Finite Group Databasebeta

← #16015920

Subgroups — #16015920

Order 3328.

684 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13127938C212yesmaximal
2C4×#88155C211yesmaximal, characteristic
3#13116601C212yesmaximal, complemented
4#13116600C214yesmaximal, complemented
5C2×#11718055C211yesmaximal, characteristic, complemented
6D13×#364C214yesmaximal, complemented
7C2×C13×#364C211yesmaximal, characteristic, complemented
8C2×#88155C411yescharacteristic
9C2×#88155C2211yescharacteristic
10C4×#6127C411yescharacteristic
11C2×C13×M32C2212yes—
12C2×C4×C8×C13C2211yescharacteristic
13#11718762C411yescharacteristic
14#11718762C2211yescharacteristic
15C2×#88052C2212yes—
16C4×#6099C411yescharacteristic
17#11718568—24no—
18D13×M32C2218yes—
19#11718562—24no—
20#11718350C412yes—
21#11718350C2212yes—
22C4×#6094C412yes—
23C4×C8×D13C2212yes—
24C13×#364C2212yes—
25C13×#364C2212yes—
26#11718103C2218yes—
27#11718055C2212yes—
28#11718055C2212yes—
29C2×#6127C2×C411yescharacteristic
30C22×C8×C13C2×C411yescharacteristic
31C22×C8×C13C2311yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C4×C22⋊D13—22no—
34#88180C2×C411yescharacteristic
35C2×#6099C2×C411yescharacteristic
36C2×#6099C2×C411yescharacteristic
37#88155C814yes—
38#88155C814yes—
39#88155D412yes—
40#88155D412yes—
41#88155Q812yes—
42#88155Q812yes—
43C2×#6094C2×C412yes—
44C2×#6094C2×C412yes—
45C2×C8×D13C2×C412yes—
46C2×C8×D13C2312yes—
47C4×D52—21no—
48#88126C2×C412yes—
49C42×D13C2×C412yes—
50C4×Dic26—21no—
51C13×M32—22no—
52C13×M32C2314yes—
53C2×C13×C16—22no—
54C4×C8×C13C2×C411yescharacteristic
55C4×C8×C13C2×C411yescharacteristic
56C4×C8×C13C2311yescharacteristic
57C4×C8×C13C2311yescharacteristic
58#88055C2×C412yes—
59#88055C2×C412yes—
60C8×Dic13C2×C412yes—
61C8×Dic13C2312yes—
62#88052—22no—
63#88052C2314yes—
64C2×#6090—22no—
65#88043C2×C412yes—
66C4×#1055C2×C412yes—
67#88038—28no—
68C16×D13—28no—
69#33401—131nomaximal, Sylow
70C22×C4×C13—21no—
71C22×C4×C13C22×C411yescharacteristic
72C2×C22⋊D13M1612yes—
73#6127C4⋊C412yes—
74#6127C4⋊C412yes—
75#6127C2×C812yes—
76#6127C2×C812yes—
77C2×D52M1611yescharacteristic
78C2×C4×D13—22no—
79C2×C4×D13C22×C412yes—
80C2×Dic26M1611yescharacteristic
81C2×C8×C13C2×C812yes—
82C2×C8×C13C2×C812yes—
83C2×C8×C13C22×C411yescharacteristic
84C2×C8×C13C22×C411yescharacteristic
85C2×C8×C13C22×C411yescharacteristic
86C2×C8×C13C2×D411yescharacteristic
87C2×C8×C13C2×D411yescharacteristic
88C2×C8×C13C2×Q811yescharacteristic
89C2×C8×C13C2×Q811yescharacteristic
90C2×C8×C13C2411yescharacteristic
91C42×C13—21no—
92C42×C13C22×C411yescharacteristic
93C42×C13C22×C411yescharacteristic
94C22⋊Dic13—21no—
95#6103—22no—
96C4⋊Dic13—21no—
97#6101—22no—
98C4×Dic13—22no—
99C4×Dic13C22×C412yes—
100#6099C4⋊C412yes—
101#6099C4⋊C412yes—
102#6099C2×C812yes—
103#6099C2×C812yes—
