Finite Group Databasebeta

← #15831963

Subgroups — #15831963

Order 3328.

666 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123949C212yesmaximal
2C4×#88155C211yesmaximal, characteristic
3#13113602C214yesmaximal, complemented
4#13113596C212yesmaximal, complemented
5#13113590C212yesmaximal, complemented
6#13113589C212yesmaximal, complemented
7C2×#11718049C211yesmaximal, characteristic, complemented
8C13×#1564C211yesmaximal, characteristic, complemented
9C2×#88155C411yescharacteristic
10C2×#88155C411yescharacteristic
11C4×#6127C2211yescharacteristic
12C13×#431C2212yes—
13C2×C4×C8×C13C2211yescharacteristic
14#11718762C411yescharacteristic
15#11718762C411yescharacteristic
16C2×C4⋊#1055C2212yes—
17C4×#6099C2211yescharacteristic
18#11718498C2214yes—
19#11718496C2214yes—
20#11718391—24no—
21#11718350C412yes—
22#11718350C412yes—
23#11718349—22no—
24C4×#6094C2212yes—
25C4×C8×D13C2212yes—
26#11718340—22no—
27C13×#335C2212yes—
28C13×#334C2211yescharacteristic
29C13×#334C2211yescharacteristic
30#11718072C2214yes—
31#11718071C2214yes—
32#11718049C2212yes—
33#11718049C2212yes—
34C2×#6127C2×C411yescharacteristic
35C22×C8×C13C2×C411yescharacteristic
36C22×C8×C13C2×C411yescharacteristic
37C2×C42×C13C2311yescharacteristic
38C4×C22⋊D13D412yes—
39C4×C22⋊D13Q812yes—
40#88180C2×C411yescharacteristic
41C2×#6099C2×C411yescharacteristic
42C2×#6099C2×C411yescharacteristic
43C22×#1055—22no—
44#88155—24no—
45#88155—24no—
46C2×#6094—24no—
47C2×#6094C2×C412yes—
48C2×#6094C2×C412yes—
49C2×C8×D13C2×C412yes—
50C2×C8×D13C2×C412yes—
51C4×D52D411yescharacteristic
52C4×D52Q811yescharacteristic
53#88126C2×C412yes—
54C42×D13C2312yes—
55C4×Dic26D411yescharacteristic
56C4×Dic26Q811yescharacteristic
57C13×C4⋊C8C2312yes—
58C13×C4⋊C8C2312yes—
59C13×C22⋊C8—22no—
60C4×C8×C13—22no—
61C4×C8×C13C2×C411yescharacteristic
62C4×C8×C13C2×C411yescharacteristic
63C4×C8×C13C2311yescharacteristic
64C4×C8×C13C2311yescharacteristic
65#88060—24no—
66#88055—24no—
67#88055C2×C412yes—
68#88055C2×C412yes—
69#88054—24no—
70C8×Dic13C2×C412yes—
71C8×Dic13C2×C412yes—
72C4⋊#1055—22no—
73C4⋊#1055C2314yes—
74#88043C2×C412yes—
75C4×#1055C2312yes—
76#17798—131nomaximal, Sylow
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×Q811yescharacteristic
80C2×C22⋊D13C4⋊C412yes—
81#6127—22no—
82#6127—22no—
83C2×D52C4⋊C411yescharacteristic
84C2×C4×D13C22×C412yes—
85C2×C4×D13C2×D412yes—
86C2×C4×D13C2×Q812yes—
87C2×Dic26C4⋊C411yescharacteristic
88C2×C8×C13—22no—
89C2×C8×C13—22no—
90C2×C8×C13—22no—
91C2×C8×C13M1614yescomplemented
92C2×C8×C13C22×C411yescharacteristic
93C2×C8×C13C22×C411yescharacteristic
94C2×C8×C13C22×C411yescharacteristic
95C2×C8×C13C22×C411yescharacteristic
96C42×C13C22×C411yescharacteristic
97C42×C13C2×D411yescharacteristic
98C42×C13C2×Q811yescharacteristic
99C42×C13C2411yescharacteristic
100C22⋊Dic13C4⋊C412yes—
101#6103C4⋊C412yes—
102#6103C4⋊C412yes—
