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13#32414yes—
181C22×C13C2×C22⋊C811yescharacteristic
182C22×C13C2×#9911yescharacteristic
183C22×C13C2×#10111yescharacteristic
184C22×C13#41611yescharacteristic
185C22×C13#41711yescharacteristic
186C22×C13C2×#10411yescharacteristic
187C22×C13#42111yescharacteristic
188C4×C13—22no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—22no—
193C4×C13—21no—
194C4×C13—22no—
195C4×C13—41no—
196Dic13—42no—
197Dic13—42no—
198Dic13—81no—
199Dic13—81no—
200C23×C4C4×D1311yescharacteristic
201C23×C4D5211yescharacteristic
202C23×C4C22⋊D1311yescharacteristic
203C22×C8—24no—
204C22×C8—22no—
205C22×C8—42no—
206C22×C8—42no—
207C22×C8—262no—
208#117—134no—
209#117—262no—
210#117—522no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—131no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C22⋊C4—261no—
220C2×C22⋊C4—261no—
221C2×C42—42no—
222C2×C42—261no—
223C2×C42—261no—
224C2×C42C4×D1311yescharacteristic
225C2×C42D5211yescharacteristic
226C2×C42C22⋊D1311yescharacteristic
227C2×C42C22×D1311yescharacteristic
228C22⋊C8—522no—
229#95—261no—
230#95—261no—
231#95—261no—
232#95—261no—
233C2×C13—24no—
234C2×C13C2×#32411yescharacteristic
235C2×C13#147611yescharacteristic
236C2×C13#147711yescharacteristic
237C2×C13#150411yescharacteristic
238C2×C13#151611yescharacteristic
239C2×C13#153111yescharacteristic
240C2×C13#155211yescharacteristic
241C24#610311yescharacteristic
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—41no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4C8×D1312yes—
256C22×C4#609412yes—
257C22×C4#610311yescharacteristic
258C22×C4#610311yescharacteristic
259C22×C4#610311yescharacteristic
260C22×C4C2×C4×D1311yescharacteristic
261C22×C4C2×D5211yescharacteristic
262C22×C4C2×C22⋊D1311yescharacteristic
263C2×C8—24no—
264C2×C8—48no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—522no—
268C2×C8—522no—
269C2×C8—522no—
270C4⋊C4—132no—
271C4⋊C4—132no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4—521no—
275C4⋊C4—521no—
276C4⋊C4—522no—
277C4⋊C4—522no—
278C4⋊C4—521no—
279C4⋊C4—521no—
280C4⋊C4—522no—
281C22⋊C4—264no—
282C22⋊C4—522no—
283C42—41no—
284C42—41no—
285C42—41no—
286C42—41no—
287C42—264no—
288C42—522no—
289C13#757911yescharacteristic, complemented, Sylow
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23#8804612yes—
295C23#8806012yes—
296C23#8806412yes—
297C23C2×#610311yescharacteristic
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—44no—
316C2×C4—262no—
317C2×C4—262no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4#8804512yes—
329C2×C4#8806012yes—
330C2×C4C2×C8×D1311yescharacteristic
331C2×C4C2×#609411yescharacteristic
332C2×C4#8815812yes—
333C2×C4#8818611yescharacteristic
334C2×C4#8819611yescharacteristic
335C8—44no—
336C8—1042no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22#1171806114yes—
344C22C2×#8804511yescharacteristic
345C22C2×#8804611yescharacteristic
346C22#1171862711yescharacteristic
347C22C2×#8806011yescharacteristic
348C22#1171877411yescharacteristic
349C22C2×#8806411yescharacteristic
350C22#1171880011yescharacteristic
351C4—22no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4—21no—
356C4—21no—
357C4—22no—
358C4—41no—
359C4—522no—
360C4—522no—
361C4—1041no—
362C4—1041no—
363C2—24no—
364C2C2×#1171806111yescharacteristic
365C2#1311321911yescharacteristic
366C2#1311322111yescharacteristic
367C2#1311333811yescharacteristic
368C2#1311339311yescharacteristic
369C2#1311345011yescharacteristic
370C2#1311353411yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC2×C13×#336C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenterC2×#336D13
hypocenterC13#7579
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
3. #13112660C2semidirect
4. #13112658C2semidirect
39. #88180C8semidirect
93. C4⋊Dic13C2×C8semidirect
94. C4⋊Dic13C2×C8semidirect
289. C13#7579semidirect

Maximal subgroups

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

subgroupindex
#131173192
#131149042
#131126602
#131126582
C2×C13×#3362
#757913