104C2×#1055C22×C412yes—
105C2×#1055C22×C412yes—
106#6094C4⋊C414yes—
107#6094C4⋊C414yes—
108#6094C2×C818yes—
109C8×D13C2×C818yes—
110C8×D13C2×D414yes—
111C8×D13C2×Q814yes—
112C13×C16—24no—
113#6090—24no—
114#3407—132no—
115C4×#131—131no—
116#2153—132no—
117#2153—134no—
118C2×#364—131no—
119C2×#364—134no—
120C2×#364D1311yescharacteristic, complemented
121C23×C13C2×M1611yescharacteristic
122C22×D13C2×M1612yes—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—42no—
126C2×C4×C13C2×C4⋊C411yescharacteristic
127C2×C4×C13C2×C4⋊C411yescharacteristic
128C2×C4×C13C22×C811yescharacteristic
129C2×C4×C13C22×C811yescharacteristic
130C2×C4×C13C2×M1611yescharacteristic
131C2×C4×C13C23×C411yescharacteristic
132C22⋊D13C4⋊C814yes—
133C22⋊D13C4⋊C814yes—
134C2×Dic13—22no—
135C2×Dic13C2×M1612yes—
136D52C4⋊C812yes—
137D52C4⋊C812yes—
138C4×D13—44no—
139C4×D13C2×C4⋊C414yes—
140C4×D13C22×C814yes—
141Dic26C4⋊C812yes—
142Dic26C4⋊C812yes—
143C8×C13C2×C4⋊C411yescharacteristic
144C8×C13C2×C4⋊C411yescharacteristic
145C8×C13C22×C812yes—
146C8×C13C22×C812yes—
147C8×C13C22×D411yescharacteristic
148C8×C13C22×Q811yescharacteristic
149#1055C2×C4⋊C414yes—
150#1055C22×C814yes—
151C2×#131—131no—
152C2×#131—131no—
153C4×#41—131no—
154#504—264no—
155#504—264no—
156C2×M32—132no—
157C2×M32—138no—
158C2×M32C2×D1312yes—
159#405—131no—
160#405—131no—
161#405—132no—
162#405—132no—
163C4×M16—131no—
164C4×M16—132no—
165C2×C4×C8—132no—
166C2×C4×C8C2×D1311yescharacteristic
167#364—138no—
168#364—132no—
169#364—132no—
170#364C2×D1312yes—
171#364C2×D1312yes—
172C22×C13—41no—
173C22×C13C2×C4⋊C811yescharacteristic
174C22×C13C2×C4⋊C811yescharacteristic
175C22×C13C22×M1611yescharacteristic
176C2×D13—42no—
177C2×D13C2×C4⋊C814yes—
178C4×C13—22no—
179C4×C13—41no—
180C4×C13C2×C4⋊C811yescharacteristic
181C4×C13C2×C4⋊C811yescharacteristic
182C4×C13C22×C4⋊C411yescharacteristic
183C4×C13C23×C811yescharacteristic
184Dic13—42no—
185Dic13C2×C4⋊C814yes—
186C2×#41—131no—
187#131—134no—
188#131—134no—
189#131—132no—
190#131—132no—
191#131—132no—
192#131—132no—
193C2×M16—131no—
194C2×M16—131no—
195C2×M16—132no—
196C2×M16—132no—
197C22×C8—132no—
198C22×C8—132no—
199C22×C8C4×D1311yescharacteristic
200C22×C8C22×D1311yescharacteristic
201C4×Q8—261no—
202C4×D4—261no—
203C4×D4—262no—
204#117—131no—
205#117—132no—
206C2×C42—132no—
207C2×C42C4×D1311yescharacteristic
208M32—22no—
209M32—134no—
210M32—268no—
211M32—262no—
212M32C22×D1314yes—
213C2×C16—22no—
214C2×C16—268no—
215C2×C16—262no—
216#97—132no—
217#97—132no—
218#97—132no—
219C4×C8—132no—
220C4×C8—132no—
221C4×C8—132no—
222C4×C8C4×D1311yescharacteristic
223C4×C8C4×D1311yescharacteristic
224C4×C8C22×D1311yescharacteristic
225C4×C8C22×D1311yescharacteristic
226C2×C13—21no—
227C2×C13—21no—
228C2×C13—21no—
229C2×C13C22×C4⋊C811yescharacteristic
230D13—24no—