103C4⋊Dic13C4⋊C411yescharacteristic
104C4⋊Dic13C4⋊C411yescharacteristic
105#6101C4⋊C412yes—
106#6101C4⋊C412yes—
107C4×Dic13C22×C412yes—
108C4×Dic13C2×D412yes—
109C4×Dic13C2×Q812yes—
110#6099—22no—
111#6099M1614yescomplemented
112C2×#1055—24no—
113C2×#1055—82no—
114C2×#1055C22×C412yes—
115C2×#1055C22×C412yes—
116#6094—24no—
117#6094—24no—
118#6094—84no—
119C8×D13—24no—
120C8×D13—24no—
121#2989—132no—
122C4×#131—131no—
123#1569—134no—
124#1568—132no—
125#1566—132no—
126#1565—132no—
127#1564D1311yescharacteristic, complemented
128C2×#334—131no—
129C23×C13C2×C4⋊C411yescharacteristic
130C22×D13C2×C4⋊C412yes—
131C2×C4×C13—22no—
132C2×C4×C13—41no—
133C2×C4×C13C2×C4⋊C411yescharacteristic
134C2×C4×C13C2×C4⋊C411yescharacteristic
135C2×C4×C13C2×C4⋊C411yescharacteristic
136C2×C4×C13C2×M1612yes—
137C2×C4×C13C2×M1612yes—
138C2×C4×C13C23×C411yescharacteristic
139C2×C4×C13C22×D411yescharacteristic
140C2×C4×C13C22×Q811yescharacteristic
141C22⋊D13—24no—
142C2×Dic13C2×C4⋊C412yes—
143C2×Dic13C2×C4⋊C412yes—
144C2×Dic13C2×C4⋊C412yes—
145D52—22no—
146C4×D13—22no—
147C4×D13—22no—
148C4×D13—24no—
149C4×D13—42no—
150Dic26—22no—
151C8×C13—21no—
152C8×C13—21no—
153C8×C13—42no—
154C8×C13—42no—
155C8×C13C2×M1612yes—
156C8×C13C2×M1612yes—
157#1055—22no—
158#1055—44no—
159#1055C2×M1614yes—
160C2×#131—131no—
161C2×#131—131no—
162C4×#41—131no—
163#446—262no—
164#436—262no—
165#435—264no—
166#432—134no—
167#431C2×D1312yes—
168#423—134no—
169C2×C4⋊C8—132no—
170#405—131no—
171#405—131no—
172#405—132no—
173#405—132no—
174C4×M16—131no—
175C4×M16—132no—
176C2×C4×C8—132no—
177C2×C4×C8C2×D1311yescharacteristic
178#335—134no—
179#335C2×D1312yes—
180#334—134no—
181#334—132no—
182#334—132no—
183#334C2×D1311yescharacteristic
184#334C2×D1311yescharacteristic
185C22×C13—21no—
186C22×C13—21no—
187C22×C13#42312yes—
188C22×C13C22×C4⋊C411yescharacteristic
189C2×D13—22no—
190C2×D13—22no—
191C2×D13—22no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13#42312yes—
196C4×C13C22×M1611yescharacteristic
197C4×C13C22×M1611yescharacteristic
198C4×C13#57712yes—
199Dic13—22no—
200Dic13—22no—
201Dic13—22no—
202C2×#41—131no—
203#131—264no—
204#131—264no—
205C2×M16—131no—
206C2×M16—131no—
207C2×M16—132no—
208C2×M16—132no—
209C2×M16—264no—
210C22×C8—132no—
211C22×C8—132no—
212C22×C8—262no—
213C22×C8C4×D1311yescharacteristic
214C22×C8C4×D1311yescharacteristic
215C4×Q8—131no—
216C4×Q8—131no—
217C4×D4—132no—
218C4×D4—132no—
219C4×D4—131no—
220C4×D4—131no—
221#117—131no—
222#117—132no—
223C2×C42—132no—
224C2×C42C22×D1311yescharacteristic
225C4⋊C8—134no—
226C4⋊C8—264no—
227C4⋊C8—262no—
228C4⋊C8C22×D1312yes—
229C4⋊C8C22×D1312yes—
230C22⋊C8—22no—
231C22⋊C8—264no—
232#97—132no—
233#97—132no—
234#97—132no—
235#97—264no—
236C4×C8—22no—
237C4×C8—132no—
238C4×C8—132no—
239C4×C8—132no—
240C4×C8C4×D1311yescharacteristic
241C4×C8C4×D1311yescharacteristic
242C4×C8C22×D1311yescharacteristic
