Finite Group Databasebeta

← #15753723

Subgroups — #15753723

Order 3328.

570 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114703C211yesmaximal, characteristic, complemented
2C4×#88072C211yesmaximal, characteristic
3C2×D4⋊#1055C211yesmaximal, characteristic
4C2×#11718046C211yesmaximal, characteristic, complemented
5#13112675C211yesmaximal, characteristic, complemented
6#13112670C211yesmaximal, characteristic, complemented
7C2×C8×D4×C13C211yesmaximal, characteristic
8C23×C8×C13—21no—
9C2×C4×D4×C13C2211yescharacteristic
10C8×D4×C13—22no—
11C8×D4×C13C414yescomplemented
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C13×C22⋊C8—21no—
14C2×C4×C8×C13C2211yescharacteristic
15C2×#88072C412yes—
16C2×#88055—21no—
17C4×C4⋊Dic13C2211yescharacteristic
18C2×C4⋊#1055C2211yescharacteristic
19C2×C4×#1055C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21#11718142—21no—
22D4⋊#1055C414yescomplemented
23#11718121C412yes—
24#11718046—22no—
25C22×D4×C13C2×C411yescharacteristic
26C23×C4×C13—21no—
27C22×C8×C13—21no—
28C22×C8×C13—24no—
29C22×C8×C13—42no—
30C22×C8×C13—42no—
31C22×C8×C13D411yescharacteristic
32C22×C8×C13D411yescharacteristic
33C4×D4×C13—21no—
34C4×D4×C13—21no—
35C4×D4×C13C2×C412yes—
36C4×D4×C13C2×C412yes—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C42×C13C2311yescharacteristic
40C2×C4⋊Dic13C2×C412yes—
41C2×C4×Dic13—21no—
42C22×#1055—21no—
43C22×#1055—21no—
44C22×#1055C2×C412yes—
45C13×C4⋊C8—21no—
46C13×C4⋊C8C2×C412yes—
47C13×C22⋊C8—24no—
48C4×C8×C13C2×C412yes—
49C4×C8×C13D412yes—
50#88072—24no—
51#88071—21no—
52#88055—42no—
53C4⋊#1055—21no—
54C4⋊#1055C2×C412yes—
55C4×#1055—21no—
56C4×#1055—21no—
57C4×#1055—21no—
58C4×#1055C2×C412yes—
59#8204—131nomaximal, Sylow
60C24×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13—22no—
63C2×D4×C13C4212yes—
64C2×D4×C13M1614yes—
65C22×C4×C13—21no—
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13#4111yescharacteristic
75C22×Dic13—22no—
76C2×C8×C13—21no—
77C2×C8×C13—21no—
78C2×C8×C13—21no—
79C2×C8×C13—21no—
80C2×C8×C13—22no—
81C2×C8×C13—48no—
82C2×C8×C13—41no—
83C2×C8×C13—41no—
84C2×C8×C13C22⋊C412yes—
85C2×C8×C13C22⋊C412yes—
86C13×C4⋊C4—21no—
87C13×C4⋊C4C4212yes—
88C13×C22⋊C4—22no—
89C13×C22⋊C4—22no—
90C42×C13C22×C411yescharacteristic
91C42×C13C22×C411yescharacteristic
92C42×C13C2×D411yescharacteristic
93C42×C13#4111yescharacteristic
94C4⋊Dic13—22no—
95C4⋊Dic13—22no—
96C4×Dic13—41no—
97C4×Dic13—41no—
98C2×#1055—24no—
99C2×#1055—22no—
100C2×#1055—22no—
101C2×#1055—22no—
102C2×#1055—22no—
103C2×#1055—22no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×C8×D4D1311yescharacteristic
107#1770—131no—
108C4×#102—131no—
109C2×D4⋊C8—131no—
110C2×#322—131no—
111#1279—131no—
112#1277—131no—
113C23×C13—22no—
114C23×C13—24no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—42no—
118C23×C13C4×D411yescharacteristic
119D4×C13—22no—
120D4×C13—24no—
121D4×C13#9714yescomplemented
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13C2×C4211yescharacteristic
131C2×C4×C13C2×C22⋊C411yescharacteristic
132C2×C4×C13#11711yescharacteristic
133C2×C4×C13C4×D411yescharacteristic
134C2×C4×C13C4×D411yescharacteristic
135C2×C4×C13C4×D411yescharacteristic
136C2×C4×C13C2×M1612yes—
137C2×C4×C13#13112yes—
138C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C13#13711yescharacteristic
142C2×Dic13—42no—
143C2×Dic13—42no—
144C2×Dic13—42no—
145C8×C13—22no—
146C8×C13—22no—
147C8×C13—42no—
148#1055—24no—
149#1055—42no—
150#1055—42no—
151C23×C8—21no—
152C2×C4×D4C2×D1311yescharacteristic
153C8×D4—22no—
154C8×D4Dic1314yescomplemented
155C2×C4⋊C8—131no—
156C2×C4⋊C8C2×D1311yescharacteristic
157C2×#102—132no—
158C2×C22⋊C8—21no—
159C2×#97—261no—
160C2×C4×C8—131no—
161C2×C4×C8—131no—
162C2×C4×C8C2×D1311yescharacteristic
163C4×C4⋊C4—131no—
164#340—132no—
165#336—261no—
166D4⋊C8—134no—
167#322—262no—
168C22×C13—24no—
169C22×C13—44no—
170C22×C13—44no—
171C22×C13—42no—
172C22×C13—42no—
173C22×C13C4×C22⋊C411yescharacteristic
174C22×C13#43512yes—
175C22×C13#44011yescharacteristic
176C22×C13#44211yescharacteristic
177C22×C13#44312yes—
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—42no—