231#41—132no—
232#41—132no—
233#41—132no—
234#41—132no—
235C2×Q8—131no—
236C2×D4—132no—
237C2×D4—131no—
238C22×C4—21no—
239C22×C4—132no—
240C22×C4—262no—
241C22×C4C2×C4×D1311yescharacteristic
242M16—132no—
243M16—132no—
244M16—132no—
245M16—132no—
246M16—134no—
247M16—134no—
248M16—138no—
249C2×C8—132no—
250C2×C8—132no—
251C2×C8—138no—
252C2×C8—134no—
253C2×C8—134no—
254C2×C8C8×D1312yes—
255C2×C8C8×D1312yes—
256C2×C8C2×C4×D1311yescharacteristic
257C2×C8C2×C4×D1311yescharacteristic
258C2×C8C2×C4×D1311yescharacteristic
259C2×C8D4×D1311yescharacteristic
260C2×C8D4×D1311yescharacteristic
261C2×C8Q8×D1311yescharacteristic
262C2×C8Q8×D1311yescharacteristic
263C2×C8C23×D1311yescharacteristic
264C4⋊C4—262no—
265C4⋊C4—261no—
266C22⋊C4—262no—
267C22⋊C4—261no—
268C42—21no—
269C42—132no—
270C42—262no—
271C42C2×C4×D1311yescharacteristic
272C42C2×C4×D1311yescharacteristic
273C16—24no—
274C16—264no—
275C13#3340111yescharacteristic, complemented, Sylow
276C23—132no—
277C23M16×D1311yescharacteristic
278Q8—132no—
279Q8—132no—
280D4—134no—
281D4—134no—
282D4—132no—
283D4—132no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—132no—
288C2×C4—134no—
289C2×C4—134no—
290C2×C4—262no—
291C2×C4—524no—
292C2×C4C4⋊C4×D1311yescharacteristic
293C2×C4C4⋊C4×D1311yescharacteristic
294C2×C4C2×C8×D1311yescharacteristic
295C2×C4C2×C8×D1311yescharacteristic
296C2×C4M16×D1311yescharacteristic
297C2×C4C22×C4×D1311yescharacteristic
298C8—134no—
299C8—134no—
300C8C4⋊C4×D1311yescharacteristic
301C8C4⋊C4×D1311yescharacteristic
302C8C2×C8×D1312yes—
303C8C2×C8×D1312yes—
304C8C2×D4×D1311yescharacteristic
305C8C2×Q8×D1311yescharacteristic
306C22—41no—
307C22—134no—
308C22—522no—
309C22D13×C4⋊C811yescharacteristic
310C22D13×C4⋊C811yescharacteristic
311C22C2×M16×D1311yescharacteristic
312C4—22no—
313C4—41no—
314C4—134no—
315C4—522no—
316C4D13×C4⋊C811yescharacteristic
317C4D13×C4⋊C811yescharacteristic
318C4C2×C4⋊C4×D1311yescharacteristic
319C4C22×C8×D1311yescharacteristic
320C2—21no—
321C2—21no—
322C2—21no—
323C2—264no—
324C2C2×D13×C4⋊C811yescharacteristic
subgroupG/H
centerC8C2×D4×D13
commutatorC4×C13C23×C8
FrattiniC2×C8C23×D13
FittingC2×C13×#364C2
socleC2×C13C22×C4⋊C8
prime radicalC2×#6127C2×C4
cosocleC2×C8×C13C24
hypercenterC2×#364D13
hypocenterC13#33401
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C22×C8 ◁ C2×#364

Complements

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

NH ≅ G/Ntype
3. #13116601C2semidirect
4. #13116600C2semidirect
5. C2×#11718055C2semidirect
6. D13×#364C2semidirect
7. C2×C13×#364C2semidirect
120. C2×#364D13semidirect
275. C13#33401semidirect

Maximal subgroups

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

subgroupindex
#131279382
C4×#881552
#131166012
#131166002
C2×#117180552
D13×#3642
C2×C13×#3642
#3340113