243C4×C8C22×D1311yescharacteristic
244C2×C13—22no—
245C2×C13C2×#42311yescharacteristic
246C2×C13#291211yescharacteristic
247C2×C13#291611yescharacteristic
248D13—42no—
249#41—262no—
250#41—262no—
251C2×Q8—131no—
252C2×D4—132no—
253C2×D4—131no—
254C22×C4—132no—
255C22×C4—132no—
256C22×C4—132no—
257C22×C4C2×C4×D1311yescharacteristic
258C22×C4D4×D1311yescharacteristic
259C22×C4Q8×D1311yescharacteristic
260M16—134no—
261M16—264no—
262M16—262no—
263M16—264no—
264M16—1044no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—132no—
269C2×C8—132no—
270C2×C8—264no—
271C2×C8—264no—
272C2×C8—264no—
273C2×C8—1042no—
274C2×C8#609414yescomplemented
275C2×C8C2×C4×D1311yescharacteristic
276C2×C8C2×C4×D1311yescharacteristic
277C2×C8C2×C4×D1311yescharacteristic
278C2×C8C2×C4×D1311yescharacteristic
279C4⋊C4—132no—
280C4⋊C4—132no—
281C4⋊C4—131no—
282C4⋊C4—131no—
283C22⋊C4—132no—
284C22⋊C4—132no—
285C22⋊C4—132no—
286C42—132no—
287C42—132no—
288C42—132no—
289C42C2×C4×D1311yescharacteristic
290C42D4×D1311yescharacteristic
291C42Q8×D1311yescharacteristic
292C42C23×D1311yescharacteristic
293C13#1779811yescharacteristic, complemented, Sylow
294C23—132no—
295C23C4⋊C4×D1311yescharacteristic
296Q8—262no—
297D4—264no—
298D4—262no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—132no—
302C2×C4—132no—
303C2×C4—132no—
304C2×C4—262no—
305C2×C4—262no—
306C2×C4—264no—
307C2×C4—522no—
308C2×C4C4⋊C4×D1311yescharacteristic
309C2×C4C4⋊C4×D1311yescharacteristic
310C2×C4C4⋊C4×D1311yescharacteristic
311C2×C4C2×#609412yes—
312C2×C4M16×D1312yes—
313C2×C4C22×C4×D1311yescharacteristic
314C2×C4C2×D4×D1311yescharacteristic
315C2×C4C2×Q8×D1311yescharacteristic
316C8—21no—
317C8—21no—
318C8—42no—
319C8—42no—
320C8—134no—
321C8—262no—
322C8—524no—
323C8C2×#609412yes—
324C8C2×#609412yes—
325C22—21no—
326C22—21no—
327C22—262no—
328C22—262no—
329C22—262no—
330C22#1171849812yes—
331C22C2×C4⋊C4×D1311yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—262no—
336C4—262no—
337C4—262no—
338C4#1171849812yes—
339C4C22×#609411yescharacteristic
340C4C2×M16×D1311yescharacteristic
341C4#1171947512yes—
342C2—22no—
343C2—522no—
344C2C2×#1171849811yescharacteristic
345C2#1312342811yescharacteristic
346C2#1312344411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1564C2
socleC22×C13C22×C4⋊C4
prime radicalC2×#6127C2×C4
cosocleC42×C13C24
hypercenter#1564D13
hypocenterC13#17798
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
3. #13113602C2semidirect
4. #13113596C2semidirect
5. #13113590C2semidirect
6. #13113589C2semidirect
7. C2×#11718049C2semidirect
8. C13×#1564C2semidirect
91. C2×C8×C13M16semidirect
111. #6099M16semidirect
127. #1564D13semidirect
274. C2×C8#6094semidirect
293. C13#17798semidirect

Maximal subgroups

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

subgroupindex
#131239492
C4×#881552
#131136022
#131135962
#131135902
#131135892
C2×#117180492
C13×#15642
#1779813