181C4×C13C2×#9711yescharacteristic
182C4×C13#40511yescharacteristic
183C4×C13#41711yescharacteristic
184C4×C13#41811yescharacteristic
185C4×C13#43512yes—
186C4×C13#44011yescharacteristic
187C4×C13#44211yescharacteristic
188Dic13—82no—
189C22×D4C4×D1311yescharacteristic
190C23×C4—21no—
191C22×C8—21no—
192C22×C8—24no—
193C22×C8—42no—
194C22×C8—42no—
195C22×C8—132no—
196C22×C8—261no—
197C22×C8—261no—
198C22×C8C22⋊D1311yescharacteristic
199C22×C8C22⋊D1311yescharacteristic
200C4×D4—21no—
201C4×D4—21no—
202C4×D4C4×D1312yes—
203C4×D4C2×Dic1312yes—
204C2×C4⋊C4—132no—
205C2×C4⋊C4C4×D1311yescharacteristic
206C2×C22⋊C4—21no—
207C2×C42—261no—
208C2×C42C22×D1311yescharacteristic
209C4⋊C8—21no—
210C4⋊C8—132no—
211C4⋊C8—261no—
212C4⋊C8C2×Dic1312yes—
213#102—264no—
214C22⋊C8—24no—
215#97—522no—
216C4×C8—132no—
217C4×C8—261no—
218C4×C8—261no—
219C4×C8—261no—
220C4×C8C2×Dic1312yes—
221C4×C8C22⋊D1312yes—
222#95—261no—
223C2×C13—44no—
224C2×C13#158512yes—
225C2×C13#158612yes—
226C2×C13#175211yescharacteristic
227C2×C13#176211yescharacteristic
228C2×C13#176411yescharacteristic
229C24—21no—
230C2×D4—22no—
231C2×D4—21no—
232C2×D4#609414yes—
233C2×D4C4×Dic1312yes—
234C22×C4—21no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—262no—
242C22×C4C2×C4×D1311yescharacteristic
243C22×C4#612711yescharacteristic
244C22×C4C2×C22⋊D1311yescharacteristic
245C2×C8—21no—
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—22no—
250C2×C8—48no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—264no—
254C2×C8—262no—
255C2×C8—262no—
256C2×C8—262no—
257C2×C8—262no—
258C2×C8—262no—
259C2×C8—521no—
260C2×C8—521no—
261C2×C8C22⋊Dic1312yes—
262C2×C8C22⋊Dic1312yes—
263C4⋊C4—21no—
264C4⋊C4—262no—
265C4⋊C4—262no—
266C4⋊C4C4×Dic1312yes—
267C22⋊C4—22no—
268C22⋊C4—22no—
269C42—521no—
270C42—521no—
271C42C2×C4×D1311yescharacteristic
272C42#612711yescharacteristic
273C42C22×Dic1311yescharacteristic
274C42C2×C22⋊D1311yescharacteristic
275C13#820411yescharacteristic, complemented, Sylow
276C23—24no—
277C23—22no—
278C23—41no—
279C23—41no—
280C23—42no—
281C23C4×C22⋊D1311yescharacteristic
282D4—22no—
283D4—24no—
284D4#8805514yescomplemented
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—522no—
294C2×C4—522no—
295C2×C4—522no—
296C2×C4C2×#609412yes—
297C2×C4#8815512yes—
298C2×C4C2×C4×Dic1311yescharacteristic
299C2×C4#8818011yescharacteristic
300C2×C4C4×C22⋊D1311yescharacteristic
301C2×C4C4×C22⋊D1311yescharacteristic
302C2×C4C4×C22⋊D1311yescharacteristic
303C2×C4#8818611yescharacteristic
304C2×C4#8818611yescharacteristic
305C2×C4#8820311yescharacteristic
306C2×C4#8820511yescharacteristic
307C2×C4C2×C22⋊Dic1311yescharacteristic
308C8—22no—
309C8—22no—
310C8—42no—
311C8—264no—
312C8—522no—
313C8—522no—
314C22—24no—
315C22—42no—
316C22—42no—
317C22—44no—
318C22—44no—
319C22#1171867511yescharacteristic
320C22#1171867911yescharacteristic
321C22#1171877212yes—
322C22#1171880512yes—
323C22C4×C22⋊Dic1311yescharacteristic
324C4—21no—
325C4—21no—
326C4—42no—
327C4—1042no—
328C4#1171867511yescharacteristic
329C4#1171867911yescharacteristic
330C4C2×#8805511yescharacteristic
331C4#1171876211yescharacteristic
332C4#1171877212yes—
333C4#1171887611yescharacteristic
334C4#1171889311yescharacteristic
335C2—44no—
336C2#1311369312yes—
337C2#1311370012yes—
338C2#1311461211yescharacteristic
339C2#1311466111yescharacteristic
340C2#1311467111yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D13
commutatorC2×C4×C13C2×C42
FrattiniC2×C42C22×D13
FittingC2×C8×D4×C13C2
socleC23×C13C4×D4
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenterC2×C8×D4D13
hypocenterC13#8204
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. #13114703C2semidirect
4. C2×#11718046C2semidirect
5. #13112675C2semidirect
6. #13112670C2semidirect
11. C8×D4×C13C4semidirect
22. D4⋊#1055C4semidirect
121. D4×C13#97semidirect
154. C8×D4Dic13semidirect
275. C13#8204semidirect
284. D4#88055semidirect

Maximal subgroups

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

subgroupindex
#131147032
C4×#880722
C2×D4⋊#10552
C2×#117180462
#131126752
#131126702
C2×C8×D4×C132
#820413